/src/moddable/xs/tools/fdlibm/k_exp.c

Source
/*-
 * SPDX-License-Identifier: BSD-2-Clause
 *
 * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 */

 #include "math_private.h"

static const uint32_t k = 1799;   /* constant for reduction */
static const double kln2 =  1246.97177782734161156; /* k * ln2 */

/*
 * Compute exp(x), scaled to avoid spurious overflow.  An exponent is
 * returned separately in 'expt'.
 *
 * Input:  ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91
 * Output: 2**1023 <= y < 2**1024
 */
static double
__frexp_exp(double x, int *expt)
{
  double exp_x;
  uint32_t hx;

  /*
   * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to
   * minimize |exp(kln2) - 2**k|.  We also scale the exponent of
   * exp_x to MAX_EXP so that the result can be multiplied by
   * a tiny number without losing accuracy due to denormalization.
   */
  exp_x = __ieee754_exp(x - kln2);
  GET_HIGH_WORD(hx, exp_x);
  *expt = (hx >> 20) - (0x3ff + 1023) + k;
  SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20));
  return (exp_x);
}

/*
 * __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt.
 * They are intended for large arguments (real part >= ln(DBL_MAX))
 * where care is needed to avoid overflow.
 *
 * The present implementation is narrowly tailored for our hyperbolic and
 * exponential functions.  We assume expt is small (0 or -1), and the caller
 * has filtered out very large x, for which overflow would be inevitable.
 */

double
__ldexp_exp(double x, int expt)
{
  double exp_x, scale;
  int ex_expt;

  exp_x = __frexp_exp(x, &ex_expt);
  expt += ex_expt;
  INSERT_WORDS(scale, (0x3ff + expt) << 20, 0);
  return (exp_x * scale);
}

Coverage Report

Created: 2025-06-24 07:03

Line	Count	Source
1		/*-
2		* SPDX-License-Identifier: BSD-2-Clause
3		*
4		* Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
5		* All rights reserved.
6		*
7		* Redistribution and use in source and binary forms, with or without
8		* modification, are permitted provided that the following conditions
9		* are met:
10		* 1. Redistributions of source code must retain the above copyright
11		* notice, this list of conditions and the following disclaimer.
12		* 2. Redistributions in binary form must reproduce the above copyright
13		* notice, this list of conditions and the following disclaimer in the
14		* documentation and/or other materials provided with the distribution.
15		*
16		* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17		* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18		* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19		* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20		* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21		* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22		* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23		* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24		* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25		* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26		* SUCH DAMAGE.
27		*/
28
29		#include "math_private.h"
30
31		static const uint32_t k = 1799; /* constant for reduction */
32		static const double kln2 = 1246.97177782734161156; /* k * ln2 */
33
34		/*
35		* Compute exp(x), scaled to avoid spurious overflow. An exponent is
36		* returned separately in 'expt'.
37		*
38		* Input: ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91
39		* Output: 21023 <= y < 21024
40		*/
41		static double
42		__frexp_exp(double x, int *expt)
43	4	{
44	4	double exp_x;
45	4	uint32_t hx;
46
47		/*
48		* We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to
49		* minimize \|exp(kln2) - 2**k\|. We also scale the exponent of
50		* exp_x to MAX_EXP so that the result can be multiplied by
51		* a tiny number without losing accuracy due to denormalization.
52		*/
53	4	exp_x = __ieee754_exp(x - kln2);
54	4	GET_HIGH_WORD(hx, exp_x);
55	4	*expt = (hx >> 20) - (0x3ff + 1023) + k;
56	4	SET_HIGH_WORD(exp_x, (hx & 0xfffff) \| ((0x3ff + 1023) << 20));
57	4	return (exp_x);
58	4	}
59
60		/*
61		* __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt.
62		* They are intended for large arguments (real part >= ln(DBL_MAX))
63		* where care is needed to avoid overflow.
64		*
65		* The present implementation is narrowly tailored for our hyperbolic and
66		* exponential functions. We assume expt is small (0 or -1), and the caller
67		* has filtered out very large x, for which overflow would be inevitable.
68		*/
69
70		double
71		__ldexp_exp(double x, int expt)
72	4	{
73	4	double exp_x, scale;
74	4	int ex_expt;
75
76	4	exp_x = __frexp_exp(x, &ex_expt);
77	4	expt += ex_expt;
78	4	INSERT_WORDS(scale, (0x3ff + expt) << 20, 0);
79	4	return (exp_x * scale);
80	4	}