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

     1  /* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */
     2  /*-
     3   * Copyright (c) 2007 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  /*
    31   * gcc doesn't implement complex multiplication or division correctly,
    32   * so we need to handle infinities specially. We turn on this pragma to
    33   * notify conforming c99 compilers that the fast-but-incorrect code that
    34   * gcc generates is acceptable, since the special cases have already been
    35   * handled.
    36   */
    37  #pragma STDC CX_LIMITED_RANGE ON
    38  
    39  /* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
    40  #define THRESH  0x1.a827999fcef32p+1022
    41  
    42  double complex csqrt(double complex z)
    43  {
    44  	double complex result;
    45  	double a, b;
    46  	double t;
    47  	int scale;
    48  
    49  	a = creal(z);
    50  	b = cimag(z);
    51  
    52  	/* Handle special cases. */
    53  	if (z == 0)
    54  		return CMPLX(0, b);
    55  	if (isinf(b))
    56  		return CMPLX(INFINITY, b);
    57  	if (isnan(a)) {
    58  		t = (b - b) / (b - b);  /* raise invalid if b is not a NaN */
    59  		return CMPLX(a, t);   /* return NaN + NaN i */
    60  	}
    61  	if (isinf(a)) {
    62  		/*
    63  		 * csqrt(inf + NaN i)  = inf +  NaN i
    64  		 * csqrt(inf + y i)    = inf +  0 i
    65  		 * csqrt(-inf + NaN i) = NaN +- inf i
    66  		 * csqrt(-inf + y i)   = 0   +  inf i
    67  		 */
    68  		if (signbit(a))
    69  			return CMPLX(fabs(b - b), copysign(a, b));
    70  		else
    71  			return CMPLX(a, copysign(b - b, b));
    72  	}
    73  	/*
    74  	 * The remaining special case (b is NaN) is handled just fine by
    75  	 * the normal code path below.
    76  	 */
    77  
    78  	/* Scale to avoid overflow. */
    79  	if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
    80  		a *= 0.25;
    81  		b *= 0.25;
    82  		scale = 1;
    83  	} else {
    84  		scale = 0;
    85  	}
    86  
    87  	/* Algorithm 312, CACM vol 10, Oct 1967. */
    88  	if (a >= 0) {
    89  		t = sqrt((a + hypot(a, b)) * 0.5);
    90  		result = CMPLX(t, b / (2 * t));
    91  	} else {
    92  		t = sqrt((-a + hypot(a, b)) * 0.5);
    93  		result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
    94  	}
    95  
    96  	/* Rescale. */
    97  	if (scale)
    98  		result *= 2;
    99  	return result;
   100  }