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-rw-r--r--math/k_casinhf.c212
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diff --git a/math/k_casinhf.c b/math/k_casinhf.c
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-/* Return arc hyperbole sine for float 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__ float
-__kernel_casinhf (__complex__ float x, int adj)
-{
- __complex__ float res;
- float rx, ix;
- __complex__ float y;
-
- /* Avoid cancellation by reducing to the first quadrant. */
- rx = fabsf (__real__ x);
- ix = fabsf (__imag__ x);
-
- if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_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 = __copysignf (__imag__ y, __imag__ x);
- __imag__ y = t;
- }
-
- res = __clogf (y);
- __real__ res += (float) M_LN2;
- }
- else if (rx >= 0.5f && ix < FLT_EPSILON / 8.0f)
- {
- float s = __ieee754_hypotf (1.0f, rx);
-
- __real__ res = __ieee754_logf (rx + s);
- if (adj)
- __imag__ res = __ieee754_atan2f (s, __imag__ x);
- else
- __imag__ res = __ieee754_atan2f (ix, s);
- }
- else if (rx < FLT_EPSILON / 8.0f && ix >= 1.5f)
- {
- float s = __ieee754_sqrtf ((ix + 1.0f) * (ix - 1.0f));
-
- __real__ res = __ieee754_logf (ix + s);
- if (adj)
- __imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
- else
- __imag__ res = __ieee754_atan2f (s, rx);
- }
- else if (ix > 1.0f && ix < 1.5f && rx < 0.5f)
- {
- if (rx < FLT_EPSILON * FLT_EPSILON)
- {
- float ix2m1 = (ix + 1.0f) * (ix - 1.0f);
- float s = __ieee754_sqrtf (ix2m1);
-
- __real__ res = __log1pf (2.0f * (ix2m1 + ix * s)) / 2.0f;
- if (adj)
- __imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
- else
- __imag__ res = __ieee754_atan2f (s, rx);
- }
- else
- {
- float ix2m1 = (ix + 1.0f) * (ix - 1.0f);
- float rx2 = rx * rx;
- float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix);
- float d = __ieee754_sqrtf (ix2m1 * ix2m1 + f);
- float dp = d + ix2m1;
- float dm = f / dp;
- float r1 = __ieee754_sqrtf ((dm + rx2) / 2.0f);
- float r2 = rx * ix / r1;
-
- __real__ res
- = __log1pf (rx2 + dp + 2.0f * (rx * r1 + ix * r2)) / 2.0f;
- if (adj)
- __imag__ res = __ieee754_atan2f (rx + r1, __copysignf (ix + r2,
- __imag__ x));
- else
- __imag__ res = __ieee754_atan2f (ix + r2, rx + r1);
- }
- }
- else if (ix == 1.0f && rx < 0.5f)
- {
- if (rx < FLT_EPSILON / 8.0f)
- {
- __real__ res = __log1pf (2.0f * (rx + __ieee754_sqrtf (rx))) / 2.0f;
- if (adj)
- __imag__ res = __ieee754_atan2f (__ieee754_sqrtf (rx),
- __copysignf (1.0f, __imag__ x));
- else
- __imag__ res = __ieee754_atan2f (1.0f, __ieee754_sqrtf (rx));
- }
- else
- {
- float d = rx * __ieee754_sqrtf (4.0f + rx * rx);
- float s1 = __ieee754_sqrtf ((d + rx * rx) / 2.0f);
- float s2 = __ieee754_sqrtf ((d - rx * rx) / 2.0f);
-
- __real__ res = __log1pf (rx * rx + d + 2.0f * (rx * s1 + s2)) / 2.0f;
- if (adj)
- __imag__ res = __ieee754_atan2f (rx + s1,
- __copysignf (1.0f + s2,
- __imag__ x));
- else
- __imag__ res = __ieee754_atan2f (1.0f + s2, rx + s1);
- }
- }
- else if (ix < 1.0f && rx < 0.5f)
- {
- if (ix >= FLT_EPSILON)
- {
- if (rx < FLT_EPSILON * FLT_EPSILON)
- {
- float onemix2 = (1.0f + ix) * (1.0f - ix);
- float s = __ieee754_sqrtf (onemix2);
-
- __real__ res = __log1pf (2.0f * rx / s) / 2.0f;
- if (adj)
- __imag__ res = __ieee754_atan2f (s, __imag__ x);
- else
- __imag__ res = __ieee754_atan2f (ix, s);
- }
- else
- {
- float onemix2 = (1.0f + ix) * (1.0f - ix);
- float rx2 = rx * rx;
- float f = rx2 * (2.0f + rx2 + 2.0f * ix * ix);
- float d = __ieee754_sqrtf (onemix2 * onemix2 + f);
- float dp = d + onemix2;
- float dm = f / dp;
- float r1 = __ieee754_sqrtf ((dp + rx2) / 2.0f);
- float r2 = rx * ix / r1;
-
- __real__ res
- = __log1pf (rx2 + dm + 2.0f * (rx * r1 + ix * r2)) / 2.0f;
- if (adj)
- __imag__ res = __ieee754_atan2f (rx + r1,
- __copysignf (ix + r2,
- __imag__ x));
- else
- __imag__ res = __ieee754_atan2f (ix + r2, rx + r1);
- }
- }
- else
- {
- float s = __ieee754_hypotf (1.0f, rx);
-
- __real__ res = __log1pf (2.0f * rx * (rx + s)) / 2.0f;
- if (adj)
- __imag__ res = __ieee754_atan2f (s, __imag__ x);
- else
- __imag__ res = __ieee754_atan2f (ix, s);
- }
- math_check_force_underflow_nonneg (__real__ res);
- }
- else
- {
- __real__ y = (rx - ix) * (rx + ix) + 1.0f;
- __imag__ y = 2.0f * rx * ix;
-
- y = __csqrtf (y);
-
- __real__ y += rx;
- __imag__ y += ix;
-
- if (adj)
- {
- float t = __real__ y;
- __real__ y = __copysignf (__imag__ y, __imag__ x);
- __imag__ y = t;
- }
-
- res = __clogf (y);
- }
-
- /* Give results the correct sign for the original argument. */
- __real__ res = __copysignf (__real__ res, __real__ x);
- __imag__ res = __copysignf (__imag__ res, (adj ? 1.0f : __imag__ x));
-
- return res;
-}
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