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132 lines
3.7 KiB
C
132 lines
3.7 KiB
C
/* Return arc hyperbole sine for float value, with the imaginary part
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of the result possibly adjusted for use in computing other
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functions.
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Copyright (C) 1997-2013 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<http://www.gnu.org/licenses/>. */
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#include <complex.h>
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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/* Return the complex inverse hyperbolic sine of finite nonzero Z,
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with the imaginary part of the result subtracted from pi/2 if ADJ
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is nonzero. */
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__complex__ float
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__kernel_casinhf (__complex__ float x, int adj)
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{
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__complex__ float res;
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float rx, ix;
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__complex__ float y;
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/* Avoid cancellation by reducing to the first quadrant. */
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rx = fabsf (__real__ x);
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ix = fabsf (__imag__ x);
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if (rx >= 1.0f / FLT_EPSILON || ix >= 1.0f / FLT_EPSILON)
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{
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/* For large x in the first quadrant, x + csqrt (1 + x * x)
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is sufficiently close to 2 * x to make no significant
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difference to the result; avoid possible overflow from
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the squaring and addition. */
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__real__ y = rx;
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__imag__ y = ix;
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if (adj)
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{
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float t = __real__ y;
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__real__ y = __copysignf (__imag__ y, __imag__ x);
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__imag__ y = t;
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}
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res = __clogf (y);
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__real__ res += (float) M_LN2;
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}
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else if (rx >= 0.5f && ix < FLT_EPSILON / 8.0f)
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{
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float s = __ieee754_hypotf (1.0f, rx);
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__real__ res = __ieee754_logf (rx + s);
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if (adj)
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__imag__ res = __ieee754_atan2f (s, __imag__ x);
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else
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__imag__ res = __ieee754_atan2f (ix, s);
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}
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else if (rx < FLT_EPSILON / 8.0f && ix >= 1.5f)
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{
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float s = __ieee754_sqrtf ((ix + 1.0f) * (ix - 1.0f));
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__real__ res = __ieee754_logf (ix + s);
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if (adj)
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__imag__ res = __ieee754_atan2f (rx, __copysignf (s, __imag__ x));
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else
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__imag__ res = __ieee754_atan2f (s, rx);
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}
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else if (ix == 1.0f && rx < 0.5f)
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{
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if (rx < FLT_EPSILON / 8.0f)
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{
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__real__ res = __log1pf (2.0f * (rx + __ieee754_sqrtf (rx))) / 2.0f;
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if (adj)
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__imag__ res = __ieee754_atan2f (__ieee754_sqrtf (rx),
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__copysignf (1.0f, __imag__ x));
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else
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__imag__ res = __ieee754_atan2f (1.0f, __ieee754_sqrtf (rx));
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}
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else
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{
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float d = rx * __ieee754_sqrtf (4.0f + rx * rx);
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float s1 = __ieee754_sqrtf ((d + rx * rx) / 2.0f);
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float s2 = __ieee754_sqrtf ((d - rx * rx) / 2.0f);
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__real__ res = __log1pf (rx * rx + d + 2.0f * (rx * s1 + s2)) / 2.0f;
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if (adj)
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__imag__ res = __ieee754_atan2f (rx + s1,
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__copysignf (1.0f + s2,
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__imag__ x));
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else
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__imag__ res = __ieee754_atan2f (1.0f + s2, rx + s1);
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}
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}
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else
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{
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__real__ y = (rx - ix) * (rx + ix) + 1.0f;
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__imag__ y = 2.0f * rx * ix;
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y = __csqrtf (y);
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__real__ y += rx;
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__imag__ y += ix;
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if (adj)
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{
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float t = __real__ y;
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__real__ y = __copysignf (__imag__ y, __imag__ x);
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__imag__ y = t;
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}
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res = __clogf (y);
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}
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/* Give results the correct sign for the original argument. */
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__real__ res = __copysignf (__real__ res, __real__ x);
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__imag__ res = __copysignf (__imag__ res, (adj ? 1.0f : __imag__ x));
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return res;
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}
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