mirror of
https://github.com/autc04/Retro68.git
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203 lines
5.5 KiB
C
203 lines
5.5 KiB
C
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/* Return arc hyperbolic sine for a complex float type, with the
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imaginary part of the result possibly adjusted for use in
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computing other functions.
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Copyright (C) 1997-2018 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 "quadmath-imp.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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__complex128
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__quadmath_kernel_casinhq (__complex128 x, int adj)
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{
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__complex128 res;
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__float128 rx, ix;
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__complex128 y;
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/* Avoid cancellation by reducing to the first quadrant. */
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rx = fabsq (__real__ x);
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ix = fabsq (__imag__ x);
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if (rx >= 1 / FLT128_EPSILON || ix >= 1 / FLT128_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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__float128 t = __real__ y;
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__real__ y = copysignq (__imag__ y, __imag__ x);
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__imag__ y = t;
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}
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res = clogq (y);
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__real__ res += (__float128) M_LN2q;
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}
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else if (rx >= 0.5Q && ix < FLT128_EPSILON / 8)
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{
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__float128 s = hypotq (1, rx);
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__real__ res = logq (rx + s);
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if (adj)
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__imag__ res = atan2q (s, __imag__ x);
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else
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__imag__ res = atan2q (ix, s);
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}
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else if (rx < FLT128_EPSILON / 8 && ix >= 1.5Q)
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{
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__float128 s = sqrtq ((ix + 1) * (ix - 1));
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__real__ res = logq (ix + s);
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if (adj)
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__imag__ res = atan2q (rx, copysignq (s, __imag__ x));
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else
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__imag__ res = atan2q (s, rx);
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}
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else if (ix > 1 && ix < 1.5Q && rx < 0.5Q)
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{
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if (rx < FLT128_EPSILON * FLT128_EPSILON)
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{
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__float128 ix2m1 = (ix + 1) * (ix - 1);
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__float128 s = sqrtq (ix2m1);
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__real__ res = log1pq (2 * (ix2m1 + ix * s)) / 2;
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if (adj)
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__imag__ res = atan2q (rx, copysignq (s, __imag__ x));
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else
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__imag__ res = atan2q (s, rx);
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}
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else
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{
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__float128 ix2m1 = (ix + 1) * (ix - 1);
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__float128 rx2 = rx * rx;
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__float128 f = rx2 * (2 + rx2 + 2 * ix * ix);
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__float128 d = sqrtq (ix2m1 * ix2m1 + f);
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__float128 dp = d + ix2m1;
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__float128 dm = f / dp;
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__float128 r1 = sqrtq ((dm + rx2) / 2);
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__float128 r2 = rx * ix / r1;
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__real__ res = log1pq (rx2 + dp + 2 * (rx * r1 + ix * r2)) / 2;
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if (adj)
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__imag__ res = atan2q (rx + r1, copysignq (ix + r2, __imag__ x));
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else
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__imag__ res = atan2q (ix + r2, rx + r1);
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}
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}
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else if (ix == 1 && rx < 0.5Q)
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{
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if (rx < FLT128_EPSILON / 8)
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{
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__real__ res = log1pq (2 * (rx + sqrtq (rx))) / 2;
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if (adj)
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__imag__ res = atan2q (sqrtq (rx), copysignq (1, __imag__ x));
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else
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__imag__ res = atan2q (1, sqrtq (rx));
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}
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else
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{
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__float128 d = rx * sqrtq (4 + rx * rx);
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__float128 s1 = sqrtq ((d + rx * rx) / 2);
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__float128 s2 = sqrtq ((d - rx * rx) / 2);
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__real__ res = log1pq (rx * rx + d + 2 * (rx * s1 + s2)) / 2;
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if (adj)
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__imag__ res = atan2q (rx + s1, copysignq (1 + s2, __imag__ x));
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else
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__imag__ res = atan2q (1 + s2, rx + s1);
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}
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}
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else if (ix < 1 && rx < 0.5Q)
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{
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if (ix >= FLT128_EPSILON)
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{
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if (rx < FLT128_EPSILON * FLT128_EPSILON)
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{
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__float128 onemix2 = (1 + ix) * (1 - ix);
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__float128 s = sqrtq (onemix2);
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__real__ res = log1pq (2 * rx / s) / 2;
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if (adj)
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__imag__ res = atan2q (s, __imag__ x);
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else
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__imag__ res = atan2q (ix, s);
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}
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else
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{
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__float128 onemix2 = (1 + ix) * (1 - ix);
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__float128 rx2 = rx * rx;
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__float128 f = rx2 * (2 + rx2 + 2 * ix * ix);
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__float128 d = sqrtq (onemix2 * onemix2 + f);
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__float128 dp = d + onemix2;
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__float128 dm = f / dp;
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__float128 r1 = sqrtq ((dp + rx2) / 2);
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__float128 r2 = rx * ix / r1;
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__real__ res = log1pq (rx2 + dm + 2 * (rx * r1 + ix * r2)) / 2;
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if (adj)
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__imag__ res = atan2q (rx + r1, copysignq (ix + r2,
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__imag__ x));
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else
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__imag__ res = atan2q (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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__float128 s = hypotq (1, rx);
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__real__ res = log1pq (2 * rx * (rx + s)) / 2;
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if (adj)
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__imag__ res = atan2q (s, __imag__ x);
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else
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__imag__ res = atan2q (ix, s);
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}
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math_check_force_underflow_nonneg (__real__ res);
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}
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else
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{
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__real__ y = (rx - ix) * (rx + ix) + 1;
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__imag__ y = 2 * rx * ix;
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y = csqrtq (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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__float128 t = __real__ y;
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__real__ y = copysignq (__imag__ y, __imag__ x);
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__imag__ y = t;
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}
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res = clogq (y);
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}
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/* Give results the correct sign for the original argument. */
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__real__ res = copysignq (__real__ res, __real__ x);
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__imag__ res = copysignq (__imag__ res, (adj ? 1 : __imag__ x));
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return res;
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}
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