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202bd7bff2
Change logb to return -infinity, +infinity, and NaN respectively. Formerly logb returned an extreme fixnum to represent infinity, but this is no longer the right thing to do now that we have bignums and there is no extreme integer. * doc/lispref/numbers.texi (Float Basics), etc/NEWS: Document. * src/floatfns.c (Flogb): Implement this.
618 lines
16 KiB
C
618 lines
16 KiB
C
/* Primitive operations on floating point for GNU Emacs Lisp interpreter.
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Copyright (C) 1988, 1993-1994, 1999, 2001-2019 Free Software Foundation,
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Inc.
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Author: Wolfgang Rupprecht (according to ack.texi)
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This file is part of GNU Emacs.
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GNU Emacs is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or (at
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your option) any later version.
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GNU Emacs is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with GNU Emacs. If not, see <https://www.gnu.org/licenses/>. */
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/* C89 requires only the following math.h functions, and Emacs omits
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the starred functions since we haven't found a use for them:
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acos, asin, atan, atan2, ceil, cos, *cosh, exp, fabs, floor, fmod,
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frexp, ldexp, log, log10 [via (log X 10)], *modf, pow, sin, *sinh,
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sqrt, tan, *tanh.
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C99 and C11 require the following math.h functions in addition to
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the C89 functions. Of these, Emacs currently exports only the
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starred ones to Lisp, since we haven't found a use for the others:
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acosh, atanh, cbrt, *copysign, erf, erfc, exp2, expm1, fdim, fma,
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fmax, fmin, fpclassify, hypot, ilogb, isfinite, isgreater,
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isgreaterequal, isinf, isless, islessequal, islessgreater, *isnan,
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isnormal, isunordered, lgamma, log1p, *log2 [via (log X 2)], *logb
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(approximately), lrint/llrint, lround/llround, nan, nearbyint,
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nextafter, nexttoward, remainder, remquo, *rint, round, scalbln,
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scalbn, signbit, tgamma, *trunc.
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*/
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#include <config.h>
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#include "lisp.h"
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#include "bignum.h"
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#include <math.h>
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#include <count-leading-zeros.h>
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/* Check that X is a floating point number. */
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static void
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CHECK_FLOAT (Lisp_Object x)
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{
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CHECK_TYPE (FLOATP (x), Qfloatp, x);
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}
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/* Extract a Lisp number as a `double', or signal an error. */
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double
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extract_float (Lisp_Object num)
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{
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CHECK_NUMBER (num);
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return XFLOATINT (num);
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}
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/* Trig functions. */
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DEFUN ("acos", Facos, Sacos, 1, 1, 0,
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doc: /* Return the inverse cosine of ARG. */)
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(Lisp_Object arg)
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{
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double d = extract_float (arg);
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d = acos (d);
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return make_float (d);
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}
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DEFUN ("asin", Fasin, Sasin, 1, 1, 0,
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doc: /* Return the inverse sine of ARG. */)
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(Lisp_Object arg)
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{
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double d = extract_float (arg);
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d = asin (d);
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return make_float (d);
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}
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DEFUN ("atan", Fatan, Satan, 1, 2, 0,
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doc: /* Return the inverse tangent of the arguments.
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If only one argument Y is given, return the inverse tangent of Y.
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If two arguments Y and X are given, return the inverse tangent of Y
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divided by X, i.e. the angle in radians between the vector (X, Y)
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and the x-axis. */)
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(Lisp_Object y, Lisp_Object x)
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{
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double d = extract_float (y);
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if (NILP (x))
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d = atan (d);
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else
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{
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double d2 = extract_float (x);
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d = atan2 (d, d2);
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}
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return make_float (d);
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}
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DEFUN ("cos", Fcos, Scos, 1, 1, 0,
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doc: /* Return the cosine of ARG. */)
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(Lisp_Object arg)
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{
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double d = extract_float (arg);
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d = cos (d);
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return make_float (d);
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}
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DEFUN ("sin", Fsin, Ssin, 1, 1, 0,
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doc: /* Return the sine of ARG. */)
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(Lisp_Object arg)
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{
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double d = extract_float (arg);
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d = sin (d);
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return make_float (d);
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}
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DEFUN ("tan", Ftan, Stan, 1, 1, 0,
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doc: /* Return the tangent of ARG. */)
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(Lisp_Object arg)
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{
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double d = extract_float (arg);
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d = tan (d);
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return make_float (d);
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}
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DEFUN ("isnan", Fisnan, Sisnan, 1, 1, 0,
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doc: /* Return non nil if argument X is a NaN. */)
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(Lisp_Object x)
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{
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CHECK_FLOAT (x);
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return isnan (XFLOAT_DATA (x)) ? Qt : Qnil;
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}
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/* Although the substitute does not work on NaNs, it is good enough
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for platforms lacking the signbit macro. */
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#ifndef signbit
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# define signbit(x) ((x) < 0 || (IEEE_FLOATING_POINT && !(x) && 1 / (x) < 0))
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#endif
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DEFUN ("copysign", Fcopysign, Scopysign, 2, 2, 0,
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doc: /* Copy sign of X2 to value of X1, and return the result.
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Cause an error if X1 or X2 is not a float. */)
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(Lisp_Object x1, Lisp_Object x2)
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{
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double f1, f2;
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CHECK_FLOAT (x1);
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CHECK_FLOAT (x2);
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f1 = XFLOAT_DATA (x1);
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f2 = XFLOAT_DATA (x2);
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/* Use signbit instead of copysign, to avoid calling make_float when
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the result is X1. */
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return signbit (f1) != signbit (f2) ? make_float (-f1) : x1;
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}
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DEFUN ("frexp", Ffrexp, Sfrexp, 1, 1, 0,
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doc: /* Get significand and exponent of a floating point number.
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Breaks the floating point number X into its binary significand SGNFCAND
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\(a floating point value between 0.5 (included) and 1.0 (excluded))
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and an integral exponent EXP for 2, such that:
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X = SGNFCAND * 2^EXP
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The function returns the cons cell (SGNFCAND . EXP).
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If X is zero, both parts (SGNFCAND and EXP) are zero. */)
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(Lisp_Object x)
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{
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double f = extract_float (x);
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int exponent;
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double sgnfcand = frexp (f, &exponent);
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return Fcons (make_float (sgnfcand), make_fixnum (exponent));
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}
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DEFUN ("ldexp", Fldexp, Sldexp, 2, 2, 0,
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doc: /* Return SGNFCAND * 2**EXPONENT, as a floating point number.
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EXPONENT must be an integer. */)
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(Lisp_Object sgnfcand, Lisp_Object exponent)
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{
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CHECK_FIXNUM (exponent);
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int e = min (max (INT_MIN, XFIXNUM (exponent)), INT_MAX);
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return make_float (ldexp (extract_float (sgnfcand), e));
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}
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DEFUN ("exp", Fexp, Sexp, 1, 1, 0,
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doc: /* Return the exponential base e of ARG. */)
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(Lisp_Object arg)
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{
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double d = extract_float (arg);
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d = exp (d);
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return make_float (d);
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}
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DEFUN ("expt", Fexpt, Sexpt, 2, 2, 0,
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doc: /* Return the exponential ARG1 ** ARG2. */)
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(Lisp_Object arg1, Lisp_Object arg2)
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{
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CHECK_NUMBER (arg1);
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CHECK_NUMBER (arg2);
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/* Common Lisp spec: don't promote if both are integers, and if the
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result is not fractional. */
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if (INTEGERP (arg1) && !NILP (Fnatnump (arg2)))
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return expt_integer (arg1, arg2);
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return make_float (pow (XFLOATINT (arg1), XFLOATINT (arg2)));
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}
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DEFUN ("log", Flog, Slog, 1, 2, 0,
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doc: /* Return the natural logarithm of ARG.
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If the optional argument BASE is given, return log ARG using that base. */)
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(Lisp_Object arg, Lisp_Object base)
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{
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double d = extract_float (arg);
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if (NILP (base))
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d = log (d);
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else
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{
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double b = extract_float (base);
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if (b == 10.0)
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d = log10 (d);
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#if HAVE_LOG2
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else if (b == 2.0)
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d = log2 (d);
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#endif
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else
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d = log (d) / log (b);
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}
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return make_float (d);
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}
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DEFUN ("sqrt", Fsqrt, Ssqrt, 1, 1, 0,
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doc: /* Return the square root of ARG. */)
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(Lisp_Object arg)
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{
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double d = extract_float (arg);
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d = sqrt (d);
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return make_float (d);
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}
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DEFUN ("abs", Fabs, Sabs, 1, 1, 0,
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doc: /* Return the absolute value of ARG. */)
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(Lisp_Object arg)
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{
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CHECK_NUMBER (arg);
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if (FIXNUMP (arg))
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{
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if (XFIXNUM (arg) < 0)
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arg = make_int (-XFIXNUM (arg));
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}
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else if (FLOATP (arg))
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{
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if (signbit (XFLOAT_DATA (arg)))
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arg = make_float (- XFLOAT_DATA (arg));
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}
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else
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{
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if (mpz_sgn (XBIGNUM (arg)->value) < 0)
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{
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mpz_neg (mpz[0], XBIGNUM (arg)->value);
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arg = make_integer_mpz ();
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}
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}
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return arg;
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}
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DEFUN ("float", Ffloat, Sfloat, 1, 1, 0,
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doc: /* Return the floating point number equal to ARG. */)
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(register Lisp_Object arg)
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{
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CHECK_NUMBER (arg);
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/* If ARG is a float, give 'em the same float back. */
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return FLOATP (arg) ? arg : make_float (XFLOATINT (arg));
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}
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static int
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ecount_leading_zeros (EMACS_UINT x)
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{
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return (EMACS_UINT_WIDTH == UINT_WIDTH ? count_leading_zeros (x)
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: EMACS_UINT_WIDTH == ULONG_WIDTH ? count_leading_zeros_l (x)
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: count_leading_zeros_ll (x));
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}
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DEFUN ("logb", Flogb, Slogb, 1, 1, 0,
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doc: /* Returns largest integer <= the base 2 log of the magnitude of ARG.
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This is the same as the exponent of a float. */)
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(Lisp_Object arg)
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{
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EMACS_INT value;
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CHECK_NUMBER (arg);
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if (FLOATP (arg))
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{
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double f = XFLOAT_DATA (arg);
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if (f == 0)
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return make_float (-HUGE_VAL);
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if (!isfinite (f))
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return f < 0 ? make_float (-f) : arg;
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int ivalue;
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frexp (f, &ivalue);
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value = ivalue - 1;
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}
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else if (!FIXNUMP (arg))
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value = mpz_sizeinbase (XBIGNUM (arg)->value, 2) - 1;
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else
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{
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EMACS_INT i = XFIXNUM (arg);
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if (i == 0)
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return make_float (-HUGE_VAL);
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value = EMACS_UINT_WIDTH - 1 - ecount_leading_zeros (eabs (i));
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}
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return make_fixnum (value);
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}
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/* True if A is exactly representable as an integer. */
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static bool
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integer_value (Lisp_Object a)
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{
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if (FLOATP (a))
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{
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double d = XFLOAT_DATA (a);
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return d == floor (d) && isfinite (d);
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}
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return true;
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}
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/* the rounding functions */
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static Lisp_Object
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rounding_driver (Lisp_Object arg, Lisp_Object divisor,
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double (*double_round) (double),
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void (*int_divide) (mpz_t, mpz_t const, mpz_t const),
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EMACS_INT (*fixnum_divide) (EMACS_INT, EMACS_INT))
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{
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CHECK_NUMBER (arg);
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double d;
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if (NILP (divisor))
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{
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if (! FLOATP (arg))
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return arg;
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d = XFLOAT_DATA (arg);
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}
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else
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{
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CHECK_NUMBER (divisor);
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if (integer_value (arg) && integer_value (divisor))
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{
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/* Divide as integers. Converting to double might lose
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info, even for fixnums; also see the FIXME below. */
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if (FLOATP (arg))
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arg = double_to_integer (XFLOAT_DATA (arg));
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if (FLOATP (divisor))
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divisor = double_to_integer (XFLOAT_DATA (divisor));
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if (FIXNUMP (divisor))
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{
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if (XFIXNUM (divisor) == 0)
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xsignal0 (Qarith_error);
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if (FIXNUMP (arg))
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return make_int (fixnum_divide (XFIXNUM (arg),
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XFIXNUM (divisor)));
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}
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int_divide (mpz[0],
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*bignum_integer (&mpz[0], arg),
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*bignum_integer (&mpz[1], divisor));
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return make_integer_mpz ();
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}
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double f1 = XFLOATINT (arg);
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double f2 = XFLOATINT (divisor);
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if (! IEEE_FLOATING_POINT && f2 == 0)
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xsignal0 (Qarith_error);
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/* FIXME: This division rounds, so the result is double-rounded. */
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d = f1 / f2;
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}
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/* Round, coarsely test for fixnum overflow before converting to
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EMACS_INT (to avoid undefined C behavior), and then exactly test
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for overflow after converting (as FIXNUM_OVERFLOW_P is inaccurate
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on floats). */
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double dr = double_round (d);
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if (fabs (dr) < 2 * (MOST_POSITIVE_FIXNUM + 1))
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{
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EMACS_INT ir = dr;
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if (! FIXNUM_OVERFLOW_P (ir))
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return make_fixnum (ir);
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}
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return double_to_integer (dr);
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}
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static EMACS_INT
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ceiling2 (EMACS_INT n, EMACS_INT d)
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{
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return n / d + ((n % d != 0) & ((n < 0) == (d < 0)));
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}
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static EMACS_INT
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floor2 (EMACS_INT n, EMACS_INT d)
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{
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return n / d - ((n % d != 0) & ((n < 0) != (d < 0)));
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}
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static EMACS_INT
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truncate2 (EMACS_INT n, EMACS_INT d)
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{
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return n / d;
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}
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static EMACS_INT
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round2 (EMACS_INT n, EMACS_INT d)
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{
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/* The C language's division operator gives us the remainder R
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corresponding to truncated division, but we want the remainder R1
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on the other side of 0 if R1 is closer to 0 than R is; because we
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want to round to even, we also want R1 if R and R1 are the same
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distance from 0 and if the truncated quotient is odd. */
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EMACS_INT q = n / d;
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EMACS_INT r = n % d;
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bool neg_d = d < 0;
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bool neg_r = r < 0;
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EMACS_INT abs_r = eabs (r);
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EMACS_INT abs_r1 = eabs (d) - abs_r;
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if (abs_r1 < abs_r + (q & 1))
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q += neg_d == neg_r ? 1 : -1;
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return q;
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}
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static void
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rounddiv_q (mpz_t q, mpz_t const n, mpz_t const d)
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{
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/* Mimic the source code of round2, using mpz_t instead of EMACS_INT. */
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mpz_t *r = &mpz[2], *abs_r = r, *abs_r1 = &mpz[3];
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mpz_tdiv_qr (q, *r, n, d);
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bool neg_d = mpz_sgn (d) < 0;
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bool neg_r = mpz_sgn (*r) < 0;
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mpz_abs (*abs_r, *r);
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mpz_abs (*abs_r1, d);
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mpz_sub (*abs_r1, *abs_r1, *abs_r);
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if (mpz_cmp (*abs_r1, *abs_r) < (mpz_odd_p (q) != 0))
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(neg_d == neg_r ? mpz_add_ui : mpz_sub_ui) (q, q, 1);
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}
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/* The code uses emacs_rint, so that it works to undefine HAVE_RINT
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if `rint' exists but does not work right. */
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#ifdef HAVE_RINT
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#define emacs_rint rint
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#else
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static double
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emacs_rint (double d)
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{
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double d1 = d + 0.5;
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double r = floor (d1);
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return r - (r == d1 && fmod (r, 2) != 0);
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}
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#endif
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#ifndef HAVE_TRUNC
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double
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trunc (double d)
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{
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return (d < 0 ? ceil : floor) (d);
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}
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#endif
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DEFUN ("ceiling", Fceiling, Sceiling, 1, 2, 0,
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doc: /* Return the smallest integer no less than ARG.
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This rounds the value towards +inf.
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With optional DIVISOR, return the smallest integer no less than ARG/DIVISOR. */)
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(Lisp_Object arg, Lisp_Object divisor)
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{
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return rounding_driver (arg, divisor, ceil, mpz_cdiv_q, ceiling2);
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}
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DEFUN ("floor", Ffloor, Sfloor, 1, 2, 0,
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doc: /* Return the largest integer no greater than ARG.
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This rounds the value towards -inf.
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With optional DIVISOR, return the largest integer no greater than ARG/DIVISOR. */)
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(Lisp_Object arg, Lisp_Object divisor)
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{
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return rounding_driver (arg, divisor, floor, mpz_fdiv_q, floor2);
|
||
}
|
||
|
||
DEFUN ("round", Fround, Sround, 1, 2, 0,
|
||
doc: /* Return the nearest integer to ARG.
|
||
With optional DIVISOR, return the nearest integer to ARG/DIVISOR.
|
||
|
||
Rounding a value equidistant between two integers may choose the
|
||
integer closer to zero, or it may prefer an even integer, depending on
|
||
your machine. For example, (round 2.5) can return 3 on some
|
||
systems, but 2 on others. */)
|
||
(Lisp_Object arg, Lisp_Object divisor)
|
||
{
|
||
return rounding_driver (arg, divisor, emacs_rint, rounddiv_q, round2);
|
||
}
|
||
|
||
/* Since rounding_driver truncates anyway, no need to call 'trunc'. */
|
||
static double
|
||
identity (double x)
|
||
{
|
||
return x;
|
||
}
|
||
|
||
DEFUN ("truncate", Ftruncate, Struncate, 1, 2, 0,
|
||
doc: /* Truncate a floating point number to an int.
|
||
Rounds ARG toward zero.
|
||
With optional DIVISOR, truncate ARG/DIVISOR. */)
|
||
(Lisp_Object arg, Lisp_Object divisor)
|
||
{
|
||
return rounding_driver (arg, divisor, identity, mpz_tdiv_q, truncate2);
|
||
}
|
||
|
||
|
||
Lisp_Object
|
||
fmod_float (Lisp_Object x, Lisp_Object y)
|
||
{
|
||
double f1 = XFLOATINT (x);
|
||
double f2 = XFLOATINT (y);
|
||
|
||
f1 = fmod (f1, f2);
|
||
|
||
/* If the "remainder" comes out with the wrong sign, fix it. */
|
||
if (f2 < 0 ? f1 > 0 : f1 < 0)
|
||
f1 += f2;
|
||
|
||
return make_float (f1);
|
||
}
|
||
|
||
DEFUN ("fceiling", Ffceiling, Sfceiling, 1, 1, 0,
|
||
doc: /* Return the smallest integer no less than ARG, as a float.
|
||
\(Round toward +inf.) */)
|
||
(Lisp_Object arg)
|
||
{
|
||
CHECK_FLOAT (arg);
|
||
double d = XFLOAT_DATA (arg);
|
||
d = ceil (d);
|
||
return make_float (d);
|
||
}
|
||
|
||
DEFUN ("ffloor", Fffloor, Sffloor, 1, 1, 0,
|
||
doc: /* Return the largest integer no greater than ARG, as a float.
|
||
\(Round toward -inf.) */)
|
||
(Lisp_Object arg)
|
||
{
|
||
CHECK_FLOAT (arg);
|
||
double d = XFLOAT_DATA (arg);
|
||
d = floor (d);
|
||
return make_float (d);
|
||
}
|
||
|
||
DEFUN ("fround", Ffround, Sfround, 1, 1, 0,
|
||
doc: /* Return the nearest integer to ARG, as a float. */)
|
||
(Lisp_Object arg)
|
||
{
|
||
CHECK_FLOAT (arg);
|
||
double d = XFLOAT_DATA (arg);
|
||
d = emacs_rint (d);
|
||
return make_float (d);
|
||
}
|
||
|
||
DEFUN ("ftruncate", Fftruncate, Sftruncate, 1, 1, 0,
|
||
doc: /* Truncate a floating point number to an integral float value.
|
||
\(Round toward zero.) */)
|
||
(Lisp_Object arg)
|
||
{
|
||
CHECK_FLOAT (arg);
|
||
double d = XFLOAT_DATA (arg);
|
||
d = trunc (d);
|
||
return make_float (d);
|
||
}
|
||
|
||
void
|
||
syms_of_floatfns (void)
|
||
{
|
||
defsubr (&Sacos);
|
||
defsubr (&Sasin);
|
||
defsubr (&Satan);
|
||
defsubr (&Scos);
|
||
defsubr (&Ssin);
|
||
defsubr (&Stan);
|
||
defsubr (&Sisnan);
|
||
defsubr (&Scopysign);
|
||
defsubr (&Sfrexp);
|
||
defsubr (&Sldexp);
|
||
defsubr (&Sfceiling);
|
||
defsubr (&Sffloor);
|
||
defsubr (&Sfround);
|
||
defsubr (&Sftruncate);
|
||
defsubr (&Sexp);
|
||
defsubr (&Sexpt);
|
||
defsubr (&Slog);
|
||
defsubr (&Ssqrt);
|
||
|
||
defsubr (&Sabs);
|
||
defsubr (&Sfloat);
|
||
defsubr (&Slogb);
|
||
defsubr (&Sceiling);
|
||
defsubr (&Sfloor);
|
||
defsubr (&Sround);
|
||
defsubr (&Struncate);
|
||
}
|