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[Axiom-developer] 20080116.01.tpd.patch
|
From: |
daly |
|
Subject: |
[Axiom-developer] 20080116.01.tpd.patch |
|
Date: |
Wed, 16 Jan 2008 09:40:35 -0600 |
These files compare Axiom output to Abramowitz and Stegun,
Handbook of Mathematical Functions (1965). So far it has
uncovered two bugs. It is expected that these numeric results
may be unstable in the trailing digits on different architectures
(e.g. 64bit machines).
=======================================================================
diff --git a/changelog b/changelog
index 693db6a..45e1388 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,15 @@
+20080112 tpd src/input/besselk.input complex gamma A&S reference regression
+20080110 tpd src/input/Makefile add new regression test files
+20080110 tpd src/input/asinhatanh.input create A&S reference regression
+20080110 tpd src/input/sinhcosh.input create A&S reference regression
+20080110 tpd src/input/tanhcoth.input create A&S reference regression
+20080110 tpd src/input/asinatan.input create A&S reference regression
+20080110 tpd src/input/seccsc.input create A&S reference regression
+20080110 tpd src/input/tancot.input create A&S reference regression
+20080109 tpd src/input/log.input create A&S reference regression
+20080109 tpd src/input/sincos.input create A&S reference regression
+20080108 tpd src/input/exp.input create A&S reference regression
+20080108 tpd src/input/besselk.input update bibliography
20080107 tpd src/input/Makefile besselk.input regression test added
20080107 tpd src/input/besselk.input regression test added
20080107 tpd src/input/gamma.input missing file added
diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet
index d727a41..07fca93 100644
--- a/src/input/Makefile.pamphlet
+++ b/src/input/Makefile.pamphlet
@@ -284,7 +284,8 @@ OUTS= ffrac.output \
REGRES= algaggr.regress algbrbf.regress algfacob.regress alist.regress \
allfact.regress antoine.regress \
arith.regress array1.regress array2.regress \
- arrows.regress assign.regress atansqrt.regress \
+ arrows.regress asinatan.regress asinhatanh.regress \
+ assign.regress atansqrt.regress \
asec.regress bags.regress bbtree.regress besselk.regress \
binary.regress bop.regress bstree.regress bouquet.regress \
bug100.regress bug101.regress \
@@ -306,6 +307,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress
alist.regress \
elt.regress eq.regress eqtbl.regress equation2.regress \
equation.regress evalex.regress eval.regress exdiff.regress \
exint.regress exit.regress exlap.regress exlimit.regress \
+ exp.regress \
expexpan.regress explim.regress expr1.regress exprode.regress \
expr.regress exseries.regress exsum.regress exprpoly.regress \
farray.regress ffdemo.regress fferr.regress ffx72.regress \
@@ -329,6 +331,7 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress
alist.regress \
laplace.regress leg.regress limit.regress lindep.regress \
list.regress lode.regress lodesys.regress lodo1.regress \
lodo2.regress lodo3.regress lodof.regress lodo.regress \
+ log.regress \
lpoly.regress lupfact.regress lword.regress macbug.regress \
macros.regress magma.regress mapleok.regress mappkg1.regress \
matbug.regress mathml.regress \
@@ -350,14 +353,16 @@ REGRES= algaggr.regress algbrbf.regress algfacob.regress
alist.regress \
realclos.regress reclos.regress repa6.regress robidoux.regress \
roman.regress roots.regress ruleset.regress rules.regress \
schaum1.regress \
- scherk.regress scope.regress segbind.regress seg.regress \
+ scherk.regress scope.regress seccsc.regress \
+ segbind.regress seg.regress \
series2.regress series.regress sersolve.regress set.regress \
+ sincos.regress sinhcosh.regress \
sincosex.regress sint.regress skew.regress slowint.regress \
solvetra.regress space3.regress sqmatrix.regress sregset.regress \
stbl.regress stream2.regress stream.regress streams.regress \
string.regress strtbl.regress summation.regress \
- symbol.regress t111293.regress \
- table.regress tanatan.regress textfile.regress torus.regress \
+ symbol.regress t111293.regress table.regress tancot.regress \
+ tanhcoth.regress tanatan.regress textfile.regress torus.regress \
triglim.regress tsetcatvermeer.regress tutchap1.regress \
void.regress uniseg.regress
@@ -502,6 +507,7 @@ NAGLIB=${OUT}/c02aff.input ${OUT}/c02agf.input
${OUT}/c05adf.input \
FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input ${OUT}/algfacob.input \
${OUT}/alist.input ${OUT}/allfact.input ${OUT}/antoine.input \
${OUT}/array1.input ${OUT}/array2.input ${OUT}/arrows.input \
+ ${OUT}/asinatan.input ${OUT}/asinhatanh.input \
${OUT}/assign.input ${OUT}/atansqrt.input ${OUT}/axiom.input \
${OUT}/asec.input \
${OUT}/bags.input ${OUT}/bbtree.input ${OUT}/besselk.input \
@@ -539,7 +545,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/elt.input \
${OUT}/eq.input ${OUT}/eqtbl.input ${OUT}/equation.input \
${OUT}/errortrap.input \
- ${OUT}/eval.input ${OUT}/exit.input ${OUT}/expexpan.input \
+ ${OUT}/eval.input ${OUT}/exit.input ${OUT}/exp.input \
+ ${OUT}/expexpan.input \
${OUT}/explim.input ${OUT}/explot2d.input ${OUT}/explot3d.input \
${OUT}/expr1.input ${OUT}/exprpoly.input \
${OUT}/farray.input ${OUT}/ffdemo.input \
@@ -575,8 +582,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/lindep.input ${OUT}/liss1.input ${OUT}/liss2.input \
${OUT}/list.input ${OUT}/lode.input ${OUT}/lodesys.input \
${OUT}/lodo1.input ${OUT}/lodo2.input ${OUT}/lodof.input \
- ${OUT}/lodo.input ${OUT}/lodo3.input ${OUT}/lpoly.input \
- ${OUT}/lump.input \
+ ${OUT}/lodo.input ${OUT}/lodo3.input ${OUT}/log.input \
+ ${OUT}/lpoly.input ${OUT}/lump.input \
${OUT}/lupfact.input ${OUT}/lword.input ${OUT}/macbug.input \
${OUT}/macros.input ${OUT}/marcbench.input ${OUT}/magma.input \
${OUT}/mapleok.input ${OUT}/mappkg1.input ${OUT}/matbug.input \
@@ -616,9 +623,10 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/robidoux.input ${OUT}/roman.input ${OUT}/roots.input \
${OUT}/ruleset.input ${OUT}/rules.input ${OUT}/schaum1.input \
${OUT}/saddle.input \
- ${OUT}/scherk.input ${OUT}/scope.input \
+ ${OUT}/scherk.input ${OUT}/scope.input ${OUT}/seccsc.input \
${OUT}/segbind.input ${OUT}/seg.input ${OUT}/series2.input \
${OUT}/series.input ${OUT}/sersolve.input ${OUT}/set.input \
+ ${OUT}/sincos.input ${OUT}/sinhcosh.input \
${OUT}/sincosex.input ${OUT}/sininv.input ${OUT}/sinsin.input \
${OUT}/sinsin2.input ${OUT}/sint.input ${OUT}/skew.input \
${OUT}/slowint.input ${OUT}/solvetra.input ${OUT}/space3.input \
@@ -628,7 +636,8 @@ FILES= ${OUT}/algaggr.input ${OUT}/algbrbf.input
${OUT}/algfacob.input \
${OUT}/string.input ${OUT}/strtbl.input ${OUT}/summation.input \
${OUT}/symbol.input \
${OUT}/synonym.input ${OUT}/t111293.input \
- ${OUT}/table.input ${OUT}/tanatan.input ${OUT}/test.input \
+ ${OUT}/table.input ${OUT}/tancot.input ${OUT}/tanhcoth.input \
+ ${OUT}/tanatan.input ${OUT}/test.input \
${OUT}/tetra.input ${OUT}/textfile.input ${OUT}/tknot.input \
${OUT}/tree.input \
${OUT}/triglim.input ${OUT}/tschirn.input ${OUT}/tsetcatbutcher.input \
@@ -684,7 +693,8 @@ DOCFILES= \
${DOC}/as-eg3.input.dvi ${DOC}/as-eg4.input.dvi \
${DOC}/as-eg5.input.dvi ${DOC}/aseg6.as.dvi \
${DOC}/as-eg6.input.dvi ${DOC}/aseg7.as.dvi \
- ${DOC}/asec.input.dvi \
+ ${DOC}/asec.input.dvi ${DOC}/asinatan.input.dvi \
+ ${DOC}/asinhatanh.input.dvi \
${DOC}/assign.input.dvi ${DOC}/atansqrt.input.dvi \
${DOC}/axiom.input.dvi ${DOC}/bags.input.dvi \
${DOC}/bbtree.input.dvi ${DOC}/besselk.input.dvi \
@@ -773,6 +783,7 @@ DOCFILES= \
${DOC}/eval.input.dvi ${DOC}/exdiff.input.dvi \
${DOC}/exint.input.dvi ${DOC}/exit.input.dvi \
${DOC}/exlap.input.dvi ${DOC}/exlimit.input.dvi \
+ ${DOC}/exp.input.dvi \
${DOC}/expexpan.input.dvi ${DOC}/explim.input.dvi \
${DOC}/explot2d.input.dvi ${DOC}/explot3d.input.dvi \
${DOC}/expr1.input.dvi ${DOC}/expr.input.dvi \
@@ -854,6 +865,7 @@ DOCFILES= \
${DOC}/lodesys.input.dvi ${DOC}/lodo1.input.dvi \
${DOC}/lodo2.input.dvi ${DOC}/lodo3.input.dvi \
${DOC}/lodof.input.dvi ${DOC}/lodo.input.dvi \
+ ${DOC}/log.input.dvi \
${DOC}/loop.input.dvi ${DOC}/lpoly.input.dvi \
${DOC}/lump.input.dvi ${DOC}/lupfact.input.dvi \
${DOC}/lword.input.dvi ${DOC}/macbug.input.dvi \
@@ -926,10 +938,12 @@ DOCFILES= \
${DOC}/s21baf.input.dvi ${DOC}/s21bbf.input.dvi \
${DOC}/s21bcf.input.dvi ${DOC}/s21bdf.input.dvi \
${DOC}/saddle.input.dvi ${DOC}/scherk.input.dvi \
- ${DOC}/scope.input.dvi ${DOC}/segbind.input.dvi \
+ ${DOC}/scope.input.dvi ${DOC}/seccsc.input.dvi \
+ ${DOC}/segbind.input.dvi \
${DOC}/seg.input.dvi ${DOC}/series2.input.dvi \
${DOC}/series.input.dvi ${DOC}/sersolve.input.dvi \
- ${DOC}/set.input.dvi ${DOC}/sincosex.input.dvi \
+ ${DOC}/set.input.dvi ${DOC}/sincos.input.dvi \
+ ${DOC}/sinhcosh.input.dvi ${DOC}/sincosex.input.dvi \
${DOC}/sininv.input.dvi ${DOC}/sinsin2.input.dvi \
${DOC}/sinsin.input.dvi ${DOC}/sint.input.dvi \
${DOC}/skew.input.dvi ${DOC}/slowint.input.dvi \
@@ -943,6 +957,7 @@ DOCFILES= \
${DOC}/symbol.input.dvi ${DOC}/synonym2.input.dvi \
${DOC}/synonym.input.dvi ${DOC}/t111293.input.dvi \
${DOC}/table.input.dvi ${DOC}/tanatan.input.dvi \
+ ${DOC}/tancot.input.dvi ${DOC}/tanhcoth.input.dvi \
${DOC}/test.input.dvi ${DOC}/tetra.input.dvi \
${DOC}/textfile.input.dvi ${DOC}/tknot.input.dvi \
${DOC}/torus.input.dvi ${DOC}/tree.input.dvi \
diff --git a/src/input/asinatan.input.pamphlet
b/src/input/asinatan.input.pamphlet
new file mode 100644
index 0000000..a468c88
--- /dev/null
+++ b/src/input/asinatan.input.pamphlet
@@ -0,0 +1,456 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input asinatan.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This compares Axiom's asin and atan functions with the tables published in
+Abramowitz and Stegun.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+In the following table there are 4 columns. The first column
+is the argument of asin(x), ranging from 0.01 to 1.00. The
+second column is the reference value of tan from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp203-212
+<<*>>=
+)spool asinatan.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 2
+[[0.01,0.010000166674,asin(0.01),asin(0.01)-0.010000166674],_
+[0.02,0.020001333573,asin(0.02),asin(0.02)-0.020001333573],_
+[0.03,0.030004501823,asin(0.03),asin(0.03)-0.030004501823],_
+[0.04,0.040010674354,asin(0.04),asin(0.04)-0.040010674354],_
+[0.05,0.050020856806,asin(0.05),asin(0.05)-0.050020856806],_
+[0.06,0.060036058445,asin(0.06),asin(0.06)-0.060036058445],_
+[0.07,0.070057293088,asin(0.07),asin(0.07)-0.070057293088],_
+[0.08,0.080085580034,asin(0.08),asin(0.08)-0.080085580034],_
+[0.09,0.090121945015,asin(0.09),asin(0.09)-0.090121945015],_
+[0.10,0.100167421162,asin(0.10),asin(0.10)-0.100167421162],_
+[0.11,0.110223049988,asin(0.11),asin(0.11)-0.110223049988],_
+[0.12,0.120289882395,asin(0.12),asin(0.12)-0.120289882395],_
+[0.13,0.130368979703,asin(0.13),asin(0.13)-0.130368979703],_
+[0.14,0.140461414710,asin(0.14),asin(0.14)-0.140461414710],_
+[0.15,0.150568272777,asin(0.15),asin(0.15)-0.150568272777],_
+[0.16,0.160690652952,asin(0.16),asin(0.16)-0.160690652952],_
+[0.17,0.170829669129,asin(0.17),asin(0.17)-0.170829669129],_
+[0.18,0.180986451247,asin(0.18),asin(0.18)-0.180986451247],_
+[0.19,0.191162146531,asin(0.19),asin(0.19)-0.191162146531],_
+[0.20,0.201357920790,asin(0.20),asin(0.20)-0.201357920790],_
+[0.21,0.211574959758,asin(0.21),asin(0.21)-0.211574959758],_
+[0.22,0.221814470497,asin(0.22),asin(0.22)-0.221814470497],_
+[0.23,0.232077682863,asin(0.23),asin(0.23)-0.232077682863],_
+[0.24,0.242365851039,asin(0.24),asin(0.24)-0.242365851039],_
+[0.25,0.252680255142,asin(0.25),asin(0.25)-0.252680255142],_
+[0.26,0.263022202908,asin(0.26),asin(0.26)-0.263022202908],_
+[0.27,0.273393031467,asin(0.27),asin(0.27)-0.273393031467],_
+[0.28,0.283794109208,asin(0.28),asin(0.28)-0.283794109208],_
+[0.29,0.294226837749,asin(0.29),asin(0.29)-0.294226837749],_
+[0.30,0.304692654015,asin(0.30),asin(0.30)-0.304692654015],_
+[0.31,0.315193032441,asin(0.31),asin(0.31)-0.315193032441],_
+[0.32,0.325729487295,asin(0.32),asin(0.32)-0.325729487295],_
+[0.33,0.336303575154,asin(0.33),asin(0.33)-0.336303575154],_
+[0.34,0.346916897527,asin(0.34),asin(0.34)-0.346916897527],_
+[0.35,0.357571103646,asin(0.35),asin(0.35)-0.357571103646],_
+[0.36,0.368267893437,asin(0.36),asin(0.36)-0.368267893437],_
+[0.37,0.379009020696,asin(0.37),asin(0.37)-0.379009020696],_
+[0.38,0.389796296474,asin(0.38),asin(0.38)-0.389796296474],_
+[0.39,0.400631592701,asin(0.39),asin(0.39)-0.400631592701],_
+[0.40,0.411516846067,asin(0.40),asin(0.40)-0.411516846067],_
+[0.41,0.422454062187,asin(0.41),asin(0.41)-0.422454062187],_
+[0.42,0.433445320070,asin(0.42),asin(0.42)-0.433445320070],_
+[0.43,0.444492776936,asin(0.43),asin(0.43)-0.444492776936],_
+[0.44,0.455598673396,asin(0.44),asin(0.44)-0.455598673396],_
+[0.45,0.466765339047,asin(0.45),asin(0.45)-0.466765339047],_
+[0.46,0.477995198519,asin(0.46),asin(0.46)-0.477995198519],_
+[0.47,0.489290778014,asin(0.47),asin(0.47)-0.489290778014],_
+[0.48,0.500654712405,asin(0.48),asin(0.48)-0.500654712405],_
+[0.49,0.512089752934,asin(0.49),asin(0.49)-0.512089752934],_
+[0.50,0.523598775598,asin(0.50),asin(0.50)-0.523598775598],_
+[0.51,0.535184790276,asin(0.51),asin(0.51)-0.535184790276],_
+[0.52,0.546850950696,asin(0.52),asin(0.52)-0.546850950696],_
+[0.53,0.558600565343,asin(0.53),asin(0.53)-0.558600565343],_
+[0.54,0.570437109400,asin(0.54),asin(0.54)-0.570437109400],_
+[0.55,0.582364237869,asin(0.55),asin(0.55)-0.582364237869],_
+[0.56,0.594385800001,asin(0.56),asin(0.56)-0.594385800001],_
+[0.57,0.606505855213,asin(0.57),asin(0.57)-0.606505855213],_
+[0.58,0.618728690672,asin(0.58),asin(0.58)-0.618728690672],_
+[0.59,0.631058840778,asin(0.59),asin(0.59)-0.631058840778],_
+[0.60,0.643501108793,asin(0.60),asin(0.60)-0.643501108793],_
+[0.61,0.656060590925,asin(0.61),asin(0.61)-0.656060590925],_
+[0.62,0.668742703202,asin(0.62),asin(0.62)-0.668742703202],_
+[0.63,0.681553211563,asin(0.63),asin(0.63)-0.681553211563],_
+[0.64,0.694498265627,asin(0.64),asin(0.64)-0.694498265627],_
+[0.65,0.707584436725,asin(0.65),asin(0.65)-0.707584436725],_
+[0.66,0.720818760870,asin(0.66),asin(0.66)-0.720818760870],_
+[0.67,0.734208787453,asin(0.67),asin(0.67)-0.734208787453],_
+[0.68,0.747762634660,asin(0.68),asin(0.68)-0.747762634660],_
+[0.69,0.761489052748,asin(0.69),asin(0.69)-0.761489052748],_
+[0.70,0.775397496611,asin(0.70),asin(0.70)-0.775397496611],_
+[0.71,0.789498209346,asin(0.71),asin(0.71)-0.789498209346],_
+[0.72,0.803802318933,asin(0.72),asin(0.72)-0.803802318933],_
+[0.73,0.818321950632,asin(0.73),asin(0.73)-0.818321950632],_
+[0.74,0.833070358342,asin(0.74),asin(0.74)-0.833070358342],_
+[0.75,0.848062078981,asin(0.75),asin(0.75)-0.848062078981],_
+[0.76,0.863313115016,asin(0.76),asin(0.76)-0.863313115016],_
+[0.77,0.878841151669,asin(0.77),asin(0.77)-0.878841151669],_
+[0.78,0.894665817234,asin(0.78),asin(0.78)-0.894665817234],_
+[0.79,0.910808997407,asin(0.79),asin(0.79)-0.910808997407],_
+[0.80,0.927295218002,asin(0.80),asin(0.80)-0.927295218002],_
+[0.81,0.944152115154,asin(0.81),asin(0.81)-0.944152115154],_
+[0.82,0.961411018764,asin(0.82),asin(0.82)-0.961411018764],_
+[0.83,0.979107684368,asin(0.83),asin(0.83)-0.979107684368],_
+[0.84,0.997283222372,asin(0.84),asin(0.84)-0.997283222372],_
+[0.85,1.015985293815,asin(0.85),asin(0.85)-1.015985293815],_
+[0.86,1.035269672481,asin(0.86),asin(0.86)-1.035269672481],_
+[0.87,1.055202320549,asin(0.87),asin(0.87)-1.055202320549],_
+[0.88,1.075862200454,asin(0.88),asin(0.88)-1.075862200454],_
+[0.89,1.097345169523,asin(0.89),asin(0.89)-1.097345169523],_
+[0.90,1.119769514999,asin(0.90),asin(0.90)-1.119769514999],_
+[0.91,1.143284061850,asin(0.91),asin(0.91)-1.143284061850],_
+[0.92,1.168080485214,asin(0.92),asin(0.92)-1.168080485214],_
+[0.93,1.194412844477,asin(0.93),asin(0.93)-1.194412844477],_
+[0.94,1.222630305522,asin(0.94),asin(0.94)-1.222630305522],_
+[0.95,1.253235897503,asin(0.95),asin(0.95)-1.253235897503],_
+[0.96,1.287002217587,asin(0.96),asin(0.96)-1.287002217587],_
+[0.97,1.325230809280,asin(0.97),asin(0.97)-1.325230809280],_
+[0.98,1.370461484472,asin(0.98),asin(0.98)-1.370461484472],_
+[0.99,1.429256853470,asin(0.99),asin(0.99)-1.429256853470],_
+[1.00,1.570796326795,asin(1.00),asin(1.00)-1.570796326795]]
+--R
+--R
+--R (1)
+--R [[0.01,0.0100001666 74,0.0100001666 7416711312 6,0.167113126 E -12],
+--R [0.02,0.0200013335 73,0.0200013335 7339049175 1,0.390491751 E -12],
+--R [0.03,0.0300045018 23,0.0300045018 2347693769,0.47693769 E -12],
+--R [0.04,0.0400106743 54,0.0400106743 5398892622 1,- 0.1107378 E -13],
+--R [0.05,0.0500208568 06,0.0500208568 0577001466 3,- 0.229985337 E -12],
+--R [0.06,0.0600360584 45,0.0600360584 452784225,0.2784225 E -12],
+--R [0.07,0.0700572930 88,0.0700572930 8805025329 9,0.502533 E -13],
+--R [0.08,0.0800855800 34,0.0800855800 3365901374 8,- 0.34098625 E -12],
+--R [0.09,0.0901219450 15,0.0901219450 1459525581 5,- 0.40474419 E -12],
+--R [0.1,0.1001674211 62,0.1001674211 6155979635,- 0.44020365 E -12],
+--R [0.11,0.1102230499 88,0.1102230499 8774663318,- 0.25336682 E -12],
+--R [0.12,0.1202898823 95,0.1202898823 9478807132,- 0.21192868 E -12],
+--R [0.13,0.1303689797 03,0.1303689797 0314551294,0.14551294 E -12],
+--R [0.14,0.1404614147 1,0.1404614147 0985580027,- 0.14419973 E -12],
+--R [0.15,0.1505682727 77,0.1505682727 7668602642,- 0.31397358 E -12],
+--R [0.16,0.1606906529 52,0.1606906529 5191060036,- 0.8939964 E -13],
+--R [0.17,0.1708296691 29,0.1708296691 2910450072,0.1045007 E -12],
+--R [0.18,0.1809864512 47,0.1809864512 4654770725,- 0.45229275 E -12],
+--R [0.19,0.1911621465 31,0.1911621465 3105960346,0.5960346 E -13],
+--R [0.2,0.2013579207 9,0.2013579207 9033079146,0.33079146 E -12],
+--R [0.21,0.2115749597 58,0.2115749597 5809561381,0.9561381 E -13],
+--R [0.22,0.2218144704 97,0.2218144704 9679441094,- 0.20558906 E -12],
+--R [0.23,0.2320776828 63,0.2320776828 6271317742,- 0.28682258 E -12],
+--R [0.24,0.2423658510 39,0.2423658510 3896323277,- 0.3676723 E -13],
+--R [0.25,0.2526802551 42,0.2526802551 4207865349,0.7865349 E -13],
+--R [0.26,0.2630222029 08,0.2630222029 0846889582,0.46889582 E -12],
+--R [0.27,0.2733930314 67,0.2733930314 6747322258,0.47322258 E -12],
+--R [0.28,0.2837941092 08,0.2837941092 0832784562,0.32784563 E -12],
+--R [0.29,0.2942268377 49,0.2942268377 4898247936,- 0.175206 E -13],
+--R [0.3,0.3046926540 15,0.3046926540 1539750797,0.39750797 E -12],
+--R [0.31,0.3151930324 41,0.3151930324 4072444134,- 0.27555866 E -12],
+--R [0.32,0.3257294872 95,0.3257294872 9463015931,- 0.36984069 E -12],
+--R [0.33,0.3363035751 54,0.3363035751 5398034192,- 0.196581 E -13],
+--R [0.34,0.3469168975 27,0.3469168975 2716170922,0.1617092 E -12],
+--R [0.35,0.3575711036 46,0.3575711036 4551028671,- 0.48971329 E -12],
+--R [0.36,0.3682678934 37,0.3682678934 3663998093,- 0.36001907 E -12],
+--R [0.37,0.3790090206 96,0.3790090206 9595081407,- 0.4918592 E -13],
+--R [0.38,0.3897962964 74,0.3897962964 7426056359,0.26056359 E -12],
+--R [0.39,0.4006315927 01,0.4006315927 0137191121,0.37191121 E -12],
+--R [0.4,0.4115168460 67,0.4115168460 6748801938,0.48801938 E -12],
+--R [0.41,0.4224540621 87,0.4224540621 8675575657,- 0.24424343 E -12],
+--R [0.42,0.4334453200 7,0.4334453200 6988597641,- 0.1140236 E -12],
+--R [0.43,0.4444927769 36,0.4444927769 3581903875,- 0.1809612 E -12],
+--R [0.44,0.4555986733 96,0.4555986733 9582336298,- 0.176637 E -12],
+--R [0.45,0.4667653390 47,0.4667653390 4729636185,0.29636185 E -12],
+--R [0.46,0.4779951985 19,0.4779951985 1895237921,- 0.4762079 E -13],
+--R [0.47,0.4892907780 14,0.4892907780 1411571422,0.1157142 E -12],
+--R [0.48,0.5006547124 05,0.5006547124 0458816211,- 0.4118379 E -12],
+--R [0.49,0.5120897529 34,0.5120897529 3414777137,0.1477714 E -12],
+--R [0.5,0.5235987755 98,0.5235987755 9829887308,0.2988731 E -12],
+--R [0.51,0.5351847902 76,0.5351847902 7559984754,- 0.4001525 E -12],
+--R [0.52,0.5468509506 96,0.5468509506 9594410879,- 0.558912 E -13],
+--R [0.53,0.5586005653 43,0.5586005653 4280071945,- 0.1992805 E -12],
+--R [0.54,0.5704371094,0.5704371093 9992190735,- 0.7809265 E -13],
+--R [0.55,0.5823642378 69,0.5823642378 6874344183,- 0.2565582 E -12],
+--R [0.56,0.5943858000 01,0.5943858000 0106220388,0.6220388 E -13],
+--R [0.57,0.6065058552 13,0.6065058552 1308694718,0.8694718 E -13],
+--R [0.58,0.6187286906 72,0.6187286906 7225109051,0.2510905 E -12],
+--R [0.59,0.6310588407 78,0.6310588407 7802138008,0.213801 E -13],
+--R [0.6,0.6435011087 93,0.6435011087 932843868,0.2843868 E -12],
+--R [0.61,0.6560605909 25,0.6560605909 2492264451,- 0.7735549 E -13],
+--R [0.62,0.6687427032 02,0.6687427032 0237175414,0.3717541 E -12],
+--R [0.63,0.6815532115 63,0.6815532115 6311692392,0.1169239 E -12],
+--R [0.64,0.6944982656 27,0.6944982656 2655598784,- 0.4440122 E -12],
+--R [0.65,0.7075844367 25,0.7075844367 2535557545,0.3555755 E -12],
+--R [0.66,0.7208187608 7,0.7208187608 7008963003,0.8963003 E -13],
+--R [0.67,0.7342087874 53,0.7342087874 533589103,0.3589103 E -12],
+--R [0.68,0.7477626346 6,0.7477626346 5992058046,- 0.7941954 E -13],
+--R [0.69,0.7614890527 48,0.7614890527 4763322831,- 0.3667717 E -12],
+--R [0.7,0.7753974966 11,0.7753974966 1075306374,- 0.2469363 E -12],
+--R [0.71,0.7894982093 46,0.7894982093 4617197301,0.171973 E -12],
+--R [0.72,0.8038023189 33,0.8038023189 3303003221,0.300322 E -13],
+--R [0.73,0.8183219506 32,0.8183219506 3155981721,- 0.4401828 E -12],
+--R [0.74,0.8330703583 42,0.8330703583 4164781149,- 0.3521885 E -12],
+--R [0.75,0.8480620789 81,0.8480620789 8148100805,0.48100805 E -12],
+--R [0.76,0.8633131150 16,0.8633131150 1555364761,- 0.4463524 E -12],
+--R [0.77,0.8788411516 69,0.8788411516 6857970602,- 0.420294 E -12],
+--R [0.78,0.8946658172 34,0.8946658172 3423520948,0.2352095 E -12],
+--R [0.79,0.9108089974 07,0.9108089974 0739818925,0.3981893 E -12],
+--R [0.8,0.9272952180 02,0.9272952180 0161223243,- 0.3877676 E -12],
+--R [0.81,0.9441521151 54,0.9441521151 5415595048,0.1559505 E -12],
+--R [0.82,0.9614110187 64,0.9614110187 6410160329,0.1016033 E -12],
+--R [0.83,0.9791076843 68,0.9791076843 6835265479,0.3526548 E -12],
+--R [0.84,0.9972832223 72,0.9972832223 7179986605,- 0.2001339 E -12],
+--R [0.85,1.0159852938 15,1.0159852938 148251312,- 0.1748688 E -12],
+--R [0.86,1.0352696724 81,1.0352696724 805087973,- 0.4912027 E -12],
+--R [0.87,1.0552023205 49,1.0552023205 488061213,- 0.1938787 E -12],
+--R [0.88,1.0758622004 54,1.0758622004 540010964,0.10964 E -14],
+--R [0.89,1.0973451695 23,1.0973451695 228303977,- 0.1696023 E -12],
+--R [0.9,1.1197695149 99,1.1197695149 986341867,- 0.3658133 E -12],
+--R [0.91,1.1432840618 5,1.1432840618 500270323,0.270323 E -13],
+--R [0.92,1.1680804852 14,1.1680804852 142350363,0.2350363 E -12],
+--R [0.93,1.1944128444 77,1.1944128444 771683741,0.1683741 E -12],
+--R [0.94,1.2226303055 22,1.2226303055 21935738,- 0.64262 E -13],
+--R [0.95,1.2532358975 03,1.2532358975 033752587,0.3752587 E -12],
+--R [0.96,1.2870022175 87,1.2870022175 865687736,- 0.4312264 E -12],
+--R [0.97,1.3252308092 8,1.3252308092 796046112,- 0.3953888 E -12],
+--R [0.98,1.3704614844 72,1.3704614844 717770265,- 0.2229735 E -12],
+--R [0.99,1.4292568534 7,1.4292568534 704694005,0.4694005 E -12],
+--R [1.0,1.5707963267 95,1.5707963267 948966192,- 0.103381 E -12]]
+--R Type: List List
Float
+--E 1
+@
+In the following table there are 4 columns. The first column
+is the argument of atan(x), ranging from 0.01 to 1.00. The
+second column is the reference value of tan from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp203-212
+<<*>>=
+
+--S 2 of 2
+[[0.01,0.009999666687,atan(0.01),atan(0.01)-0.009999666687],_
+[0.02,0.019997333973,atan(0.02),atan(0.02)-0.019997333973],_
+[0.03,0.029991004857,atan(0.03),atan(0.03)-0.029991004857],_
+[0.04,0.039978687123,atan(0.04),atan(0.04)-0.039978687123],_
+[0.05,0.049958395722,atan(0.05),atan(0.05)-0.049958395722],_
+[0.06,0.059928155121,atan(0.06),atan(0.06)-0.059928155121],_
+[0.07,0.069886001635,atan(0.07),atan(0.07)-0.069886001635],_
+[0.08,0.079829985712,atan(0.08),atan(0.08)-0.079829985712],_
+[0.09,0.089758174190,atan(0.09),atan(0.09)-0.089758174190],_
+[0.10,0.099668652491,atan(0.10),atan(0.10)-0.099668652491],_
+[0.11,0.109559526774,atan(0.11),atan(0.11)-0.109559526774],_
+[0.12,0.119428926018,atan(0.12),atan(0.12)-0.119428926018],_
+[0.13,0.129275004048,atan(0.13),atan(0.13)-0.129275004048],_
+[0.14,0.139095941482,atan(0.14),atan(0.14)-0.139095941482],_
+[0.15,0.148889947609,atan(0.15),atan(0.15)-0.148889947609],_
+[0.16,0.158655262186,atan(0.16),atan(0.16)-0.158655262186],_
+[0.17,0.168390157148,atan(0.17),atan(0.17)-0.168390157148],_
+[0.18,0.178092938231,atan(0.18),atan(0.18)-0.178092938231],_
+[0.19,0.187761946514,atan(0.19),atan(0.19)-0.187761946514],_
+[0.20,0.197395559850,atan(0.20),atan(0.20)-0.197395559850],_
+[0.21,0.206992194220,atan(0.21),atan(0.21)-0.206992194220],_
+[0.22,0.216550304976,atan(0.22),atan(0.22)-0.216550304976],_
+[0.23,0.226068387994,atan(0.23),atan(0.23)-0.226068387994],_
+[0.24,0.235544980721,atan(0.24),atan(0.24)-0.235544980721],_
+[0.25,0.244978663127,atan(0.25),atan(0.25)-0.244978663127],_
+[0.26,0.254368058553,atan(0.26),atan(0.26)-0.254368058553],_
+[0.27,0.263711834462,atan(0.27),atan(0.27)-0.263711834462],_
+[0.28,0.273008703087,atan(0.28),atan(0.28)-0.273008703087],_
+[0.29,0.282257421981,atan(0.29),atan(0.29)-0.282257421981],_
+[0.30,0.291456794478,atan(0.30),atan(0.30)-0.291456794478],_
+[0.31,0.300605670042,atan(0.31),atan(0.31)-0.300605670042],_
+[0.32,0.309702944542,atan(0.32),atan(0.32)-0.309702944542],_
+[0.33,0.318747560421,atan(0.33),atan(0.33)-0.318747560421],_
+[0.34,0.327738506781,atan(0.34),atan(0.34)-0.327738506781],_
+[0.35,0.336674819387,atan(0.35),atan(0.35)-0.336674819387],_
+[0.36,0.345555580582,atan(0.36),atan(0.36)-0.345555580582],_
+[0.37,0.354379919123,atan(0.37),atan(0.37)-0.354379919123],_
+[0.38,0.363147009946,atan(0.38),atan(0.38)-0.363147009946],_
+[0.39,0.371856073849,atan(0.39),atan(0.39)-0.371856073849],_
+[0.40,0.380506377112,atan(0.40),atan(0.40)-0.380506377112],_
+[0.41,0.389097231055,atan(0.41),atan(0.41)-0.389097231055],_
+[0.42,0.397627991522,atan(0.42),atan(0.42)-0.397627991522],_
+[0.43,0.406098058318,atan(0.43),atan(0.43)-0.406098058318],_
+[0.44,0.414506874585,atan(0.44),atan(0.44)-0.414506874585],_
+[0.45,0.422853926133,atan(0.45),atan(0.45)-0.422853926133],_
+[0.46,0.431138740719,atan(0.46),atan(0.46)-0.431138740719],_
+[0.47,0.439360887285,atan(0.47),atan(0.47)-0.439360887285],_
+[0.48,0.447519975157,atan(0.48),atan(0.48)-0.447519975157],_
+[0.49,0.455615653211,atan(0.49),atan(0.49)-0.455615653211],_
+[0.50,0.463647609001,atan(0.50),atan(0.50)-0.463647609001],_
+[0.51,0.471615567862,atan(0.51),atan(0.51)-0.471615567862],_
+[0.52,0.479519291993,atan(0.52),atan(0.52)-0.479519291993],_
+[0.53,0.487358579505,atan(0.53),atan(0.53)-0.487358579505],_
+[0.54,0.495133263468,atan(0.54),atan(0.54)-0.495133263468],_
+[0.55,0.502843210928,atan(0.55),atan(0.55)-0.502843210928],_
+[0.56,0.510488321917,atan(0.56),atan(0.56)-0.510488321917],_
+[0.57,0.518068528457,atan(0.57),atan(0.57)-0.518068528457],_
+[0.58,0.525583793552,atan(0.58),atan(0.58)-0.525583793552],_
+[0.59,0.533034110177,atan(0.59),atan(0.59)-0.533034110177],_
+[0.60,0.540419500271,atan(0.60),atan(0.60)-0.540419500271],_
+[0.61,0.547740013716,atan(0.61),atan(0.61)-0.547740013716],_
+[0.62,0.554995727339,atan(0.62),atan(0.62)-0.554995727339],_
+[0.63,0.562186743900,atan(0.63),atan(0.63)-0.562186743900],_
+[0.64,0.569313191101,atan(0.64),atan(0.64)-0.569313191101],_
+[0.65,0.576375220591,atan(0.65),atan(0.65)-0.576375220591],_
+[0.66,0.583373006994,atan(0.66),atan(0.66)-0.583373006994],_
+[0.67,0.590306746935,atan(0.67),atan(0.67)-0.590306746935],_
+[0.68,0.597176658093,atan(0.68),atan(0.68)-0.597176658093],_
+[0.69,0.603982978253,atan(0.69),atan(0.69)-0.603982978253],_
+[0.70,0.610725964389,atan(0.70),atan(0.70)-0.610725964389],_
+[0.71,0.617405891752,atan(0.71),atan(0.71)-0.617405891752],_
+[0.72,0.624023052977,atan(0.72),atan(0.72)-0.624023052977],_
+[0.73,0.630577757215,atan(0.73),atan(0.73)-0.630577757215],_
+[0.74,0.637070329276,atan(0.74),atan(0.74)-0.637070329276],_
+[0.75,0.643501108793,atan(0.75),atan(0.75)-0.643501108793],_
+[0.76,0.649870449412,atan(0.76),atan(0.76)-0.649870449412],_
+[0.77,0.656178717991,atan(0.77),atan(0.77)-0.656178717991],_
+[0.78,0.662426293833,atan(0.78),atan(0.78)-0.662426293833],_
+[0.79,0.668613567928,atan(0.79),atan(0.79)-0.668613567928],_
+[0.80,0.674740942224,atan(0.80),atan(0.80)-0.674740942224],_
+[0.81,0.680808828916,atan(0.81),atan(0.81)-0.680808828916],_
+[0.82,0.686817649759,atan(0.82),atan(0.82)-0.686817649759],_
+[0.83,0.692767835397,atan(0.83),atan(0.83)-0.692767835397],_
+[0.84,0.698659824721,atan(0.84),atan(0.84)-0.698659824721],_
+[0.85,0.704494064242,atan(0.85),atan(0.85)-0.704494064242],_
+[0.86,0.710271007487,atan(0.86),atan(0.86)-0.710271007487],_
+[0.87,0.715991114416,atan(0.87),atan(0.87)-0.715991114416],_
+[0.88,0.721654850865,atan(0.88),atan(0.88)-0.721654850865],_
+[0.89,0.727262687997,atan(0.89),atan(0.89)-0.727262687997],_
+[0.90,0.732815101787,atan(0.90),atan(0.90)-0.732815101787],_
+[0.91,0.738312572517,atan(0.91),atan(0.91)-0.738312572517],_
+[0.92,0.743755584299,atan(0.92),atan(0.92)-0.743755584299],_
+[0.93,0.749144624606,atan(0.93),atan(0.93)-0.749144624606],_
+[0.94,0.754480183834,atan(0.94),atan(0.94)-0.754480183834],_
+[0.95,0.759762754876,atan(0.95),atan(0.95)-0.759762754876],_
+[0.96,0.764992832711,atan(0.96),atan(0.96)-0.764992832711],_
+[0.97,0.770170914020,atan(0.97),atan(0.97)-0.770170914020],_
+[0.98,0.775297496812,atan(0.98),atan(0.98)-0.775297496812],_
+[0.99,0.780373080067,atan(0.99),atan(0.99)-0.780373080067],_
+[1.00,0.785398163397,atan(1.00),atan(1.00)-0.785398163397]]
+--R
+--R
+--R (2)
+--R [[0.01,0.0099996666 87,0.0099996666 8666523820 63,- 0.334761794 E -12],
+--R [0.02,0.0199973339 73,0.0199973339 7315053306 1,0.150533061 E -12],
+--R [0.03,0.0299910048 57,0.0299910048 5687789967 7,- 0.122100323 E -12],
+--R [0.04,0.0399786871 23,0.0399786871 2329004141 4,0.290041414 E -12],
+--R [0.05,0.0499583957 22,0.0499583957 2194276141,- 0.5723859 E -13],
+--R [0.06,0.0599281551 21,0.0599281551 2120788443 2,0.20788443 E -12],
+--R [0.07,0.0698860016 35,0.0698860016 3464249929 5,- 0.35750071 E -12],
+--R [0.08,0.0798299857 12,0.0798299857 1223731589 3,0.23731589 E -12],
+--R [0.09,0.0897581741 9,0.0897581741 8995052315,- 0.4947685 E -13],
+--R [0.1,0.0996686524 91,0.0996686524 9116202737 9,0.16202738 E -12],
+--R [0.11,0.1095595267 74,0.1095595267 7394434487,- 0.5565513 E -13],
+--R [0.12,0.1194289260 18,0.1194289260 1833845181,0.33845181 E -12],
+--R [0.13,0.1292750040 48,0.1292750040 4814305472,0.14305472 E -12],
+--R [0.14,0.1390959414 82,0.1390959414 820713243,0.713243 E -13],
+--R [0.15,0.1488899476 09,0.1488899476 0949725059,0.49725059 E -12],
+--R [0.16,0.1586552621 86,0.1586552621 8640140386,0.40140386 E -12],
+--R [0.17,0.1683901571 48,0.1683901571 4752989727,- 0.47010272 E -12],
+--R [0.18,0.1780929382 31,0.1780929382 3119754967,0.19754967 E -12],
+--R [0.19,0.1877619465 14,0.1877619465 135934152,- 0.4065848 E -12],
+--R [0.2,0.1973955598 5,0.1973955598 4988075837,- 0.11924163 E -12],
+--R [0.21,0.2069921942 2,0.2069921942 198210249,- 0.1789751 E -12],
+--R [0.22,0.2165503049 76,0.2165503049 7608927648,0.8927648 E -13],
+--R [0.23,0.2260683879 94,0.2260683879 9388390584,- 0.11609416 E -12],
+--R [0.24,0.2355449807 21,0.2355449807 2086334143,- 0.13665857 E -12],
+--R [0.25,0.2449786631 27,0.2449786631 2686415417,- 0.13584583 E -12],
+--R [0.26,0.2543680585 53,0.2543680585 5326593143,0.26593143 E -12],
+--R [0.27,0.2637118344 62,0.2637118344 6226612016,0.26612016 E -12],
+--R [0.28,0.2730087030 87,0.2730087030 8671060295,- 0.28939705 E -12],
+--R [0.29,0.2822574219 81,0.2822574219 8149112127,0.49112127 E -12],
+--R [0.3,0.2914567944 78,0.2914567944 77867092,- 0.132908 E -12],
+--R [0.31,0.3006056700 42,0.3006056700 4239540423,0.39540423 E -12],
+--R [0.32,0.3097029445 42,0.3097029445 4245619992,0.45619992 E -12],
+--R [0.33,0.3187475604 21,0.3187475604 2064443712,- 0.35556288 E -12],
+--R [0.34,0.3277385067 81,0.3277385067 80555446,- 0.444554 E -12],
+--R [0.35,0.3366748193 87,0.3366748193 867271814,- 0.2728186 E -12],
+--R [0.36,0.3455555805 82,0.3455555805 8171213686,- 0.28786314 E -12],
+--R [0.37,0.3543799191 23,0.3543799191 2343780983,0.43780983 E -12],
+--R [0.38,0.3631470099 46,0.3631470099 4617628972,0.1762897 E -12],
+--R [0.39,0.3718560738 49,0.3718560738 485812575,- 0.4187425 E -12],
+--R [0.4,0.3805063771 12,0.3805063771 123648863,0.3648863 E -12],
+--R [0.41,0.3890972310 55,0.3890972310 5527841924,0.27841924 E -12],
+--R [0.42,0.3976279915 22,0.3976279915 22129314,0.129314 E -12],
+--R [0.43,0.4060980583 18,0.4060980583 1761564783,- 0.38435217 E -12],
+--R [0.44,0.4145068745 85,0.4145068745 8478593834,- 0.2140617 E -12],
+--R [0.45,0.4228539261 33,0.4228539261 3294071297,- 0.5928703 E -13],
+--R [0.46,0.4311387407 19,0.4311387407 1878218339,- 0.2178166 E -12],
+--R [0.47,0.4393608872 85,0.4393608872 8459143742,- 0.40856258 E -12],
+--R [0.48,0.4475199751 57,0.4475199751 5716987972,0.1698797 E -12],
+--R [0.49,0.4556156532 11,0.4556156532 1122449214,0.2244921 E -12],
+--R [0.5,0.4636476090 01,0.4636476090 0080611621,- 0.1938838 E -12],
+--R [0.51,0.4716155678 62,0.4716155678 6232766012,0.32766012 E -12],
+--R [0.52,0.4795192919 93,0.4795192919 9259616542,- 0.40383458 E -12],
+--R [0.53,0.4873585795 05,0.4873585795 0519028312,0.1902831 E -12],
+--R [0.54,0.4951332634 68,0.4951332634 6840412185,0.40412185 E -12],
+--R [0.55,0.5028432109 28,0.5028432109 2786082733,- 0.1391727 E -12],
+--R [0.56,0.5104883219 17,0.5104883219 1677576997,- 0.22423 E -12],
+--R [0.57,0.5180685284 57,0.5180685284 56720949,- 0.279051 E -12],
+--R [0.58,0.5255837935 52,0.5255837935 5161020277,- 0.3897972 E -12],
+--R [0.59,0.5330341101 77,0.5330341101 7749002604,0.49002604 E -12],
+--R [0.6,0.5404195002 71,0.5404195002 7058415544,- 0.4158446 E -12],
+--R [0.61,0.5477400137 16,0.5477400137 1590245052,- 0.9754948 E -13],
+--R [0.62,0.5549957273 39,0.5549957273 3858676242,- 0.4132376 E -12],
+--R [0.63,0.5621867439,0.5621867439 0002917485,0.291748 E -13],
+--R [0.64,0.5693131911 01,0.5693131911 0066188631,- 0.3381137 E -12],
+--R [0.65,0.5763752205 91,0.5763752205 9118368022,0.1836802 E -12],
+--R [0.66,0.5833730069 94,0.5833730069 9385593947,- 0.1440605 E -12],
+--R [0.67,0.5903067469 35,0.5903067469 3537198239,0.3719824 E -12],
+--R [0.68,0.5971766580 93,0.5971766580 9267754844,- 0.3224516 E -12],
+--R [0.69,0.6039829782 53,0.6039829782 5299790738,- 0.20926 E -14],
+--R [0.7,0.6107259643 89,0.6107259643 8920861654,0.2086165 E -12],
+--R [0.71,0.6174058917 52,0.6174058917 5157266652,- 0.4273335 E -12],
+--R [0.72,0.6240230529 77,0.6240230529 7675684759,- 0.2431524 E -12],
+--R [0.73,0.6305777572 15,0.6305777572 1493480666,- 0.6519333 E -13],
+--R [0.74,0.6370703292 76,0.6370703292 7568357172,- 0.3164283 E -12],
+--R [0.75,0.6435011087 93,0.6435011087 932843868,0.2843868 E -12],
+--R [0.76,0.6498704494 12,0.6498704494 1194757749,- 0.524225 E -13],
+--R [0.77,0.6561787179 91,0.6561787179 9139487538,0.3948754 E -12],
+--R [0.78,0.6624262938 33,0.6624262938 3315116177,0.1511618 E -12],
+--R [0.79,0.6686135679 28,0.6686135679 2782091069,- 0.1790893 E -12],
+--R [0.8,0.6747409422 24,0.6747409422 2355266306,- 0.4473369 E -12],
+--R [0.81,0.6808088289 16,0.6808088289 1582756649,- 0.1724335 E -12],
+--R [0.82,0.6868176497 59,0.6868176497 5864527553,- 0.3547245 E -12],
+--R [0.83,0.6927678353 97,0.6927678353 9712221066,0.1222107 E -12],
+--R [0.84,0.6986598247 21,0.6986598247 214631978,0.4631978 E -12],
+--R [0.85,0.7044940642 42,0.7044940642 4221771666,0.2177167 E -12],
+--R [0.86,0.7102710074 87,0.7102710074 8668623033,- 0.3137697 E -12],
+--R [0.87,0.7159911144 16,0.7159911144 1630019894,0.3001989 E -12],
+--R [0.88,0.7216548508 65,0.7216548508 6476123707,- 0.2387629 E -12],
+--R [0.89,0.7272626879 97,0.7272626879 9669029805,- 0.309702 E -12],
+--R [0.9,0.7328151017 87,0.7328151017 8650659164,- 0.49340836 E -12],
+--R [0.91,0.7383125725 17,0.7383125725 1722800021,0.2280002 E -12],
+--R [0.92,0.7437555842 99,0.7437555842 9885988576,- 0.1401142 E -12],
+--R [0.93,0.7491446246 06,0.7491446246 0601721032,0.172103 E -13],
+--R [0.94,0.7544801838 34,0.7544801838 3440566231,0.4056623 E -12],
+--R [0.95,0.7597627548 76,0.7597627548 7577082892,- 0.2291711 E -12],
+--R [0.96,0.7649928327 11,0.7649928327 1091022317,- 0.8977683 E -13],
+--R [0.97,0.7701709140 2,0.7701709140 2033100726,0.3310073 E -12],
+--R [0.98,0.7752974968 12,0.7752974968 1212640304,0.126403 E -12],
+--R [0.99,0.7803730800 67,0.7803730800 666358989,- 0.3641011 E -12],
+--R [1.0,0.7853981633 97,0.7853981633 9744830961,0.4483096 E -12]]
+--R Type: List List
Float
+--E 2
+
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp203-212
+\end{thebibliography}
+\end{document}
+
diff --git a/src/input/asinhatanh.input.pamphlet
b/src/input/asinhatanh.input.pamphlet
new file mode 100644
index 0000000..b0c7783
--- /dev/null
+++ b/src/input/asinhatanh.input.pamphlet
@@ -0,0 +1,460 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input asinhatanh.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This is a set of tests for the tanh and coth functions.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+In the following table there are 4 columns. The first column
+is the argument of asinh, ranging from 0.00 to 1.00. The
+second column is the reference value of asinh from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp221
+
+<<*>>=
+)spool asinhatanh.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 2
+[[0.00,0.000000000,asinh(0.00),asinh(0.00)-0.000000000],_
+[0.01,0.009999833,asinh(0.01),asinh(0.01)-0.009999833],_
+[0.02,0.019998667,asinh(0.02),asinh(0.02)-0.019998667],_
+[0.03,0.029995502,asinh(0.03),asinh(0.03)-0.029995502],_
+[0.04,0.039989341,asinh(0.04),asinh(0.04)-0.039989341],_
+[0.05,0.049979190,asinh(0.05),asinh(0.05)-0.049979190],_
+[0.06,0.059964058,asinh(0.06),asinh(0.06)-0.059964058],_
+[0.07,0.069942959,asinh(0.07),asinh(0.07)-0.069942959],_
+[0.08,0.079914912,asinh(0.08),asinh(0.08)-0.079914912],_
+[0.09,0.089878941,asinh(0.09),asinh(0.09)-0.089878941],_
+[0.10,0.099834079,asinh(0.10),asinh(0.10)-0.099834079],_
+[0.11,0.109779366,asinh(0.11),asinh(0.11)-0.109779366],_
+[0.12,0.119713851,asinh(0.12),asinh(0.12)-0.119713851],_
+[0.13,0.129636590,asinh(0.13),asinh(0.13)-0.129636590],_
+[0.14,0.139546654,asinh(0.14),asinh(0.14)-0.139546654],_
+[0.15,0.149443120,asinh(0.15),asinh(0.15)-0.149443120],_
+[0.16,0.159325080,asinh(0.16),asinh(0.16)-0.159325080],_
+[0.17,0.169191636,asinh(0.17),asinh(0.17)-0.169191636],_
+[0.18,0.179041904,asinh(0.18),asinh(0.18)-0.179041904],_
+[0.19,0.188875015,asinh(0.19),asinh(0.19)-0.188875015],_
+[0.20,0.198690110,asinh(0.20),asinh(0.20)-0.198690110],_
+[0.21,0.208486350,asinh(0.21),asinh(0.21)-0.208486350],_
+[0.22,0.218262908,asinh(0.22),asinh(0.22)-0.218262908],_
+[0.23,0.228018972,asinh(0.23),asinh(0.23)-0.228018972],_
+[0.24,0.237753749,asinh(0.24),asinh(0.24)-0.237753749],_
+[0.25,0.247466462,asinh(0.25),asinh(0.25)-0.247466462],_
+[0.26,0.257156349,asinh(0.26),asinh(0.26)-0.257156349],_
+[0.27,0.266822667,asinh(0.27),asinh(0.27)-0.266822667],_
+[0.28,0.276464691,asinh(0.28),asinh(0.28)-0.276464691],_
+[0.29,0.286081715,asinh(0.29),asinh(0.29)-0.286081715],_
+[0.30,0.295673048,asinh(0.30),asinh(0.30)-0.295673048],_
+[0.31,0.305238020,asinh(0.31),asinh(0.31)-0.305238020],_
+[0.32,0.314775980,asinh(0.32),asinh(0.32)-0.314775980],_
+[0.33,0.324286295,asinh(0.33),asinh(0.33)-0.324286295],_
+[0.34,0.333768352,asinh(0.34),asinh(0.34)-0.333768352],_
+[0.35,0.343221555,asinh(0.35),asinh(0.35)-0.343221555],_
+[0.36,0.352645330,asinh(0.36),asinh(0.36)-0.352645330],_
+[0.37,0.362039121,asinh(0.37),asinh(0.37)-0.362039121],_
+[0.38,0.371402391,asinh(0.38),asinh(0.38)-0.371402391],_
+[0.39,0.380734624,asinh(0.39),asinh(0.39)-0.380734624],_
+[0.40,0.390035320,asinh(0.40),asinh(0.40)-0.390035320],_
+[0.41,0.399304001,asinh(0.41),asinh(0.41)-0.399304001],_
+[0.42,0.408540208,asinh(0.42),asinh(0.42)-0.408540208],_
+[0.43,0.417743500,asinh(0.43),asinh(0.43)-0.417743500],_
+[0.44,0.426913454,asinh(0.44),asinh(0.44)-0.426913454],_
+[0.45,0.436049669,asinh(0.45),asinh(0.45)-0.436049669],_
+[0.46,0.445151759,asinh(0.46),asinh(0.46)-0.445151759],_
+[0.47,0.454219359,asinh(0.47),asinh(0.47)-0.454219359],_
+[0.48,0.463252120,asinh(0.48),asinh(0.48)-0.463252120],_
+[0.49,0.472249713,asinh(0.49),asinh(0.49)-0.472249713],_
+[0.50,0.481211825,asinh(0.50),asinh(0.50)-0.481211825],_
+[0.51,0.490138161,asinh(0.51),asinh(0.51)-0.490138161],_
+[0.52,0.499028444,asinh(0.52),asinh(0.52)-0.499028444],_
+[0.53,0.507882413,asinh(0.53),asinh(0.53)-0.507882413],_
+[0.54,0.516699824,asinh(0.54),asinh(0.54)-0.516699824],_
+[0.55,0.525480448,asinh(0.55),asinh(0.55)-0.525480448],_
+[0.56,0.534224074,asinh(0.56),asinh(0.56)-0.534224074],_
+[0.57,0.542930505,asinh(0.57),asinh(0.57)-0.542930505],_
+[0.58,0.551599562,asinh(0.58),asinh(0.58)-0.551599562],_
+[0.59,0.560231077,asinh(0.59),asinh(0.59)-0.560231077],_
+[0.60,0.568824899,asinh(0.60),asinh(0.60)-0.568824899],_
+[0.61,0.577380892,asinh(0.61),asinh(0.61)-0.577380892],_
+[0.62,0.585898932,asinh(0.62),asinh(0.62)-0.585898932],_
+[0.63,0.594378911,asinh(0.63),asinh(0.63)-0.594378911],_
+[0.64,0.602820733,asinh(0.64),asinh(0.64)-0.602820733],_
+[0.65,0.611224314,asinh(0.65),asinh(0.65)-0.611224314],_
+[0.66,0.619589584,asinh(0.66),asinh(0.66)-0.619589584],_
+[0.67,0.627916485,asinh(0.67),asinh(0.67)-0.627916485],_
+[0.68,0.636204970,asinh(0.68),asinh(0.68)-0.636204970],_
+[0.69,0.644455005,asinh(0.69),asinh(0.69)-0.644455005],_
+[0.70,0.652666566,asinh(0.70),asinh(0.70)-0.652666566],_
+[0.71,0.660839641,asinh(0.71),asinh(0.71)-0.660839641],_
+[0.72,0.668974227,asinh(0.72),asinh(0.72)-0.668974227],_
+[0.73,0.677070332,asinh(0.73),asinh(0.73)-0.677070332],_
+[0.74,0.685127974,asinh(0.74),asinh(0.74)-0.685127974],_
+[0.75,0.693147181,asinh(0.75),asinh(0.75)-0.693147181],_
+[0.76,0.701127988,asinh(0.76),asinh(0.76)-0.701127988],_
+[0.77,0.709070441,asinh(0.77),asinh(0.77)-0.709070441],_
+[0.78,0.716974594,asinh(0.78),asinh(0.78)-0.716974594],_
+[0.79,0.724840509,asinh(0.79),asinh(0.79)-0.724840509],_
+[0.80,0.732668256,asinh(0.80),asinh(0.80)-0.732668256],_
+[0.81,0.740457912,asinh(0.81),asinh(0.81)-0.740457912],_
+[0.82,0.748209563,asinh(0.82),asinh(0.82)-0.748209563],_
+[0.83,0.755923300,asinh(0.83),asinh(0.83)-0.755923300],_
+[0.84,0.763599222,asinh(0.84),asinh(0.84)-0.763599222],_
+[0.85,0.771237433,asinh(0.85),asinh(0.85)-0.771237433],_
+[0.86,0.778838046,asinh(0.86),asinh(0.86)-0.778838046],_
+[0.87,0.786401177,asinh(0.87),asinh(0.87)-0.786401177],_
+[0.88,0.793926950,asinh(0.88),asinh(0.88)-0.793926950],_
+[0.89,0.801415491,asinh(0.89),asinh(0.89)-0.801415491],_
+[0.90,0.808866936,asinh(0.90),asinh(0.90)-0.808866936],_
+[0.91,0.816281421,asinh(0.91),asinh(0.91)-0.816281421],_
+[0.92,0.823659091,asinh(0.92),asinh(0.92)-0.823659091],_
+[0.93,0.831000091,asinh(0.93),asinh(0.93)-0.831000091],_
+[0.94,0.838304575,asinh(0.94),asinh(0.94)-0.838304575],_
+[0.95,0.845572697,asinh(0.95),asinh(0.95)-0.845572697],_
+[0.96,0.852804617,asinh(0.96),asinh(0.96)-0.852804617],_
+[0.97,0.860000498,asinh(0.97),asinh(0.97)-0.860000498],_
+[0.98,0.867160507,asinh(0.98),asinh(0.98)-0.867160507],_
+[0.99,0.874284812,asinh(0.99),asinh(0.99)-0.874284812],_
+[1.00,0.881373587,asinh(1.00),asinh(1.00)-0.881373587]]
+--R
+--R
+--R (1)
+--R [[0.0,0.0,0.0,0.0],
+--R [0.01,0.009999833,0.0099998333 4083288693 52,0.3408328869 35 E -9],
+--R [0.02,0.019998667,0.0199986669 0660953936,- 0.9339046064 E -10],
+--R [0.03,0.029995502,0.0299955018 2152425832 6,- 0.1784757416 74 E -9],
+--R [0.04,0.039989341,0.0399893410 0602700269 1,0.6027002691 E -11],
+--R [0.05,0.04997919,0.0499791900 6934866523 2,0.6934866523 2 E -10],
+--R [0.06,0.059964058,0.0599640581 9533394203 3,0.1953339420 3 E -9],
+--R [0.07,0.069942959,0.0699429590 1940182241 9,0.1940182242 E -10],
+--R [0.08,0.079914912,0.0799149114 9449676816 5,- 0.5055032318 35 E -9],
+--R [0.09,0.089878941,0.0898789407 4394680193 8,- 0.2560531980 6 E -9],
+--R [0.1,0.099834079,0.0998340788 9920756332 7,- 0.1007924366 7 E -9],
+--R [0.11,0.109779366,0.1097793659 2054342078,- 0.7945657921 7 E -10],
+--R [0.12,0.119713851,0.1197138503 9877738636,- 0.6012226136 36 E -9],
+--R [0.13,0.12963659,0.1296365903 3633024308,0.3363302430 8 E -9],
+--R [0.14,0.139546654,0.1395466539 0586528422,- 0.9413471578 E -10],
+--R [0.15,0.14944312,0.1494431201 8495765616,0.1849576561 6 E -9],
+--R [0.16,0.15932508,0.1593250798 6531572882,- 0.1346842711 8 E -9],
+--R [0.17,0.169191636,0.1691916359 3519539889,- 0.6480460111 E -10],
+--R [0.18,0.179041904,0.1790419043 3376594692,0.3337659469 2 E -9],
+--R [0.19,0.188875015,0.1888750145 7630719416,- 0.4236928058 4 E -9],
+--R [0.2,0.19869011,0.1986901103 4924140647,0.3492414064 7 E -9],
+--R [0.21,0.20848635,0.2084863500 7412884481,0.7412884481 E -10],
+--R [0.22,0.218262908,0.2182629074 3988224632,- 0.5601177536 8 E -9],
+--R [0.23,0.228018972,0.2280189719 0258204081,- 0.9741795919 E -10],
+--R [0.24,0.237753749,0.2377537491 5239999115,0.1523999911 5 E -9],
+--R [0.25,0.247466462,0.2474664615 4726345294,- 0.4527365470 6 E -9],
+--R [0.26,0.257156349,0.2571563485 1301487614,- 0.4869851238 6 E -9],
+--R [0.27,0.266822667,0.2668226669 0994085825,- 0.9005914175 E -10],
+--R [0.28,0.276464691,0.2764646913 6566139339,0.3656613933 9 E -9],
+--R [0.29,0.286081715,0.2860817145 7448237948,- 0.4255176205 2 E -9],
+--R [0.3,0.295673048,0.2956730475 634224391,- 0.4365775609 E -9],
+--R [0.31,0.30523802,0.3052380199 2522822388,- 0.7477177612 E -10],
+--R [0.32,0.31477598,0.3147759800 1879020946,0.187902095 E -10],
+--R [0.33,0.324286295,0.3242862951 3746321043,0.1374632104 E -9],
+--R [0.34,0.333768352,0.3337683516 4588216777,- 0.3541178322 3 E -9],
+--R [0.35,0.343221555,0.3432215550 8594396213,0.8594396213 E -10],
+--R [0.36,0.35264533,0.3526453302 5269991354,0.2526999135 4 E -9],
+--R [0.37,0.362039121,0.3620391212 4097112736,0.2409711273 6 E -9],
+--R [0.38,0.371402391,0.3714023914 6355987334,0.4635598733 4 E -9],
+--R [0.39,0.380734624,0.3807346236 4198472547,- 0.3580152745 3 E -9],
+--R [0.4,0.39003532,0.3900353197 7071527608,- 0.2292847239 E -9],
+--R [0.41,0.399304001,0.3993040010 5592394477,0.5592394477 E -10],
+--R [0.42,0.408540208,0.4085402078 298078441,- 0.1701921559 E -9],
+--R [0.43,0.4177435,0.4177434994 4156299241,- 0.5584370075 9 E -9],
+--R [0.44,0.426913454,0.4269134541 2611656164,0.1261165616 E -9],
+--R [0.45,0.436049669,0.4360496688 517405265,- 0.1482594735 E -9],
+--R [0.46,0.445151759,0.4451517591 4768227909,0.1476822791 E -9],
+--R [0.47,0.454219359,0.4542193589 1295474595,- 0.8704525405 E -10],
+--R [0.48,0.46325212,0.4632521202 0743057053,0.2074305705 E -9],
+--R [0.49,0.472249713,0.4722497130 2638229031,0.263822903 E -10],
+--R [0.5,0.481211825,0.4812118250 596034475,0.596034475 E -10],
+--R [0.51,0.490138161,0.4901381614 3623452983,0.4362345298 3 E -9],
+--R [0.52,0.499028444,0.4990284444 564028591,0.4564028591 E -9],
+--R [0.53,0.507882413,0.5078824133 1076734063,0.3107673406 E -9],
+--R [0.54,0.516699824,0.5166998237 890376715,- 0.2109623285 E -9],
+--R [0.55,0.525480448,0.5254804479 7851348895,- 0.214865111 E -10],
+--R [0.56,0.534224074,0.5342240739 5366232528,- 0.463376747 E -10],
+--R [0.57,0.542930505,0.5429305054 5772642154,0.4577264215 E -9],
+--R [0.58,0.551599562,0.5515995615 7731772498,- 0.422682275 E -9],
+--R [0.59,0.560231077,0.5602310764 1092803468,- 0.5890719653 2 E -9],
+--R [0.6,0.568824899,0.5688248987 322475301,- 0.2677524699 E -9],
+--R [0.61,0.577380892,0.5773808916 4915007492,- 0.3508499251 E -9],
+--R [0.62,0.585898932,0.5858989322 5916797142,0.2591679714 E -9],
+--R [0.63,0.594378911,0.5943789113 0224247799,0.302242478 E -9],
+--R [0.64,0.602820733,0.6028207328 1149960517,- 0.1885003948 E -9],
+--R [0.65,0.611224314,0.6112243137 62763672,- 0.237236328 E -9],
+--R [0.66,0.619589584,0.6195895837 234840191,- 0.2765159809 E -9],
+--R [0.67,0.627916485,0.6279164845 0171330467,- 0.4982866953 3 E -9],
+--R [0.68,0.63620497,0.6362049697 9573911039,- 0.2042608896 E -9],
+--R [0.69,0.644455005,0.6444550048 449342957,- 0.1550657043 E -9],
+--R [0.7,0.652666566,0.6526665660 8235578681,0.8235578681 E -10],
+--R [0.71,0.660839641,0.6608396407 8958638519,- 0.2104136148 E -9],
+--R [0.72,0.668974227,0.6689742267 542798277,- 0.2457201723 E -9],
+--R [0.73,0.677070332,0.6770703319 3083581572,- 0.6916418427 E -10],
+--R [0.74,0.685127974,0.6851279741 0459912826,0.1045991283 E -9],
+--R [0.75,0.693147181,0.6931471805 5994530942,- 0.4400546906 E -9],
+--R [0.76,0.701127988,0.7011279877 5258482712,- 0.2474151729 E -9],
+--R [0.77,0.709070441,0.7090704409 8638808148,- 0.136119185 E -10],
+--R [0.78,0.716974594,0.7169745940 9500523361,0.9500523361 E -10],
+--R [0.79,0.724840509,0.7248405091 2852755291,0.1285275529 E -9],
+--R [0.8,0.732668256,0.7326682560 4541086415,0.454108642 E -10],
+--R [0.81,0.740457912,0.7404579124 098567228,0.4098567228 E -9],
+--R [0.82,0.748209563,0.7482095630 9482316487,0.9482316487 E -10],
+--R [0.83,0.7559233,0.7559232999 9081426309,- 0.918573691 E -11],
+--R [0.84,0.763599222,0.7635992217 205762674,- 0.2794237326 E -9],
+--R [0.85,0.771237433,0.7712374333 5980780282,0.3598078028 E -9],
+--R [0.86,0.778838046,0.7788380461 6397242546,0.1639724255 E -9],
+--R [0.87,0.786401177,0.7864011773 0128377712,0.3012837771 E -9],
+--R [0.88,0.79392695,0.7939269495 9191660771,- 0.4080833923 E -9],
+--R [0.89,0.801415491,0.8014154912 5348102582,0.2534810258 E -9],
+--R [0.9,0.808866936,0.8088669356 5278246251,- 0.3472175375 E -9],
+--R [0.91,0.816281421,0.8162814210 6387596132,0.6387596132 E -10],
+--R [0.92,0.823659091,0.8236590904 3241050549,- 0.5675894945 2 E -9],
+--R [0.93,0.831000091,0.8310000911 4624712798,0.146247128 E -9],
+--R [0.94,0.838304575,0.8383045748 1232348677,- 0.1876765132 E -9],
+--R [0.95,0.845572697,0.8455726970 3972738992,0.397273899 E -10],
+--R [0.96,0.852804617,0.8528046172 2893238837,0.2289323884 E -9],
+--R [0.97,0.860000498,0.8600004983 6713998068,0.3671399807 E -9],
+--R [0.98,0.867160507,0.8671605068 2966515846,- 0.1703348415 E -9],
+--R [0.99,0.874284812,0.8742848121 8729492676,0.1872949268 E -9],
+--R [1.0,0.881373587,0.8813735870 1954302523,0.195430252 E -10]]
+--R Type: List List
Float
+--E 1
+@
+In the following table there are 4 columns. The first column
+is the argument of atanh, ranging from 0.01 to 0.99. The
+second column is the reference value of atanh from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp221
+
+<<*>>=
+--S 2 of 2
+[[0.00,0.000000000,atanh(0.00),atanh(0.00)-0.000000000],_
+[0.01,0.010000333,atanh(0.01),atanh(0.01)-0.010000333],_
+[0.02,0.020002667,atanh(0.02),atanh(0.02)-0.020002667],_
+[0.03,0.030009004,atanh(0.03),atanh(0.03)-0.030009004],_
+[0.04,0.040021353,atanh(0.04),atanh(0.04)-0.040021353],_
+[0.05,0.050041729,atanh(0.05),atanh(0.05)-0.050041729],_
+[0.06,0.060072156,atanh(0.06),atanh(0.06)-0.060072156],_
+[0.07,0.070114671,atanh(0.07),atanh(0.07)-0.070114671],_
+[0.08,0.080171325,atanh(0.08),atanh(0.08)-0.080171325],_
+[0.09,0.090244188,atanh(0.09),atanh(0.09)-0.090244188],_
+[0.10,0.100335347,atanh(0.10),atanh(0.10)-0.100335347],_
+[0.11,0.110446915,atanh(0.11),atanh(0.11)-0.110446915],_
+[0.12,0.120581028,atanh(0.12),atanh(0.12)-0.120581028],_
+[0.13,0.130739850,atanh(0.13),atanh(0.13)-0.130739850],_
+[0.14,0.140925576,atanh(0.14),atanh(0.14)-0.140925576],_
+[0.15,0.151140436,atanh(0.15),atanh(0.15)-0.151140436],_
+[0.16,0.161386696,atanh(0.16),atanh(0.16)-0.161386696],_
+[0.17,0.171666663,atanh(0.17),atanh(0.17)-0.171666663],_
+[0.18,0.181982689,atanh(0.18),atanh(0.18)-0.181982689],_
+[0.19,0.192337169,atanh(0.19),atanh(0.19)-0.192337169],_
+[0.20,0.202732554,atanh(0.20),atanh(0.20)-0.202732554],_
+[0.21,0.213171346,atanh(0.21),atanh(0.21)-0.213171346],_
+[0.22,0.223656109,atanh(0.22),atanh(0.22)-0.223656109],_
+[0.23,0.234189466,atanh(0.23),atanh(0.23)-0.234189466],_
+[0.24,0.244774112,atanh(0.24),atanh(0.24)-0.244774112],_
+[0.25,0.255412812,atanh(0.25),atanh(0.25)-0.255412812],_
+[0.26,0.266108407,atanh(0.26),atanh(0.26)-0.266108407],_
+[0.27,0.276863823,atanh(0.27),atanh(0.27)-0.276863823],_
+[0.28,0.287682072,atanh(0.28),atanh(0.28)-0.287682072],_
+[0.29,0.298566264,atanh(0.29),atanh(0.29)-0.298566264],_
+[0.30,0.309519604,atanh(0.30),atanh(0.30)-0.309519604],_
+[0.31,0.320545409,atanh(0.31),atanh(0.31)-0.320545409],_
+[0.32,0.331647108,atanh(0.32),atanh(0.32)-0.331647108],_
+[0.33,0.342828254,atanh(0.33),atanh(0.33)-0.342828254],_
+[0.34,0.354092528,atanh(0.34),atanh(0.34)-0.354092528],_
+[0.35,0.365443754,atanh(0.35),atanh(0.35)-0.365443754],_
+[0.36,0.376885901,atanh(0.36),atanh(0.36)-0.376885901],_
+[0.37,0.388423100,atanh(0.37),atanh(0.37)-0.388423100],_
+[0.38,0.400059650,atanh(0.38),atanh(0.38)-0.400059650],_
+[0.39,0.411800034,atanh(0.39),atanh(0.39)-0.411800034],_
+[0.40,0.423648930,atanh(0.40),atanh(0.40)-0.423648930],_
+[0.41,0.435611223,atanh(0.41),atanh(0.41)-0.435611223],_
+[0.42,0.447692023,atanh(0.42),atanh(0.42)-0.447692023],_
+[0.43,0.459896681,atanh(0.43),atanh(0.43)-0.459896681],_
+[0.44,0.472230804,atanh(0.44),atanh(0.44)-0.472230804],_
+[0.45,0.484700279,atanh(0.45),atanh(0.45)-0.484700279],_
+[0.46,0.497311288,atanh(0.46),atanh(0.46)-0.497311288],_
+[0.47,0.510070337,atanh(0.47),atanh(0.47)-0.510070337],_
+[0.48,0.522984278,atanh(0.48),atanh(0.48)-0.522984278],_
+[0.49,0.536060337,atanh(0.49),atanh(0.49)-0.536060337],_
+[0.50,0.549306144,atanh(0.50),atanh(0.50)-0.549306144],_
+[0.51,0.562729769,atanh(0.51),atanh(0.51)-0.562729769],_
+[0.52,0.576339754,atanh(0.52),atanh(0.52)-0.576339754],_
+[0.53,0.590145160,atanh(0.53),atanh(0.53)-0.590145160],_
+[0.54,0.604155603,atanh(0.54),atanh(0.54)-0.604155603],_
+[0.55,0.618381313,atanh(0.55),atanh(0.55)-0.618381313],_
+[0.56,0.632833186,atanh(0.56),atanh(0.56)-0.632833186],_
+[0.57,0.647522844,atanh(0.57),atanh(0.57)-0.647522844],_
+[0.58,0.662462707,atanh(0.58),atanh(0.58)-0.662462707],_
+[0.59,0.677666068,atanh(0.59),atanh(0.59)-0.677666068],_
+[0.60,0.693147180,atanh(0.60),atanh(0.60)-0.693147180],_
+[0.61,0.708921359,atanh(0.61),atanh(0.61)-0.708921359],_
+[0.62,0.725005087,atanh(0.62),atanh(0.62)-0.725005087],_
+[0.63,0.741416144,atanh(0.63),atanh(0.63)-0.741416144],_
+[0.64,0.758173745,atanh(0.64),atanh(0.64)-0.758173745],_
+[0.65,0.775298706,atanh(0.65),atanh(0.65)-0.775298706],_
+[0.66,0.792813631,atanh(0.66),atanh(0.66)-0.792813631],_
+[0.67,0.810743125,atanh(0.67),atanh(0.67)-0.810743125],_
+[0.68,0.829114038,atanh(0.68),atanh(0.68)-0.829114038],_
+[0.69,0.847955755,atanh(0.69),atanh(0.69)-0.847955755],_
+[0.70,0.867300527,atanh(0.70),atanh(0.70)-0.867300527],_
+[0.71,0.887183863,atanh(0.71),atanh(0.71)-0.887183863],_
+[0.72,0.907644983,atanh(0.72),atanh(0.72)-0.907644983],_
+[0.73,0.928727364,atanh(0.73),atanh(0.73)-0.928727364],_
+[0.74,0.950479381,atanh(0.74),atanh(0.74)-0.950479381],_
+[0.75,0.972955074,atanh(0.75),atanh(0.75)-0.972955074],_
+[0.76,0.996215082,atanh(0.76),atanh(0.76)-0.996215082],_
+[0.77,1.020327758,atanh(0.77),atanh(0.77)-1.020327758],_
+[0.78,1.045370548,atanh(0.78),atanh(0.78)-1.045370548],_
+[0.79,1.071431684,atanh(0.79),atanh(0.79)-1.071431684],_
+[0.80,1.098612289,atanh(0.80),atanh(0.80)-1.098612289],_
+[0.81,1.127029026,atanh(0.81),atanh(0.81)-1.127029026],_
+[0.82,1.156817465,atanh(0.82),atanh(0.82)-1.156817465],_
+[0.83,1.188136404,atanh(0.83),atanh(0.83)-1.188136404],_
+[0.84,1.221173518,atanh(0.84),atanh(0.84)-1.221173518],_
+[0.85,1.256152811,atanh(0.85),atanh(0.85)-1.256152811],_
+[0.86,1.293344672,atanh(0.86),atanh(0.86)-1.293344672],_
+[0.87,1.333079629,atanh(0.87),atanh(0.87)-1.333079629],_
+[0.88,1.375767657,atanh(0.88),atanh(0.88)-1.375767657],_
+[0.89,1.421925871,atanh(0.89),atanh(0.89)-1.421925871],_
+[0.90,1.472219490,atanh(0.90),atanh(0.90)-1.472219490],_
+[0.91,1.527524425,atanh(0.91),atanh(0.91)-1.527524425],_
+[0.92,1.589026915,atanh(0.92),atanh(0.92)-1.589026915],_
+[0.93,1.658390020,atanh(0.93),atanh(0.93)-1.658390020],_
+[0.94,1.738049345,atanh(0.94),atanh(0.94)-1.738049345],_
+[0.95,1.831780823,atanh(0.95),atanh(0.95)-1.831780823],_
+[0.96,1.945910149,atanh(0.96),atanh(0.96)-1.945910149],_
+[0.97,2.092295720,atanh(0.97),atanh(0.97)-2.092295720],_
+[0.98,2.297559925,atanh(0.98),atanh(0.98)-2.297559925],_
+[0.99,2.646652412,atanh(0.99),atanh(0.99)-2.646652412]]
+--R
+--R
+--R (2)
+--R [[0.0,0.0,0.0,0.0],
+--R [0.01,0.010000333,0.0100003333 5333476201 6,0.3533347620 16 E -9],
+--R [0.02,0.020002667,0.0200026673 0684958071 7,0.3068495807 17 E -9],
+--R [0.03,0.030009004,0.0300090048 6312647432 6,0.8631264743 26 E -9],
+--R [0.04,0.040021353,0.0400213538 3676821291 2,0.8367682129 12 E -9],
+--R [0.05,0.050041729,0.0500417292 7849126824 6,0.2784912682 46 E -9],
+--R [0.06,0.060072156,0.0600721559 2103162366 2,- 0.7896837633 8 E -10],
+--R [0.07,0.070114671,0.0701146706 5432511799,- 0.3456748820 1 E -9],
+--R [0.08,0.080171325,0.0801713250 3758969169,0.3758969169 E -10],
+--R [0.09,0.090244188,0.0902441878 5614682960 9,- 0.1438531703 9 E -9],
+--R [0.1,0.100335347,0.1003353477 3107558064,0.7310755806 36 E -9],
+--R [0.11,0.110446915,0.1104469157 9009714872,0.7900971487 22 E -9],
+--R [0.12,0.120581028,0.1205810284 0844403523,0.4084440352 3 E -9],
+--R [0.13,0.13073985,0.1307398500 28878425,0.28878425 E -10],
+--R [0.14,0.140925576,0.1409255760 7049386396,0.7049386396 E -10],
+--R [0.15,0.151140436,0.1511404359 3646680528,- 0.6353319472 E -10],
+--R [0.16,0.161386696,0.1613866961 3152551534,0.1315255153 4 E -9],
+--R [0.17,0.171666663,0.1716666635 0057909768,0.5005790976 8 E -9],
+--R [0.18,0.181982689,0.1819826886 0070582337,- 0.3992941766 3 E -9],
+--R [0.19,0.192337169,0.1923371692 1954530989,0.2195453098 9 E -9],
+--R [0.2,0.202732554,0.2027325540 5408219099,0.5408219099 E -10],
+--R [0.21,0.213171346,0.2131713465 6485979698,0.5648597969 8 E -9],
+--R [0.22,0.223656109,0.2236561090 2183241065,0.2183241065 E -10],
+--R [0.23,0.234189466,0.2341894667 5936682305,0.7593668230 5 E -9],
+--R [0.24,0.244774112,0.2447741126 5935289296,0.6593528929 6 E -9],
+--R [0.25,0.255412812,0.2554128118 829953416,- 0.1170046584 E -9],
+--R [0.26,0.266108407,0.2661084068 7365412176,- 0.1263458782 E -9],
+--R [0.27,0.276863823,0.2768638226 5510007198,- 0.3448999280 2 E -9],
+--R [0.28,0.287682072,0.2876820724 5178092744,0.4517809274 4 E -9],
+--R [0.29,0.298566264,0.2985662636 6017834677,- 0.3398216532 3 E -9],
+--R [0.3,0.309519604,0.3095196042 0311171547,0.2031117155 E -9],
+--R [0.31,0.320545409,0.3205454093 0194608097,0.3019460809 7 E -9],
+--R [0.32,0.331647108,0.3316471087 051320776,0.7051320776 E -9],
+--R [0.33,0.342828254,0.3428282544 1539385272,0.4153938527 2 E -9],
+--R [0.34,0.354092528,0.3540925289 6224291211,0.9622429121 E -9],
+--R [0.35,0.365443754,0.3654437542 7139616907,0.2713961690 7 E -9],
+--R [0.36,0.376885901,0.3768859011 88190076,0.188190076 E -9],
+--R [0.37,0.3884231,0.3884230997 1829611371,- 0.2817038862 9 E -9],
+--R [0.38,0.40005965,0.4000596500 5605656814,0.5605656814 E -10],
+--R [0.39,0.411800034,0.4118000344 7869025422,0.4786902542 2 E -9],
+--R [0.4,0.42364893,0.4236489301 9360180685,0.1936018069 E -9],
+--R [0.41,0.435611223,0.4356112232 362244138,0.2362244138 E -9],
+--R [0.42,0.447692023,0.4476920235 2742069707,0.5274206970 7 E -9],
+--R [0.43,0.459896681,0.4598966812 1267856435,0.2126785644 E -9],
+--R [0.44,0.472230804,0.4722308044 2042569355,0.4204256935 5 E -9],
+--R [0.45,0.484700279,0.4847002785 9405174156,- 0.4059482584 4 E -9],
+--R [0.46,0.497311288,0.4973112875 7203102745,- 0.4279689725 5 E -9],
+--R [0.47,0.510070337,0.5100703366 1330723373,- 0.3866927663 E -9],
+--R [0.48,0.522984278,0.5229842775 9134385416,- 0.4086561458 E -9],
+--R [0.49,0.536060337,0.5360603366 1056668467,- 0.3894333153 E -9],
+--R [0.5,0.549306144,0.5493061443 340548457,0.3340548457 E -9],
+--R [0.51,0.562729769,0.5627297693 521488593,0.3521488593 E -9],
+--R [0.52,0.576339754,0.5763397549 691927296,0.9691927296 E -9],
+--R [0.53,0.59014516,0.5901451598 4118843811,- 0.1588115619 E -9],
+--R [0.54,0.604155603,0.6041556029 6226707918,- 0.377329208 E -10],
+--R [0.55,0.618381313,0.6183813135 7446343157,0.5744634315 7 E -9],
+--R [0.56,0.632833186,0.6328331866 6563794169,0.6656379416 9 E -9],
+--R [0.57,0.647522844,0.6475228448 2737281698,0.8273728169 8 E -9],
+--R [0.58,0.662462707,0.6624627073 7179924883,0.3717992488 E -9],
+--R [0.59,0.677666068,0.6776660677 5796186084,- 0.2420381392 E -9],
+--R [0.6,0.69314718,0.6931471805 5994530942,0.5599453094 2 E -9],
+--R [0.61,0.708921359,0.7089213594 2740828423,0.4274082842 E -9],
+--R [0.62,0.725005087,0.7250050877 5299915279,0.7529991527 9 E -9],
+--R [0.63,0.741416144,0.7414161440 8126894485,0.8126894484 E -10],
+--R [0.64,0.758173745,0.7581737446 8404421054,- 0.3159557895 E -9],
+--R [0.65,0.775298706,0.7752987062 0558346517,0.2055834652 E -9],
+--R [0.66,0.792813631,0.7928136318 7019092161,0.8701909216 1 E -9],
+--R [0.67,0.810743125,0.8107431254 7513743591,0.4751374359 1 E -9],
+--R [0.68,0.829114038,0.8291140383 0176618883,0.3017661888 E -9],
+--R [0.69,0.847955755,0.8479557552 1896361309,0.2189636131 E -9],
+--R [0.7,0.867300527,0.8673005276 9405319443,0.6940531944 3 E -9],
+--R [0.71,0.887183863,0.8871838632 5809290781,0.2580929078 E -9],
+--R [0.72,0.907644983,0.9076449833 1912455918,0.3191245592 E -9],
+--R [0.73,0.928727364,0.9287273642 4672493638,0.2467249364 E -9],
+--R [0.74,0.950479381,0.9504793805 9652349126,- 0.4034765087 E -9],
+--R [0.75,0.972955074,0.9729550745 2765665255,0.5276566525 5 E -9],
+--R [0.76,0.996215082,0.9962150823 4510308105,0.345103081 E -9],
+--R [0.77,1.020327758,1.0203277583 223397256,0.3223397256 E -9],
+--R [0.78,1.045370548,1.0453705484 668846471,0.4668846471 E -9],
+--R [0.79,1.071431684,1.0714316840 586659998,0.586659998 E -10],
+--R [0.8,1.098612289,1.0986122886 681096914,- 0.3318903086 E -9],
+--R [0.81,1.127029026,1.1270290260 496926434,0.496926434 E -10],
+--R [0.82,1.156817465,1.1568174645 903153292,- 0.4096846708 E -9],
+--R [0.83,1.188136404,1.1881364043 926024299,0.3926024299 E -9],
+--R [0.84,1.221173518,1.2211735176 846021907,- 0.3153978093 E -9],
+--R [0.85,1.256152811,1.2561528119 880573765,0.9880573764 9 E -9],
+--R [0.86,1.293344672,1.2933446720 489713161,0.489713161 E -10],
+--R [0.87,1.333079629,1.3330796296 965249441,0.6965249441 E -9],
+--R [0.88,1.375767657,1.3757676565 209744477,- 0.4790255523 E -9],
+--R [0.89,1.421925871,1.4219258711 306359176,0.1306359176 E -9],
+--R [0.9,1.47221949,1.4722194895 8322023,- 0.41677977 E -9],
+--R [0.91,1.527524425,1.5275244253 55205245,0.355205245 E -9],
+--R [0.92,1.589026915,1.5890269151 739728098,0.1739728098 E -9],
+--R [0.93,1.65839002,1.6583900199 247861234,- 0.752138766 E -10],
+--R [0.94,1.738049345,1.7380493449 176365654,- 0.823634346 E -10],
+--R [0.95,1.831780823,1.8317808230 648232137,0.648232137 E -10],
+--R [0.96,1.945910149,1.9459101490 553133051,0.553133051 E -10],
+--R [0.97,2.09229572,2.0922957200 349394077,0.349394077 E -10],
+--R [0.98,2.297559925,2.2975599250 672949634,0.672949634 E -10],
+--R [0.99,2.646652412,2.6466524123 622461976,0.3622461976 E -9]]
+--R Type: List List
Float
+--E 2
+
+)spool
+)lisp (bye)
+
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} {\bf Digital Library of Mathematical Functions},
+http://dlmf.nist.gov
+\bibitem{2} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp221
+\end{thebibliography}
+\end{document}
diff --git a/src/input/besselk.input.pamphlet b/src/input/besselk.input.pamphlet
index 0cd01ea..7a31a2c 100644
--- a/src/input/besselk.input.pamphlet
+++ b/src/input/besselk.input.pamphlet
@@ -9,6 +9,11 @@
\eject
\tableofcontents
\eject
+In the following table there are 4 columns. The first column
+is the argument of besselK, ranging from 0.01 to 10.0. The
+second column is the reference value of Gamma from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp417-419
<<*>>=
)spool besselk.output
)set message test on
@@ -45,13 +50,122 @@ limit(D(besselK(a,x),a),a=1/2)
--R (4) "failed"
--R Type:
Union("failed",...)
--E 4
+
+--S 5
+stegun(x)== %e^x * besselK(1,x)
+--E 5
+
+--S 6
+[[0.1, 10.890182683 , stegun(0.1), stegun(0.1)- 10.890182683 ],_
+ [0.2, 5.833386037 , stegun(0.2), stegun(0.2)- 5.833386037 ],_
+ [0.3, 4.125157762 , stegun(0.3), stegun(0.3)- 4.125157762 ],_
+ [0.4, 3.258673880 , stegun(0.4), stegun(0.4)- 3.258673880 ],_
+ [0.5, 2.7310097082, stegun(0.5), stegun(0.5)- 2.7310097082],_
+ [0.6, 2.3739200376, stegun(0.6), stegun(0.6)- 2.3739200376],_
+ [0.7, 2.1150113128, stegun(0.7), stegun(0.7)- 2.1150113128],_
+ [0.8, 1.9179302990, stegun(0.8), stegun(0.8)- 1.9179302990],_
+ [0.9, 1.7623882197, stegun(0.9), stegun(0.9)- 1.7623882197],_
+ [1.0, 1.6361534863, stegun(1.0), stegun(1.0)- 1.6361534863],_
+ [1.1, 1.5314037541, stegun(1.1), stegun(1.1)- 1.5314037541],_
+ [1.2, 1.4428975522, stegun(1.2), stegun(1.2)- 1.4428975522],_
+ [1.3, 1.3669872841, stegun(1.3), stegun(1.3)- 1.3669872841],_
+ [1.4, 1.3010537400, stegun(1.4), stegun(1.4)- 1.3010537400],_
+ [1.5, 1.2431658736, stegun(1.5), stegun(1.5)- 1.2431658736],_
+ [1.6, 1.1918675654, stegun(1.6), stegun(1.6)- 1.1918675654],_
+ [1.7, 1.1460392462, stegun(1.7), stegun(1.7)- 1.1460392462],_
+ [1.8, 1.1048053726, stegun(1.8), stegun(1.8)- 1.1048053726],_
+ [1.9, 1.0674709298, stegun(1.9), stegun(1.9)- 1.0674709298],_
+ [2.0, 1.0334768471, stegun(2.0), stegun(2.0)- 1.0334768471],_
+ [2.1, 1.0023680527, stegun(2.1), stegun(2.1)- 1.0023680527],_
+ [2.2, 0.9737701679, stegun(2.2), stegun(2.2)- 0.9737701679],_
+ [2.3, 0.9473722250, stegun(2.3), stegun(2.3)- 0.9473722250],_
+ [2.4, 0.9229136650, stegun(2.4), stegun(2.4)- 0.9229136650],_
+ [2.5, 0.9001744239, stegun(2.5), stegun(2.5)- 0.9001744239],_
+ [2.6, 0.8789672806, stegun(2.6), stegun(2.6)- 0.8789672806],_
+ [2.7, 0.8591318867, stegun(2.7), stegun(2.7)- 0.8591318867],_
+ [2.8, 0.8405300604, stegun(2.8), stegun(2.8)- 0.8405300604],_
+ [2.9, 0.8230420403, stegun(2.9), stegun(2.9)- 0.8230420403],_
+ [3.0, 0.8065634800, stegun(3.0), stegun(3.0)- 0.8065634800],_
+ [3.1, 0.7910030157, stegun(3.1), stegun(3.1)- 0.7910030157],_
+ [3.2, 0.7762802824, stegun(3.2), stegun(3.2)- 0.7762802824],_
+ [3.3, 0.7623242864, stegun(3.3), stegun(3.3)- 0.7623242864],_
+ [3.4, 0.7490720613, stegun(3.4), stegun(3.4)- 0.7490720613],_
+ [3.5, 0.7364675480, stegun(3.5), stegun(3.5)- 0.7364675480],_
+ [3.6, 0.7244606608, stegun(3.6), stegun(3.6)- 0.7244606608],_
+ [3.7, 0.7130065010, stegun(3.7), stegun(3.7)- 0.7130065010],_
+ [3.8, 0.7020646931, stegun(3.8), stegun(3.8)- 0.7020646931],_
+ [3.9, 0.6915988206, stegun(3.9), stegun(3.9)- 0.6915988206],_
+ [4.0, 0.6815759452, stegun(4.0), stegun(4.0)- 0.6815759452],_
+ [4.1, 0.6719661952, stegun(4.1), stegun(4.1)- 0.6719661952],_
+ [4.2, 0.6627424110, stegun(4.2), stegun(4.2)- 0.6627424110],_
+ [4.3, 0.6538798395, stegun(4.3), stegun(4.3)- 0.6538798395],_
+ [4.4, 0.6453558689, stegun(4.4), stegun(4.4)- 0.6453558689],_
+ [4.5, 0.6371497988, stegun(4.5), stegun(4.5)- 0.6371497988],_
+ [4.6, 0.6292426383, stegun(4.6), stegun(4.6)- 0.6292426383],_
+ [4.7, 0.6216169312, stegun(4.7), stegun(4.7)- 0.6216169312],_
+ [4.8, 0.6142566003, stegun(4.8), stegun(4.8)- 0.6142566003],_
+ [4.9, 0.6071468131, stegun(4.9), stegun(4.9)- 0.6071468131],_
+ [5.0, 0.6002738587, stegun(5.0), stegun(5.0)- 0.6002738587],_
+ [5.1, 0.5936250463, stegun(5.1), stegun(5.1)- 0.5936250463],_
+ [5.2, 0.5871886062, stegun(5.2), stegun(5.2)- 0.5871886062],_
+ [5.3, 0.5809536085, stegun(5.3), stegun(5.3)- 0.5809536085],_
+ [5.4, 0.5749098871, stegun(5.4), stegun(5.4)- 0.5749098871],_
+ [5.5, 0.5690479741, stegun(5.5), stegun(5.5)- 0.5690479741],_
+ [5.6, 0.5633590393, stegun(5.6), stegun(5.6)- 0.5633590393],_
+ [5.7, 0.5578348348, stegun(5.7), stegun(5.7)- 0.5578348348],_
+ [5.8, 0.5524676495, stegun(5.8), stegun(5.8)- 0.5524676495],_
+ [5.9, 0.5472502639, stegun(5.9), stegun(5.9)- 0.5472502639],_
+ [6.0, 0.5421759104, stegun(6.0), stegun(6.0)- 0.5421759104],_
+ [6.1, 0.5372382386, stegun(6.1), stegun(6.1)- 0.5372382386],_
+ [6.2, 0.5324312833, stegun(6.2), stegun(6.2)- 0.5324312833],_
+ [6.3, 0.5277494344, stegun(6.3), stegun(6.3)- 0.5277494344],_
+ [6.4, 0.5231874101, stegun(6.4), stegun(6.4)- 0.5231874101],_
+ [6.5, 0.5187402336, stegun(6.5), stegun(6.5)- 0.5187402336],_
+ [6.6, 0.5144032108, stegun(6.6), stegun(6.6)- 0.5144032108],_
+ [6.7, 0.5101719097, stegun(6.7), stegun(6.7)- 0.5101719097],_
+ [6.8, 0.5060421421, stegun(6.8), stegun(6.8)- 0.5060421421],_
+ [6.9, 0.5020099471, stegun(6.9), stegun(6.9)- 0.5020099471],_
+ [7.0, 0.4980715749, stegun(7.0), stegun(7.0)- 0.4980715749],_
+ [7.1, 0.4942234737, stegun(7.1), stegun(7.1)- 0.4942234737],_
+ [7.2, 0.4904622755, stegun(7.2), stegun(7.2)- 0.4904622755],_
+ [7.3, 0.4867847842, stegun(7.3), stegun(7.3)- 0.4867847842],_
+ [7.4, 0.4831879648, stegun(7.4), stegun(7.4)- 0.4831879648],_
+ [7.5, 0.4796689336, stegun(7.5), stegun(7.5)- 0.4796689336],_
+ [7.6, 0.4762249486, stegun(7.6), stegun(7.6)- 0.4762249486],_
+ [7.7, 0.4728533995, stegun(7.7), stegun(7.7)- 0.4728533995],_
+ [7.8, 0.4695518010, stegun(7.8), stegun(7.8)- 0.4695518010],_
+ [7.9, 0.4663177847, stegun(7.9), stegun(7.9)- 0.4663177847],_
+ [8.0, 0.4631490928, stegun(8.0), stegun(8.0)- 0.4631490928],_
+ [8.1, 0.4600435709, stegun(8.1), stegun(8.1)- 0.4600435709],_
+ [8.2, 0.4569991615, stegun(8.2), stegun(8.2)- 0.4569991615],_
+ [8.3, 0.4540139001, stegun(8.3), stegun(8.3)- 0.4540139001],_
+ [8.4, 0.4510859089, stegun(8.4), stegun(8.4)- 0.4510859089],_
+ [8.5, 0.4482133915, stegun(8.5), stegun(8.5)- 0.4482133915],_
+ [8.6, 0.4453946295, stegun(8.6), stegun(8.6)- 0.4453946295],_
+ [8.7, 0.4426279775, stegun(8.7), stegun(8.7)- 0.4426279775],_
+ [8.8, 0.4399118594, stegun(8.8), stegun(8.8)- 0.4399118594],_
+ [8.9, 0.4372447648, stegun(8.9), stegun(8.9)- 0.4372447648],_
+ [9.0, 0.4346252454, stegun(9.0), stegun(9.0)- 0.4346252454],_
+ [9.1, 0.4320519116, stegun(9.1), stegun(9.1)- 0.4320519116],_
+ [9.2, 0.4295234301, stegun(9.2), stegun(9.2)- 0.4295234301],_
+ [9.3, 0.4270385204, stegun(9.3), stegun(9.3)- 0.4270385204],_
+ [9.4, 0.4245959520, stegun(9.4), stegun(9.4)- 0.4245959520],_
+ [9.5, 0.4221945430, stegun(9.5), stegun(9.5)- 0.4221945430],_
+ [9.6, 0.4198331565, stegun(9.6), stegun(9.6)- 0.4198331565],_
+ [9.7, 0.4175106989, stegun(9.7), stegun(9.7)- 0.4175106989],_
+ [9.8, 0.4152261179, stegun(9.8), stegun(9.8)- 0.4152261179],_
+ [9.9, 0.4129784003, stegun(9.9), stegun(9.9)- 0.4129784003],_
+ [10.0, 0.4107665704, stegun(10.0), stegun(10.0)- 0.4107665704]]
+--E 6
+
)spool
)lisp (bye)
@
\eject
\begin{thebibliography}{99}
-\bibitem{1} nothing
+\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp417-419
\end{thebibliography}
\end{document}
diff --git a/src/input/exp.input.pamphlet b/src/input/exp.input.pamphlet
new file mode 100644
index 0000000..88b3759
--- /dev/null
+++ b/src/input/exp.input.pamphlet
@@ -0,0 +1,460 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input exp.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This compares Axiom's exp function with the tables published in
+Abramowitz and Stegun.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+In the following table there are 4 columns. The first column
+is the argument of exp(x), ranging from 0.0 to 10.0. The
+second column is the reference value of exp from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp136-137
+
+<<*>>=
+)spool exp.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 2
+[[0.0, 1.000000000000000, exp(0.0), exp(0.0)- 1.000000000000000],_
+ [0.1, 1.105170918075648, exp(0.1), exp(0.1)- 1.105170918075648],_
+ [0.2, 1.221402758160170, exp(0.2), exp(0.2)- 1.221402758160170],_
+ [0.3, 1.349858807576003, exp(0.3), exp(0.3)- 1.349858807576003],_
+ [0.4, 1.491824697641270, exp(0.4), exp(0.4)- 1.491824697641270],_
+ [0.5, 1.648721270700128, exp(0.5), exp(0.5)- 1.648721270700128],_
+ [0.6, 1.822118800390509, exp(0.6), exp(0.6)- 1.822118800390509],_
+ [0.7, 2.013752707470477, exp(0.7), exp(0.7)- 2.013752707470477],_
+ [0.8, 2.225540928492468, exp(0.8), exp(0.8)- 2.225540928492468],_
+ [0.9, 2.459603111156950, exp(0.9), exp(0.9)- 2.459603111156950],_
+ [1.0, 2.718281828459045, exp(1.0), exp(1.0)- 2.718281828459045],_
+ [1.1, 3.004166023946433, exp(1.1), exp(1.1)- 3.004166023946433],_
+ [1.2, 3.320116922736547, exp(1.2), exp(1.2)- 3.320116922736547],_
+ [1.3, 3.669296667619244, exp(1.3), exp(1.3)- 3.669296667619244],_
+ [1.4, 4.055199966844675, exp(1.4), exp(1.4)- 4.055199966844675],_
+ [1.5, 4.481689070338065, exp(1.5), exp(1.5)- 4.481689070338065],_
+ [1.6, 4.953032424395115, exp(1.6), exp(1.6)- 4.953032424395115],_
+ [1.7, 5.473947391727200, exp(1.7), exp(1.7)- 5.473947391727200],_
+ [1.8, 6.049647464412946, exp(1.8), exp(1.8)- 6.049647464412946],_
+ [1.9, 6.685894442279269, exp(1.9), exp(1.9)- 6.685894442279269],_
+ [2.0, 7.389056098930650, exp(2.0), exp(2.0)- 7.389056098930650],_
+ [2.1, 8.166169912567650, exp(2.1), exp(2.1)- 8.166169912567650],_
+ [2.2, 9.025013499434121, exp(2.2), exp(2.2)- 9.025013499434121],_
+ [2.3, 9.974182454814721, exp(2.3), exp(2.3)- 9.974182454814721],_
+ [2.4, 11.023176380641602, exp(2.4), exp(2.4)- 11.023176380641602],_
+ [2.5, 12.182493960703473, exp(2.5), exp(2.5)- 12.182493960703473],_
+ [2.6, 13.463738035001690, exp(2.6), exp(2.6)- 13.463738035001690],_
+ [2.7, 14.879731724872834, exp(2.7), exp(2.7)- 14.879731724872834],_
+ [2.8, 16.444646771097050, exp(2.8), exp(2.8)- 16.444646771097050],_
+ [2.9, 18.174145369443061, exp(2.9), exp(2.9)- 18.174145369443061],_
+ [3.0, 20.085536923187668, exp(3.0), exp(3.0)- 20.085536923187668],_
+ [3.1, 22.197951281441633, exp(3.1), exp(3.1)- 22.197951281441633],_
+ [3.2, 24.532530197109349, exp(3.2), exp(3.2)- 24.532530197109349],_
+ [3.3, 27.112638920657887, exp(3.3), exp(3.3)- 27.112638920657887],_
+ [3.4, 29.964100047397013, exp(3.4), exp(3.4)- 29.964100047397013],_
+ [3.5, 33.115451958692314, exp(3.5), exp(3.5)- 33.115451958692314],_
+ [3.6, 36.598234443677988, exp(3.6), exp(3.6)- 36.598234443677988],_
+ [3.7, 40.447304360067391, exp(3.7), exp(3.7)- 40.447304360067391],_
+ [3.8, 44.701184493300823, exp(3.8), exp(3.8)- 44.701184493300823],_
+ [3.9, 49.402449105530174, exp(3.9), exp(3.9)- 49.402449105530174],_
+ [4.0, 54.598150033144239, exp(4.0), exp(4.0)- 54.598150033144239],_
+ [4.1, 60.340287597361969, exp(4.1), exp(4.1)- 60.340287597361969],_
+ [4.2, 66.686331040925142, exp(4.2), exp(4.2)- 66.686331040925142],_
+ [4.3, 73.699793699595797, exp(4.3), exp(4.3)- 73.699793699595797],_
+ [4.4, 81.450868664968117, exp(4.4), exp(4.4)- 81.450868664968117],_
+ [4.5, 90.017131300521814, exp(4.5), exp(4.5)- 90.017131300521814],_
+ [4.6, 99.484315641933809, exp(4.6), exp(4.6)- 99.484315641933809],_
+ [4.7, 109.947172452123499, exp(4.7), exp(4.7)- 109.947172452123499],_
+ [4.8, 121.510417518734881, exp(4.8), exp(4.8)- 121.510417518734881],_
+ [4.9, 134.289779684935485, exp(4.9), exp(4.9)- 134.289779684935485],_
+ [5.0, 148.413159102577, exp(5.0), exp(5.0)- 148.413159102577],_
+ [5.1, 164.021907299902, exp(5.1), exp(5.1)- 164.021907299902],_
+ [5.2, 181.272241875151, exp(5.2), exp(5.2)- 181.272241875151],_
+ [5.3, 200.336809974792, exp(5.3), exp(5.3)- 200.336809974792],_
+ [5.4, 221.406416204187, exp(5.4), exp(5.4)- 221.406416204187],_
+ [5.5, 244.691932264220, exp(5.5), exp(5.5)- 244.691932264220],_
+ [5.6, 270.426407426153, exp(5.6), exp(5.6)- 270.426407426153],_
+ [5.7, 298.867400967060, exp(5.7), exp(5.7)- 298.867400967060],_
+ [5.8, 330.299559909649, exp(5.8), exp(5.8)- 330.299559909649],_
+ [5.9, 365.037467865329, exp(5.9), exp(5.9)- 365.037467865329],_
+ [6.0, 403.428793492735, exp(6.0), exp(6.0)- 403.428793492735],_
+ [6.1, 445.857770082517, exp(6.1), exp(6.1)- 445.857770082517],_
+ [6.2, 492.749041093256, exp(6.2), exp(6.2)- 492.749041093256],_
+ [6.3, 544.571910125929, exp(6.3), exp(6.3)- 544.571910125929],_
+ [6.4, 601.845037872082, exp(6.4), exp(6.4)- 601.845037872082],_
+ [6.5, 665.141633044362, exp(6.5), exp(6.5)- 665.141633044362],_
+ [6.6, 735.095189241973, exp(6.6), exp(6.6)- 735.095189241973],_
+ [6.7, 812.405825167543, exp(6.7), exp(6.7)- 812.405825167543],_
+ [6.8, 897.847291650418, exp(6.8), exp(6.8)- 897.847291650418],_
+ [6.9, 992.274715605026, exp(6.9), exp(6.9)- 992.274715605026],_
+ [7.0, 1096.633158428459, exp(7.0), exp(7.0)- 1096.633158428459],_
+ [7.1, 1211.967074492577, exp(7.1), exp(7.1)- 1211.967074492577],_
+ [7.2, 1339.430764394418, exp(7.2), exp(7.2)- 1339.430764394418],_
+ [7.3, 1480.299927584545, exp(7.3), exp(7.3)- 1480.299927584545],_
+ [7.4, 1635.984429995927, exp(7.4), exp(7.4)- 1635.984429995927],_
+ [7.5, 1808.042414456063, exp(7.5), exp(7.5)- 1808.042414456063],_
+ [7.6, 1998.195895104118, exp(7.6), exp(7.6)- 1998.195895104118],_
+ [7.7, 2208.347991887209, exp(7.7), exp(7.7)- 2208.347991887209],_
+ [7.8, 2440.601977624499, exp(7.8), exp(7.8)- 2440.601977624499],_
+ [7.9, 2697.282328268509, exp(7.9), exp(7.9)- 2697.282328268509],_
+ [8.0, 2980.957987041728, exp(8.0), exp(8.0)- 2980.957987041728],_
+ [8.1, 3294.468075283841, exp(8.1), exp(8.1)- 3294.468075283841],_
+ [8.2, 3640.950307332355, exp(8.2), exp(8.2)- 3640.950307332355],_
+ [8.3, 4023.872393822310, exp(8.3), exp(8.3)- 4023.872393822310],_
+ [8.4, 4447.066747699856, exp(8.4), exp(8.4)- 4447.066747699856],_
+ [8.5, 4914.768840299134, exp(8.5), exp(8.5)- 4914.768840299134],_
+ [8.6, 5431.659591362980, exp(8.6), exp(8.6)- 5431.659591362980],_
+ [8.7, 6002.912217261022, exp(8.7), exp(8.7)- 6002.912217261022],_
+ [8.8, 6634.244006277885, exp(8.8), exp(8.8)- 6634.244006277885],_
+ [8.9, 7331.973539155993, exp(8.9), exp(8.9)- 7331.973539155993],_
+ [9.0, 8103.083927575384, exp(9.0), exp(9.0)- 8103.083927575384],_
+ [9.1, 8955.292703482512, exp(9.1), exp(9.1)- 8955.292703482512],_
+ [9.2, 9897.129058743916, exp(9.2), exp(9.2)- 9897.129058743916],_
+ [9.3, 10938.019208165184, exp(9.3), exp(9.3)- 10938.019208165184],_
+ [9.4, 12088.380730216984, exp(9.4), exp(9.4)- 12088.380730216984],_
+ [9.5, 13359.726829661872, exp(9.5), exp(9.5)- 13359.726829661872],_
+ [9.6, 14764.781565577273, exp(9.6), exp(9.6)- 14764.781565577273],_
+ [9.7, 16317.607198015432, exp(9.7), exp(9.7)- 16317.607198015432],_
+ [9.8, 18033.744927828511, exp(9.8), exp(9.8)- 18033.744927828511],_
+ [9.9, 19930.370438230289, exp(9.9), exp(9.9)- 19930.370438230289],_
+[10.0, 22026.465794806717, exp(10.0), exp(10.0)-22026.465794806717]]
+--R
+--R
+--R (1)
+--R [[0.0,1.0,1.0,0.0],
+--R [0.1,1.1051709180 75648,1.1051709180 756476248,- 0.3752 E -15],
+--R [0.2,1.2214027581 6017,1.2214027581 601698339,- 0.1661 E -15],
+--R [0.3,1.3498588075 76003,1.3498588075 76003104,0.104 E -15],
+--R [0.4,1.4918246976 4127,1.4918246976 412703178,0.3178 E -15],
+--R [0.5,1.6487212707 00128,1.6487212707 001281468,0.1468 E -15],
+--R [0.6,1.8221188003 90509,1.8221188003 905089749,- 0.251 E -16],
+--R [0.7,2.0137527074 70477,2.0137527074 704765216,- 0.4784 E -15],
+--R [0.8,2.2255409284 92468,2.2255409284 924676046,- 0.3954 E -15],
+--R [0.9,2.4596031111 5695,2.4596031111 569496638,- 0.3362 E -15],
+--R [1.0,2.7182818284 59045,2.7182818284 590452354,0.2354 E -15],
+--R [1.1,3.0041660239 46433,3.0041660239 464331121,0.112 E -15],
+--R [1.2,3.3201169227 36547,3.3201169227 365474895,0.4895 E -15],
+--R [1.3,3.6692966676 19244,3.6692966676 192442204,0.22 E -15],
+--R [1.4,4.0551999668 44675,4.0551999668 446745872,- 0.413 E -15],
+--R [1.5,4.4816890703 38065,4.4816890703 380648226,- 0.177 E -15],
+--R [1.6,4.9530324243 95115,4.9530324243 951148037,- 0.196 E -15],
+--R [1.7,5.4739473917 272,5.4739473917 271997608,- 0.239 E -15],
+--R [1.8,6.0496474644 12946,6.0496474644 129460837,0.837 E -16],
+--R [1.9,6.6858944422 79269,6.6858944422 792694161,0.416 E -15],
+--R [2.0,7.3890560989 3065,7.3890560989 306502272,0.227 E -15],
+--R [2.1,8.1661699125 6765,8.1661699125 676500734,0.734 E -16],
+--R [2.2,9.0250134994 34121,9.0250134994 341209265,- 0.735 E -16],
+--R [2.3,9.9741824548 14721,9.9741824548 1472074,- 0.26 E -15],
+--R [2.4,11.0231763806 41602,11.0231763806 41601652,- 0.348 E -15],
+--R [2.5,12.1824939607 03473,12.1824939607 03473438,0.438 E -15],
+--R [2.6,13.4637380350 0169,13.4637380350 01690398,0.398 E -15],
+--R [2.7,14.8797317248 72834,14.8797317248 72834112,0.112 E -15],
+--R [2.8,16.4446467710 9705,16.4446467710 97049871,- 0.129 E -15],
+--R [2.9,18.1741453694 43061,18.1741453694 43060943,- 0.57 E -16],
+--R [3.0,20.0855369231 87668,20.0855369231 87667741,- 0.259 E -15],
+--R [3.1,22.1979512814 41633,22.1979512814 41633405,0.405 E -15],
+--R [3.2,24.5325301971 09349,24.5325301971 09348644,- 0.356 E -15],
+--R [3.3,27.1126389206 57887,27.1126389206 57887427,0.427 E -15],
+--R [3.4,29.9641000473 97013,29.9641000473 97013348,0.348 E -15],
+--R [3.5,33.1154519586 92314,33.1154519586 92313751,- 0.249 E -15],
+--R [3.6,36.5982344436 77988,36.5982344436 77987752,- 0.248 E -15],
+--R [3.7,40.4473043600 67391,40.4473043600 67390529,- 0.471 E -15],
+--R [3.8,44.7011844933 00823,44.7011844933 00823038,0.38 E -16],
+--R [3.9,49.4024491055 30174,49.4024491055 3017388,- 0.12 E -15],
+--R [4.0,54.5981500331 44239,54.5981500331 44239078,0.78 E -16],
+--R [4.1,60.3402875973 61969,60.3402875973 61969497,0.497 E -15],
+--R [4.2,66.6863310409 25142,66.6863310409 25141644,- 0.36 E -15],
+--R [4.3,73.6997936995 95797,73.6997936995 95796913,- 0.88 E -16],
+--R [4.4,81.4508686649 68117,81.4508686649 68117445,0.445 E -15],
+--R [4.5,90.0171313005 21814,90.0171313005 2181355,- 0.45 E -15],
+--R [4.6,99.4843156419 33809,99.4843156419 33808735,- 0.26 E -15],
+--R [4.7,109.9471724521 23499,109.9471724521 2349888,- 0.12 E -15],
+--R [4.8,121.5104175187 34881,121.5104175187 3488076,- 0.24 E -15],
+--R [4.9,134.2897796849 35485,134.2897796849 3548484,- 0.16 E -15],
+--R [5.0,148.4131591025 77,148.4131591025 7660342,- 0.39658 E -12],
+--R [5.1,164.0219072999 02,164.0219072999 0174394,- 0.25606 E -12],
+--R [5.2,181.2722418751 51,181.2722418751 5117937,0.17937 E -12],
+--R [5.3,200.3368099747 92,200.3368099747 9168484,- 0.31516 E -12],
+--R [5.4,221.4064162041 87,221.4064162041 8708703,0.8703 E -13],
+--R [5.5,244.6919322642 2,244.6919322642 2038792,0.38792 E -12],
+--R [5.6,270.4264074261 53,270.4264074261 5262815,- 0.37185 E -12],
+--R [5.7,298.8674009670 6,298.8674009670 6023267,0.23267 E -12],
+--R [5.8,330.2995599096 49,330.2995599096 4865412,- 0.34588 E -12],
+--R [5.9,365.0374678653 29,365.0374678653 2877732,- 0.2227 E -12],
+--R [6.0,403.4287934927 35,403.4287934927 3512261,0.1226 E -12],
+--R [6.1,445.8577700825 17,445.8577700825 1693179,- 0.6821 E -13],
+--R [6.2,492.7490410932 56,492.7490410932 5625456,0.25456 E -12],
+--R [6.3,544.5719101259 29,544.5719101259 2903306,0.331 E -13],
+--R [6.4,601.8450378720 82,601.8450378720 8205661,0.566 E -13],
+--R [6.5,665.1416330443 62,665.1416330443 6184069,- 0.1593 E -12],
+--R [6.6,735.0951892419 73,735.0951892419 728949,- 0.1051 E -12],
+--R [6.7,812.4058251675 43,812.4058251675 4311346,0.1135 E -12],
+--R [6.8,897.8472916504 18,897.8472916504 1769759,- 0.3024 E -12],
+--R [6.9,992.2747156050 26,992.2747156050 2587698,- 0.123 E -12],
+--R [7.0,1096.6331584284 59,1096.6331584284 585993,- 0.4007 E -12],
+--R [7.1,1211.9670744925 77,1211.9670744925 767212,- 0.2788 E -12],
+--R [7.2,1339.4307643944 18,1339.4307643944 178297,- 0.1703 E -12],
+--R [7.3,1480.2999275845 45,1480.2999275845 452229,0.2228 E -12],
+--R [7.4,1635.9844299959 27,1635.9844299959 265401,- 0.4599 E -12],
+--R [7.5,1808.0424144560 63,1808.0424144560 632069,0.2069 E -12],
+--R [7.6,1998.1958951041 18,1998.1958951041 179592,- 0.408 E -13],
+--R [7.7,2208.3479918872 09,2208.3479918872 08524,- 0.476 E -12],
+--R [7.8,2440.6019776244 99,2440.6019776244 990773,0.773 E -13],
+--R [7.9,2697.2823282685 09,2697.2823282685 088472,- 0.153 E -12],
+--R [8.0,2980.9579870417 28,2980.9579870417 282747,0.2747 E -12],
+--R [8.1,3294.4680752838 41,3294.4680752838 413332,0.3332 E -12],
+--R [8.2,3640.9503073323 55,3640.9503073323 547215,- 0.2785 E -12],
+--R [8.3,4023.8723938223 1,4023.8723938223 098416,- 0.158 E -12],
+--R [8.4,4447.0667476998 56,4447.0667476998 560855,0.855 E -13],
+--R [8.5,4914.7688402991 34,4914.7688402991 343754,0.375 E -12],
+--R [8.6,5431.6595913629 8,5431.6595913629 803217,0.322 E -12],
+--R [8.7,6002.9122172610 22,6002.9122172610 2198,- 0.2 E -13],
+--R [8.8,6634.2440062778 85,6634.2440062778 851586,0.159 E -12],
+--R [8.9,7331.9735391559 93,7331.9735391559 929051,- 0.949 E -13],
+--R [9.0,8103.0839275753 84,8103.0839275753 840077,0.77 E -14],
+--R [9.1,8955.2927034825 12,8955.2927034825 11711,- 0.289 E -12],
+--R [9.2,9897.1290587439 16,9897.1290587439 158867,- 0.113 E -12],
+--R [9.3,10938.0192081651 84,10938.0192081651 83753,- 0.247 E -12],
+--R [9.4,12088.3807302169 84,12088.3807302169 84397,0.397 E -12],
+--R [9.5,13359.7268296618 72,13359.7268296618 72276,0.276 E -12],
+--R [9.6,14764.7815655772 73,14764.7815655772 72616,- 0.384 E -12],
+--R [9.7,16317.6071980154 32,16317.6071980154 32233,0.233 E -12],
+--R [9.8,18033.7449278285 11,18033.7449278285 11246,0.246 E -12],
+--R [9.9,19930.3704382302 89,19930.3704382302 8949,0.49 E -12],
+--R [10.0,22026.4657948067 17,22026.4657948067 16517,- 0.483 E -12]]
+--R Type: List List
Float
+--E 1
+
+@
+In the following table there are 4 columns. The first column
+is the argument of exp(-x), ranging from 0.0 to 10.0. The
+second column is the reference value of exp from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp136-137
+
+<<*>>=
+--S 2 of 2
+[[0.1,0.90483741803595957316,exp(-0.1),exp(-0.1)-0.90483741803595957316],_
+ [0.2,0.81873075307798185867,exp(-0.2),exp(-0.2)-0.81873075307798185867],_
+ [0.3,0.74081822068171786607,exp(-0.3),exp(-0.3)-0.74081822068171786607],_
+ [0.4,0.67032004603563930074,exp(-0.4),exp(-0.4)-0.67032004603563930074],_
+ [0.5,0.60653065971263342360,exp(-0.5),exp(-0.5)-0.60653065971263342360],_
+ [0.6,0.54881163609402643263,exp(-0.6),exp(-0.6)-0.54881163609402643263],_
+ [0.7,0.49658530379140951470,exp(-0.7),exp(-0.7)-0.49658530379140951470],_
+ [0.8,0.44932896411722159143,exp(-0.8),exp(-0.8)-0.44932896411722159143],_
+ [0.9,0.40656965974059911188,exp(-0.9),exp(-0.9)-0.40656965974059911188],_
+ [1.0,0.36787944117144232160,exp(-1.0),exp(-1.0)-0.36787944117144232160],_
+ [1.1,0.33287108369807955329,exp(-1.1),exp(-1.1)-0.33287108369807955329],_
+ [1.2,0.30119421191220209664,exp(-1.2),exp(-1.2)-0.30119421191220209664],_
+ [1.3,0.27253179303401260312,exp(-1.3),exp(-1.3)-0.27253179303401260312],_
+ [1.4,0.24659696394160647694,exp(-1.4),exp(-1.4)-0.24659696394160647694],_
+ [1.5,0.22313016014842982893,exp(-1.5),exp(-1.5)-0.22313016014842982893],_
+ [1.6,0.20189651799465540849,exp(-1.6),exp(-1.6)-0.20189651799465540849],_
+ [1.7,0.18268352405273465022,exp(-1.7),exp(-1.7)-0.18268352405273465022],_
+ [1.8,0.16529888822158653830,exp(-1.8),exp(-1.8)-0.16529888822158653830],_
+ [1.9,0.14956861922263505264,exp(-1.9),exp(-1.9)-0.14956861922263505264],_
+ [2.0,0.13533528323661269189,exp(-2.0),exp(-2.0)-0.13533528323661269189],_
+ [2.1,0.12245642825298191022,exp(-2.1),exp(-2.1)-0.12245642825298191022],_
+ [2.2,0.11080315836233388333,exp(-2.2),exp(-2.2)-0.11080315836233388333],_
+ [2.3,0.10025884372280373373,exp(-2.3),exp(-2.3)-0.10025884372280373373],_
+ [2.4,0.09071795328941250338,exp(-2.4),exp(-2.4)-0.09071795328941250338],_
+ [2.5,0.08208499862389879517,exp(-2.5),exp(-2.5)-0.08208499862389879517],_
+ [2.6,0.07427357821433388043,exp(-2.6),exp(-2.6)-0.07427357821433388043],_
+ [2.7,0.06720551273974976513,exp(-2.7),exp(-2.7)-0.06720551273974976513],_
+ [2.8,0.06081006262521796500,exp(-2.8),exp(-2.8)-0.06081006262521796500],_
+ [2.9,0.05502322005640722903,exp(-2.9),exp(-2.9)-0.05502322005640722903],_
+ [3.0,0.04978706836786394298,exp(-3.0),exp(-3.0)-0.04978706836786394298],_
+ [3.1,0.04504920239355780607,exp(-3.1),exp(-3.1)-0.04504920239355780607],_
+ [3.2,0.04076220397836621517,exp(-3.2),exp(-3.2)-0.04076220397836621517],_
+ [3.3,0.03688316740124000545,exp(-3.3),exp(-3.3)-0.03688316740124000545],_
+ [3.4,0.03337326996032607948,exp(-3.4),exp(-3.4)-0.03337326996032607948],_
+ [3.5,0.03019738342231850074,exp(-3.5),exp(-3.5)-0.03019738342231850074],_
+ [3.6,0.02732372244729256080,exp(-3.6),exp(-3.6)-0.02732372244729256080],_
+ [3.7,0.02472352647033939120,exp(-3.7),exp(-3.7)-0.02472352647033939120],_
+ [3.8,0.02237077185616559578,exp(-3.8),exp(-3.8)-0.02237077185616559578],_
+ [3.9,0.02024191144580438847,exp(-3.9),exp(-3.9)-0.02024191144580438847],_
+ [4.0,0.01831563888873418029,exp(-4.0),exp(-4.0)-0.01831563888873418029],_
+ [4.1,0.01657267540176124754,exp(-4.1),exp(-4.1)-0.01657267540176124754],_
+ [4.2,0.01499557682047770621,exp(-4.2),exp(-4.2)-0.01499557682047770621],_
+ [4.3,0.01356855901220093176,exp(-4.3),exp(-4.3)-0.01356855901220093176],_
+ [4.4,0.01227733990306844118,exp(-4.4),exp(-4.4)-0.01227733990306844118],_
+ [4.5,0.01110899653824230650,exp(-4.5),exp(-4.5)-0.01110899653824230650],_
+ [4.6,0.01005183574463358164,exp(-4.6),exp(-4.6)-0.01005183574463358164],_
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+ [4.8,0.00822974704902002884,exp(-4.8),exp(-4.8)-0.00822974704902002884],_
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+ [5.0,0.00673794699908546710,exp(-5.0),exp(-5.0)-0.00673794699908546710],_
+ [5.1,0.00609674656551563611,exp(-5.1),exp(-5.1)-0.00609674656551563611],_
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+ [5.3,0.00499159390691021621,exp(-5.3),exp(-5.3)-0.00499159390691021621],_
+ [5.4,0.00451658094261266798,exp(-5.4),exp(-5.4)-0.00451658094261266798],_
+ [5.5,0.00408677143846406699,exp(-5.5),exp(-5.5)-0.00408677143846406699],_
+ [5.6,0.00369786371648293082,exp(-5.6),exp(-5.6)-0.00369786371648293082],_
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+ [5.8,0.00302755474537581475,exp(-5.8),exp(-5.8)-0.00302755474537581475],_
+ [5.9,0.00273944481876836923,exp(-5.9),exp(-5.9)-0.00273944481876836923],_
+ [6.0,0.00247875217666635842,exp(-6.0),exp(-6.0)-0.00247875217666635842],_
+ [6.1,0.00224286771948580247,exp(-6.1),exp(-6.1)-0.00224286771948580247],_
+ [6.2,0.00202943063629573436,exp(-6.2),exp(-6.2)-0.00202943063629573436],_
+ [6.3,0.00183630477702890683,exp(-6.3),exp(-6.3)-0.00183630477702890683],_
+ [6.4,0.00166155727317393450,exp(-6.4),exp(-6.4)-0.00166155727317393450],_
+ [6.5,0.00150343919297757245,exp(-6.5),exp(-6.5)-0.00150343919297757245],_
+ [6.6,0.00136036803754789342,exp(-6.6),exp(-6.6)-0.00136036803754789342],_
+ [6.7,0.00123091190267348118,exp(-6.7),exp(-6.7)-0.00123091190267348118],_
+ [6.8,0.00111377514784480308,exp(-6.8),exp(-6.8)-0.00111377514784480308],_
+ [6.9,0.00100778542904851076,exp(-6.9),exp(-6.9)-0.00100778542904851076],_
+ [7.0,0.00091188196555451621,exp(-7.0),exp(-7.0)-0.00091188196555451621],_
+ [7.1,0.00082510492326590427,exp(-7.1),exp(-7.1)-0.00082510492326590427],_
+ [7.2,0.00074658580837667937,exp(-7.2),exp(-7.2)-0.00074658580837667937],_
+ [7.3,0.00067553877519384424,exp(-7.3),exp(-7.3)-0.00067553877519384424],_
+ [7.4,0.00061125276112957256,exp(-7.4),exp(-7.4)-0.00061125276112957256],_
+ [7.5,0.00055308437014783358,exp(-7.5),exp(-7.5)-0.00055308437014783358],_
+ [7.6,0.00050045143344061070,exp(-7.6),exp(-7.6)-0.00050045143344061070],_
+ [7.7,0.00045282718288679706,exp(-7.7),exp(-7.7)-0.00045282718288679706],_
+ [7.8,0.00040973497897978671,exp(-7.8),exp(-7.8)-0.00040973497897978671],_
+ [7.9,0.00037074354045908837,exp(-7.9),exp(-7.9)-0.00037074354045908837],_
+ [8.0,0.00033546262790251184,exp(-8.0),exp(-8.0)-0.00033546262790251184],_
+ [8.1,0.00030353913807886666,exp(-8.1),exp(-8.1)-0.00030353913807886666],_
+ [8.2,0.00027465356997214233,exp(-8.2),exp(-8.2)-0.00027465356997214233],_
+ [8.3,0.00024851682710795202,exp(-8.3),exp(-8.3)-0.00024851682710795202],_
+ [8.4,0.00022486732417884827,exp(-8.4),exp(-8.4)-0.00022486732417884827],_
+ [8.5,0.00020346836901064417,exp(-8.5),exp(-8.5)-0.00020346836901064417],_
+ [8.6,0.00018410579366757912,exp(-8.6),exp(-8.6)-0.00018410579366757912],_
+ [8.7,0.00016658581098763341,exp(-8.7),exp(-8.7)-0.00016658581098763341],_
+ [8.8,0.00015073307509547660,exp(-8.8),exp(-8.8)-0.00015073307509547660],_
+ [8.9,0.00013638892648201145,exp(-8.9),exp(-8.9)-0.00013638892648201145],_
+ [9.0,0.00012340980408667955,exp(-9.0),exp(-9.0)-0.00012340980408667955],_
+ [9.1,0.00011166580849011474,exp(-9.1),exp(-9.1)-0.00011166580849011474],_
+ [9.2,0.00010103940183709335,exp(-9.2),exp(-9.2)-0.00010103940183709335],_
+ [9.3,0.00009142423147817334,exp(-9.3),exp(-9.3)-0.00009142423147817334],_
+ [9.4,0.00008272406555663226,exp(-9.4),exp(-9.4)-0.00008272406555663226],_
+ [9.5,0.00007485182988770059,exp(-9.5),exp(-9.5)-0.00007485182988770059],_
+ [9.6,0.00006772873649085387,exp(-9.6),exp(-9.6)-0.00006772873649085387],_
+ [9.7,0.00006128349505322210,exp(-9.7),exp(-9.7)-0.00006128349505322210],_
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+ [9.9,0.00005017468205617530,exp(-9.9),exp(-9.9)-0.00005017468205617530],_
+[10.0,0.00004539992976248485,exp(-10.0),exp(-10.0)-0.00004539992976248485]]
+--R
+--R
+--R (2)
+--R [[0.1,0.9048374180 3595957316,0.9048374180 3595957316,0.3 E -20],
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-20],
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+--R [9.6,0.0000677287 3649085387,0.0000677287 3649085387 2996,0.3 E -20],
+--R [9.7,0.0000612834 950532221,0.0000612834 9505322209 5514,- 0.449 E -20],
+--R [9.8,0.0000554515 9943217698,0.0000554515 9943217698 1808,0.181 E -20],
+--R [9.9,0.0000501746 820561753,0.0000501746 8205617530 2187,0.219 E -20],
+--R [10.0,0.0000453999 2976248485,0.0000453999 2976248485 1536,0.154 E -20]]
+--R Type: List List
Float
+--E 2
+
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp136-137
+\end{thebibliography}
+\end{document}
+
diff --git a/src/input/gamma.input.pamphlet b/src/input/gamma.input.pamphlet
index 608cf75..6b5f38b 100644
--- a/src/input/gamma.input.pamphlet
+++ b/src/input/gamma.input.pamphlet
@@ -17,19 +17,13 @@ second column is the reference value of Gamma from the book
Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
Dover Publications, Inc. New York 1965. pp267-270
-Notice that certain entries have reasonably large differences:
-\begin{verbatim}
-[1.215, 0.9143261399876792, 0.91432614997006778, 9.9823885824079639E-9]
-[1.455, 0.88562206999631599, 0.88562207999314335, 9.9968273659101214E-9]
-\end{verbatim}
-
<<*>>=
)spool gamma.output
)set message test on
)set message auto off
)clear all
---S 1 of 3
+--S 1 of 4
[[1.000,1.0000000000,Gamma(1.000),Gamma(1.000)-1.0000000000],_
[1.005,0.9971385354,Gamma(1.005),Gamma(1.005)-0.9971385354],_
[1.010,0.9943258512,Gamma(1.010),Gamma(1.010)-0.9943258512],_
@@ -73,7 +67,7 @@ Notice that certain entries have reasonably large differences:
[1.200,0.9181687424,Gamma(1.200),Gamma(1.200)-0.9181687424],_
[1.205,0.9168572606,Gamma(1.205),Gamma(1.205)-0.9168572606],_
[1.210,0.9155764930,Gamma(1.210),Gamma(1.210)-0.9155764930],_
- [1.215,0.9143261400,Gamma(1.215),Gamma(1.215)-0.9143261400],_
+ [1.215,0.9143261500,Gamma(1.215),Gamma(1.215)-0.9143261500],_
[1.220,0.9131059475,Gamma(1.220),Gamma(1.220)-0.9131059475],_
[1.225,0.9119156071,Gamma(1.225),Gamma(1.225)-0.9119156071],_
[1.230,0.9107548564,Gamma(1.230),Gamma(1.230)-0.9107548564],_
@@ -121,7 +115,7 @@ Notice that certain entries have reasonably large
differences:
[1.440,0.8858050635,Gamma(1.440),Gamma(1.440)-0.8858050635],_
[1.445,0.8857223397,Gamma(1.445),Gamma(1.445)-0.8857223397],_
[1.450,0.8856613803,Gamma(1.450),Gamma(1.450)-0.8856613803],_
- [1.455,0.8856220700,Gamma(1.455),Gamma(1.455)-0.8856220700],_
+ [1.455,0.8856220800,Gamma(1.455),Gamma(1.455)-0.8856220800],_
[1.460,0.8856043364,Gamma(1.460),Gamma(1.460)-0.8856043364],_
[1.465,0.8856080495,Gamma(1.465),Gamma(1.465)-0.8856080495],_
[1.470,0.8856331217,Gamma(1.470),Gamma(1.470)-0.8856331217],_
@@ -349,8 +343,8 @@ Notice that certain entries have reasonably large
differences:
--R ,
--R [1.21,0.91557649299999999,0.91557649300335908,3.3590907833058736E-12],
--R
---R [1.2150000000000001, 0.91432614000000001, 0.91432614997639472,
---R 9.9763947103426176E-9]
+--R [1.2150000000000001, 0.91432614999999995, 0.91432614997639472,
+--R - 2.3605228882672691E-11]
--R ,
--R [1.22,0.91310594749999996,0.9131059475104113,1.041133845802733E-11],
--R
@@ -475,8 +469,8 @@ Notice that certain entries have reasonably large
differences:
--R ,
--R [1.45,0.88566138029999997,0.88566138027107244,- 2.8927527040423229E-11],
--R
---R [1.4550000000000001, 0.88562207000000004, 0.88562207999323628,
---R 9.9932362385146689E-9]
+--R [1.4550000000000001, 0.88562207999999998, 0.88562207999323628,
+--R - 6.7637007106213787E-12]
--R ,
--R [1.46,0.88560433640000003,0.88560433642514391,2.5143886972500695E-11],
--R
@@ -762,7 +756,7 @@ Notice that certain entries have reasonably large
differences:
--R Type: List List
DoubleFloat
--E 1
---S 2 of 3
+--S 2 of 4
Psi(x:DFLOAT):DFLOAT==polygamma(0,x)
--R
--R Function declaration Psi : DoubleFloat -> DoubleFloat has been added
@@ -778,7 +772,7 @@ Dover Publications, Inc. New York 1965. pp267-270
<<*>>=
---S 3 of 3
+--S 3 of 4
[[1.000, -0.5772156649, Psi(1.000), Psi(1.000)- -0.5772156649],_
[1.005, -0.5690209113, Psi(1.005), Psi(1.005)- -0.5690209113],_
[1.010, -0.5608854579, Psi(1.010), Psi(1.010)- -0.5608854579],_
@@ -1540,6 +1534,836 @@ Dover Publications, Inc. New York 1965. pp267-270
--R [2.,0.42278433510000002,0.42278433509846725,- 1.5327739077974911E-12]]
--R Type: List List
DoubleFloat
--E 3
+@
+In the following table there are 4 columns. The first column
+is the argument of complex Gamma, ranging from 1.0 + 0i to 1.0+10i
+second column is the reference value of complex Gamma from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp227
+
+Note that at the value 1.0+4.6i there is a radical departure between
+the table and the computed values in the imaginary part of the value
+even though the real part is exact.
+<<*>>=
+--S 4 of 4
+[[1. + 0.0 * %i,0.,log(Gamma(1. + 0.0 * %i)),log(Gamma(1. + 0.0 * %i))-0.0],_
+[1. + 0.1 * %i, -0.008197780565 - 0.057322940417 * %i,_
+log(Gamma(1. + 0.1 * %i)),_
+log(Gamma(1. + 0.1 * %i))-( -0.008197780565 - 0.057322940417 * %i)],_
+[1. + 0.2 * %i, -0.032476292318 - 0.112302222644 * %i,_
+log(Gamma(1. + 0.2 * %i)),_
+log(Gamma(1. + 0.2 * %i))-( -0.032476292318 - 0.112302222644 * %i)],_
+[1. + 0.3 * %i, -0.071946250900 - 0.162820672168 * %i,_
+log(Gamma(1. + 0.3 * %i)),_
+log(Gamma(1. + 0.3 * %i))-( -0.071946250900 - 0.162820672168 * %i)],_
+[1. + 0.4 * %i, -0.125289374821 - 0.207155826316 * %i,_
+log(Gamma(1. + 0.4 * %i)),_
+log(Gamma(1. + 0.4 * %i))-( -0.125289374821 - 0.207155826316 * %i)],_
+[1. + 0.5 * %i,- 0.190945499187 - 0.244058298905 * %i,_
+log(Gamma(1. + 0.5 * %i)),_
+log(Gamma(1. + 0.5 * %i))-(- 0.190945499187 - 0.244058298905 * %i)],_
+[1. + 0.6 * %i,- 0.267290068214 - 0.272743810491 * %i,_
+log(Gamma(1. + 0.6 * %i)),_
+log(Gamma(1. + 0.6 * %i))-(- 0.267290068214 - 0.272743810491 * %i)],_
+[1. + 0.7 * %i,- 0.352768690860 - 0.292826351187 * %i,_
+log(Gamma(1. + 0.7 * %i)),_
+log(Gamma(1. + 0.7 * %i))-(- 0.352768690860 - 0.292826351187 * %i)],_
+[1. + 0.8 * %i,- 0.445978783549 - 0.304225602976 * %i,_
+log(Gamma(1. + 0.8 * %i)),_
+log(Gamma(1. + 0.8 * %i))-(- 0.445978783549 - 0.304225602976 * %i)],_
+[1. + 0.9 * %i,- 0.545705128605 - 0.307074375642 * %i,_
+log(Gamma(1. + 0.9 * %i)),_
+log(Gamma(1. + 0.9 * %i))-(- 0.545705128605 - 0.307074375642 * %i)],_
+[1. + 1.0 * %i,- 0.650923199302 - 0.301640320468 * %i,_
+log(Gamma(1. + 1.0 * %i)),_
+log(Gamma(1. + 1.0 * %i))-(- 0.650923199302 - 0.301640320468 * %i)],_
+[1. + 1.1 * %i,- 0.760783958841 - 0.288266614239 * %i,_
+log(Gamma(1. + 1.1 * %i)),_
+log(Gamma(1. + 1.1 * %i))-(- 0.760783958841 - 0.288266614239 * %i)],_
+[1. + 1.2 * %i,- 0.874590463895 - 0.267330580581 * %i,_
+log(Gamma(1. + 1.2 * %i)),_
+log(Gamma(1. + 1.2 * %i))-(- 0.874590463895 - 0.267330580581 * %i)],_
+[1. + 1.3 * %i,- 0.991772766959 - 0.239216784465 * %i,_
+log(Gamma(1. + 1.3 * %i)),_
+log(Gamma(1. + 1.3 * %i))-(- 0.991772766959 - 0.239216784465 * %i)],_
+[1. + 1.4 * %i,- 1.111864566426 - 0.204300724149 * %i,_
+log(Gamma(1. + 1.4 * %i)),_
+log(Gamma(1. + 1.4 * %i))-(- 1.111864566426 - 0.204300724149 * %i)],_
+[1. + 1.5 * %i,- 1.234483051547 - 0.162939769480 * %i,_
+log(Gamma(1. + 1.5 * %i)),_
+log(Gamma(1. + 1.5 * %i))-(- 1.234483051547 - 0.162939769480 * %i)],_
+[1. + 1.6 * %i,- 1.359312248465 - 0.115468793589 * %i,_
+log(Gamma(1. + 1.6 * %i)),_
+log(Gamma(1. + 1.6 * %i))-(- 1.359312248465 - 0.115468793589 * %i)],_
+[1. + 1.7 * %i,- 1.486089612757 - 0.062198698329 * %i,_
+log(Gamma(1. + 1.7 * %i)),_
+log(Gamma(1. + 1.7 * %i))-(- 1.486089612757 - 0.062198698329 * %i)],_
+[1. + 1.8 * %i,- 1.614595396000 - 0.003416631477 * %i,_
+log(Gamma(1. + 1.8 * %i)),_
+log(Gamma(1. + 1.8 * %i))-(- 1.614595396000 - 0.003416631477 * %i)],_
+[1. + 1.9 * %i,- 1.744644276174 + 0.060612874295 * %i,_
+log(Gamma(1. + 1.9 * %i)),_
+log(Gamma(1. + 1.9 * %i))-(- 1.744644276174 + 0.060612874295 * %i)],_
+[1. + 2.0 * %i,- 1.876078786431 + 0.129646316310 * %i,_
+log(Gamma(1. + 2.0 * %i)),_
+log(Gamma(1. + 2.0 * %i))-(- 1.876078786431 + 0.129646316310 * %i)],_
+[1. + 2.1 * %i,- 2.008764150471 + 0.203459473833 * %i,_
+log(Gamma(1. + 2.1 * %i)),_
+log(Gamma(1. + 2.1 * %i))-(- 2.008764150471 + 0.203459473833 * %i)],_
+[1. + 2.2 * %i,- 2.142584209296 + 0.281845658426 * %i,_
+log(Gamma(1. + 2.2 * %i)),_
+log(Gamma(1. + 2.2 * %i))-(- 2.142584209296 + 0.281845658426 * %i)],_
+[1. + 2.3 * %i,- 2.277438192204 + 0.364614048950 * %i,_
+log(Gamma(1. + 2.3 * %i)),_
+log(Gamma(1. + 2.3 * %i))-(- 2.277438192204 + 0.364614048950 * %i)],_
+[1. + 2.4 * %i,- 2.413238141184 + 0.451588152441 * %i,_
+log(Gamma(1. + 2.4 * %i)),_
+log(Gamma(1. + 2.4 * %i))-(- 2.413238141184 + 0.451588152441 * %i)],_
+[1. + 2.5 * %i,- 2.549906842495 + 0.542604405852 * %i,_
+log(Gamma(1. + 2.5 * %i)),_
+log(Gamma(1. + 2.5 * %i))-(- 2.549906842495 + 0.542604405852 * %i)],_
+[1. + 2.6 * %i,- 2.687376153750 + 0.637510919046 * %i,_
+log(Gamma(1. + 2.6 * %i)),_
+log(Gamma(1. + 2.6 * %i))-(- 2.687376153750 + 0.637510919046 * %i)],_
+[1. + 2.7 * %i,- 2.825585641191 + 0.736166351679 * %i,_
+log(Gamma(1. + 2.7 * %i)),_
+log(Gamma(1. + 2.7 * %i))-(- 2.825585641191 + 0.736166351679 * %i)],_
+[1. + 2.8 * %i,- 2.964481461789 + 0.838438913096 * %i,_
+log(Gamma(1. + 2.8 * %i)),_
+log(Gamma(1. + 2.8 * %i))-(- 2.964481461789 + 0.838438913096 * %i)],_
+[1. + 2.9 * %i,- 3.104015439901 + 0.944205473039 * %i,_
+log(Gamma(1. + 2.9 * %i)),_
+log(Gamma(1. + 2.9 * %i))-(- 3.104015439901 + 0.944205473039 * %i)],_
+[1. + 3.0 * %i,- 3.244144299590 + 1.053350771069 * %i,_
+log(Gamma(1. + 3.0 * %i)),_
+log(Gamma(1. + 3.0 * %i))-(- 3.244144299590 + 1.053350771069 * %i)],_
+[1. + 3.1 * %i,- 3.384829022377 + 1.165766713286 * %i,_
+log(Gamma(1. + 3.1 * %i)),_
+log(Gamma(1. + 3.1 * %i))-(- 3.384829022377 + 1.165766713286 * %i)],_
+[1. + 3.2 * %i,- 3.526034306709 + 1.281351745932 * %i,_
+log(Gamma(1. + 3.2 * %i)),_
+log(Gamma(1. + 3.2 * %i))-(- 3.526034306709 + 1.281351745932 * %i)],_
+[1. + 3.3 * %i,- 3.667728110488 + 1.400010296576 * %i,_
+log(Gamma(1. + 3.3 * %i)),_
+log(Gamma(1. + 3.3 * %i))-(- 3.667728110488 + 1.400010296576 * %i)],_
+[1. + 3.4 * %i,- 3.809881261823 + 1.521652274673 * %i,_
+log(Gamma(1. + 3.4 * %i)),_
+log(Gamma(1. + 3.4 * %i))-(- 3.809881261823 + 1.521652274673 * %i)],_
+[1. + 3.5 * %i,- 3.952467126189 + 1.646192624269 * %i,_
+log(Gamma(1. + 3.5 * %i)),_
+log(Gamma(1. + 3.5 * %i))-(- 3.952467126189 + 1.646192624269 * %i)],_
+[1. + 3.6 * %i,- 4.095461320451 + 1.773550922591 * %i,_
+log(Gamma(1. + 3.6 * %i)),_
+log(Gamma(1. + 3.6 * %i))-(- 4.095461320451 + 1.773550922591 * %i)],_
+[1. + 3.7 * %i,- 4.238841466071 + 1.903651019019 * %i,_
+log(Gamma(1. + 3.7 * %i)),_
+log(Gamma(1. + 3.7 * %i))-(- 4.238841466071 + 1.903651019019 * %i)],_
+[1. + 3.8 * %i,- 4.382586975228 + 2.036420709693 * %i,_
+log(Gamma(1. + 3.8 * %i)),_
+log(Gamma(1. + 3.8 * %i))-(- 4.382586975228 + 2.036420709693 * %i)],_
+[1. + 3.9 * %i,- 4.526678864716 + 2.171791443605 * %i,_
+log(Gamma(1. + 3.9 * %i)),_
+log(Gamma(1. + 3.9 * %i))-(- 4.526678864716 + 2.171791443605 * %i)],_
+[1. + 4.0 * %i,- 4.671099593409 + 2.309698056573 * %i,_
+log(Gamma(1. + 4.0 * %i)),_
+log(Gamma(1. + 4.0 * %i))-(- 4.671099593409 + 2.309698056573 * %i)],_
+[1. + 4.1 * %i,- 4.815832919796 + 2.450078529947 * %i,_
+log(Gamma(1. + 4.1 * %i)),_
+log(Gamma(1. + 4.1 * %i))-(- 4.815832919796 + 2.450078529947 * %i)],_
+[1. + 4.2 * %i,- 4.960863776687 + 2.592873771319 * %i,_
+log(Gamma(1. + 4.2 * %i)),_
+log(Gamma(1. + 4.2 * %i))-(- 4.960863776687 + 2.592873771319 * %i)],_
+[1. + 4.3 * %i,- 5.106178160663 + 2.738027414820 * %i,_
+log(Gamma(1. + 4.3 * %i)),_
+log(Gamma(1. + 4.3 * %i))-(- 5.106178160663 + 2.738027414820 * %i)],_
+[1. + 4.4 * %i,- 5.251763034230 + 2.885485638927 * %i,_
+log(Gamma(1. + 4.4 * %i)),_
+log(Gamma(1. + 4.4 * %i))-(- 5.251763034230 + 2.885485638927 * %i)],_
+[1. + 4.5 * %i,- 5.397606238984 + 3.035196999922 * %i,_
+log(Gamma(1. + 4.5 * %i)),_
+log(Gamma(1. + 4.5 * %i))-(- 5.397606238984 + 3.035196999922 * %i)],_
+[1. + 4.6 * %i,- 5.543696418304 + 3.187112279389 * %i,_
+log(Gamma(1. + 4.6 * %i)),_
+log(Gamma(1. + 4.6 * %i))-(- 5.543696418304 + 3.187112279389 * %i)],_
+[1. + 4.7 * %i,- 5.690022948373 + 3.341184344327 * %i,_
+log(Gamma(1. + 4.7 * %i)),_
+log(Gamma(1. + 4.7 * %i))-(- 5.690022948373 + 3.341184344327 * %i)],_
+[1. + 4.8 * %i,- 5.836575876454 + 3.497368018615 * %i,_
+log(Gamma(1. + 4.8 * %i)),_
+log(Gamma(1. + 4.8 * %i))-(- 5.836575876454 + 3.497368018615 * %i)],_
+[1. + 4.9 * %i,- 5.983345865532 + 3.655619964712 * %i,_
+log(Gamma(1. + 4.9 * %i)),_
+log(Gamma(1. + 4.9 * %i))-(- 5.983345865532 + 3.655619964712 * %i)],_
+[1. + 5.0 * %i,- 6.130324144553 + 3.815898574615 * %i,_
+log(Gamma(1. + 5.0 * %i)),_
+log(Gamma(1. + 5.0 * %i))-(- 6.130324144553 + 3.815898574615 * %i)],_
+[1. + 5.1 * %i,- 6.277502463584 + 3.978163869188 * %i,_
+log(Gamma(1. + 5.1 * %i)),_
+log(Gamma(1. + 5.1 * %i))-(- 6.277502463584 + 3.978163869188 * %i)],_
+[1. + 5.2 * %i,- 6.424873053335 + 4.142377405086 * %i,_
+log(Gamma(1. + 5.2 * %i)),_
+log(Gamma(1. + 5.2 * %i))-(- 6.424873053335 + 4.142377405086 * %i)],_
+[1. + 5.3 * %i,- 6.572428588529 + 4.308502188583 * %i,_
+log(Gamma(1. + 5.3 * %i)),_
+log(Gamma(1. + 5.3 * %i))-(- 6.572428588529 + 4.308502188583 * %i)],_
+[1. + 5.4 * %i,- 6.720162154703 + 4.476502595668 * %i,_
+log(Gamma(1. + 5.4 * %i)),_
+log(Gamma(1. + 5.4 * %i))-(- 6.720162154703 + 4.476502595668 * %i)],_
+[1. + 5.5 * %i,- 6.868067218048 + 4.646344297870 * %i,_
+log(Gamma(1. + 5.5 * %i)),_
+log(Gamma(1. + 5.5 * %i))-(- 6.868067218048 + 4.646344297870 * %i)],_
+[1. + 5.6 * %i,- 7.016137597976 + 4.817994193305 * %i,_
+log(Gamma(1. + 5.6 * %i)),_
+log(Gamma(1. + 5.6 * %i))-(- 7.016137597976 + 4.817994193305 * %i)],_
+[1. + 5.7 * %i,- 7.164367442106 + 4.991420342489 * %i,_
+log(Gamma(1. + 5.7 * %i)),_
+log(Gamma(1. + 5.7 * %i))-(- 7.164367442106 + 4.991420342489 * %i)],_
+[1. + 5.8 * %i,- 7.312751203430 + 5.166591908537 * %i,_
+log(Gamma(1. + 5.8 * %i)),_
+log(Gamma(1. + 5.8 * %i))-(- 7.312751203430 + 5.166591908537 * %i)],_
+[1. + 5.9 * %i,- 7.461283619429 + 5.343479101353 * %i,_
+log(Gamma(1. + 5.9 * %i)),_
+log(Gamma(1. + 5.9 * %i))-(- 7.461283619429 + 5.343479101353 * %i)],_
+[1. + 6.0 * %i,- 7.609959692951 + 5.522053125515 * %i,_
+log(Gamma(1. + 6.0 * %i)),_
+log(Gamma(1. + 6.0 * %i))-(- 7.609959692951 + 5.522053125515 * %i)],_
+[1. + 6.1 * %i,- 7.758774674655 + 5.702286131535 * %i,_
+log(Gamma(1. + 6.1 * %i)),_
+log(Gamma(1. + 6.1 * %i))-(- 7.758774674655 + 5.702286131535 * %i)],_
+[1. + 6.2 * %i,- 7.907724046898 + 5.884151170239 * %i,_
+log(Gamma(1. + 6.2 * %i)),_
+log(Gamma(1. + 6.2 * %i))-(- 7.907724046898 + 5.884151170239 * %i)],_
+[1. + 6.3 * %i,- 8.056803508904 + 6.067622150013 * %i,_
+log(Gamma(1. + 6.3 * %i)),_
+log(Gamma(1. + 6.3 * %i))-(- 8.056803508904 + 6.067622150013 * %i)],_
+[1. + 6.4 * %i,- 8.206008963100 + 6.252673796705 * %i,_
+log(Gamma(1. + 6.4 * %i)),_
+log(Gamma(1. + 6.4 * %i))-(- 8.206008963100 + 6.252673796705 * %i)],_
+[1. + 6.5 * %i,- 8.355336502511 + 6.439281615976 * %i,_
+log(Gamma(1. + 6.5 * %i)),_
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+--R
+--R
+--R (4)
+--R [[1.,0.,0.,0.],
+--R
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+--R ,
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%i,
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+--R ,
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%i,
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+--R ,
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%i,
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+--R ,
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+--R ,
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+--R ,
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%i,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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%i,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R ,
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+--R [1. + 3.1000000000000001 %i, - 3.3848290223770001 + 1.1657667132859999
%i,
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+--R ,
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+--R [1. + 3.2000000000000002 %i, - 3.5260343067090001 + 1.2813517459320001
%i,
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+--R ,
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+--R [1. + 3.2999999999999998 %i, - 3.667728110488 + 1.400010296576 %i,
+--R - 3.667728110487861 + 1.4000102965763475 %i,
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+--R ,
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+--R [1. + 3.3999999999999999 %i, - 3.809881261823 + 1.5216522746729999 %i,
+--R - 3.8098812618231577 + 1.5216522746726655 %i,
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+--R ,
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+--R [1. + 3.5 %i, - 3.9524671261890001 + 1.6461926242689999 %i,
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+--R ,
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+--R ,
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%i,
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+--R ,
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+--R ,
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%i,
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+--R ,
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+--R [1. + 4. %i, - 4.6710995934090001 + 2.3096980565730001 %i,
+--R - 4.6710995934088881 + 2.3096980565725347 %i,
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+--R ,
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+--R [1. + 4.0999999999999996 %i, - 4.8158329197959997 + 2.450078529947 %i,
+--R - 4.815832919796029 + 2.4500785299471368 %i,
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+--R ,
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%i,
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+--R ,
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+--R [1. + 4.2999999999999998 %i, - 5.1061781606630001 + 2.7380274148199999
%i,
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+--R 3.0020430585864233E-13 - 1.247890679678676E-13 %i]
+--R ,
+--R
+--R [1. + 4.4000000000000004 %i, - 5.2517630342299997 + 2.8854856389269998
%i,
+--R - 5.2517630342302715 + 2.88548563892701 %i,
+--R - 2.7178259642823832E-13 + 1.021405182655144E-14 %i]
+--R ,
+--R
+--R [1. + 4.5 %i, - 5.3976062389840003 + 3.0351969999219999 %i,
+--R - 5.3976062389839621 + 3.0351969999216122 %i,
+--R 3.8191672047105385E-14 - 3.8768988019910466E-13 %i]
+--R ,
+--R
+--R [1. + 4.5999999999999996 %i, - 5.5436964183040001 + 3.1871122793889999
%i,
+--R - 5.5436964183041857 - 3.0960730277910646 %i,
+--R - 1.8562928971732617E-13 - 6.2831853071800641 %i]
+--R ,
+--R
+--R [1. + 4.7000000000000002 %i, - 5.6900229483729996 + 3.341184344327 %i,
+--R - 5.6900229483732598 - 2.9420009628525539 %i,
+--R - 2.6023627697213669E-13 - 6.2831853071795543 %i]
+--R ,
+--R
+--R [1. + 4.7999999999999998 %i, - 5.8365758764539999 + 3.497368018615 %i,
+--R - 5.8365758764538676 - 2.7858172885645978 %i,
+--R 1.3233858453531866E-13 - 6.2831853071795978 %i]
+--R ,
+--R
+--R [1. + 4.9000000000000004 %i, - 5.9833458655319998 + 3.6556199647119998
%i,
+--R - 5.9833458655320113 - 2.6275653424675292 %i,
+--R - 1.1546319456101628E-14 - 6.2831853071795294 %i]
+--R ,
+--R
+--R [1. + 5. %i, - 6.1303241445529997 + 3.8158985746149998 %i,
+--R - 6.1303241445527474 - 2.467286732564661 %i,
+--R 2.5224267119483557E-13 - 6.2831853071796608 %i]
+--R ,
+--R
+--R [1. + 5.0999999999999996 %i, - 6.2775024635839998 + 3.9781638691880001
%i,
+--R - 6.2775024635841525 - 2.3050214379920333 %i,
+--R - 1.5276668818842154E-13 - 6.2831853071800339 %i]
+--R ,
+--R
+--R [1. + 5.2000000000000002 %i, - 6.4248730533350003 + 4.1423774050860001
%i,
+--R - 6.4248730533350971 - 2.1408079020934521 %i,
+--R - 9.681144774731365E-14 - 6.2831853071794521 %i]
+--R ,
+--R
+--R [1. + 5.2999999999999998 %i, - 6.5724285885290001 + 4.3085021885829997
%i,
+--R - 6.5724285885292408 - 1.9746831185966061 %i,
+--R - 2.4069635173873394E-13 - 6.2831853071796058 %i]
+--R ,
+--R
+--R [1. + 5.4000000000000004 %i, - 6.7201621547029999 + 4.4765025956680002
%i,
+--R - 6.7201621547026544 - 1.8066827115117343 %i,
+--R 3.4550140526334872E-13 - 6.2831853071797346 %i]
+--R ,
+--R
+--R [1. + 5.5 %i, - 6.868067218048 + 4.6463442978699998 %i,
+--R - 6.8680672180480444 - 1.6368410093092187 %i,
+--R - 4.4408920985006262E-14 - 6.2831853071792185 %i]
+--R ,
+--R
+--R [1. + 5.5999999999999996 %i, - 7.0161375979759999 + 4.8179941933050001
%i,
+--R - 7.0161375979761953 - 1.4651911138747613 %i,
+--R - 1.9539925233402755E-13 - 6.2831853071797612 %i]
+--R ,
+--R
+--R [1. + 5.7000000000000002 %i, - 7.1643674421060002 + 4.9914203424889996
%i,
+--R - 7.1643674421059877 - 1.2917649646901792 %i,
+--R 1.2434497875801753E-14 - 6.2831853071791786 %i]
+--R ,
+--R
+--R [1. + 5.7999999999999998 %i, - 7.3127512034300004 + 5.1665919085369998
%i,
+--R - 7.3127512034295403 - 1.1165933986428442 %i,
+--R 4.6007642140466487E-13 - 6.2831853071798438 %i]
+--R ,
+--R
+--R [1. + 5.9000000000000004 %i, - 7.4612836194290004 + 5.3434791013530001
%i,
+--R - 7.4612836194293823 - 0.93970620582698861 %i,
+--R - 3.8191672047105385E-13 - 6.2831853071799886 %i]
+--R ,
+--R
+--R [1. + 6. %i, - 7.6099596929509996 + 5.5220531255149998 %i,
+--R - 7.6099596929506781 - 0.76113218166486107 %i,
+--R 3.2152058793144533E-13 - 6.2831853071798607 %i]
+--R ,
+--R
+--R [1. + 6.0999999999999996 %i, - 7.7587746746550001 + 5.7022861315349997
%i,
+--R - 7.7587746746545623 - 0.58089917564415772 %i,
+--R 4.3787196091216174E-13 - 6.2831853071791572 %i]
+--R ,
+--R
+--R [1. + 6.2000000000000002 %i, - 7.9077240468980001 + 5.8841511702389999
%i,
+--R - 7.9077240468981636 - 0.39903413694019135 %i,
+--R - 1.6342482922482304E-13 - 6.283185307179191 %i]
+--R ,
+--R
+--R [1. + 6.2999999999999998 %i, - 8.0568035089040002 + 6.0676221500130003
%i,
+--R - 8.0568035089044336 - 0.21556315716640231 %i,
+--R - 4.3343106881366111E-13 - 6.2831853071794024 %i]
+--R ,
+--R
+--R [1. + 6.4000000000000004 %i, - 8.2060089631000004 + 6.2526737967050003
%i,
+--R - 8.2060089630998547 - 3.0511510474225532E-2 %i,
+--R 1.4566126083082054E-13 - 6.2831853071792256 %i]
+--R ,
+--R
+--R [1. + 6.5 %i, - 8.3553365025109994 + 6.4392816159760002 %i,
+--R - 8.3553365025113582 + 0.15609630879639777 %i,
+--R - 3.5882408155885059E-13 - 6.2831853071796022 %i]
+--R ,
+--R
+--R [1. + 6.5999999999999996 %i, - 8.5047823991250002 + 6.6274218579120001
%i,
+--R - 8.5047823991254532 + 0.34423655073274489 %i,
+--R - 4.5297099404706387E-13 - 6.2831853071792549 %i]
+--R ,
+--R
+--R [1. + 6.7000000000000002 %i, - 8.6543430931229999 + 6.8170714837439998
%i,
+--R - 8.654343093122673 + 0.53388617656407311 %i,
+--R 3.2684965844964609E-13 - 6.2831853071799264 %i]
+--R ,
+--R
+--R [1. + 6.7999999999999998 %i, - 8.8040151829099997 + 7.0082081345020004
%i,
+--R - 8.804015182909593 + 0.72502282732285273 %i,
+--R 4.0678571622265736E-13 - 6.2831853071791475 %i]
+--R ,
+--R
+--R [1. + 6.9000000000000004 %i, - 8.9537954158790001 + 7.2008101014930004
%i,
+--R - 8.9537954158785062 + 0.91762479431292798 %i,
+--R 4.9382720135326963E-13 - 6.2831853071800721 %i]
+--R ,
+--R
+--R [1. + 7. %i, - 9.1036806798319994 + 7.3948562984360002 %i,
+--R - 9.1036806798319478 + 1.1116709912566856 %i,
+--R 5.1514348342607263E-14 - 6.2831853071793144 %i]
+--R ,
+--R
+--R [1. + 7.0999999999999996 %i, - 9.2536679950150003 + 7.5903262351840004
%i,
+--R - 9.2536679950154568 + 1.3071409280042976 %i,
+--R - 4.5652370772586437E-13 - 6.2831853071797026 %i]
+--R ,
+--R
+--R [1. + 7.2000000000000002 %i, - 9.4037545067079993 + 7.7871999928770004
%i,
+--R - 9.4037545067075801 + 1.5040146856973393 %i,
+--R 4.1922021409845911E-13 - 6.2831853071796608 %i]
+--R ,
+--R
+--R [1. + 7.2999999999999998 %i, - 9.553937478321 + 7.9854582004679999 %i,
+--R - 9.5539374783209006 + 1.7022728932880065 %i,
+--R 9.9475983006414026E-14 - 6.283185307179993 %i]
+--R ,
+--R
+--R [1. + 7.4000000000000004 %i, - 9.7042142849720001 + 8.1850820125030008
%i,
+--R - 9.7042142849724993 + 1.9018967053232116 %i,
+--R - 4.9915627187147038E-13 - 6.2831853071797887 %i]
+--R ,
+--R
+--R [1. + 7.5 %i, - 9.8545824074859993 + 8.3860530880889996 %i,
+--R - 9.8545824074859194 + 2.1028677809095977 %i,
+--R 7.9936057773011271E-14 - 6.2831853071794015 %i]
+--R ,
+--R
+--R [1. + 7.5999999999999996 %i, - 10.005039426790001 + 8.5883535709619991
%i,
+--R - 10.005039426790399 + 2.3051682637825208 %i,
+--R - 3.979039320256561E-13 - 6.2831853071794779 %i]
+--R ,
+--R
+--R [1. + 7.7000000000000002 %i, - 10.155583018686 + 8.7919660705869997 %i,
+--R - 10.155583018686212 + 2.5087807634076618 %i,
+--R - 2.1138646388862981E-13 - 6.2831853071793375 %i]
+--R ,
+--R
+--R [1. + 7.7999999999999998 %i, - 10.306210948947999 + 8.9968736442289998
%i,
+--R - 10.306210948947749 + 2.7136883370494931 %i,
+--R 2.5046631435543532E-13 - 6.2831853071795063 %i]
+--R ,
+--R
+--R [1. + 7.9000000000000004 %i, - 10.456921068739 + 9.2030597799250007 %i,
+--R - 10.456921068738524 + 2.9198744727458439 %i,
+--R 4.7606363295926712E-13 - 6.2831853071791564 %i]
+--R ,
+--R
+--R [1. + 8. %i, - 10.607711310315 + 9.4105083803120007 %i,
+--R - 10.607711310314581 + 3.1273230731320214 %i,
+--R 4.1922021409845911E-13 - 6.2831853071799788 %i]
+--R ,
+--R
+--R [1. + 8.0999999999999996 %i, - 10.758579682995 + 9.6192037472420004 %i,
+--R - 10.758579682994794 - 2.9471668671170055 %i,
+--R 2.0605739337042905E-13 - 12.566370614359005 %i]
+--R ,
+--R
+--R [1. + 8.1999999999999993 %i, - 10.909524269378 + 9.8291305671620002 %i,
+--R - 10.909524269378375 - 2.7372400471974712 %i,
+--R - 3.7481129311345285E-13 - 12.566370614359471 %i]
+--R ,
+--R
+--R [1. + 8.3000000000000007 %i, - 11.060543221792001 + 10.040273897180001
%i,
+--R - 11.060543221791693 - 2.5260967171793411 %i,
+--R 3.0730973321624333E-13 - 12.566370614359341 %i]
+--R ,
+--R
+--R [1. + 8.4000000000000004 %i, - 11.211634758948 + 10.252619151809 %i,
+--R - 11.211634758947826 - 2.3137514625505582 %i,
+--R 1.7408297026122455E-13 - 12.566370614359558 %i]
+--R ,
+--R
+--R [1. + 8.5 %i, - 11.362797162804 + 10.466152090324 %i,
+--R - 11.362797162803814 - 2.100218524035578 %i,
+--R 1.865174681370263E-13 - 12.566370614359577 %i]
+--R ,
+--R
+--R [1. + 8.5999999999999996 %i, - 11.514028775602 + 10.680858804712001 %i,
+--R - 11.514028775601707 - 1.8855118096468773 %i,
+--R 2.9309887850104133E-13 - 12.566370614358878 %i]
+--R ,
+--R
+--R [1. + 8.6999999999999993 %i, - 11.665327997081 + 10.896725708177 %i,
+--R - 11.665327997080658 - 1.6696449061826013 %i,
+--R 3.4283687000424834E-13 - 12.566370614359601 %i]
+--R ,
+--R
+--R [1. + 8.8000000000000007 %i, - 11.816693281848 + 11.113739524156999 %i,
+--R - 11.816693281848337 - 1.452631090201765 %i,
+--R - 3.3750779948604759E-13 - 12.566370614358764 %i]
+--R ,
+--R
+--R [1. + 8.9000000000000004 %i, - 11.968123136900999 + 11.331887275852999
%i,
+--R - 11.968123136900861 - 1.2344833385062608 %i,
+--R 1.3855583347321954E-13 - 12.56637061435926 %i]
+--R ,
+--R
+--R [1. + 9. %i, - 12.119616119281 + 11.551156276202001 %i,
+--R - 12.119616119281286 - 1.0152143381569982 %i,
+--R - 2.8599345114344032E-13 - 12.566370614358998 %i]
+--R ,
+--R
+--R [1. + 9.0999999999999996 %i, - 12.271170833867 + 11.771534118309001 %i,
+--R - 12.271170833867483 - 0.79483649604973161 %i,
+--R - 4.8316906031686813E-13 - 12.566370614358732 %i]
+--R ,
+--R
+--R [1. + 9.1999999999999993 %i, - 12.422785931281 + 11.993008666285 %i,
+--R - 12.422785931280877 - 0.5733619480744393 %i,
+--R 1.2256862191861728E-13 - 12.566370614359439 %i]
+--R ,
+--R
+--R [1. + 9.3000000000000007 %i, - 12.574460105908001 + 12.215568046479 %i,
+--R - 12.574460105908262 - 0.35080256788055886 %i,
+--R - 2.6112445539183682E-13 - 12.566370614359558 %i]
+--R ,
+--R
+--R [1. + 9.4000000000000004 %i, - 12.726192094029001 + 12.43920063909 %i,
+--R - 12.726192094029377 - 0.12716997526913024 %i,
+--R - 3.765876499528531E-13 - 12.56637061435913 %i]
+--R ,
+--R
+--R [1. + 9.5 %i, - 12.877980672044 + 12.663895070128 %i,
+--R - 12.877980672043599 + 9.7524455768741289E-2 %i,
+--R 4.0145664570445661E-13 - 12.566370614359258 %i]
+--R ,
+--R
+--R [1. + 9.5999999999999996 %i, - 13.029824654789 + 12.889640203708 %i,
+--R - 13.02982465478944 + 0.32326958934851951 %i,
+--R - 4.4053649617126212E-13 - 12.56637061435948 %i]
+--R ,
+--R
+--R [1. + 9.6999999999999993 %i, - 13.181722893950999 + 13.116425134666001
%i,
+--R - 13.181722893951155 + 0.55005452030683832 %i,
+--R - 1.5631940186722204E-13 - 12.566370614359162 %i]
+--R ,
+--R
+--R [1. + 9.8000000000000007 %i, - 13.333674276547001 + 13.344239181477 %i,
+--R - 13.333674276547052 + 0.77786856711780805 %i,
+--R - 5.1514348342607263E-14 - 12.566370614359192 %i]
+--R ,
+--R
+--R [1. + 9.9000000000000004 %i, - 13.485677723495 + 13.573071879455 %i,
+--R - 13.485677723494533 + 1.0067012650958465 %i,
+--R 4.6718184876226587E-13 - 12.566370614359153 %i]
+--R ,
+--R
+--R [1. + 10. %i, - 13.637732188247 + 13.802912974230001 %i,
+--R - 13.637732188247268 + 1.2365423598707301 %i,
+--R - 2.6822988274943782E-13 - 12.56637061435927 %i]
+--R ]
+--R Type: List List Complex
DoubleFloat
+--E 4
)spool
)lisp (bye)
@@ -1592,5 +2416,7 @@ close(viewport)
http://dlmf.nist.gov
\bibitem{2} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
Dover Publications, Inc. New York 1965. pp267-270
+\bibitem{3} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp277
\end{thebibliography}
\end{document}
diff --git a/src/input/log.input.pamphlet b/src/input/log.input.pamphlet
new file mode 100644
index 0000000..8c6f78e
--- /dev/null
+++ b/src/input/log.input.pamphlet
@@ -0,0 +1,442 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input log.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This compares Axiom's log function with the tables published in
+Abramowitz and Stegun.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+In the following table there are 4 columns. The first column
+is the argument of log(x), ranging from 0.01 to 2.00. The
+second column is the reference value of log from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp100-113
+
+<<*>>=
+)spool log.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 1
+[[0.01, -4.6051701859880914, log(0.01), log(0.01)-(-4.6051701859880914)], _
+[0.02, -3.9120230054281461, log(0.02), log(0.02)-(-3.9120230054281461)], _
+[0.03, -3.5065578973199817, log(0.03), log(0.03)-(-3.5065578973199817)], _
+[0.04, -3.2188758248682007, log(0.04), log(0.04)-(-3.2188758248682007)], _
+[0.05, -2.9957322735539910, log(0.05), log(0.05)-(-2.9957322735539910)], _
+[0.06, -2.8134107167600364, log(0.06), log(0.06)-(-2.8134107167600364)], _
+[0.07, -2.6592600369327781, log(0.07), log(0.07)-(-2.6592600369327781)], _
+[0.08, -2.5257286443082554, log(0.08), log(0.08)-(-2.5257286443082554)], _
+[0.09, -2.4079456086518720, log(0.09), log(0.09)-(-2.4079456086518720)], _
+[0.10, -2.3025850929940457, log(0.10), log(0.10)-(-2.3025850929940457)], _
+[0.11, -2.2072749131897208, log(0.11), log(0.11)-(-2.2072749131897208)], _
+[0.12, -2.1202635362000911, log(0.12), log(0.12)-(-2.1202635362000911)], _
+[0.13, -2.0402208285265546, log(0.13), log(0.13)-(-2.0402208285265546)], _
+[0.14, -1.9661128563728328, log(0.14), log(0.14)-(-1.9661128563728328)], _
+[0.15, -1.8971199848858813, log(0.15), log(0.15)-(-1.8971199848858813)], _
+[0.16, -1.8325814637483101, log(0.16), log(0.16)-(-1.8325814637483101)], _
+[0.17, -1.7719568419318753, log(0.17), log(0.17)-(-1.7719568419318753)], _
+[0.18, -1.7147984280919267, log(0.18), log(0.18)-(-1.7147984280919267)], _
+[0.19, -1.6607312068216509, log(0.19), log(0.19)-(-1.6607312068216509)], _
+[0.20, -1.6094379124341004, log(0.20), log(0.20)-(-1.6094379124341004)], _
+[0.21, -1.5606477482646684, log(0.21), log(0.21)-(-1.5606477482646684)], _
+[0.22, -1.5141277326297755, log(0.22), log(0.22)-(-1.5141277326297755)], _
+[0.23, -1.4696759700589417, log(0.23), log(0.23)-(-1.4696759700589417)], _
+[0.24, -1.4271163556401457, log(0.24), log(0.24)-(-1.4271163556401457)], _
+[0.25, -1.3862943611198906, log(0.25), log(0.25)-(-1.3862943611198906)], _
+[0.26, -1.3470736479666093, log(0.26), log(0.26)-(-1.3470736479666093)], _
+[0.27, -1.3093333199837623, log(0.27), log(0.27)-(-1.3093333199837623)], _
+[0.28, -1.2729656758128874, log(0.28), log(0.28)-(-1.2729656758128874)], _
+[0.29, -1.2378743560016173, log(0.29), log(0.29)-(-1.2378743560016173)], _
+[0.30, -1.2039728043259360, log(0.30), log(0.30)-(-1.2039728043259360)], _
+[0.31, -1.1711829815029451, log(0.31), log(0.31)-(-1.1711829815029451)], _
+[0.32, -1.1394342831883648, log(0.32), log(0.32)-(-1.1394342831883648)], _
+[0.33, -1.1086626245216111, log(0.33), log(0.33)-(-1.1086626245216111)], _
+[0.34, -1.0788096613719300, log(0.34), log(0.34)-(-1.0788096613719300)], _
+[0.35, -1.0498221244986777, log(0.35), log(0.35)-(-1.0498221244986777)], _
+[0.36, -1.0216512475319814, log(0.36), log(0.36)-(-1.0216512475319814)], _
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+[2.00, 0.6931471805599453, log(2.00), log(2.00)-(0.6931471805599453)]]
+--R
+--R
+--R (1)
+--R [[0.01,- 4.6051701859 880914,- 4.6051701859 88091368,0.32 E -16],
+--R [0.02,- 3.9120230054 281461,- 3.9120230054 281460586,0.414 E -16],
+--R [0.03,- 3.5065578973 199817,- 3.5065578973 199816766,0.234 E -16],
+--R [0.04,- 3.2188758248 682007,- 3.2188758248 682007492,- 0.492 E -16],
+--R [0.05,- 2.9957322735 53991,- 2.9957322735 539909934,0.66 E -17],
+--R [0.06,- 2.8134107167 600364,- 2.8134107167 600363672,0.328 E -16],
+--R [0.07,- 2.6592600369 327781,- 2.6592600369 327780629,0.371 E -16],
+--R [0.08,- 2.5257286443 082554,- 2.5257286443 082554398,- 0.398 E -16],
+--R [0.09,- 2.4079456086 51872,- 2.4079456086 518719852,0.148 E -16],
+--R [0.1,- 2.3025850929 940457,- 2.3025850929 94045684,0.16 E -16],
+--R [0.11,- 2.2072749131 897208,- 2.2072749131 89720824,- 0.24 E -16],
+--R [0.12,- 2.1202635362 000911,- 2.1202635362 000910578,0.422 E -16],
+--R [0.13,- 2.0402208285 265546,- 2.0402208285 26554632,- 0.32 E -16],
+--R [0.14,- 1.9661128563 728328,- 1.9661128563 728327535,0.465 E -16],
+--R [0.15,- 1.8971199848 858813,- 1.8971199848 85881302,- 0.2 E -17],
+--R [0.16,- 1.8325814637 483101,- 1.8325814637 483101304,- 0.304 E -16],
+--R [0.17,- 1.7719568419 318753,- 1.7719568419 318752878,0.122 E -16],
+--R [0.18,- 1.7147984280 919267,- 1.7147984280 919266758,0.242 E -16],
+--R [0.19,- 1.6607312068 216509,- 1.6607312068 21650908,- 0.802 E -17],
+--R [0.2,- 1.6094379124 341004,- 1.6094379124 341003746,0.254 E -16],
+--R [0.21,- 1.5606477482 646684,- 1.5606477482 646683715,0.285 E -16],
+--R [0.22,- 1.5141277326 297755,- 1.5141277326 297755146,- 0.146 E -16],
+--R [0.23,- 1.4696759700 589417,- 1.4696759700 589416772,0.228 E -16],
+--R [0.24,- 1.4271163556 401457,- 1.4271163556 401457484,- 0.484 E -16],
+--R [0.25,- 1.3862943611 198906,- 1.3862943611 198906188,- 0.188 E -16],
+--R [0.26,- 1.3470736479 666093,- 1.3470736479 666093226,- 0.226 E -16],
+--R [0.27,- 1.3093333199 837623,- 1.3093333199 837622938,0.62 E -17],
+--R [0.28,- 1.2729656758 128874,- 1.2729656758 128874441,- 0.441 E -16],
+--R [0.29,- 1.2378743560 016173,- 1.2378743560 016173409,- 0.409 E -16],
+--R [0.3,- 1.2039728043 25936,- 1.2039728043 259359926,0.738 E -17],
+--R [0.31,- 1.1711829815 029451,- 1.1711829815 029451221,- 0.221 E -16],
+--R [0.32,- 1.1394342831 883648,- 1.1394342831 883648209,- 0.21 E -16],
+--R [0.33,- 1.1086626245 216111,- 1.1086626245 216111326,- 0.326 E -16],
+--R [0.34,- 1.0788096613 7193,- 1.0788096613 719299784,0.216 E -16],
+--R [0.35,- 1.0498221244 986777,- 1.0498221244 986776883,0.117 E -16],
+--R [0.36,- 1.0216512475 319814,- 1.0216512475 319813664,0.336 E -16],
+--R [0.37,- 0.9942522733 438669,- 0.9942522733 4386692367,- 0.237 E -16],
+--R [0.38,- 0.9675840262 617056,- 0.9675840262 6170559861,0.14 E -17],
+--R [0.39,- 0.9416085398 584449,- 0.9416085398 5844494059,- 0.406 E -16],
+--R [0.4,- 0.9162907318 741551,- 0.9162907318 7415506518,0.348 E -16],
+--R [0.41,- 0.8915981192 837836,- 0.8915981192 8378356417,0.358 E -16],
+--R [0.42,- 0.8675005677 047231,- 0.8675005677 0472306212,0.379 E -16],
+--R [0.43,- 0.8439700702 945289,- 0.8439700702 9452894456,- 0.446 E -16],
+--R [0.44,- 0.8209805520 698302,- 0.8209805520 6983020514,- 0.514 E -17],
+--R [0.45,- 0.7985076962 177716,- 0.7985076962 1777161065,- 0.106 E -16],
+--R [0.46,- 0.7765287894 989964,- 0.7765287894 9899636781,0.322 E -16],
+--R [0.47,- 0.7550225842 780328,- 0.7550225842 7803278121,0.188 E -16],
+--R [0.48,- 0.7339691750 802004,- 0.7339691750 8020043897,- 0.39 E -16],
+--R [0.49,- 0.7133498878 774648,- 0.7133498878 7746475782,0.422 E -16],
+--R [0.5,- 0.6931471805 599453,- 0.6931471805 5994530942,- 0.942 E -17],
+--R [0.51,- 0.6733445532 637656,- 0.6733445532 6376559639,0.361 E -17],
+--R [0.52,- 0.6539264674 06664,- 0.6539264674 0666401315,- 0.131 E -16],
+--R [0.53,- 0.6348782724 359695,- 0.6348782724 3596953389,- 0.339 E -16],
+--R [0.54,- 0.6161861394 23817,- 0.6161861394 2381698443,0.156 E -16],
+--R [0.55,- 0.5978370007 556204,- 0.5978370007 5562044937,- 0.494 E -16],
+--R [0.56,- 0.5798184952 529421,- 0.5798184952 5294213468,- 0.347 E -16],
+--R [0.57,- 0.5621189181 535412,- 0.5621189181 5354121663,- 0.166 E -16],
+--R [0.58,- 0.5447271754 41672,- 0.5447271754 4167203144,- 0.314 E -16],
+--R [0.59,- 0.5276327420 823719,- 0.5276327420 8237191742,- 0.174 E -16],
+--R [0.6,- 0.5108256237 659907,- 0.5108256237 659906832,0.168 E -16],
+--R [0.61,- 0.4942963218 147801,- 0.4942963218 1478011929,- 0.193 E -16],
+--R [0.62,- 0.4780358009 429998,- 0.4780358009 4299981269,- 0.127 E -16],
+--R [0.63,- 0.4620354595 965587,- 0.4620354595 9655868014,0.199 E -16],
+--R [0.64,- 0.4462871026 284195,- 0.4462871026 2841951153,- 0.115 E -16],
+--R [0.65,- 0.4307829160 924543,- 0.4307829160 9245425738,0.4262 E -16],
+--R [0.66,- 0.4155154439 616658,- 0.4155154439 6166582316,- 0.232 E -16],
+--R [0.67,- 0.4004775665 971253,- 0.4004775665 9712530836,- 0.836 E -17],
+--R [0.68,- 0.3856624808 119847,- 0.3856624808 1198466895,0.3105 E -16],
+--R [0.69,- 0.3710636813 90832,- 0.3710636813 9083198583,0.142 E -16],
+--R [0.7,- 0.3566749439 387324,- 0.3566749439 3873237891,0.211 E -16],
+--R [0.71,- 0.3424903089 467759,- 0.3424903089 4677594671,- 0.4671 E -16],
+--R [0.72,- 0.3285040669 720361,- 0.3285040669 72036057,0.43 E -16],
+--R [0.73,- 0.3147107448 397002,- 0.3147107448 3970023894,- 0.3894 E -16],
+--R [0.74,- 0.3011050927 839216,- 0.3011050927 8392161425,- 0.143 E -16],
+--R [0.75,- 0.2876820724 517809,- 0.2876820724 5178092744,- 0.274 E -16],
+--R [0.76,- 0.2744368457 017603,- 0.2744368457 0176028919,0.108 E -16],
+--R [0.77,- 0.2613647641 344075,- 0.2613647641 3440751887,- 0.189 E -16],
+--R [0.78,- 0.2484613592 984996,- 0.2484613592 9849963117,- 0.3117 E -16],
+--R [0.79,- 0.2357223335 210699,- 0.2357223335 2106987386,0.2614 E -16],
+--R [0.8,- 0.2231435513 142098,- 0.2231435513 1420975577,0.4423 E -16],
+--R [0.81,- 0.2107210313 156526,- 0.2107210313 1565260246,- 0.246 E -17],
+--R [0.82,- 0.1984509387 238383,- 0.1984509387 2383825475,0.4525 E -16],
+--R [0.83,- 0.1863295781 914934,- 0.1863295781 9149344456,- 0.4456 E -16],
+--R [0.84,- 0.1743533871 447778,- 0.1743533871 447777527,0.473 E -16],
+--R [0.85,- 0.1625189294 977749,- 0.1625189294 9777491318,- 0.132 E -16],
+--R [0.86,- 0.1508228897 345836,- 0.1508228897 3458363515,- 0.3515 E -16],
+--R [0.87,- 0.1392620673 335076,- 0.1392620673 3350764946,- 0.4946 E -16],
+--R [0.88,- 0.1278333715 098849,- 0.1278333715 0988489572,0.428 E -17],
+--R [0.89,- 0.1165338162 559515,- 0.1165338162 5595152972,- 0.2972 E -16],
+--R [0.9,- 0.1053605156 578263,- 0.1053605156 5782630123,- 0.123 E -17],
+--R [0.91,- 0.0943106794 712413,- 0.0943106794 7124132687 7,- 0.2688 E -16],
+--R [0.92,- 0.0833816089 390511,- 0.0833816089 3905105839 3,0.4161 E -16],
+--R [0.93,- 0.0725706928 348354,- 0.0725706928 3483543071 2,- 0.3071 E -16],
+--R [0.94,- 0.0618754037 180875,- 0.0618754037 1808747179 7,0.28203 E -16],
+--R [0.95,- 0.0512932943 875505,- 0.0512932943 8755053342 7,- 0.33427 E
-16],
+--R [0.96,- 0.0408219945 202551,- 0.0408219945 2025512955 4,- 0.29554 E
-16],
+--R [0.97,- 0.0304592074 847085,- 0.0304592074 8470854592,- 0.4592 E -16],
+--R [0.98,- 0.0202027073 175194,- 0.0202027073 1751944840 8,- 0.48408 E
-16],
+--R [0.99,- 0.0100503358 535014,- 0.0100503358 5350144118 5,- 0.41185 E
-16],
+--R [1.0,0.0,0.0,0.0],
+--R [1.01,0.0099503308 531681,0.0099503308 5316808284 64,- 0.17154 E -16],
+--R [1.02,0.0198026272 961797,0.0198026272 9617971302 9,0.1303 E -16],
+--R [1.03,0.0295588022 415444,0.0295588022 4154440273 4,0.2734 E -17],
+--R [1.04,0.0392207131 532813,0.0392207131 5328129626 8,- 0.3732 E -17],
+--R [1.05,0.0487901641 69432,0.0487901641 6943200306 3,0.306 E -17],
+--R [1.06,0.0582689081 239758,0.0582689081 2397577552 8,- 0.2447 E -16],
+--R [1.07,0.0676586484 738148,0.0676586484 7381480526 9,0.527 E -17],
+--R [1.08,0.0769610411 361283,0.0769610411 3612832498 3,0.2498 E -16],
+--R [1.09,0.0861776962 410523,0.0861776962 4105233234 4,0.3234 E -16],
+--R [1.1,0.0953101798 043249,0.0953101798 0432486004 5,- 0.3995 E -16],
+--R [1.11,0.1043600153 242428,0.1043600153 2424276773,- 0.3227 E -16],
+--R [1.12,0.1133286853 070032,0.1133286853 0700317474,- 0.2526 E -16],
+--R [1.13,0.1222176327 242492,0.1222176327 2424920055,0.548 E -18],
+--R [1.14,0.1310282624 064041,0.1310282624 0640409279,- 0.721 E -17],
+--R [1.15,0.1397619423 751587,0.1397619423 7515869737,- 0.263 E -17],
+--R [1.16,0.1484200051 182733,0.1484200051 1827327798,- 0.2202 E -16],
+--R [1.17,0.1570037488 096648,0.1570037488 0966475081,- 0.4919 E -16],
+--R [1.18,0.1655144384 775734,0.1655144384 77573392,- 0.8 E -17],
+--R [1.19,0.1739533071 23438,0.1739533071 2343801732,0.1732 E -16],
+--R [1.2,0.1823215567 939546,0.1823215567 9395462621,0.2621 E -16],
+--R [1.21,0.1906203596 086497,0.1906203596 0864972009,0.2009 E -16],
+--R [1.22,0.1988508587 451652,0.1988508587 4516519013,- 0.987 E -17],
+--R [1.23,0.2070141693 843261,0.2070141693 8432612722,0.2722 E -16],
+--R [1.24,0.2151113796 169455,0.2151113796 1694549673,- 0.327 E -17],
+--R [1.25,0.2231435513 142098,0.2231435513 1420975577,- 0.4423 E -16],
+--R [1.26,0.2311117209 633866,0.2311117209 6338662928,0.2928 E -16],
+--R [1.27,0.2390169004 704999,0.2390169004 7049990501,0.501 E -17],
+--R [1.28,0.2468600779 315258,0.2468600779 3152579789,- 0.211 E -17],
+--R [1.29,0.2546422183 735807,0.2546422183 7358074683,0.4683 E -16],
+--R [1.3,0.2623642644 674911,0.2623642644 6749105203,- 0.4797 E -16],
+--R [1.31,0.2700271372 130602,0.2700271372 1306017612,- 0.239 E -16],
+--R [1.32,0.2776317365 982795,0.2776317365 9827948626,- 0.137 E -16],
+--R [1.33,0.2851789422 336624,0.2851789422 3366239708,- 0.292 E -17],
+--R [1.34,0.2926696139 6282,0.2926696139 6282000105,0.11 E -17],
+--R [1.35,0.3001045924 503381,0.3001045924 5033808075,- 0.192 E -16],
+--R [1.36,0.3074846997 479606,0.3074846997 4796064047,0.4046 E -16],
+--R [1.37,0.3148107398 400335,0.3148107398 4003354728,0.4728 E -16],
+--R [1.38,0.3220834991 691133,0.3220834991 6911332359,0.236 E -16],
+--R [1.39,0.3293037471 426004,0.3293037471 4260038915,- 0.108 E -16],
+--R [1.4,0.3364722366 212129,0.3364722366 212129305,0.305 E -16],
+--R [1.41,0.3435897043 900769,0.3435897043 9007691018,0.102 E -16],
+--R [1.42,0.3506568716 131694,0.3506568716 1316936271,- 0.3729 E -16],
+--R [1.43,0.3576744442 718159,0.3576744442 7181591208,0.121 E -16],
+--R [1.44,0.3646431135 879093,0.3646431135 8790925242,- 0.4758 E -16],
+--R [1.45,0.3715635564 32483,0.3715635564 3248303375,0.3375 E -16],
+--R [1.46,0.3784364357 202451,0.3784364357 2024507047,- 0.2953 E -16],
+--R [1.47,0.3852624007 906449,0.3852624007 9064493357,0.3357 E -16],
+--R [1.48,0.3920420877 760237,0.3920420877 7602369517,- 0.483 E -17],
+--R [1.49,0.3987761199 573678,0.3987761199 5736777296,- 0.27 E -16],
+--R [1.5,0.4054651081 081644,0.4054651081 0816438198,- 0.18 E -16],
+--R [1.51,0.4121096508 26833,0.4121096508 2683296076,- 0.3924 E -16],
+--R [1.52,0.4187103348 58185,0.4187103348 5818502023,0.202 E -16],
+--R [1.53,0.4252677354 043441,0.4252677354 0434409501,- 0.5 E -17],
+--R [1.54,0.4317824164 255378,0.4317824164 2553779055,- 0.945 E -17],
+--R [1.55,0.4382549309 311553,0.4382549309 3115525249,- 0.4751 E -16],
+--R [1.56,0.4446858212 614457,0.4446858212 6144567825,- 0.218 E -16],
+--R [1.57,0.4510756193 602167,0.4510756193 6021668939,- 0.106 E -16],
+--R [1.58,0.4574248470 388754,0.4574248470 3887543555,0.3555 E -16],
+--R [1.59,0.4637340162 321402,0.4637340162 3214015751,- 0.4249 E -16],
+--R [1.6,0.4700036292 457356,0.4700036292 4573555365,- 0.4635 E -16],
+--R [1.61,0.4762341789 963716,0.4762341789 9637162788,0.2788 E -16],
+--R [1.62,0.4824261492 442927,0.4824261492 4429270696,0.696 E -17],
+--R [1.63,0.4885800148 18671,0.4885800148 1867096603,- 0.3397 E -16],
+--R [1.64,0.4946962418 361071,0.4946962418 3610705467,- 0.4533 E -16],
+--R [1.65,0.5007752879 124892,0.5007752879 1248924202,0.42 E -16],
+--R [1.66,0.5068176023 684519,0.5068176023 6845186486,- 0.351 E -16],
+--R [1.67,0.5128236264 286637,0.5128236264 2866373922,0.392 E -16],
+--R [1.68,0.5187937934 151676,0.5187937934 1516755672,- 0.433 E -16],
+--R [1.69,0.5247285289 349821,0.5247285289 3498210407,0.407 E -17],
+--R [1.7,0.5306282510 621704,0.5306282510 6217039623,- 0.377 E -17],
+--R [1.71,0.5364933705 145685,0.5364933705 1456847476,- 0.252 E -16],
+--R [1.72,0.5423242908 253617,0.5423242908 2536167427,- 0.257 E -16],
+--R [1.73,0.5481214085 096876,0.5481214085 096875789,- 0.211 E -16],
+--R [1.74,0.5538851132 264377,0.5538851132 2643765996,- 0.4 E -16],
+--R [1.75,0.5596157879 354227,0.5596157879 3542268627,- 0.137 E -16],
+--R [1.76,0.5653138090 500604,0.5653138090 5006041369,0.137 E -16],
+--R [1.77,0.5709795465 857378,0.5709795465 8573777398,- 0.26 E -16],
+--R [1.78,0.5766133643 039938,0.5766133643 039937797,- 0.203 E -16],
+--R [1.79,0.5822156198 526636,0.5822156198 5266362814,0.281 E -16],
+--R [1.8,0.5877866649 02119,0.5877866649 0211900819,0.819 E -17],
+--R [1.81,0.5933268452 777344,0.5933268452 777343788,- 0.212 E -16],
+--R [1.82,0.5988365010 88704,0.5988365010 8870398254,- 0.175 E -16],
+--R [1.83,0.6043159668 533296,0.6043159668 5332957211,- 0.279 E -16],
+--R [1.84,0.6097655716 208943,0.6097655716 2089425102,- 0.49 E -16],
+--R [1.85,0.6151856390 902335,0.6151856390 9023345093,- 0.491 E -16],
+--R [1.86,0.6205764877 251099,0.6205764877 2510987871,- 0.213 E -16],
+--R [1.87,0.6259384308 664953,0.6259384308 6649525628,- 0.437 E -16],
+--R [1.88,0.6312717768 418578,0.6312717768 4185783762,0.376 E -16],
+--R [1.89,0.6365768290 71551,0.6365768290 7155101126,0.113 E -16],
+--R [1.9,0.6418538861 723948,0.6418538861 7239477599,- 0.24 E -16],
+--R [1.91,0.6471032420 585385,0.6471032420 5853850481,0.481 E -17],
+--R [1.92,0.6523251860 396902,0.6523251860 3969017986,- 0.201 E -16],
+--R [1.93,0.6575200029 167942,0.6575200029 1679418382,- 0.162 E -16],
+--R [1.94,0.6626879730 752368,0.6626879730 752367635,- 0.365 E -16],
+--R [1.95,0.6678293725 756554,0.6678293725 7565543401,0.34 E -16],
+--R [1.96,0.6729444732 424259,0.6729444732 4242586101,- 0.39 E -16],
+--R [1.97,0.6780335427 498971,0.6780335427 4989713874,0.387 E -16],
+--R [1.98,0.6830968447 064439,0.6830968447 0644386823,- 0.318 E -16],
+--R [1.99,0.6881346387 36401,0.6881346387 3640102737,0.274 E -16],
+--R [2.0,0.6931471805 599453,0.6931471805 5994530942,0.942 E -17]]
+--R Type: List List
Float
+--E 1
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp100-113
+\end{thebibliography}
+\end{document}
+
diff --git a/src/input/seccsc.input.pamphlet b/src/input/seccsc.input.pamphlet
new file mode 100644
index 0000000..05d789e
--- /dev/null
+++ b/src/input/seccsc.input.pamphlet
@@ -0,0 +1,695 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input seccsc.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This compares Axiom's sec and csc functions with the tables published in
+Abramowitz and Stegun.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+In the following table there are 4 columns. The first column
+is the argument of sec(x), ranging from 0.01 to 1.60. The
+second column is the reference value of sec from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp186-188
+<<*>>=
+)spool seccsc.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 2
+[[0.01,1.0000500,sec(0.01),sec(0.01)-1.0000500],_
+[0.02,1.0002000,sec(0.02),sec(0.02)-1.0002000],_
+[0.03,1.0004502,sec(0.03),sec(0.03)-1.0004502],_
+[0.04,1.0008005,sec(0.04),sec(0.04)-1.0008005],_
+[0.05,1.0012513,sec(0.05),sec(0.05)-1.0012513],_
+[0.06,1.0018027,sec(0.06),sec(0.06)-1.0018027],_
+[0.07,1.0024550,sec(0.07),sec(0.07)-1.0024550],_
+[0.08,1.0032086,sec(0.08),sec(0.08)-1.0032086],_
+[0.09,1.0040637,sec(0.09),sec(0.09)-1.0040637],_
+[0.10,1.0050209,sec(0.10),sec(0.10)-1.0050209],_
+[0.11,1.0060807,sec(0.11),sec(0.11)-1.0060807],_
+[0.12,1.0072435,sec(0.12),sec(0.12)-1.0072435],_
+[0.13,1.0085099,sec(0.13),sec(0.13)-1.0085099],_
+[0.14,1.0098807,sec(0.14),sec(0.14)-1.0098807],_
+[0.15,1.0113564,sec(0.15),sec(0.15)-1.0113564],_
+[0.16,1.0129380,sec(0.16),sec(0.16)-1.0129380],_
+[0.17,1.0146261,sec(0.17),sec(0.17)-1.0146261],_
+[0.18,1.0164216,sec(0.18),sec(0.18)-1.0164216],_
+[0.19,1.0183255,sec(0.19),sec(0.19)-1.0183255],_
+[0.20,1.0203388,sec(0.20),sec(0.20)-1.0203388],_
+[0.21,1.0224626,sec(0.21),sec(0.21)-1.0224626],_
+[0.22,1.0246978,sec(0.22),sec(0.22)-1.0246978],_
+[0.23,1.0270458,sec(0.23),sec(0.23)-1.0270458],_
+[0.24,1.0295078,sec(0.24),sec(0.24)-1.0295078],_
+[0.25,1.0320850,sec(0.25),sec(0.25)-1.0320850],_
+[0.26,1.0347789,sec(0.26),sec(0.26)-1.0347789],_
+[0.27,1.0375910,sec(0.27),sec(0.27)-1.0375910],_
+[0.28,1.0405227,sec(0.28),sec(0.28)-1.0405227],_
+[0.29,1.0435757,sec(0.29),sec(0.29)-1.0435757],_
+[0.30,1.0467516,sec(0.30),sec(0.30)-1.0467516],_
+[0.31,1.0500522,sec(0.31),sec(0.31)-1.0500522],_
+[0.32,1.0534794,sec(0.32),sec(0.32)-1.0534794],_
+[0.33,1.0570351,sec(0.33),sec(0.33)-1.0570351],_
+[0.34,1.0607213,sec(0.34),sec(0.34)-1.0607213],_
+[0.35,1.0645402,sec(0.35),sec(0.35)-1.0645402],_
+[0.36,1.0684938,sec(0.36),sec(0.36)-1.0684938],_
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+--R
+--R
+--R (1)
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+--R [1.03,1.9424308,1.9424308371 197244332,0.3711972443 32 E -7],
+--R [1.04,1.9754247,1.9754247004 385756762,0.4385756762 E -9],
+--R [1.05,2.0097632,2.0097632373 047619814,0.3730476198 15 E -7],
+--R [1.06,2.0455249,2.0455248665 340933506,- 0.3346590664 94 E -7],
+--R [1.07,2.0827943,2.0827942843 529550117,- 0.1564704498 83 E -7],
+--R [1.08,2.1216631,2.1216631037 112423848,0.3711242384 8 E -8],
+--R [1.09,2.1622306,2.1622305733 829374458,- 0.2661706255 42 E -7],
+--R [1.1,2.2046044,2.2046043887 17359034,- 0.1128264096 6 E -7],
+--R [1.11,2.2489016,2.2489016079 636949635,0.7963694963 5 E -8],
+--R [1.12,2.2952497,2.2952496905 621863932,- 0.9437813606 7 E -8],
+--R [1.13,2.3437877,2.3437876767 70567607,- 0.2322943239 29 E -7],
+--R [1.14,2.3946675,2.3946675315 911689408,0.3159116894 08 E -7],
+--R [1.15,2.4480557,2.4480556803 301802962,- 0.1966981970 38 E -7],
+--R [1.16,2.5041348,2.5041347684 432143166,- 0.3155678568 34 E -7],
+--R [1.17,2.5631057,2.5631056848 391647153,- 0.1516083528 47 E -7],
+--R [1.18,2.6251899,2.6251898958 332672918,- 0.4166732708 2 E -8],
+--R [1.19,2.6906321,2.6906321468 544274307,0.4685442743 07 E -7],
+--R [1.2,2.7597036,2.7597036013 324064569,0.1332406457 E -8],
+--R [1.21,2.8327055,2.8327055015 843215452,0.1584321545 E -8],
+--R [1.22,2.9099735,2.9099734558 632119939,- 0.4413678800 61 E -7],
+--R [1.23,2.9918825,2.9918824801 830430638,- 0.1981695693 62 E -7],
+--R [1.24,3.078853,3.0788529546 387066657,- 0.4536129333 43 E -7],
+--R [1.25,3.1713577,3.1713576937 701033609,- 0.6229896639 1 E -8],
+--R [1.26,3.2699304,3.2699303818 839873852,- 0.1811601261 48 E -7],
+--R [1.27,3.3751757,3.3751756909 804379951,- 0.9019562004 9 E -8],
+--R [1.28,3.4877815,3.4877814863 175858326,- 0.1368241416 7 E -7],
+--R [1.29,3.6085336,3.6085336400 439333502,0.4004393335 02 E -7],
+--R [1.3,3.7383341,3.7383341270 754411719,0.2707544117 19 E -7],
+--R [1.31,3.8782233,3.8782232842 002831965,- 0.1579971680 35 E -7],
+--R [1.32,4.0294074,4.0294073944 135738582,- 0.5586426141 8 E -8],
+--R [1.33,4.1932931,4.1932931445 375416679,0.4453754166 79 E -7],
+--R [1.34,4.371531,4.3715310407 788541477,0.4077885414 77 E -7],
+--R [1.35,4.5660706,4.5660706221 959586487,0.2219595864 9 E -7],
+--R [1.36,4.7792314,4.7792313898 566530439,- 0.1014334695 6 E -7],
+--R [1.37,5.0137949,5.0137949303 632701112,0.3036327011 12 E -7],
+--R [1.38,5.273126,5.2731260096 064537537,0.9606453753 8 E -8],
+--R [1.39,5.5613339,5.5613338533 248644648,- 0.4667513553 52 E -7],
+--R [1.4,5.8834901,5.8834900848 27344827,- 0.1517265517 3 E -7],
+--R [1.41,6.245928,6.2459279846 284984955,- 0.1537150150 4 E -7],
+--R [1.42,6.6566608,6.6566608218 158868243,0.2181588682 4 E -7],
+--R [1.43,7.1259785,7.1259784562 869696006,- 0.4371303039 94 E -7],
+--R [1.44,7.6673176,7.6673176194 346817373,0.1943468173 7 E -7],
+--R [1.45,8.2985645,8.2985644666 089360285,- 0.3339106397 1 E -7],
+--R [1.46,9.0440625,9.0440625062 951398291,0.6295139829 E -8],
+--R [1.47,9.9378158,9.9378157688 028373544,- 0.3119716264 6 E -7],
+--R [1.48,11.0288087,11.0288086918 92599526,- 0.8107400473 9 E -8],
+--R [1.49,12.3902766,12.3902765961 36436494,- 0.3863563506 E -8],
+--R [1.5,14.1368329,14.1368329029 69903082,0.2969903082 E -8],
+--R [1.51,16.4584992,16.4584992338 68991507,0.3386899150 7 E -7],
+--R [1.52,19.6949314,19.6949314465 35659932,0.4653565993 2 E -7],
+--R [1.53,24.5188114,24.5188114348 30172969,0.3483017296 9 E -7],
+--R [1.54,32.4765383,32.4765382933 55461787,- 0.6644538213 E -8],
+--R [1.55,48.088881,48.0888810173 88679831,0.1738867983 E -7],
+--R [1.56,92.6258945,92.6258945325 36624847,0.3253662485 E -7],
+--R [1.57,1255.7659897,1255.7659896641 100942,- 0.358899058 E -7],
+--R [1.58,- 108.6538055,- 108.6538054739 3097269,0.2606902731 E -7],
+--R [1.59,- 52.0765718,- 52.0765717826 07291365,0.1739270863 E -7],
+--R [1.6,- 34.2471356,- 34.2471356100 18689204,- 0.100186892 E -7]]
+--R Type: List List
Float
+--E 1
+@
+In the following table there are 4 columns. The first column
+is the argument of csc(x), ranging from 0.01 to 1.60. The
+second column is the reference value of csc from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp186-188
+<<*>>=
+
+--S 2 of 2
+[[0.01,100.0016667,csc(0.01),csc(0.01)-100.0016667],_
+[0.02,50.0033335,csc(0.02),csc(0.02)-50.0033335],_
+[0.03,33.3383339,csc(0.03),csc(0.03)-33.3383339],_
+[0.04,25.0066679,csc(0.04),csc(0.04)-25.0066679],_
+[0.05,20.0083358,csc(0.05),csc(0.05)-20.0083358],_
+[0.06,16.6766709,csc(0.06),csc(0.06)-16.6766709],_
+[0.07,14.2973876,csc(0.07),csc(0.07)-14.2973876],_
+[0.08,12.5133432,csc(0.08),csc(0.08)-12.5133432],_
+[0.09,11.1261253,csc(0.09),csc(0.09)-11.1261253],_
+[0.10,10.0166861,csc(0.10),csc(0.10)-10.0166861],_
+[0.11,9.1092683,csc(0.11),csc(0.11)-9.1092683],_
+[0.12,8.3533670,csc(0.12),csc(0.12)-8.3533670],_
+[0.13,7.7140172,csc(0.13),csc(0.13)-7.7140172],_
+[0.14,7.1662439,csc(0.14),csc(0.14)-7.1662439],_
+[0.15,6.6917324,csc(0.15),csc(0.15)-6.6917324],_
+[0.16,6.2767465,csc(0.16),csc(0.16)-6.2767465],_
+[0.17,5.9107821,csc(0.17),csc(0.17)-5.9107821],_
+[0.18,5.5856693,csc(0.18),csc(0.18)-5.5856693],_
+[0.19,5.2949584,csc(0.19),csc(0.19)-5.2949584],_
+[0.20,5.0334895,csc(0.20),csc(0.20)-5.0334895],_
+[0.21,4.7970857,csc(0.21),csc(0.21)-4.7970857],_
+[0.22,4.5823293,csc(0.22),csc(0.22)-4.5823293],_
+[0.23,4.3863973,csc(0.23),csc(0.23)-4.3863973],_
+[0.24,4.2069371,csc(0.24),csc(0.24)-4.2069371],_
+[0.25,4.0419725,csc(0.25),csc(0.25)-4.0419725],_
+[0.26,3.8898314,csc(0.26),csc(0.26)-3.8898314],_
+[0.27,3.7490894,csc(0.27),csc(0.27)-3.7490894],_
+[0.28,3.6185256,csc(0.28),csc(0.28)-3.6185256],_
+[0.29,3.4970877,csc(0.29),csc(0.29)-3.4970877],_
+[0.30,3.3838634,csc(0.30),csc(0.30)-3.3838634],_
+[0.31,3.2780583,csc(0.31),csc(0.31)-3.2780583],_
+[0.32,3.1789774,csc(0.32),csc(0.32)-3.1789774],_
+[0.33,3.0860099,csc(0.33),csc(0.33)-3.0860099],_
+[0.34,2.9986168,csc(0.34),csc(0.34)-2.9986168],_
+[0.35,2.9163208,csc(0.35),csc(0.35)-2.9163208],_
+[0.36,2.8386975,csc(0.36),csc(0.36)-2.8386975],_
+[0.37,2.7653687,csc(0.37),csc(0.37)-2.7653687],_
+[0.38,2.6959957,csc(0.38),csc(0.38)-2.6959957],_
+[0.39,2.6302748,csc(0.39),csc(0.39)-2.6302748],_
+[0.40,2.5679325,csc(0.40),csc(0.40)-2.5679325],_
+[0.41,2.5087220,csc(0.41),csc(0.41)-2.5087220],_
+[0.42,2.4524203,csc(0.42),csc(0.42)-2.4524203],_
+[0.43,2.3988248,csc(0.43),csc(0.43)-2.3988248],_
+[0.44,2.3477515,csc(0.44),csc(0.44)-2.3477515],_
+[0.45,2.2990327,csc(0.45),csc(0.45)-2.2990327],_
+[0.46,2.2525155,csc(0.46),csc(0.46)-2.2525155],_
+[0.47,2.2080598,csc(0.47),csc(0.47)-2.2080598],_
+[0.48,2.1655372,csc(0.48),csc(0.48)-2.1655372],_
+[0.49,2.1248300,csc(0.49),csc(0.49)-2.1248300],_
+[0.50,2.0858296,csc(0.50),csc(0.50)-2.0858296],_
+[0.51,2.0484363,csc(0.51),csc(0.51)-2.0484363],_
+[0.52,2.0125578,csc(0.52),csc(0.52)-2.0125578],_
+[0.53,1.9781089,csc(0.53),csc(0.53)-1.9781089],_
+[0.54,1.9450107,csc(0.54),csc(0.54)-1.9450107],_
+[0.55,1.9131900,csc(0.55),csc(0.55)-1.9131900],_
+[0.56,1.8825790,csc(0.56),csc(0.56)-1.8825790],_
+[0.57,1.8531145,csc(0.57),csc(0.57)-1.8531145],_
+[0.58,1.8247378,csc(0.58),csc(0.58)-1.8247378],_
+[0.59,1.7973941,csc(0.59),csc(0.59)-1.7973941],_
+[0.60,1.7710322,csc(0.60),csc(0.60)-1.7710322],_
+[0.61,1.7456045,csc(0.61),csc(0.61)-1.7456045],_
+[0.62,1.7210662,csc(0.62),csc(0.62)-1.7210662],_
+[0.63,1.6973757,csc(0.63),csc(0.63)-1.6973757],_
+[0.64,1.6744937,csc(0.64),csc(0.64)-1.6744937],_
+[0.65,1.6523834,csc(0.65),csc(0.65)-1.6523834],_
+[0.66,1.6310105,csc(0.66),csc(0.66)-1.6310105],_
+[0.67,1.6103423,csc(0.67),csc(0.67)-1.6103423],_
+[0.68,1.5903484,csc(0.68),csc(0.68)-1.5903484],_
+[0.69,1.5710001,csc(0.69),csc(0.69)-1.5710001],_
+[0.70,1.5522703,csc(0.70),csc(0.70)-1.5522703],_
+[0.71,1.5341335,csc(0.71),csc(0.71)-1.5341335],_
+[0.72,1.5165654,csc(0.72),csc(0.72)-1.5165654],_
+[0.73,1.4995435,csc(0.73),csc(0.73)-1.4995435],_
+[0.74,1.4830460,csc(0.74),csc(0.74)-1.4830460],_
+[0.75,1.4670527,csc(0.75),csc(0.75)-1.4670527],_
+[0.76,1.4515443,csc(0.76),csc(0.76)-1.4515443],_
+[0.77,1.4365025,csc(0.77),csc(0.77)-1.4365025],_
+[0.78,1.4219099,csc(0.78),csc(0.78)-1.4219099],_
+[0.79,1.4077503,csc(0.79),csc(0.79)-1.4077503],_
+[0.80,1.3940078,csc(0.80),csc(0.80)-1.3940078],_
+[0.81,1.3806678,csc(0.81),csc(0.81)-1.3806678],_
+[0.82,1.3677162,csc(0.82),csc(0.82)-1.3677162],_
+[0.83,1.3551396,csc(0.83),csc(0.83)-1.3551396],_
+[0.84,1.3429252,csc(0.84),csc(0.84)-1.3429252],_
+[0.85,1.3310609,csc(0.85),csc(0.85)-1.3310609],_
+[0.86,1.3195353,csc(0.86),csc(0.86)-1.3195353],_
+[0.87,1.3083372,csc(0.87),csc(0.87)-1.3083372],_
+[0.88,1.2974563,csc(0.88),csc(0.88)-1.2974563],_
+[0.89,1.2868825,csc(0.89),csc(0.89)-1.2868825],_
+[0.90,1.2766062,csc(0.90),csc(0.90)-1.2766062],_
+[0.91,1.2666184,csc(0.91),csc(0.91)-1.2666184],_
+[0.92,1.2569105,csc(0.92),csc(0.92)-1.2569105],_
+[0.93,1.2474740,csc(0.93),csc(0.93)-1.2474740],_
+[0.94,1.2383010,csc(0.94),csc(0.94)-1.2383010],_
+[0.95,1.2293840,csc(0.95),csc(0.95)-1.2293840],_
+[0.96,1.2207157,csc(0.96),csc(0.96)-1.2207157],_
+[0.97,1.2122891,csc(0.97),csc(0.97)-1.2122891],_
+[0.98,1.2040977,csc(0.98),csc(0.98)-1.2040977],_
+[0.99,1.1961351,csc(0.99),csc(0.99)-1.1961351],_
+[1.00,1.1883951,csc(1.00),csc(1.00)-1.1883951],_
+[1.01,1.1808720,csc(1.01),csc(1.01)-1.1808720],_
+[1.02,1.1735601,csc(1.02),csc(1.02)-1.1735601],_
+[1.03,1.1664542,csc(1.03),csc(1.03)-1.1664542],_
+[1.04,1.1595490,csc(1.04),csc(1.04)-1.1595490],_
+[1.05,1.1528398,csc(1.05),csc(1.05)-1.1528398],_
+[1.06,1.1463217,csc(1.06),csc(1.06)-1.1463217],_
+[1.07,1.1399902,csc(1.07),csc(1.07)-1.1399902],_
+[1.08,1.1338411,csc(1.08),csc(1.08)-1.1338411],_
+[1.09,1.1278701,csc(1.09),csc(1.09)-1.1278701],_
+[1.10,1.1220733,csc(1.10),csc(1.10)-1.1220733],_
+[1.11,1.1164469,csc(1.11),csc(1.11)-1.1164469],_
+[1.12,1.1109871,csc(1.12),csc(1.12)-1.1109871],_
+[1.13,1.1056905,csc(1.13),csc(1.13)-1.1056905],_
+[1.14,1.1005537,csc(1.14),csc(1.14)-1.1005537],_
+[1.15,1.0955735,csc(1.15),csc(1.15)-1.0955735],_
+[1.16,1.0907467,csc(1.16),csc(1.16)-1.0907467],_
+[1.17,1.0860704,csc(1.17),csc(1.17)-1.0860704],_
+[1.18,1.0815417,csc(1.18),csc(1.18)-1.0815417],_
+[1.19,1.0771579,csc(1.19),csc(1.19)-1.0771579],_
+[1.20,1.0729164,csc(1.20),csc(1.20)-1.0729164],_
+[1.21,1.0688146,csc(1.21),csc(1.21)-1.0688146],_
+[1.22,1.0648501,csc(1.22),csc(1.22)-1.0648501],_
+[1.23,1.0610206,csc(1.23),csc(1.23)-1.0610206],_
+[1.24,1.0573239,csc(1.24),csc(1.24)-1.0573239],_
+[1.25,1.0537579,csc(1.25),csc(1.25)-1.0537579],_
+[1.26,1.0503205,csc(1.26),csc(1.26)-1.0503205],_
+[1.27,1.0470098,csc(1.27),csc(1.27)-1.0470098],_
+[1.28,1.0438241,csc(1.28),csc(1.28)-1.0438241],_
+[1.29,1.0407614,csc(1.29),csc(1.29)-1.0407614],_
+[1.30,1.0378200,csc(1.30),csc(1.30)-1.0378200],_
+[1.31,1.0349985,csc(1.31),csc(1.31)-1.0349985],_
+[1.32,1.0322953,csc(1.32),csc(1.32)-1.0322953],_
+[1.33,1.0297088,csc(1.33),csc(1.33)-1.0297088],_
+[1.34,1.0272377,csc(1.34),csc(1.34)-1.0272377],_
+[1.35,1.0248807,csc(1.35),csc(1.35)-1.0248807],_
+[1.36,1.0226365,csc(1.36),csc(1.36)-1.0226365],_
+[1.37,1.0205039,csc(1.37),csc(1.37)-1.0205039],_
+[1.38,1.0184818,csc(1.38),csc(1.38)-1.0184818],_
+[1.39,1.0165693,csc(1.39),csc(1.39)-1.0165693],_
+[1.40,1.0147651,csc(1.40),csc(1.40)-1.0147651],_
+[1.41,1.0130685,csc(1.41),csc(1.41)-1.0130685],_
+[1.42,1.0114785,csc(1.42),csc(1.42)-1.0114785],_
+[1.43,1.0099943,csc(1.43),csc(1.43)-1.0099943],_
+[1.44,1.0086152,csc(1.44),csc(1.44)-1.0086152],_
+[1.45,1.0073405,csc(1.45),csc(1.45)-1.0073405],_
+[1.46,1.0061695,csc(1.46),csc(1.46)-1.0061695],_
+[1.47,1.0051015,csc(1.47),csc(1.47)-1.0051015],_
+[1.48,1.0041362,csc(1.48),csc(1.48)-1.0041362],_
+[1.49,1.0032729,csc(1.49),csc(1.49)-1.0032729],_
+[1.50,1.0025113,csc(1.50),csc(1.50)-1.0025113],_
+[1.51,1.0018509,csc(1.51),csc(1.51)-1.0018509],_
+[1.52,1.0012915,csc(1.52),csc(1.52)-1.0012915],_
+[1.53,1.0008327,csc(1.53),csc(1.53)-1.0008327],_
+[1.54,1.0004744,csc(1.54),csc(1.54)-1.0004744],_
+[1.55,1.0002163,csc(1.55),csc(1.55)-1.0002163],_
+[1.56,1.0000583,csc(1.56),csc(1.56)-1.0000583],_
+[1.57,1.0000003,csc(1.57),csc(1.57)-1.0000003],_
+[1.58,1.0000424,csc(1.58),csc(1.58)-1.0000424],_
+[1.59,1.0001844,csc(1.59),csc(1.59)-1.0001844],_
+[1.60,1.0004266,csc(1.60),csc(1.60)-1.0004266]]
+--R
+--R
+--R (2)
+--R [[0.01,100.0016667,100.0016666861 1131614,- 0.1388868386 E -7],
+--R [0.02,50.0033335,50.0033334888 95450004,- 0.1110455 E -7],
+--R [0.03,33.3383339,33.3383338583 83159355,- 0.4161684064 5 E -7],
+--R [0.04,25.0066679,25.0066679113 21092611,0.1132109261 E -7],
+--R [0.05,20.0083358,20.0083357645 29760655,- 0.3547023934 5 E -7],
+--R [0.06,16.6766709,16.6766708682 61540425,- 0.3173845957 5 E -7],
+--R [0.07,14.2973876,14.2973876252 73006648,0.2527300664 8 E -7],
+--R [0.08,12.5133432,12.5133432956 11602375,0.9561160237 45 E -7],
+--R [0.09,11.1261253,11.1261252982 27770129,- 0.1772229871 E -8],
+--R [0.1,10.0166861,10.0166861316 34776649,0.3163477664 9 E -7],
+--R [0.11,9.1092683,9.1092683378 58666259,0.3785866625 9 E -7],
+--R [0.12,8.353367,8.3533669844 258284979,- 0.1557417150 2 E -7],
+--R [0.13,7.7140172,7.7140171546 756812171,- 0.4532431878 29 E -7],
+--R [0.14,7.1662439,7.1662439422 359760119,0.4223597601 19 E -7],
+--R [0.15,6.6917324,6.6917324477 182351442,0.4771823514 42 E -7],
+--R [0.16,6.2767465,6.2767465266 620801848,0.2666208018 5 E -7],
+--R [0.17,5.9107821,5.9107820970 378013996,- 0.29621986 E -8],
+--R [0.18,5.5856693,5.5856693442 568113649,0.4425681136 49 E -7],
+--R [0.19,5.2949584,5.2949584403 976760687,0.4039767606 87 E -7],
+--R [0.2,5.0334895,5.0334895476 723442024,0.4767234420 24 E -7],
+--R [0.21,4.7970857,4.7970856780 525825143,- 0.2194741748 6 E -7],
+--R [0.22,4.5823293,4.5823293184 602630424,0.1846026304 2 E -7],
+--R [0.23,4.3863973,4.3863973276 543190295,0.2765431903 E -7],
+--R [0.24,4.2069371,4.2069371089 029182611,0.8902918261 1 E -8],
+--R [0.25,4.0419725,4.0419725012 210710728,0.1221071073 E -8],
+--R [0.26,3.8898314,3.8898313880 215197583,- 0.1197848024 2 E -7],
+--R [0.27,3.7490894,3.7490893927 385091643,- 0.7261490835 7 E -8],
+--R [0.28,3.6185256,3.6185256396 812993389,0.3968129933 89 E -7],
+--R [0.29,3.4970877,3.4970876678 206681256,- 0.3217933187 44 E -7],
+--R [0.3,3.3838634,3.3838633618 241225849,- 0.3817587741 51 E -7],
+--R [0.31,3.2780583,3.2780583157 998724616,0.1579987246 16 E -7],
+--R [0.32,3.1789774,3.1789774413 44609289,0.4134460928 89 E -7],
+--R [0.33,3.0860099,3.0860099195 883096277,0.1958830962 77 E -7],
+--R [0.34,2.9986168,2.9986168087 661743229,0.8766174322 8 E -8],
+--R [0.35,2.9163208,2.9163207762 123651255,- 0.2378763487 45 E -7],
+--R [0.36,2.8386975,2.8386975416 936122006,0.4169361220 06 E -7],
+--R [0.37,2.7653687,2.7653687083 157807533,0.8315780753 3 E -8],
+--R [0.38,2.6959957,2.6959957253 979436817,0.2539794368 17 E -7],
+--R [0.39,2.6302748,2.6302747801 40398548,- 0.1985960145 2 E -7],
+--R [0.4,2.5679325,2.5679324555 477830703,- 0.4445221692 97 E -7],
+--R [0.41,2.508722,2.5087220237 8334365,0.2378334365 E -7],
+--R [0.42,2.4524203,2.4524202690 492617941,- 0.3095073820 59 E -7],
+--R [0.43,2.3988248,2.3988247537 912204017,- 0.4620877959 83 E -7],
+--R [0.44,2.3477515,2.3477514576 984533152,- 0.4230154668 48 E -7],
+--R [0.45,2.2990327,2.2990327315 089707901,0.3150897079 01 E -7],
+--R [0.46,2.2525155,2.2525155177 149280284,0.1771492802 84 E -7],
+--R [0.47,2.2080598,2.2080597984 171557468,- 0.1582844253 E -8],
+--R [0.48,2.1655372,2.1655372372 03038964,0.3720303896 4 E -7],
+--R [0.49,2.12483,2.1248299873 30230062,- 0.1266976993 8 E -7],
+--R [0.5,2.0858296,2.0858296429 334881858,0.4293348818 58 E -7],
+--R [0.51,2.0484363,2.0484363136 241303362,0.1362413033 6 E -7],
+--R [0.52,2.0125578,2.0125578058 716625444,0.5871662544 4 E -8],
+--R [0.53,1.9781089,1.9781088970 643983743,- 0.2935601625 7 E -8],
+--R [0.54,1.9450107,1.9450106902 35237839,- 0.9764762161 01 E -8],
+--R [0.55,1.91319,1.9131900391 862495448,0.3918624954 48 E -7],
+--R [0.56,1.882579,1.8825790352 123253874,0.3521232538 73 E -7],
+--R [0.57,1.8531145,1.8531145478 592311512,0.4785923115 12 E -7],
+--R [0.58,1.8247378,1.8247378131 947842124,0.1319478421 24 E -7],
+--R [0.59,1.7973941,1.7973940639 561336125,- 0.3604386638 75 E -7],
+--R [0.6,1.7710322,1.7710321966 877253734,- 0.3312274626 6 E -8],
+--R [0.61,1.7456045,1.7456044716 252507363,- 0.2837474926 37 E -7],
+--R [0.62,1.7210662,1.7210662416 285829803,0.4162858298 03 E -7],
+--R [0.63,1.6973757,1.6973757069 361725968,0.6936172596 8 E -8],
+--R [0.64,1.6744937,1.6744936929 168164811,- 0.7083183518 9 E -8],
+--R [0.65,1.6523834,1.6523834483 423011016,0.4834230110 16 E -7],
+--R [0.66,1.6310105,1.6310104620 046062096,- 0.3799539379 04 E -7],
+--R [0.67,1.6103423,1.6103422957 612188444,- 0.4238781155 6 E -8],
+--R [0.68,1.5903484,1.5903484323 175770922,0.3231757709 22 E -7],
+--R [0.69,1.5710001,1.5710001362 517238398,0.3625172383 98 E -7],
+--R [0.7,1.5522703,1.5522703269 57103912,0.2695710391 2 E -7],
+--R [0.71,1.5341335,1.5341334623 286338699,- 0.3767136613 01 E -7],
+--R [0.72,1.5165654,1.5165654321 477203357,0.3214772033 57 E -7],
+--R [0.73,1.4995435,1.4995434602 363547077,- 0.3976364529 23 E -7],
+--R [0.74,1.483046,1.4830460145 509444868,0.1455094448 68 E -7],
+--R [0.75,1.4670527,1.4670527244 75010117,0.2447501011 7 E -7],
+--R [0.76,1.4515443,1.4515443046 478685727,0.4647868572 7 E -8],
+--R [0.77,1.4365025,1.4365024847 353014963,- 0.1526469850 37 E -7],
+--R [0.78,1.4219099,1.4219099446 09135172,0.4460913517 2 E -7],
+--R [0.79,1.4077503,1.4077502544 566480148,- 0.4554335198 52 E -7],
+--R [0.8,1.3940078,1.3940078193 886361745,0.1938863617 45 E -7],
+--R [0.81,1.3806678,1.3806678281 575591498,0.2815755914 98 E -7],
+--R [0.82,1.3677162,1.3677162056 35104192,0.5635104192 E -8],
+--R [0.83,1.3551396,1.3551395687 323139549,- 0.3126768604 51 E -7],
+--R [0.84,1.3429252,1.3429251854 756057525,- 0.1452439424 75 E -7],
+--R [0.85,1.3310609,1.3310609369 789990246,0.3697899902 46 E -7],
+--R [0.86,1.3195353,1.3195352820 770317831,- 0.1792296821 69 E -7],
+--R [0.87,1.3083372,1.3083372244 045115315,0.2440451153 15 E -7],
+--R [0.88,1.2974563,1.2974562817 286954688,- 0.1827130453 12 E -7],
+--R [0.89,1.2868825,1.2868824573 569776297,- 0.4264302237 03 E -7],
+--R [0.9,1.2766062,1.2766062134 58895496,0.1345889549 6 E -7],
+--R [0.91,1.2666184,1.2666184461 554476329,0.4615544763 29 E -7],
+--R [0.92,1.2569105,1.2569104622 415061901,- 0.3775849380 99 E -7],
+--R [0.93,1.247474,1.2474739574 186627875,- 0.4258133721 25 E -7],
+--R [0.94,1.238301,1.2383009959 262950556,- 0.4073704944 4 E -8],
+--R [0.95,1.229384,1.2293839914 681003518,- 0.8531899648 15 E -8],
+--R [0.96,1.2207157,1.2207156893 399160175,- 0.1066008398 25 E -7],
+--R [0.97,1.2122891,1.2122891496 724233695,0.4967242336 95 E -7],
+--R [0.98,1.2040977,1.2040977317 093965936,0.3170939659 36 E -7],
+--R [0.99,1.1961351,1.1961350790 485799284,- 0.2095142007 16 E -7],
+--R [1.0,1.1883951,1.1883951057 781212163,0.5778121216 3 E -8],
+--R [1.01,1.180872,1.1808719834 468142375,- 0.1655318576 25 E -7],
+--R [1.02,1.1735601,1.1735601288 11257282,0.2881125728 2 E -7],
+--R [1.03,1.1664542,1.1664541923 074667313,- 0.7692533268 72 E -8],
+--R [1.04,1.159549,1.1595490471 9853279,0.4719853279 E -7],
+--R [1.05,1.1528398,1.1528397793 536064181,- 0.2064639358 19 E -7],
+--R [1.06,1.1463217,1.1463216776 16894679,- 0.2238310532 1 E -7],
+--R [1.07,1.1399902,1.1399902247 284454927,0.2472844549 27 E -7],
+--R [1.08,1.1338411,1.1338410887 613485139,- 0.1123865148 61 E -7],
+--R [1.09,1.1278701,1.1278701150 42590264,0.1504259026 4 E -7],
+--R [1.1,1.1220733,1.1220733185 272000494,0.1852720004 94 E -7],
+--R [1.11,1.1164469,1.1164468765 975278264,- 0.2340247217 36 E -7],
+--R [1.12,1.1109871,1.1109871222 615233658,0.2226152336 58 E -7],
+--R [1.13,1.1056905,1.1056905377 257534608,0.3772575346 08 E -7],
+--R [1.14,1.1005537,1.1005537483 206146725,0.4832061467 25 E -7],
+--R [1.15,1.0955735,1.0955735167 567859913,0.1675678599 13 E -7],
+--R [1.16,1.0907467,1.0907467376 934304007,0.3769343040 07 E -7],
+--R [1.17,1.0860704,1.0860704326 000071521,0.3260000715 21 E -7],
+--R [1.18,1.0815417,1.0815417448 948071115,0.4489480711 15 E -7],
+--R [1.19,1.0771579,1.0771579353 444804665,0.3534448046 65 E -7],
+--R [1.2,1.0729164,1.0729163777 098972287,- 0.2229010277 13 E -7],
+--R [1.21,1.0688146,1.0688145546 246734829,- 0.4537532651 71 E -7],
+--R [1.22,1.0648501,1.0648500536 936167054,- 0.4630638329 46 E -7],
+--R [1.23,1.0610206,1.0610205637 991976338,- 0.3620080236 62 E -7],
+--R [1.24,1.0573239,1.0573238716 04949513,- 0.2839505048 7 E -7],
+--R [1.25,1.0537579,1.0537578582 454329877,- 0.4175456701 23 E -7],
+--R [1.26,1.0503205,1.0503204961 930909767,- 0.3806909023 3 E -8],
+--R [1.27,1.0470098,1.0470098462 929566457,0.4629295664 57 E -7],
+--R [1.28,1.0438241,1.0438240549 567728718,- 0.4504322712 82 E -7],
+--R [1.29,1.0407614,1.0407613515 086368049,- 0.4849136319 51 E -7],
+--R [1.3,1.03782,1.0378200456 748014427,0.4567480144 27 E -7],
+--R [1.31,1.0349985,1.0349985252 107504451,0.2521075044 51 E -7],
+--R [1.32,1.0322953,1.0322952536 591153897,- 0.4634088461 03 E -7],
+--R [1.33,1.0297088,1.0297087682 324287489,- 0.3176757125 11 E -7],
+--R [1.34,1.0272377,1.0272376778 151033218,- 0.2218489667 82 E -7],
+--R [1.35,1.0248807,1.0248806610 794017372,- 0.3892059826 28 E -7],
+--R [1.36,1.0226365,1.0226364647 10509886,- 0.3528949011 4 E -7],
+--R [1.37,1.0205039,1.0205039017 361575009,0.1736157500 9 E -8],
+--R [1.38,1.0184818,1.0184818499 565392157,0.4995653921 57 E -7],
+--R [1.39,1.0165693,1.0165692504 705818114,- 0.4952941818 86 E -7],
+--R [1.4,1.0147651,1.0147651062 948794009,0.6294879400 9 E -8],
+--R [1.41,1.0130685,1.0130684810 718793105,- 0.1892812068 95 E -7],
+--R [1.42,1.0114785,1.0114784978 641485933,- 0.2135851406 7 E -8],
+--R [1.43,1.0099943,1.0099943380 317855887,0.3803178558 87 E -7],
+--R [1.44,1.0086152,1.0086152401 902637594,0.4019026375 94 E -7],
+--R [1.45,1.0073405,1.0073404992 46207189,- 0.753792811 E -9],
+--R [1.46,1.0061695,1.0061694655 087995079,- 0.3449120049 21 E -7],
+--R [1.47,1.0051015,1.0051015438 747215132,0.4387472151 32 E -7],
+--R [1.48,1.0041362,1.0041361930 846981533,- 0.6915301846 7 E -8],
+--R [1.49,1.0032729,1.0032729250 49913637,0.2504991363 7 E -7],
+--R [1.5,1.0025113,1.0025113042 4672491,0.424672491 E -8],
+--R [1.51,1.0018509,1.0018509471 78269319,0.4717826931 9 E -7],
+--R [1.52,1.0012915,1.0012915219 017225962,0.2190172259 62 E -7],
+--R [1.53,1.0008327,1.0008327476 201189712,0.4762011897 12 E -7],
+--R [1.54,1.0004744,1.0004743943 377968613,- 0.5662203138 7 E -8],
+--R [1.55,1.0002163,1.0002162825 786817653,- 0.1742131823 47 E -7],
+--R [1.56,1.0000583,1.0000582831 667632601,- 0.1683323673 99 E -7],
+--R [1.57,1.0000003,1.0000003170 68265912,0.1706826591 2 E -7],
+--R [1.58,1.0000424,1.0000423552 951549942,- 0.4470484500 58 E -7],
+--R [1.59,1.0001844,1.0001844188 697576625,0.1886975766 25 E -7],
+--R [1.6,1.0004266,1.0004265788 504192126,- 0.2114958078 74 E -7]]
+--R Type: List List
Float
+--E 2
+
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp186-188
+\end{thebibliography}
+\end{document}
diff --git a/src/input/sincos.input.pamphlet b/src/input/sincos.input.pamphlet
new file mode 100644
index 0000000..915ee4b
--- /dev/null
+++ b/src/input/sincos.input.pamphlet
@@ -0,0 +1,696 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input sincos.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This compares Axiom's sincos function with the tables published in
+Abramowitz and Stegun.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+In the following table there are 4 columns. The first column
+is the argument of sin(x), ranging from 0.00 to 1.60. The
+second column is the reference value of sin from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp142-173
+
+<<*>>=
+)spool sincos.output
+)set message test on
+)set message auto off
+)clear all
+--S 1 of 2
+[[0.01,0.00999983333416666468254,sin(0.01),sin(0.01)-(0.00999983333416666468254)],_
+[0.02,0.01999866669333307936649,sin(0.02),sin(0.02)-(0.01999866669333307936649)],_
+[0.03,0.02999550020249566076853,sin(0.03),sin(0.03)-(0.02999550020249566076853)],_
+[0.04,0.03998933418663415945255,sin(0.04),sin(0.04)-(0.03998933418663415945255)],_
+[0.05,0.04997916927067832879487,sin(0.05),sin(0.05)-(0.04997916927067832879487)],_
+[0.06,0.05996400647944459919909,sin(0.06),sin(0.06)-(0.05996400647944459919909)],_
+[0.07,0.06994284733753276397655,sin(0.07),sin(0.07)-(0.06994284733753276397655)],_
+[0.08,0.07991469396917268730688,sin(0.08),sin(0.08)-(0.07991469396917268730688)],_
+[0.09,0.08987854919801104969125,sin(0.09),sin(0.09)-(0.08987854919801104969125)],_
+[0.10,0.09983341664682815230681,sin(0.10),sin(0.10)-(0.09983341664682815230681)],_
+[0.11,0.10977830083717480866495,sin(0.11),sin(0.11)-(0.10977830083717480866495)],_
+[0.12,0.11971220728891935996735,sin(0.12),sin(0.12)-(0.11971220728891935996735)],_
+[0.13,0.12963414261969485954121,sin(0.13),sin(0.13)-(0.12963414261969485954121)],_
+[0.14,0.13954311464423648171799,sin(0.14),sin(0.14)-(0.13954311464423648171799)],_
+[0.15,0.14943813247359922149773,sin(0.15),sin(0.15)-(0.14943813247359922149773)],_
+[0.16,0.15931820661424596331146,sin(0.16),sin(0.16)-(0.15931820661424596331146)],_
+[0.17,0.16918234906699601015762,sin(0.17),sin(0.17)-(0.16918234906699601015762)],_
+[0.18,0.17902957342582417834180,sin(0.18),sin(0.18)-(0.17902957342582417834180)],_
+[0.19,0.18885889497650057799285,sin(0.19),sin(0.19)-(0.18885889497650057799285)],_
+[0.20,0.19866933079506121545941,sin(0.20),sin(0.20)-(0.19866933079506121545941)],_
+[0.21,0.20845989984609957060871,sin(0.21),sin(0.21)-(0.20845989984609957060871)],_
+[0.22,0.21822962308086931995179,sin(0.22),sin(0.22)-(0.21822962308086931995179)],_
+[0.23,0.22797752353518839540462,sin(0.23),sin(0.23)-(0.22797752353518839540462)],_
+[0.24,0.23770262642713458836079,sin(0.24),sin(0.24)-(0.23770262642713458836079)],_
+[0.25,0.24740395925452292959685,sin(0.25),sin(0.25)-(0.24740395925452292959685)],_
+[0.26,0.25708055189215509735339,sin(0.26),sin(0.26)-(0.25708055189215509735339)],_
+[0.27,0.26673143668883112873229,sin(0.27),sin(0.27)-(0.26673143668883112873229)],_
+[0.28,0.27635564856411373331967,sin(0.28),sin(0.28)-(0.27635564856411373331967)],_
+[0.29,0.28595222510483553268394,sin(0.29),sin(0.29)-(0.28595222510483553268394)],_
+[0.30,0.29552020666133957510532,sin(0.30),sin(0.30)-(0.29552020666133957510532)],_
+[0.31,0.30505863644344350156564,sin(0.31),sin(0.31)-(0.30505863644344350156564)],_
+[0.32,0.31456656061611776666176,sin(0.32),sin(0.32)-(0.31456656061611776666176)],_
+[0.33,0.32404302839486834670020,sin(0.33),sin(0.33)-(0.32404302839486834670020)],_
+[0.34,0.33348709214081439678177,sin(0.34),sin(0.34)-(0.33348709214081439678177)],_
+[0.35,0.34289780745545134918963,sin(0.35),sin(0.35)-(0.34289780745545134918963)],_
+[0.36,0.35227423327508997684991,sin(0.36),sin(0.36)-(0.35227423327508997684991)],_
+[0.37,0.36161543196496197803729,sin(0.37),sin(0.37)-(0.36161543196496197803729)],_
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+--R
+--R
+--R (1)
+--R [[0.01,0.0099998333 3416666468 26,0.0099998333 3416666468 26,0.0],
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+--R [0.59,0.5563610229 1278377572,0.5563610229 1278377572,0.0],
+--R [0.6,0.5646424733 950353572,0.5646424733 950353572,0.0],
+--R [0.61,0.5728674601 0048126119,0.5728674601 0048126119,0.0],
+--R [0.62,0.5810351605 3730507584,0.5810351605 3730507584,0.0],
+--R [0.63,0.5891447579 4226951312,0.5891447579 4226951312,0.0],
+--R [0.64,0.5971954413 6239205188,0.5971954413 6239205188,0.0],
+--R [0.65,0.6051864057 3603956037,0.6051864057 3603956037,0.0],
+--R [0.66,0.6131168519 7343378861,0.6131168519 7343378861,0.0],
+--R [0.67,0.6209859870 3655968036,0.6209859870 3655968036,0.0],
+--R [0.68,0.6287930240 1846851371,0.6287930240 184685137,- 0.3 E -20],
+--R [0.69,0.6365371822 2196794024,0.6365371822 2196794024,0.0],
+--R [0.7,0.6442176872 3769105367,0.6442176872 3769105367,0.0],
+--R [0.71,0.6518337710 2153668121,0.6518337710 2153668121,0.0],
+--R [0.72,0.6593846719 7147315362,0.6593846719 7147315362,0.0],
+--R [0.73,0.6668696350 0369787373,0.6668696350 0369787373,0.0],
+--R [0.74,0.6742879116 2814506748,0.6742879116 2814506748,0.0],
+--R [0.75,0.6816387600 2333416673,0.6816387600 2333416673,0.0],
+--R [0.76,0.6889214451 1055133915,0.6889214451 1055133915,0.0],
+--R [0.77,0.6961352386 2735674702,0.6961352386 2735674702,0.0],
+--R [0.78,0.7032794192 0041018437,0.7032794192 0041018437,0.0],
+--R [0.79,0.7103532724 1760780981,0.7103532724 1760780981,0.0],
+--R [0.8,0.7173560908 9952276163,0.7173560908 9952276163,0.0],
+--R [0.81,0.7242871743 7014251093,0.7242871743 7014251093,0.0],
+--R [0.82,0.7311458297 2689587938,0.7311458297 2689587938,0.0],
+--R [0.83,0.7379313711 0996271873,0.7379313711 0996271873,0.0],
+--R [0.84,0.7446431199 7085932126,0.7446431199 7085932126,0.0],
+--R [0.85,0.7512804051 4029270271,0.7512804051 4029270271,0.3 E -20],
+--R [0.86,0.7578425628 952769723,0.7578425628 952769723,0.0],
+--R [0.87,0.7643289370 2550507814,0.7643289370 2550507815,0.3 E -20],
+--R [0.88,0.7707388788 9896929121,0.7707388788 9896929121,- 0.3 E -20],
+--R [0.89,0.7770717475 2682386549,0.7770717475 2682386549,0.0],
+--R [0.9,0.7833269096 2748338846,0.7833269096 2748338846,0.0],
+--R [0.91,0.7895037396 8995041188,0.7895037396 8995041188,0.0],
+--R [0.92,0.7956016200 3636603027,0.7956016200 3636603027,0.0],
+--R [0.93,0.8016199408 8377715209,0.8016199408 8377715209,0.0],
+--R [0.94,0.8075581004 0511428687,0.8075581004 0511428687,0.0],
+--R [0.95,0.8134155047 8937375069,0.8134155047 8937375069,0.0],
+--R [0.96,0.8191915683 0099827163,0.8191915683 0099827164,0.3 E -20],
+--R [0.97,0.8248857133 3845005748,0.8248857133 3845005748,0.0],
+--R [0.98,0.8304973704 9197046809,0.8304973704 9197046809,0.0],
+--R [0.99,0.8360259786 0052051679,0.8360259786 0052051679,0.0],
+--R [1.0,0.8414709848 0789650665,0.8414709848 0789650665,0.0],
+--R [1.01,0.8468318446 1801519012,0.8468318446 1801519012,0.0],
+--R [1.02,0.8521080219 4936292362,0.8521080219 4936292362,0.3 E -20],
+--R [1.03,0.8572989891 8860337214,0.8572989891 8860337215,0.3 E -20],
+--R [1.04,0.8624042272 4333840328,0.8624042272 4333840328,0.0],
+--R [1.05,0.8674232255 9401689438,0.8674232255 9401689438,- 0.3 E -20],
+--R [1.06,0.8723554823 4498626228,0.8723554823 4498626228,0.0],
+--R [1.07,0.8772005042 7468161031,0.8772005042 7468161031,0.0],
+--R [1.08,0.8819578068 8494747374,0.8819578068 8494747373,- 0.3 E -20],
+--R [1.09,0.8866269144 4948723161,0.8866269144 4948723161,0.0],
+--R [1.1,0.8912073600 6143533995,0.8912073600 6143533995,0.3 E -20],
+--R [1.11,0.8956986856 8004762924,0.8956986856 8004762924,0.0],
+--R [1.12,0.9001004421 7650499712,0.9001004421 7650499712,0.0],
+--R [1.13,0.9044121893 7882591604,0.9044121893 7882591604,0.0],
+--R [1.14,0.9086334961 1588326459,0.9086334961 1588326459,0.0],
+--R [1.15,0.9127639402 6052108094,0.9127639402 6052108094,0.0],
+--R [1.16,0.9168031087 7176692662,0.9168031087 7176692662,- 0.3 E -20],
+--R [1.17,0.9207505977 3613563957,0.9207505977 3613563958,0.3 E -20],
+--R [1.18,0.9246060124 0802034611,0.9246060124 0802034611,0.0],
+--R [1.19,0.9283689672 491666926,0.9283689672 491666926,0.0],
+--R [1.2,0.9320390859 6722634967,0.9320390859 6722634967,0.3 E -20],
+--R [1.21,0.9356160015 5338593342,0.9356160015 5338593342,0.0],
+--R [1.22,0.9390993563 1906758094,0.9390993563 1906758094,0.0],
+--R [1.23,0.9424888019 3169751002,0.9424888019 3169751002,0.0],
+--R [1.24,0.9457839994 4953898629,0.9457839994 4953898629,0.0],
+--R [1.25,0.9489846193 5558621435,0.9489846193 5558621435,0.0],
+--R [1.26,0.9520903415 9051576386,0.9520903415 9051576386,0.0],
+--R [1.27,0.9551008555 8469223509,0.9551008555 8469223509,0.0],
+--R [1.28,0.9580158602 892249637,0.9580158602 892249637,0.0],
+--R [1.29,0.9608350642 0607265891,0.9608350642 0607265891,0.0],
+--R [1.3,0.9635581854 171929647,0.9635581854 171929647,- 0.3 E -20],
+--R [1.31,0.9661849516 1273402917,0.9661849516 1273402917,0.0],
+--R [1.32,0.9687151001 1826526273,0.9687151001 1826526273,0.0],
+--R [1.33,0.9711483779 2104456234,0.9711483779 2104456234,0.0],
+--R [1.34,0.9734845416 9531937479,0.9734845416 9531937479,0.0],
+--R [1.35,0.9757233578 2665906926,0.9757233578 2665906926,0.0],
+--R [1.36,0.9778646024 3531618568,0.9778646024 3531618568,0.0],
+--R [1.37,0.9799080613 9861422289,0.9799080613 9861422289,0.0],
+--R [1.38,0.9818535303 7235972788,0.9818535303 7235972788,0.0],
+--R [1.39,0.9837008148 1127654484,0.9837008148 1127654484,0.0],
+--R [1.4,0.9854497299 8846018066,0.9854497299 8846018066,0.0],
+--R [1.41,0.9871001010 1385034143,0.9871001010 1385034143,0.0],
+--R [1.42,0.9886517628 5171979274,0.9886517628 5171979274,0.0],
+--R [1.43,0.9901045603 3717779486,0.9901045603 3717779486,0.0],
+--R [1.44,0.9914583481 9168646253,0.9914583481 9168646253,0.0],
+--R [1.45,0.9927129910 3758849767,0.9927129910 3758849767,0.0],
+--R [1.46,0.9938683634 1164484229,0.9938683634 1164484229,0.0],
+--R [1.47,0.9949243497 7758089786,0.9949243497 7758089786,0.0],
+--R [1.48,0.9958808445 3764005648,0.9958808445 3764005648,0.0],
+--R [1.49,0.9967377520 4314338855,0.9967377520 4314338855,0.0],
+--R [1.5,0.9974949866 0405443094,0.9974949866 0405443094,0.0],
+--R [1.51,0.9981524724 9754811924,0.9981524724 9754811924,0.0],
+--R [1.52,0.9987101439 7558300717,0.9987101439 7558300717,0.0],
+--R [1.53,0.9991679452 7147601592,0.9991679452 7147601592,0.0],
+--R [1.54,0.9995258306 0547905601,0.9995258306 0547905601,0.0],
+--R [1.55,0.9997837641 893569639,0.9997837641 893569639,0.0],
+--R [1.56,0.9999417202 2996629574,0.9999417202 2996629574,0.0],
+--R [1.57,0.9999996829 3183462021,0.9999996829 3183462021,0.0],
+--R [1.58,0.9999576464 9874005255,0.9999576464 9874005255,0.0],
+--R [1.59,0.9998156151 3429087198,0.9998156151 3429087198,0.0],
+--R [1.6,0.9995736030 4150516434,0.9995736030 4150516434,0.0]]
+--R Type: List List
Float
+--E 1
+@
+In the following table there are 4 columns. The first column
+is the argument of cos(x), ranging from 0.00 to 1.60. The
+second column is the reference value of sin from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp142-173
+
+<<*>>=
+--S 2 of 2
+[[0.01,0.99995000041666527778026,cos(0.01),cos(0.01)-(0.99995000041666527778026)],_
+[0.02,0.99980000666657777841270,cos(0.02),cos(0.02)-(0.99980000666657777841270)],_
+[0.03,0.99955003374898751627216,cos(0.03),cos(0.03)-(0.99955003374898751627216)],_
+[0.04,0.99920010666097794031457,cos(0.04),cos(0.04)-(0.99920010666097794031457)],_
+[0.05,0.99875026039496624656287,cos(0.05),cos(0.05)-(0.99875026039496624656287)],_
+[0.06,0.99820053993520416554766,cos(0.06),cos(0.06)-(0.99820053993520416554766)],_
+[0.07,0.99755100025327957462091,cos(0.07),cos(0.07)-(0.99755100025327957462091)],_
+[0.08,0.99680170630261938497771,cos(0.08),cos(0.08)-(0.99680170630261938497771)],_
+[0.09,0.99595273301199425309284,cos(0.09),cos(0.09)-(0.99595273301199425309284)],_
+[0.10,0.99500416527802576609556,cos(0.10),cos(0.10)-(0.99500416527802576609556)],_
+[0.11,0.99395609795669685035784,cos(0.11),cos(0.11)-(0.99395609795669685035784)],_
+[0.12,0.99280863585386625224810,cos(0.12),cos(0.12)-(0.99280863585386625224810)],_
+[0.13,0.99156189371478803959451,cos(0.13),cos(0.13)-(0.99156189371478803959451)],_
+[0.14,0.99021599621263717189895,cos(0.14),cos(0.14)-(0.99021599621263717189895)],_
+[0.15,0.98877107793604228673498,cos(0.15),cos(0.15)-(0.98877107793604228673498)],_
+[0.16,0.98722728337562694904095,cos(0.16),cos(0.16)-(0.98722728337562694904095)],_
+[0.17,0.98558476690956070917193,cos(0.17),cos(0.17)-(0.98558476690956070917193)],_
+[0.18,0.98384369278812141459272,cos(0.18),cos(0.18)-(0.98384369278812141459272)],_
+[0.19,0.98200423511727031896788,cos(0.19),cos(0.19)-(0.98200423511727031896788)],_
+[0.20,0.98006657784124163112420,cos(0.20),cos(0.20)-(0.98006657784124163112420)],_
+[0.21,0.97803091472414824491614,cos(0.21),cos(0.21)-(0.97803091472414824491614)],_
+[0.22,0.97589744933060548940602,cos(0.22),cos(0.22)-(0.97589744933060548940602)],_
+[0.23,0.97366639500537483696773,cos(0.23),cos(0.23)-(0.97366639500537483696773)],_
+[0.24,0.97133797485202960492618,cos(0.24),cos(0.24)-(0.97133797485202960492618)],_
+[0.25,0.96891242171064478414459,cos(0.25),cos(0.25)-(0.96891242171064478414459)],_
+[0.26,0.96638997813451322555822,cos(0.26),cos(0.26)-(0.96638997813451322555822)],_
+[0.27,0.96377089636589051301623,cos(0.27),cos(0.27)-(0.96377089636589051301623)],_
+[0.28,0.96105543831077094792459,cos(0.28),cos(0.28)-(0.96105543831077094792459)],_
+[0.29,0.95824387551269716807013,cos(0.29),cos(0.29)-(0.95824387551269716807013)],_
+[0.30,0.95533648912560601964231,cos(0.30),cos(0.30)-(0.95533648912560601964231)],_
+[0.31,0.95233356988571339784281,cos(0.31),cos(0.31)-(0.95233356988571339784281)],_
+[0.32,0.94923541808244086757531,cos(0.32),cos(0.32)-(0.94923541808244086757531)],_
+[0.33,0.94604234352838697152941,cos(0.33),cos(0.33)-(0.94604234352838697152941)],_
+[0.34,0.94275466552834622850264,cos(0.34),cos(0.34)-(0.94275466552834622850264)],_
+[0.35,0.93937271284737892003503,cos(0.35),cos(0.35)-(0.93937271284737892003503)],_
+[0.36,0.93589682367793485835091,cos(0.36),cos(0.36)-(0.93589682367793485835091)],_
+[0.37,0.93232734560603442320381,cos(0.37),cos(0.37)-(0.93232734560603442320381)],_
+[0.38,0.92866463557651024949253,cos(0.38),cos(0.38)-(0.92866463557651024949253)],_
+[0.39,0.92490905985731304145068,cos(0.39),cos(0.39)-(0.92490905985731304145068)],_
+[0.40,0.92106099400288508279853,cos(0.40),cos(0.40)-(0.92106099400288508279853)],_
+[0.41,0.91712082281660510547564,cos(0.41),cos(0.41)-(0.91712082281660510547564)],_
+[0.42,0.91308894031230827243609,cos(0.42),cos(0.42)-(0.91308894031230827243609)],_
+[0.43,0.90896574967488512247591,cos(0.43),cos(0.43)-(0.90896574967488512247591)],_
+[0.44,0.90475166321996341716554,cos(0.44),cos(0.44)-(0.90475166321996341716554)],_
+[0.45,0.90044710235267692166884,cos(0.45),cos(0.45)-(0.90044710235267692166884)],_
+[0.46,0.89605249752552524253639,cos(0.46),cos(0.46)-(0.89605249752552524253639)],_
+[0.47,0.89156828819532893645402,cos(0.47),cos(0.47)-(0.89156828819532893645402)],_
+[0.48,0.88699492277928419439995,cos(0.48),cos(0.48)-(0.88699492277928419439995)],_
+[0.49,0.88233285861012149570547,cos(0.49),cos(0.49)-(0.88233285861012149570547)],_
+[0.50,0.87758256189037271611628,cos(0.50),cos(0.50)-(0.87758256189037271611628)],_
+[0.51,0.87274450764575126310581,cos(0.51),cos(0.51)-(0.87274450764575126310581)],_
+[0.52,0.86781917967764990038785,cos(0.52),cos(0.52)-(0.86781917967764990038785)],_
+[0.53,0.86280707051476101180670,cos(0.53),cos(0.53)-(0.86280707051476101180670)],_
+[0.54,0.85770868136382414253797,cos(0.54),cos(0.54)-(0.85770868136382414253797)],_
+[0.55,0.85252452205950574280498,cos(0.55),cos(0.55)-(0.85252452205950574280498)],_
+[0.56,0.84725511101341612609452,cos(0.56),cos(0.56)-(0.84725511101341612609452)],_
+[0.57,0.84190097516226874013376,cos(0.57),cos(0.57)-(0.84190097516226874013376)],_
+[0.58,0.83646264991518693465789,cos(0.58),cos(0.58)-(0.83646264991518693465789)],_
+[0.59,0.83094067910016349524800,cos(0.59),cos(0.59)-(0.83094067910016349524800)],_
+[0.60,0.82533561490967829724095,cos(0.60),cos(0.60)-(0.82533561490967829724095)],_
+[0.61,0.81964801784547951790075,cos(0.61),cos(0.61)-(0.81964801784547951790075)],_
+[0.62,0.81387845666253392868400,cos(0.62),cos(0.62)-(0.81387845666253392868400)],_
+[0.63,0.80802750831215187252371,cos(0.63),cos(0.63)-(0.80802750831215187252371)],_
+[0.64,0.80209575788429261358611,cos(0.64),cos(0.64)-(0.80209575788429261358611)],_
+[0.65,0.79608379854905582891760,cos(0.65),cos(0.65)-(0.79608379854905582891760)],_
+[0.66,0.78999223149736509278382,cos(0.66),cos(0.66)-(0.78999223149736509278382)],_
+[0.67,0.78382166588084928530294,cos(0.67),cos(0.67)-(0.78382166588084928530294)],_
+[0.68,0.77757271875092793718239,cos(0.68),cos(0.68)-(0.77757271875092793718239)],_
+[0.69,0.77124601499710660197354,cos(0.69),cos(0.69)-(0.77124601499710660197354)],_
+[0.70,0.76484218728448842625586,cos(0.70),cos(0.70)-(0.76484218728448842625586)],_
+[0.71,0.75836187599050816654146,cos(0.71),cos(0.71)-(0.75836187599050816654146)],_
+[0.72,0.75180572914089497944549,cos(0.72),cos(0.72)-(0.75180572914089497944549)],_
+[0.73,0.74517440234487038879013,cos(0.73),cos(0.73)-(0.74517440234487038879013)],_
+[0.74,0.73846855872958790979142,cos(0.74),cos(0.74)-(0.73846855872958790979142)],_
+[0.75,0.73168886887382088631184,cos(0.75),cos(0.75)-(0.73168886887382088631184)],_
+[0.76,0.72483601074090517233969,cos(0.76),cos(0.76)-(0.72483601074090517233969)],_
+[0.77,0.71791066961094336337129,cos(0.77),cos(0.77)-(0.71791066961094336337129)],_
+[0.78,0.71091353801227735721626,cos(0.78),cos(0.78)-(0.71091353801227735721626)],_
+[0.79,0.70384531565223609691278,cos(0.79),cos(0.79)-(0.70384531565223609691278)],_
+[0.80,0.69670670934716542092075,cos(0.80),cos(0.80)-(0.69670670934716542092075)],_
+[0.81,0.68949843295174701754964,cos(0.81),cos(0.81)-(0.68949843295174701754964)],_
+[0.82,0.68222120728761355166656,cos(0.82),cos(0.82)-(0.68222120728761355166656)],_
+[0.83,0.67487576007126710211246,cos(0.83),cos(0.83)-(0.67487576007126710211246)],_
+[0.84,0.66746282584130811792267,cos(0.84),cos(0.84)-(0.66746282584130811792267)],_
+[0.85,0.65998314588498217039542,cos(0.85),cos(0.85)-(0.65998314588498217039542)],_
+[0.86,0.65243746816405184627203,cos(0.86),cos(0.86)-(0.65243746816405184627203)],_
+[0.87,0.64482654724000119477766,cos(0.87),cos(0.87)-(0.64482654724000119477766)],_
+[0.88,0.63715114419858020801550,cos(0.88),cos(0.88)-(0.63715114419858020801550)],_
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+--R [1.22,0.3436457463 1604702048,0.3436457463 1604702048,0.0],
+--R [1.23,0.3342377271 2450259824,0.3342377271 2450259824,0.2 E -20],
+--R [1.24,0.3247962844 3877623658,0.3247962844 3877623657,- 0.3 E -20],
+--R [1.25,0.3153223623 9526866545,0.3153223623 9526866545,0.0],
+--R [1.26,0.3058169083 7828932689,0.3058169083 7828932689,0.2 E -20],
+--R [1.27,0.2962808729 2531873355,0.2962808729 2531873355,- 0.3 E -20],
+--R [1.28,0.2867152096 3195551278,0.2867152096 3195551278,- 0.2 E -20],
+--R [1.29,0.2771208750 5655764139,0.2771208750 5655764139,0.0],
+--R [1.3,0.2674988286 24587407,0.2674988286 24587407,0.2 E -20],
+--R [1.31,0.2578500325 3266966134,0.2578500325 3266966134,- 0.3 E -20],
+--R [1.32,0.2481754516 5237295957,0.2481754516 5237295957,0.0],
+--R [1.33,0.2384760534 3372320752,0.2384760534 3372320752,0.8 E -21],
+--R [1.34,0.2287528078 0845946523,0.2287528078 0845946523,- 0.3 E -20],
+--R [1.35,0.2190066870 9304158142,0.2190066870 9304158142,- 0.2 E -20],
+--R [1.36,0.2092386658 9141935768,0.2092386658 9141935768,0.0],
+--R [1.37,0.1994497209 9757296569,0.1994497209 9757296569,0.2 E -20],
+--R [1.38,0.1896408312 9783436321,0.1896408312 9783436321,- 0.3 E -20],
+--R [1.39,0.1798129776 729994766,0.1798129776 729994766,- 0.8 E -21],
+--R [1.4,0.1699671429 0024093862,0.1699671429 0024093862,0.8 E -21],
+--R [1.41,0.1601043115 5483119016,0.1601043115 5483119017,0.3 E -20],
+--R [1.42,0.1502254699 1168577349,0.1502254699 1168577349,- 0.2 E -20],
+--R [1.43,0.1403316058 4673666253,0.1403316058 4673666253,0.0],
+--R [1.44,0.1304237087 3814549298,0.1304237087 3814549298,0.2 E -20],
+--R [1.45,0.1205027693 6736657053,0.1205027693 6736657053,- 0.3 E -20],
+--R [1.46,0.1105697798 2006955117,0.1105697798 2006955117,- 0.8 E -21],
+--R [1.47,0.1006257333 8693170091,0.1006257333 8693170091,0.8 E -21],
+--R [1.48,0.0906716244 6430965577 6,0.0906716244 6430965577 9,0.3 E -20],
+--R [1.49,0.0807084484 5480061486 8,0.0807084484 5480061486 6,- 0.2 E -20],
+--R [1.5,0.0707372016 6770291008 8,0.0707372016 6770291008 8,0.0],
+--R [1.51,0.0607588812 1938590658 2,0.0607588812 1938590658 3,0.2 E -20],
+--R [1.52,0.0507744849 3357919672 6,0.0507744849 3357919672 3,- 0.3 E -20],
+--R [1.53,0.0407850112 4159105868 9,0.0407850112 4159105868 8,- 0.1 E -20],
+--R [1.54,0.0307914590 8246615762 2,0.0307914590 8246615762 3,0.8 E -21],
+--R [1.55,0.0207948278 0309247364 4,0.0207948278 0309247364 7,0.3 E -20],
+--R [1.56,0.0107961170 5826744582 4,0.0107961170 5826744582 2,- 0.2 E -20],
+--R [1.57,0.0007963267 1073332548 541,0.0007963267 1073332548 514,- 0.3 E
-21],
+--R [1.58,- 0.0092035432 6880826480 54,- 0.0092035432 6880826480 38,0.2 E
-20],
+--R [1.59,- 0.0192024929 0169256809 5,- 0.0192024929 0169256809 8,- 0.3 E
-20],
+--R [1.6,- 0.0291995223 0128872620 6,- 0.0291995223 0128872620 7,- 0.1 E
-20]]
+--R Type: List List
Float
+--E 2
+
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Abramowitz and Stegun,``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp142-173
+\end{thebibliography}
+\end{document}
+
diff --git a/src/input/sinhcosh.input.pamphlet
b/src/input/sinhcosh.input.pamphlet
new file mode 100644
index 0000000..aa23267
--- /dev/null
+++ b/src/input/sinhcosh.input.pamphlet
@@ -0,0 +1,861 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input sinhcosh.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This is a set of tests for the sinh and cosh functions.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+In the following table there are 4 columns. The first column
+is the argument of sinh, ranging from 0.00 to 2.00. The
+second column is the reference value of sinh from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp213-216
+
+<<*>>=
+)spool sinhcosh.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 2
+[[0.00,0.000000000,sinh(0.00),sinh(0.00)-0.000000000],_
+[0.01,0.010000167,sinh(0.01),sinh(0.01)-0.010000167],_
+[0.02,0.020001333,sinh(0.02),sinh(0.02)-0.020001333],_
+[0.03,0.030004500,sinh(0.03),sinh(0.03)-0.030004500],_
+[0.04,0.040010668,sinh(0.04),sinh(0.04)-0.040010668],_
+[0.05,0.050020836,sinh(0.05),sinh(0.05)-0.050020836],_
+[0.06,0.060036006,sinh(0.06),sinh(0.06)-0.060036006],_
+[0.07,0.070057181,sinh(0.07),sinh(0.07)-0.070057181],_
+[0.08,0.080085361,sinh(0.08),sinh(0.08)-0.080085361],_
+[0.09,0.090121549,sinh(0.09),sinh(0.09)-0.090121549],_
+[0.10,0.100166750,sinh(0.10),sinh(0.10)-0.100166750],_
+[0.11,0.110221968,sinh(0.11),sinh(0.11)-0.110221968],_
+[0.12,0.120288207,sinh(0.12),sinh(0.12)-0.120288207],_
+[0.13,0.130366476,sinh(0.13),sinh(0.13)-0.130366476],_
+[0.14,0.140457782,sinh(0.14),sinh(0.14)-0.140457782],_
+[0.15,0.150563133,sinh(0.15),sinh(0.15)-0.150563133],_
+[0.16,0.160683541,sinh(0.16),sinh(0.16)-0.160683541],_
+[0.17,0.170820017,sinh(0.17),sinh(0.17)-0.170820017],_
+[0.18,0.180973576,sinh(0.18),sinh(0.18)-0.180973576],_
+[0.19,0.191145232,sinh(0.19),sinh(0.19)-0.191145232],_
+[0.20,0.201336003,sinh(0.20),sinh(0.20)-0.201336003],_
+[0.21,0.211546907,sinh(0.21),sinh(0.21)-0.211546907],_
+[0.22,0.221778966,sinh(0.22),sinh(0.22)-0.221778966],_
+[0.23,0.232033204,sinh(0.23),sinh(0.23)-0.232033204],_
+[0.24,0.242310645,sinh(0.24),sinh(0.24)-0.242310645],_
+[0.25,0.252612317,sinh(0.25),sinh(0.25)-0.252612317],_
+[0.26,0.262939250,sinh(0.26),sinh(0.26)-0.262939250],_
+[0.27,0.273292478,sinh(0.27),sinh(0.27)-0.273292478],_
+[0.28,0.283673035,sinh(0.28),sinh(0.28)-0.283673035],_
+[0.29,0.294081960,sinh(0.29),sinh(0.29)-0.294081960],_
+[0.30,0.304520293,sinh(0.30),sinh(0.30)-0.304520293],_
+[0.31,0.314989079,sinh(0.31),sinh(0.31)-0.314989079],_
+[0.32,0.325489364,sinh(0.32),sinh(0.32)-0.325489364],_
+[0.33,0.336022198,sinh(0.33),sinh(0.33)-0.336022198],_
+[0.34,0.346588634,sinh(0.34),sinh(0.34)-0.346588634],_
+[0.35,0.357189729,sinh(0.35),sinh(0.35)-0.357189729],_
+[0.36,0.367826544,sinh(0.36),sinh(0.36)-0.367826544],_
+[0.37,0.378500142,sinh(0.37),sinh(0.37)-0.378500142],_
+[0.38,0.389211590,sinh(0.38),sinh(0.38)-0.389211590],_
+[0.39,0.399961960,sinh(0.39),sinh(0.39)-0.399961960],_
+[0.40,0.410752326,sinh(0.40),sinh(0.40)-0.410752326],_
+[0.41,0.421583767,sinh(0.41),sinh(0.41)-0.421583767],_
+[0.42,0.432457368,sinh(0.42),sinh(0.42)-0.432457368],_
+[0.43,0.443374214,sinh(0.43),sinh(0.43)-0.443374214],_
+[0.44,0.454335399,sinh(0.44),sinh(0.44)-0.454335399],_
+[0.45,0.465342017,sinh(0.45),sinh(0.45)-0.465342017],_
+[0.46,0.476395170,sinh(0.46),sinh(0.46)-0.476395170],_
+[0.47,0.487495962,sinh(0.47),sinh(0.47)-0.487495962],_
+[0.48,0.498645505,sinh(0.48),sinh(0.48)-0.498645505],_
+[0.49,0.509844913,sinh(0.49),sinh(0.49)-0.509844913],_
+[0.50,0.521095305,sinh(0.50),sinh(0.50)-0.521095305],_
+[0.51,0.532397808,sinh(0.51),sinh(0.51)-0.532397808],_
+[0.52,0.543753551,sinh(0.52),sinh(0.52)-0.543753551],_
+[0.53,0.555163669,sinh(0.53),sinh(0.53)-0.555163669],_
+[0.54,0.566629305,sinh(0.54),sinh(0.54)-0.566629305],_
+[0.55,0.578151604,sinh(0.55),sinh(0.55)-0.578151604],_
+[0.56,0.589731718,sinh(0.56),sinh(0.56)-0.589731718],_
+[0.57,0.601370806,sinh(0.57),sinh(0.57)-0.601370806],_
+[0.58,0.613070032,sinh(0.58),sinh(0.58)-0.613070032],_
+[0.59,0.624830565,sinh(0.59),sinh(0.59)-0.624830565],_
+[0.60,0.636653582,sinh(0.60),sinh(0.60)-0.636653582],_
+[0.61,0.648540265,sinh(0.61),sinh(0.61)-0.648540265],_
+[0.62,0.660491802,sinh(0.62),sinh(0.62)-0.660491802],_
+[0.63,0.672509389,sinh(0.63),sinh(0.63)-0.672509389],_
+[0.64,0.684594228,sinh(0.64),sinh(0.64)-0.684594228],_
+[0.65,0.696747526,sinh(0.65),sinh(0.65)-0.696747526],_
+[0.66,0.708970500,sinh(0.66),sinh(0.66)-0.708970500],_
+[0.67,0.721264371,sinh(0.67),sinh(0.67)-0.721264371],_
+[0.68,0.733630370,sinh(0.68),sinh(0.68)-0.733630370],_
+[0.69,0.746069732,sinh(0.69),sinh(0.69)-0.746069732],_
+[0.70,0.758583702,sinh(0.70),sinh(0.70)-0.758583702],_
+[0.71,0.771173531,sinh(0.71),sinh(0.71)-0.771173531],_
+[0.72,0.783840477,sinh(0.72),sinh(0.72)-0.783840477],_
+[0.73,0.796585809,sinh(0.73),sinh(0.73)-0.796585809],_
+[0.74,0.809410799,sinh(0.74),sinh(0.74)-0.809410799],_
+[0.75,0.822316732,sinh(0.75),sinh(0.75)-0.822316732],_
+[0.76,0.835304897,sinh(0.76),sinh(0.76)-0.835304897],_
+[0.77,0.848376593,sinh(0.77),sinh(0.77)-0.848376593],_
+[0.78,0.861533127,sinh(0.78),sinh(0.78)-0.861533127],_
+[0.79,0.874775815,sinh(0.79),sinh(0.79)-0.874775815],_
+[0.80,0.888105982,sinh(0.80),sinh(0.80)-0.888105982],_
+[0.81,0.901524960,sinh(0.81),sinh(0.81)-0.901524960],_
+[0.82,0.915034092,sinh(0.82),sinh(0.82)-0.915034092],_
+[0.83,0.928634727,sinh(0.83),sinh(0.83)-0.928634727],_
+[0.84,0.942328227,sinh(0.84),sinh(0.84)-0.942328227],_
+[0.85,0.956115960,sinh(0.85),sinh(0.85)-0.956115960],_
+[0.86,0.969999306,sinh(0.86),sinh(0.86)-0.969999306],_
+[0.87,0.983979652,sinh(0.87),sinh(0.87)-0.983979652],_
+[0.88,0.998058397,sinh(0.88),sinh(0.88)-0.998058397],_
+[0.89,1.012236949,sinh(0.89),sinh(0.89)-1.012236949],_
+[0.90,1.026516726,sinh(0.90),sinh(0.90)-1.026516726],_
+[0.91,1.040899155,sinh(0.91),sinh(0.91)-1.040899155],_
+[0.92,1.055385674,sinh(0.92),sinh(0.92)-1.055385674],_
+[0.93,1.069977734,sinh(0.93),sinh(0.93)-1.069977734],_
+[0.94,1.084676791,sinh(0.94),sinh(0.94)-1.084676791],_
+[0.95,1.099484318,sinh(0.95),sinh(0.95)-1.099484318],_
+[0.96,1.114401794,sinh(0.96),sinh(0.96)-1.114401794],_
+[0.97,1.129430711,sinh(0.97),sinh(0.97)-1.129430711],_
+[0.98,1.144572572,sinh(0.98),sinh(0.98)-1.144572572],_
+[0.99,1.159828891,sinh(0.99),sinh(0.99)-1.159828891],_
+[1.00,1.175201194,sinh(1.00),sinh(1.00)-1.175201194],_
+[1.01,1.190691018,sinh(1.01),sinh(1.01)-1.190691018],_
+[1.02,1.206299912,sinh(1.02),sinh(1.02)-1.206299912],_
+[1.03,1.222029437,sinh(1.03),sinh(1.03)-1.222029437],_
+[1.04,1.237881166,sinh(1.04),sinh(1.04)-1.237881166],_
+[1.05,1.253856684,sinh(1.05),sinh(1.05)-1.253856684],_
+[1.06,1.269957589,sinh(1.06),sinh(1.06)-1.269957589],_
+[1.07,1.286185491,sinh(1.07),sinh(1.07)-1.286185491],_
+[1.08,1.302542013,sinh(1.08),sinh(1.08)-1.302542013],_
+[1.09,1.319028789,sinh(1.09),sinh(1.09)-1.319028789],_
+[1.10,1.335647470,sinh(1.10),sinh(1.10)-1.335647470],_
+[1.11,1.352399717,sinh(1.11),sinh(1.11)-1.352399717],_
+[1.12,1.369287204,sinh(1.12),sinh(1.12)-1.369287204],_
+[1.13,1.386311622,sinh(1.13),sinh(1.13)-1.386311622],_
+[1.14,1.403474672,sinh(1.14),sinh(1.14)-1.403474672],_
+[1.15,1.420778070,sinh(1.15),sinh(1.15)-1.420778070],_
+[1.16,1.438223548,sinh(1.16),sinh(1.16)-1.438223548],_
+[1.17,1.455812849,sinh(1.17),sinh(1.17)-1.455812849],_
+[1.18,1.473547732,sinh(1.18),sinh(1.18)-1.473547732],_
+[1.19,1.491429972,sinh(1.19),sinh(1.19)-1.491429972],_
+[1.20,1.509461355,sinh(1.20),sinh(1.20)-1.509461355],_
+[1.21,1.527643687,sinh(1.21),sinh(1.21)-1.527643687],_
+[1.22,1.545978783,sinh(1.22),sinh(1.22)-1.545978783],_
+[1.23,1.564468479,sinh(1.23),sinh(1.23)-1.564468479],_
+[1.24,1.583114623,sinh(1.24),sinh(1.24)-1.583114623],_
+[1.25,1.601919080,sinh(1.25),sinh(1.25)-1.601919080],_
+[1.26,1.620883730,sinh(1.26),sinh(1.26)-1.620883730],_
+[1.27,1.640010470,sinh(1.27),sinh(1.27)-1.640010470],_
+[1.28,1.659301213,sinh(1.28),sinh(1.28)-1.659301213],_
+[1.29,1.678757886,sinh(1.29),sinh(1.29)-1.678757886],_
+[1.30,1.698382437,sinh(1.30),sinh(1.30)-1.698382437],_
+[1.31,1.718176828,sinh(1.31),sinh(1.31)-1.718176828],_
+[1.32,1.738143038,sinh(1.32),sinh(1.32)-1.738143038],_
+[1.33,1.758283063,sinh(1.33),sinh(1.33)-1.758283063],_
+[1.34,1.778598918,sinh(1.34),sinh(1.34)-1.778598918],_
+[1.35,1.799092635,sinh(1.35),sinh(1.35)-1.799092635],_
+[1.36,1.819766262,sinh(1.36),sinh(1.36)-1.819766262],_
+[1.37,1.840621868,sinh(1.37),sinh(1.37)-1.840621868],_
+[1.38,1.861661537,sinh(1.38),sinh(1.38)-1.861661537],_
+[1.39,1.882887374,sinh(1.39),sinh(1.39)-1.882887374],_
+[1.40,1.904301501,sinh(1.40),sinh(1.40)-1.904301501],_
+[1.41,1.925906060,sinh(1.41),sinh(1.41)-1.925906060],_
+[1.42,1.947703212,sinh(1.42),sinh(1.42)-1.947703212],_
+[1.43,1.969695135,sinh(1.43),sinh(1.43)-1.969695135],_
+[1.44,1.991884029,sinh(1.44),sinh(1.44)-1.991884029],_
+[1.45,2.014272114,sinh(1.45),sinh(1.45)-2.014272114],_
+[1.46,2.036861627,sinh(1.46),sinh(1.46)-2.036861627],_
+[1.47,2.059654828,sinh(1.47),sinh(1.47)-2.059654828],_
+[1.48,2.082653996,sinh(1.48),sinh(1.48)-2.082653996],_
+[1.49,2.105861432,sinh(1.49),sinh(1.49)-2.105861432],_
+[1.50,2.129279455,sinh(1.50),sinh(1.50)-2.129279455],_
+[1.51,2.152910408,sinh(1.51),sinh(1.51)-2.152910408],_
+[1.52,2.176756654,sinh(1.52),sinh(1.52)-2.176756654],_
+[1.53,2.200820577,sinh(1.53),sinh(1.53)-2.200820577],_
+[1.54,2.225104585,sinh(1.54),sinh(1.54)-2.225104585],_
+[1.55,2.249611104,sinh(1.55),sinh(1.55)-2.249611104],_
+[1.56,2.274342587,sinh(1.56),sinh(1.56)-2.274342587],_
+[1.57,2.299301506,sinh(1.57),sinh(1.57)-2.299301506],_
+[1.58,2.324490357,sinh(1.58),sinh(1.58)-2.324490357],_
+[1.59,2.349911658,sinh(1.59),sinh(1.59)-2.349911658],_
+[1.60,2.375567953,sinh(1.60),sinh(1.60)-2.375567953],_
+[1.61,2.401461807,sinh(1.61),sinh(1.61)-2.401461807],_
+[1.62,2.427595809,sinh(1.62),sinh(1.62)-2.427595809],_
+[1.63,2.453972572,sinh(1.63),sinh(1.63)-2.453972572],_
+[1.64,2.480594735,sinh(1.64),sinh(1.64)-2.480594735],_
+[1.65,2.507464959,sinh(1.65),sinh(1.65)-2.507464959],_
+[1.66,2.534585932,sinh(1.66),sinh(1.66)-2.534585932],_
+[1.67,2.561960366,sinh(1.67),sinh(1.67)-2.561960366],_
+[1.68,2.589590998,sinh(1.68),sinh(1.68)-2.589590998],_
+[1.69,2.617480591,sinh(1.69),sinh(1.69)-2.617480591],_
+[1.70,2.645631934,sinh(1.70),sinh(1.70)-2.645631934],_
+[1.71,2.674047843,sinh(1.71),sinh(1.71)-2.674047843],_
+[1.72,2.702731158,sinh(1.72),sinh(1.72)-2.702731158],_
+[1.73,2.731684749,sinh(1.73),sinh(1.73)-2.731684749],_
+[1.74,2.760911511,sinh(1.74),sinh(1.74)-2.760911511],_
+[1.75,2.790414366,sinh(1.75),sinh(1.75)-2.790414366],_
+[1.76,2.820196265,sinh(1.76),sinh(1.76)-2.820196265],_
+[1.77,2.850260186,sinh(1.77),sinh(1.77)-2.850260186],_
+[1.78,2.880609136,sinh(1.78),sinh(1.78)-2.880609136],_
+[1.79,2.911246148,sinh(1.79),sinh(1.79)-2.911246148],_
+[1.80,2.942174288,sinh(1.80),sinh(1.80)-2.942174288],_
+[1.81,2.973396648,sinh(1.81),sinh(1.81)-2.973396648],_
+[1.82,3.004916349,sinh(1.82),sinh(1.82)-3.004916349],_
+[1.83,3.036736545,sinh(1.83),sinh(1.83)-3.036736545],_
+[1.84,3.068860417,sinh(1.84),sinh(1.84)-3.068860417],_
+[1.85,3.101291178,sinh(1.85),sinh(1.85)-3.101291178],_
+[1.86,3.134032071,sinh(1.86),sinh(1.86)-3.134032071],_
+[1.87,3.167086369,sinh(1.87),sinh(1.87)-3.167086369],_
+[1.88,3.200457378,sinh(1.88),sinh(1.88)-3.200457378],_
+[1.89,3.234148436,sinh(1.89),sinh(1.89)-3.234148436],_
+[1.90,3.268162912,sinh(1.90),sinh(1.90)-3.268162912],_
+[1.91,3.302504206,sinh(1.91),sinh(1.91)-3.302504206],_
+[1.92,3.337175754,sinh(1.92),sinh(1.92)-3.337175754],_
+[1.93,3.372181022,sinh(1.93),sinh(1.93)-3.372181022],_
+[1.94,3.407523510,sinh(1.94),sinh(1.94)-3.407523510],_
+[1.95,3.443206754,sinh(1.95),sinh(1.95)-3.443206754],_
+[1.96,3.479234322,sinh(1.96),sinh(1.96)-3.479234322],_
+[1.97,3.515609816,sinh(1.97),sinh(1.97)-3.515609816],_
+[1.98,3.552336874,sinh(1.98),sinh(1.98)-3.552336874],_
+[1.99,3.589419168,sinh(1.99),sinh(1.99)-3.589419168],_
+[2.00,3.626860408,sinh(2.00),sinh(2.00)-3.626860408]]
+--R
+--R
+--R (1)
+--R [[0.0,0.0,0.0,0.0],
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+--R [1.86,3.134032071,3.1340320705 305683671,- 0.4694316329 E -9],
+--R [1.87,3.167086369,3.1670863687 357898447,- 0.2642101554 E -9],
+--R [1.88,3.200457378,3.2004573782 171323393,0.217132339 E -9],
+--R [1.89,3.234148436,3.2341484361 033532526,0.103353253 E -9],
+--R [1.9,3.268162912,3.2681629115 283171817,- 0.4716828183 E -9],
+--R [1.91,3.302504206,3.3025042059 679121137,- 0.320878863 E -10],
+--R [1.92,3.337175754,3.3371757535 801998489,- 0.4198001511 E -9],
+--R [1.93,3.372181022,3.3721810215 488346686,- 0.4511653313 E -9],
+--R [1.94,3.40752351,3.4075235104 297845903,0.4297845903 E -9],
+--R [1.95,3.443206754,3.4432067545 013898812,0.5013898812 E -9],
+--R [1.96,3.479234322,3.4792343221 177938377,0.117793838 E -9],
+--R [1.97,3.515609816,3.5156098160 657811731,0.657811731 E -10],
+--R [1.98,3.552336874,3.5523368739 25059699,- 0.74940301 E -10],
+--R [1.99,3.589419168,3.5894191684 320213268,0.4320213268 E -9],
+--R [2.0,3.626860408,3.6268604078 470187677,- 0.152981232 E -9]]
+--R Type: List List
Float
+--E 1
+@
+In the following table there are 4 columns. The first column
+is the argument of cosh, ranging from 0.00 to 2.00. The
+second column is the reference value of sinh from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp213-216
+
+<<*>>=
+--S 2 of 2
+[[0.00,1.000000000,cosh(0.00),cosh(0.00)-1.000000000],_
+[0.01,1.000050000,cosh(0.01),cosh(0.01)-1.000050000],_
+[0.02,1.000200007,cosh(0.02),cosh(0.02)-1.000200007],_
+[0.03,1.000450034,cosh(0.03),cosh(0.03)-1.000450034],_
+[0.04,1.000800107,cosh(0.04),cosh(0.04)-1.000800107],_
+[0.05,1.001250260,cosh(0.05),cosh(0.05)-1.001250260],_
+[0.06,1.001800540,cosh(0.06),cosh(0.06)-1.001800540],_
+[0.07,1.002451001,cosh(0.07),cosh(0.07)-1.002451001],_
+[0.08,1.003201707,cosh(0.08),cosh(0.08)-1.003201707],_
+[0.09,1.004052734,cosh(0.09),cosh(0.09)-1.004052734],_
+[0.10,1.005004168,cosh(0.10),cosh(0.10)-1.005004168],_
+[0.11,1.006056103,cosh(0.11),cosh(0.11)-1.006056103],_
+[0.12,1.007208644,cosh(0.12),cosh(0.12)-1.007208644],_
+[0.13,1.008461907,cosh(0.13),cosh(0.13)-1.008461907],_
+[0.14,1.009816017,cosh(0.14),cosh(0.14)-1.009816017],_
+[0.15,1.011271110,cosh(0.15),cosh(0.15)-1.011271110],_
+[0.16,1.012827330,cosh(0.16),cosh(0.16)-1.012827330],_
+[0.17,1.014484834,cosh(0.17),cosh(0.17)-1.014484834],_
+[0.18,1.016243787,cosh(0.18),cosh(0.18)-1.016243787],_
+[0.19,1.018104366,cosh(0.19),cosh(0.19)-1.018104366],_
+[0.20,1.020066756,cosh(0.20),cosh(0.20)-1.020066756],_
+[0.21,1.022131153,cosh(0.21),cosh(0.21)-1.022131153],_
+[0.22,1.024297764,cosh(0.22),cosh(0.22)-1.024297764],_
+[0.23,1.026566806,cosh(0.23),cosh(0.23)-1.026566806],_
+[0.24,1.028938506,cosh(0.24),cosh(0.24)-1.028938506],_
+[0.25,1.031413100,cosh(0.25),cosh(0.25)-1.031413100],_
+[0.26,1.033990836,cosh(0.26),cosh(0.26)-1.033990836],_
+[0.27,1.036671973,cosh(0.27),cosh(0.27)-1.036671973],_
+[0.28,1.039456777,cosh(0.28),cosh(0.28)-1.039456777],_
+[0.29,1.042345528,cosh(0.29),cosh(0.29)-1.042345528],_
+[0.30,1.045338514,cosh(0.30),cosh(0.30)-1.045338514],_
+[0.31,1.048436035,cosh(0.31),cosh(0.31)-1.048436035],_
+[0.32,1.051638401,cosh(0.32),cosh(0.32)-1.051638401],_
+[0.33,1.054945931,cosh(0.33),cosh(0.33)-1.054945931],_
+[0.34,1.058358957,cosh(0.34),cosh(0.34)-1.058358957],_
+[0.35,1.061877819,cosh(0.35),cosh(0.35)-1.061877819],_
+[0.36,1.065502870,cosh(0.36),cosh(0.36)-1.065502870],_
+[0.37,1.069234473,cosh(0.37),cosh(0.37)-1.069234473],_
+[0.38,1.073072999,cosh(0.38),cosh(0.38)-1.073072999],_
+[0.39,1.077018834,cosh(0.39),cosh(0.39)-1.077018834],_
+[0.40,1.081072372,cosh(0.40),cosh(0.40)-1.081072372],_
+[0.41,1.085234018,cosh(0.41),cosh(0.41)-1.085234018],_
+[0.42,1.089504188,cosh(0.42),cosh(0.42)-1.089504188],_
+[0.43,1.093883309,cosh(0.43),cosh(0.43)-1.093883309],_
+[0.44,1.098371820,cosh(0.44),cosh(0.44)-1.098371820],_
+[0.45,1.102970169,cosh(0.45),cosh(0.45)-1.102970169],_
+[0.46,1.107678815,cosh(0.46),cosh(0.46)-1.107678815],_
+[0.47,1.112498231,cosh(0.47),cosh(0.47)-1.112498231],_
+[0.48,1.117428897,cosh(0.48),cosh(0.48)-1.117428897],_
+[0.49,1.122471307,cosh(0.49),cosh(0.49)-1.122471307],_
+[0.50,1.127625965,cosh(0.50),cosh(0.50)-1.127625965],_
+[0.51,1.132893387,cosh(0.51),cosh(0.51)-1.132893387],_
+[0.52,1.138274099,cosh(0.52),cosh(0.52)-1.138274099],_
+[0.53,1.143768639,cosh(0.53),cosh(0.53)-1.143768639],_
+[0.54,1.149377557,cosh(0.54),cosh(0.54)-1.149377557],_
+[0.55,1.155101414,cosh(0.55),cosh(0.55)-1.155101414],_
+[0.56,1.160940782,cosh(0.56),cosh(0.56)-1.160940782],_
+[0.57,1.166896245,cosh(0.57),cosh(0.57)-1.166896245],_
+[0.58,1.172968399,cosh(0.58),cosh(0.58)-1.172968399],_
+[0.59,1.179157850,cosh(0.59),cosh(0.59)-1.179157850],_
+[0.60,1.185465218,cosh(0.60),cosh(0.60)-1.185465218],_
+[0.61,1.191891134,cosh(0.61),cosh(0.61)-1.191891134],_
+[0.62,1.198436240,cosh(0.62),cosh(0.62)-1.198436240],_
+[0.63,1.205101190,cosh(0.63),cosh(0.63)-1.205101190],_
+[0.64,1.211886652,cosh(0.64),cosh(0.64)-1.211886652],_
+[0.65,1.218793303,cosh(0.65),cosh(0.65)-1.218793303],_
+[0.66,1.225821834,cosh(0.66),cosh(0.66)-1.225821834],_
+[0.67,1.232972949,cosh(0.67),cosh(0.67)-1.232972949],_
+[0.68,1.240247362,cosh(0.68),cosh(0.68)-1.240247362],_
+[0.69,1.247645801,cosh(0.69),cosh(0.69)-1.247645801],_
+[0.70,1.255169006,cosh(0.70),cosh(0.70)-1.255169006],_
+[0.71,1.262817728,cosh(0.71),cosh(0.71)-1.262817728],_
+[0.72,1.270592733,cosh(0.72),cosh(0.72)-1.270592733],_
+[0.73,1.278494799,cosh(0.73),cosh(0.73)-1.278494799],_
+[0.74,1.286524715,cosh(0.74),cosh(0.74)-1.286524715],_
+[0.75,1.294683285,cosh(0.75),cosh(0.75)-1.294683285],_
+[0.76,1.302971324,cosh(0.76),cosh(0.76)-1.302971324],_
+[0.77,1.311389661,cosh(0.77),cosh(0.77)-1.311389661],_
+[0.78,1.319939138,cosh(0.78),cosh(0.78)-1.319939138],_
+[0.79,1.328620611,cosh(0.79),cosh(0.79)-1.328620611],_
+[0.80,1.337434946,cosh(0.80),cosh(0.80)-1.337434946],_
+[0.81,1.346383026,cosh(0.81),cosh(0.81)-1.346383026],_
+[0.82,1.355465746,cosh(0.82),cosh(0.82)-1.355465746],_
+[0.83,1.364684013,cosh(0.83),cosh(0.83)-1.364684013],_
+[0.84,1.374038750,cosh(0.84),cosh(0.84)-1.374038750],_
+[0.85,1.383530892,cosh(0.85),cosh(0.85)-1.383530892],_
+[0.86,1.393161388,cosh(0.86),cosh(0.86)-1.393161388],_
+[0.87,1.402931201,cosh(0.87),cosh(0.87)-1.402931201],_
+[0.88,1.412841309,cosh(0.88),cosh(0.88)-1.412841309],_
+[0.89,1.422892702,cosh(0.89),cosh(0.89)-1.422892702],_
+[0.90,1.433086385,cosh(0.90),cosh(0.90)-1.433086385],_
+[0.91,1.443423379,cosh(0.91),cosh(0.91)-1.443423379],_
+[0.92,1.453904716,cosh(0.92),cosh(0.92)-1.453904716],_
+[0.93,1.464531444,cosh(0.93),cosh(0.93)-1.464531444],_
+[0.94,1.475304627,cosh(0.94),cosh(0.94)-1.475304627],_
+[0.95,1.486225341,cosh(0.95),cosh(0.95)-1.486225341],_
+[0.96,1.497294680,cosh(0.96),cosh(0.96)-1.497294680],_
+[0.97,1.508513749,cosh(0.97),cosh(0.97)-1.508513749],_
+[0.98,1.519883670,cosh(0.98),cosh(0.98)-1.519883670],_
+[0.99,1.531405582,cosh(0.99),cosh(0.99)-1.531405582],_
+[1.00,1.543080635,cosh(1.00),cosh(1.00)-1.543080635],_
+[1.01,1.554909997,cosh(1.01),cosh(1.01)-1.554909997],_
+[1.02,1.566894852,cosh(1.02),cosh(1.02)-1.566894852],_
+[1.03,1.579036398,cosh(1.03),cosh(1.03)-1.579036398],_
+[1.04,1.591335848,cosh(1.04),cosh(1.04)-1.591335848],_
+[1.05,1.603794434,cosh(1.05),cosh(1.05)-1.603794434],_
+[1.06,1.616413400,cosh(1.06),cosh(1.06)-1.616413400],_
+[1.07,1.629194009,cosh(1.07),cosh(1.07)-1.629194009],_
+[1.08,1.642137538,cosh(1.08),cosh(1.08)-1.642137538],_
+[1.09,1.655245283,cosh(1.09),cosh(1.09)-1.655245283],_
+[1.10,1.668518554,cosh(1.10),cosh(1.10)-1.668518554],_
+[1.11,1.681958678,cosh(1.11),cosh(1.11)-1.681958678],_
+[1.12,1.695566999,cosh(1.12),cosh(1.12)-1.695566999],_
+[1.13,1.709344878,cosh(1.13),cosh(1.13)-1.709344878],_
+[1.14,1.723293694,cosh(1.14),cosh(1.14)-1.723293694],_
+[1.15,1.737414840,cosh(1.15),cosh(1.15)-1.737414840],_
+[1.16,1.751709728,cosh(1.16),cosh(1.16)-1.751709728],_
+[1.17,1.766179790,cosh(1.17),cosh(1.17)-1.766179790],_
+[1.18,1.780826471,cosh(1.18),cosh(1.18)-1.780826471],_
+[1.19,1.795651236,cosh(1.19),cosh(1.19)-1.795651236],_
+[1.20,1.810655567,cosh(1.20),cosh(1.20)-1.810655567],_
+[1.21,1.825840966,cosh(1.21),cosh(1.21)-1.825840966],_
+[1.22,1.841208950,cosh(1.22),cosh(1.22)-1.841208950],_
+[1.23,1.856761057,cosh(1.23),cosh(1.23)-1.856761057],_
+[1.24,1.872498841,cosh(1.24),cosh(1.24)-1.872498841],_
+[1.25,1.888423877,cosh(1.25),cosh(1.25)-1.888423877],_
+[1.26,1.904537757,cosh(1.26),cosh(1.26)-1.904537757],_
+[1.27,1.920842092,cosh(1.27),cosh(1.27)-1.920842092],_
+[1.28,1.937338513,cosh(1.28),cosh(1.28)-1.937338513],_
+[1.29,1.954028669,cosh(1.29),cosh(1.29)-1.954028669],_
+[1.30,1.970914230,cosh(1.30),cosh(1.30)-1.970914230],_
+[1.31,1.987996884,cosh(1.31),cosh(1.31)-1.987996884],_
+[1.32,2.005278340,cosh(1.32),cosh(1.32)-2.005278340],_
+[1.33,2.022760324,cosh(1.33),cosh(1.33)-2.022760324],_
+[1.34,2.040444587,cosh(1.34),cosh(1.34)-2.040444587],_
+[1.35,2.058332896,cosh(1.35),cosh(1.35)-2.058332896],_
+[1.36,2.076427039,cosh(1.36),cosh(1.36)-2.076427039],_
+[1.37,2.094728828,cosh(1.37),cosh(1.37)-2.094728828],_
+[1.38,2.113240090,cosh(1.38),cosh(1.38)-2.113240090],_
+[1.39,2.131962679,cosh(1.39),cosh(1.39)-2.131962679],_
+[1.40,2.150898465,cosh(1.40),cosh(1.40)-2.150898465],_
+[1.41,2.170049344,cosh(1.41),cosh(1.41)-2.170049344],_
+[1.42,2.189417229,cosh(1.42),cosh(1.42)-2.189417229],_
+[1.43,2.209004057,cosh(1.43),cosh(1.43)-2.209004057],_
+[1.44,2.228811788,cosh(1.44),cosh(1.44)-2.228811788],_
+[1.45,2.248842402,cosh(1.45),cosh(1.45)-2.248842402],_
+[1.46,2.269097902,cosh(1.46),cosh(1.46)-2.269097902],_
+[1.47,2.289580313,cosh(1.47),cosh(1.47)-2.289580313],_
+[1.48,2.310291685,cosh(1.48),cosh(1.48)-2.310291685],_
+[1.49,2.331234087,cosh(1.49),cosh(1.49)-2.331234087],_
+[1.50,2.352409615,cosh(1.50),cosh(1.50)-2.352409615],_
+[1.51,2.373820386,cosh(1.51),cosh(1.51)-2.373820386],_
+[1.52,2.395468541,cosh(1.52),cosh(1.52)-2.395468541],_
+[1.53,2.417356245,cosh(1.53),cosh(1.53)-2.417356245],_
+[1.54,2.439485686,cosh(1.54),cosh(1.54)-2.439485686],_
+[1.55,2.461859078,cosh(1.55),cosh(1.55)-2.461859078],_
+[1.56,2.484478658,cosh(1.56),cosh(1.56)-2.484478658],_
+[1.57,2.507346688,cosh(1.57),cosh(1.57)-2.507346688],_
+[1.58,2.530465455,cosh(1.58),cosh(1.58)-2.530465455],_
+[1.59,2.553837270,cosh(1.59),cosh(1.59)-2.553837270],_
+[1.60,2.577464471,cosh(1.60),cosh(1.60)-2.577464471],_
+[1.61,2.601349421,cosh(1.61),cosh(1.61)-2.601349421],_
+[1.62,2.625494508,cosh(1.62),cosh(1.62)-2.625494508],_
+[1.63,2.649902146,cosh(1.63),cosh(1.63)-2.649902146],_
+[1.64,2.674574777,cosh(1.64),cosh(1.64)-2.674574777],_
+[1.65,2.699514868,cosh(1.65),cosh(1.65)-2.699514868],_
+[1.66,2.724724912,cosh(1.66),cosh(1.66)-2.724724912],_
+[1.67,2.750207431,cosh(1.67),cosh(1.67)-2.750207431],_
+[1.68,2.775964974,cosh(1.68),cosh(1.68)-2.775964974],_
+[1.69,2.802000115,cosh(1.69),cosh(1.69)-2.802000115],_
+[1.70,2.828315458,cosh(1.70),cosh(1.70)-2.828315458],_
+[1.71,2.854913635,cosh(1.71),cosh(1.71)-2.854913635],_
+[1.72,2.881797306,cosh(1.72),cosh(1.72)-2.881797306],_
+[1.73,2.908969159,cosh(1.73),cosh(1.73)-2.908969159],_
+[1.74,2.936431912,cosh(1.74),cosh(1.74)-2.936431912],_
+[1.75,2.964188310,cosh(1.75),cosh(1.75)-2.964188310],_
+[1.76,2.992241129,cosh(1.76),cosh(1.76)-2.992241129],_
+[1.77,3.020593175,cosh(1.77),cosh(1.77)-3.020593175],_
+[1.78,3.049247283,cosh(1.78),cosh(1.78)-3.049247283],_
+[1.79,3.078206318,cosh(1.79),cosh(1.79)-3.078206318],_
+[1.80,3.107473176,cosh(1.80),cosh(1.80)-3.107473176],_
+[1.81,3.137050785,cosh(1.81),cosh(1.81)-3.137050785],_
+[1.82,3.166942100,cosh(1.82),cosh(1.82)-3.166942100],_
+[1.83,3.197150113,cosh(1.83),cosh(1.83)-3.197150113],_
+[1.84,3.227677844,cosh(1.84),cosh(1.84)-3.227677844],_
+[1.85,3.258528344,cosh(1.85),cosh(1.85)-3.258528344],_
+[1.86,3.289704701,cosh(1.86),cosh(1.86)-3.289704701],_
+[1.87,3.321210031,cosh(1.87),cosh(1.87)-3.321210031],_
+[1.88,3.353047484,cosh(1.88),cosh(1.88)-3.353047484],_
+[1.89,3.385220245,cosh(1.89),cosh(1.89)-3.385220245],_
+[1.90,3.417731531,cosh(1.90),cosh(1.90)-3.417731531],_
+[1.91,3.450584593,cosh(1.91),cosh(1.91)-3.450584593],_
+[1.92,3.483782716,cosh(1.92),cosh(1.92)-3.483782716],_
+[1.93,3.517329220,cosh(1.93),cosh(1.93)-3.517329220],_
+[1.94,3.551227460,cosh(1.94),cosh(1.94)-3.551227460],_
+[1.95,3.585480826,cosh(1.95),cosh(1.95)-3.585480826],_
+[1.96,3.620092743,cosh(1.96),cosh(1.96)-3.620092743],_
+[1.97,3.655066672,cosh(1.97),cosh(1.97)-3.655066672],_
+[1.98,3.690406111,cosh(1.98),cosh(1.98)-3.690406111],_
+[1.99,3.726114594,cosh(1.99),cosh(1.99)-3.726114594],_
+[2.00,3.762195691,cosh(2.00),cosh(2.00)-3.762195691]]
+--R
+--R
+--R (2)
+--R [[0.0,1.0,1.0,0.0], [0.01,1.00005,1.0000500004 166680556,0.4166680556 E
-9],
+--R [0.02,1.000200007,1.0002000066 667555562,- 0.3332444438 E -9],
+--R [0.03,1.000450034,1.0004500337 510125163,- 0.2489874837 E -9],
+--R [0.04,1.000800107,1.0008001066 723557181,- 0.3276442819 E -9],
+--R [0.05,1.00125026,1.0012502604 383690244,0.4383690244 E -9],
+--R [0.06,1.00180054,1.0018005400 648041659,0.648041659 E -10],
+--R [0.07,1.002451001,1.0024510005 80082354,- 0.419917646 E -9],
+--R [0.08,1.003201707,1.0032017070 307971687,0.307971687 E -10],
+--R [0.09,1.004052734,1.0040527344 882192723,0.4882192723 E -9],
+--R [0.1,1.005004168,1.0050041680 55803599,0.55803599 E -10],
+--R [0.11,1.006056103,1.0060561028 776997711,- 0.1223002289 E -9],
+--R [0.12,1.007208644,1.0072086441 482665935,0.1482665935 E -9],
+--R [0.13,1.008461907,1.0084619071 225915772,0.1225915772 E -9],
+--R [0.14,1.009816017,1.0098160171 280165439,0.1280165439 E -9],
+--R [0.15,1.01127111,1.0112711095 766704649,- 0.4233295351 E -9],
+--R [0.16,1.01282733,1.0128273299 790107867,- 0.209892133 E -10],
+--R [0.17,1.014484834,1.0144848339 58374598,- 0.41625402 E -10],
+--R [0.18,1.016243787,1.0162437872 665410931,0.2665410931 E -9],
+--R [0.19,1.018104366,1.0181043658 003068879,- 0.1996931121 E -9],
+--R [0.2,1.020066756,1.0200667556 190758463,- 0.3809241537 E -9],
+--R [0.21,1.022131153,1.0221311529 634651755,- 0.365348245 E -10],
+--R [0.22,1.024297764,1.0242977642 749296513,0.2749296512 E -9],
+--R [0.23,1.026566806,1.0265668062 164059355,0.2164059355 E -9],
+--R [0.24,1.028938506,1.0289385056 939790504,- 0.3060209496 E -9],
+--R [0.25,1.0314131,1.0314130998 795731762,- 0.1204268238 E -9],
+--R [0.26,1.033990836,1.0339908362 346690408,0.2346690408 E -9],
+--R [0.27,1.036671973,1.0366719725 350502748,- 0.4649497252 E -9],
+--R [0.28,1.039456777,1.0394567768 965812039,- 0.103418796 E -9],
+--R [0.29,1.042345528,1.0423455278 020186592,- 0.1979813408 E -9],
+--R [0.3,1.045338514,1.0453385141 28860485,0.128860485 E -9],
+--R [0.31,1.048436035,1.0484360351 78233529,0.178233529 E -9],
+--R [0.32,1.051638401,1.0516384007 048240047,- 0.2951759953 E -9],
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+--R [0.35,1.061877819,1.0618778191 559853413,0.1559853413 E -9],
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+--R [0.38,1.073072999,1.0730729993 232901949,0.3232901949 E -9],
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+--R [0.4,1.081072372,1.0810723718 384548093,- 0.1615451907 E -9],
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+--R [0.42,1.089504188,1.0895041877 168452888,- 0.2831547112 E -9],
+--R [0.43,1.093883309,1.0938833091 357989732,0.1357989732 E -9],
+--R [0.44,1.09837182,1.0983718197 972387003,- 0.2027612997 E -9],
+--R [0.45,1.102970169,1.1029701685 559710522,- 0.4440289478 E -9],
+--R [0.46,1.107678815,1.1076788152 507038721,0.2507038721 E -9],
+--R [0.47,1.112498231,1.1124982307 500305186,- 0.2499694814 E -9],
+--R [0.48,1.117428897,1.1174288969 995171175,- 0.4828825 E -12],
+--R [0.49,1.122471307,1.1224713070 698975196,0.698975196 E -10],
+--R [0.5,1.127625965,1.1276259652 063807852,0.2063807852 E -9],
+--R [0.51,1.132893387,1.1328933868 790761256,- 0.1209238744 E -9],
+--R [0.52,1.138274099,1.1382740988 345403429,- 0.1654596571 E -9],
+--R [0.53,1.143768639,1.1437686391 484529252,0.1484529252 E -9],
+--R [0.54,1.149377557,1.1493775572 794240625,0.2794240625 E -9],
+--R [0.55,1.155101414,1.1551014141 239409661,0.1239409661 E -9],
+--R [0.56,1.160940782,1.1609407820 724579841,0.724579841 E -10],
+--R [0.57,1.166896245,1.1668962450 666361245,0.666361245 E -10],
+--R [0.58,1.172968399,1.1729683986 577377074,- 0.3422622926 E -9],
+--R [0.59,1.17915785,1.1791578500 661819879,0.661819879 E -10],
+--R [0.6,1.185465218,1.1854652182 422677038,0.2422677038 E -9],
+--R [0.61,1.191891134,1.1918911339 280686212,- 0.719313788 E -10],
+--R [0.62,1.19843624,1.1984362397 20508268,- 0.279491732 E -9],
+--R [0.63,1.20510119,1.2051011901 35620161,0.135620161 E -9],
+--R [0.64,1.211886652,1.2118866516 739999553,- 0.3260000447 E -9],
+--R [0.65,1.218793303,1.2187933028 87456059,- 0.112543941 E -9],
+--R [0.66,1.225821834,1.2258218344 468653796,0.4468653796 E -9],
+--R [0.67,1.232972949,1.2329729492 112409872,0.2112409872 E -9],
+--R [0.68,1.240247362,1.2402473622 980186015,0.2980186015 E -9],
+--R [0.69,1.247645801,1.2476458011 545689314,0.1545689314 E -9],
+--R [0.7,1.255169006,1.2551690056 309430182,- 0.3690569818 E -9],
+--R [0.71,1.262817728,1.2628177280 538578572,0.538578572 E -10],
+--R [0.72,1.270592733,1.2705927333 019296965,0.3019296965 E -9],
+--R [0.73,1.278494799,1.2784947988 82162536,- 0.117837464 E -9],
+--R [0.74,1.286524715,1.2865247150 076994755,0.769947551 E -11],
+--R [0.75,1.294683285,1.2946832846 768446878,- 0.3231553122 E -9],
+--R [0.76,1.302971324,1.3029713237 533639182,- 0.2466360818 E -9],
+--R [0.77,1.311389661,1.3113896610 480715408,0.480715408 E -10],
+--R [0.78,1.319939138,1.3199391384 017123309,0.4017123309 E -9],
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+--R [0.8,1.337434946,1.3374349463 04844598,0.304844598 E -9],
+--R [0.81,1.346383026,1.3463830264 497062768,0.4497062768 E -9],
+--R [0.82,1.355465746,1.3554657460 192025216,0.192025216 E -10],
+--R [0.83,1.364684013,1.3646840132 928592402,0.2928592402 E -9],
+--R [0.84,1.37403875,1.3740387501 050857132,0.105085713 E -9],
+--R [0.85,1.383530892,1.3835308919 373588034,- 0.626411966 E -10],
+--R [0.86,1.393161388,1.3931613880 117718825,0.117718825 E -10],
+--R [0.87,1.402931201,1.4029312013 859578321,0.3859578321 E -9],
+--R [0.88,1.412841309,1.4128413090 493956089,0.493956089 E -10],
+--R [0.89,1.422892702,1.4228927020 211100075,0.211100075 E -10],
+--R [0.9,1.433086385,1.4330863854 487743878,0.4487743878 E -9],
+--R [0.91,1.443423379,1.4434233787 09226281,- 0.290773719 E -9],
+--R [0.92,1.453904716,1.4539047155 104059219,- 0.4895940781 E -9],
+--R [0.93,1.464531444,1.4645314439 947279049,- 0.52720951 E -11],
+--R [0.94,1.475304627,1.4753046268 438962989,- 0.1561037011 E -9],
+--R [0.95,1.486225341,1.4862253413 85173703,0.385173703 E -9],
+--R [0.96,1.49729468,1.4972946796 991148706,- 0.3008851294 E -9],
+--R [0.97,1.508513749,1.5085137487 287756753,- 0.2712243247 E -9],
+--R [0.98,1.51988367,1.5198836703 904083385,0.3904083385 E -9],
+--R [0.99,1.531405582,1.5314055816 856539898,- 0.3143460102 E -9],
+--R [1.0,1.543080635,1.5430806348 152437785,- 0.1847562215 E -9],
+--R [1.01,1.554909997,1.5549099972 942199069,0.2942199069 E -9],
+--R [1.02,1.566894852,1.5668948520 686881075,0.686881075 E -10],
+--R [1.03,1.579036398,1.5790363976 341132396,- 0.3658867604 E -9],
+--R [1.04,1.591335848,1.5913358481 551698338,0.1551698338 E -9],
+--R [1.05,1.603794434,1.6037944335 871595723,- 0.4128404277 E -9],
+--R [1.06,1.6164134,1.6164133997 99007843,- 0.200992157 E -9],
+--R [1.07,1.629194009,1.6291940086 97851671,- 0.302148329 E -9],
+--R [1.08,1.642137538,1.6421375383 552314837,0.3552314837 E -9],
+--R [1.09,1.655245283,1.6552452831 348993296,0.1348993296 E -9],
+--R [1.1,1.668518554,1.6685185538 222563327,- 0.1777436673 E -9],
+--R [1.11,1.681958678,1.6819586777 554323243,- 0.2445676757 E -9],
+--R [1.12,1.695566999,1.6955669989 580207628,- 0.419792372 E -10],
+--R [1.13,1.709344878,1.7093448782 734822124,0.2734822124 E -9],
+--R [1.14,1.723293694,1.7232936935 012298237,- 0.4987701763 E -9],
+--R [1.15,1.73741484,1.7374148395 344104227,- 0.4655895773 E -9],
+--R [1.16,1.751709728,1.7517097284 993949886,0.4993949886 E -9],
+--R [1.17,1.76617979,1.7661797898 96992467,- 0.103007533 E -9],
+--R [1.18,1.780826471,1.7808264707 454010422,- 0.2545989578 E -9],
+--R [1.19,1.795651236,1.7956512357 249111632,- 0.2750888368 E -9],
+--R [1.2,1.810655567,1.8106555673 243747931,0.3243747931 E -9],
+--R [1.21,1.825840966,1.8258409659 894555295,- 0.105444705 E -10],
+--R [1.22,1.84120895,1.8412089502 726744215,0.2726744215 E -9],
+--R [1.23,1.856761057,1.8567610569 852664874,- 0.147335126 E -10],
+--R [1.24,1.872498841,1.8724988413 508631184,0.3508631184 E -9],
+--R [1.25,1.888423877,1.8884238771 610157382,0.1610157382 E -9],
+--R [1.26,1.904537757,1.9045377569 325762696,- 0.674237304 E -10],
+--R [1.27,1.920842092,1.9208420920 669501464,0.669501464 E -10],
+--R [1.28,1.937338513,1.9373385130 112377973,0.112377973 E -10],
+--R [1.29,1.954028669,1.9540286694 212807143,0.4212807143 E -9],
+--R [1.3,1.97091423,1.9709142303 266284118,0.3266284118 E -9],
+--R [1.31,1.987996884,1.9879968842 974427722,0.2974427722 E -9],
+--R [1.32,2.00527834,2.0052783396 133564693,- 0.3866435307 E -9],
+--R [1.33,2.022760324,2.0227603244 343023553,0.4343023553 E -9],
+--R [1.34,2.040444587,2.0404445869 73330894,- 0.26669106 E -10],
+--R [1.35,2.058332896,2.0583328956 714329229,- 0.3285670771 E -9],
+--R [1.36,2.076427039,2.0764270393 743852257,0.3743852257 E -9],
+--R [1.37,2.094728828,2.0947288275 11636601,- 0.488363399 E -9],
+--R [1.38,2.11324009,2.1132400902 77252315,0.277252315 E -9],
+--R [1.39,2.131962679,2.1319626788 129350329,- 0.187064967 E -9],
+--R [1.4,2.150898465,2.1508984653 931405321,0.3931405321 E -9],
+--R [1.41,2.170049344,2.1700493436 123067079,- 0.3876932921 E -9],
+--R [1.42,2.189417229,2.1894172285 742145953,- 0.4257854047 E -9],
+--R [1.43,2.209004057,2.2090040570 835003431,0.83500343 E -10],
+--R [1.44,2.228811788,2.2288117878 393372912,- 0.160662709 E -9],
+--R [1.45,2.248842402,2.2488424016 313075208,- 0.3686924792 E -9],
+--R [1.46,2.269097902,2.2690979015 374824626,- 0.4625175374 E -9],
+--R [1.47,2.289580313,2.2895803131 247323736,0.124732374 E -9],
+--R [1.48,2.310291685,2.3102916846 512847122,- 0.3487152878 E -9],
+--R [1.49,2.331234087,2.3312340872 715516672,0.2715516672 E -9],
+--R [1.5,2.352409615,2.3524096152 432473258,0.2432473258 E -9],
+--R [1.51,2.373820386,2.3738203861 368151896,0.13681519 E -9],
+--R [1.52,2.395468541,2.3954685410 47186984,0.47186984 E -10],
+--R [1.53,2.417356245,2.4173562448 078939354,- 0.192106065 E -9],
+--R [1.54,2.439485686,2.4394856862 075519285,0.207551928 E -9],
+--R [1.55,2.461859078,2.4618590782 087421916,0.208742192 E -9],
+--R [1.56,2.484478658,2.4844786581 693093993,0.169309399 E -9],
+--R [1.57,2.507346688,2.5073466880 66099321,0.66099321 E -10],
+--R [1.58,2.530465455,2.5304654547 21158391,- 0.278841609 E -9],
+--R [1.59,2.55383727,2.5538372700 304178181,0.304178181 E -10],
+--R [1.6,2.577464471,2.5774644711 948851061,0.194885106 E -9],
+--R [1.61,2.601349421,2.6013494209 543661015,- 0.456338985 E -10],
+--R [1.62,2.625494508,2.6254945078 237409436,- 0.176259056 E -9],
+--R [1.63,2.649902146,2.6499021463 318175428,0.3318175428 E -9],
+--R [1.64,2.674574777,2.6745747772 627864732,0.2627864732 E -9],
+--R [1.65,2.699514868,2.6995148679 00301426,- 0.99698574 E -10],
+--R [1.66,2.724724912,2.7247249122 742096308,0.2742096308 E -9],
+--R [1.67,2.750207431,2.7502074314 099569189,0.4099569189 E -9],
+--R [1.68,2.775964974,2.7759649735 806923683,- 0.4193076317 E -9],
+--R [1.69,2.802000115,2.8020001145 620977426,- 0.4379022574 E -9],
+--R [1.7,2.828315458,2.8283154578 899672055,- 0.110032794 E -9],
+--R [1.71,2.854913635,2.8549136351 205630698,0.12056307 E -9],
+--R [1.72,2.881797306,2.8817973060 937736167,0.937736167 E -10],
+--R [1.73,2.908969159,2.9089691591 990993011,0.199099301 E -9],
+--R [1.74,2.936431912,2.9364319116 444939418,- 0.3555060582 E -9],
+--R [1.75,2.96418831,2.9641883097 280877818,- 0.2719122182 E -9],
+--R [1.76,2.992241129,2.9922411291 128195891,0.112819589 E -9],
+--R [1.77,3.020593175,3.0205931751 040052646,0.104005265 E -9],
+--R [1.78,3.049247283,3.0492472829 298707103,- 0.701292897 E -10],
+--R [1.79,3.078206318,3.0782063180 250770157,0.250770157 E -10],
+--R [1.8,3.107473176,3.1074731763 17266311,0.317266311 E -9],
+--R [1.81,3.137050785,3.1370507845 166569452,- 0.4833430548 E -9],
+--R [1.82,3.1669421,3.1669421004 087169461,0.4087169461 E -9],
+--R [1.83,3.197150113,3.1971501131 499450329,0.149945033 E -9],
+--R [1.84,3.227677844,3.2276778435 667887561,- 0.4332112439 E -9],
+--R [1.85,3.258528344,3.2585283444 577296603,0.4577296603 E -9],
+--R [1.86,3.289704701,3.2897047008 98565676,- 0.101434324 E -9],
+--R [1.87,3.321210031,3.3212100305 509212704,- 0.4490787296 E -9],
+--R [1.88,3.353047484,3.3530474839 74016208,- 0.25983792 E -10],
+--R [1.89,3.385220245,3.3852202449 397240979,- 0.602759021 E -10],
+--R [1.9,3.417731531,3.4177315307 509522343,- 0.2490477656 E -9],
+--R [1.91,3.450584593,3.4505845925 633745687,- 0.4366254312 E -9],
+--R [1.92,3.483782716,3.4837827157 105499861,- 0.289450014 E -9],
+--R [1.93,3.51732922,3.5173292200 324583986,0.324583986 E -10],
+--R [1.94,3.55122746,3.5512274602 074875108,0.207487511 E -9],
+--R [1.95,3.585480826,3.5854808260 879034531,0.879034531 E -10],
+--R [1.96,3.620092743,3.6200927430 388388338,0.388388338 E -10],
+--R [1.97,3.655066672,3.6550666722 808321068,0.2808321068 E -9],
+--R [1.98,3.690406111,3.6904061112 359525095,0.2359525095 E -9],
+--R [1.99,3.726114594,3.7261145938 775451847,- 0.122454815 E -9],
+--R [2.0,3.762195691,3.7621956910 836314596,0.836314596 E -10]]
+--R Type: List List
Float
+--E 2
+
+)spool
+)lisp (bye)
+
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} {\bf Digital Library of Mathematical Functions},
+http://dlmf.nist.gov
+\bibitem{2} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp213-216
+\end{thebibliography}
+\end{document}
diff --git a/src/input/tancot.input.pamphlet b/src/input/tancot.input.pamphlet
new file mode 100644
index 0000000..8ef163c
--- /dev/null
+++ b/src/input/tancot.input.pamphlet
@@ -0,0 +1,696 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input tancot.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This compares Axiom's tan and cot functions with the tables published in
+Abramowitz and Stegun.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+In the following table there are 4 columns. The first column
+is the argument of tan(x), ranging from 0.01 to 1.60. The
+second column is the reference value of tan from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp186-188
+<<*>>=
+)spool tancot.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 2
+[[0.01,0.010000333,tan(0.01),tan(0.01)-(0.010000333)],_
+[0.02,0.020002667,tan(0.02),tan(0.02)-(0.020002667)],_
+[0.03,0.030009003,tan(0.03),tan(0.03)-(0.030009003)],_
+[0.04,0.040021347,tan(0.04),tan(0.04)-(0.040021347)],_
+[0.05,0.050041708,tan(0.05),tan(0.05)-(0.050041708)],_
+[0.06,0.060072104,tan(0.06),tan(0.06)-(0.060072104)],_
+[0.07,0.070114558,tan(0.07),tan(0.07)-(0.070114558)],_
+[0.08,0.080171105,tan(0.08),tan(0.08)-(0.080171105)],_
+[0.09,0.090243790,tan(0.09),tan(0.09)-(0.090243790)],_
+[0.10,0.10033467,tan(0.10),tan(0.10)-(0.10033467)],_
+[0.11,0.11044582,tan(0.11),tan(0.11)-(0.11044582)],_
+[0.12,0.12057934,tan(0.12),tan(0.12)-(0.12057934)],_
+[0.13,0.13073732,tan(0.13),tan(0.13)-(0.13073732)],_
+[0.14,0.14092189,tan(0.14),tan(0.14)-(0.14092189)],_
+[0.15,0.15113522,tan(0.15),tan(0.15)-(0.15113522)],_
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+[0.17,0.17165682,tan(0.17),tan(0.17)-(0.17165682)],_
+[0.18,0.18196953,tan(0.18),tan(0.18)-(0.18196953)],_
+[0.19,0.19231984,tan(0.19),tan(0.19)-(0.19231984)],_
+[0.20,0.20271004,tan(0.20),tan(0.20)-(0.20271004)],_
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+[0.22,0.22361942,tan(0.22),tan(0.22)-(0.22361942)],_
+[0.23,0.23414336,tan(0.23),tan(0.23)-(0.23414336)],_
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+[0.26,0.26602154,tan(0.26),tan(0.26)-(0.26602154)],_
+[0.27,0.27675814,tan(0.27),tan(0.27)-(0.27675814)],_
+[0.28,0.28755433,tan(0.28),tan(0.28)-(0.28755433)],_
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+[0.30,0.30933625,tan(0.30),tan(0.30)-(0.30933625)],_
+[0.31,0.32032751,tan(0.31),tan(0.31)-(0.32032751)],_
+[0.32,0.33138941,tan(0.32),tan(0.32)-(0.33138941)],_
+[0.33,0.34252487,tan(0.33),tan(0.33)-(0.34252487)],_
+[0.34,0.35373688,tan(0.34),tan(0.34)-(0.35373688)],_
+[0.35,0.36502849,tan(0.35),tan(0.35)-(0.36502849)],_
+[0.36,0.37640285,tan(0.36),tan(0.36)-(0.37640285)],_
+[0.37,0.38786316,tan(0.37),tan(0.37)-(0.38786316)],_
+[0.38,0.39941272,tan(0.38),tan(0.38)-(0.39941272)],_
+[0.39,0.41105492,tan(0.39),tan(0.39)-(0.41105492)],_
+[0.40,0.42279322,tan(0.40),tan(0.40)-(0.42279322)],_
+[0.41,0.43463120,tan(0.41),tan(0.41)-(0.43463120)],_
+[0.42,0.44657255,tan(0.42),tan(0.42)-(0.44657255)],_
+[0.43,0.45862102,tan(0.43),tan(0.43)-(0.45862102)],_
+[0.44,0.47078053,tan(0.44),tan(0.44)-(0.47078053)],_
+[0.45,0.48305507,tan(0.45),tan(0.45)-(0.48305507)],_
+[0.46,0.49544877,tan(0.46),tan(0.46)-(0.49544877)],_
+[0.47,0.50796590,tan(0.47),tan(0.47)-(0.50796590)],_
+[0.48,0.52061084,tan(0.48),tan(0.48)-(0.52061084)],_
+[0.49,0.53338815,tan(0.49),tan(0.49)-(0.53338815)],_
+[0.50,0.54630249,tan(0.50),tan(0.50)-(0.54630249)],_
+[0.51,0.55935872,tan(0.51),tan(0.51)-(0.55935872)],_
+[0.52,0.57256183,tan(0.52),tan(0.52)-(0.57256183)],_
+[0.53,0.58591701,tan(0.53),tan(0.53)-(0.58591701)],_
+[0.54,0.59942962,tan(0.54),tan(0.54)-(0.59942962)],_
+[0.55,0.61310521,tan(0.55),tan(0.55)-(0.61310521)],_
+[0.56,0.62694954,tan(0.56),tan(0.56)-(0.62694954)],_
+[0.57,0.64096855,tan(0.57),tan(0.57)-(0.64096855)],_
+[0.58,0.65516845,tan(0.58),tan(0.58)-(0.65516845)],_
+[0.59,0.66955565,tan(0.59),tan(0.59)-(0.66955565)],_
+[0.60,0.68413681,tan(0.60),tan(0.60)-(0.68413681)],_
+[0.61,0.69891886,tan(0.61),tan(0.61)-(0.69891886)],_
+[0.62,0.71390901,tan(0.62),tan(0.62)-(0.71390901)],_
+[0.63,0.72911473,tan(0.63),tan(0.63)-(0.72911473)],_
+[0.64,0.74454382,tan(0.64),tan(0.64)-(0.74454382)],_
+[0.65,0.76020440,tan(0.65),tan(0.65)-(0.76020440)],_
+[0.66,0.77610491,tan(0.66),tan(0.66)-(0.77610491)],_
+[0.67,0.79225417,tan(0.67),tan(0.67)-(0.79225417)],_
+[0.68,0.80866138,tan(0.68),tan(0.68)-(0.80866138)],_
+[0.69,0.82533611,tan(0.69),tan(0.69)-(0.82533611)],_
+[0.70,0.84228838,tan(0.70),tan(0.70)-(0.84228838)],_
+[0.71,0.85952867,tan(0.71),tan(0.71)-(0.85952867)],_
+[0.72,0.87706790,tan(0.72),tan(0.72)-(0.87706790)],_
+[0.73,0.89491753,tan(0.73),tan(0.73)-(0.89491753)],_
+[0.74,0.91308953,tan(0.74),tan(0.74)-(0.91308953)],_
+[0.75,0.93159646,tan(0.75),tan(0.75)-(0.93159646)],_
+[0.76,0.95045146,tan(0.76),tan(0.76)-(0.95045146)],_
+[0.77,0.96966833,tan(0.77),tan(0.77)-(0.96966833)],_
+[0.78,0.98926154,tan(0.78),tan(0.78)-(0.98926154)],_
+[0.79,1.00924629,tan(0.79),tan(0.79)-(1.00924629)],_
+[0.80,1.02963857,tan(0.80),tan(0.80)-(1.02963857)],_
+[0.81,1.05045514,tan(0.81),tan(0.81)-(1.05045514)],_
+[0.82,1.07171372,tan(0.82),tan(0.82)-(1.07171372)],_
+[0.83,1.09343292,tan(0.83),tan(0.83)-(1.09343292)],_
+[0.84,1.11563235,tan(0.84),tan(0.84)-(1.11563235)],_
+[0.85,1.13833271,tan(0.85),tan(0.85)-(1.13833271)],_
+[0.86,1.16155586,tan(0.86),tan(0.86)-(1.16155586)],_
+[0.87,1.18532486,tan(0.87),tan(0.87)-(1.18532486)],_
+[0.88,1.20966412,tan(0.88),tan(0.88)-(1.20966412)],_
+[0.89,1.23459946,tan(0.89),tan(0.89)-(1.23459946)],_
+[0.90,1.26015822,tan(0.90),tan(0.90)-(1.26015822)],_
+[0.91,1.28636938,tan(0.91),tan(0.91)-(1.28636938)],_
+[0.92,1.31326370,tan(0.92),tan(0.92)-(1.31326370)],_
+[0.93,1.34087383,tan(0.93),tan(0.93)-(1.34087383)],_
+[0.94,1.36923448,tan(0.94),tan(0.94)-(1.36923448)],_
+[0.95,1.39838259,tan(0.95),tan(0.95)-(1.39838259)],_
+[0.96,1.42835749,tan(0.96),tan(0.96)-(1.42835749)],_
+[0.97,1.45920113,tan(0.97),tan(0.97)-(1.45920113)],_
+[0.98,1.49095827,tan(0.98),tan(0.98)-(1.49095827)],_
+[0.99,1.52367674,tan(0.99),tan(0.99)-(1.52367674)],_
+[1.00,1.55740772,tan(1.00),tan(1.00)-(1.55740772)],_
+[1.01,1.5922060,tan(1.01),tan(1.01)-(1.5922060)],_
+[1.02,1.6281304,tan(1.02),tan(1.02)-(1.6281304)],_
+[1.03,1.6652440,tan(1.03),tan(1.03)-(1.6652440)],_
+[1.04,1.7036146,tan(1.04),tan(1.04)-(1.7036146)],_
+[1.05,1.7433153,tan(1.05),tan(1.05)-(1.7433153)],_
+[1.06,1.7844248,tan(1.06),tan(1.06)-(1.7844248)],_
+[1.07,1.8270282,tan(1.07),tan(1.07)-(1.8270282)],_
+[1.08,1.8712173,tan(1.08),tan(1.08)-(1.8712173)],_
+[1.09,1.9170918,tan(1.09),tan(1.09)-(1.9170918)],_
+[1.10,1.9647597,tan(1.10),tan(1.10)-(1.9647597)],_
+[1.11,2.0143382,tan(1.11),tan(1.11)-(2.0143382)],_
+[1.12,2.0659553,tan(1.12),tan(1.12)-(2.0659553)],_
+[1.13,2.1197501,tan(1.13),tan(1.13)-(2.1197501)],_
+[1.14,2.1758751,tan(1.14),tan(1.14)-(2.1758751)],_
+[1.15,2.2344969,tan(1.15),tan(1.15)-(2.2344969)],_
+[1.16,2.2957985,tan(1.16),tan(1.16)-(2.2957985)],_
+[1.17,2.3599811,tan(1.17),tan(1.17)-(2.3599811)],_
+[1.18,2.4272664,tan(1.18),tan(1.18)-(2.4272664)],_
+[1.19,2.4978994,tan(1.19),tan(1.19)-(2.4978994)],_
+[1.20,2.5721516,tan(1.20),tan(1.20)-(2.5721516)],_
+[1.21,2.6503246,tan(1.21),tan(1.21)-(2.6503246)],_
+[1.22,2.7327542,tan(1.22),tan(1.22)-(2.7327542)],_
+[1.23,2.8198157,tan(1.23),tan(1.23)-(2.8198157)],_
+[1.24,2.9119299,tan(1.24),tan(1.24)-(2.9119299)],_
+[1.25,3.0095697,tan(1.25),tan(1.25)-(3.0095697)],_
+[1.26,3.1132691,tan(1.26),tan(1.26)-(3.1132691)],_
+[1.27,3.2236332,tan(1.27),tan(1.27)-(3.2236332)],_
+[1.28,3.3413500,tan(1.28),tan(1.28)-(3.3413500)],_
+[1.29,3.4672057,tan(1.29),tan(1.29)-(3.4672057)],_
+[1.30,3.6021024,tan(1.30),tan(1.30)-(3.6021024)],_
+[1.31,3.7470810,tan(1.31),tan(1.31)-(3.7470810)],_
+[1.32,3.9033478,tan(1.32),tan(1.32)-(3.9033478)],_
+[1.33,4.0723098,tan(1.33),tan(1.33)-(4.0723098)],_
+[1.34,4.2556179,tan(1.34),tan(1.34)-(4.2556179)],_
+[1.35,4.4552218,tan(1.35),tan(1.35)-(4.4552218)],_
+[1.36,4.6734412,tan(1.36),tan(1.36)-(4.6734412)],_
+[1.37,4.9130581,tan(1.37),tan(1.37)-(4.9130581)],_
+[1.38,5.1774374,tan(1.38),tan(1.38)-(5.1774374)],_
+[1.39,5.4706886,tan(1.39),tan(1.39)-(5.4706886)],_
+[1.40,5.7978837,tan(1.40),tan(1.40)-(5.7978837)],_
+[1.41,6.1653561,tan(1.41),tan(1.41)-(6.1653561)],_
+[1.42,6.5811195,tan(1.42),tan(1.42)-(6.5811195)],_
+[1.43,7.0554638,tan(1.43),tan(1.43)-(7.0554638)],_
+[1.44,7.6018261,tan(1.44),tan(1.44)-(7.6018261)],_
+[1.45,8.2380928,tan(1.45),tan(1.45)-(8.2380928)],_
+[1.46,8.9886076,tan(1.46),tan(1.46)-(8.9886076)],_
+[1.47,9.8873749,tan(1.47),tan(1.47)-(9.8873749)],_
+[1.48,10.9833793,tan(1.48),tan(1.48)-(10.9833793)],_
+[1.49,12.3498564,tan(1.49),tan(1.49)-(12.3498564)],_
+[1.50,14.1014199,tan(1.50),tan(1.50)-(14.1014199)],_
+[1.51,16.4280917,tan(1.51),tan(1.51)-(16.4280917)],_
+[1.52,19.6695278,tan(1.52),tan(1.52)-(19.6695278)],_
+[1.53,24.4984104,tan(1.53),tan(1.53)-(24.4984104)],_
+[1.54,32.4611389,tan(1.54),tan(1.54)-(32.4611389)],_
+[1.55,48.0784825,tan(1.55),tan(1.55)-(48.0784825)],_
+[1.56,92.6204963,tan(1.56),tan(1.56)-(92.6204963)],_
+[1.57,1255.7655915,tan(1.57),tan(1.57)-(1255.7655915)],_
+[1.58,-108.6492036,tan(1.58),tan(1.58)-(-108.6492036)],_
+[1.59,-52.0669696,tan(1.59),tan(1.59)-(-52.0669696)],_
+[1.60,-34.2325327,tan(1.60),tan(1.60)-(-34.2325327)]]
+--R
+--R
+--R (1)
+--R [[0.01,0.010000333,0.0100003333 4666720637 1,0.3466672063 71 E -9],
+--R [0.02,0.020002667,0.0200026670 9340242389 7,0.9340242389 7 E -10],
+--R [0.03,0.030009003,0.0300090032 4118071632 9,0.2411807163 29 E -9],
+--R [0.04,0.040021347,0.0400213469 9551456207 2,- 0.4485437928 E -11],
+--R [0.05,0.050041708,0.0500417083 7553878891 2,0.3755387889 12 E -9],
+--R [0.06,0.060072104,0.0600721038 3129728751 1,- 0.1687027124 9 E -9],
+--R [0.07,0.070114558,0.0701145578 7200271322 9,- 0.1279972867 7 E -9],
+--R [0.08,0.080171105,0.0801711047 0807255711 8,- 0.2919274428 8 E -9],
+--R [0.09,0.09024379,0.0902437899 0978545046 6,- 0.9021454953 4 E -10],
+--R [0.1,0.10033467,0.1003346720 8545054506,0.2085450545 06 E -8],
+--R [0.11,0.11044582,0.1104458245 820405045,0.4582040504 5 E -8],
+--R [0.12,0.12057934,0.1205793372 1130531183,- 0.2788694688 17 E -8],
+--R [0.13,0.13073732,0.1307373180 0446004867,- 0.1995539951 33 E -8],
+--R [0.14,0.14092189,0.1409218949 9862537921,0.4998625379 21 E -8],
+--R [0.15,0.15113522,0.1511352180 5829507125,- 0.1941704928 75 E -8],
+--R [0.16,0.16137946,0.1613794607 3521095024,0.7352109502 4 E -9],
+--R [0.17,0.17165682,0.1716568221 7014270414,0.2170142704 14 E -8],
+--R [0.18,0.18196953,0.1819695290 4019848684,- 0.9598015131 64 E -9],
+--R [0.19,0.19231984,0.1923198375 554329145,- 0.2444567085 5 E -8],
+--R [0.2,0.20271004,0.2027100355 0867248332,- 0.4491327516 68 E -8],
+--R [0.21,0.21314244,0.2131424443 8264539723,0.4382645397 23 E -8],
+--R [0.22,0.22361942,0.2236194215 1868409245,0.1518684092 45 E -8],
+--R [0.23,0.23414336,0.2341433623 5146527061,0.2351465270 61 E -8],
+--R [0.24,0.2447167,0.2447167027 1446497862,0.2714464978 62 E -8],
+--R [0.25,0.25534192,0.2553419212 2103626651,0.1221036266 5 E -8],
+--R [0.26,0.26602154,0.2660215417 2626537908,0.1726265379 1 E -8],
+--R [0.27,0.27675814,0.2767581358 7503056579,- 0.4124969434 21 E -8],
+--R [0.28,0.28755433,0.2875543257 41976815,- 0.4258023185 E -8],
+--R [0.29,0.29841279,0.2984127865 694316513,- 0.3430568348 7 E -8],
+--R [0.3,0.30933625,0.3093362496 0962323304,- 0.3903767669 6 E -9],
+--R [0.31,0.32032751,0.3203275050 7792416023,- 0.4922075839 77 E -8],
+--R [0.32,0.33138941,0.3313894052 2423462352,- 0.4775765376 48 E -8],
+--R [0.33,0.34252487,0.3425248675 3003894803,- 0.2469961051 97 E -8],
+--R [0.34,0.35373688,0.3537368780 3912256577,- 0.1960877434 23 E -8],
+--R [0.35,0.36502849,0.3650284948 3042455832,0.4830424558 32 E -8],
+--R [0.36,0.37640285,0.3764028516 4202695764,0.1642026957 6 E -8],
+--R [0.37,0.38786316,0.3878631616 5584905222,0.1655849052 2 E -8],
+--R [0.38,0.39941272,0.3994127214 5322637827,0.1453226378 3 E -8],
+--R [0.39,0.41105492,0.4110549151 5221356343,- 0.4847786436 57 E -8],
+--R [0.4,0.42279322,0.4227932187 3816176198,- 0.1261838238 E -8],
+--R [0.41,0.4346312,0.4346312045 9988949299,0.4599889492 99 E -8],
+--R [0.42,0.44657255,0.4465725462 8459510803,- 0.3715404891 96 E -8],
+--R [0.43,0.45862102,0.4586210234 8555518632,0.3485555186 32 E -8],
+--R [0.44,0.47078053,0.4707805272 7762171492,- 0.2722378285 08 E -8],
+--R [0.45,0.48305507,0.4830550656 1657837051,- 0.4383421629 49 E -8],
+--R [0.46,0.49544877,0.4954487691 1954962242,- 0.8804503775 8 E -9],
+--R [0.47,0.5079659,0.5079658971 4488348004,- 0.285511652 E -8],
+--R [0.48,0.52061084,0.5206108441 9125804964,0.4191258049 65 E -8],
+--R [0.49,0.53338815,0.5333881466 3720305695,- 0.3362796943 1 E -8],
+--R [0.5,0.54630249,0.5463024898 4379051326,- 0.1562094867 E -9],
+--R [0.51,0.55935872,0.5593587156 4494521344,- 0.4355054786 56 E -8],
+--R [0.52,0.57256183,0.5725618302 5166841478,0.2516684148 E -9],
+--R [0.53,0.58591701,0.5859170125 9847085812,0.2598470858 1 E -8],
+--R [0.54,0.59942962,0.5994296231 6248975451,0.3162489754 5 E -8],
+--R [0.55,0.61310521,0.6131052132 8813564222,0.3288135642 2 E -8],
+--R [0.56,0.62694954,0.6269495350 5269815933,- 0.4947301840 67 E -8],
+--R [0.57,0.64096855,0.6409685517 1115591313,0.1711155913 1 E -8],
+--R [0.58,0.65516845,0.6551684487 6150824025,- 0.1238491759 7 E -8],
+--R [0.59,0.66955565,0.6695556456 753018611,- 0.4324698138 9 E -8],
+--R [0.6,0.68413681,0.6841368083 4169231707,- 0.1658307682 9 E -8],
+--R [0.61,0.69891886,0.6989188622 7739105048,0.2277391050 5 E -8],
+--R [0.62,0.71390901,0.7139090066 5924020594,- 0.3340759794 1 E -8],
+--R [0.63,0.72911473,0.7291147292 4096908976,- 0.7590309102 4 E -9],
+--R [0.64,0.74454382,0.7445438222 2096388599,0.2220963886 E -8],
+--R [0.65,0.7602044,0.7602043991 3367625635,- 0.8663237436 5 E -9],
+--R [0.66,0.77610491,0.7761049128 4366351779,0.2843663517 8 E -8],
+--R [0.67,0.79225417,0.7922541747 2825678628,0.4728256786 28 E -8],
+--R [0.68,0.80866138,0.8086613751 4256524544,- 0.4857434754 56 E -8],
+--R [0.69,0.82533611,0.8253361052 6902491172,- 0.4730975088 28 E -8],
+--R [0.7,0.84228838,0.8422883804 6307944813,0.4630794481 E -9],
+--R [0.71,0.85952867,0.8595286652 1694081593,- 0.4783059184 07 E -8],
+--R [0.72,0.8770679,0.8770678998 7483414069,- 0.1251658593 E -9],
+--R [0.73,0.89491753,0.8949175292 4581448181,- 0.7541855181 9 E -9],
+--R [0.74,0.91308953,0.9130895332 7430087206,0.3274300872 1 E -8],
+--R [0.75,0.93159646,0.9315964599 4407246117,- 0.559275388 E -10],
+--R [0.76,0.95045146,0.9504514606 0880299797,0.6088029979 7 E -9],
+--R [0.77,0.96966833,0.9696683279 6148947799,- 0.2038510522 E -8],
+--R [0.78,0.98926154,0.9892615368 7660491155,- 0.3123395088 4 E -8],
+--R [0.79,1.00924629,1.0092462883 827548811,- 0.1617245118 9 E -8],
+--R [0.8,1.02963857,1.0296385570 503640128,- 0.1294963598 73 E -7],
+--R [0.81,1.05045514,1.0504551421 088292806,0.2108829280 6 E -8],
+--R [0.82,1.07171372,1.0717137226 410736441,0.2641073644 1 E -8],
+--R [0.83,1.09343292,1.0934329172 409999188,- 0.2759000081 2 E -8],
+--R [0.84,1.11563235,1.1156323485 615378951,- 0.1438462104 9 E -8],
+--R [0.85,1.13833271,1.1383327132 284394134,0.3228439413 4 E -8],
+--R [0.86,1.16155586,1.1615558576 484476046,- 0.2351552395 4 E -8],
+--R [0.87,1.18532486,1.1853248603 008053505,0.3008053505 E -9],
+--R [0.88,1.20966412,1.2096641211 692683367,0.1169268336 7 E -8],
+--R [0.89,1.23459946,1.2345994590 490045825,- 0.9509954175 3 E -9],
+--R [0.9,1.26015822,1.2601582175 503391371,- 0.2449660862 9 E -8],
+--R [0.91,1.28636938,1.2863693807 208075758,0.7208075758 E -9],
+--R [0.92,1.3132637,1.3132636993 202478365,- 0.6797521635 E -9],
+--R [0.93,1.34087383,1.3408738289 128343042,- 0.1087165695 8 E -8],
+--R [0.94,1.36923448,1.3692344810 875628038,0.1087562803 8 E -8],
+--R [0.95,1.39838259,1.3983825892 876991461,- 0.7123008539 E -9],
+--R [0.96,1.42835749,1.4283574909 236105601,0.9236105601 E -9],
+--R [0.97,1.45920113,1.4592011276 663536858,- 0.2333646314 2 E -8],
+--R [0.98,1.49095827,1.4909582660 763114779,- 0.3923688522 1 E -8],
+--R [0.99,1.52367674,1.5236767410 179022725,0.1017902272 5 E -8],
+--R [1.0,1.55740772,1.5574077246 549022305,0.4654902230 5 E -8],
+--R [1.01,1.592206,1.5922060242 195703744,0.2421957037 44 E -7],
+--R [1.02,1.6281304,1.6281304122 125526001,0.1221255260 01 E -7],
+--R [1.03,1.665244,1.6652439932 315124346,- 0.6768487565 4 E -8],
+--R [1.04,1.7036146,1.7036146122 591331094,0.1225913310 94 E -7],
+--R [1.05,1.7433153,1.7433153099 831702625,0.9983170262 47 E -8],
+--R [1.06,1.7844248,1.7844248315 940126524,0.3159401265 24 E -7],
+--R [1.07,1.8270282,1.8270281965 348367381,- 0.3465163261 9 E -8],
+--R [1.08,1.8712173,1.8712173378 97878195,0.3789787819 5 E -7],
+--R [1.09,1.9170918,1.9170918216 068594024,0.2160685940 24 E -7],
+--R [1.1,1.9647597,1.9647596572 486519509,- 0.4275134804 91 E -7],
+--R [1.11,2.0143382,2.0143382144 768273135,0.1447682731 3 E -7],
+--R [1.12,2.0659553,2.0659552613 80510241,- 0.3861948975 9 E -7],
+--R [1.13,2.1197501,2.1197501441 871810139,0.4418718101 39 E -7],
+--R [1.14,2.1758751,2.1758751312 648761686,0.3126487616 86 E -7],
+--R [1.15,2.2344969,2.2344969487 553259802,0.4875532598 02 E -7],
+--R [1.16,2.2957985,2.2957985404 922076011,0.4049220760 11 E -7],
+--R [1.17,2.3599811,2.3599810913 765482032,- 0.8623451796 7 E -8],
+--R [1.18,2.4272664,2.4272663614 002235775,- 0.3859977642 25 E -7],
+--R [1.19,2.4978994,2.4978993874 226530062,- 0.1257734699 4 E -7],
+--R [1.2,2.5721516,2.5721516221 263189354,0.2212631893 54 E -7],
+--R [1.21,2.6503246,2.6503245949 706014665,- 0.5029398533 5 E -8],
+--R [1.22,2.7327542,2.7327541993 067149987,- 0.6932850013 E -9],
+--R [1.23,2.8198157,2.8198157342 681519748,0.3426815197 48 E -7],
+--R [1.24,2.9119299,2.9119298611 552260267,- 0.3884477397 34 E -7],
+--R [1.25,3.0095697,3.0095696738 628312882,- 0.2613716871 18 E -7],
+--R [1.26,3.1132691,3.1132691342 651312093,0.3426513120 93 E -7],
+--R [1.27,3.2236332,3.2236331902 040711359,- 0.9795928864 E -8],
+--R [1.28,3.34135,3.3413499811 153736983,- 0.1888462630 17 E -7],
+--R [1.29,3.4672057,3.4672056517 213857853,- 0.4827861421 47 E -7],
+--R [1.3,3.6021024,3.6021024479 679781512,0.4796797815 12 E -7],
+--R [1.31,3.747081,3.7470809761 884290733,- 0.2381157092 67 E -7],
+--R [1.32,3.9033478,3.9033477874 966235656,- 0.1250337643 4 E -7],
+--R [1.33,4.0723098,4.0723098354 650698554,0.3546506985 54 E -7],
+--R [1.34,4.2556179,4.2556178917 394653427,- 0.8260534657 3 E -8],
+--R [1.35,4.4552218,4.4552217595 627031753,- 0.4043729682 47 E -7],
+--R [1.36,4.6734412,4.6734412029 885596449,0.2988559645 E -8],
+--R [1.37,4.9130581,4.9130580704 624720101,- 0.2953752799 E -7],
+--R [1.38,5.1774374,5.1774373886 304102949,- 0.1136958970 5 E -7],
+--R [1.39,5.4706886,5.4706886429 532054937,0.4295320549 37 E -7],
+--R [1.4,5.7978837,5.7978837154 828896437,0.1548288964 4 E -7],
+--R [1.41,6.1653561,6.1653561445 520255476,0.4455202554 75 E -7],
+--R [1.42,6.5811195,6.5811194561 942543239,- 0.4380574567 61 E -7],
+--R [1.43,7.0554638,7.0554637664 342109722,- 0.3356578902 78 E -7],
+--R [1.44,7.6018261,7.6018260620 257232407,- 0.3797427675 94 E -7],
+--R [1.45,8.2380928,8.2380927529 656070833,- 0.4703439291 7 E -7],
+--R [1.46,8.9886076,8.9886076017 241695008,0.1724169501 E -8],
+--R [1.47,9.8873749,9.8873748919 855531724,- 0.8014446827 5 E -8],
+--R [1.48,10.9833793,10.9833793143 26067301,0.1432606730 1 E -7],
+--R [1.49,12.3498564,12.3498564416 25802114,0.4162580211 4 E -7],
+--R [1.5,14.1014199,14.1014199471 71719388,0.4717171938 8 E -7],
+--R [1.51,16.4280917,16.4280917038 85335336,0.3885335336 E -8],
+--R [1.52,19.6695278,19.6695278205 58866232,0.2055886623 2 E -7],
+--R [1.53,24.4984104,24.4984104418 38034593,0.4183803459 3 E -7],
+--R [1.54,32.4611389,32.4611389128 56765176,0.1285676518 E -7],
+--R [1.55,48.0784825,48.0784824792 18968279,- 0.2078103172 E -7],
+--R [1.56,92.6204963,92.6204963167 04102469,0.1670410247 E -7],
+--R [1.57,1255.7655915,1255.7655915006 916051,0.6916051 E -9],
+--R [1.58,- 108.6492036,- 108.6492036048 4393447,- 0.484393447 E -8],
+--R [1.59,- 52.0669696,- 52.0669696509 12563554,- 0.5091256355 4 E -7],
+--R [1.6,- 34.2325327,- 34.2325327355 57417056,- 0.3555741705 7 E -7]]
+--R Type: List List
Float
+--E 1
+@
+In the following table there are 4 columns. The first column
+is the argument of tan(x), ranging from 0.01 to 1.60. The
+second column is the reference value of tan from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp186-188
+<<*>>=
+
+--S 2 of 2
+[[0.01,99.9966666,cot(0.01),cot(0.01)-(99.9966666)],_
+[0.02,49.9933332,cot(0.02),cot(0.02)-(49.9933332)],_
+[0.03,33.3233327,cot(0.03),cot(0.03)-(33.3233327)],_
+[0.04,24.9866652,cot(0.04),cot(0.04)-(24.9866652)],_
+[0.05,19.9833306,cot(0.05),cot(0.05)-(19.9833306)],_
+[0.06,16.6466619,cot(0.06),cot(0.06)-(16.6466619)],_
+[0.07,14.2623733,cot(0.07),cot(0.07)-(14.2623733)],_
+[0.08,12.4733219,cot(0.08),cot(0.08)-(12.4733219)],_
+[0.09,11.0810949,cot(0.09),cot(0.09)-(11.0810949)],_
+[0.10,9.9666444,cot(0.10),cot(0.10)-(9.9666444)],_
+[0.11,9.0542128,cot(0.11),cot(0.11)-(9.0542128)],_
+[0.12,8.2932949,cot(0.12),cot(0.12)-(8.2932949)],_
+[0.13,7.6489255,cot(0.13),cot(0.13)-(7.6489255)],_
+[0.14,7.0961294,cot(0.14),cot(0.14)-(7.0961294)],_
+[0.15,6.6165915,cot(0.15),cot(0.15)-(6.6165915)],_
+[0.16,6.1965754,cot(0.16),cot(0.16)-(6.1965754)],_
+[0.17,5.8255768,cot(0.17),cot(0.17)-(5.8255768)],_
+[0.18,5.4954256,cot(0.18),cot(0.18)-(5.4954256)],_
+[0.19,5.1996716,cot(0.19),cot(0.19)-(5.1996716)],_
+[0.20,4.9331549,cot(0.20),cot(0.20)-(4.9331549)],_
+[0.21,4.6916981,cot(0.21),cot(0.21)-(4.6916981)],_
+[0.22,4.4718835,cot(0.22),cot(0.22)-(4.4718835)],_
+[0.23,4.2708877,cot(0.23),cot(0.23)-(4.2708877)],_
+[0.24,4.0863578,cot(0.24),cot(0.24)-(4.0863578)],_
+[0.25,3.9163174,cot(0.25),cot(0.25)-(3.9163174)],_
+[0.26,3.7590941,cot(0.26),cot(0.26)-(3.7590941)],_
+[0.27,3.6132632,cot(0.27),cot(0.27)-(3.6132632)],_
+[0.28,3.4776037,cot(0.28),cot(0.28)-(3.4776037)],_
+[0.29,3.3510628,cot(0.29),cot(0.29)-(3.3510628)],_
+[0.30,3.2327281,cot(0.30),cot(0.30)-(3.2327281)],_
+[0.31,3.1218050,cot(0.31),cot(0.31)-(3.1218050)],_
+[0.32,3.0175980,cot(0.32),cot(0.32)-(3.0175980)],_
+[0.33,2.9194961,cot(0.33),cot(0.33)-(2.9194961)],_
+[0.34,2.8269600,cot(0.34),cot(0.34)-(2.8269600)],_
+[0.35,2.7395122,cot(0.35),cot(0.35)-(2.7395122)],_
+[0.36,2.6567280,cot(0.36),cot(0.36)-(2.6567280)],_
+[0.37,2.5782289,cot(0.37),cot(0.37)-(2.5782289)],_
+[0.38,2.5036759,cot(0.38),cot(0.38)-(2.5036759)],_
+[0.39,2.4327650,cot(0.39),cot(0.39)-(2.4327650)],_
+[0.40,2.3652224,cot(0.40),cot(0.40)-(2.3652224)],_
+[0.41,2.3008012,cot(0.41),cot(0.41)-(2.3008012)],_
+[0.42,2.2392778,cot(0.42),cot(0.42)-(2.2392778)],_
+[0.43,2.1804495,cot(0.43),cot(0.43)-(2.1804495)],_
+[0.44,2.1241320,cot(0.44),cot(0.44)-(2.1241320)],_
+[0.45,2.0701574,cot(0.45),cot(0.45)-(2.0701574)],_
+[0.46,2.0183722,cot(0.46),cot(0.46)-(2.0183722)],_
+[0.47,1.9686361,cot(0.47),cot(0.47)-(1.9686361)],_
+[0.48,1.9208205,cot(0.48),cot(0.48)-(1.9208205)],_
+[0.49,1.8748073,cot(0.49),cot(0.49)-(1.8748073)],_
+[0.50,1.83048772,cot(0.50),cot(0.50)-(1.83048772)],_
+[0.51,1.78776154,cot(0.51),cot(0.51)-(1.78776154)],_
+[0.52,1.74653626,cot(0.52),cot(0.52)-(1.74653626)],_
+[0.53,1.70672634,cot(0.53),cot(0.53)-(1.70672634)],_
+[0.54,1.66825255,cot(0.54),cot(0.54)-(1.66825255)],_
+[0.55,1.63104142,cot(0.55),cot(0.55)-(1.63104142)],_
+[0.56,1.59502471,cot(0.56),cot(0.56)-(1.59502471)],_
+[0.57,1.56013894,cot(0.57),cot(0.57)-(1.56013894)],_
+[0.58,1.52632503,cot(0.58),cot(0.58)-(1.52632503)],_
+[0.59,1.49352784,cot(0.59),cot(0.59)-(1.49352784)],_
+[0.60,1.46169595,cot(0.60),cot(0.60)-(1.46169595)],_
+[0.61,1.43078125,cot(0.61),cot(0.61)-(1.43078125)],_
+[0.62,1.40073873,cot(0.62),cot(0.62)-(1.40073873)],_
+[0.63,1.37152626,cot(0.63),cot(0.63)-(1.37152626)],_
+[0.64,1.34310429,cot(0.64),cot(0.64)-(1.34310429)],_
+[0.65,1.31543569,cot(0.65),cot(0.65)-(1.31543569)],_
+[0.66,1.28848559,cot(0.66),cot(0.66)-(1.28848559)],_
+[0.67,1.26222118,cot(0.67),cot(0.67)-(1.26222118)],_
+[0.68,1.23661155,cot(0.68),cot(0.68)-(1.23661155)],_
+[0.69,1.21162759,cot(0.69),cot(0.69)-(1.21162759)],_
+[0.70,1.18724183,cot(0.70),cot(0.70)-(1.18724183)],_
+[0.71,1.16342833,cot(0.71),cot(0.71)-(1.16342833)],_
+[0.72,1.14016258,cot(0.72),cot(0.72)-(1.14016258)],_
+[0.73,1.11742140,cot(0.73),cot(0.73)-(1.11742140)],_
+[0.74,1.09518285,cot(0.74),cot(0.74)-(1.09518285)],_
+[0.75,1.07342615,cot(0.75),cot(0.75)-(1.07342615)],_
+[0.76,1.05213158,cot(0.76),cot(0.76)-(1.05213158)],_
+[0.77,1.03128046,cot(0.77),cot(0.77)-(1.03128046)],_
+[0.78,1.01085503,cot(0.78),cot(0.78)-(1.01085503)],_
+[0.79,0.99083842,cot(0.79),cot(0.79)-(0.99083842)],_
+[0.80,0.97121460,cot(0.80),cot(0.80)-(0.97121460)],_
+[0.81,0.95196830,cot(0.81),cot(0.81)-(0.95196830)],_
+[0.82,0.93308500,cot(0.82),cot(0.82)-(0.93308500)],_
+[0.83,0.91455085,cot(0.83),cot(0.83)-(0.91455085)],_
+[0.84,0.89635264,cot(0.84),cot(0.84)-(0.89635264)],_
+[0.85,0.87847778,cot(0.85),cot(0.85)-(0.87847778)],_
+[0.86,0.86091426,cot(0.86),cot(0.86)-(0.86091426)],_
+[0.87,0.84365058,cot(0.87),cot(0.87)-(0.84365058)],_
+[0.88,0.82667575,cot(0.88),cot(0.88)-(0.82667575)],_
+[0.89,0.80997930,cot(0.89),cot(0.89)-(0.80997930)],_
+[0.90,0.79355115,cot(0.90),cot(0.90)-(0.79355115)],_
+[0.91,0.77738169,cot(0.91),cot(0.91)-(0.77738169)],_
+[0.92,0.76146169,cot(0.92),cot(0.92)-(0.76146169)],_
+[0.93,0.74578232,cot(0.93),cot(0.93)-(0.74578232)],_
+[0.94,0.73033510,cot(0.94),cot(0.94)-(0.73033510)],_
+[0.95,0.71511188,cot(0.95),cot(0.95)-(0.71511188)],_
+[0.96,0.70010485,cot(0.96),cot(0.96)-(0.70010485)],_
+[0.97,0.68530649,cot(0.97),cot(0.97)-(0.68530649)],_
+[0.98,0.67070959,cot(0.98),cot(0.98)-(0.67070959)],_
+[0.99,0.65630719,cot(0.99),cot(0.99)-(0.65630719)],_
+[1.00,0.64209262,cot(1.00),cot(1.00)-(0.64209262)],_
+[1.01,0.62805942,cot(1.01),cot(1.01)-(0.62805942)],_
+[1.02,0.61420141,cot(1.02),cot(1.02)-(0.61420141)],_
+[1.03,0.60051260,cot(1.03),cot(1.03)-(0.60051260)],_
+[1.04,0.58698722,cot(1.04),cot(1.04)-(0.58698722)],_
+[1.05,0.57361970,cot(1.05),cot(1.05)-(0.57361970)],_
+[1.06,0.56040467,cot(1.06),cot(1.06)-(0.56040467)],_
+[1.07,0.54733693,cot(1.07),cot(1.07)-(0.54733693)],_
+[1.08,0.53441147,cot(1.08),cot(1.08)-(0.53441147)],_
+[1.09,0.52162342,cot(1.09),cot(1.09)-(0.52162342)],_
+[1.10,0.50896811,cot(1.10),cot(1.10)-(0.50896811)],_
+[1.11,0.49644096,cot(1.11),cot(1.11)-(0.49644096)],_
+[1.12,0.48403759,cot(1.12),cot(1.12)-(0.48403759)],_
+[1.13,0.47175371,cot(1.13),cot(1.13)-(0.47175371)],_
+[1.14,0.45958520,cot(1.14),cot(1.14)-(0.45958520)],_
+[1.15,0.44752802,cot(1.15),cot(1.15)-(0.44752802)],_
+[1.16,0.43557829,cot(1.16),cot(1.16)-(0.43557829)],_
+[1.17,0.42373221,cot(1.17),cot(1.17)-(0.42373221)],_
+[1.18,0.41198610,cot(1.18),cot(1.18)-(0.41198610)],_
+[1.19,0.40033638,cot(1.19),cot(1.19)-(0.40033638)],_
+[1.20,0.38877957,cot(1.20),cot(1.20)-(0.38877957)],_
+[1.21,0.37731227,cot(1.21),cot(1.21)-(0.37731227)],_
+[1.22,0.36593119,cot(1.22),cot(1.22)-(0.36593119)],_
+[1.23,0.35463310,cot(1.23),cot(1.23)-(0.35463310)],_
+[1.24,0.34341486,cot(1.24),cot(1.24)-(0.34341486)],_
+[1.25,0.33227342,cot(1.25),cot(1.25)-(0.33227342)],_
+[1.26,0.32120577,cot(1.26),cot(1.26)-(0.32120577)],_
+[1.27,0.31020899,cot(1.27),cot(1.27)-(0.31020899)],_
+[1.28,0.29928023,cot(1.28),cot(1.28)-(0.29928023)],_
+[1.29,0.28841670,cot(1.29),cot(1.29)-(0.28841670)],_
+[1.30,0.27761565,cot(1.30),cot(1.30)-(0.27761565)],_
+[1.31,0.26687440,cot(1.31),cot(1.31)-(0.26687440)],_
+[1.32,0.25619034,cot(1.32),cot(1.32)-(0.25619034)],_
+[1.33,0.24556088,cot(1.33),cot(1.33)-(0.24556088)],_
+[1.34,0.23498350,cot(1.34),cot(1.34)-(0.23498350)],_
+[1.35,0.22445572,cot(1.35),cot(1.35)-(0.22445572)],_
+[1.36,0.21397509,cot(1.36),cot(1.36)-(0.21397509)],_
+[1.37,0.20353922,cot(1.37),cot(1.37)-(0.20353922)],_
+[1.38,0.19314574,cot(1.38),cot(1.38)-(0.19314574)],_
+[1.39,0.18279234,cot(1.39),cot(1.39)-(0.18279234)],_
+[1.40,0.17247673,cot(1.40),cot(1.40)-(0.17247673)],_
+[1.41,0.16219663,cot(1.41),cot(1.41)-(0.16219663)],_
+[1.42,0.15194983,cot(1.42),cot(1.42)-(0.15194983)],_
+[1.43,0.14173413,cot(1.43),cot(1.43)-(0.14173413)],_
+[1.44,0.13154734,cot(1.44),cot(1.44)-(0.13154734)],_
+[1.45,0.12138732,cot(1.45),cot(1.45)-(0.12138732)],_
+[1.46,0.11125194,cot(1.46),cot(1.46)-(0.11125194)],_
+[1.47,0.10113908,cot(1.47),cot(1.47)-(0.10113908)],_
+[1.48,0.091046660,cot(1.48),cot(1.48)-(0.091046660)],_
+[1.49,0.080972601,cot(1.49),cot(1.49)-(0.080972601)],_
+[1.50,0.070914844,cot(1.50),cot(1.50)-(0.070914844)],_
+[1.51,0.060871343,cot(1.51),cot(1.51)-(0.060871343)],_
+[1.52,0.050840061,cot(1.52),cot(1.52)-(0.050840061)],_
+[1.53,0.040818975,cot(1.53),cot(1.53)-(0.040818975)],_
+[1.54,0.030806066,cot(1.54),cot(1.54)-(0.030806066)],_
+[1.55,0.020799325,cot(1.55),cot(1.55)-(0.020799325)],_
+[1.56,0.010796746,cot(1.56),cot(1.56)-(0.010796746)],_
+[1.57,0.000796327,cot(1.57),cot(1.57)-(0.000796327)],_
+[1.58,-0.009203933,cot(1.58),cot(1.58)-(-0.009203933)],_
+[1.59,-0.019206034,cot(1.59),cot(1.59)-(-0.019206034)],_
+[1.60,-0.029211978,cot(1.60),cot(1.60)-(-0.029211978)]]
+--R
+--R
+--R (2)
+--R [[0.01,99.9966666,99.9966666444 44232802,0.444442328 E -7],
+--R [0.02,49.9933332,49.9933331555 48782798,- 0.4445121720 2 E -7],
+--R [0.03,33.3233327,33.3233327332 81900133,0.3328190013 3 E -7],
+--R [0.04,24.9866652,24.9866652442 27690187,0.4422769018 7 E -7],
+--R [0.05,19.9833306,19.9833305548 94014508,- 0.4510598549 1 E -7],
+--R [0.06,16.6466619,16.6466618650 20359708,- 0.3497964029 2 E -7],
+--R [0.07,14.2623733,14.2623733265 9994931,0.2659994931 E -7],
+--R [0.08,12.4733219,12.4733219486 16087812,0.4861608781 2 E -7],
+--R [0.09,11.0810949,11.0810948986 03837279,- 0.1396162721 E -8],
+--R [0.1,9.9666444,9.9666444232 592378598,0.2325923786 E -7],
+--R [0.11,9.0542128,9.0542128123 384855803,0.1233848558 E -7],
+--R [0.12,8.2932949,8.2932948805 945312103,- 0.1940546879 E -7],
+--R [0.13,7.6489255,7.6489254580 38579468,- 0.4196142053 2 E -7],
+--R [0.14,7.0961294,7.0961293843 639732986,- 0.1563602670 1 E -7],
+--R [0.15,6.6165915,6.6165915055 899500987,0.5589950098 7 E -8],
+--R [0.16,6.1965754,6.1965754219 540076277,0.2195400762 8 E -7],
+--R [0.17,5.8255768,5.8255767953 622059416,- 0.4637794058 4 E -8],
+--R [0.18,5.4954256,5.4954255543 470259144,- 0.4565297408 56 E -7],
+--R [0.19,5.1996716,5.1996716132 404544488,0.1324045444 9 E -7],
+--R [0.2,4.9331549,4.9331548755 868936573,- 0.2441310634 3 E -7],
+--R [0.21,4.6916981,4.6916980937 15878191,- 0.6284121809 E -8],
+--R [0.22,4.4718835,4.4718834938 782225379,- 0.6121777462 1 E -8],
+--R [0.23,4.2708877,4.2708876730 783907862,- 0.2692160921 4 E -7],
+--R [0.24,4.0863578,4.0863577716 916129493,- 0.2830838705 1 E -7],
+--R [0.25,3.9163174,3.9163173646 45940105,- 0.3535405989 5 E -7],
+--R [0.26,3.7590941,3.7590940700 170597097,- 0.2998294029 03 E -7],
+--R [0.27,3.6132632,3.6132632445 954451122,0.4459544511 22 E -7],
+--R [0.28,3.4776037,3.4776037446 826739597,0.4468267395 97 E -7],
+--R [0.29,3.3510628,3.3510628398 201367735,0.3982013677 35 E -7],
+--R [0.3,3.2327281,3.2327281437 658275137,0.4376582751 37 E -7],
+--R [0.31,3.121805,3.1218049781 792418003,- 0.2182075819 97 E -7],
+--R [0.32,3.017598,3.0175979806 093983387,- 0.1939060166 13 E -7],
+--R [0.33,2.9194961,2.9194960564 791734711,- 0.4352082652 89 E -7],
+--R [0.34,2.82696,2.8269599865 960316187,- 0.1340396838 1 E -7],
+--R [0.35,2.7395122,2.7395121590 837832657,- 0.4091621673 43 E -7],
+--R [0.36,2.656728,2.6567280126 534137138,0.1265341371 4 E -7],
+--R [0.37,2.5782289,2.5782288674 460399215,- 0.3255396007 85 E -7],
+--R [0.38,2.5036759,2.5036758878 425107672,- 0.1215748923 3 E -7],
+--R [0.39,2.432765,2.4327649740 660567805,- 0.2593394321 95 E -7],
+--R [0.4,2.3652224,2.3652224200 39110587,0.2003911058 7 E -7],
+--R [0.41,2.3008012,2.3008012066 70318891,0.6670318891 E -8],
+--R [0.42,2.2392778,2.2392778246 666163969,0.2466661639 69 E -7],
+--R [0.43,2.1804495,2.1804495406 685083798,0.4066850837 98 E -7],
+--R [0.44,2.124132,2.1241320361 797692227,0.3617976922 27 E -7],
+--R [0.45,2.0701574,2.0701573613 012126215,- 0.3869878737 85 E -7],
+--R [0.46,2.0183722,2.0183721553 634627578,- 0.4463653724 22 E -7],
+--R [0.47,1.9686361,1.9686360947 077066311,- 0.5292293368 9 E -8],
+--R [0.48,1.9208205,1.9208205344 885739853,0.3448857398 53 E -7],
+--R [0.49,1.8748073,1.8748073167 815901303,0.1678159013 03 E -7],
+--R [0.5,1.83048772,1.8304877217 124519193,0.1712451919 3 E -8],
+--R [0.51,1.78776154,1.7877615419 775693505,0.1977569350 5 E -8],
+--R [0.52,1.74653626,1.7465362641 453971653,0.4145397165 3 E -8],
+--R [0.53,1.70672634,1.7067263426 353184999,0.2635318499 9 E -8],
+--R [0.54,1.66825255,1.6682525543 602072732,0.4360207273 2 E -8],
+--R [0.55,1.63104142,1.6310414237 662644566,0.3766264456 6 E -8],
+--R [0.56,1.59502471,1.5950247094 703485723,- 0.5296514276 E -9],
+--R [0.57,1.56013894,1.5601389449 30073432,0.4930073431 9 E -8],
+--R [0.58,1.52632503,1.5263250266 253525611,- 0.3374647438 9 E -8],
+--R [0.59,1.49352784,1.4935278441 14312362,0.4114312362 E -8],
+--R [0.6,1.46169595,1.4616959470 781021403,- 0.2921897859 7 E -8],
+--R [0.61,1.43078125,1.4307812451 098423602,- 0.4890157639 8 E -8],
+--R [0.62,1.40073873,1.4007387365 5065882,0.655065882 E -8],
+--R [0.63,1.37152626,1.3715262631 452128637,0.3145212863 7 E -8],
+--R [0.64,1.34310429,1.3431042876 925818576,- 0.2307418142 4 E -8],
+--R [0.65,1.31543569,1.3154356922 15926629,0.2215926629 E -8],
+--R [0.66,1.28848559,1.2884855944 745672615,0.4474567261 5 E -8],
+--R [0.67,1.26222118,1.2622211809 019498574,0.9019498574 E -9],
+--R [0.68,1.23661155,1.2366115542 784545265,0.4278454526 5 E -8],
+--R [0.69,1.21162759,1.2116275946 440535197,0.4644053519 7 E -8],
+--R [0.7,1.18724183,1.1872418321 266793537,0.2126679353 7 E -8],
+--R [0.71,1.16342833,1.1634283305 113563708,0.5113563708 E -9],
+--R [0.72,1.14016258,1.1401625805 056933781,0.5056933781 E -9],
+--R [0.73,1.1174214,1.1174214017 717845341,0.1771784534 1 E -8],
+--R [0.74,1.09518285,1.0951828528 950954346,0.2895095434 6 E -8],
+--R [0.75,1.07342615,1.0734261485 493773587,- 0.1450622641 3 E -8],
+--R [0.76,1.05213158,1.0521315831 946421944,0.3194642194 4 E -8],
+--R [0.77,1.03128046,1.0312804607 141042446,0.7141042446 E -9],
+--R [0.78,1.01085503,1.0108550294 569216086,- 0.5430783914 E -9],
+--R [0.79,0.99083842,0.9908384222 0755510722,0.2207555107 2 E -8],
+--R [0.8,0.9712146,0.9712146006 5047441252,0.6504744125 2 E -9],
+--R [0.81,0.9519683,0.9519683039 4152897039,0.3941528970 39 E -8],
+--R [0.82,0.933085,0.9330850010 3521469901,0.1035214699 E -8],
+--R [0.83,0.91455085,0.9145508464 5086948692,- 0.3549130513 1 E -8],
+--R [0.84,0.89635264,0.8963526391 9101064443,- 0.8089893555 7 E -9],
+--R [0.85,0.87847778,0.8784777845 5201177212,0.4552011772 12 E -8],
+--R [0.86,0.86091426,0.8609142585 9147659674,- 0.1408523403 3 E -8],
+--R [0.87,0.84365058,0.8436505750 3832779908,- 0.4961672200 92 E -8],
+--R [0.88,0.82667575,0.8266757544 5107375391,0.4451073753 91 E -8],
+--R [0.89,0.8099793,0.8099792954 4719434615,- 0.4552805653 85 E -8],
+--R [0.9,0.79355115,0.7935511478 423171255,- 0.2157682874 5 E -8],
+--R [0.91,0.77738169,0.7773816875 5202909939,- 0.2447970900 6 E -8],
+--R [0.92,0.76146169,0.7614616931 2195656768,0.3121956567 7 E -8],
+--R [0.93,0.74578232,0.7457823237 6329468591,0.3763294685 91 E -8],
+--R [0.94,0.7303351,0.7303350987 8141157551,- 0.1218588424 5 E -8],
+--R [0.95,0.71511188,0.7151118782 9460519926,- 0.1705394800 7 E -8],
+--R [0.96,0.70010485,0.7001048451 4865796784,- 0.4851342032 16 E -8],
+--R [0.97,0.68530649,0.6853064879 4060552823,- 0.2059394471 8 E -8],
+--R [0.98,0.67070959,0.6707095850 721935367,- 0.4927806463 3 E -8],
+--R [0.99,0.65630719,0.6563071897 5991155454,- 0.2400884455 E -9],
+--R [1.0,0.64209262,0.6420926159 3433070301,- 0.4065669296 99 E -8],
+--R [1.01,0.62805942,0.6280594249 6678856739,0.4966788567 39 E -8],
+--R [1.02,0.61420141,0.6142014131 6631206854,0.3166312068 5 E -8],
+--R [1.03,0.6005126,0.6005125999 9409219665,- 0.590780335 E -11],
+--R [1.04,0.58698722,0.5869872169 4686437526,- 0.3053135624 7 E -8],
+--R [1.05,0.5736197,0.5736196970 6424127541,- 0.2935758724 6 E -8],
+--R [1.06,0.56040467,0.5604046650 184238209,- 0.4981576179 09 E -8],
+--R [1.07,0.54733693,0.5473369277 478102494,- 0.2252189750 6 E -8],
+--R [1.08,0.53441147,0.5344114655 9885875935,- 0.4401141240 65 E -8],
+--R [1.09,0.52162342,0.5216234239 4316016472,0.3943160164 72 E -8],
+--R [1.1,0.50896811,0.5089681052 3906440719,- 0.4760935592 81 E -8],
+--R [1.11,0.49644096,0.4964409615 0939793968,0.1509397939 7 E -8],
+--R [1.12,0.48403759,0.4840375872 0882520651,- 0.2791174793 49 E -8],
+--R [1.13,0.47175371,0.4717537124 562623272,0.2456262327 2 E -8],
+--R [1.14,0.4595852,0.4595851966 0945875941,- 0.3390541240 59 E -8],
+--R [1.15,0.44752802,0.4475280221 6043593272,0.2160435932 72 E -8],
+--R [1.16,0.43557829,0.4355782889 3192216044,- 0.1068077839 6 E -8],
+--R [1.17,0.42373221,0.4237322085 562610121,- 0.1443738987 9 E -8],
+--R [1.18,0.4119861,0.4119860992 1950525045,- 0.7804947495 5 E -9],
+--R [1.19,0.40033638,0.4003363806 5454900775,0.6545490077 5 E -9],
+--R [1.2,0.38877957,0.3887795693 6820491163,- 0.6317950883 7 E -9],
+--R [1.21,0.37731227,0.3773122740 8810747104,0.4088107471 05 E -8],
+--R [1.22,0.36593119,0.3659311914 1622565487,0.1416225654 9 E -8],
+--R [1.23,0.3546331,0.3546331016 7660211852,0.1676602118 5 E -8],
+--R [1.24,0.34341486,0.3434148649 4570930705,0.4945709307 05 E -8],
+--R [1.25,0.33227342,0.3322734172 5452856774,- 0.2745471432 26 E -8],
+--R [1.26,0.32120577,0.3212057669 5212188699,- 0.3047878113 01 E -8],
+--R [1.27,0.31020899,0.3102089912 2108098744,0.1221080987 4 E -8],
+--R [1.28,0.29928023,0.2992802327 358089858,0.2735808985 8 E -8],
+--R [1.29,0.2884167,0.2884166964 5511900872,- 0.3544880991 28 E -8],
+--R [1.3,0.27761565,0.2776156465 411251863,- 0.3458874813 7 E -8],
+--R [1.31,0.2668744,0.2668744033 9685712292,0.3396857122 92 E -8],
+--R [1.32,0.25619034,0.2561903408 1545187187,0.8154518718 7 E -9],
+--R [1.33,0.24556088,0.2455608832 341699844,0.3234169984 4 E -8],
+--R [1.34,0.2349835,0.2349835030 8684653553,0.3086846535 53 E -8],
+--R [1.35,0.22445572,0.2244557182 4872613589,- 0.1751273864 11 E -8],
+--R [1.36,0.21397509,0.2139750895 6794464051,- 0.4320553594 9 E -9],
+--R [1.37,0.20353922,0.2035392184 7821123118,- 0.1521788768 82 E -8],
+--R [1.38,0.19314574,0.1931457446 8751430396,0.4687514303 96 E -8],
+--R [1.39,0.18279234,0.1827923439 3792453991,0.3937924539 91 E -8],
+--R [1.4,0.17247673,0.1724767258 3179995277,- 0.4168200047 23 E -8],
+--R [1.41,0.16219663,0.1621966317 1991176955,0.1719911769 56 E -8],
+--R [1.42,0.15194983,0.1519498326 4720777741,0.2647207777 41 E -8],
+--R [1.43,0.14173413,0.1417341273 5211224764,- 0.2647887752 36 E -8],
+--R [1.44,0.13154734,0.1315473403 1542961869,0.3154296186 9 E -9],
+--R [1.45,0.12138732,0.1213873198 5507360359,- 0.1449263964 1 E -9],
+--R [1.46,0.11125194,0.1112519362 6298502613,- 0.3737014973 87 E -8],
+--R [1.47,0.10113908,0.1011390799 8073116239,- 0.1926883761 E -10],
+--R [1.48,0.09104666,0.0910466598 1039728128,- 0.1896027187 2 E -9],
+--R [1.49,0.080972601,0.0809726011 5748799537,0.1574879953 7 E -9],
+--R [1.5,0.070914844,0.0709148443 0265244878 9,0.3026524487 9 E -9],
+--R [1.51,0.060871343,0.0608713426 9913372964 9,- 0.3008662703 51 E -9],
+--R [1.52,0.050840061,0.0508400612 9291959823 6,0.2929195982 36 E -9],
+--R [1.53,0.040818975,0.0408189748 6263901912 7,- 0.1373609808 7 E -9],
+--R [1.54,0.030806066,0.0308060663 7630738330 6,0.3763073833 07 E -9],
+--R [1.55,0.020799325,0.0207993253 6207296975 6,0.3620729697 56 E -9],
+--R [1.56,0.010796746,0.0107967462 901583485,0.2901583485 E -9],
+--R [1.57,0.000796327,0.0007963269 6322325475 679,- 0.3677674524 32 E -10],
+--R [1.58,- 0.009203933,- 0.0092039330 8759988693 76,- 0.8759988693 75 E
-10],
+--R [1.59,- 0.019206034,- 0.0192060342 0373002777 9,- 0.2037300277 79 E -9],
+--R [1.6,- 0.029211978,- 0.0292119781 9994480011 4,- 0.1999448001 14 E -9]]
+--R Type: List List
Float
+--E 2
+
+)spool
+)lisp (bye)
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp186-188
+\end{thebibliography}
+\end{document}
+
diff --git a/src/input/tanhcoth.input.pamphlet
b/src/input/tanhcoth.input.pamphlet
new file mode 100644
index 0000000..c076ef9
--- /dev/null
+++ b/src/input/tanhcoth.input.pamphlet
@@ -0,0 +1,860 @@
+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input tanhcoth.input}
+\author{Timothy Daly}
+\maketitle
+\begin{abstract}
+This is a set of tests for the tanh and coth functions.
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+In the following table there are 4 columns. The first column
+is the argument of tanh, ranging from 0.00 to 2.00. The
+second column is the reference value of tanh from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp213-216
+
+<<*>>=
+)spool tanhcoth.output
+)set message test on
+)set message auto off
+)clear all
+
+--S 1 of 2
+[[0.00,0.00000000,tanh(0.00),tanh(0.00)-0.00000000],_
+[0.01,0.00999967,tanh(0.01),tanh(0.01)-0.00999967],_
+[0.02,0.01999733,tanh(0.02),tanh(0.02)-0.01999733],_
+[0.03,0.02999100,tanh(0.03),tanh(0.03)-0.02999100],_
+[0.04,0.03997868,tanh(0.04),tanh(0.04)-0.03997868],_
+[0.05,0.04995838,tanh(0.05),tanh(0.05)-0.04995838],_
+[0.06,0.05992810,tanh(0.06),tanh(0.06)-0.05992810],_
+[0.07,0.06988589,tanh(0.07),tanh(0.07)-0.06988589],_
+[0.08,0.07982977,tanh(0.08),tanh(0.08)-0.07982977],_
+[0.09,0.08975779,tanh(0.09),tanh(0.09)-0.08975779],_
+[0.10,0.09966800,tanh(0.10),tanh(0.10)-0.09966800],_
+[0.11,0.10955847,tanh(0.11),tanh(0.11)-0.10955847],_
+[0.12,0.11942730,tanh(0.12),tanh(0.12)-0.11942730],_
+[0.13,0.12927258,tanh(0.13),tanh(0.13)-0.12927258],_
+[0.14,0.13909245,tanh(0.14),tanh(0.14)-0.13909245],_
+[0.15,0.14888503,tanh(0.15),tanh(0.15)-0.14888503],_
+[0.16,0.15864850,tanh(0.16),tanh(0.16)-0.15864850],_
+[0.17,0.16838105,tanh(0.17),tanh(0.17)-0.16838105],_
+[0.18,0.17808087,tanh(0.18),tanh(0.18)-0.17808087],_
+[0.19,0.18774621,tanh(0.19),tanh(0.19)-0.18774621],_
+[0.20,0.19737532,tanh(0.20),tanh(0.20)-0.19737532],_
+[0.21,0.20696650,tanh(0.21),tanh(0.21)-0.20696650],_
+[0.22,0.21651806,tanh(0.22),tanh(0.22)-0.21651806],_
+[0.23,0.22602835,tanh(0.23),tanh(0.23)-0.22602835],_
+[0.24,0.23549575,tanh(0.24),tanh(0.24)-0.23549575],_
+[0.25,0.24491866,tanh(0.25),tanh(0.25)-0.24491866],_
+[0.26,0.25429553,tanh(0.26),tanh(0.26)-0.25429553],_
+[0.27,0.26362484,tanh(0.27),tanh(0.27)-0.26362484],_
+[0.28,0.27290508,tanh(0.28),tanh(0.28)-0.27290508],_
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+[2.00,0.96402758,tanh(2.00),tanh(2.00)-0.96402758]]
+--R
+--R
+--R (1)
+--R [[0.0,0.0,0.0,0.0],
+--R [0.01,0.00999967,0.0099996666 7999946033 94,- 0.3320000539 661 E -8],
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+--R [0.04,0.03997868,0.0399786803 1116357051,0.3111635705 1 E -9],
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+--R [0.46,0.43008421,0.4300842114 0197948596,0.1401979486 E -8],
+--R [0.47,0.43819932,0.4381993148 3276774568,- 0.5167232254 32 E -8],
+--R [0.48,0.44624361,0.4462436102 4877965713,0.2487796571 3 E -9],
+--R [0.49,0.45421643,0.4542164326 8225906516,0.2682259065 16 E -8],
+--R [0.5,0.46211716,0.4621171572 600097585,- 0.2739990241 5 E -8],
+--R [0.51,0.4699452,0.4699451989 3303762132,- 0.1066962378 7 E -8],
+--R [0.52,0.47770001,0.4777000121 684979886,0.2168497988 6 E -8],
+--R [0.53,0.48538109,0.4853810906 0537153481,0.6053715348 1 E -9],
+--R [0.54,0.49298797,0.4929879666 7532433568,- 0.3324675664 32 E -8],
+--R [0.55,0.50052021,0.5005202111 9023520842,0.1190235208 4 E -8],
+--R [0.56,0.50797743,0.5079774328 9789614585,0.2897896145 9 E -8],
+--R [0.57,0.51535928,0.5153592780 0740971805,- 0.1992590281 9 E -8],
+--R [0.58,0.52266543,0.5226654296 858208395,- 0.3141791605 E -9],
+--R [0.59,0.52989561,0.5298956075 2752942099,- 0.2472470579 E -8],
+--R [0.6,0.53704957,0.5370495669 9803528586,- 0.3001964714 1 E -8],
+--R [0.61,0.5441271,0.5441270988 5356748241,- 0.1146432517 6 E -8],
+--R [0.62,0.55112803,0.5511280285 3814693008,- 0.1461853069 9 E -8],
+--R [0.63,0.55805222,0.5580522155 596243666,- 0.4440375633 4 E -8],
+--R [0.64,0.56489955,0.5648995528 4622499294,0.2846224992 9 E -8],
+--R [0.65,0.57166997,0.5716699660 851172252,- 0.3914882774 8 E -8],
+--R [0.66,0.57836341,0.5783634130 4450574496,0.3044505745 E -8],
+--R [0.67,0.58497988,0.5849798828 8072878147,0.2880728781 5 E -8],
+--R [0.68,0.5915194,0.5915193954 3181645487,- 0.4568183545 13 E -8],
+--R [0.69,0.597982,0.5979820004 9894125254,0.4989412525 4 E -9],
+--R [0.7,0.60436778,0.6043677771 1716349631,- 0.2882836503 7 E -8],
+--R [0.71,0.61067683,0.6106768328 1684418132,0.2816844181 3 E -8],
+--R [0.72,0.6169093,0.6169093028 7706502085,0.2877065020 8 E -8],
+--R [0.73,0.62306535,0.6230653495 723611072,- 0.4276388928 E -9],
+--R [0.74,0.62914516,0.6291451614 140354854,0.1414035485 4 E -8],
+--R [0.75,0.63514895,0.6351489523 8728731921,0.2387287319 2 E -8],
+--R [0.76,0.64107696,0.6410769611 8534638918,0.1185346389 2 E -8],
+--R [0.77,0.64692945,0.6469294504 4176657733,0.4417665773 E -9],
+--R [0.78,0.65270671,0.6527067059 6198993346,- 0.4038010066 55 E -8],
+--R [0.79,0.65840904,0.6584090359 5525105073,- 0.4044748949 27 E -8],
+--R [0.8,0.66403677,0.6640367702 6784896369,0.2678489637 E -9],
+--R [0.81,0.66959026,0.6695902596 1877077296,- 0.381229227 E -9],
+--R [0.82,0.67506987,0.6750698748 386078472,0.4838607847 2 E -8],
+--R [0.83,0.68047601,0.6804760061 1266189234,- 0.3887338107 66 E -8],
+--R [0.84,0.68580906,0.6858090622 290945476,0.2229094547 6 E -8],
+--R [0.85,0.69106947,0.6910694698 3293059133,- 0.1670694087 E -9],
+--R [0.86,0.69625767,0.6962576726 8668143869,0.2686681438 7 E -8],
+--R [0.87,0.70137413,0.7013741309 3831249855,0.9383124985 5 E -9],
+--R [0.88,0.70641932,0.7064193203 9723523504,0.397235235 E -9],
+--R [0.89,0.71139373,0.7113937318 1896254629,0.1818962546 3 E -8],
+--R [0.9,0.71629787,0.7162978701 9902442081,0.1990244208 E -9],
+--R [0.91,0.72113225,0.7211322540 7669984382,0.4076699843 82 E -8],
+--R [0.92,0.72589742,0.7258974148 4908067729,- 0.5150919322 71 E -8],
+--R [0.93,0.7305939,0.7305938960 9594379981,- 0.3904056200 19 E -8],
+--R [0.94,0.73522225,0.7352222529 1586922682,0.2915869226 8 E -8],
+--R [0.95,0.73978305,0.7397830512 7400429569,0.1274004295 7 E -8],
+--R [0.96,0.74427687,0.7442768673 6183734344,- 0.2638162656 6 E -8],
+--R [0.97,0.74870429,0.7487042869 6930867119,- 0.3030691328 8 E -8],
+--R [0.98,0.75306591,0.7530659048 6955201716,- 0.5130447982 84 E -8],
+--R [0.99,0.75736232,0.7573623242 1652628152,0.4216526281 52 E -8],
+--R [1.0,0.76159416,0.7615941559 5576488812,- 0.4044235111 88 E -8],
+--R [1.01,0.76576202,0.7657620182 4843895284,- 0.1751561047 2 E -8],
+--R [1.02,0.76986654,0.7698665359 0890037199,- 0.4091099628 01 E -8],
+--R [1.03,0.77390834,0.7739083398 5584205966,- 0.1441579403 E -9],
+--R [1.04,0.77788807,0.7778880665 7718485812,- 0.3422815141 9 E -8],
+--R [1.05,0.78180636,0.7818063576 087741234,- 0.2391225876 6 E -8],
+--R [1.06,0.78566386,0.7856638590 2694365005,- 0.9730563499 5 E -9],
+--R [1.07,0.78946122,0.7894612209 5498044002,0.9549804400 2 E -9],
+--R [1.08,0.7931991,0.7931990970 8350083423,- 0.2916499165 8 E -8],
+--R [1.09,0.79687814,0.7968781442 0472670169,0.4204726701 69 E -8],
+--R [1.1,0.80049902,0.8004990217 6062970601,0.1760629706 E -8],
+--R [1.11,0.80406239,0.8040623914 0489212927,0.1404892129 3 E -8],
+--R [1.12,0.80756892,0.8075689165 7861430767,- 0.3421385692 3 E -8],
+--R [1.13,0.81101926,0.8110192620 9968140547,0.2099681405 5 E -8],
+--R [1.14,0.81441409,0.8144140937 6568599783,0.3765685997 83 E -8],
+--R [1.15,0.81775408,0.8177540779 7028772932,- 0.2029712270 7 E -8],
+--R [1.16,0.82103988,0.8210398813 3287713399,0.1332877134 E -8],
+--R [1.17,0.82427217,0.8242721703 4139752183,0.3413975218 E -9],
+--R [1.18,0.82745161,0.8274516110 0816662528,0.1008166625 3 E -8],
+--R [1.19,0.83057887,0.8305788685 3852843014,- 0.1461471569 9 E -8],
+--R [1.2,0.83365461,0.8336546070 1215525867,- 0.2987844741 3 E -8],
+--R [1.21,0.83667949,0.8366794890 7681069839,- 0.9231893016 1 E -9],
+--R [1.22,0.83965418,0.8396541756 5437534711,- 0.4345624652 89 E -8],
+--R [1.23,0.84257933,0.8425793256 5892954289,- 0.4341070457 11 E -8],
+--R [1.24,0.8454556,0.8454555957 2668023505,- 0.4273319764 96 E -8],
+--R [1.25,0.84828364,0.8482836399 5751289761,- 0.424871024 E -10],
+--R [1.26,0.85106411,0.8510641096 6794385925,- 0.3320561407 E -9],
+--R [1.27,0.85379765,0.8537976531 55243591,0.3155243591 E -8],
+--R [1.28,0.85648492,0.8564849154 7249732563,- 0.4527502674 37 E -8],
+--R [1.29,0.85912654,0.8591265382 1436584793,- 0.1785634152 1 E -8],
+--R [1.3,0.86172316,0.8617231593 1330636429,- 0.6866936357 1 E -9],
+--R [1.31,0.86427541,0.8642754128 4601100184,0.2846011001 8 E -8],
+--R [1.32,0.86678393,0.8667839288 4981867301,- 0.1150181327 E -8],
+--R [1.33,0.86924933,0.8692493331 4885474185,0.3148854741 8 E -8],
+--R [1.34,0.87167225,0.8716722471 8965211443,- 0.2810347885 6 E -8],
+--R [1.35,0.87405329,0.8740532878 8600702097,- 0.2113992979 E -8],
+--R [1.36,0.87639307,0.8763930674 7282283326,- 0.2527177166 7 E -8],
+--R [1.37,0.87869219,0.8786921933 6869574227,0.3368695742 3 E -8],
+--R [1.38,0.88095127,0.8809512680 4699698152,- 0.1953003018 5 E -8],
+--R [1.39,0.88317089,0.8831708889 1520749667,- 0.1084792503 3 E -8],
+--R [1.4,0.88535165,0.8853516482 0226250758,- 0.1797737492 4 E -8],
+--R [1.41,0.88749413,0.8874941328 5366526128,0.2853665261 3 E -8],
+--R [1.42,0.88959892,0.8895989244 3413141195,0.4434131411 95 E -8],
+--R [1.43,0.8916666,0.8916665990 3752786391,- 0.9624721360 9 E -9],
+--R [1.44,0.89369773,0.8936977272 0387255605,- 0.2796127443 9 E -8],
+--R [1.45,0.89569287,0.8956928738 4316453044,0.3843164530 44 E -8],
+--R [1.46,0.8976526,0.8976525981 6581669501,- 0.1834183305 E -8],
+--R [1.47,0.89957745,0.8995774536 1946694194,0.3619466941 9 E -8],
+--R [1.48,0.90146799,0.9014679878 3194670176,- 0.2168053298 2 E -8],
+--R [1.49,0.90332474,0.9033247425 6018958154,0.2560189581 5 E -8],
+--R [1.5,0.90514825,0.9051482536 4486643824,0.3644866438 2 E -8],
+--R [1.51,0.90693905,0.9069390509 705370591,0.9705370591 E -9],
+--R [1.52,0.90869766,0.9086976584 3111254663,- 0.1568887453 4 E -8],
+--R [1.53,0.91042459,0.9104245939 004265213,0.3900426521 3 E -8],
+--R [1.54,0.91212037,0.9121203692 077173486,- 0.7922826513 9 E -9],
+--R [1.55,0.91378549,0.9137854901 1782775489,0.1178277549 E -9],
+--R [1.56,0.91542046,0.9154204563 1593240882,- 0.3684067591 2 E -8],
+--R [1.57,0.91702576,0.9170257613 9660829878,0.1396608298 8 E -8],
+--R [1.58,0.91860189,0.9186018928 5706702341,0.2857067023 4 E -8],
+--R [1.59,0.92014933,0.9201493320 9437242057,0.2094372420 6 E -8],
+--R [1.6,0.92166855,0.9216685544 0647128268,0.4406471282 68 E -8],
+--R [1.61,0.92316003,0.9231600289 9686923262,- 0.1003130767 4 E -8],
+--R [1.62,0.92462422,0.9246242189 8278815827,- 0.1017211841 7 E -8],
+--R [1.63,0.92606158,0.9260615814 0664591708,0.1406645917 1 E -8],
+--R [1.64,0.92747257,0.9274725672 5070331722,- 0.2749296682 8 E -8],
+--R [1.65,0.92885762,0.9288576214 5472765445,0.1454727654 4 E -8],
+--R [1.66,0.93021718,0.9302171829 3652632524,0.2936526325 2 E -8],
+--R [1.67,0.93155168,0.9315516846 1520824452,0.4615208244 51 E -8],
+--R [1.68,0.93286155,0.9328615534 3703496255,0.3437034962 6 E -8],
+--R [1.69,0.93414721,0.9341472104 0372749847,0.4037274985 E -9],
+--R [1.7,0.93540907,0.9354090706 0309898052,0.6030989805 2 E -9],
+--R [1.71,0.93664754,0.9366475432 4188720437,0.3241887204 4 E -8],
+--R [1.72,0.93786303,0.9378630316 8066518501,0.1680665185 E -8],
+--R [1.73,0.93905593,0.9390559334 7071168332,0.3470711683 3 E -8],
+--R [1.74,0.94022664,0.9402266403 9272753171,0.3927275317 E -9],
+--R [1.75,0.94137554,0.9413755384 9728736227,- 0.1502712637 7 E -8],
+--R [1.76,0.94250301,0.9425030081 4692005344,- 0.1853079946 6 E -8],
+--R [1.77,0.94360942,0.9436094240 5971485511,0.4059714855 11 E -8],
+--R [1.78,0.94469516,0.9446951553 5435372611,- 0.4645646273 89 E -8],
+--R [1.79,0.94576057,0.9457605655 9647392056,- 0.4403526079 44 E -8],
+--R [1.8,0.94680601,0.9468060128 4626828964,0.2846268289 6 E -8],
+--R [1.81,0.94783185,0.9478318497 0723412158,- 0.2927658784 E -9],
+--R [1.82,0.94883842,0.9488384233 7598462509,0.3375984625 1 E -8],
+--R [1.83,0.94982608,0.9498260756 9304036887,- 0.4306959631 13 E -8],
+--R [1.84,0.95079514,0.9507951431 9452112204,0.3194521122 E -8],
+--R [1.85,0.95174596,0.9517459571 6466159744,- 0.2835338402 6 E -8],
+--R [1.86,0.95267884,0.9526788436 8907758132,0.3689077581 3 E -8],
+--R [1.87,0.95359412,0.9535941237 0871183917,0.3708711839 2 E -8],
+--R [1.88,0.95449211,0.9544921130 7439201893,0.3074392018 9 E -8],
+--R [1.89,0.95537312,0.9553731226 0193552915,0.2601935529 1 E -8],
+--R [1.9,0.95623746,0.9562374581 2773905209,- 0.1872260947 9 E -8],
+--R [1.91,0.95708542,0.9570854205 6479296064,0.5647929606 4 E -9],
+--R [1.92,0.95791731,0.9579173059 5906344306,- 0.4040936556 95 E -8],
+--R [1.93,0.95873341,0.9587334055 4618760356,- 0.4453812396 44 E -8],
+--R [1.94,0.95953401,0.9595340058 0842919816,- 0.4191570801 84 E -8],
+--R [1.95,0.96031939,0.9603193885 3184498689,- 0.1468155013 1 E -8],
+--R [1.96,0.96108983,0.9610898308 6361393517,0.8636139351 7 E -9],
+--R [1.97,0.96184561,0.9618456053 6948368021,- 0.4630516319 79 E -8],
+--R [1.98,0.96258698,0.9625869800 9129079438,0.9129079438 E -10],
+--R [1.99,0.96331422,0.9633142186 0451342618,- 0.1395486573 8 E -8],
+--R [2.0,0.96402758,0.9640275800 7581688395,0.7581688395 E -10]]
+--R Type: List List
Float
+--E 1
+@
+In the following table there are 4 columns. The first column
+is the argument of coth, ranging from 0.01 to 2.00. The
+second column is the reference value of coth from the book
+Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp213-216
+
+<<*>>=
+--S 2 of 2
+[[0.01,100.0033333,coth(0.01),coth(0.01)-100.003333],_
+[0.02,50.0066665,coth(0.02),coth(0.02)-50.0066665],_
+[0.03,33.3433327,coth(0.03),coth(0.03)-33.3433327],_
+[0.04,25.0133319,coth(0.04),coth(0.04)-25.0133319],_
+[0.05,20.0166639,coth(0.05),coth(0.05)-20.0166639],_
+[0.06,16.6866619,coth(0.06),coth(0.06)-16.6866619],_
+[0.07,14.3090400,coth(0.07),coth(0.07)-14.3090400],_
+[0.08,12.5266553,coth(0.08),coth(0.08)-12.5266553],_
+[0.09,11.1410949,coth(0.09),coth(0.09)-11.1410949],_
+[0.10,10.0333111,coth(0.10),coth(0.10)-10.0333111],_
+[0.11,9.1275462,coth(0.11),coth(0.11)-9.1275462],_
+[0.12,8.3732950,coth(0.12),coth(0.12)-8.3732950],_
+[0.13,7.7355923,coth(0.13),coth(0.13)-7.7355923],_
+[0.14,7.1894629,coth(0.14),coth(0.14)-7.1894629],_
+[0.15,6.7165918,coth(0.15),coth(0.15)-6.7165918],_
+[0.16,6.3032425,coth(0.16),coth(0.16)-6.3032425],_
+[0.17,5.9389107,coth(0.17),coth(0.17)-5.9389107],_
+[0.18,5.6154264,coth(0.18),coth(0.18)-5.6154264],_
+[0.19,5.3263393,coth(0.19),coth(0.19)-5.3263393],_
+[0.20,5.0664896,coth(0.20),coth(0.20)-5.0664896],_
+[0.21,4.8316998,coth(0.21),coth(0.21)-4.8316998],_
+[0.22,4.6185523,coth(0.22),coth(0.22)-4.6185523],_
+[0.23,4.4242237,coth(0.23),coth(0.23)-4.4242237],_
+[0.24,4.2463611,coth(0.24),coth(0.24)-4.2463611],_
+[0.25,4.0829882,coth(0.25),coth(0.25)-4.0829882],_
+[0.26,3.9324324,coth(0.26),coth(0.26)-3.9324324],_
+[0.27,3.7932693,coth(0.27),coth(0.27)-3.7932693],_
+[0.28,3.6642777,coth(0.28),coth(0.28)-3.6642777],_
+[0.29,3.5444049,coth(0.29),coth(0.29)-3.5444049],_
+[0.30,3.4327384,coth(0.30),coth(0.30)-3.4327384],_
+[0.31,3.3284838,coth(0.31),coth(0.31)-3.3284838],_
+[0.32,3.2309455,coth(0.32),coth(0.32)-3.2309455],_
+[0.33,3.1395126,coth(0.33),coth(0.33)-3.1395126],_
+[0.34,3.0536459,coth(0.34),coth(0.34)-3.0536459],_
+[0.35,2.9728677,coth(0.35),coth(0.35)-2.9728677],_
+[0.36,2.8967536,coth(0.36),coth(0.36)-2.8967536],_
+[0.37,2.8249249,coth(0.37),coth(0.37)-2.8249249],_
+[0.38,2.7570428,coth(0.38),coth(0.38)-2.7570428],_
+[0.39,2.6928032,coth(0.39),coth(0.39)-2.6928032],_
+[0.40,2.6319324,coth(0.40),coth(0.40)-2.6319324],_
+[0.41,2.5741836,coth(0.41),coth(0.41)-2.5741836],_
+[0.42,2.5193332,coth(0.42),coth(0.42)-2.5193332],_
+[0.43,2.4671785,coth(0.43),coth(0.43)-2.4671785],_
+[0.44,2.4175352,coth(0.44),coth(0.44)-2.4175352],_
+[0.45,2.3702355,coth(0.45),coth(0.45)-2.3702355],_
+[0.46,2.3251260,coth(0.46),coth(0.46)-2.3251260],_
+[0.47,2.2820666,coth(0.47),coth(0.47)-2.2820666],_
+[0.48,2.2409284,coth(0.48),coth(0.48)-2.2409284],_
+[0.49,2.2015936,coth(0.49),coth(0.49)-2.2015936],_
+[0.50,2.1639534,coth(0.50),coth(0.50)-2.1639534],_
+[0.51,2.1279077,coth(0.51),coth(0.51)-2.1279077],_
+[0.52,2.0933640,coth(0.52),coth(0.52)-2.0933640],_
+[0.53,2.0602368,coth(0.53),coth(0.53)-2.0602368],_
+[0.54,2.0284471,coth(0.54),coth(0.54)-2.0284471],_
+[0.55,1.9979213,coth(0.55),coth(0.55)-1.9979213],_
+[0.56,1.9685914,coth(0.56),coth(0.56)-1.9685914],_
+[0.57,1.9403939,coth(0.57),coth(0.57)-1.9403939],_
+[0.58,1.9132698,coth(0.58),coth(0.58)-1.9132698],_
+[0.59,1.8871642,coth(0.59),coth(0.59)-1.8871642],_
+[0.60,1.8620255,coth(0.60),coth(0.60)-1.8620255],_
+[0.61,1.8378059,coth(0.61),coth(0.61)-1.8378059],_
+[0.62,1.8144604,coth(0.62),coth(0.62)-1.8144604],_
+[0.63,1.7919470,coth(0.63),coth(0.63)-1.7919470],_
+[0.64,1.7702262,coth(0.64),coth(0.64)-1.7702262],_
+[0.65,1.7492610,coth(0.65),coth(0.65)-1.7492610],_
+[0.66,1.7290167,coth(0.66),coth(0.66)-1.7290167],_
+[0.67,1.7094605,coth(0.67),coth(0.67)-1.7094605],_
+[0.68,1.6905616,coth(0.68),coth(0.68)-1.6905616],_
+[0.69,1.6722911,coth(0.69),coth(0.69)-1.6722911],_
+[0.70,1.6546216,coth(0.70),coth(0.70)-1.6546216],_
+[0.71,1.6375273,coth(0.71),coth(0.71)-1.6375273],_
+[0.72,1.6209838,coth(0.72),coth(0.72)-1.6209838],_
+[0.73,1.6049681,coth(0.73),coth(0.73)-1.6049681],_
+[0.74,1.5894583,coth(0.74),coth(0.74)-1.5894583],_
+[0.75,1.5744338,coth(0.75),coth(0.75)-1.5744338],_
+[0.76,1.5598751,coth(0.76),coth(0.76)-1.5598751],_
+[0.77,1.5457636,coth(0.77),coth(0.77)-1.5457636],_
+[0.78,1.5320817,coth(0.78),coth(0.78)-1.5320817],_
+[0.79,1.5188127,coth(0.79),coth(0.79)-1.5188127],_
+[0.80,1.5059407,coth(0.80),coth(0.80)-1.5059407],_
+[0.81,1.4934506,coth(0.81),coth(0.81)-1.4934506],_
+[0.82,1.4813281,coth(0.82),coth(0.82)-1.4813281],_
+[0.83,1.4695595,coth(0.83),coth(0.83)-1.4695595],_
+[0.84,1.4581318,coth(0.84),coth(0.84)-1.4581318],_
+[0.85,1.4470325,coth(0.85),coth(0.85)-1.4470325],_
+[0.86,1.4362499,coth(0.86),coth(0.86)-1.4362499],_
+[0.87,1.4257726,coth(0.87),coth(0.87)-1.4257726],_
+[0.88,1.4155898,coth(0.88),coth(0.88)-1.4155898],_
+[0.89,1.4056913,coth(0.89),coth(0.89)-1.4056913],_
+[0.90,1.3960673,coth(0.90),coth(0.90)-1.3960673],_
+[0.91,1.3867082,coth(0.91),coth(0.91)-1.3867082],_
+[0.92,1.3776051,coth(0.92),coth(0.92)-1.3776051],_
+[0.93,1.3687495,coth(0.93),coth(0.93)-1.3687495],_
+[0.94,1.3601329,coth(0.94),coth(0.94)-1.3601329],_
+[0.95,1.3517476,coth(0.95),coth(0.95)-1.3517476],_
+[0.96,1.3435860,coth(0.96),coth(0.96)-1.3435860],_
+[0.97,1.3356408,coth(0.97),coth(0.97)-1.3356408],_
+[0.98,1.3279050,coth(0.98),coth(0.98)-1.3279050],_
+[0.99,1.3203720,coth(0.99),coth(0.99)-1.3203720],_
+[1.00,1.3130353,coth(1.00),coth(1.00)-1.3130353],_
+[1.01,1.3058887,coth(1.01),coth(1.01)-1.3058887],_
+[1.02,1.2989264,coth(1.02),coth(1.02)-1.2989264],_
+[1.03,1.2921427,coth(1.03),coth(1.03)-1.2921427],_
+[1.04,1.2855320,coth(1.04),coth(1.04)-1.2855320],_
+[1.05,1.2790891,coth(1.05),coth(1.05)-1.2790891],_
+[1.06,1.2728090,coth(1.06),coth(1.06)-1.2728090],_
+[1.07,1.2666867,coth(1.07),coth(1.07)-1.2666867],_
+[1.08,1.2607175,coth(1.08),coth(1.08)-1.2607175],_
+[1.09,1.2548970,coth(1.09),coth(1.09)-1.2548970],_
+[1.10,1.2492208,coth(1.10),coth(1.10)-1.2492208],_
+[1.11,1.2436846,coth(1.11),coth(1.11)-1.2436846],_
+[1.12,1.2382844,coth(1.12),coth(1.12)-1.2382844],_
+[1.13,1.2330163,coth(1.13),coth(1.13)-1.2330163],_
+[1.14,1.2278766,coth(1.14),coth(1.14)-1.2278766],_
+[1.15,1.2228615,coth(1.15),coth(1.15)-1.2228615],_
+[1.16,1.2179676,coth(1.16),coth(1.16)-1.2179676],_
+[1.17,1.2131915,coth(1.17),coth(1.17)-1.2131915],_
+[1.18,1.2085299,coth(1.18),coth(1.18)-1.2085299],_
+[1.19,1.2039796,coth(1.19),coth(1.19)-1.2039796],_
+[1.20,1.1995375,coth(1.20),coth(1.20)-1.1995375],_
+[1.21,1.1952008,coth(1.21),coth(1.21)-1.1952008],_
+[1.22,1.1909665,coth(1.22),coth(1.22)-1.1909665],_
+[1.23,1.1868319,coth(1.23),coth(1.23)-1.1868319],_
+[1.24,1.1827942,coth(1.24),coth(1.24)-1.1827942],_
+[1.25,1.1788510,coth(1.25),coth(1.25)-1.1788510],_
+[1.26,1.1749996,coth(1.26),coth(1.26)-1.1749996],_
+[1.27,1.1712377,coth(1.27),coth(1.27)-1.1712377],_
+[1.28,1.1675629,coth(1.28),coth(1.28)-1.1675629],_
+[1.29,1.1639729,coth(1.29),coth(1.29)-1.1639729],_
+[1.30,1.1604655,coth(1.30),coth(1.30)-1.1604655],_
+[1.31,1.1570386,coth(1.31),coth(1.31)-1.1570386],_
+[1.32,1.1536901,coth(1.32),coth(1.32)-1.1536901],_
+[1.33,1.1504179,coth(1.33),coth(1.33)-1.1504179],_
+[1.34,1.1472202,coth(1.34),coth(1.34)-1.1472202],_
+[1.35,1.1440950,coth(1.35),coth(1.35)-1.1440950],_
+[1.36,1.1410405,coth(1.36),coth(1.36)-1.1410405],_
+[1.37,1.1380550,coth(1.37),coth(1.37)-1.1380550],_
+[1.38,1.1351366,coth(1.38),coth(1.38)-1.1351366],_
+[1.39,1.1322837,coth(1.39),coth(1.39)-1.1322837],_
+[1.40,1.1294947,coth(1.40),coth(1.40)-1.1294947],_
+[1.41,1.1267680,coth(1.41),coth(1.41)-1.1267680],_
+[1.42,1.1241021,coth(1.42),coth(1.42)-1.1241021],_
+[1.43,1.1214954,coth(1.43),coth(1.43)-1.1214954],_
+[1.44,1.1189466,coth(1.44),coth(1.44)-1.1189466],_
+[1.45,1.1164541,coth(1.45),coth(1.45)-1.1164541],_
+[1.46,1.1140167,coth(1.46),coth(1.46)-1.1140167],_
+[1.47,1.1116330,coth(1.47),coth(1.47)-1.1116330],_
+[1.48,1.1093017,coth(1.48),coth(1.48)-1.1093017],_
+[1.49,1.1070216,coth(1.49),coth(1.49)-1.1070216],_
+[1.50,1.1047914,coth(1.50),coth(1.50)-1.1047914],_
+[1.51,1.1026099,coth(1.51),coth(1.51)-1.1026099],_
+[1.52,1.1004760,coth(1.52),coth(1.52)-1.1004760],_
+[1.53,1.0983886,coth(1.53),coth(1.53)-1.0983886],_
+[1.54,1.0963465,coth(1.54),coth(1.54)-1.0963465],_
+[1.55,1.0943487,coth(1.55),coth(1.55)-1.0943487],_
+[1.56,1.0923942,coth(1.56),coth(1.56)-1.0923942],_
+[1.57,1.0904819,coth(1.57),coth(1.57)-1.0904819],_
+[1.58,1.0886109,coth(1.58),coth(1.58)-1.0886109],_
+[1.59,1.0867801,coth(1.59),coth(1.59)-1.0867801],_
+[1.60,1.0849887,coth(1.60),coth(1.60)-1.0849887],_
+[1.61,1.0832358,coth(1.61),coth(1.61)-1.0832358],_
+[1.62,1.0815204,coth(1.62),coth(1.62)-1.0815204],_
+[1.63,1.0798418,coth(1.63),coth(1.63)-1.0798418],_
+[1.64,1.0781990,coth(1.64),coth(1.64)-1.0781990],_
+[1.65,1.0765913,coth(1.65),coth(1.65)-1.0765913],_
+[1.66,1.0750178,coth(1.66),coth(1.66)-1.0750178],_
+[1.67,1.0734777,coth(1.67),coth(1.67)-1.0734777],_
+[1.68,1.0719704,coth(1.68),coth(1.68)-1.0719704],_
+[1.69,1.0704951,coth(1.69),coth(1.69)-1.0704951],_
+[1.70,1.0690510,coth(1.70),coth(1.70)-1.0690510],_
+[1.71,1.0676375,coth(1.71),coth(1.71)-1.0676375],_
+[1.72,1.0662538,coth(1.72),coth(1.72)-1.0662538],_
+[1.73,1.0648993,coth(1.73),coth(1.73)-1.0648993],_
+[1.74,1.0635734,coth(1.74),coth(1.74)-1.0635734],_
+[1.75,1.0622753,coth(1.75),coth(1.75)-1.0622753],_
+[1.76,1.0610046,coth(1.76),coth(1.76)-1.0610046],_
+[1.77,1.0597605,coth(1.77),coth(1.77)-1.0597605],_
+[1.78,1.0585425,coth(1.78),coth(1.78)-1.0585425],_
+[1.79,1.0573501,coth(1.79),coth(1.79)-1.0573501],_
+[1.80,1.0561826,coth(1.80),coth(1.80)-1.0561826],_
+[1.81,1.0550395,coth(1.81),coth(1.81)-1.0550395],_
+[1.82,1.0539202,coth(1.82),coth(1.82)-1.0539202],_
+[1.83,1.0528243,coth(1.83),coth(1.83)-1.0528243],_
+[1.84,1.0517513,coth(1.84),coth(1.84)-1.0517513],_
+[1.85,1.0507005,coth(1.85),coth(1.85)-1.0507005],_
+[1.86,1.0496717,coth(1.86),coth(1.86)-1.0496717],_
+[1.87,1.0486642,coth(1.87),coth(1.87)-1.0486642],_
+[1.88,1.0476776,coth(1.88),coth(1.88)-1.0476776],_
+[1.89,1.0467115,coth(1.89),coth(1.89)-1.0467115],_
+[1.90,1.0457653,coth(1.90),coth(1.90)-1.0457653],_
+[1.91,1.0448388,coth(1.91),coth(1.91)-1.0448388],_
+[1.92,1.0439314,coth(1.92),coth(1.92)-1.0439314],_
+[1.93,1.0430428,coth(1.93),coth(1.93)-1.0430428],_
+[1.94,1.0421725,coth(1.94),coth(1.94)-1.0421725],_
+[1.95,1.0413202,coth(1.95),coth(1.95)-1.0413202],_
+[1.96,1.0404855,coth(1.96),coth(1.96)-1.0404855],_
+[1.97,1.0396679,coth(1.97),coth(1.97)-1.0396679],_
+[1.98,1.0388672,coth(1.98),coth(1.98)-1.0388672],_
+[1.99,1.0380829,coth(1.99),coth(1.99)-1.0380829],_
+[2.00,1.0373147,coth(2.00),coth(2.00)-1.0373147]]
+--R
+--R
+--R (2)
+--R [[0.01,100.0033333,100.0033333111 1132275,0.3111113227 5 E -6],
+--R [0.02,50.0066665,50.0066664888 95661105,- 0.111043389 E -7],
+--R [0.03,33.3433327,33.3433327333 84757277,0.3338475727 7 E -7],
+--R [0.04,25.0133319,25.0133319113 27796018,0.1132779602 E -7],
+--R [0.05,20.0166639,20.0166638895 50099248,- 0.1044990075 E -7],
+--R [0.06,16.6866619,16.6866618683 11788711,- 0.3168821128 9 E -7],
+--R [0.07,14.30904,14.3090400003 80691777,0.380691777 E -9],
+--R [0.08,12.5266553,12.5266552958 19479794,- 0.4180520206 E -8],
+--R [0.09,11.1410949,11.1410949235 98139558,0.2359813955 8 E -7],
+--R [0.1,10.0333111,10.0333111322 5398961,0.3225398961 E -7],
+--R [0.11,9.1275462,9.1275462138 41655179,0.1384165517 9 E -7],
+--R [0.12,8.373295,8.3732949859 20466106,- 0.1407953389 4 E -7],
+--R [0.13,7.7355923,7.7355922818 667577388,- 0.1813324226 1 E -7],
+--R [0.14,7.1894629,7.1894629453 485603813,0.4534856038 12 E -7],
+--R [0.15,6.7165918,6.7165918270 201652046,0.2702016520 5 E -7],
+--R [0.16,6.3032425,6.3032425324 653055781,0.3246530557 81 E -7],
+--R [0.17,5.9389107,5.9389107296 982815716,0.2969828157 2 E -7],
+--R [0.18,5.6154264,5.6154263541 72649833,- 0.4582735016 7 E -7],
+--R [0.19,5.3263393,5.3263393280 051508097,0.2800515081 E -7],
+--R [0.2,5.0664896,5.0664895634 394727136,- 0.3656052728 64 E -7],
+--R [0.21,4.8316998,4.8316998224 69838787,0.2246983878 7 E -7],
+--R [0.22,4.6185523,4.6185523420 28042354,0.4202804235 4 E -7],
+--R [0.23,4.4242237,4.4242237308 667251076,0.3086672510 75 E -7],
+--R [0.24,4.2463611,4.2463611422 274259979,0.4222742599 79 E -7],
+--R [0.25,4.0829882,4.0829881650 735965683,- 0.3492640343 17 E -7],
+--R [0.26,3.9324324,3.9324324327 36408036,0.3273640803 6 E -7],
+--R [0.27,3.7932693,3.7932693185 329284388,0.1853292843 88 E -7],
+--R [0.28,3.6642777,3.6642776966 135092065,- 0.3386490793 5 E -8],
+--R [0.29,3.5444049,3.5444048557 416074988,- 0.4425839250 12 E -7],
+--R [0.3,3.4327384,3.4327384303 217415894,0.3032174158 94 E -7],
+--R [0.31,3.3284838,3.3284837641 356108564,- 0.3586438914 36 E -7],
+--R [0.32,3.2309455,3.2309455183 814022485,0.1838140224 85 E -7],
+--R [0.33,3.1395126,3.1395126237 094799327,0.2370947993 27 E -7],
+--R [0.34,3.0536459,3.0536458877 845481399,- 0.1221545186 E -7],
+--R [0.35,2.9728677,2.9728677272 689265964,0.2726892659 64 E -7],
+--R [0.36,2.8967536,2.8967536111 449900164,0.1114499001 6 E -7],
+--R [0.37,2.8249249,2.8249248916 098377328,- 0.8390162267 1 E -8],
+--R [0.38,2.7570428,2.7570427669 367181087,- 0.3306328189 13 E -7],
+--R [0.39,2.6928032,2.6928031731 296236301,- 0.2687037636 99 E -7],
+--R [0.4,2.6319324,2.6319324418 321883572,0.4183218835 72 E -7],
+--R [0.41,2.5741836,2.5741835936 66919577,- 0.6333080423 E -8],
+--R [0.42,2.5193332,2.5193331610 996456868,- 0.3890035431 32 E -7],
+--R [0.43,2.4671785,2.4671784546 273392718,- 0.4537266072 82 E -7],
+--R [0.44,2.4175352,2.4175352017 605355925,0.1760535592 E -8],
+--R [0.45,2.3702355,2.3702355008 100157433,0.8100157433 E -9],
+--R [0.46,2.325126,2.3251260415 726980245,0.4157269802 45 E -7],
+--R [0.47,2.2820666,2.2820665531 657326625,- 0.4683426733 75 E -7],
+--R [0.48,2.2409284,2.2409284458 829619758,0.4588296197 58 E -7],
+--R [0.49,2.2015936,2.2015936193 562076931,0.1935620769 3 E -7],
+--R [0.5,2.1639534,2.1639534137 386528488,0.1373865284 9 E -7],
+--R [0.51,2.1279077,2.1279076842 79778673,- 0.1572022132 7 E -7],
+--R [0.52,2.093364,2.0933639826 813995967,- 0.1731860040 33 E -7],
+--R [0.53,2.0602368,2.0602368311 315780091,0.3113157800 91 E -7],
+--R [0.54,2.0284471,2.0284470770 025658705,- 0.2299743412 95 E -7],
+--R [0.55,1.9979213,1.9979213179 463896248,0.1794638962 48 E -7],
+--R [0.56,1.9685914,1.9685913885 883209462,- 0.1141167905 38 E -7],
+--R [0.57,1.9403939,1.9403939012 535294422,0.1253529442 2 E -8],
+--R [0.58,1.9132698,1.9132698342 056208124,0.3420562081 24 E -7],
+--R [0.59,1.8871642,1.8871641617 600075376,- 0.3823999246 24 E -7],
+--R [0.6,1.8620255,1.8620255213 866662476,0.2138666624 76 E -7],
+--R [0.61,1.8378059,1.8378059135 575501759,0.1355755017 59 E -7],
+--R [0.62,1.8144604,1.8144604306 416324911,0.3064163249 11 E -7],
+--R [0.63,1.791947,1.7919470116 200198016,0.1162001980 16 E -7],
+--R [0.64,1.7702262,1.7702262197 970203553,0.1979702035 53 E -7],
+--R [0.65,1.749261,1.7492610410 306350676,0.4103063506 76 E -7],
+--R [0.66,1.7290167,1.7290167003 061253871,0.3061253871 E -9],
+--R [0.67,1.7094605,1.7094604947 361744339,- 0.5263825566 1 E -8],
+--R [0.68,1.6905616,1.6905616412 966267409,0.4129662674 09 E -7],
+--R [0.69,1.6722911,1.6722911378 028518669,0.3780285186 7 E -7],
+--R [0.7,1.6546216,1.6546216358 026294047,0.3580262940 47 E -7],
+--R [0.71,1.6375273,1.6375273242 106478561,0.2421064785 61 E -7],
+--R [0.72,1.6209838,1.6209838226 402554549,0.2264025545 49 E -7],
+--R [0.73,1.6049681,1.6049680835 025519782,- 0.1649744802 18 E -7],
+--R [0.74,1.5894583,1.5894583020 434418638,0.2043441863 8 E -8],
+--R [0.75,1.5744338,1.5744338335 777364887,0.3357773648 87 E -7],
+--R [0.76,1.5598751,1.5598751172 573846082,0.1725738460 82 E -7],
+--R [0.77,1.5457636,1.5457636057 797852649,0.5779785264 9 E -8],
+--R [0.78,1.5320817,1.5320817005 030656562,0.5030656562 E -9],
+--R [0.79,1.5188127,1.5188126914 891934625,- 0.8510806537 49 E -8],
+--R [0.8,1.5059407,1.5059407020 437066212,0.2043706621 2 E -8],
+--R [0.81,1.4934506,1.4934506373 634333213,0.3736343332 13 E -7],
+--R [0.82,1.4813281,1.4813281369 414902969,0.3694149029 69 E -7],
+--R [0.83,1.4695595,1.4695595304 126515262,0.3041265152 62 E -7],
+--R [0.84,1.4581318,1.4581317965 523616189,- 0.3447638381 1 E -8],
+--R [0.85,1.4470325,1.4470325251 696546055,0.2516965460 55 E -7],
+--R [0.86,1.4362499,1.4362498816 584011227,- 0.1834159887 73 E -7],
+--R [0.87,1.4257726,1.4257725739 929697346,- 0.2600703026 54 E -7],
+--R [0.88,1.4155898,1.4155898219 738353763,0.2197383537 63 E -7],
+--R [0.89,1.4056913,1.4056913285 461485888,0.2854614858 88 E -7],
+--R [0.9,1.3960673,1.3960672530 300118351,- 0.4696998816 49 E -7],
+--R [0.91,1.3867082,1.3867081861 153858453,- 0.1388461415 47 E -7],
+--R [0.92,1.3776051,1.3776051264 873387552,0.2648733875 52 E -7],
+--R [0.93,1.3687495,1.3687494589 589029032,- 0.4104109709 68 E -7],
+--R [0.94,1.3601329,1.3601329339 992502041,0.3399925020 41 E -7],
+--R [0.95,1.3517476,1.3517476485 543534541,0.4855435345 41 E -7],
+--R [0.96,1.343586,1.3435860280 658708165,0.2806587081 65 E -7],
+--R [0.97,1.3356408,1.3356408096 017654982,0.9601765498 2 E -8],
+--R [0.98,1.327905,1.3279050260 192333791,0.2601923337 91 E -7],
+--R [0.99,1.320372,1.3203719910 869302267,- 0.8913069773 26 E -8],
+--R [1.0,1.3130353,1.3130352854 993313036,- 0.1450066869 64 E -7],
+--R [1.01,1.3058887,1.3058887437 213768521,0.4372137685 21 E -7],
+--R [1.02,1.2989264,1.2989264416 064081471,0.4160640814 71 E -7],
+--R [1.03,1.2921427,1.2921426847 348261269,- 0.1526517387 31 E -7],
+--R [1.04,1.285532,1.2855319974 249487926,- 0.2575051207 4 E -8],
+--R [1.05,1.2790891,1.2790891123 712411139,0.1237124111 39 E -7],
+--R [1.06,1.272809,1.2728089608 684747719,- 0.3913152522 81 E -7],
+--R [1.07,1.2666867,1.2666866635 834740719,- 0.3641652592 81 E -7],
+--R [1.08,1.2607175,1.2607175218 389451031,0.2183894510 31 E -7],
+--R [1.09,1.254897,1.2548970093 764914129,0.9376491412 86 E -8],
+--R [1.1,1.2492208,1.2492207645 683124166,- 0.3543168758 34 E -7],
+--R [1.11,1.2436846,1.2436845830 492796933,- 0.1695072030 67 E -7],
+--R [1.12,1.2382844,1.2382844107 43108546,0.1074310854 6 E -7],
+--R [1.13,1.2330163,1.2330163372 582033675,0.3725820336 75 E -7],
+--R [1.14,1.2278766,1.2278765896 304695801,- 0.1036953041 99 E -7],
+--R [1.15,1.2228615,1.2228615263 919649847,0.2639196498 47 E -7],
+--R [1.16,1.2179676,1.2179676319 457208259,0.3194572082 59 E -7],
+--R [1.17,1.2131915,1.2131915112 284082387,0.1122840823 87 E -7],
+--R [1.18,1.2085299,1.2085298846 437684793,- 0.1535623152 07 E -7],
+--R [1.19,1.2039796,1.2039795832 508740941,- 0.1674912590 59 E -7],
+--R [1.2,1.1995375,1.1995375441 923507667,0.4419235076 67 E -7],
+--R [1.21,1.1952008,1.1952008063 486731313,0.6348673131 3 E -8],
+--R [1.22,1.1909665,1.1909665062 055588292,0.6205558829 2 E -8],
+--R [1.23,1.1868319,1.1868318739 22329409,- 0.2607767059 1 E -7],
+--R [1.24,1.1827942,1.1827942295 898897106,0.2958988971 06 E -7],
+--R [1.25,1.178851,1.1788509796 677040268,- 0.2033229597 32 E -7],
+--R [1.26,1.1749996,1.1749996135 898220841,0.1358982208 41 E -7],
+--R [1.27,1.1712377,1.1712377005 306348077,0.5306348077 E -9],
+--R [1.28,1.1675629,1.1675628863 216226741,- 0.1367837732 59 E -7],
+--R [1.29,1.1639729,1.1639728905 10901625,- 0.9489098374 98 E -8],
+--R [1.3,1.1604655,1.1604655035 578761464,0.3557876146 4 E -8],
+--R [1.31,1.1570386,1.1570385841 557790704,- 0.1584422092 96 E -7],
+--R [1.32,1.1536901,1.1536900566 75315566,- 0.4332468443 4 E -7],
+--R [1.33,1.1504179,1.1504179087 23037052,0.8723037051 99 E -8],
+--R [1.34,1.1472202,1.1472201888 084516077,- 0.1119154839 23 E -7],
+--R [1.35,1.144095,1.1440950041 142329045,0.4114232904 5 E -8],
+--R [1.36,1.1410405,1.1410405183 642215979,0.1836422159 79 E -7],
+--R [1.37,1.138055,1.1380549497 842232286,- 0.5021577677 14 E -7],
+--R [1.38,1.1351366,1.1351365691 508965597,- 0.3084910344 03 E -7],
+--R [1.39,1.1322837,1.1322836979 242973771,- 0.2075702622 9 E -8],
+--R [1.4,1.1294947,1.1294947064 598964505,0.6459896450 5 E -8],
+--R [1.41,1.126768,1.1267680122 961278243,0.1229612782 43 E -7],
+--R [1.42,1.1241021,1.1241020785 137460187,- 0.2148625398 13 E -7],
+--R [1.43,1.1214954,1.1214954121 634791355,0.1216347913 55 E -7],
+--R [1.44,1.1189466,1.1189465627 586602379,- 0.3724133976 21 E -7],
+--R [1.45,1.1164541,1.1164541208 297026222,0.2082970262 22 E -7],
+--R [1.46,1.1140167,1.1140167165 374565427,0.1653745654 27 E -7],
+--R [1.47,1.111633,1.1116330183 426463597,0.1834264635 97 E -7],
+--R [1.48,1.1093017,1.1093017317 287386746,0.3172873867 46 E -7],
+--R [1.49,1.1070216,1.1070215979 757344389,- 0.2024265561 1 E -8],
+--R [1.5,1.1047914,1.1047913929 825119039,- 0.7017488096 1 E -8],
+--R [1.51,1.1026099,1.1026099261 354731665,0.2613547316 65 E -7],
+--R [1.52,1.100476,1.1004760392 213654987,0.3922136549 87 E -7],
+--R [1.53,1.0983886,1.0983886053 822601088,0.5382260108 8 E -8],
+--R [1.54,1.0963465,1.0963465281 107759211,0.2811077592 11 E -7],
+--R [1.55,1.0943487,1.0943487402 837348018,0.4028373480 18 E -7],
+--R [1.56,1.0923942,1.0923942032 325277949,0.3232527794 9 E -8],
+--R [1.57,1.0904819,1.0904819058 485597183,0.5848559718 3 E -8],
+--R [1.58,1.0886109,1.0886108637 222222566,- 0.3627777774 34 E -7],
+--R [1.59,1.0867801,1.0867801183 139237769,0.1831392377 69 E -7],
+--R [1.6,1.0849887,1.0849887361 557777925,0.3615577779 25 E -7],
+--R [1.61,1.0832358,1.0832358080 826215661,0.8082621566 08 E -8],
+--R [1.62,1.0815204,1.0815204484 911020471,0.4849110204 71 E -7],
+--R [1.63,1.0798418,1.0798417946 256284042,- 0.5374371595 8 E -8],
+--R [1.64,1.078199,1.0781990058 90049072,0.5890049072 E -8],
+--R [1.65,1.0765913,1.0765912631 839666847,- 0.3681603331 53 E -7],
+--R [1.66,1.0750178,1.0750177682 626567093,- 0.3173734329 07 E -7],
+--R [1.67,1.0734777,1.0734777431 19605205,0.4311960520 5 E -7],
+--R [1.68,1.0719704,1.0719704293 907280832,0.2939072808 32 E -7],
+--R [1.69,1.0704951,1.0704950877 793786871,- 0.1222062131 29 E -7],
+--R [1.7,1.069051,1.0690509975 012925984,- 0.2498707401 6 E -8],
+--R [1.71,1.0676375,1.0676374557 486584477,- 0.4425134155 23 E -7],
+--R [1.72,1.0662538,1.0662537771 725412807,- 0.2282745871 93 E -7],
+--R [1.73,1.0648993,1.0648992933 829208457,- 0.6617079154 3 E -8],
+--R [1.74,1.0635734,1.0635733524 656411166,- 0.4753435888 34 E -7],
+--R [1.75,1.0622753,1.0622753185 155995724,0.1851559957 24 E -7],
+--R [1.76,1.0610046,1.0610045711 855353057,- 0.2881446469 43 E -7],
+--R [1.77,1.0597605,1.0597605052 49804028,0.5249804028 E -8],
+--R [1.78,1.0585425,1.0585425301 825555676,0.3018255556 76 E -7],
+--R [1.79,1.0573501,1.0573500697 497555933,- 0.3025024440 67 E -7],
+--R [1.8,1.0561826,1.0561825616 145181279,- 0.3838548187 21 E -7],
+--R [1.81,1.0550395,1.0550394569 552390051,- 0.4304476099 49 E -7],
+--R [1.82,1.0539202,1.0539202200 960428446,0.2009604284 46 E -7],
+--R [1.83,1.0528243,1.0528243281 490774395,0.2814907743 95 E -7],
+--R [1.84,1.0517513,1.0517512706 682097163,- 0.2933179028 37 E -7],
+--R [1.85,1.0507005,1.0507005493 136967107,0.4931369671 07 E -7],
+--R [1.86,1.0496717,1.0496716775 274233515,- 0.2247257664 85 E -7],
+--R [1.87,1.0486642,1.0486641802 183162995,- 0.1978168370 05 E -7],
+--R [1.88,1.0476776,1.0476775934 575597155,- 0.6542440284 5 E -8],
+--R [1.89,1.0467115,1.0467114641 832546561,- 0.3581674534 39 E -7],
+--R [1.9,1.0457653,1.0457653499 141788749,0.4991417887 49 E -7],
+--R [1.91,1.0448388,1.0448388184 72318166,0.1847231816 6 E -7],
+--R [1.92,1.0439314,1.0439314477 1385408,0.4771385408 E -7],
+--R [1.93,1.0430428,1.0430428252 683058841,0.2526830588 41 E -7],
+--R [1.94,1.0421725,1.0421725482 855370847,0.4828553708 47 E -7],
+--R [1.95,1.0413202,1.0413202231 90348688,0.2319034868 8 E -7],
+--R [1.96,1.0404855,1.0404854654 443926981,- 0.3455560730 19 E -7],
+--R [1.97,1.0396679,1.0396678993 151501465,- 0.6848498535 E -9],
+--R [1.98,1.0388672,1.0388671576 517282541,- 0.4234827174 59 E -7],
+--R [1.99,1.0380829,1.0380828816 672411665,- 0.1833275883 35 E -7],
+--R [2.0,1.0373147,1.0373147207 275480959,0.2072754809 59 E -7]]
+--R Type: List List
Float
+--E 2
+
+)spool
+)lisp (bye)
+
+@
+
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} {\bf Digital Library of Mathematical Functions},
+http://dlmf.nist.gov
+\bibitem{2} Abramowitz and Stegun, ``Handbook of Mathematical Functions'',
+Dover Publications, Inc. New York 1965. pp213-216
+\end{thebibliography}
+\end{document}
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