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 "libm.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 39float 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} 83