407 lines
9.6 KiB
C
407 lines
9.6 KiB
C
/* $NetBSD: catrigf.c,v 1.1 2016/09/19 22:05:05 christos Exp $ */
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/*-
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* Copyright (c) 2012 Stephen Montgomery-Smith <stephen@FreeBSD.ORG>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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/*
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* The algorithm is very close to that in "Implementing the complex arcsine
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* and arccosine functions using exception handling" by T. E. Hull, Thomas F.
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* Fairgrieve, and Ping Tak Peter Tang, published in ACM Transactions on
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* Mathematical Software, Volume 23 Issue 3, 1997, Pages 299-335,
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* http://dl.acm.org/citation.cfm?id=275324.
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*
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* See catrig.c for complete comments.
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*
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* XXX comments were removed automatically, and even short ones on the right
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* of statements were removed (all of them), contrary to normal style. Only
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* a few comments on the right of declarations remain.
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*/
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#include <sys/cdefs.h>
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#if 0
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__FBSDID("$FreeBSD: head/lib/msun/src/catrigf.c 275819 2014-12-16 09:21:56Z ed $");
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#endif
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__RCSID("$NetBSD: catrigf.c,v 1.1 2016/09/19 22:05:05 christos Exp $");
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#include "namespace.h"
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#ifdef __weak_alias
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__weak_alias(casinf, _casinf)
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#endif
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#ifdef __weak_alias
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__weak_alias(catanf, _catanf)
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#endif
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#include <complex.h>
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#include <float.h>
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#include "math.h"
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#include "math_private.h"
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#undef isinf
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#define isinf(x) (fabsf(x) == INFINITY)
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#undef isnan
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#define isnan(x) ((x) != (x))
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#define raise_inexact() do { volatile float junk __unused = /*LINTED*/1 + tiny; } while(/*CONSTCOND*/0)
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#undef signbit
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#define signbit(x) (__builtin_signbitf(x))
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static const float
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A_crossover = 10,
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B_crossover = 0.6417,
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FOUR_SQRT_MIN = 0x1p-61,
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QUARTER_SQRT_MAX = 0x1p61,
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m_e = 2.7182818285e0, /* 0xadf854.0p-22 */
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m_ln2 = 6.9314718056e-1, /* 0xb17218.0p-24 */
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pio2_hi = 1.5707962513e0, /* 0xc90fda.0p-23 */
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RECIP_EPSILON = 1 / FLT_EPSILON,
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SQRT_3_EPSILON = 5.9801995673e-4, /* 0x9cc471.0p-34 */
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SQRT_6_EPSILON = 8.4572793338e-4, /* 0xddb3d7.0p-34 */
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SQRT_MIN = 0x1p-63;
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static const volatile float
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pio2_lo = 7.5497899549e-8, /* 0xa22169.0p-47 */
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tiny = 0x1p-100;
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static float complex clog_for_large_values(float complex z);
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static inline float
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f(float a, float b, float hypot_a_b)
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{
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if (b < 0)
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return ((hypot_a_b - b) / 2);
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if (b == 0)
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return (a / 2);
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return (a * a / (hypot_a_b + b) / 2);
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}
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static inline void
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do_hard_work(float x, float y, float *rx, int *B_is_usable, float *B,
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float *sqrt_A2my2, float *new_y)
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{
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float R, S, A;
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float Am1, Amy;
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R = hypotf(x, y + 1);
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S = hypotf(x, y - 1);
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A = (R + S) / 2;
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if (A < 1)
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A = 1;
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if (A < A_crossover) {
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if (y == 1 && x < FLT_EPSILON * FLT_EPSILON / 128) {
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*rx = sqrtf(x);
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} else if (x >= FLT_EPSILON * fabsf(y - 1)) {
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Am1 = f(x, 1 + y, R) + f(x, 1 - y, S);
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*rx = log1pf(Am1 + sqrtf(Am1 * (A + 1)));
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} else if (y < 1) {
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*rx = x / sqrtf((1 - y) * (1 + y));
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} else {
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*rx = log1pf((y - 1) + sqrtf((y - 1) * (y + 1)));
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}
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} else {
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*rx = logf(A + sqrtf(A * A - 1));
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}
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*new_y = y;
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if (y < FOUR_SQRT_MIN) {
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*B_is_usable = 0;
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*sqrt_A2my2 = A * (2 / FLT_EPSILON);
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*new_y = y * (2 / FLT_EPSILON);
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return;
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}
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*B = y / A;
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*B_is_usable = 1;
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if (*B > B_crossover) {
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*B_is_usable = 0;
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if (y == 1 && x < FLT_EPSILON / 128) {
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*sqrt_A2my2 = sqrtf(x) * sqrtf((A + y) / 2);
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} else if (x >= FLT_EPSILON * fabsf(y - 1)) {
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Amy = f(x, y + 1, R) + f(x, y - 1, S);
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*sqrt_A2my2 = sqrtf(Amy * (A + y));
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} else if (y > 1) {
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*sqrt_A2my2 = x * (4 / FLT_EPSILON / FLT_EPSILON) * y /
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sqrtf((y + 1) * (y - 1));
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*new_y = y * (4 / FLT_EPSILON / FLT_EPSILON);
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} else {
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*sqrt_A2my2 = sqrtf((1 - y) * (1 + y));
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}
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}
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}
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float complex
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casinhf(float complex z)
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{
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float x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y;
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int B_is_usable;
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float complex w;
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x = crealf(z);
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y = cimagf(z);
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ax = fabsf(x);
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ay = fabsf(y);
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if (isnan(x) || isnan(y)) {
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if (isinf(x))
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return (CMPLXF(x, y + y));
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if (isinf(y))
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return (CMPLXF(y, x + x));
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if (y == 0)
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return (CMPLXF(x + x, y));
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return (CMPLXF(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
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}
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if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
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if (signbit(x) == 0)
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w = clog_for_large_values(z) + m_ln2;
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else
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w = clog_for_large_values(-z) + m_ln2;
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return (CMPLXF(copysignf(crealf(w), x),
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copysignf(cimagf(w), y)));
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}
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if (x == 0 && y == 0)
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return (z);
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raise_inexact();
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if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
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return (z);
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do_hard_work(ax, ay, &rx, &B_is_usable, &B, &sqrt_A2my2, &new_y);
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if (B_is_usable)
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ry = asinf(B);
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else
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ry = atan2f(new_y, sqrt_A2my2);
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return (CMPLXF(copysignf(rx, x), copysignf(ry, y)));
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}
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float complex
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casinf(float complex z)
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{
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float complex w = casinhf(CMPLXF(cimagf(z), crealf(z)));
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return (CMPLXF(cimagf(w), crealf(w)));
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}
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float complex
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cacosf(float complex z)
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{
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float x, y, ax, ay, rx, ry, B, sqrt_A2mx2, new_x;
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int sx, sy;
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int B_is_usable;
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float complex w;
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x = crealf(z);
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y = cimagf(z);
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sx = signbit(x);
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sy = signbit(y);
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ax = fabsf(x);
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ay = fabsf(y);
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if (isnan(x) || isnan(y)) {
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if (isinf(x))
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return (CMPLXF(y + y, -INFINITY));
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if (isinf(y))
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return (CMPLXF(x + x, -y));
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if (x == 0)
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return (CMPLXF(pio2_hi + pio2_lo, y + y));
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return (CMPLXF(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
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}
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if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) {
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w = clog_for_large_values(z);
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rx = fabsf(cimagf(w));
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ry = crealf(w) + m_ln2;
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if (sy == 0)
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ry = -ry;
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return (CMPLXF(rx, ry));
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}
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if (x == 1 && y == 0)
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return (CMPLXF(0, -y));
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raise_inexact();
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if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4)
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return (CMPLXF(pio2_hi - (x - pio2_lo), -y));
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do_hard_work(ay, ax, &ry, &B_is_usable, &B, &sqrt_A2mx2, &new_x);
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if (B_is_usable) {
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if (sx == 0)
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rx = acosf(B);
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else
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rx = acosf(-B);
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} else {
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if (sx == 0)
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rx = atan2f(sqrt_A2mx2, new_x);
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else
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rx = atan2f(sqrt_A2mx2, -new_x);
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}
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if (sy == 0)
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ry = -ry;
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return (CMPLXF(rx, ry));
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}
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float complex
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cacoshf(float complex z)
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{
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float complex w;
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float rx, ry;
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w = cacosf(z);
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rx = crealf(w);
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ry = cimagf(w);
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if (isnan(rx) && isnan(ry))
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return (CMPLXF(ry, rx));
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if (isnan(rx))
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return (CMPLXF(fabsf(ry), rx));
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if (isnan(ry))
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return (CMPLXF(ry, ry));
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return (CMPLXF(fabsf(ry), copysignf(rx, cimagf(z))));
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}
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static float complex
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clog_for_large_values(float complex z)
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{
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float x, y;
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float ax, ay, t;
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x = crealf(z);
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y = cimagf(z);
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ax = fabsf(x);
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ay = fabsf(y);
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if (ax < ay) {
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t = ax;
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ax = ay;
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ay = t;
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}
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if (ax > FLT_MAX / 2)
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return (CMPLXF(logf(hypotf(x / m_e, y / m_e)) + 1,
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atan2f(y, x)));
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if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN)
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return (CMPLXF(logf(hypotf(x, y)), atan2f(y, x)));
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return (CMPLXF(logf(ax * ax + ay * ay) / 2, atan2f(y, x)));
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}
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static inline float
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sum_squares(float x, float y)
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{
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if (y < SQRT_MIN)
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return (x * x);
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return (x * x + y * y);
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}
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static inline float
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real_part_reciprocal(float x, float y)
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{
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float scale;
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uint32_t hx, hy;
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int32_t ix, iy;
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GET_FLOAT_WORD(hx, x);
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ix = hx & 0x7f800000;
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GET_FLOAT_WORD(hy, y);
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iy = hy & 0x7f800000;
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#define BIAS (FLT_MAX_EXP - 1)
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#define CUTOFF (FLT_MANT_DIG / 2 + 1)
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if (ix - iy >= CUTOFF << 23 || isinf(x))
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return (1 / x);
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if (iy - ix >= CUTOFF << 23)
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return (x / y / y);
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if (ix <= (BIAS + FLT_MAX_EXP / 2 - CUTOFF) << 23)
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return (x / (x * x + y * y));
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SET_FLOAT_WORD(scale, 0x7f800000 - ix);
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x *= scale;
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y *= scale;
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return (x / (x * x + y * y) * scale);
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}
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float complex
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catanhf(float complex z)
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{
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float x, y, ax, ay, rx, ry;
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x = crealf(z);
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y = cimagf(z);
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ax = fabsf(x);
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ay = fabsf(y);
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if (y == 0 && ax <= 1)
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return (CMPLXF(atanhf(x), y));
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if (x == 0)
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return (CMPLXF(x, atanf(y)));
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if (isnan(x) || isnan(y)) {
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if (isinf(x))
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return (CMPLXF(copysignf(0, x), y + y));
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if (isinf(y))
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return (CMPLXF(copysignf(0, x),
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copysignf(pio2_hi + pio2_lo, y)));
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return (CMPLXF(x + 0.0L + (y + 0), x + 0.0L + (y + 0)));
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}
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if (ax > RECIP_EPSILON || ay > RECIP_EPSILON)
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return (CMPLXF(real_part_reciprocal(x, y),
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copysignf(pio2_hi + pio2_lo, y)));
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if (ax < SQRT_3_EPSILON / 2 && ay < SQRT_3_EPSILON / 2) {
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raise_inexact();
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return (z);
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}
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if (ax == 1 && ay < FLT_EPSILON)
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rx = (m_ln2 - logf(ay)) / 2;
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else
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rx = log1pf(4 * ax / sum_squares(ax - 1, ay)) / 4;
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if (ax == 1)
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ry = atan2f(2, -ay) / 2;
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else if (ay < FLT_EPSILON)
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ry = atan2f(2 * ay, (1 - ax) * (1 + ax)) / 2;
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else
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ry = atan2f(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2;
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return (CMPLXF(copysignf(rx, x), copysignf(ry, y)));
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}
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float complex
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catanf(float complex z)
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{
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float complex w = catanhf(CMPLXF(cimagf(z), crealf(z)));
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return (CMPLXF(cimagf(w), crealf(w)));
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}
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