Add casinl() cacosl() catanl() casinhl() cacoshl() catanhl() APIs to msun
to improve C11 conformance. PR: 216850 216851 216852 216856 216857 216858 Submitted by: mmokhi Reported by: sgk@troutmask.apl.washington.edu Reviewed by: bde, mat, theraven Approved by: bde (src committer), mat (mentor) Differential Revision: https://reviews.freebsd.org/D9491
This commit is contained in:
mmokhi
parent
face0f2538
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4d5cf50c32
@ -107,7 +107,7 @@ COMMON_SRCS+= e_acoshl.c e_acosl.c e_asinl.c e_atan2l.c e_atanhl.c \
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.endif
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# C99 complex functions
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COMMON_SRCS+= catrig.c catrigf.c \
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COMMON_SRCS+= catrig.c catrigf.c catrigl.c \
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s_ccosh.c s_ccoshf.c s_cexp.c s_cexpf.c \
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s_cimag.c s_cimagf.c s_cimagl.c \
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s_conj.c s_conjf.c s_conjl.c \
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@ -285,3 +285,13 @@ FBSD_1.3 {
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FBSD_1.4 {
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lgammal_r;
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};
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/* First added in 12.0-CURRENT */
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FBSD_1.5 {
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cacoshl;
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cacosl;
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casinhl;
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casinl;
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catanl;
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catanhl;
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};
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412
lib/msun/src/catrigl.c
Normal file
412
lib/msun/src/catrigl.c
Normal file
@ -0,0 +1,412 @@
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/*-
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* Copyright (c) 2012 Stephen Montgomery-Smith <stephen@FreeBSD.ORG>
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* Copyright (c) 2017 Mahdi Mokhtari <mmokhi@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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__FBSDID("$FreeBSD$");
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#include <complex.h>
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#include <float.h>
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#include "invtrig.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) (fabsl(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 = 1 + tiny; } while(0)
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#undef signbit
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#define signbit(x) (__builtin_signbitl(x))
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static const long double
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A_crossover = 10,
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B_crossover = 0.6417,
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FOUR_SQRT_MIN = 0x1p-8189L,
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QUARTER_SQRT_MAX = 0x1p8189L,
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RECIP_EPSILON = 1 / LDBL_EPSILON,
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SQRT_MIN = 0x1p-8191L;
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#if LDBL_MANT_DIG == 64
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static const union IEEEl2bits
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um_e = LD80C(0xadf85458a2bb4a9b, 1, 2.71828182845904523536e+0L),
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um_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L);
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#define m_e um_e.e
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#define m_ln2 um_ln2.e
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static const long double
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/* The next 2 literals for non-i386. Misrounding them on i386 is harmless. */
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SQRT_3_EPSILON = 5.70316273435758915310e-10, /* 0x9cc470a0490973e8.0p-94 */
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SQRT_6_EPSILON = 8.06549008734932771664e-10; /* 0xddb3d742c265539e.0p-94 */
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#elif LDBL_MANT_DIG == 113
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static const long double
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m_e = 2.71828182845904523536028747135266250e0L, /* 0x15bf0a8b1457695355fb8ac404e7a.0p-111 */
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m_ln2 = 6.93147180559945309417232121458176568e-1L, /* 0x162e42fefa39ef35793c7673007e6.0p-113 */
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SQRT_3_EPSILON = 2.40370335797945490975336727199878124e-17, /* 0x1bb67ae8584caa73b25742d7078b8.0p-168 */
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SQRT_6_EPSILON = 3.39934988877629587239082586223300391e-17; /* 0x13988e1409212e7d0321914321a55.0p-167 */
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#else
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#error "Unsupported long double format"
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#endif
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static const volatile float
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tiny = 0x1p-100;
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static long double complex clog_for_large_values(long double complex z);
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static inline long double
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f(long double a, long double b, long double 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(long double x, long double y, long double *rx, int *B_is_usable,
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long double *B, long double *sqrt_A2my2, long double *new_y)
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{
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long double R, S, A;
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long double Am1, Amy;
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R = hypotl(x, y + 1);
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S = hypotl(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 < LDBL_EPSILON * LDBL_EPSILON / 128) {
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*rx = sqrtl(x);
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} else if (x >= LDBL_EPSILON * fabsl(y - 1)) {
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Am1 = f(x, 1 + y, R) + f(x, 1 - y, S);
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*rx = log1pl(Am1 + sqrtl(Am1 * (A + 1)));
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} else if (y < 1) {
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*rx = x / sqrtl((1 - y) * (1 + y));
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} else {
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*rx = log1pl((y - 1) + sqrtl((y - 1) * (y + 1)));
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}
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} else {
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*rx = logl(A + sqrtl(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 / LDBL_EPSILON);
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*new_y = y * (2 / LDBL_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 < LDBL_EPSILON / 128) {
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*sqrt_A2my2 = sqrtl(x) * sqrtl((A + y) / 2);
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} else if (x >= LDBL_EPSILON * fabsl(y - 1)) {
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Amy = f(x, y + 1, R) + f(x, y - 1, S);
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*sqrt_A2my2 = sqrtl(Amy * (A + y));
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} else if (y > 1) {
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*sqrt_A2my2 = x * (4 / LDBL_EPSILON / LDBL_EPSILON) * y /
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sqrtl((y + 1) * (y - 1));
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*new_y = y * (4 / LDBL_EPSILON / LDBL_EPSILON);
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} else {
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*sqrt_A2my2 = sqrtl((1 - y) * (1 + y));
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}
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}
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}
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long double complex
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casinhl(long double complex z)
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{
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long double x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y;
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int B_is_usable;
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long double complex w;
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x = creall(z);
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y = cimagl(z);
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ax = fabsl(x);
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ay = fabsl(y);
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if (isnan(x) || isnan(y)) {
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if (isinf(x))
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return (CMPLXL(x, y + y));
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if (isinf(y))
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return (CMPLXL(y, x + x));
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if (y == 0)
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return (CMPLXL(x + x, y));
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return (CMPLXL(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 (CMPLXL(copysignl(creall(w), x),
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copysignl(cimagl(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 = asinl(B);
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else
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ry = atan2l(new_y, sqrt_A2my2);
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return (CMPLXL(copysignl(rx, x), copysignl(ry, y)));
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}
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long double complex
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casinl(long double complex z)
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{
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long double complex w;
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w = casinhl(CMPLXL(cimagl(z), creall(z)));
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return (CMPLXL(cimagl(w), creall(w)));
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}
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long double complex
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cacosl(long double complex z)
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{
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long double 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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long double complex w;
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x = creall(z);
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y = cimagl(z);
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sx = signbit(x);
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sy = signbit(y);
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ax = fabsl(x);
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ay = fabsl(y);
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if (isnan(x) || isnan(y)) {
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if (isinf(x))
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return (CMPLXL(y + y, -INFINITY));
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if (isinf(y))
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return (CMPLXL(x + x, -y));
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if (x == 0)
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return (CMPLXL(pio2_hi + pio2_lo, y + y));
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return (CMPLXL(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 = fabsl(cimagl(w));
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ry = creall(w) + m_ln2;
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if (sy == 0)
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ry = -ry;
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return (CMPLXL(rx, ry));
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}
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if (x == 1 && y == 0)
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return (CMPLXL(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 (CMPLXL(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 = acosl(B);
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else
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rx = acosl(-B);
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} else {
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if (sx == 0)
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rx = atan2l(sqrt_A2mx2, new_x);
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else
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rx = atan2l(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 (CMPLXL(rx, ry));
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}
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long double complex
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cacoshl(long double complex z)
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{
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long double complex w;
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long double rx, ry;
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w = cacosl(z);
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rx = creall(w);
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ry = cimagl(w);
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if (isnan(rx) && isnan(ry))
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return (CMPLXL(ry, rx));
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if (isnan(rx))
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return (CMPLXL(fabsl(ry), rx));
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if (isnan(ry))
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return (CMPLXL(ry, ry));
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return (CMPLXL(fabsl(ry), copysignl(rx, cimagl(z))));
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}
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static long double complex
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clog_for_large_values(long double complex z)
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{
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long double x, y;
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long double ax, ay, t;
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x = creall(z);
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y = cimagl(z);
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ax = fabsl(x);
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ay = fabsl(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 > LDBL_MAX / 2)
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return (CMPLXL(logl(hypotl(x / m_e, y / m_e)) + 1,
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atan2l(y, x)));
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if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN)
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return (CMPLXL(logl(hypotl(x, y)), atan2l(y, x)));
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return (CMPLXL(logl(ax * ax + ay * ay) / 2, atan2l(y, x)));
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}
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static inline long double
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sum_squares(long double x, long double 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 long double
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real_part_reciprocal(long double x, long double y)
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{
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long double scale;
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uint16_t hx, hy;
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int16_t ix, iy;
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GET_LDBL_EXPSIGN(hx, x);
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ix = hx & 0x7fff;
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GET_LDBL_EXPSIGN(hy, y);
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iy = hy & 0x7fff;
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#define BIAS (LDBL_MAX_EXP - 1)
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#define CUTOFF (LDBL_MANT_DIG / 2 + 1)
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if (ix - iy >= CUTOFF || isinf(x))
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return (1 / x);
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if (iy - ix >= CUTOFF)
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return (x / y / y);
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if (ix <= BIAS + LDBL_MAX_EXP / 2 - CUTOFF)
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return (x / (x * x + y * y));
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scale = 1;
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SET_LDBL_EXPSIGN(scale, 0x7fff - 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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long double complex
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catanhl(long double complex z)
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{
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long double x, y, ax, ay, rx, ry;
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x = creall(z);
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y = cimagl(z);
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ax = fabsl(x);
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ay = fabsl(y);
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if (y == 0 && ax <= 1)
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return (CMPLXL(atanhl(x), y));
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if (x == 0)
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return (CMPLXL(x, atanl(y)));
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if (isnan(x) || isnan(y)) {
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if (isinf(x))
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return (CMPLXL(copysignl(0, x), y + y));
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if (isinf(y))
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return (CMPLXL(copysignl(0, x),
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copysignl(pio2_hi + pio2_lo, y)));
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return (CMPLXL(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 (CMPLXL(real_part_reciprocal(x, y),
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copysignl(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 < LDBL_EPSILON)
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rx = (m_ln2 - logl(ay)) / 2;
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else
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rx = log1pl(4 * ax / sum_squares(ax - 1, ay)) / 4;
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if (ax == 1)
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ry = atan2l(2, -ay) / 2;
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else if (ay < LDBL_EPSILON)
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ry = atan2l(2 * ay, (1 - ax) * (1 + ax)) / 2;
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else
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ry = atan2l(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2;
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return (CMPLXL(copysignl(rx, x), copysignl(ry, y)));
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||||
}
|
||||
|
||||
long double complex
|
||||
catanl(long double complex z)
|
||||
{
|
||||
long double complex w;
|
||||
|
||||
w = catanhl(CMPLXL(cimagl(z), creall(z)));
|
||||
return (CMPLXL(cimagl(w), creall(w)));
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user