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

     1  /* origin: FreeBSD /usr/src/lib/msun/src/s_csinh.c */
     2  /*-
     3   * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
     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 unmodified, this list of conditions, and the following
    11   *    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 ``AS IS'' AND ANY EXPRESS OR
    17   * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
    18   * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
    19   * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
    20   * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
    21   * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
    22   * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
    23   * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
    24   * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
    25   * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
    26   */
    27  /*
    28   * Hyperbolic sine of a complex argument z = x + i y.
    29   *
    30   * sinh(z) = sinh(x+iy)
    31   *         = sinh(x) cos(y) + i cosh(x) sin(y).
    32   *
    33   * Exceptional values are noted in the comments within the source code.
    34   * These values and the return value were taken from n1124.pdf.
    35   */
    36  
    37  #include "complex_impl.h"
    38  
    39  static const double huge = 0x1p1023;
    40  
    41  double complex csinh(double complex z)
    42  {
    43  	double x, y, h;
    44  	int32_t hx, hy, ix, iy, lx, ly;
    45  
    46  	x = creal(z);
    47  	y = cimag(z);
    48  
    49  	EXTRACT_WORDS(hx, lx, x);
    50  	EXTRACT_WORDS(hy, ly, y);
    51  
    52  	ix = 0x7fffffff & hx;
    53  	iy = 0x7fffffff & hy;
    54  
    55  	/* Handle the nearly-non-exceptional cases where x and y are finite. */
    56  	if (ix < 0x7ff00000 && iy < 0x7ff00000) {
    57  		if ((iy | ly) == 0)
    58  			return CMPLX(sinh(x), y);
    59  		if (ix < 0x40360000)    /* small x: normal case */
    60  			return CMPLX(sinh(x) * cos(y), cosh(x) * sin(y));
    61  
    62  		/* |x| >= 22, so cosh(x) ~= exp(|x|) */
    63  		if (ix < 0x40862e42) {
    64  			/* x < 710: exp(|x|) won't overflow */
    65  			h = exp(fabs(x)) * 0.5;
    66  			return CMPLX(copysign(h, x) * cos(y), h * sin(y));
    67  		} else if (ix < 0x4096bbaa) {
    68  			/* x < 1455: scale to avoid overflow */
    69  			z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
    70  			return CMPLX(creal(z) * copysign(1, x), cimag(z));
    71  		} else {
    72  			/* x >= 1455: the result always overflows */
    73  			h = huge * x;
    74  			return CMPLX(h * cos(y), h * h * sin(y));
    75  		}
    76  	}
    77  
    78  	/*
    79  	 * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN.
    80  	 * The sign of 0 in the result is unspecified.  Choice = normally
    81  	 * the same as dNaN.  Raise the invalid floating-point exception.
    82  	 *
    83  	 * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN).
    84  	 * The sign of 0 in the result is unspecified.  Choice = normally
    85  	 * the same as d(NaN).
    86  	 */
    87  	if ((ix | lx) == 0 && iy >= 0x7ff00000)
    88  		return CMPLX(copysign(0, x * (y - y)), y - y);
    89  
    90  	/*
    91  	 * sinh(+-Inf +- I 0) = +-Inf + I +-0.
    92  	 *
    93  	 * sinh(NaN +- I 0)   = d(NaN) + I +-0.
    94  	 */
    95  	if ((iy | ly) == 0 && ix >= 0x7ff00000) {
    96  		if (((hx & 0xfffff) | lx) == 0)
    97  			return CMPLX(x, y);
    98  		return CMPLX(x, copysign(0, y));
    99  	}
   100  
   101  	/*
   102  	 * sinh(x +- I Inf) = dNaN + I dNaN.
   103  	 * Raise the invalid floating-point exception for finite nonzero x.
   104  	 *
   105  	 * sinh(x + I NaN) = d(NaN) + I d(NaN).
   106  	 * Optionally raises the invalid floating-point exception for finite
   107  	 * nonzero x.  Choice = don't raise (except for signaling NaNs).
   108  	 */
   109  	if (ix < 0x7ff00000 && iy >= 0x7ff00000)
   110  		return CMPLX(y - y, x * (y - y));
   111  
   112  	/*
   113  	 * sinh(+-Inf + I NaN)  = +-Inf + I d(NaN).
   114  	 * The sign of Inf in the result is unspecified.  Choice = normally
   115  	 * the same as d(NaN).
   116  	 *
   117  	 * sinh(+-Inf +- I Inf) = +Inf + I dNaN.
   118  	 * The sign of Inf in the result is unspecified.  Choice = always +.
   119  	 * Raise the invalid floating-point exception.
   120  	 *
   121  	 * sinh(+-Inf + I y)   = +-Inf cos(y) + I Inf sin(y)
   122  	 */
   123  	if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
   124  		if (iy >= 0x7ff00000)
   125  			return CMPLX(x * x, x * (y - y));
   126  		return CMPLX(x * cos(y), INFINITY * sin(y));
   127  	}
   128  
   129  	/*
   130  	 * sinh(NaN + I NaN)  = d(NaN) + I d(NaN).
   131  	 *
   132  	 * sinh(NaN +- I Inf) = d(NaN) + I d(NaN).
   133  	 * Optionally raises the invalid floating-point exception.
   134  	 * Choice = raise.
   135  	 *
   136  	 * sinh(NaN + I y)    = d(NaN) + I d(NaN).
   137  	 * Optionally raises the invalid floating-point exception for finite
   138  	 * nonzero y.  Choice = don't raise (except for signaling NaNs).
   139  	 */
   140  	return CMPLX((x * x) * (y - y), (x + x) * (y - y));
   141  }