blob: af384efd611fc37058a38e72ff3c45b58ed74405 [file] [log] [blame]
 /* 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 . */ #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; }