147 lines
3.8 KiB
C
147 lines
3.8 KiB
C
/* Complex square root of double value.
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Copyright (C) 1997-2014 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Based on an algorithm by Stephen L. Moshier <moshier@world.std.com>.
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Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <complex.h>
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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__complex__ double
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__csqrt (__complex__ double x)
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{
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__complex__ double res;
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int rcls = fpclassify (__real__ x);
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int icls = fpclassify (__imag__ x);
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if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE))
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{
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if (icls == FP_INFINITE)
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{
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__real__ res = HUGE_VAL;
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__imag__ res = __imag__ x;
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}
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else if (rcls == FP_INFINITE)
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{
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if (__real__ x < 0.0)
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{
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__real__ res = icls == FP_NAN ? __nan ("") : 0;
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__imag__ res = __copysign (HUGE_VAL, __imag__ x);
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}
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else
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{
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__real__ res = __real__ x;
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__imag__ res = (icls == FP_NAN
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? __nan ("") : __copysign (0.0, __imag__ x));
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}
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}
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else
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{
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__real__ res = __nan ("");
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__imag__ res = __nan ("");
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}
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}
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else
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{
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if (__glibc_unlikely (icls == FP_ZERO))
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{
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if (__real__ x < 0.0)
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{
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__real__ res = 0.0;
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__imag__ res = __copysign (__ieee754_sqrt (-__real__ x),
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__imag__ x);
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}
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else
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{
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__real__ res = fabs (__ieee754_sqrt (__real__ x));
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__imag__ res = __copysign (0.0, __imag__ x);
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}
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}
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else if (__glibc_unlikely (rcls == FP_ZERO))
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{
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double r;
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if (fabs (__imag__ x) >= 2.0 * DBL_MIN)
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r = __ieee754_sqrt (0.5 * fabs (__imag__ x));
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else
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r = 0.5 * __ieee754_sqrt (2.0 * fabs (__imag__ x));
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__real__ res = r;
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__imag__ res = __copysign (r, __imag__ x);
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}
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else
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{
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double d, r, s;
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int scale = 0;
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if (fabs (__real__ x) > DBL_MAX / 4.0)
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{
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scale = 1;
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__real__ x = __scalbn (__real__ x, -2 * scale);
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__imag__ x = __scalbn (__imag__ x, -2 * scale);
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}
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else if (fabs (__imag__ x) > DBL_MAX / 4.0)
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{
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scale = 1;
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if (fabs (__real__ x) >= 4.0 * DBL_MIN)
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__real__ x = __scalbn (__real__ x, -2 * scale);
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else
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__real__ x = 0.0;
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__imag__ x = __scalbn (__imag__ x, -2 * scale);
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}
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else if (fabs (__real__ x) < DBL_MIN
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&& fabs (__imag__ x) < DBL_MIN)
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{
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scale = -(DBL_MANT_DIG / 2);
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__real__ x = __scalbn (__real__ x, -2 * scale);
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__imag__ x = __scalbn (__imag__ x, -2 * scale);
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}
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d = __ieee754_hypot (__real__ x, __imag__ x);
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/* Use the identity 2 Re res Im res = Im x
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to avoid cancellation error in d +/- Re x. */
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if (__real__ x > 0)
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{
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r = __ieee754_sqrt (0.5 * (d + __real__ x));
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s = 0.5 * (__imag__ x / r);
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}
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else
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{
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s = __ieee754_sqrt (0.5 * (d - __real__ x));
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r = fabs (0.5 * (__imag__ x / s));
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}
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if (scale)
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{
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r = __scalbn (r, scale);
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s = __scalbn (s, scale);
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}
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__real__ res = r;
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__imag__ res = __copysign (s, __imag__ x);
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}
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}
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return res;
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}
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weak_alias (__csqrt, csqrt)
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#ifdef NO_LONG_DOUBLE
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strong_alias (__csqrt, __csqrtl)
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weak_alias (__csqrt, csqrtl)
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#endif
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