[Emacs-diffs] Changes to obsolete/float.el

[Stefan Monnier]

CVSROOT:        /sources/emacs
Module name:    emacs
Changes by:     Stefan Monnier <monnier>        08/06/03 08:08:01

Index: obsolete/float.el
===================================================================
RCS file: obsolete/float.el
diff -N obsolete/float.el
--- obsolete/float.el   6 May 2008 04:27:25 -0000       1.14
+++ /dev/null   1 Jan 1970 00:00:00 -0000
@@ -1,460 +0,0 @@
-;;; float.el --- obsolete floating point arithmetic package
-
-;; Copyright (C) 1986, 2001, 2002, 2003, 2004, 2005,
-;;   2006, 2007, 2008 Free Software Foundation, Inc.
-
-;; Author: Bill Rosenblatt
-;; Maintainer: FSF
-;; Keywords: extensions
-
-;; This file is part of GNU Emacs.
-
-;; GNU Emacs is free software: you can redistribute it and/or modify
-;; it under the terms of the GNU General Public License as published by
-;; the Free Software Foundation, either version 3 of the License, or
-;; (at your option) any later version.
-
-;; GNU Emacs is distributed in the hope that it will be useful,
-;; but WITHOUT ANY WARRANTY; without even the implied warranty of
-;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-;; GNU General Public License for more details.
-
-;; You should have received a copy of the GNU General Public License
-;; along with GNU Emacs.  If not, see <http://www.gnu.org/licenses/>.
-
-;;; Commentary:
-
-;; This file has been obsolete since Emacs 22.1.
-
-;; Floating point numbers are represented by dot-pairs (mant . exp)
-;; where mant is the 24-bit signed integral mantissa and exp is the
-;; base 2 exponent.
-;;
-;; Emacs LISP supports a 24-bit signed integer data type, which has a
-;; range of -(2**23) to +(2**23)-1, or -8388608 to 8388607 decimal.
-;; This gives six significant decimal digit accuracy.  Exponents can
-;; be anything in the range -(2**23) to +(2**23)-1.
-;;
-;; User interface:
-;; function f converts from integer to floating point
-;; function string-to-float converts from string to floating point
-;; function fint converts a floating point to integer (with truncation)
-;; function float-to-string converts from floating point to string
-;;
-;; Caveats:
-;; -  Exponents outside of the range of +/-100 or so will cause certain
-;;    functions (especially conversion routines) to take forever.
-;; -  Very little checking is done for fixed point overflow/underflow.
-;; -  No checking is done for over/underflow of the exponent
-;;    (hardly necessary when exponent can be 2**23).
-;;
-;;
-;; Bill Rosenblatt
-;; June 20, 1986
-;;
-
-;;; Code:
-
-;; fundamental implementation constants
-(defconst exp-base 2
-  "Base of exponent in this floating point representation.")
-
-(defconst mantissa-bits 24
-  "Number of significant bits in this floating point representation.")
-
-(defconst decimal-digits 6
-  "Number of decimal digits expected to be accurate.")
-
-(defconst expt-digits 2
-  "Maximum permitted digits in a scientific notation exponent.")
-
-;; other constants
-(defconst maxbit (1- mantissa-bits)
-  "Number of highest bit")
-
-(defconst mantissa-maxval (1- (ash 1 maxbit))
-  "Maximum permissible value of mantissa")
-
-(defconst mantissa-minval (ash 1 maxbit)
-  "Minimum permissible value of mantissa")
-
-(defconst floating-point-regexp
-  "^[ \t]*\\(-?\\)\\([0-9]*\\)\
-\\(\\.\\([0-9]*\\)\\|\\)\
-\\(\\(\\([Ee]\\)\\(-?\\)\\([0-9][0-9]*\\)\\)\\|\\)[ \t]*$"
-  "Regular expression to match floating point numbers.  Extract matches:
-1 - minus sign
-2 - integer part
-4 - fractional part
-8 - minus sign for power of ten
-9 - power of ten
-")
-
-(defconst high-bit-mask (ash 1 maxbit)
-  "Masks all bits except the high-order (sign) bit.")
-
-(defconst second-bit-mask (ash 1 (1- maxbit))
-  "Masks all bits except the highest-order magnitude bit")
-
-;; various useful floating point constants
-(defconst _f0 '(0 . 1))
-
-(defconst _f1/2 '(4194304 . -23))
-
-(defconst _f1 '(4194304 . -22))
-
-(defconst _f10 '(5242880 . -19))
-
-;; support for decimal conversion routines
-(defvar powers-of-10 (make-vector (1+ decimal-digits) _f1))
-(aset powers-of-10 1 _f10)
-(aset powers-of-10 2 '(6553600 . -16))
-(aset powers-of-10 3 '(8192000 . -13))
-(aset powers-of-10 4 '(5120000 . -9))
-(aset powers-of-10 5 '(6400000 . -6))
-(aset powers-of-10 6 '(8000000 . -3))
-
-(defconst all-decimal-digs-minval (aref powers-of-10 (1- decimal-digits)))
-(defconst highest-power-of-10 (aref powers-of-10 decimal-digits))
-
-(defun fashl (fnum)                    ; floating-point arithmetic shift left
-  (cons (ash (car fnum) 1) (1- (cdr fnum))))
-
-(defun fashr (fnum)                    ; floating point arithmetic shift right
-  (cons (ash (car fnum) -1) (1+ (cdr fnum))))
-
-(defun normalize (fnum)
-  (if (> (car fnum) 0)                 ; make sure next-to-highest bit is set
-      (while (zerop (logand (car fnum) second-bit-mask))
-       (setq fnum (fashl fnum)))
-    (if (< (car fnum) 0)               ; make sure highest bit is set
-       (while (zerop (logand (car fnum) high-bit-mask))
-         (setq fnum (fashl fnum)))
-      (setq fnum _f0)))                        ; "standard 0"
-  fnum)
-
-(defun abs (n)                         ; integer absolute value
-  (if (>= n 0) n (- n)))
-
-(defun fabs (fnum)                     ; re-normalize after taking abs value
-  (normalize (cons (abs (car fnum)) (cdr fnum))))
-
-(defun xor (a b)                       ; logical exclusive or
-  (and (or a b) (not (and a b))))
-
-(defun same-sign (a b)                 ; two f-p numbers have same sign?
-  (not (xor (natnump (car a)) (natnump (car b)))))
-
-(defun extract-match (str i)           ; used after string-match
-  (condition-case ()
-      (substring str (match-beginning i) (match-end i))
-    (error "")))
-
-;; support for the multiplication function
-(defconst halfword-bits (/ mantissa-bits 2)) ; bits in a halfword
-(defconst masklo (1- (ash 1 halfword-bits))) ; isolate the lower halfword
-(defconst maskhi (lognot masklo))      ; isolate the upper halfword
-(defconst round-limit (ash 1 (/ halfword-bits 2)))
-
-(defun hihalf (n)                      ; return high halfword, shifted down
-  (ash (logand n maskhi) (- halfword-bits)))
-
-(defun lohalf (n)                      ; return low halfword
-  (logand n masklo))
-
-;; Visible functions
-
-;; Arithmetic functions
-(defun f+ (a1 a2)
-  "Returns the sum of two floating point numbers."
-  (let ((f1 (fmax a1 a2))
-       (f2 (fmin a1 a2)))
-    (if (same-sign a1 a2)
-       (setq f1 (fashr f1)             ; shift right to avoid overflow
-             f2 (fashr f2)))
-    (normalize
-     (cons (+ (car f1) (ash (car f2) (- (cdr f2) (cdr f1))))
-          (cdr f1)))))
-
-(defun f- (a1 &optional a2)            ; unary or binary minus
-  "Returns the difference of two floating point numbers."
-  (if a2
-      (f+ a1 (f- a2))
-    (normalize (cons (- (car a1)) (cdr a1)))))
-
-(defun f* (a1 a2)                      ; multiply in halfword chunks
-  "Returns the product of two floating point numbers."
-  (let* ((i1 (car (fabs a1)))
-        (i2 (car (fabs a2)))
-        (sign (not (same-sign a1 a2)))
-        (prodlo (+ (hihalf (* (lohalf i1) (lohalf i2)))
-                   (lohalf (* (hihalf i1) (lohalf i2)))
-                   (lohalf (* (lohalf i1) (hihalf i2)))))
-        (prodhi (+ (* (hihalf i1) (hihalf i2))
-                   (hihalf (* (hihalf i1) (lohalf i2)))
-                   (hihalf (* (lohalf i1) (hihalf i2)))
-                   (hihalf prodlo))))
-    (if (> (lohalf prodlo) round-limit)
-       (setq prodhi (1+ prodhi)))      ; round off truncated bits
-    (normalize
-     (cons (if sign (- prodhi) prodhi)
-          (+ (cdr (fabs a1)) (cdr (fabs a2)) mantissa-bits)))))
-
-(defun f/ (a1 a2)                      ; SLOW subtract-and-shift algorithm
-  "Returns the quotient of two floating point numbers."
-  (if (zerop (car a2))                 ; if divide by 0
-      (signal 'arith-error (list "attempt to divide by zero" a1 a2))
-    (let ((bits (1- maxbit))
-         (quotient 0)
-         (dividend (car (fabs a1)))
-         (divisor (car (fabs a2)))
-         (sign (not (same-sign a1 a2))))
-      (while (natnump bits)
-       (if (< (- dividend divisor) 0)
-           (setq quotient (ash quotient 1))
-         (setq quotient (1+ (ash quotient 1))
-               dividend (- dividend divisor)))
-       (setq dividend (ash dividend 1)
-             bits (1- bits)))
-      (normalize
-       (cons (if sign (- quotient) quotient)
-            (- (cdr (fabs a1)) (cdr (fabs a2)) (1- maxbit)))))))
-
-(defun f% (a1 a2)
-  "Returns the remainder of first floating point number divided by second."
-  (f- a1 (f* (ftrunc (f/ a1 a2)) a2)))
-
-
-;; Comparison functions
-(defun f= (a1 a2)
-  "Returns t if two floating point numbers are equal, nil otherwise."
-  (equal a1 a2))
-
-(defun f> (a1 a2)
-  "Returns t if first floating point number is greater than second,
-nil otherwise."
-  (cond ((and (natnump (car a1)) (< (car a2) 0))
-        t)                             ; a1 nonnegative, a2 negative
-       ((and (> (car a1) 0) (<= (car a2) 0))
-        t)                             ; a1 positive, a2 nonpositive
-       ((and (<= (car a1) 0) (natnump (car a2)))
-        nil)                           ; a1 nonpos, a2 nonneg
-       ((/= (cdr a1) (cdr a2))         ; same signs.  exponents differ
-        (> (cdr a1) (cdr a2)))         ; compare the mantissas.
-       (t
-        (> (car a1) (car a2)))))       ; same exponents.
-
-(defun f>= (a1 a2)
-  "Returns t if first floating point number is greater than or equal to
-second, nil otherwise."
-  (or (f> a1 a2) (f= a1 a2)))
-
-(defun f< (a1 a2)
-  "Returns t if first floating point number is less than second,
-nil otherwise."
-  (not (f>= a1 a2)))
-
-(defun f<= (a1 a2)
-  "Returns t if first floating point number is less than or equal to
-second, nil otherwise."
-  (not (f> a1 a2)))
-
-(defun f/= (a1 a2)
-  "Returns t if first floating point number is not equal to second,
-nil otherwise."
-  (not (f= a1 a2)))
-
-(defun fmin (a1 a2)
-  "Returns the minimum of two floating point numbers."
-  (if (f< a1 a2) a1 a2))
-
-(defun fmax (a1 a2)
-  "Returns the maximum of two floating point numbers."
-  (if (f> a1 a2) a1 a2))
-
-(defun fzerop (fnum)
-  "Returns t if the floating point number is zero, nil otherwise."
-  (= (car fnum) 0))
-
-(defun floatp (fnum)
-  "Returns t if the arg is a floating point number, nil otherwise."
-  (and (consp fnum) (integerp (car fnum)) (integerp (cdr fnum))))
-
-;; Conversion routines
-(defun f (int)
-  "Convert the integer argument to floating point, like a C cast operator."
-  (normalize (cons int '0)))
-
-(defun int-to-hex-string (int)
-  "Convert the integer argument to a C-style hexadecimal string."
-  (let ((shiftval -20)
-       (str "0x")
-       (hex-chars "0123456789ABCDEF"))
-    (while (<= shiftval 0)
-      (setq str (concat str (char-to-string
-                       (aref hex-chars
-                             (logand (lsh int shiftval) 15))))
-           shiftval (+ shiftval 4)))
-    str))
-
-(defun ftrunc (fnum)                   ; truncate fractional part
-  "Truncate the fractional part of a floating point number."
-  (cond ((natnump (cdr fnum))          ; it's all integer, return number as is
-        fnum)
-       ((<= (cdr fnum) (- maxbit))     ; it's all fractional, return 0
-        '(0 . 1))
-       (t                              ; otherwise mask out fractional bits
-        (let ((mant (car fnum)) (exp (cdr fnum)))
-          (normalize
-           (cons (if (natnump mant)    ; if negative, use absolute value
-                     (ash (ash mant exp) (- exp))
-                   (- (ash (ash (- mant) exp) (- exp))))
-                 exp))))))
-
-(defun fint (fnum)                     ; truncate and convert to integer
-  "Convert the floating point number to integer, with truncation,
-like a C cast operator."
-  (let* ((tf (ftrunc fnum)) (tint (car tf)) (texp (cdr tf)))
-    (cond ((>= texp mantissa-bits)     ; too high, return "maxint"
-          mantissa-maxval)
-         ((<= texp (- mantissa-bits))  ; too low, return "minint"
-          mantissa-minval)
-         (t                            ; in range
-          (ash tint texp)))))          ; shift so that exponent is 0
-
-(defun float-to-string (fnum &optional sci)
-  "Convert the floating point number to a decimal string.
-Optional second argument non-nil means use scientific notation."
-  (let* ((value (fabs fnum)) (sign (< (car fnum) 0))
-        (power 0) (result 0) (str "")
-        (temp 0) (pow10 _f1))
-
-    (if (f= fnum _f0)
-       "0"
-      (if (f>= value _f1)                      ; find largest power of 10 <= 
value
-         (progn                                ; value >= 1, power is positive
-           (while (f<= (setq temp (f* pow10 highest-power-of-10)) value)
-             (setq pow10 temp
-                   power (+ power decimal-digits)))
-           (while (f<= (setq temp (f* pow10 _f10)) value)
-             (setq pow10 temp
-                   power (1+ power))))
-       (progn                          ; value < 1, power is negative
-         (while (f> (setq temp (f/ pow10 highest-power-of-10)) value)
-           (setq pow10 temp
-                 power (- power decimal-digits)))
-         (while (f> pow10 value)
-           (setq pow10 (f/ pow10 _f10)
-                 power (1- power)))))
-                                         ; get value in range 100000 to 999999
-      (setq value (f* (f/ value pow10) all-decimal-digs-minval)
-           result (ftrunc value))
-      (let (int)
-       (if (f> (f- value result) _f1/2)        ; round up if remainder > 0.5
-           (setq int (1+ (fint result)))
-         (setq int (fint result)))
-       (setq str (int-to-string int))
-       (if (>= int 1000000)
-           (setq power (1+ power))))
-
-      (if sci                          ; scientific notation
-         (setq str (concat (substring str 0 1) "." (substring str 1)
-                           "E" (int-to-string power)))
-
-                                         ; regular decimal string
-       (cond ((>= power (1- decimal-digits))
-                                         ; large power, append zeroes
-              (let ((zeroes (- power decimal-digits)))
-                (while (natnump zeroes)
-                  (setq str (concat str "0")
-                        zeroes (1- zeroes)))))
-
-                                         ; negative power, prepend decimal
-             ((< power 0)              ; point and zeroes
-              (let ((zeroes (- (- power) 2)))
-                (while (natnump zeroes)
-                  (setq str (concat "0" str)
-                        zeroes (1- zeroes)))
-                (setq str (concat "0." str))))
-
-             (t                                ; in range, insert decimal point
-              (setq str (concat
-                         (substring str 0 (1+ power))
-                         "."
-                         (substring str (1+ power)))))))
-
-      (if sign                         ; if negative, prepend minus sign
-         (concat "-" str)
-       str))))
-
-
-;; string to float conversion.
-;; accepts scientific notation, but ignores anything after the first two
-;; digits of the exponent.
-(defun string-to-float (str)
-  "Convert the string to a floating point number.
-Accepts a decimal string in scientific notation, with exponent preceded
-by either E or e.  Only the six most significant digits of the integer
-and fractional parts are used; only the first two digits of the exponent
-are used.  Negative signs preceding both the decimal number and the exponent
-are recognized."
-
-  (if (string-match floating-point-regexp str 0)
-      (let (power)
-       (f*
-        ; calculate the mantissa
-        (let* ((int-subst (extract-match str 2))
-               (fract-subst (extract-match str 4))
-               (digit-string (concat int-subst fract-subst))
-               (mant-sign (equal (extract-match str 1) "-"))
-               (leading-0s 0) (round-up nil))
-
-          ; get rid of leading 0's
-          (setq power (- (length int-subst) decimal-digits))
-          (while (and (< leading-0s (length digit-string))
-                      (= (aref digit-string leading-0s) ?0))
-            (setq leading-0s (1+ leading-0s)))
-          (setq power (- power leading-0s)
-                digit-string (substring digit-string leading-0s))
-
-          ; if more than 6 digits, round off
-          (if (> (length digit-string) decimal-digits)
-              (setq round-up (>= (aref digit-string decimal-digits) ?5)
-                    digit-string (substring digit-string 0 decimal-digits))
-            (setq power (+ power (- decimal-digits (length digit-string)))))
-
-          ; round up and add minus sign, if necessary
-          (f (* (+ (string-to-number digit-string)
-                   (if round-up 1 0))
-                (if mant-sign -1 1))))
-
-        ; calculate the exponent (power of ten)
-        (let* ((expt-subst (extract-match str 9))
-               (expt-sign (equal (extract-match str 8) "-"))
-               (expt 0) (chunks 0) (tens 0) (exponent _f1)
-               (func 'f*))
-
-          (setq expt (+ (* (string-to-number
-                            (substring expt-subst 0
-                                       (min expt-digits (length expt-subst))))
-                           (if expt-sign -1 1))
-                        power))
-          (if (< expt 0)               ; if power of 10 negative
-              (setq expt (- expt)      ; take abs val of exponent
-                    func 'f/))         ; and set up to divide, not multiply
-
-          (setq chunks (/ expt decimal-digits)
-                tens (% expt decimal-digits))
-          ; divide or multiply by "chunks" of 10**6
-          (while (> chunks 0)
-            (setq exponent (funcall func exponent highest-power-of-10)
-                  chunks (1- chunks)))
-          ; divide or multiply by remaining power of ten
-          (funcall func exponent (aref powers-of-10 tens)))))
-
-    _f0))                              ; if invalid, return 0
-
-(provide 'float)
-
-;; arch-tag: cc0c89c6-5718-49af-978e-585f6b14e347
-;;; float.el ends here