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-;;; 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
generated by cgit v1.2.3 (git 2.46.0) at 2024-11-13 01:11:34 +0000