| /* Complex square root of double value. |
| Copyright (C) 1997-2015 Free Software Foundation, Inc. |
| This file is part of the GNU C Library. |
| Based on an algorithm by Stephen L. Moshier <moshier@world.std.com>. |
| Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. |
| |
| The GNU C Library is free software; you can redistribute it and/or |
| modify it under the terms of the GNU Lesser General Public |
| License as published by the Free Software Foundation; either |
| version 2.1 of the License, or (at your option) any later version. |
| |
| The GNU C Library is distributed in the hope that it will be useful, |
| but WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| Lesser General Public License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public |
| License along with the GNU C Library; if not, see |
| <http://www.gnu.org/licenses/>. */ |
| |
| #include <complex.h> |
| #include <math.h> |
| #include <math_private.h> |
| #include <float.h> |
| |
| __complex__ double |
| __csqrt (__complex__ double x) |
| { |
| __complex__ double res; |
| int rcls = fpclassify (__real__ x); |
| int icls = fpclassify (__imag__ x); |
| |
| if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE)) |
| { |
| if (icls == FP_INFINITE) |
| { |
| __real__ res = HUGE_VAL; |
| __imag__ res = __imag__ x; |
| } |
| else if (rcls == FP_INFINITE) |
| { |
| if (__real__ x < 0.0) |
| { |
| __real__ res = icls == FP_NAN ? __nan ("") : 0; |
| __imag__ res = __copysign (HUGE_VAL, __imag__ x); |
| } |
| else |
| { |
| __real__ res = __real__ x; |
| __imag__ res = (icls == FP_NAN |
| ? __nan ("") : __copysign (0.0, __imag__ x)); |
| } |
| } |
| else |
| { |
| __real__ res = __nan (""); |
| __imag__ res = __nan (""); |
| } |
| } |
| else |
| { |
| if (__glibc_unlikely (icls == FP_ZERO)) |
| { |
| if (__real__ x < 0.0) |
| { |
| __real__ res = 0.0; |
| __imag__ res = __copysign (__ieee754_sqrt (-__real__ x), |
| __imag__ x); |
| } |
| else |
| { |
| __real__ res = fabs (__ieee754_sqrt (__real__ x)); |
| __imag__ res = __copysign (0.0, __imag__ x); |
| } |
| } |
| else if (__glibc_unlikely (rcls == FP_ZERO)) |
| { |
| double r; |
| if (fabs (__imag__ x) >= 2.0 * DBL_MIN) |
| r = __ieee754_sqrt (0.5 * fabs (__imag__ x)); |
| else |
| r = 0.5 * __ieee754_sqrt (2.0 * fabs (__imag__ x)); |
| |
| __real__ res = r; |
| __imag__ res = __copysign (r, __imag__ x); |
| } |
| else |
| { |
| double d, r, s; |
| int scale = 0; |
| |
| if (fabs (__real__ x) > DBL_MAX / 4.0) |
| { |
| scale = 1; |
| __real__ x = __scalbn (__real__ x, -2 * scale); |
| __imag__ x = __scalbn (__imag__ x, -2 * scale); |
| } |
| else if (fabs (__imag__ x) > DBL_MAX / 4.0) |
| { |
| scale = 1; |
| if (fabs (__real__ x) >= 4.0 * DBL_MIN) |
| __real__ x = __scalbn (__real__ x, -2 * scale); |
| else |
| __real__ x = 0.0; |
| __imag__ x = __scalbn (__imag__ x, -2 * scale); |
| } |
| else if (fabs (__real__ x) < DBL_MIN |
| && fabs (__imag__ x) < DBL_MIN) |
| { |
| scale = -(DBL_MANT_DIG / 2); |
| __real__ x = __scalbn (__real__ x, -2 * scale); |
| __imag__ x = __scalbn (__imag__ x, -2 * scale); |
| } |
| |
| d = __ieee754_hypot (__real__ x, __imag__ x); |
| /* Use the identity 2 Re res Im res = Im x |
| to avoid cancellation error in d +/- Re x. */ |
| if (__real__ x > 0) |
| { |
| r = __ieee754_sqrt (0.5 * (d + __real__ x)); |
| if (scale == 1 && fabs (__imag__ x) < 1.0) |
| { |
| /* Avoid possible intermediate underflow. */ |
| s = __imag__ x / r; |
| r = __scalbn (r, scale); |
| scale = 0; |
| } |
| else |
| s = 0.5 * (__imag__ x / r); |
| } |
| else |
| { |
| s = __ieee754_sqrt (0.5 * (d - __real__ x)); |
| if (scale == 1 && fabs (__imag__ x) < 1.0) |
| { |
| /* Avoid possible intermediate underflow. */ |
| r = fabs (__imag__ x / s); |
| s = __scalbn (s, scale); |
| scale = 0; |
| } |
| else |
| r = fabs (0.5 * (__imag__ x / s)); |
| } |
| |
| if (scale) |
| { |
| r = __scalbn (r, scale); |
| s = __scalbn (s, scale); |
| } |
| |
| __real__ res = r; |
| __imag__ res = __copysign (s, __imag__ x); |
| } |
| } |
| |
| return res; |
| } |
| weak_alias (__csqrt, csqrt) |
| #ifdef NO_LONG_DOUBLE |
| strong_alias (__csqrt, __csqrtl) |
| weak_alias (__csqrt, csqrtl) |
| #endif |