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

     1  /* origin: FreeBSD /usr/src/lib/msun/src/s_csqrtf.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  float complex csqrtf(float complex z)
    40  {
    41  	float a = crealf(z), b = cimagf(z);
    42  	double t;
    43  
    44  	/* Handle special cases. */
    45  	if (z == 0)
    46  		return CMPLXF(0, b);
    47  	if (isinf(b))
    48  		return CMPLXF(INFINITY, b);
    49  	if (isnan(a)) {
    50  		t = (b - b) / (b - b);  /* raise invalid if b is not a NaN */
    51  		return CMPLXF(a, t);  /* return NaN + NaN i */
    52  	}
    53  	if (isinf(a)) {
    54  		/*
    55  		 * csqrtf(inf + NaN i)  = inf +  NaN i
    56  		 * csqrtf(inf + y i)    = inf +  0 i
    57  		 * csqrtf(-inf + NaN i) = NaN +- inf i
    58  		 * csqrtf(-inf + y i)   = 0   +  inf i
    59  		 */
    60  		if (signbit(a))
    61  			return CMPLXF(fabsf(b - b), copysignf(a, b));
    62  		else
    63  			return CMPLXF(a, copysignf(b - b, b));
    64  	}
    65  	/*
    66  	 * The remaining special case (b is NaN) is handled just fine by
    67  	 * the normal code path below.
    68  	 */
    69  
    70  	/*
    71  	 * We compute t in double precision to avoid overflow and to
    72  	 * provide correct rounding in nearly all cases.
    73  	 * This is Algorithm 312, CACM vol 10, Oct 1967.
    74  	 */
    75  	if (a >= 0) {
    76  		t = sqrt((a + hypot(a, b)) * 0.5);
    77  		return CMPLXF(t, b / (2.0 * t));
    78  	} else {
    79  		t = sqrt((-a + hypot(a, b)) * 0.5);
    80  		return CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b));
    81  	}
    82  }