| /* 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 <complex.h> |
| #include <math.h> |
| #include <math_private.h> |
| #include <float.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. */ |
| |
| CFLOAT |
| M_DECL_FUNC (__kernel_casinh) (CFLOAT x, int adj) |
| { |
| CFLOAT res; |
| FLOAT rx, ix; |
| CFLOAT y; |
| |
| /* Avoid cancellation by reducing to the first quadrant. */ |
| rx = M_FABS (__real__ x); |
| ix = M_FABS (__imag__ x); |
| |
| if (rx >= 1 / M_EPSILON || ix >= 1 / M_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) |
| { |
| FLOAT t = __real__ y; |
| __real__ y = M_COPYSIGN (__imag__ y, __imag__ x); |
| __imag__ y = t; |
| } |
| |
| res = M_SUF (__clog) (y); |
| __real__ res += (FLOAT) M_MLIT (M_LN2); |
| } |
| else if (rx >= M_LIT (0.5) && ix < M_EPSILON / 8) |
| { |
| FLOAT s = M_HYPOT (1, rx); |
| |
| __real__ res = M_LOG (rx + s); |
| if (adj) |
| __imag__ res = M_ATAN2 (s, __imag__ x); |
| else |
| __imag__ res = M_ATAN2 (ix, s); |
| } |
| else if (rx < M_EPSILON / 8 && ix >= M_LIT (1.5)) |
| { |
| FLOAT s = M_SQRT ((ix + 1) * (ix - 1)); |
| |
| __real__ res = M_LOG (ix + s); |
| if (adj) |
| __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x)); |
| else |
| __imag__ res = M_ATAN2 (s, rx); |
| } |
| else if (ix > 1 && ix < M_LIT (1.5) && rx < M_LIT (0.5)) |
| { |
| if (rx < M_EPSILON * M_EPSILON) |
| { |
| FLOAT ix2m1 = (ix + 1) * (ix - 1); |
| FLOAT s = M_SQRT (ix2m1); |
| |
| __real__ res = M_LOG1P (2 * (ix2m1 + ix * s)) / 2; |
| if (adj) |
| __imag__ res = M_ATAN2 (rx, M_COPYSIGN (s, __imag__ x)); |
| else |
| __imag__ res = M_ATAN2 (s, rx); |
| } |
| else |
| { |
| FLOAT ix2m1 = (ix + 1) * (ix - 1); |
| FLOAT rx2 = rx * rx; |
| FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix); |
| FLOAT d = M_SQRT (ix2m1 * ix2m1 + f); |
| FLOAT dp = d + ix2m1; |
| FLOAT dm = f / dp; |
| FLOAT r1 = M_SQRT ((dm + rx2) / 2); |
| FLOAT r2 = rx * ix / r1; |
| |
| __real__ res = M_LOG1P (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2; |
| if (adj) |
| __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, __imag__ x)); |
| else |
| __imag__ res = M_ATAN2 (ix + r2, rx + r1); |
| } |
| } |
| else if (ix == 1 && rx < M_LIT (0.5)) |
| { |
| if (rx < M_EPSILON / 8) |
| { |
| __real__ res = M_LOG1P (2 * (rx + M_SQRT (rx))) / 2; |
| if (adj) |
| __imag__ res = M_ATAN2 (M_SQRT (rx), M_COPYSIGN (1, __imag__ x)); |
| else |
| __imag__ res = M_ATAN2 (1, M_SQRT (rx)); |
| } |
| else |
| { |
| FLOAT d = rx * M_SQRT (4 + rx * rx); |
| FLOAT s1 = M_SQRT ((d + rx * rx) / 2); |
| FLOAT s2 = M_SQRT ((d - rx * rx) / 2); |
| |
| __real__ res = M_LOG1P (rx * rx + d + 2 * (rx * s1 + s2)) / 2; |
| if (adj) |
| __imag__ res = M_ATAN2 (rx + s1, M_COPYSIGN (1 + s2, __imag__ x)); |
| else |
| __imag__ res = M_ATAN2 (1 + s2, rx + s1); |
| } |
| } |
| else if (ix < 1 && rx < M_LIT (0.5)) |
| { |
| if (ix >= M_EPSILON) |
| { |
| if (rx < M_EPSILON * M_EPSILON) |
| { |
| FLOAT onemix2 = (1 + ix) * (1 - ix); |
| FLOAT s = M_SQRT (onemix2); |
| |
| __real__ res = M_LOG1P (2 * rx / s) / 2; |
| if (adj) |
| __imag__ res = M_ATAN2 (s, __imag__ x); |
| else |
| __imag__ res = M_ATAN2 (ix, s); |
| } |
| else |
| { |
| FLOAT onemix2 = (1 + ix) * (1 - ix); |
| FLOAT rx2 = rx * rx; |
| FLOAT f = rx2 * (2 + rx2 + 2 * ix * ix); |
| FLOAT d = M_SQRT (onemix2 * onemix2 + f); |
| FLOAT dp = d + onemix2; |
| FLOAT dm = f / dp; |
| FLOAT r1 = M_SQRT ((dp + rx2) / 2); |
| FLOAT r2 = rx * ix / r1; |
| |
| __real__ res = M_LOG1P (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2; |
| if (adj) |
| __imag__ res = M_ATAN2 (rx + r1, M_COPYSIGN (ix + r2, |
| __imag__ x)); |
| else |
| __imag__ res = M_ATAN2 (ix + r2, rx + r1); |
| } |
| } |
| else |
| { |
| FLOAT s = M_HYPOT (1, rx); |
| |
| __real__ res = M_LOG1P (2 * rx * (rx + s)) / 2; |
| if (adj) |
| __imag__ res = M_ATAN2 (s, __imag__ x); |
| else |
| __imag__ res = M_ATAN2 (ix, s); |
| } |
| math_check_force_underflow_nonneg (__real__ res); |
| } |
| else |
| { |
| __real__ y = (rx - ix) * (rx + ix) + 1; |
| __imag__ y = 2 * rx * ix; |
| |
| y = M_SUF (__csqrt) (y); |
| |
| __real__ y += rx; |
| __imag__ y += ix; |
| |
| if (adj) |
| { |
| FLOAT t = __real__ y; |
| __real__ y = M_COPYSIGN (__imag__ y, __imag__ x); |
| __imag__ y = t; |
| } |
| |
| res = M_SUF (__clog) (y); |
| } |
| |
| /* Give results the correct sign for the original argument. */ |
| __real__ res = M_COPYSIGN (__real__ res, __real__ x); |
| __imag__ res = M_COPYSIGN (__imag__ res, (adj ? 1 : __imag__ x)); |
| |
| return res; |
| } |