1181076Sdas/*- 2181076Sdas * Copyright (c) 2008 David Schultz <das@FreeBSD.org> 3181076Sdas * All rights reserved. 4181076Sdas * 5181076Sdas * Redistribution and use in source and binary forms, with or without 6181076Sdas * modification, are permitted provided that the following conditions 7181076Sdas * are met: 8181076Sdas * 1. Redistributions of source code must retain the above copyright 9181076Sdas * notice, this list of conditions and the following disclaimer. 10181076Sdas * 2. Redistributions in binary form must reproduce the above copyright 11181076Sdas * notice, this list of conditions and the following disclaimer in the 12181076Sdas * documentation and/or other materials provided with the distribution. 13181076Sdas * 14181076Sdas * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 15181076Sdas * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16181076Sdas * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17181076Sdas * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 18181076Sdas * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 19181076Sdas * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 20181076Sdas * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21181076Sdas * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22181076Sdas * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23181076Sdas * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24181076Sdas * SUCH DAMAGE. 25181076Sdas */ 26181076Sdas 27181076Sdas/* 28181076Sdas * Tests for corner cases in the inverse trigonometric functions. Some 29181076Sdas * accuracy tests are included as well, but these are very basic 30181076Sdas * sanity checks, not intended to be comprehensive. 31181076Sdas */ 32181076Sdas 33181076Sdas#include <sys/cdefs.h> 34181076Sdas__FBSDID("$FreeBSD$"); 35181076Sdas 36181076Sdas#include <assert.h> 37181076Sdas#include <fenv.h> 38181076Sdas#include <float.h> 39181076Sdas#include <math.h> 40181076Sdas#include <stdio.h> 41181076Sdas 42251241Sdas#include "test-utils.h" 43181076Sdas 44181076Sdas#define LEN(a) (sizeof(a) / sizeof((a)[0])) 45181076Sdas 46181076Sdas#pragma STDC FENV_ACCESS ON 47181076Sdas 48181076Sdas/* 49181076Sdas * Test that a function returns the correct value and sets the 50181076Sdas * exception flags correctly. A tolerance specifying the maximum 51181076Sdas * relative error allowed may be specified. For the 'testall' 52181076Sdas * functions, the tolerance is specified in ulps. 53181076Sdas * 54181076Sdas * These are macros instead of functions so that assert provides more 55181076Sdas * meaningful error messages. 56181076Sdas */ 57181076Sdas#define test_tol(func, x, result, tol, excepts) do { \ 58181076Sdas volatile long double _in = (x), _out = (result); \ 59181076Sdas assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 60251241Sdas assert(fpequal_tol(func(_in), _out, (tol), CS_BOTH)); \ 61251241Sdas assert(((void)func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \ 62181076Sdas} while (0) 63181076Sdas#define test(func, x, result, excepts) \ 64181076Sdas test_tol(func, (x), (result), 0, (excepts)) 65181076Sdas 66181076Sdas#define testall_tol(prefix, x, result, tol, excepts) do { \ 67181076Sdas test_tol(prefix, (double)(x), (double)(result), \ 68181076Sdas (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \ 69181076Sdas test_tol(prefix##f, (float)(x), (float)(result), \ 70181076Sdas (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \ 71181076Sdas test_tol(prefix##l, (x), (result), \ 72181076Sdas (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \ 73181076Sdas} while (0) 74181076Sdas#define testall(prefix, x, result, excepts) \ 75181076Sdas testall_tol(prefix, (x), (result), 0, (excepts)) 76181076Sdas 77181076Sdas#define test2_tol(func, y, x, result, tol, excepts) do { \ 78181076Sdas volatile long double _iny = (y), _inx = (x), _out = (result); \ 79181076Sdas assert(feclearexcept(FE_ALL_EXCEPT) == 0); \ 80251241Sdas assert(fpequal_tol(func(_iny, _inx), _out, (tol), CS_BOTH)); \ 81251241Sdas assert(((void)func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \ 82181076Sdas} while (0) 83181076Sdas#define test2(func, y, x, result, excepts) \ 84181076Sdas test2_tol(func, (y), (x), (result), 0, (excepts)) 85181076Sdas 86181076Sdas#define testall2_tol(prefix, y, x, result, tol, excepts) do { \ 87181076Sdas test2_tol(prefix, (double)(y), (double)(x), (double)(result), \ 88181076Sdas (tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \ 89181076Sdas test2_tol(prefix##f, (float)(y), (float)(x), (float)(result), \ 90181076Sdas (tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \ 91181076Sdas test2_tol(prefix##l, (y), (x), (result), \ 92181076Sdas (tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \ 93181076Sdas} while (0) 94181076Sdas#define testall2(prefix, y, x, result, excepts) \ 95181076Sdas testall2_tol(prefix, (y), (x), (result), 0, (excepts)) 96181076Sdas 97181076Sdaslong double 98181076Sdaspi = 3.14159265358979323846264338327950280e+00L, 99181076Sdaspio3 = 1.04719755119659774615421446109316766e+00L, 100181076Sdasc3pi = 9.42477796076937971538793014983850839e+00L, 101181076Sdasc5pi = 1.57079632679489661923132169163975140e+01L, 102181076Sdasc7pi = 2.19911485751285526692385036829565196e+01L, 103181076Sdasc5pio3 = 5.23598775598298873077107230546583851e+00L, 104181076Sdassqrt2m1 = 4.14213562373095048801688724209698081e-01L; 105181076Sdas 106181076Sdas 107181076Sdas/* 108181076Sdas * Test special case inputs in asin(), acos() and atan(): signed 109181076Sdas * zeroes, infinities, and NaNs. 110181076Sdas */ 111181076Sdasstatic void 112181076Sdastest_special(void) 113181076Sdas{ 114181076Sdas 115181076Sdas testall(asin, 0.0, 0.0, 0); 116181076Sdas testall(acos, 0.0, pi / 2, FE_INEXACT); 117181076Sdas testall(atan, 0.0, 0.0, 0); 118181076Sdas testall(asin, -0.0, -0.0, 0); 119181076Sdas testall(acos, -0.0, pi / 2, FE_INEXACT); 120181076Sdas testall(atan, -0.0, -0.0, 0); 121181076Sdas 122181076Sdas testall(asin, INFINITY, NAN, FE_INVALID); 123181076Sdas testall(acos, INFINITY, NAN, FE_INVALID); 124181076Sdas testall(atan, INFINITY, pi / 2, FE_INEXACT); 125181076Sdas testall(asin, -INFINITY, NAN, FE_INVALID); 126181076Sdas testall(acos, -INFINITY, NAN, FE_INVALID); 127181076Sdas testall(atan, -INFINITY, -pi / 2, FE_INEXACT); 128181076Sdas 129181076Sdas testall(asin, NAN, NAN, 0); 130181076Sdas testall(acos, NAN, NAN, 0); 131181076Sdas testall(atan, NAN, NAN, 0); 132181076Sdas} 133181076Sdas 134181076Sdas/* 135181076Sdas * Test special case inputs in atan2(), where the exact value of y/x is 136181076Sdas * zero or non-finite. 137181076Sdas */ 138181076Sdasstatic void 139181076Sdastest_special_atan2(void) 140181076Sdas{ 141181076Sdas long double z; 142181076Sdas int e; 143181076Sdas 144181076Sdas testall2(atan2, 0.0, -0.0, pi, FE_INEXACT); 145181076Sdas testall2(atan2, -0.0, -0.0, -pi, FE_INEXACT); 146181076Sdas testall2(atan2, 0.0, 0.0, 0.0, 0); 147181076Sdas testall2(atan2, -0.0, 0.0, -0.0, 0); 148181076Sdas 149181076Sdas testall2(atan2, INFINITY, -INFINITY, c3pi / 4, FE_INEXACT); 150181076Sdas testall2(atan2, -INFINITY, -INFINITY, -c3pi / 4, FE_INEXACT); 151181076Sdas testall2(atan2, INFINITY, INFINITY, pi / 4, FE_INEXACT); 152181076Sdas testall2(atan2, -INFINITY, INFINITY, -pi / 4, FE_INEXACT); 153181076Sdas 154181076Sdas /* Tests with one input in the range (0, Inf]. */ 155181076Sdas z = 1.23456789L; 156181076Sdas for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP; e++) { 157181076Sdas test2(atan2f, 0.0, ldexpf(z, e), 0.0, 0); 158181076Sdas test2(atan2f, -0.0, ldexpf(z, e), -0.0, 0); 159181076Sdas test2(atan2f, 0.0, ldexpf(-z, e), (float)pi, FE_INEXACT); 160181076Sdas test2(atan2f, -0.0, ldexpf(-z, e), (float)-pi, FE_INEXACT); 161181076Sdas test2(atan2f, ldexpf(z, e), 0.0, (float)pi / 2, FE_INEXACT); 162181076Sdas test2(atan2f, ldexpf(z, e), -0.0, (float)pi / 2, FE_INEXACT); 163181076Sdas test2(atan2f, ldexpf(-z, e), 0.0, (float)-pi / 2, FE_INEXACT); 164181076Sdas test2(atan2f, ldexpf(-z, e), -0.0, (float)-pi / 2, FE_INEXACT); 165181076Sdas } 166181076Sdas for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP; e++) { 167181076Sdas test2(atan2, 0.0, ldexp(z, e), 0.0, 0); 168181076Sdas test2(atan2, -0.0, ldexp(z, e), -0.0, 0); 169181076Sdas test2(atan2, 0.0, ldexp(-z, e), (double)pi, FE_INEXACT); 170181076Sdas test2(atan2, -0.0, ldexp(-z, e), (double)-pi, FE_INEXACT); 171181076Sdas test2(atan2, ldexp(z, e), 0.0, (double)pi / 2, FE_INEXACT); 172181076Sdas test2(atan2, ldexp(z, e), -0.0, (double)pi / 2, FE_INEXACT); 173181076Sdas test2(atan2, ldexp(-z, e), 0.0, (double)-pi / 2, FE_INEXACT); 174181076Sdas test2(atan2, ldexp(-z, e), -0.0, (double)-pi / 2, FE_INEXACT); 175181076Sdas } 176181076Sdas for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP; e++) { 177181076Sdas test2(atan2l, 0.0, ldexpl(z, e), 0.0, 0); 178181076Sdas test2(atan2l, -0.0, ldexpl(z, e), -0.0, 0); 179181076Sdas test2(atan2l, 0.0, ldexpl(-z, e), pi, FE_INEXACT); 180181076Sdas test2(atan2l, -0.0, ldexpl(-z, e), -pi, FE_INEXACT); 181181076Sdas test2(atan2l, ldexpl(z, e), 0.0, pi / 2, FE_INEXACT); 182181076Sdas test2(atan2l, ldexpl(z, e), -0.0, pi / 2, FE_INEXACT); 183181076Sdas test2(atan2l, ldexpl(-z, e), 0.0, -pi / 2, FE_INEXACT); 184181076Sdas test2(atan2l, ldexpl(-z, e), -0.0, -pi / 2, FE_INEXACT); 185181076Sdas } 186181076Sdas 187181076Sdas /* Tests with one input in the range (0, Inf). */ 188181076Sdas for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP - 1; e++) { 189181076Sdas test2(atan2f, ldexpf(z, e), INFINITY, 0.0, 0); 190181076Sdas test2(atan2f, ldexpf(-z,e), INFINITY, -0.0, 0); 191181076Sdas test2(atan2f, ldexpf(z, e), -INFINITY, (float)pi, FE_INEXACT); 192181076Sdas test2(atan2f, ldexpf(-z,e), -INFINITY, (float)-pi, FE_INEXACT); 193181076Sdas test2(atan2f, INFINITY, ldexpf(z,e), (float)pi/2, FE_INEXACT); 194181076Sdas test2(atan2f, INFINITY, ldexpf(-z,e), (float)pi/2, FE_INEXACT); 195181076Sdas test2(atan2f, -INFINITY, ldexpf(z,e), (float)-pi/2,FE_INEXACT); 196181076Sdas test2(atan2f, -INFINITY, ldexpf(-z,e),(float)-pi/2,FE_INEXACT); 197181076Sdas } 198181076Sdas for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP - 1; e++) { 199181076Sdas test2(atan2, ldexp(z, e), INFINITY, 0.0, 0); 200181076Sdas test2(atan2, ldexp(-z,e), INFINITY, -0.0, 0); 201181076Sdas test2(atan2, ldexp(z, e), -INFINITY, (double)pi, FE_INEXACT); 202181076Sdas test2(atan2, ldexp(-z,e), -INFINITY, (double)-pi, FE_INEXACT); 203181076Sdas test2(atan2, INFINITY, ldexp(z,e), (double)pi/2, FE_INEXACT); 204181076Sdas test2(atan2, INFINITY, ldexp(-z,e), (double)pi/2, FE_INEXACT); 205181076Sdas test2(atan2, -INFINITY, ldexp(z,e), (double)-pi/2,FE_INEXACT); 206181076Sdas test2(atan2, -INFINITY, ldexp(-z,e),(double)-pi/2,FE_INEXACT); 207181076Sdas } 208181076Sdas for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP - 1; e++) { 209181076Sdas test2(atan2l, ldexpl(z, e), INFINITY, 0.0, 0); 210181076Sdas test2(atan2l, ldexpl(-z,e), INFINITY, -0.0, 0); 211181076Sdas test2(atan2l, ldexpl(z, e), -INFINITY, pi, FE_INEXACT); 212181076Sdas test2(atan2l, ldexpl(-z,e), -INFINITY, -pi, FE_INEXACT); 213181076Sdas test2(atan2l, INFINITY, ldexpl(z, e), pi / 2, FE_INEXACT); 214181076Sdas test2(atan2l, INFINITY, ldexpl(-z, e), pi / 2, FE_INEXACT); 215181076Sdas test2(atan2l, -INFINITY, ldexpl(z, e), -pi / 2, FE_INEXACT); 216181076Sdas test2(atan2l, -INFINITY, ldexpl(-z, e), -pi / 2, FE_INEXACT); 217181076Sdas } 218181076Sdas} 219181076Sdas 220181076Sdas/* 221181076Sdas * Test various inputs to asin(), acos() and atan() and verify that the 222181076Sdas * results are accurate to within 1 ulp. 223181076Sdas */ 224181076Sdasstatic void 225181076Sdastest_accuracy(void) 226181076Sdas{ 227181076Sdas 228181076Sdas /* We expect correctly rounded results for these basic cases. */ 229181076Sdas testall(asin, 1.0, pi / 2, FE_INEXACT); 230181076Sdas testall(acos, 1.0, 0, 0); 231181076Sdas testall(atan, 1.0, pi / 4, FE_INEXACT); 232181076Sdas testall(asin, -1.0, -pi / 2, FE_INEXACT); 233181076Sdas testall(acos, -1.0, pi, FE_INEXACT); 234181076Sdas testall(atan, -1.0, -pi / 4, FE_INEXACT); 235181076Sdas 236181076Sdas /* 237181076Sdas * Here we expect answers to be within 1 ulp, although inexactness 238181076Sdas * in the input, combined with double rounding, could cause larger 239181076Sdas * errors. 240181076Sdas */ 241181076Sdas 242181076Sdas testall_tol(asin, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT); 243181076Sdas testall_tol(acos, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT); 244181076Sdas testall_tol(asin, -sqrtl(2) / 2, -pi / 4, 1, FE_INEXACT); 245181076Sdas testall_tol(acos, -sqrtl(2) / 2, c3pi / 4, 1, FE_INEXACT); 246181076Sdas 247181076Sdas testall_tol(asin, sqrtl(3) / 2, pio3, 1, FE_INEXACT); 248181076Sdas testall_tol(acos, sqrtl(3) / 2, pio3 / 2, 1, FE_INEXACT); 249181076Sdas testall_tol(atan, sqrtl(3), pio3, 1, FE_INEXACT); 250181076Sdas testall_tol(asin, -sqrtl(3) / 2, -pio3, 1, FE_INEXACT); 251181076Sdas testall_tol(acos, -sqrtl(3) / 2, c5pio3 / 2, 1, FE_INEXACT); 252181076Sdas testall_tol(atan, -sqrtl(3), -pio3, 1, FE_INEXACT); 253181076Sdas 254181076Sdas testall_tol(atan, sqrt2m1, pi / 8, 1, FE_INEXACT); 255181076Sdas testall_tol(atan, -sqrt2m1, -pi / 8, 1, FE_INEXACT); 256181076Sdas} 257181076Sdas 258181076Sdas/* 259181076Sdas * Test inputs to atan2() where x is a power of 2. These are easy cases 260181076Sdas * because y/x is exact. 261181076Sdas */ 262181076Sdasstatic void 263181076Sdastest_p2x_atan2(void) 264181076Sdas{ 265181076Sdas 266181076Sdas testall2(atan2, 1.0, 1.0, pi / 4, FE_INEXACT); 267181076Sdas testall2(atan2, 1.0, -1.0, c3pi / 4, FE_INEXACT); 268181076Sdas testall2(atan2, -1.0, 1.0, -pi / 4, FE_INEXACT); 269181076Sdas testall2(atan2, -1.0, -1.0, -c3pi / 4, FE_INEXACT); 270181076Sdas 271181076Sdas testall2_tol(atan2, sqrt2m1 * 2, 2.0, pi / 8, 1, FE_INEXACT); 272181076Sdas testall2_tol(atan2, sqrt2m1 * 2, -2.0, c7pi / 8, 1, FE_INEXACT); 273181076Sdas testall2_tol(atan2, -sqrt2m1 * 2, 2.0, -pi / 8, 1, FE_INEXACT); 274181076Sdas testall2_tol(atan2, -sqrt2m1 * 2, -2.0, -c7pi / 8, 1, FE_INEXACT); 275181076Sdas 276181076Sdas testall2_tol(atan2, sqrtl(3) * 0.5, 0.5, pio3, 1, FE_INEXACT); 277181076Sdas testall2_tol(atan2, sqrtl(3) * 0.5, -0.5, pio3 * 2, 1, FE_INEXACT); 278181076Sdas testall2_tol(atan2, -sqrtl(3) * 0.5, 0.5, -pio3, 1, FE_INEXACT); 279181076Sdas testall2_tol(atan2, -sqrtl(3) * 0.5, -0.5, -pio3 * 2, 1, FE_INEXACT); 280181076Sdas} 281181076Sdas 282181076Sdas/* 283181076Sdas * Test inputs very close to 0. 284181076Sdas */ 285181076Sdasstatic void 286181076Sdastest_tiny(void) 287181076Sdas{ 288181076Sdas float tiny = 0x1.23456p-120f; 289181076Sdas 290181076Sdas testall(asin, tiny, tiny, FE_INEXACT); 291181076Sdas testall(acos, tiny, pi / 2, FE_INEXACT); 292181076Sdas testall(atan, tiny, tiny, FE_INEXACT); 293181076Sdas 294181076Sdas testall(asin, -tiny, -tiny, FE_INEXACT); 295181076Sdas testall(acos, -tiny, pi / 2, FE_INEXACT); 296181076Sdas testall(atan, -tiny, -tiny, FE_INEXACT); 297181076Sdas 298181076Sdas /* Test inputs to atan2() that would cause y/x to underflow. */ 299181076Sdas test2(atan2f, 0x1.0p-100, 0x1.0p100, 0.0, FE_INEXACT | FE_UNDERFLOW); 300181076Sdas test2(atan2, 0x1.0p-1000, 0x1.0p1000, 0.0, FE_INEXACT | FE_UNDERFLOW); 301181076Sdas test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP), 302181076Sdas ldexpl(1.0, LDBL_MAX_EXP - 100), 0.0, FE_INEXACT | FE_UNDERFLOW); 303181076Sdas test2(atan2f, -0x1.0p-100, 0x1.0p100, -0.0, FE_INEXACT | FE_UNDERFLOW); 304181076Sdas test2(atan2, -0x1.0p-1000, 0x1.0p1000, -0.0, FE_INEXACT | FE_UNDERFLOW); 305181076Sdas test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP), 306181076Sdas ldexpl(1.0, LDBL_MAX_EXP - 100), -0.0, FE_INEXACT | FE_UNDERFLOW); 307181076Sdas test2(atan2f, 0x1.0p-100, -0x1.0p100, (float)pi, FE_INEXACT); 308181076Sdas test2(atan2, 0x1.0p-1000, -0x1.0p1000, (double)pi, FE_INEXACT); 309181076Sdas test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP), 310181076Sdas -ldexpl(1.0, LDBL_MAX_EXP - 100), pi, FE_INEXACT); 311181076Sdas test2(atan2f, -0x1.0p-100, -0x1.0p100, (float)-pi, FE_INEXACT); 312181076Sdas test2(atan2, -0x1.0p-1000, -0x1.0p1000, (double)-pi, FE_INEXACT); 313181076Sdas test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP), 314181076Sdas -ldexpl(1.0, LDBL_MAX_EXP - 100), -pi, FE_INEXACT); 315181076Sdas} 316181076Sdas 317181076Sdas/* 318181076Sdas * Test very large inputs to atan(). 319181076Sdas */ 320181076Sdasstatic void 321181076Sdastest_atan_huge(void) 322181076Sdas{ 323181076Sdas float huge = 0x1.23456p120; 324181076Sdas 325181076Sdas testall(atan, huge, pi / 2, FE_INEXACT); 326181076Sdas testall(atan, -huge, -pi / 2, FE_INEXACT); 327181076Sdas 328181076Sdas /* Test inputs to atan2() that would cause y/x to overflow. */ 329181076Sdas test2(atan2f, 0x1.0p100, 0x1.0p-100, (float)pi / 2, FE_INEXACT); 330181076Sdas test2(atan2, 0x1.0p1000, 0x1.0p-1000, (double)pi / 2, FE_INEXACT); 331181076Sdas test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100), 332181076Sdas ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT); 333181076Sdas test2(atan2f, -0x1.0p100, 0x1.0p-100, (float)-pi / 2, FE_INEXACT); 334181076Sdas test2(atan2, -0x1.0p1000, 0x1.0p-1000, (double)-pi / 2, FE_INEXACT); 335181076Sdas test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100), 336181076Sdas ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT); 337181206Sdas 338181206Sdas test2(atan2f, 0x1.0p100, -0x1.0p-100, (float)pi / 2, FE_INEXACT); 339181206Sdas test2(atan2, 0x1.0p1000, -0x1.0p-1000, (double)pi / 2, FE_INEXACT); 340181206Sdas test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100), 341181206Sdas -ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT); 342181206Sdas test2(atan2f, -0x1.0p100, -0x1.0p-100, (float)-pi / 2, FE_INEXACT); 343181206Sdas test2(atan2, -0x1.0p1000, -0x1.0p-1000, (double)-pi / 2, FE_INEXACT); 344181206Sdas test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100), 345181206Sdas -ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT); 346181076Sdas} 347181076Sdas 348181076Sdas/* 349181076Sdas * Test that sin(asin(x)) == x, and similarly for acos() and atan(). 350181076Sdas * You need to have a working sinl(), cosl(), and tanl() for these 351181076Sdas * tests to pass. 352181076Sdas */ 353181076Sdasstatic long double 354181076Sdassinasinf(float x) 355181076Sdas{ 356181076Sdas 357181076Sdas return (sinl(asinf(x))); 358181076Sdas} 359181076Sdas 360181076Sdasstatic long double 361181076Sdassinasin(double x) 362181076Sdas{ 363181076Sdas 364181076Sdas return (sinl(asin(x))); 365181076Sdas} 366181076Sdas 367181076Sdasstatic long double 368181076Sdassinasinl(long double x) 369181076Sdas{ 370181076Sdas 371181076Sdas return (sinl(asinl(x))); 372181076Sdas} 373181076Sdas 374181076Sdasstatic long double 375181076Sdascosacosf(float x) 376181076Sdas{ 377181076Sdas 378181076Sdas return (cosl(acosf(x))); 379181076Sdas} 380181076Sdas 381181076Sdasstatic long double 382181076Sdascosacos(double x) 383181076Sdas{ 384181076Sdas 385181076Sdas return (cosl(acos(x))); 386181076Sdas} 387181076Sdas 388181076Sdasstatic long double 389181076Sdascosacosl(long double x) 390181076Sdas{ 391181076Sdas 392181076Sdas return (cosl(acosl(x))); 393181076Sdas} 394181076Sdas 395181076Sdasstatic long double 396181076Sdastanatanf(float x) 397181076Sdas{ 398181076Sdas 399181076Sdas return (tanl(atanf(x))); 400181076Sdas} 401181076Sdas 402181076Sdasstatic long double 403181076Sdastanatan(double x) 404181076Sdas{ 405181076Sdas 406181076Sdas return (tanl(atan(x))); 407181076Sdas} 408181076Sdas 409181076Sdasstatic long double 410181076Sdastanatanl(long double x) 411181076Sdas{ 412181076Sdas 413181076Sdas return (tanl(atanl(x))); 414181076Sdas} 415181076Sdas 416181076Sdasstatic void 417181076Sdastest_inverse(void) 418181076Sdas{ 419181076Sdas float i; 420181076Sdas 421181076Sdas for (i = -1; i <= 1; i += 0x1.0p-12f) { 422181076Sdas testall_tol(sinasin, i, i, 2, i == 0 ? 0 : FE_INEXACT); 423181076Sdas /* The relative error for cosacos is very large near x=0. */ 424181076Sdas if (fabsf(i) > 0x1.0p-4f) 425181076Sdas testall_tol(cosacos, i, i, 16, i == 1 ? 0 : FE_INEXACT); 426181076Sdas testall_tol(tanatan, i, i, 2, i == 0 ? 0 : FE_INEXACT); 427181076Sdas } 428181076Sdas} 429181076Sdas 430181076Sdasint 431181076Sdasmain(int argc, char *argv[]) 432181076Sdas{ 433181076Sdas 434181076Sdas printf("1..7\n"); 435181076Sdas 436181076Sdas test_special(); 437181076Sdas printf("ok 1 - special\n"); 438181076Sdas 439181076Sdas test_special_atan2(); 440181076Sdas printf("ok 2 - atan2 special\n"); 441181076Sdas 442181076Sdas test_accuracy(); 443181076Sdas printf("ok 3 - accuracy\n"); 444181076Sdas 445181076Sdas test_p2x_atan2(); 446181076Sdas printf("ok 4 - atan2 p2x\n"); 447181076Sdas 448181076Sdas test_tiny(); 449181076Sdas printf("ok 5 - tiny inputs\n"); 450181076Sdas 451181076Sdas test_atan_huge(); 452181076Sdas printf("ok 6 - atan huge inputs\n"); 453181076Sdas 454181076Sdas test_inverse(); 455181076Sdas printf("ok 7 - inverse\n"); 456181076Sdas 457181076Sdas return (0); 458181076Sdas} 459