143 lines
3.8 KiB
C
143 lines
3.8 KiB
C
/* Complex square root of long double value.
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Copyright (C) 1997-2013 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__ long double
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__csqrtl (__complex__ long double x)
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{
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__complex__ long 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 (__builtin_expect (rcls <= FP_INFINITE || icls <= FP_INFINITE, 0))
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{
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if (icls == FP_INFINITE)
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{
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__real__ res = HUGE_VALL;
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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 ? __nanl ("") : 0;
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__imag__ res = __copysignl (HUGE_VALL, __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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? __nanl ("") : __copysignl (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 = __nanl ("");
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__imag__ res = __nanl ("");
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}
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}
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else
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{
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if (__builtin_expect (icls == FP_ZERO, 0))
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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 = __copysignl (__ieee754_sqrtl (-__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 = fabsl (__ieee754_sqrtl (__real__ x));
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__imag__ res = __copysignl (0.0, __imag__ x);
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}
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}
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else if (__builtin_expect (rcls == FP_ZERO, 0))
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{
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long double r;
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if (fabsl (__imag__ x) >= 2.0L * LDBL_MIN)
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r = __ieee754_sqrtl (0.5L * fabsl (__imag__ x));
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else
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r = 0.5L * __ieee754_sqrtl (2.0L * fabsl (__imag__ x));
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__real__ res = r;
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__imag__ res = __copysignl (r, __imag__ x);
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}
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else
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{
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long double d, r, s;
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int scale = 0;
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if (fabsl (__real__ x) > LDBL_MAX / 4.0L)
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{
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scale = 1;
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__real__ x = __scalbnl (__real__ x, -2 * scale);
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__imag__ x = __scalbnl (__imag__ x, -2 * scale);
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}
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else if (fabsl (__imag__ x) > LDBL_MAX / 4.0L)
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{
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scale = 1;
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if (fabsl (__real__ x) >= 4.0L * LDBL_MIN)
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__real__ x = __scalbnl (__real__ x, -2 * scale);
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else
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__real__ x = 0.0L;
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__imag__ x = __scalbnl (__imag__ x, -2 * scale);
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}
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else if (fabsl (__real__ x) < LDBL_MIN
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&& fabsl (__imag__ x) < LDBL_MIN)
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{
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scale = -(LDBL_MANT_DIG / 2);
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__real__ x = __scalbnl (__real__ x, -2 * scale);
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__imag__ x = __scalbnl (__imag__ x, -2 * scale);
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}
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d = __ieee754_hypotl (__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_sqrtl (0.5L * (d + __real__ x));
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s = 0.5L * (__imag__ x / r);
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}
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else
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{
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s = __ieee754_sqrtl (0.5L * (d - __real__ x));
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r = fabsl (0.5L * (__imag__ x / s));
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}
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if (scale)
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{
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r = __scalbnl (r, scale);
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s = __scalbnl (s, scale);
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}
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__real__ res = r;
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__imag__ res = __copysignl (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 (__csqrtl, csqrtl)
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