github.com/afumu/libc@v0.0.6/musl/src/complex/__cexp.c (about)

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