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Diffstat (limited to 'math/k_casinh_template.c')
| -rw-r--r-- | math/k_casinh_template.c | 210 |
1 files changed, 210 insertions, 0 deletions
diff --git a/math/k_casinh_template.c b/math/k_casinh_template.c new file mode 100644 index 0000000000..354dde1f3e --- /dev/null +++ b/math/k_casinh_template.c @@ -0,0 +1,210 @@ +/* Return arc hyperbole sine for double value, with the imaginary part + of the result possibly adjusted for use in computing other + functions. + Copyright (C) 1997-2016 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. */ + +__complex__ double +__kernel_casinh (__complex__ double x, int adj) +{ + __complex__ double res; + double rx, ix; + __complex__ double y; + + /* Avoid cancellation by reducing to the first quadrant. */ + rx = fabs (__real__ x); + ix = fabs (__imag__ x); + + if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_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) + { + double t = __real__ y; + __real__ y = __copysign (__imag__ y, __imag__ x); + __imag__ y = t; + } + + res = __clog (y); + __real__ res += M_LN2; + } + else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0) + { + double s = __ieee754_hypot (1.0, rx); + + __real__ res = __ieee754_log (rx + s); + if (adj) + __imag__ res = __ieee754_atan2 (s, __imag__ x); + else + __imag__ res = __ieee754_atan2 (ix, s); + } + else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5) + { + double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0)); + + __real__ res = __ieee754_log (ix + s); + if (adj) + __imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x)); + else + __imag__ res = __ieee754_atan2 (s, rx); + } + else if (ix > 1.0 && ix < 1.5 && rx < 0.5) + { + if (rx < DBL_EPSILON * DBL_EPSILON) + { + double ix2m1 = (ix + 1.0) * (ix - 1.0); + double s = __ieee754_sqrt (ix2m1); + + __real__ res = __log1p (2.0 * (ix2m1 + ix * s)) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x)); + else + __imag__ res = __ieee754_atan2 (s, rx); + } + else + { + double ix2m1 = (ix + 1.0) * (ix - 1.0); + double rx2 = rx * rx; + double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix); + double d = __ieee754_sqrt (ix2m1 * ix2m1 + f); + double dp = d + ix2m1; + double dm = f / dp; + double r1 = __ieee754_sqrt ((dm + rx2) / 2.0); + double r2 = rx * ix / r1; + + __real__ res = __log1p (rx2 + dp + 2.0 * (rx * r1 + ix * r2)) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (rx + r1, __copysign (ix + r2, + __imag__ x)); + else + __imag__ res = __ieee754_atan2 (ix + r2, rx + r1); + } + } + else if (ix == 1.0 && rx < 0.5) + { + if (rx < DBL_EPSILON / 8.0) + { + __real__ res = __log1p (2.0 * (rx + __ieee754_sqrt (rx))) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (__ieee754_sqrt (rx), + __copysign (1.0, __imag__ x)); + else + __imag__ res = __ieee754_atan2 (1.0, __ieee754_sqrt (rx)); + } + else + { + double d = rx * __ieee754_sqrt (4.0 + rx * rx); + double s1 = __ieee754_sqrt ((d + rx * rx) / 2.0); + double s2 = __ieee754_sqrt ((d - rx * rx) / 2.0); + + __real__ res = __log1p (rx * rx + d + 2.0 * (rx * s1 + s2)) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (rx + s1, __copysign (1.0 + s2, + __imag__ x)); + else + __imag__ res = __ieee754_atan2 (1.0 + s2, rx + s1); + } + } + else if (ix < 1.0 && rx < 0.5) + { + if (ix >= DBL_EPSILON) + { + if (rx < DBL_EPSILON * DBL_EPSILON) + { + double onemix2 = (1.0 + ix) * (1.0 - ix); + double s = __ieee754_sqrt (onemix2); + + __real__ res = __log1p (2.0 * rx / s) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (s, __imag__ x); + else + __imag__ res = __ieee754_atan2 (ix, s); + } + else + { + double onemix2 = (1.0 + ix) * (1.0 - ix); + double rx2 = rx * rx; + double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix); + double d = __ieee754_sqrt (onemix2 * onemix2 + f); + double dp = d + onemix2; + double dm = f / dp; + double r1 = __ieee754_sqrt ((dp + rx2) / 2.0); + double r2 = rx * ix / r1; + + __real__ res + = __log1p (rx2 + dm + 2.0 * (rx * r1 + ix * r2)) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (rx + r1, + __copysign (ix + r2, + __imag__ x)); + else + __imag__ res = __ieee754_atan2 (ix + r2, rx + r1); + } + } + else + { + double s = __ieee754_hypot (1.0, rx); + + __real__ res = __log1p (2.0 * rx * (rx + s)) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (s, __imag__ x); + else + __imag__ res = __ieee754_atan2 (ix, s); + } + math_check_force_underflow_nonneg (__real__ res); + } + else + { + __real__ y = (rx - ix) * (rx + ix) + 1.0; + __imag__ y = 2.0 * rx * ix; + + y = __csqrt (y); + + __real__ y += rx; + __imag__ y += ix; + + if (adj) + { + double t = __real__ y; + __real__ y = __copysign (__imag__ y, __imag__ x); + __imag__ y = t; + } + + res = __clog (y); + } + + /* Give results the correct sign for the original argument. */ + __real__ res = __copysign (__real__ res, __real__ x); + __imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x)); + + return res; +} |