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Diffstat (limited to 'REORG.TODO/math/k_casinh_template.c')
| -rw-r--r-- | REORG.TODO/math/k_casinh_template.c | 205 |
1 files changed, 205 insertions, 0 deletions
diff --git a/REORG.TODO/math/k_casinh_template.c b/REORG.TODO/math/k_casinh_template.c new file mode 100644 index 0000000000..4ab7d4b836 --- /dev/null +++ b/REORG.TODO/math/k_casinh_template.c @@ -0,0 +1,205 @@ +/* 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) 1997-2017 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; +} |