compiler/stdc/math/k_exp.c

   1 /*-
   2  * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
   3  * All rights reserved.
   4  *
   5  * Redistribution and use in source and binary forms, with or without
   6  * modification, are permitted provided that the following conditions
   7  * are met:
   8  * 1. Redistributions of source code must retain the above copyright
   9  *    notice, this list of conditions and the following disclaimer.
  10  * 2. Redistributions in binary form must reproduce the above copyright
  11  *    notice, this list of conditions and the following disclaimer in the
  12  *    documentation and/or other materials provided with the distribution.
  13  *
  14  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
  15  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  16  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  17  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  18  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  19  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  20  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  21  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  22  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  23  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  24  * SUCH DAMAGE.
  25  */
  26
  27 #ifndef lint
  28 static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_exp.c,v 1.1 2011/10/21 06:27:56 das Exp $";
  29 #endif
  30
  31 #include "math.h"
  32 #include "math_private.h"
  33
  34 static const uint32_t k = 1799;         /* constant for reduction */
  35 static const double kln2 =  1246.97177782734161156;     /* k * ln2 */
  36
  37 /*
  38  * Compute exp(x), scaled to avoid spurious overflow.  An exponent is
  39  * returned separately in 'expt'.
  40  *
  41  * Input:  ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91
  42  * Output: 2**1023 <= y < 2**1024
  43  */
  44 static double
  45 __frexp_exp(double x, int *expt)
  46 {
  47         double exp_x;
  48         uint32_t hx;
  49
  50         /*
  51          * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to
  52          * minimize |exp(kln2) - 2**k|.  We also scale the exponent of
  53          * exp_x to MAX_EXP so that the result can be multiplied by
  54          * a tiny number without losing accuracy due to denormalization.
  55          */
  56         exp_x = exp(x - kln2);
  57         GET_HIGH_WORD(hx, exp_x);
  58         *expt = (hx >> 20) - (0x3ff + 1023) + k;
  59         SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20));
  60         return (exp_x);
  61 }
  62
  63 /*
  64  * __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt.
  65  * They are intended for large arguments (real part >= ln(DBL_MAX))
  66  * where care is needed to avoid overflow.
  67  *
  68  * The present implementation is narrowly tailored for our hyperbolic and
  69  * exponential functions.  We assume expt is small (0 or -1), and the caller
  70  * has filtered out very large x, for which overflow would be inevitable.
  71  */
  72
  73 double
  74 __ldexp_exp(double x, int expt)
  75 {
  76         double exp_x, scale;
  77         int ex_expt;
  78
  79         exp_x = __frexp_exp(x, &ex_expt);
  80         expt += ex_expt;
  81         INSERT_WORDS(scale, (0x3ff + expt) << 20, 0);
  82         return (exp_x * scale);
  83 }
  84
  85 double complex
  86 __ldexp_cexp(double complex z, int expt)
  87 {
  88         double x, y, exp_x, scale1, scale2;
  89         int ex_expt, half_expt;
  90
  91         x = creal(z);
  92         y = cimag(z);
  93         exp_x = __frexp_exp(x, &ex_expt);
  94         expt += ex_expt;
  95
  96         /*
  97          * Arrange so that scale1 * scale2 == 2**expt.  We use this to
  98          * compensate for scalbn being horrendously slow.
  99          */
 100         half_expt = expt / 2;
 101         INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0);
 102         half_expt = expt - half_expt;
 103         INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0);
 104
 105         return (CMPLX(cos(y) * exp_x * scale1 * scale2,
 106             sin(y) * exp_x * scale1 * scale2));
 107 }