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224 lines
6.5 KiB
C
224 lines
6.5 KiB
C
/* Return arc hyperbole sine for long double value, with the imaginary
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part of the result possibly adjusted for use in computing other
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functions.
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Copyright (C) 1997-2014 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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/* To avoid spurious overflows, use this definition to treat IBM long
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double as approximating an IEEE-style format. */
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#if LDBL_MANT_DIG == 106
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# undef LDBL_EPSILON
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# define LDBL_EPSILON 0x1p-106L
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#endif
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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__ long double
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__kernel_casinhl (__complex__ long double x, int adj)
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{
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__complex__ long double res;
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long double rx, ix;
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__complex__ long double y;
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/* Avoid cancellation by reducing to the first quadrant. */
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rx = fabsl (__real__ x);
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ix = fabsl (__imag__ x);
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if (rx >= 1.0L / LDBL_EPSILON || ix >= 1.0L / LDBL_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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long double t = __real__ y;
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__real__ y = __copysignl (__imag__ y, __imag__ x);
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__imag__ y = t;
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}
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res = __clogl (y);
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__real__ res += M_LN2l;
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}
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else if (rx >= 0.5L && ix < LDBL_EPSILON / 8.0L)
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{
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long double s = __ieee754_hypotl (1.0L, rx);
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__real__ res = __ieee754_logl (rx + s);
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if (adj)
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__imag__ res = __ieee754_atan2l (s, __imag__ x);
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else
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__imag__ res = __ieee754_atan2l (ix, s);
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}
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else if (rx < LDBL_EPSILON / 8.0L && ix >= 1.5L)
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{
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long double s = __ieee754_sqrtl ((ix + 1.0L) * (ix - 1.0L));
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__real__ res = __ieee754_logl (ix + s);
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if (adj)
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__imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
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else
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__imag__ res = __ieee754_atan2l (s, rx);
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}
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else if (ix > 1.0L && ix < 1.5L && rx < 0.5L)
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{
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if (rx < LDBL_EPSILON * LDBL_EPSILON)
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{
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long double ix2m1 = (ix + 1.0L) * (ix - 1.0L);
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long double s = __ieee754_sqrtl (ix2m1);
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__real__ res = __log1pl (2.0L * (ix2m1 + ix * s)) / 2.0L;
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if (adj)
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__imag__ res = __ieee754_atan2l (rx, __copysignl (s, __imag__ x));
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else
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__imag__ res = __ieee754_atan2l (s, rx);
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}
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else
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{
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long double ix2m1 = (ix + 1.0L) * (ix - 1.0L);
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long double rx2 = rx * rx;
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long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix);
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long double d = __ieee754_sqrtl (ix2m1 * ix2m1 + f);
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long double dp = d + ix2m1;
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long double dm = f / dp;
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long double r1 = __ieee754_sqrtl ((dm + rx2) / 2.0L);
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long double r2 = rx * ix / r1;
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__real__ res
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= __log1pl (rx2 + dp + 2.0L * (rx * r1 + ix * r2)) / 2.0L;
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if (adj)
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__imag__ res = __ieee754_atan2l (rx + r1, __copysignl (ix + r2,
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__imag__ x));
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else
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__imag__ res = __ieee754_atan2l (ix + r2, rx + r1);
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}
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}
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else if (ix == 1.0L && rx < 0.5L)
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{
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if (rx < LDBL_EPSILON / 8.0L)
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{
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__real__ res = __log1pl (2.0L * (rx + __ieee754_sqrtl (rx))) / 2.0L;
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if (adj)
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__imag__ res = __ieee754_atan2l (__ieee754_sqrtl (rx),
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__copysignl (1.0L, __imag__ x));
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else
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__imag__ res = __ieee754_atan2l (1.0L, __ieee754_sqrtl (rx));
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}
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else
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{
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long double d = rx * __ieee754_sqrtl (4.0L + rx * rx);
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long double s1 = __ieee754_sqrtl ((d + rx * rx) / 2.0L);
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long double s2 = __ieee754_sqrtl ((d - rx * rx) / 2.0L);
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__real__ res = __log1pl (rx * rx + d + 2.0L * (rx * s1 + s2)) / 2.0L;
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if (adj)
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__imag__ res = __ieee754_atan2l (rx + s1,
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__copysignl (1.0L + s2,
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__imag__ x));
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else
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__imag__ res = __ieee754_atan2l (1.0L + s2, rx + s1);
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}
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}
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else if (ix < 1.0L && rx < 0.5L)
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{
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if (ix >= LDBL_EPSILON)
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{
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if (rx < LDBL_EPSILON * LDBL_EPSILON)
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{
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long double onemix2 = (1.0L + ix) * (1.0L - ix);
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long double s = __ieee754_sqrtl (onemix2);
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__real__ res = __log1pl (2.0L * rx / s) / 2.0L;
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if (adj)
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__imag__ res = __ieee754_atan2l (s, __imag__ x);
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else
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__imag__ res = __ieee754_atan2l (ix, s);
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}
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else
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{
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long double onemix2 = (1.0L + ix) * (1.0L - ix);
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long double rx2 = rx * rx;
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long double f = rx2 * (2.0L + rx2 + 2.0L * ix * ix);
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long double d = __ieee754_sqrtl (onemix2 * onemix2 + f);
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long double dp = d + onemix2;
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long double dm = f / dp;
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long double r1 = __ieee754_sqrtl ((dp + rx2) / 2.0L);
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long double r2 = rx * ix / r1;
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__real__ res
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= __log1pl (rx2 + dm + 2.0L * (rx * r1 + ix * r2)) / 2.0L;
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if (adj)
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__imag__ res = __ieee754_atan2l (rx + r1,
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__copysignl (ix + r2,
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__imag__ x));
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else
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__imag__ res = __ieee754_atan2l (ix + r2, rx + r1);
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}
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}
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else
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{
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long double s = __ieee754_hypotl (1.0L, rx);
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__real__ res = __log1pl (2.0L * rx * (rx + s)) / 2.0L;
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if (adj)
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__imag__ res = __ieee754_atan2l (s, __imag__ x);
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else
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__imag__ res = __ieee754_atan2l (ix, s);
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}
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if (__real__ res < LDBL_MIN)
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{
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volatile long double force_underflow = __real__ res * __real__ res;
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(void) force_underflow;
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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) + 1.0L;
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__imag__ y = 2.0L * rx * ix;
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y = __csqrtl (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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long double t = __real__ y;
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__real__ y = __copysignl (__imag__ y, __imag__ x);
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__imag__ y = t;
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}
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res = __clogl (y);
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}
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/* Give results the correct sign for the original argument. */
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__real__ res = __copysignl (__real__ res, __real__ x);
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__imag__ res = __copysignl (__imag__ res, (adj ? 1.0L : __imag__ x));
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return res;
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}
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