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106 lines
3.0 KiB
C
106 lines
3.0 KiB
C
/* Return arc hyperbole sine for double 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__ double
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__kernel_casinh (__complex__ double x, int adj)
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{
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__complex__ double res;
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double rx, ix;
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__complex__ double y;
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/* Avoid cancellation by reducing to the first quadrant. */
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rx = fabs (__real__ x);
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ix = fabs (__imag__ x);
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if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_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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double t = __real__ y;
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__real__ y = __copysign (__imag__ y, __imag__ x);
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__imag__ y = t;
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}
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res = __clog (y);
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__real__ res += M_LN2;
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}
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else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0)
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{
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double s = __ieee754_hypot (1.0, rx);
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__real__ res = __ieee754_log (rx + s);
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if (adj)
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__imag__ res = __ieee754_atan2 (s, __imag__ x);
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else
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__imag__ res = __ieee754_atan2 (ix, s);
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}
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else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5)
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{
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double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0));
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__real__ res = __ieee754_log (ix + s);
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if (adj)
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__imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
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else
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__imag__ res = __ieee754_atan2 (s, rx);
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}
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else
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{
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__real__ y = (rx - ix) * (rx + ix) + 1.0;
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__imag__ y = 2.0 * rx * ix;
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y = __csqrt (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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double t = __real__ y;
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__real__ y = copysign (__imag__ y, __imag__ x);
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__imag__ y = t;
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}
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res = __clog (y);
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}
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/* Give results the correct sign for the original argument. */
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__real__ res = __copysign (__real__ res, __real__ x);
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__imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x));
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return res;
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}
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