emacs/src/floatfns.c

/* Primitive operations on floating point for GNU Emacs Lisp interpreter.

Copyright (C) 1988, 1993-1994, 1999, 2001-2019 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 <https://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 "bignum.h"

#include <math.h>

#include <count-leading-zeros.h>

/* Emacs needs proper handling of +/-inf; correct printing as well as
   important packages depend on it.  Make sure the user didn't specify
   -ffinite-math-only, either directly or implicitly with -Ofast or
   -ffast-math.  */
#if defined __FINITE_MATH_ONLY__ && __FINITE_MATH_ONLY__
 #error Emacs cannot be built with -ffinite-math-only
#endif

/* 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 (num);
  return XFLOATINT (num);
}

/* 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;
}

/* Although the substitute does not work on NaNs, it is good enough
   for platforms lacking the signbit macro.  */
#ifndef signbit
# define signbit(x) ((x) < 0 || (IEEE_FLOATING_POINT && !(x) && 1 / (x) < 0))
#endif

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);

  /* Use signbit instead of copysign, to avoid calling make_float when
     the result is X1.  */
  return signbit (f1) != signbit (f2) ? make_float (-f1) : x1;
}

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 = extract_float (x);
  int exponent;
  double sgnfcand = frexp (f, &exponent);
  return Fcons (make_float (sgnfcand), make_fixnum (exponent));
}

DEFUN ("ldexp", Fldexp, Sldexp, 2, 2, 0,
       doc: /* Return SGNFCAND * 2**EXPONENT, as a floating point number.
EXPONENT must be an integer.   */)
  (Lisp_Object sgnfcand, Lisp_Object exponent)
{
  CHECK_FIXNUM (exponent);
  int e = min (max (INT_MIN, XFIXNUM (exponent)), INT_MAX);
  return make_float (ldexp (extract_float (sgnfcand), e));
}

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)
{
  CHECK_NUMBER (arg1);
  CHECK_NUMBER (arg2);

  /* Common Lisp spec: don't promote if both are integers, and if the
     result is not fractional.  */
  if (INTEGERP (arg1) && !NILP (Fnatnump (arg2)))
    return expt_integer (arg1, arg2);

  return make_float (pow (XFLOATINT (arg1), XFLOATINT (arg2)));
}

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);
}

DEFUN ("abs", Fabs, Sabs, 1, 1, 0,
       doc: /* Return the absolute value of ARG.  */)
  (Lisp_Object arg)
{
  CHECK_NUMBER (arg);

  if (FIXNUMP (arg))
    {
      if (XFIXNUM (arg) < 0)
	arg = make_int (-XFIXNUM (arg));
    }
  else if (FLOATP (arg))
    {
      if (signbit (XFLOAT_DATA (arg)))
	arg = make_float (- XFLOAT_DATA (arg));
    }
  else
    {
      if (mpz_sgn (*xbignum_val (arg)) < 0)
	{
	  mpz_neg (mpz[0], *xbignum_val (arg));
	  arg = make_integer_mpz ();
	}
    }

  return arg;
}

DEFUN ("float", Ffloat, Sfloat, 1, 1, 0,
       doc: /* Return the floating point number equal to ARG.  */)
  (register Lisp_Object arg)
{
  CHECK_NUMBER (arg);
  /* If ARG is a float, give 'em the same float back.  */
  return FLOATP (arg) ? arg : make_float (XFLOATINT (arg));
}

static int
ecount_leading_zeros (EMACS_UINT x)
{
  return (EMACS_UINT_WIDTH == UINT_WIDTH ? count_leading_zeros (x)
	  : EMACS_UINT_WIDTH == ULONG_WIDTH ? count_leading_zeros_l (x)
	  : count_leading_zeros_ll (x));
}

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)
{
  EMACS_INT value;
  CHECK_NUMBER (arg);

  if (FLOATP (arg))
    {
      double f = XFLOAT_DATA (arg);
      if (f == 0)
	return make_float (-HUGE_VAL);
      if (!isfinite (f))
	return f < 0 ? make_float (-f) : arg;
      int ivalue;
      frexp (f, &ivalue);
      value = ivalue - 1;
    }
  else if (!FIXNUMP (arg))
    value = mpz_sizeinbase (*xbignum_val (arg), 2) - 1;
  else
    {
      EMACS_INT i = XFIXNUM (arg);
      if (i == 0)
	return make_float (-HUGE_VAL);
      value = EMACS_UINT_WIDTH - 1 - ecount_leading_zeros (eabs (i));
    }

  return make_fixnum (value);
}

/* True if A is exactly representable as an integer.  */

static bool
integer_value (Lisp_Object a)
{
  if (FLOATP (a))
    {
      double d = XFLOAT_DATA (a);
      return d == floor (d) && isfinite (d);
    }
  return true;
}

/* the rounding functions  */

static Lisp_Object
rounding_driver (Lisp_Object arg, Lisp_Object divisor,
		 double (*double_round) (double),
		 void (*int_divide) (mpz_t, mpz_t const, mpz_t const),
		 EMACS_INT (*fixnum_divide) (EMACS_INT, EMACS_INT))
{
  CHECK_NUMBER (arg);

  double d;
  if (NILP (divisor))
    {
      if (! FLOATP (arg))
	return arg;
      d = XFLOAT_DATA (arg);
    }
  else
    {
      CHECK_NUMBER (divisor);
      if (integer_value (arg) && integer_value (divisor))
	{
	  /* Divide as integers.  Converting to double might lose
	     info, even for fixnums; also see the FIXME below.  */

	  if (FLOATP (arg))
	    arg = double_to_integer (XFLOAT_DATA (arg));
	  if (FLOATP (divisor))
	    divisor = double_to_integer (XFLOAT_DATA (divisor));

	  if (FIXNUMP (divisor))
	    {
	      if (XFIXNUM (divisor) == 0)
		xsignal0 (Qarith_error);
	      if (FIXNUMP (arg))
		return make_int (fixnum_divide (XFIXNUM (arg),
						XFIXNUM (divisor)));
	    }
	  int_divide (mpz[0],
		      *bignum_integer (&mpz[0], arg),
		      *bignum_integer (&mpz[1], divisor));
	  return make_integer_mpz ();
	}

      double f1 = XFLOATINT (arg);
      double f2 = XFLOATINT (divisor);
      if (! IEEE_FLOATING_POINT && f2 == 0)
	xsignal0 (Qarith_error);
      /* FIXME: This division rounds, so the result is double-rounded.  */
      d = f1 / f2;
    }

  /* Round, coarsely test for fixnum overflow before converting to
     EMACS_INT (to avoid undefined C behavior), and then exactly test
     for overflow after converting (as FIXNUM_OVERFLOW_P is inaccurate
     on floats).  */
  double dr = double_round (d);
  if (fabs (dr) < 2 * (MOST_POSITIVE_FIXNUM + 1))
    {
      EMACS_INT ir = dr;
      if (! FIXNUM_OVERFLOW_P (ir))
	return make_fixnum (ir);
    }
  return double_to_integer (dr);
}

static EMACS_INT
ceiling2 (EMACS_INT n, EMACS_INT d)
{
  return n / d + ((n % d != 0) & ((n < 0) == (d < 0)));
}

static EMACS_INT
floor2 (EMACS_INT n, EMACS_INT d)
{
  return n / d - ((n % d != 0) & ((n < 0) != (d < 0)));
}

static EMACS_INT
truncate2 (EMACS_INT n, EMACS_INT d)
{
  return n / d;
}

static EMACS_INT
round2 (EMACS_INT n, EMACS_INT d)
{
  /* The C language's division operator gives us the remainder R
     corresponding to truncated division, 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 the truncated quotient is odd.  */
  EMACS_INT q = n / d;
  EMACS_INT r = n % d;
  bool neg_d = d < 0;
  bool neg_r = r < 0;
  EMACS_INT abs_r = eabs (r);
  EMACS_INT abs_r1 = eabs (d) - abs_r;
  if (abs_r1 < abs_r + (q & 1))
    q += neg_d == neg_r ? 1 : -1;
  return q;
}

static void
rounddiv_q (mpz_t q, mpz_t const n, mpz_t const d)
{
  /* Mimic the source code of round2, using mpz_t instead of EMACS_INT.  */
  mpz_t *r = &mpz[2], *abs_r = r, *abs_r1 = &mpz[3];
  mpz_tdiv_qr (q, *r, n, d);
  bool neg_d = mpz_sgn (d) < 0;
  bool neg_r = mpz_sgn (*r) < 0;
  mpz_abs (*abs_r, *r);
  mpz_abs (*abs_r1, d);
  mpz_sub (*abs_r1, *abs_r1, *abs_r);
  if (mpz_cmp (*abs_r1, *abs_r) < (mpz_odd_p (q) != 0))
    (neg_d == neg_r ? mpz_add_ui : mpz_sub_ui) (q, q, 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

#ifndef HAVE_TRUNC
double
trunc (double d)
{
  return (d < 0 ? ceil : floor) (d);
}
#endif

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, mpz_cdiv_q, ceiling2);
}

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, 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);
}