From 4d5cf50c32e474e9f29fd6959e54d719cd33f236 Mon Sep 17 00:00:00 2001 From: mmokhi Date: Wed, 15 Feb 2017 07:59:54 +0000 Subject: [PATCH] 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 --- lib/msun/Makefile | 2 +- lib/msun/Symbol.map | 10 + lib/msun/src/catrigl.c | 412 +++++++++++++++++++++++++++++++++++++++++ 3 files changed, 423 insertions(+), 1 deletion(-) create mode 100644 lib/msun/src/catrigl.c diff --git a/lib/msun/Makefile b/lib/msun/Makefile index 69011345a0d6..b2502742ac83 100644 --- a/lib/msun/Makefile +++ b/lib/msun/Makefile @@ -107,7 +107,7 @@ COMMON_SRCS+= e_acoshl.c e_acosl.c e_asinl.c e_atan2l.c e_atanhl.c \ .endif # C99 complex functions -COMMON_SRCS+= catrig.c catrigf.c \ +COMMON_SRCS+= catrig.c catrigf.c catrigl.c \ s_ccosh.c s_ccoshf.c s_cexp.c s_cexpf.c \ s_cimag.c s_cimagf.c s_cimagl.c \ s_conj.c s_conjf.c s_conjl.c \ diff --git a/lib/msun/Symbol.map b/lib/msun/Symbol.map index d5b7f4699f10..5ba7c49c1413 100644 --- a/lib/msun/Symbol.map +++ b/lib/msun/Symbol.map @@ -285,3 +285,13 @@ FBSD_1.3 { FBSD_1.4 { lgammal_r; }; + +/* First added in 12.0-CURRENT */ +FBSD_1.5 { + cacoshl; + cacosl; + casinhl; + casinl; + catanl; + catanhl; +}; diff --git a/lib/msun/src/catrigl.c b/lib/msun/src/catrigl.c new file mode 100644 index 000000000000..f71a3118de7e --- /dev/null +++ b/lib/msun/src/catrigl.c @@ -0,0 +1,412 @@ +/*- + * Copyright (c) 2012 Stephen Montgomery-Smith + * Copyright (c) 2017 Mahdi Mokhtari + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +/* + * The algorithm is very close to that in "Implementing the complex arcsine + * and arccosine functions using exception handling" by T. E. Hull, Thomas F. + * Fairgrieve, and Ping Tak Peter Tang, published in ACM Transactions on + * Mathematical Software, Volume 23 Issue 3, 1997, Pages 299-335, + * http://dl.acm.org/citation.cfm?id=275324. + * + * See catrig.c for complete comments. + * + * XXX comments were removed automatically, and even short ones on the right + * of statements were removed (all of them), contrary to normal style. Only + * a few comments on the right of declarations remain. + */ + +#include +__FBSDID("$FreeBSD$"); + +#include +#include + +#include "invtrig.h" +#include "math.h" +#include "math_private.h" + +#undef isinf +#define isinf(x) (fabsl(x) == INFINITY) +#undef isnan +#define isnan(x) ((x) != (x)) +#define raise_inexact() do { volatile float junk = 1 + tiny; } while(0) +#undef signbit +#define signbit(x) (__builtin_signbitl(x)) + +static const long double +A_crossover = 10, +B_crossover = 0.6417, +FOUR_SQRT_MIN = 0x1p-8189L, +QUARTER_SQRT_MAX = 0x1p8189L, +RECIP_EPSILON = 1 / LDBL_EPSILON, +SQRT_MIN = 0x1p-8191L; + +#if LDBL_MANT_DIG == 64 +static const union IEEEl2bits +um_e = LD80C(0xadf85458a2bb4a9b, 1, 2.71828182845904523536e+0L), +um_ln2 = LD80C(0xb17217f7d1cf79ac, -1, 6.93147180559945309417e-1L); +#define m_e um_e.e +#define m_ln2 um_ln2.e +static const long double +/* The next 2 literals for non-i386. Misrounding them on i386 is harmless. */ +SQRT_3_EPSILON = 5.70316273435758915310e-10, /* 0x9cc470a0490973e8.0p-94 */ +SQRT_6_EPSILON = 8.06549008734932771664e-10; /* 0xddb3d742c265539e.0p-94 */ +#elif LDBL_MANT_DIG == 113 +static const long double +m_e = 2.71828182845904523536028747135266250e0L, /* 0x15bf0a8b1457695355fb8ac404e7a.0p-111 */ +m_ln2 = 6.93147180559945309417232121458176568e-1L, /* 0x162e42fefa39ef35793c7673007e6.0p-113 */ +SQRT_3_EPSILON = 2.40370335797945490975336727199878124e-17, /* 0x1bb67ae8584caa73b25742d7078b8.0p-168 */ +SQRT_6_EPSILON = 3.39934988877629587239082586223300391e-17; /* 0x13988e1409212e7d0321914321a55.0p-167 */ +#else +#error "Unsupported long double format" +#endif + +static const volatile float +tiny = 0x1p-100; + +static long double complex clog_for_large_values(long double complex z); + +static inline long double +f(long double a, long double b, long double hypot_a_b) +{ + if (b < 0) + return ((hypot_a_b - b) / 2); + if (b == 0) + return (a / 2); + return (a * a / (hypot_a_b + b) / 2); +} + +static inline void +do_hard_work(long double x, long double y, long double *rx, int *B_is_usable, + long double *B, long double *sqrt_A2my2, long double *new_y) +{ + long double R, S, A; + long double Am1, Amy; + + R = hypotl(x, y + 1); + S = hypotl(x, y - 1); + + A = (R + S) / 2; + if (A < 1) + A = 1; + + if (A < A_crossover) { + if (y == 1 && x < LDBL_EPSILON * LDBL_EPSILON / 128) { + *rx = sqrtl(x); + } else if (x >= LDBL_EPSILON * fabsl(y - 1)) { + Am1 = f(x, 1 + y, R) + f(x, 1 - y, S); + *rx = log1pl(Am1 + sqrtl(Am1 * (A + 1))); + } else if (y < 1) { + *rx = x / sqrtl((1 - y) * (1 + y)); + } else { + *rx = log1pl((y - 1) + sqrtl((y - 1) * (y + 1))); + } + } else { + *rx = logl(A + sqrtl(A * A - 1)); + } + + *new_y = y; + + if (y < FOUR_SQRT_MIN) { + *B_is_usable = 0; + *sqrt_A2my2 = A * (2 / LDBL_EPSILON); + *new_y = y * (2 / LDBL_EPSILON); + return; + } + + *B = y / A; + *B_is_usable = 1; + + if (*B > B_crossover) { + *B_is_usable = 0; + if (y == 1 && x < LDBL_EPSILON / 128) { + *sqrt_A2my2 = sqrtl(x) * sqrtl((A + y) / 2); + } else if (x >= LDBL_EPSILON * fabsl(y - 1)) { + Amy = f(x, y + 1, R) + f(x, y - 1, S); + *sqrt_A2my2 = sqrtl(Amy * (A + y)); + } else if (y > 1) { + *sqrt_A2my2 = x * (4 / LDBL_EPSILON / LDBL_EPSILON) * y / + sqrtl((y + 1) * (y - 1)); + *new_y = y * (4 / LDBL_EPSILON / LDBL_EPSILON); + } else { + *sqrt_A2my2 = sqrtl((1 - y) * (1 + y)); + } + } +} + +long double complex +casinhl(long double complex z) +{ + long double x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y; + int B_is_usable; + long double complex w; + + x = creall(z); + y = cimagl(z); + ax = fabsl(x); + ay = fabsl(y); + + if (isnan(x) || isnan(y)) { + if (isinf(x)) + return (CMPLXL(x, y + y)); + if (isinf(y)) + return (CMPLXL(y, x + x)); + if (y == 0) + return (CMPLXL(x + x, y)); + return (CMPLXL(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); + } + + if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) { + if (signbit(x) == 0) + w = clog_for_large_values(z) + m_ln2; + else + w = clog_for_large_values(-z) + m_ln2; + return (CMPLXL(copysignl(creall(w), x), + copysignl(cimagl(w), y))); + } + + if (x == 0 && y == 0) + return (z); + + raise_inexact(); + + if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4) + return (z); + + do_hard_work(ax, ay, &rx, &B_is_usable, &B, &sqrt_A2my2, &new_y); + if (B_is_usable) + ry = asinl(B); + else + ry = atan2l(new_y, sqrt_A2my2); + return (CMPLXL(copysignl(rx, x), copysignl(ry, y))); +} + +long double complex +casinl(long double complex z) +{ + long double complex w; + + w = casinhl(CMPLXL(cimagl(z), creall(z))); + return (CMPLXL(cimagl(w), creall(w))); +} + +long double complex +cacosl(long double complex z) +{ + long double x, y, ax, ay, rx, ry, B, sqrt_A2mx2, new_x; + int sx, sy; + int B_is_usable; + long double complex w; + + x = creall(z); + y = cimagl(z); + sx = signbit(x); + sy = signbit(y); + ax = fabsl(x); + ay = fabsl(y); + + if (isnan(x) || isnan(y)) { + if (isinf(x)) + return (CMPLXL(y + y, -INFINITY)); + if (isinf(y)) + return (CMPLXL(x + x, -y)); + if (x == 0) + return (CMPLXL(pio2_hi + pio2_lo, y + y)); + return (CMPLXL(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); + } + + if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) { + w = clog_for_large_values(z); + rx = fabsl(cimagl(w)); + ry = creall(w) + m_ln2; + if (sy == 0) + ry = -ry; + return (CMPLXL(rx, ry)); + } + + if (x == 1 && y == 0) + return (CMPLXL(0, -y)); + + raise_inexact(); + + if (ax < SQRT_6_EPSILON / 4 && ay < SQRT_6_EPSILON / 4) + return (CMPLXL(pio2_hi - (x - pio2_lo), -y)); + + do_hard_work(ay, ax, &ry, &B_is_usable, &B, &sqrt_A2mx2, &new_x); + if (B_is_usable) { + if (sx == 0) + rx = acosl(B); + else + rx = acosl(-B); + } else { + if (sx == 0) + rx = atan2l(sqrt_A2mx2, new_x); + else + rx = atan2l(sqrt_A2mx2, -new_x); + } + if (sy == 0) + ry = -ry; + return (CMPLXL(rx, ry)); +} + +long double complex +cacoshl(long double complex z) +{ + long double complex w; + long double rx, ry; + + w = cacosl(z); + rx = creall(w); + ry = cimagl(w); + if (isnan(rx) && isnan(ry)) + return (CMPLXL(ry, rx)); + if (isnan(rx)) + return (CMPLXL(fabsl(ry), rx)); + if (isnan(ry)) + return (CMPLXL(ry, ry)); + return (CMPLXL(fabsl(ry), copysignl(rx, cimagl(z)))); +} + +static long double complex +clog_for_large_values(long double complex z) +{ + long double x, y; + long double ax, ay, t; + + x = creall(z); + y = cimagl(z); + ax = fabsl(x); + ay = fabsl(y); + if (ax < ay) { + t = ax; + ax = ay; + ay = t; + } + + if (ax > LDBL_MAX / 2) + return (CMPLXL(logl(hypotl(x / m_e, y / m_e)) + 1, + atan2l(y, x))); + + if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN) + return (CMPLXL(logl(hypotl(x, y)), atan2l(y, x))); + + return (CMPLXL(logl(ax * ax + ay * ay) / 2, atan2l(y, x))); +} + +static inline long double +sum_squares(long double x, long double y) +{ + + if (y < SQRT_MIN) + return (x * x); + + return (x * x + y * y); +} + +static inline long double +real_part_reciprocal(long double x, long double y) +{ + long double scale; + uint16_t hx, hy; + int16_t ix, iy; + + GET_LDBL_EXPSIGN(hx, x); + ix = hx & 0x7fff; + GET_LDBL_EXPSIGN(hy, y); + iy = hy & 0x7fff; +#define BIAS (LDBL_MAX_EXP - 1) +#define CUTOFF (LDBL_MANT_DIG / 2 + 1) + if (ix - iy >= CUTOFF || isinf(x)) + return (1 / x); + if (iy - ix >= CUTOFF) + return (x / y / y); + if (ix <= BIAS + LDBL_MAX_EXP / 2 - CUTOFF) + return (x / (x * x + y * y)); + scale = 1; + SET_LDBL_EXPSIGN(scale, 0x7fff - ix); + x *= scale; + y *= scale; + return (x / (x * x + y * y) * scale); +} + +long double complex +catanhl(long double complex z) +{ + long double x, y, ax, ay, rx, ry; + + x = creall(z); + y = cimagl(z); + ax = fabsl(x); + ay = fabsl(y); + + if (y == 0 && ax <= 1) + return (CMPLXL(atanhl(x), y)); + + if (x == 0) + return (CMPLXL(x, atanl(y))); + + if (isnan(x) || isnan(y)) { + if (isinf(x)) + return (CMPLXL(copysignl(0, x), y + y)); + if (isinf(y)) + return (CMPLXL(copysignl(0, x), + copysignl(pio2_hi + pio2_lo, y))); + return (CMPLXL(x + 0.0L + (y + 0), x + 0.0L + (y + 0))); + } + + if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) + return (CMPLXL(real_part_reciprocal(x, y), + copysignl(pio2_hi + pio2_lo, y))); + + if (ax < SQRT_3_EPSILON / 2 && ay < SQRT_3_EPSILON / 2) { + raise_inexact(); + return (z); + } + + if (ax == 1 && ay < LDBL_EPSILON) + rx = (m_ln2 - logl(ay)) / 2; + else + rx = log1pl(4 * ax / sum_squares(ax - 1, ay)) / 4; + + if (ax == 1) + ry = atan2l(2, -ay) / 2; + else if (ay < LDBL_EPSILON) + ry = atan2l(2 * ay, (1 - ax) * (1 + ax)) / 2; + else + ry = atan2l(2 * ay, (1 - ax) * (1 + ax) - ay * ay) / 2; + + return (CMPLXL(copysignl(rx, x), copysignl(ry, y))); +} + +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))); +}