2 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
5 * Redistribution and use in source and binary forms, with or without
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26 * $FreeBSD: head/lib/msun/src/s_csqrtf.c 181402 2008-08-08 00:15:16Z das $
32 #include "math_private.h"
35 * gcc doesn't implement complex multiplication or division correctly,
36 * so we need to handle infinities specially. We turn on this pragma to
37 * notify conforming c99 compilers that the fast-but-incorrect code that
38 * gcc generates is acceptable, since the special cases have already been
41 #pragma STDC CX_LIMITED_RANGE ON
44 csqrtf(float complex z)
46 float a = crealf(z), b = cimagf(z);
49 /* Handle special cases. */
51 return (cpackf(0, b));
53 return (cpackf(INFINITY, b));
55 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
56 return (cpackf(a, t)); /* return NaN + NaN i */
60 * csqrtf(inf + NaN i) = inf + NaN i
61 * csqrtf(inf + y i) = inf + 0 i
62 * csqrtf(-inf + NaN i) = NaN +- inf i
63 * csqrtf(-inf + y i) = 0 + inf i
66 return (cpackf(fabsf(b - b), copysignf(a, b)));
68 return (cpackf(a, copysignf(b - b, b)));
71 * The remaining special case (b is NaN) is handled just fine by
72 * the normal code path below.
76 * We compute t in double precision to avoid overflow and to
77 * provide correct rounding in nearly all cases.
78 * This is Algorithm 312, CACM vol 10, Oct 1967.
81 t = sqrt((a + hypot(a, b)) * 0.5);
82 return (cpackf(t, b / (2.0 * t)));
84 t = sqrt((-a + hypot(a, b)) * 0.5);
85 return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b)));