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-rw-r--r--math/k_casinhl.c219
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diff --git a/math/k_casinhl.c b/math/k_casinhl.c
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-/* Return arc hyperbole sine for long 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>
-
-/* To avoid spurious overflows, use this definition to treat IBM long
- double as approximating an IEEE-style format. */
-#if LDBL_MANT_DIG == 106
-# undef LDBL_EPSILON
-# define LDBL_EPSILON 0x1p-106L
-#endif
-
-/* 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__ long double
-__kernel_casinhl (__complex__ long double x, int adj)
-{
- __complex__ long double res;
- long double rx, ix;
- __complex__ long double y;
-
- /* Avoid cancellation by reducing to the first quadrant. */
- rx = fabsl (__real__ x);
- ix = fabsl (__imag__ x);
-
- if (rx >= 1.0L / LDBL_EPSILON || ix >= 1.0L / LDBL_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)
- {
- long double t = __real__ y;
- __real__ y = __copysignl (__imag__ y, __imag__ x);
- __imag__ y = t;
- }
-
- res = __clogl (y);
- __real__ res += M_LN2l;
- }
- else if (rx >= 0.5L && ix < LDBL_EPSILON / 8.0L)
- {
- long double s = __ieee754_hypotl (1.0L, rx);
-
- __real__ res = __ieee754_logl (rx + s);
- if (adj)
- __imag__ res = __ieee754_atan2l (s, __imag__ x);
- else
- __imag__ res = __ieee754_atan2l (ix, s);
- }
- else if (rx < LDBL_EPSILON / 8.0L && ix >= 1.5L)
- {
- long double s = __ieee754_sqrtl ((ix + 1.0L) * (ix - 1.0L));
-
- __real__ res = __ieee754_logl (ix + s);
- if (adj)
- __imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
- else
- __imag__ res = __ieee754_atan2l (s, rx);
- }
- else if (ix > 1.0L && ix < 1.5L && rx < 0.5L)
- {
- if (rx < LDBL_EPSILON * LDBL_EPSILON)
- {
- long double ix2m1 = (ix + 1.0L) * (ix - 1.0L);
- long double s = __ieee754_sqrtl (ix2m1);
-
- __real__ res = __log1pl (2.0L * (ix2m1 + ix * s)) / 2.0L;
- if (adj)
- __imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
- else
- __imag__ res = __ieee754_atan2l (s, rx);
- }
- else
- {
- long double ix2m1 = (ix + 1.0L) * (ix - 1.0L);
- long double rx2 = rx * rx;
- long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix);
- long double d = __ieee754_sqrtl (ix2m1 * ix2m1 + f);
- long double dp = d + ix2m1;
- long double dm = f / dp;
- long double r1 = __ieee754_sqrtl ((dm + rx2) / 2.0L);
- long double r2 = rx * ix / r1;
-
- __real__ res
- = __log1pl (rx2 + dp + 2.0L * (rx * r1 + ix * r2)) / 2.0L;
- if (adj)
- __imag__ res = __ieee754_atan2l (rx + r1, __copysignl (ix + r2,
- __imag__ x));
- else
- __imag__ res = __ieee754_atan2l (ix + r2, rx + r1);
- }
- }
- else if (ix == 1.0L && rx < 0.5L)
- {
- if (rx < LDBL_EPSILON / 8.0L)
- {
- __real__ res = __log1pl (2.0L * (rx + __ieee754_sqrtl (rx))) / 2.0L;
- if (adj)
- __imag__ res = __ieee754_atan2l (__ieee754_sqrtl (rx),
- __copysignl (1.0L, __imag__ x));
- else
- __imag__ res = __ieee754_atan2l (1.0L, __ieee754_sqrtl (rx));
- }
- else
- {
- long double d = rx * __ieee754_sqrtl (4.0L + rx * rx);
- long double s1 = __ieee754_sqrtl ((d + rx * rx) / 2.0L);
- long double s2 = __ieee754_sqrtl ((d - rx * rx) / 2.0L);
-
- __real__ res = __log1pl (rx * rx + d + 2.0L * (rx * s1 + s2)) / 2.0L;
- if (adj)
- __imag__ res = __ieee754_atan2l (rx + s1,
- __copysignl (1.0L + s2,
- __imag__ x));
- else
- __imag__ res = __ieee754_atan2l (1.0L + s2, rx + s1);
- }
- }
- else if (ix < 1.0L && rx < 0.5L)
- {
- if (ix >= LDBL_EPSILON)
- {
- if (rx < LDBL_EPSILON * LDBL_EPSILON)
- {
- long double onemix2 = (1.0L + ix) * (1.0L - ix);
- long double s = __ieee754_sqrtl (onemix2);
-
- __real__ res = __log1pl (2.0L * rx / s) / 2.0L;
- if (adj)
- __imag__ res = __ieee754_atan2l (s, __imag__ x);
- else
- __imag__ res = __ieee754_atan2l (ix, s);
- }
- else
- {
- long double onemix2 = (1.0L + ix) * (1.0L - ix);
- long double rx2 = rx * rx;
- long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix);
- long double d = __ieee754_sqrtl (onemix2 * onemix2 + f);
- long double dp = d + onemix2;
- long double dm = f / dp;
- long double r1 = __ieee754_sqrtl ((dp + rx2) / 2.0L);
- long double r2 = rx * ix / r1;
-
- __real__ res
- = __log1pl (rx2 + dm + 2.0L * (rx * r1 + ix * r2)) / 2.0L;
- if (adj)
- __imag__ res = __ieee754_atan2l (rx + r1,
- __copysignl (ix + r2,
- __imag__ x));
- else
- __imag__ res = __ieee754_atan2l (ix + r2, rx + r1);
- }
- }
- else
- {
- long double s = __ieee754_hypotl (1.0L, rx);
-
- __real__ res = __log1pl (2.0L * rx * (rx + s)) / 2.0L;
- if (adj)
- __imag__ res = __ieee754_atan2l (s, __imag__ x);
- else
- __imag__ res = __ieee754_atan2l (ix, s);
- }
- math_check_force_underflow_nonneg (__real__ res);
- }
- else
- {
- __real__ y = (rx - ix) * (rx + ix) + 1.0L;
- __imag__ y = 2.0L * rx * ix;
-
- y = __csqrtl (y);
-
- __real__ y += rx;
- __imag__ y += ix;
-
- if (adj)
- {
- long double t = __real__ y;
- __real__ y = __copysignl (__imag__ y, __imag__ x);
- __imag__ y = t;
- }
-
- res = __clogl (y);
- }
-
- /* Give results the correct sign for the original argument. */
- __real__ res = __copysignl (__real__ res, __real__ x);
- __imag__ res = __copysignl (__imag__ res, (adj ? 1.0L : __imag__ x));
-
- return res;
-}
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