-/* Primitive operations on floating point for GNU Emacs Lisp interpreter.
-
-Copyright (C) 1988, 1993-1994, 1999, 2001-2012
- Free Software Foundation, Inc.
-
-Author: Wolfgang Rupprecht
-(according to ack.texi)
-
-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/>. */
-
-
-/* ANSI C requires only these float functions:
- acos, asin, atan, atan2, ceil, cos, cosh, exp, fabs, floor, fmod,
- frexp, ldexp, log, log10, modf, pow, sin, sinh, sqrt, tan, tanh.
-
- Define HAVE_INVERSE_HYPERBOLIC if you have acosh, asinh, and atanh.
- Define HAVE_CBRT if you have cbrt.
- Define HAVE_RINT if you have a working rint.
- If you don't define these, then the appropriate routines will be simulated.
-
- Define HAVE_MATHERR if on a system supporting the SysV matherr callback.
- (This should happen automatically.)
-
- Define FLOAT_CHECK_ERRNO if the float library routines set errno.
- This has no effect if HAVE_MATHERR is defined.
-
- Define FLOAT_CATCH_SIGILL if the float library routines signal SIGILL.
- (What systems actually do this? Please let us know.)
-
- Define FLOAT_CHECK_DOMAIN if the float library doesn't handle errors by
- either setting errno, or signaling SIGFPE/SIGILL. Otherwise, domain and
- range checking will happen before calling the float routines. This has
- no effect if HAVE_MATHERR is defined (since matherr will be called when
- a domain error occurs.)
- */
-
-#include <config.h>
-#include <signal.h>
-#include <setjmp.h>
-#include "lisp.h"
-#include "syssignal.h"
-
-#include <float.h>
-/* If IEEE_FLOATING_POINT isn't defined, default it from FLT_*. */
-#ifndef IEEE_FLOATING_POINT
-#if (FLT_RADIX == 2 && FLT_MANT_DIG == 24 \
- && FLT_MIN_EXP == -125 && FLT_MAX_EXP == 128)
-#define IEEE_FLOATING_POINT 1
-#else
-#define IEEE_FLOATING_POINT 0
-#endif
-#endif
-
-#include <math.h>
-
-/* This declaration is omitted on some systems, like Ultrix. */
-#if !defined (HPUX) && defined (HAVE_LOGB) && !defined (logb)
-extern double logb (double);
-#endif /* not HPUX and HAVE_LOGB and no logb macro */
-
-#if defined (DOMAIN) && defined (SING) && defined (OVERFLOW)
- /* If those are defined, then this is probably a `matherr' machine. */
-# ifndef HAVE_MATHERR
-# define HAVE_MATHERR
-# endif
-#endif
-
-#ifdef NO_MATHERR
-#undef HAVE_MATHERR
-#endif
-
-#ifdef HAVE_MATHERR
-# ifdef FLOAT_CHECK_ERRNO
-# undef FLOAT_CHECK_ERRNO
-# endif
-# ifdef FLOAT_CHECK_DOMAIN
-# undef FLOAT_CHECK_DOMAIN
-# endif
-#endif
-
-#ifndef NO_FLOAT_CHECK_ERRNO
-#define FLOAT_CHECK_ERRNO
-#endif
-
-#ifdef FLOAT_CHECK_ERRNO
-# include <errno.h>
-#endif
-
-#ifdef FLOAT_CATCH_SIGILL
-static void float_error ();
-#endif
-
-/* Nonzero while executing in floating point.
- This tells float_error what to do. */
-
-static int in_float;
-
-/* If an argument is out of range for a mathematical function,
- here is the actual argument value to use in the error message.
- These variables are used only across the floating point library call
- so there is no need to staticpro them. */
-
-static Lisp_Object float_error_arg, float_error_arg2;
-
-static const char *float_error_fn_name;
-
-/* Evaluate the floating point expression D, recording NUM
- as the original argument for error messages.
- D is normally an assignment expression.
- Handle errors which may result in signals or may set errno.
-
- Note that float_error may be declared to return void, so you can't
- just cast the zero after the colon to (void) to make the types
- check properly. */
-
-#ifdef FLOAT_CHECK_ERRNO
-#define IN_FLOAT(d, name, num) \
- do { \
- float_error_arg = num; \
- float_error_fn_name = name; \
- in_float = 1; errno = 0; (d); in_float = 0; \
- switch (errno) { \
- case 0: break; \
- case EDOM: domain_error (float_error_fn_name, float_error_arg); \
- case ERANGE: range_error (float_error_fn_name, float_error_arg); \
- default: arith_error (float_error_fn_name, float_error_arg); \
- } \
- } while (0)
-#define IN_FLOAT2(d, name, num, num2) \
- do { \
- float_error_arg = num; \
- float_error_arg2 = num2; \
- float_error_fn_name = name; \
- in_float = 1; errno = 0; (d); in_float = 0; \
- switch (errno) { \
- case 0: break; \
- case EDOM: domain_error (float_error_fn_name, float_error_arg); \
- case ERANGE: range_error (float_error_fn_name, float_error_arg); \
- default: arith_error (float_error_fn_name, float_error_arg); \
- } \
- } while (0)
-#else
-#define IN_FLOAT(d, name, num) (in_float = 1, (d), in_float = 0)
-#define IN_FLOAT2(d, name, num, num2) (in_float = 1, (d), in_float = 0)
-#endif
-
-/* Convert float to Lisp_Int if it fits, else signal a range error
- using the given arguments. */
-#define FLOAT_TO_INT(x, i, name, num) \
- do \
- { \
- if (FIXNUM_OVERFLOW_P (x)) \
- range_error (name, num); \
- XSETINT (i, (EMACS_INT)(x)); \
- } \
- while (0)
-#define FLOAT_TO_INT2(x, i, name, num1, num2) \
- do \
- { \
- if (FIXNUM_OVERFLOW_P (x)) \
- range_error2 (name, num1, num2); \
- XSETINT (i, (EMACS_INT)(x)); \
- } \
- while (0)
-
-#define arith_error(op,arg) \
- xsignal2 (Qarith_error, build_string ((op)), (arg))
-#define range_error(op,arg) \
- xsignal2 (Qrange_error, build_string ((op)), (arg))
-#define range_error2(op,a1,a2) \
- xsignal3 (Qrange_error, build_string ((op)), (a1), (a2))
-#define domain_error(op,arg) \
- xsignal2 (Qdomain_error, build_string ((op)), (arg))
-#ifdef FLOAT_CHECK_DOMAIN
-#define domain_error2(op,a1,a2) \
- xsignal3 (Qdomain_error, build_string ((op)), (a1), (a2))
-#endif
-
-/* Extract a Lisp number as a `double', or signal an error. */
-
-double
-extract_float (Lisp_Object num)
-{
- CHECK_NUMBER_OR_FLOAT (num);
-
- if (FLOATP (num))
- return XFLOAT_DATA (num);
- return (double) XINT (num);
-}
-\f
-/* Trig functions. */
-
-DEFUN ("acos", Facos, Sacos, 1, 1, 0,
- doc: /* Return the inverse cosine of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef FLOAT_CHECK_DOMAIN
- if (d > 1.0 || d < -1.0)
- domain_error ("acos", arg);
-#endif
- IN_FLOAT (d = acos (d), "acos", arg);
- return make_float (d);
-}
-
-DEFUN ("asin", Fasin, Sasin, 1, 1, 0,
- doc: /* Return the inverse sine of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef FLOAT_CHECK_DOMAIN
- if (d > 1.0 || d < -1.0)
- domain_error ("asin", arg);
-#endif
- IN_FLOAT (d = asin (d), "asin", arg);
- return make_float (d);
-}
-
-DEFUN ("atan", Fatan, Satan, 1, 2, 0,
- doc: /* Return the inverse tangent of the arguments.
-If only one argument Y is given, return the inverse tangent of Y.
-If two arguments Y and X are given, return the inverse tangent of Y
-divided by X, i.e. the angle in radians between the vector (X, Y)
-and the x-axis. */)
- (register Lisp_Object y, Lisp_Object x)
-{
- double d = extract_float (y);
-
- if (NILP (x))
- IN_FLOAT (d = atan (d), "atan", y);
- else
- {
- double d2 = extract_float (x);
-
- IN_FLOAT2 (d = atan2 (d, d2), "atan", y, x);
- }
- return make_float (d);
-}
-
-DEFUN ("cos", Fcos, Scos, 1, 1, 0,
- doc: /* Return the cosine of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = cos (d), "cos", arg);
- return make_float (d);
-}
-
-DEFUN ("sin", Fsin, Ssin, 1, 1, 0,
- doc: /* Return the sine of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = sin (d), "sin", arg);
- return make_float (d);
-}
-
-DEFUN ("tan", Ftan, Stan, 1, 1, 0,
- doc: /* Return the tangent of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- double c = cos (d);
-#ifdef FLOAT_CHECK_DOMAIN
- if (c == 0.0)
- domain_error ("tan", arg);
-#endif
- IN_FLOAT (d = sin (d) / c, "tan", arg);
- return make_float (d);
-}
-
-#undef isnan
-#define isnan(x) ((x) != (x))
-
-DEFUN ("isnan", Fisnan, Sisnan, 1, 1, 0,
- doc: /* Return non nil iff argument X is a NaN. */)
- (Lisp_Object x)
-{
- CHECK_FLOAT (x);
- return isnan (XFLOAT_DATA (x)) ? Qt : Qnil;
-}
-
-#ifdef HAVE_COPYSIGN
-DEFUN ("copysign", Fcopysign, Scopysign, 2, 2, 0,
- doc: /* Copy sign of X2 to value of X1, and return the result.
-Cause an error if X1 or X2 is not a float. */)
- (Lisp_Object x1, Lisp_Object x2)
-{
- double f1, f2;
-
- CHECK_FLOAT (x1);
- CHECK_FLOAT (x2);
-
- f1 = XFLOAT_DATA (x1);
- f2 = XFLOAT_DATA (x2);
-
- return make_float (copysign (f1, f2));
-}
-
-DEFUN ("frexp", Ffrexp, Sfrexp, 1, 1, 0,
- doc: /* Get significand and exponent of a floating point number.
-Breaks the floating point number X into its binary significand SGNFCAND
-\(a floating point value between 0.5 (included) and 1.0 (excluded))
-and an integral exponent EXP for 2, such that:
-
- X = SGNFCAND * 2^EXP
-
-The function returns the cons cell (SGNFCAND . EXP).
-If X is zero, both parts (SGNFCAND and EXP) are zero. */)
- (Lisp_Object x)
-{
- double f = XFLOATINT (x);
-
- if (f == 0.0)
- return Fcons (make_float (0.0), make_number (0));
- else
- {
- int exponent;
- double sgnfcand = frexp (f, &exponent);
- return Fcons (make_float (sgnfcand), make_number (exponent));
- }
-}
-
-DEFUN ("ldexp", Fldexp, Sldexp, 1, 2, 0,
- doc: /* Construct number X from significand SGNFCAND and exponent EXP.
-Returns the floating point value resulting from multiplying SGNFCAND
-(the significand) by 2 raised to the power of EXP (the exponent). */)
- (Lisp_Object sgnfcand, Lisp_Object exponent)
-{
- CHECK_NUMBER (exponent);
- return make_float (ldexp (XFLOATINT (sgnfcand), XINT (exponent)));
-}
-#endif
-\f
-#if 0 /* Leave these out unless we find there's a reason for them. */
-
-DEFUN ("bessel-j0", Fbessel_j0, Sbessel_j0, 1, 1, 0,
- doc: /* Return the bessel function j0 of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = j0 (d), "bessel-j0", arg);
- return make_float (d);
-}
-
-DEFUN ("bessel-j1", Fbessel_j1, Sbessel_j1, 1, 1, 0,
- doc: /* Return the bessel function j1 of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = j1 (d), "bessel-j1", arg);
- return make_float (d);
-}
-
-DEFUN ("bessel-jn", Fbessel_jn, Sbessel_jn, 2, 2, 0,
- doc: /* Return the order N bessel function output jn of ARG.
-The first arg (the order) is truncated to an integer. */)
- (register Lisp_Object n, Lisp_Object arg)
-{
- int i1 = extract_float (n);
- double f2 = extract_float (arg);
-
- IN_FLOAT (f2 = jn (i1, f2), "bessel-jn", n);
- return make_float (f2);
-}
-
-DEFUN ("bessel-y0", Fbessel_y0, Sbessel_y0, 1, 1, 0,
- doc: /* Return the bessel function y0 of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = y0 (d), "bessel-y0", arg);
- return make_float (d);
-}
-
-DEFUN ("bessel-y1", Fbessel_y1, Sbessel_y1, 1, 1, 0,
- doc: /* Return the bessel function y1 of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = y1 (d), "bessel-y0", arg);
- return make_float (d);
-}
-
-DEFUN ("bessel-yn", Fbessel_yn, Sbessel_yn, 2, 2, 0,
- doc: /* Return the order N bessel function output yn of ARG.
-The first arg (the order) is truncated to an integer. */)
- (register Lisp_Object n, Lisp_Object arg)
-{
- int i1 = extract_float (n);
- double f2 = extract_float (arg);
-
- IN_FLOAT (f2 = yn (i1, f2), "bessel-yn", n);
- return make_float (f2);
-}
-
-#endif
-\f
-#if 0 /* Leave these out unless we see they are worth having. */
-
-DEFUN ("erf", Ferf, Serf, 1, 1, 0,
- doc: /* Return the mathematical error function of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = erf (d), "erf", arg);
- return make_float (d);
-}
-
-DEFUN ("erfc", Ferfc, Serfc, 1, 1, 0,
- doc: /* Return the complementary error function of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = erfc (d), "erfc", arg);
- return make_float (d);
-}
-
-DEFUN ("log-gamma", Flog_gamma, Slog_gamma, 1, 1, 0,
- doc: /* Return the log gamma of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = lgamma (d), "log-gamma", arg);
- return make_float (d);
-}
-
-DEFUN ("cube-root", Fcube_root, Scube_root, 1, 1, 0,
- doc: /* Return the cube root of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef HAVE_CBRT
- IN_FLOAT (d = cbrt (d), "cube-root", arg);
-#else
- if (d >= 0.0)
- IN_FLOAT (d = pow (d, 1.0/3.0), "cube-root", arg);
- else
- IN_FLOAT (d = -pow (-d, 1.0/3.0), "cube-root", arg);
-#endif
- return make_float (d);
-}
-
-#endif
-\f
-DEFUN ("exp", Fexp, Sexp, 1, 1, 0,
- doc: /* Return the exponential base e of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef FLOAT_CHECK_DOMAIN
- if (d > 709.7827) /* Assume IEEE doubles here */
- range_error ("exp", arg);
- else if (d < -709.0)
- return make_float (0.0);
- else
-#endif
- IN_FLOAT (d = exp (d), "exp", arg);
- return make_float (d);
-}
-
-DEFUN ("expt", Fexpt, Sexpt, 2, 2, 0,
- doc: /* Return the exponential ARG1 ** ARG2. */)
- (register Lisp_Object arg1, Lisp_Object arg2)
-{
- double f1, f2, f3;
-
- CHECK_NUMBER_OR_FLOAT (arg1);
- CHECK_NUMBER_OR_FLOAT (arg2);
- if (INTEGERP (arg1) /* common lisp spec */
- && INTEGERP (arg2) /* don't promote, if both are ints, and */
- && 0 <= XINT (arg2)) /* we are sure the result is not fractional */
- { /* this can be improved by pre-calculating */
- EMACS_INT y; /* some binary powers of x then accumulating */
- EMACS_UINT acc, x; /* Unsigned so that overflow is well defined. */
- Lisp_Object val;
-
- x = XINT (arg1);
- y = XINT (arg2);
- acc = (y & 1 ? x : 1);
-
- while ((y >>= 1) != 0)
- {
- x *= x;
- if (y & 1)
- acc *= x;
- }
- XSETINT (val, acc);
- return val;
- }
- f1 = FLOATP (arg1) ? XFLOAT_DATA (arg1) : XINT (arg1);
- f2 = FLOATP (arg2) ? XFLOAT_DATA (arg2) : XINT (arg2);
- /* Really should check for overflow, too */
- if (f1 == 0.0 && f2 == 0.0)
- f1 = 1.0;
-#ifdef FLOAT_CHECK_DOMAIN
- else if ((f1 == 0.0 && f2 < 0.0) || (f1 < 0 && f2 != floor (f2)))
- domain_error2 ("expt", arg1, arg2);
-#endif
- IN_FLOAT2 (f3 = pow (f1, f2), "expt", arg1, arg2);
- /* Check for overflow in the result. */
- if (f1 != 0.0 && f3 == 0.0)
- range_error ("expt", arg1);
- return make_float (f3);
-}
-
-DEFUN ("log", Flog, Slog, 1, 2, 0,
- doc: /* Return the natural logarithm of ARG.
-If the optional argument BASE is given, return log ARG using that base. */)
- (register Lisp_Object arg, Lisp_Object base)
-{
- double d = extract_float (arg);
-
-#ifdef FLOAT_CHECK_DOMAIN
- if (d <= 0.0)
- domain_error2 ("log", arg, base);
-#endif
- if (NILP (base))
- IN_FLOAT (d = log (d), "log", arg);
- else
- {
- double b = extract_float (base);
-
-#ifdef FLOAT_CHECK_DOMAIN
- if (b <= 0.0 || b == 1.0)
- domain_error2 ("log", arg, base);
-#endif
- if (b == 10.0)
- IN_FLOAT2 (d = log10 (d), "log", arg, base);
- else
- IN_FLOAT2 (d = log (d) / log (b), "log", arg, base);
- }
- return make_float (d);
-}
-
-DEFUN ("log10", Flog10, Slog10, 1, 1, 0,
- doc: /* Return the logarithm base 10 of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef FLOAT_CHECK_DOMAIN
- if (d <= 0.0)
- domain_error ("log10", arg);
-#endif
- IN_FLOAT (d = log10 (d), "log10", arg);
- return make_float (d);
-}
-
-DEFUN ("sqrt", Fsqrt, Ssqrt, 1, 1, 0,
- doc: /* Return the square root of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef FLOAT_CHECK_DOMAIN
- if (d < 0.0)
- domain_error ("sqrt", arg);
-#endif
- IN_FLOAT (d = sqrt (d), "sqrt", arg);
- return make_float (d);
-}
-\f
-#if 0 /* Not clearly worth adding. */
-
-DEFUN ("acosh", Facosh, Sacosh, 1, 1, 0,
- doc: /* Return the inverse hyperbolic cosine of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef FLOAT_CHECK_DOMAIN
- if (d < 1.0)
- domain_error ("acosh", arg);
-#endif
-#ifdef HAVE_INVERSE_HYPERBOLIC
- IN_FLOAT (d = acosh (d), "acosh", arg);
-#else
- IN_FLOAT (d = log (d + sqrt (d*d - 1.0)), "acosh", arg);
-#endif
- return make_float (d);
-}
-
-DEFUN ("asinh", Fasinh, Sasinh, 1, 1, 0,
- doc: /* Return the inverse hyperbolic sine of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef HAVE_INVERSE_HYPERBOLIC
- IN_FLOAT (d = asinh (d), "asinh", arg);
-#else
- IN_FLOAT (d = log (d + sqrt (d*d + 1.0)), "asinh", arg);
-#endif
- return make_float (d);
-}
-
-DEFUN ("atanh", Fatanh, Satanh, 1, 1, 0,
- doc: /* Return the inverse hyperbolic tangent of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef FLOAT_CHECK_DOMAIN
- if (d >= 1.0 || d <= -1.0)
- domain_error ("atanh", arg);
-#endif
-#ifdef HAVE_INVERSE_HYPERBOLIC
- IN_FLOAT (d = atanh (d), "atanh", arg);
-#else
- IN_FLOAT (d = 0.5 * log ((1.0 + d) / (1.0 - d)), "atanh", arg);
-#endif
- return make_float (d);
-}
-
-DEFUN ("cosh", Fcosh, Scosh, 1, 1, 0,
- doc: /* Return the hyperbolic cosine of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef FLOAT_CHECK_DOMAIN
- if (d > 710.0 || d < -710.0)
- range_error ("cosh", arg);
-#endif
- IN_FLOAT (d = cosh (d), "cosh", arg);
- return make_float (d);
-}
-
-DEFUN ("sinh", Fsinh, Ssinh, 1, 1, 0,
- doc: /* Return the hyperbolic sine of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
-#ifdef FLOAT_CHECK_DOMAIN
- if (d > 710.0 || d < -710.0)
- range_error ("sinh", arg);
-#endif
- IN_FLOAT (d = sinh (d), "sinh", arg);
- return make_float (d);
-}
-
-DEFUN ("tanh", Ftanh, Stanh, 1, 1, 0,
- doc: /* Return the hyperbolic tangent of ARG. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = tanh (d), "tanh", arg);
- return make_float (d);
-}
-#endif
-\f
-DEFUN ("abs", Fabs, Sabs, 1, 1, 0,
- doc: /* Return the absolute value of ARG. */)
- (register Lisp_Object arg)
-{
- CHECK_NUMBER_OR_FLOAT (arg);
-
- if (FLOATP (arg))
- IN_FLOAT (arg = make_float (fabs (XFLOAT_DATA (arg))), "abs", arg);
- else if (XINT (arg) < 0)
- XSETINT (arg, - XINT (arg));
-
- return arg;
-}
-
-DEFUN ("float", Ffloat, Sfloat, 1, 1, 0,
- doc: /* Return the floating point number equal to ARG. */)
- (register Lisp_Object arg)
-{
- CHECK_NUMBER_OR_FLOAT (arg);
-
- if (INTEGERP (arg))
- return make_float ((double) XINT (arg));
- else /* give 'em the same float back */
- return arg;
-}
-
-DEFUN ("logb", Flogb, Slogb, 1, 1, 0,
- doc: /* Returns largest integer <= the base 2 log of the magnitude of ARG.
-This is the same as the exponent of a float. */)
- (Lisp_Object arg)
-{
- Lisp_Object val;
- EMACS_INT value;
- double f = extract_float (arg);
-
- if (f == 0.0)
- value = MOST_NEGATIVE_FIXNUM;
- else
- {
-#ifdef HAVE_LOGB
- IN_FLOAT (value = logb (f), "logb", arg);
-#else
-#ifdef HAVE_FREXP
- int ivalue;
- IN_FLOAT (frexp (f, &ivalue), "logb", arg);
- value = ivalue - 1;
-#else
- int i;
- double d;
- if (f < 0.0)
- f = -f;
- value = -1;
- while (f < 0.5)
- {
- for (i = 1, d = 0.5; d * d >= f; i += i)
- d *= d;
- f /= d;
- value -= i;
- }
- while (f >= 1.0)
- {
- for (i = 1, d = 2.0; d * d <= f; i += i)
- d *= d;
- f /= d;
- value += i;
- }
-#endif
-#endif
- }
- XSETINT (val, value);
- return val;
-}
-
-
-/* the rounding functions */
-
-static Lisp_Object
-rounding_driver (Lisp_Object arg, Lisp_Object divisor,
- double (*double_round) (double),
- EMACS_INT (*int_round2) (EMACS_INT, EMACS_INT),
- const char *name)
-{
- CHECK_NUMBER_OR_FLOAT (arg);
-
- if (! NILP (divisor))
- {
- EMACS_INT i1, i2;
-
- CHECK_NUMBER_OR_FLOAT (divisor);
-
- if (FLOATP (arg) || FLOATP (divisor))
- {
- double f1, f2;
-
- f1 = FLOATP (arg) ? XFLOAT_DATA (arg) : XINT (arg);
- f2 = (FLOATP (divisor) ? XFLOAT_DATA (divisor) : XINT (divisor));
- if (! IEEE_FLOATING_POINT && f2 == 0)
- xsignal0 (Qarith_error);
-
- IN_FLOAT2 (f1 = (*double_round) (f1 / f2), name, arg, divisor);
- FLOAT_TO_INT2 (f1, arg, name, arg, divisor);
- return arg;
- }
-
- i1 = XINT (arg);
- i2 = XINT (divisor);
-
- if (i2 == 0)
- xsignal0 (Qarith_error);
-
- XSETINT (arg, (*int_round2) (i1, i2));
- return arg;
- }
-
- if (FLOATP (arg))
- {
- double d;
-
- IN_FLOAT (d = (*double_round) (XFLOAT_DATA (arg)), name, arg);
- FLOAT_TO_INT (d, arg, name, arg);
- }
-
- return arg;
-}
-
-/* With C's /, the result is implementation-defined if either operand
- is negative, so take care with negative operands in the following
- integer functions. */
-
-static EMACS_INT
-ceiling2 (EMACS_INT i1, EMACS_INT i2)
-{
- return (i2 < 0
- ? (i1 < 0 ? ((-1 - i1) / -i2) + 1 : - (i1 / -i2))
- : (i1 <= 0 ? - (-i1 / i2) : ((i1 - 1) / i2) + 1));
-}
-
-static EMACS_INT
-floor2 (EMACS_INT i1, EMACS_INT i2)
-{
- return (i2 < 0
- ? (i1 <= 0 ? -i1 / -i2 : -1 - ((i1 - 1) / -i2))
- : (i1 < 0 ? -1 - ((-1 - i1) / i2) : i1 / i2));
-}
-
-static EMACS_INT
-truncate2 (EMACS_INT i1, EMACS_INT i2)
-{
- return (i2 < 0
- ? (i1 < 0 ? -i1 / -i2 : - (i1 / -i2))
- : (i1 < 0 ? - (-i1 / i2) : i1 / i2));
-}
-
-static EMACS_INT
-round2 (EMACS_INT i1, EMACS_INT i2)
-{
- /* The C language's division operator gives us one remainder R, but
- we want the remainder R1 on the other side of 0 if R1 is closer
- to 0 than R is; because we want to round to even, we also want R1
- if R and R1 are the same distance from 0 and if C's quotient is
- odd. */
- EMACS_INT q = i1 / i2;
- EMACS_INT r = i1 % i2;
- EMACS_INT abs_r = r < 0 ? -r : r;
- EMACS_INT abs_r1 = (i2 < 0 ? -i2 : i2) - abs_r;
- return q + (abs_r + (q & 1) <= abs_r1 ? 0 : (i2 ^ r) < 0 ? -1 : 1);
-}
-
-/* The code uses emacs_rint, so that it works to undefine HAVE_RINT
- if `rint' exists but does not work right. */
-#ifdef HAVE_RINT
-#define emacs_rint rint
-#else
-static double
-emacs_rint (double d)
-{
- return floor (d + 0.5);
-}
-#endif
-
-static double
-double_identity (double d)
-{
- return d;
-}
-
-DEFUN ("ceiling", Fceiling, Sceiling, 1, 2, 0,
- doc: /* Return the smallest integer no less than ARG.
-This rounds the value towards +inf.
-With optional DIVISOR, return the smallest integer no less than ARG/DIVISOR. */)
- (Lisp_Object arg, Lisp_Object divisor)
-{
- return rounding_driver (arg, divisor, ceil, ceiling2, "ceiling");
-}
-
-DEFUN ("floor", Ffloor, Sfloor, 1, 2, 0,
- doc: /* Return the largest integer no greater than ARG.
-This rounds the value towards -inf.
-With optional DIVISOR, return the largest integer no greater than ARG/DIVISOR. */)
- (Lisp_Object arg, Lisp_Object divisor)
-{
- return rounding_driver (arg, divisor, floor, floor2, "floor");
-}
-
-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, round2, "round");
-}
-
-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, double_identity, truncate2,
- "truncate");
-}
-
-
-Lisp_Object
-fmod_float (Lisp_Object x, Lisp_Object y)
-{
- double f1, f2;
-
- f1 = FLOATP (x) ? XFLOAT_DATA (x) : XINT (x);
- f2 = FLOATP (y) ? XFLOAT_DATA (y) : XINT (y);
-
- if (! IEEE_FLOATING_POINT && f2 == 0)
- xsignal0 (Qarith_error);
-
- /* If the "remainder" comes out with the wrong sign, fix it. */
- IN_FLOAT2 ((f1 = fmod (f1, f2),
- f1 = (f2 < 0 ? f1 > 0 : f1 < 0) ? f1 + f2 : f1),
- "mod", x, y);
- return make_float (f1);
-}
-\f
-/* It's not clear these are worth adding. */
-
-DEFUN ("fceiling", Ffceiling, Sfceiling, 1, 1, 0,
- doc: /* Return the smallest integer no less than ARG, as a float.
-\(Round toward +inf.\) */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = ceil (d), "fceiling", arg);
- return make_float (d);
-}
-
-DEFUN ("ffloor", Fffloor, Sffloor, 1, 1, 0,
- doc: /* Return the largest integer no greater than ARG, as a float.
-\(Round towards -inf.\) */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = floor (d), "ffloor", arg);
- return make_float (d);
-}
-
-DEFUN ("fround", Ffround, Sfround, 1, 1, 0,
- doc: /* Return the nearest integer to ARG, as a float. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- IN_FLOAT (d = emacs_rint (d), "fround", arg);
- return make_float (d);
-}
-
-DEFUN ("ftruncate", Fftruncate, Sftruncate, 1, 1, 0,
- doc: /* Truncate a floating point number to an integral float value.
-Rounds the value toward zero. */)
- (register Lisp_Object arg)
-{
- double d = extract_float (arg);
- if (d >= 0.0)
- IN_FLOAT (d = floor (d), "ftruncate", arg);
- else
- IN_FLOAT (d = ceil (d), "ftruncate", arg);
- return make_float (d);
-}
-\f
-#ifdef FLOAT_CATCH_SIGILL
-static void
-float_error (int signo)
-{
- if (! in_float)
- fatal_error_signal (signo);
-
-#ifdef BSD_SYSTEM
- sigsetmask (SIGEMPTYMASK);
-#else
- /* Must reestablish handler each time it is called. */
- signal (SIGILL, float_error);
-#endif /* BSD_SYSTEM */
-
- SIGNAL_THREAD_CHECK (signo);
- in_float = 0;
-
- xsignal1 (Qarith_error, float_error_arg);
-}
-
-/* Another idea was to replace the library function `infnan'
- where SIGILL is signaled. */
-
-#endif /* FLOAT_CATCH_SIGILL */
-
-#ifdef HAVE_MATHERR
-int
-matherr (struct exception *x)
-{
- Lisp_Object args;
- const char *name = x->name;
-
- if (! in_float)
- /* Not called from emacs-lisp float routines; do the default thing. */
- return 0;
- if (!strcmp (x->name, "pow"))
- name = "expt";
-
- args
- = Fcons (build_string (name),
- Fcons (make_float (x->arg1),
- ((!strcmp (name, "log") || !strcmp (name, "pow"))
- ? Fcons (make_float (x->arg2), Qnil)
- : Qnil)));
- switch (x->type)
- {
- case DOMAIN: xsignal (Qdomain_error, args); break;
- case SING: xsignal (Qsingularity_error, args); break;
- case OVERFLOW: xsignal (Qoverflow_error, args); break;
- case UNDERFLOW: xsignal (Qunderflow_error, args); break;
- default: xsignal (Qarith_error, args); break;
- }
- return (1); /* don't set errno or print a message */
-}
-#endif /* HAVE_MATHERR */
-
-void
-init_floatfns (void)
-{
-#ifdef FLOAT_CATCH_SIGILL
- signal (SIGILL, float_error);
-#endif
- in_float = 0;
-}
-
-void
-syms_of_floatfns (void)
-{
- defsubr (&Sacos);
- defsubr (&Sasin);
- defsubr (&Satan);
- defsubr (&Scos);
- defsubr (&Ssin);
- defsubr (&Stan);
- defsubr (&Sisnan);
-#ifdef HAVE_COPYSIGN
- defsubr (&Scopysign);
- defsubr (&Sfrexp);
- defsubr (&Sldexp);
-#endif
-#if 0
- defsubr (&Sacosh);
- defsubr (&Sasinh);
- defsubr (&Satanh);
- defsubr (&Scosh);
- defsubr (&Ssinh);
- defsubr (&Stanh);
- defsubr (&Sbessel_y0);
- defsubr (&Sbessel_y1);
- defsubr (&Sbessel_yn);
- defsubr (&Sbessel_j0);
- defsubr (&Sbessel_j1);
- defsubr (&Sbessel_jn);
- defsubr (&Serf);
- defsubr (&Serfc);
- defsubr (&Slog_gamma);
- defsubr (&Scube_root);
-#endif
- defsubr (&Sfceiling);
- defsubr (&Sffloor);
- defsubr (&Sfround);
- defsubr (&Sftruncate);
- defsubr (&Sexp);
- defsubr (&Sexpt);
- defsubr (&Slog);
- defsubr (&Slog10);
- defsubr (&Ssqrt);
-
- defsubr (&Sabs);
- defsubr (&Sfloat);
- defsubr (&Slogb);
- defsubr (&Sceiling);
- defsubr (&Sfloor);
- defsubr (&Sround);
- defsubr (&Struncate);
-}
+/* Primitive operations on floating point for GNU Emacs Lisp interpreter.
+
+Copyright (C) 1988, 1993-1994, 1999, 2001-2014 Free Software Foundation, Inc.
+
+Author: Wolfgang Rupprecht
+(according to ack.texi)
+
+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/>. */
+
+
+/* C89 requires only the following math.h functions, and Emacs omits
+ the starred functions since we haven't found a use for them:
+ acos, asin, atan, atan2, ceil, cos, *cosh, exp, fabs, floor, fmod,
+ frexp, ldexp, log, log10 [via (log X 10)], *modf, pow, sin, *sinh,
+ sqrt, tan, *tanh.
+
+ C99 and C11 require the following math.h functions in addition to
+ the C89 functions. Of these, Emacs currently exports only the
+ starred ones to Lisp, since we haven't found a use for the others:
+ acosh, atanh, cbrt, *copysign, erf, erfc, exp2, expm1, fdim, fma,
+ fmax, fmin, fpclassify, hypot, ilogb, isfinite, isgreater,
+ isgreaterequal, isinf, isless, islessequal, islessgreater, *isnan,
+ isnormal, isunordered, lgamma, log1p, *log2 [via (log X 2)], *logb
+ (approximately), lrint/llrint, lround/llround, nan, nearbyint,
+ nextafter, nexttoward, remainder, remquo, *rint, round, scalbln,
+ scalbn, signbit, tgamma, trunc.
+ */
+
+#include <config.h>
+
+#include "lisp.h"
+
+#include <math.h>
+
+/* 'isfinite' and 'isnan' cause build failures on Solaris 10 with the
+ bundled GCC in c99 mode. Work around the bugs with simple
+ implementations that are good enough. */
+#undef isfinite
+#define isfinite(x) ((x) - (x) == 0)
+#undef isnan
+#define isnan(x) ((x) != (x))
+
+/* Check that X is a floating point number. */
+
+static void
+CHECK_FLOAT (Lisp_Object x)
+{
+ CHECK_TYPE (FLOATP (x), Qfloatp, x);
+}
+
+/* Extract a Lisp number as a `double', or signal an error. */
+
+double
+extract_float (Lisp_Object num)
+{
+ CHECK_NUMBER_OR_FLOAT (num);
+
+ if (FLOATP (num))
+ return XFLOAT_DATA (num);
+ return (double) XINT (num);
+}
+\f
+/* Trig functions. */
+
+DEFUN ("acos", Facos, Sacos, 1, 1, 0,
+ doc: /* Return the inverse cosine of ARG. */)
+ (Lisp_Object arg)
+{
+ double d = extract_float (arg);
+ d = acos (d);
+ return make_float (d);
+}
+
+DEFUN ("asin", Fasin, Sasin, 1, 1, 0,
+ doc: /* Return the inverse sine of ARG. */)
+ (Lisp_Object arg)
+{
+ double d = extract_float (arg);
+ d = asin (d);
+ return make_float (d);
+}
+
+DEFUN ("atan", Fatan, Satan, 1, 2, 0,
+ doc: /* Return the inverse tangent of the arguments.
+If only one argument Y is given, return the inverse tangent of Y.
+If two arguments Y and X are given, return the inverse tangent of Y
+divided by X, i.e. the angle in radians between the vector (X, Y)
+and the x-axis. */)
+ (Lisp_Object y, Lisp_Object x)
+{
+ double d = extract_float (y);
+
+ if (NILP (x))
+ d = atan (d);
+ else
+ {
+ double d2 = extract_float (x);
+ d = atan2 (d, d2);
+ }
+ return make_float (d);
+}
+
+DEFUN ("cos", Fcos, Scos, 1, 1, 0,
+ doc: /* Return the cosine of ARG. */)
+ (Lisp_Object arg)
+{
+ double d = extract_float (arg);
+ d = cos (d);
+ return make_float (d);
+}
+
+DEFUN ("sin", Fsin, Ssin, 1, 1, 0,
+ doc: /* Return the sine of ARG. */)
+ (Lisp_Object arg)
+{
+ double d = extract_float (arg);
+ d = sin (d);
+ return make_float (d);
+}
+
+DEFUN ("tan", Ftan, Stan, 1, 1, 0,
+ doc: /* Return the tangent of ARG. */)
+ (Lisp_Object arg)
+{
+ double d = extract_float (arg);
+ d = tan (d);
+ return make_float (d);
+}
+
+DEFUN ("isnan", Fisnan, Sisnan, 1, 1, 0,
+ doc: /* Return non nil if argument X is a NaN. */)
+ (Lisp_Object x)
+{
+ CHECK_FLOAT (x);
+ return isnan (XFLOAT_DATA (x)) ? Qt : Qnil;
+}
+
+#ifdef HAVE_COPYSIGN
+DEFUN ("copysign", Fcopysign, Scopysign, 2, 2, 0,
+ doc: /* Copy sign of X2 to value of X1, and return the result.
+Cause an error if X1 or X2 is not a float. */)
+ (Lisp_Object x1, Lisp_Object x2)
+{
+ double f1, f2;
+
+ CHECK_FLOAT (x1);
+ CHECK_FLOAT (x2);
+
+ f1 = XFLOAT_DATA (x1);
+ f2 = XFLOAT_DATA (x2);
+
+ return make_float (copysign (f1, f2));
+}
+#endif
+
+DEFUN ("frexp", Ffrexp, Sfrexp, 1, 1, 0,
+ doc: /* Get significand and exponent of a floating point number.
+Breaks the floating point number X into its binary significand SGNFCAND
+\(a floating point value between 0.5 (included) and 1.0 (excluded))
+and an integral exponent EXP for 2, such that:
+
+ X = SGNFCAND * 2^EXP
+
+The function returns the cons cell (SGNFCAND . EXP).
+If X is zero, both parts (SGNFCAND and EXP) are zero. */)
+ (Lisp_Object x)
+{
+ double f = XFLOATINT (x);
+ int exponent;
+ double sgnfcand = frexp (f, &exponent);
+ return Fcons (make_float (sgnfcand), make_number (exponent));
+}
+
+DEFUN ("ldexp", Fldexp, Sldexp, 1, 2, 0,
+ doc: /* Construct number X from significand SGNFCAND and exponent EXP.
+Returns the floating point value resulting from multiplying SGNFCAND
+(the significand) by 2 raised to the power of EXP (the exponent). */)
+ (Lisp_Object sgnfcand, Lisp_Object exponent)
+{
+ CHECK_NUMBER (exponent);
+ return make_float (ldexp (XFLOATINT (sgnfcand), XINT (exponent)));
+}
+\f
+DEFUN ("exp", Fexp, Sexp, 1, 1, 0,
+ doc: /* Return the exponential base e of ARG. */)
+ (Lisp_Object arg)
+{
+ double d = extract_float (arg);
+ d = exp (d);
+ return make_float (d);
+}
+
+DEFUN ("expt", Fexpt, Sexpt, 2, 2, 0,
+ doc: /* Return the exponential ARG1 ** ARG2. */)
+ (Lisp_Object arg1, Lisp_Object arg2)
+{
+ double f1, f2, f3;
+
+ CHECK_NUMBER_OR_FLOAT (arg1);
+ CHECK_NUMBER_OR_FLOAT (arg2);
+ if (INTEGERP (arg1) /* common lisp spec */
+ && INTEGERP (arg2) /* don't promote, if both are ints, and */
+ && XINT (arg2) >= 0) /* we are sure the result is not fractional */
+ { /* this can be improved by pre-calculating */
+ EMACS_INT y; /* some binary powers of x then accumulating */
+ EMACS_UINT acc, x; /* Unsigned so that overflow is well defined. */
+ Lisp_Object val;
+
+ x = XINT (arg1);
+ y = XINT (arg2);
+ acc = (y & 1 ? x : 1);
+
+ while ((y >>= 1) != 0)
+ {
+ x *= x;
+ if (y & 1)
+ acc *= x;
+ }
+ XSETINT (val, acc);
+ return val;
+ }
+ f1 = FLOATP (arg1) ? XFLOAT_DATA (arg1) : XINT (arg1);
+ f2 = FLOATP (arg2) ? XFLOAT_DATA (arg2) : XINT (arg2);
+ f3 = pow (f1, f2);
+ return make_float (f3);
+}
+
+DEFUN ("log", Flog, Slog, 1, 2, 0,
+ doc: /* Return the natural logarithm of ARG.
+If the optional argument BASE is given, return log ARG using that base. */)
+ (Lisp_Object arg, Lisp_Object base)
+{
+ double d = extract_float (arg);
+
+ if (NILP (base))
+ d = log (d);
+ else
+ {
+ double b = extract_float (base);
+
+ if (b == 10.0)
+ d = log10 (d);
+#if HAVE_LOG2
+ else if (b == 2.0)
+ d = log2 (d);
+#endif
+ else
+ d = log (d) / log (b);
+ }
+ return make_float (d);
+}
+
+DEFUN ("sqrt", Fsqrt, Ssqrt, 1, 1, 0,
+ doc: /* Return the square root of ARG. */)
+ (Lisp_Object arg)
+{
+ double d = extract_float (arg);
+ d = sqrt (d);
+ return make_float (d);
+}
+\f
+DEFUN ("abs", Fabs, Sabs, 1, 1, 0,
+ doc: /* Return the absolute value of ARG. */)
+ (register Lisp_Object arg)
+{
+ CHECK_NUMBER_OR_FLOAT (arg);
+
+ if (FLOATP (arg))
+ arg = make_float (fabs (XFLOAT_DATA (arg)));
+ else if (XINT (arg) < 0)
+ XSETINT (arg, - XINT (arg));
+
+ return arg;
+}
+
+DEFUN ("float", Ffloat, Sfloat, 1, 1, 0,
+ doc: /* Return the floating point number equal to ARG. */)
+ (register Lisp_Object arg)
+{
+ CHECK_NUMBER_OR_FLOAT (arg);
+
+ if (INTEGERP (arg))
+ return make_float ((double) XINT (arg));
+ else /* give 'em the same float back */
+ return arg;
+}
+
+DEFUN ("logb", Flogb, Slogb, 1, 1, 0,
+ doc: /* Returns largest integer <= the base 2 log of the magnitude of ARG.
+This is the same as the exponent of a float. */)
+ (Lisp_Object arg)
+{
+ Lisp_Object val;
+ EMACS_INT value;
+ double f = extract_float (arg);
+
+ if (f == 0.0)
+ value = MOST_NEGATIVE_FIXNUM;
+ else if (isfinite (f))
+ {
+ int ivalue;
+ frexp (f, &ivalue);
+ value = ivalue - 1;
+ }
+ else
+ value = MOST_POSITIVE_FIXNUM;
+
+ XSETINT (val, value);
+ return val;
+}
+
+
+/* the rounding functions */
+
+static Lisp_Object
+rounding_driver (Lisp_Object arg, Lisp_Object divisor,
+ double (*double_round) (double),
+ EMACS_INT (*int_round2) (EMACS_INT, EMACS_INT),
+ const char *name)
+{
+ CHECK_NUMBER_OR_FLOAT (arg);
+
+ if (! NILP (divisor))
+ {
+ EMACS_INT i1, i2;
+
+ CHECK_NUMBER_OR_FLOAT (divisor);
+
+ if (FLOATP (arg) || FLOATP (divisor))
+ {
+ double f1, f2;
+
+ f1 = FLOATP (arg) ? XFLOAT_DATA (arg) : XINT (arg);
+ f2 = (FLOATP (divisor) ? XFLOAT_DATA (divisor) : XINT (divisor));
+ if (! IEEE_FLOATING_POINT && f2 == 0)
+ xsignal0 (Qarith_error);
+
+ f1 = (*double_round) (f1 / f2);
+ if (FIXNUM_OVERFLOW_P (f1))
+ xsignal3 (Qrange_error, build_string (name), arg, divisor);
+ arg = make_number (f1);
+ return arg;
+ }
+
+ i1 = XINT (arg);
+ i2 = XINT (divisor);
+
+ if (i2 == 0)
+ xsignal0 (Qarith_error);
+
+ XSETINT (arg, (*int_round2) (i1, i2));
+ return arg;
+ }
+
+ if (FLOATP (arg))
+ {
+ double d = (*double_round) (XFLOAT_DATA (arg));
+ if (FIXNUM_OVERFLOW_P (d))
+ xsignal2 (Qrange_error, build_string (name), arg);
+ arg = make_number (d);
+ }
+
+ return arg;
+}
+
+/* With C's /, the result is implementation-defined if either operand
+ is negative, so take care with negative operands in the following
+ integer functions. */
+
+static EMACS_INT
+ceiling2 (EMACS_INT i1, EMACS_INT i2)
+{
+ return (i2 < 0
+ ? (i1 < 0 ? ((-1 - i1) / -i2) + 1 : - (i1 / -i2))
+ : (i1 <= 0 ? - (-i1 / i2) : ((i1 - 1) / i2) + 1));
+}
+
+static EMACS_INT
+floor2 (EMACS_INT i1, EMACS_INT i2)
+{
+ return (i2 < 0
+ ? (i1 <= 0 ? -i1 / -i2 : -1 - ((i1 - 1) / -i2))
+ : (i1 < 0 ? -1 - ((-1 - i1) / i2) : i1 / i2));
+}
+
+static EMACS_INT
+truncate2 (EMACS_INT i1, EMACS_INT i2)
+{
+ return (i2 < 0
+ ? (i1 < 0 ? -i1 / -i2 : - (i1 / -i2))
+ : (i1 < 0 ? - (-i1 / i2) : i1 / i2));
+}
+
+static EMACS_INT
+round2 (EMACS_INT i1, EMACS_INT i2)
+{
+ /* The C language's division operator gives us one remainder R, but
+ we want the remainder R1 on the other side of 0 if R1 is closer
+ to 0 than R is; because we want to round to even, we also want R1
+ if R and R1 are the same distance from 0 and if C's quotient is
+ odd. */
+ EMACS_INT q = i1 / i2;
+ EMACS_INT r = i1 % i2;
+ EMACS_INT abs_r = eabs (r);
+ EMACS_INT abs_r1 = eabs (i2) - abs_r;
+ return q + (abs_r + (q & 1) <= abs_r1 ? 0 : (i2 ^ r) < 0 ? -1 : 1);
+}
+
+/* The code uses emacs_rint, so that it works to undefine HAVE_RINT
+ if `rint' exists but does not work right. */
+#ifdef HAVE_RINT
+#define emacs_rint rint
+#else
+static double
+emacs_rint (double d)
+{
+ double d1 = d + 0.5;
+ double r = floor (d1);
+ return r - (r == d1 && fmod (r, 2) != 0);
+}
+#endif
+
+static double
+double_identity (double d)
+{
+ return d;
+}
+
+DEFUN ("ceiling", Fceiling, Sceiling, 1, 2, 0,
+ doc: /* Return the smallest integer no less than ARG.
+This rounds the value towards +inf.
+With optional DIVISOR, return the smallest integer no less than ARG/DIVISOR. */)
+ (Lisp_Object arg, Lisp_Object divisor)
+{
+ return rounding_driver (arg, divisor, ceil, ceiling2, "ceiling");
+}
+
+DEFUN ("floor", Ffloor, Sfloor, 1, 2, 0,
+ doc: /* Return the largest integer no greater than ARG.
+This rounds the value towards -inf.
+With optional DIVISOR, return the largest integer no greater than ARG/DIVISOR. */)
+ (Lisp_Object arg, Lisp_Object divisor)
+{
+ return rounding_driver (arg, divisor, floor, floor2, "floor");
+}
+
+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, round2, "round");
+}
+
+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, double_identity, truncate2,
+ "truncate");
+}
+
+
+Lisp_Object
+fmod_float (Lisp_Object x, Lisp_Object y)
+{
+ double f1, f2;
+
+ f1 = FLOATP (x) ? XFLOAT_DATA (x) : XINT (x);
+ f2 = FLOATP (y) ? XFLOAT_DATA (y) : XINT (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);
+}
+\f
+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)
+{
+ double d = extract_float (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.
+\(Round towards -inf.\) */)
+ (Lisp_Object arg)
+{
+ double d = extract_float (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)
+{
+ double d = extract_float (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.
+Rounds the value toward zero. */)
+ (Lisp_Object arg)
+{
+ double d = extract_float (arg);
+ if (d >= 0.0)
+ d = floor (d);
+ else
+ d = ceil (d);
+ return make_float (d);
+}
+\f
+void
+syms_of_floatfns (void)
+{
+#include "floatfns.x"
+}
HCoop / bpt / emacs.git / blobdiff