Mercurial > hg > CbC > CbC_gcc
diff libquadmath/math/casinhq_kernel.c @ 145:1830386684a0
gcc-9.2.0
author | anatofuz |
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date | Thu, 13 Feb 2020 11:34:05 +0900 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/libquadmath/math/casinhq_kernel.c Thu Feb 13 11:34:05 2020 +0900 @@ -0,0 +1,202 @@ +/* Return arc hyperbolic sine for a complex float type, with the + imaginary part of the result possibly adjusted for use in + computing other functions. + Copyright (C) 1997-2018 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + 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 "quadmath-imp.h" + +/* Return the complex inverse hyperbolic sine of finite nonzero Z, + with the imaginary part of the result subtracted from pi/2 if ADJ + is nonzero. */ + +__complex128 +__quadmath_kernel_casinhq (__complex128 x, int adj) +{ + __complex128 res; + __float128 rx, ix; + __complex128 y; + + /* Avoid cancellation by reducing to the first quadrant. */ + rx = fabsq (__real__ x); + ix = fabsq (__imag__ x); + + if (rx >= 1 / FLT128_EPSILON || ix >= 1 / FLT128_EPSILON) + { + /* For large x in the first quadrant, x + csqrt (1 + x * x) + is sufficiently close to 2 * x to make no significant + difference to the result; avoid possible overflow from + the squaring and addition. */ + __real__ y = rx; + __imag__ y = ix; + + if (adj) + { + __float128 t = __real__ y; + __real__ y = copysignq (__imag__ y, __imag__ x); + __imag__ y = t; + } + + res = clogq (y); + __real__ res += (__float128) M_LN2q; + } + else if (rx >= 0.5Q && ix < FLT128_EPSILON / 8) + { + __float128 s = hypotq (1, rx); + + __real__ res = logq (rx + s); + if (adj) + __imag__ res = atan2q (s, __imag__ x); + else + __imag__ res = atan2q (ix, s); + } + else if (rx < FLT128_EPSILON / 8 && ix >= 1.5Q) + { + __float128 s = sqrtq ((ix + 1) * (ix - 1)); + + __real__ res = logq (ix + s); + if (adj) + __imag__ res = atan2q (rx, copysignq (s, __imag__ x)); + else + __imag__ res = atan2q (s, rx); + } + else if (ix > 1 && ix < 1.5Q && rx < 0.5Q) + { + if (rx < FLT128_EPSILON * FLT128_EPSILON) + { + __float128 ix2m1 = (ix + 1) * (ix - 1); + __float128 s = sqrtq (ix2m1); + + __real__ res = log1pq (2 * (ix2m1 + ix * s)) / 2; + if (adj) + __imag__ res = atan2q (rx, copysignq (s, __imag__ x)); + else + __imag__ res = atan2q (s, rx); + } + else + { + __float128 ix2m1 = (ix + 1) * (ix - 1); + __float128 rx2 = rx * rx; + __float128 f = rx2 * (2 + rx2 + 2 * ix * ix); + __float128 d = sqrtq (ix2m1 * ix2m1 + f); + __float128 dp = d + ix2m1; + __float128 dm = f / dp; + __float128 r1 = sqrtq ((dm + rx2) / 2); + __float128 r2 = rx * ix / r1; + + __real__ res = log1pq (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2; + if (adj) + __imag__ res = atan2q (rx + r1, copysignq (ix + r2, __imag__ x)); + else + __imag__ res = atan2q (ix + r2, rx + r1); + } + } + else if (ix == 1 && rx < 0.5Q) + { + if (rx < FLT128_EPSILON / 8) + { + __real__ res = log1pq (2 * (rx + sqrtq (rx))) / 2; + if (adj) + __imag__ res = atan2q (sqrtq (rx), copysignq (1, __imag__ x)); + else + __imag__ res = atan2q (1, sqrtq (rx)); + } + else + { + __float128 d = rx * sqrtq (4 + rx * rx); + __float128 s1 = sqrtq ((d + rx * rx) / 2); + __float128 s2 = sqrtq ((d - rx * rx) / 2); + + __real__ res = log1pq (rx * rx + d + 2 * (rx * s1 + s2)) / 2; + if (adj) + __imag__ res = atan2q (rx + s1, copysignq (1 + s2, __imag__ x)); + else + __imag__ res = atan2q (1 + s2, rx + s1); + } + } + else if (ix < 1 && rx < 0.5Q) + { + if (ix >= FLT128_EPSILON) + { + if (rx < FLT128_EPSILON * FLT128_EPSILON) + { + __float128 onemix2 = (1 + ix) * (1 - ix); + __float128 s = sqrtq (onemix2); + + __real__ res = log1pq (2 * rx / s) / 2; + if (adj) + __imag__ res = atan2q (s, __imag__ x); + else + __imag__ res = atan2q (ix, s); + } + else + { + __float128 onemix2 = (1 + ix) * (1 - ix); + __float128 rx2 = rx * rx; + __float128 f = rx2 * (2 + rx2 + 2 * ix * ix); + __float128 d = sqrtq (onemix2 * onemix2 + f); + __float128 dp = d + onemix2; + __float128 dm = f / dp; + __float128 r1 = sqrtq ((dp + rx2) / 2); + __float128 r2 = rx * ix / r1; + + __real__ res = log1pq (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2; + if (adj) + __imag__ res = atan2q (rx + r1, copysignq (ix + r2, + __imag__ x)); + else + __imag__ res = atan2q (ix + r2, rx + r1); + } + } + else + { + __float128 s = hypotq (1, rx); + + __real__ res = log1pq (2 * rx * (rx + s)) / 2; + if (adj) + __imag__ res = atan2q (s, __imag__ x); + else + __imag__ res = atan2q (ix, s); + } + math_check_force_underflow_nonneg (__real__ res); + } + else + { + __real__ y = (rx - ix) * (rx + ix) + 1; + __imag__ y = 2 * rx * ix; + + y = csqrtq (y); + + __real__ y += rx; + __imag__ y += ix; + + if (adj) + { + __float128 t = __real__ y; + __real__ y = copysignq (__imag__ y, __imag__ x); + __imag__ y = t; + } + + res = clogq (y); + } + + /* Give results the correct sign for the original argument. */ + __real__ res = copysignq (__real__ res, __real__ x); + __imag__ res = copysignq (__imag__ res, (adj ? 1 : __imag__ x)); + + return res; +}