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

[Miles Bader]

Index: emacs/lisp/obsolete/float.el
diff -c /dev/null emacs/lisp/obsolete/float.el:1.2.2.1
*** /dev/null   Tue Oct 14 19:52:12 2003
--- emacs/lisp/obsolete/float.el        Tue Oct 14 19:51:32 2003
***************
*** 0 ****
--- 1,459 ----
+ ;;; float.el --- obsolete floating point arithmetic package
+ 
+ ;; Copyright (C) 1986 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 2, 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; see the file COPYING.  If not, write to the
+ ;; Free Software Foundation, Inc., 59 Temple Place - Suite 330,
+ ;; Boston, MA 02111-1307, USA.
+ 
+ ;;; Commentary:
+ 
+ ;; 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-int 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-int
+                            (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