487 lines
16 KiB
C
487 lines
16 KiB
C
/*-
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* Copyright (c) 2008 David Schultz <das@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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* Tests for corner cases in the inverse trigonometric functions. Some
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* accuracy tests are included as well, but these are very basic
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* sanity checks, not intended to be comprehensive.
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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#include <assert.h>
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#include <fenv.h>
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#include <float.h>
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#include <math.h>
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#include <stdio.h>
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#define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \
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FE_OVERFLOW | FE_UNDERFLOW)
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#define LEN(a) (sizeof(a) / sizeof((a)[0]))
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#pragma STDC FENV_ACCESS ON
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/*
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* Test that a function returns the correct value and sets the
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* exception flags correctly. A tolerance specifying the maximum
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* relative error allowed may be specified. For the 'testall'
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* functions, the tolerance is specified in ulps.
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*
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* These are macros instead of functions so that assert provides more
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* meaningful error messages.
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*/
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#define test_tol(func, x, result, tol, excepts) do { \
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volatile long double _in = (x), _out = (result); \
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assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
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assert(fpequal(func(_in), _out, (tol))); \
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assert((func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \
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} while (0)
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#define test(func, x, result, excepts) \
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test_tol(func, (x), (result), 0, (excepts))
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#define testall_tol(prefix, x, result, tol, excepts) do { \
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test_tol(prefix, (double)(x), (double)(result), \
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(tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \
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test_tol(prefix##f, (float)(x), (float)(result), \
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(tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \
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test_tol(prefix##l, (x), (result), \
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(tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \
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} while (0)
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#define testall(prefix, x, result, excepts) \
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testall_tol(prefix, (x), (result), 0, (excepts))
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#define test2_tol(func, y, x, result, tol, excepts) do { \
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volatile long double _iny = (y), _inx = (x), _out = (result); \
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assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
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assert(fpequal(func(_iny, _inx), _out, (tol))); \
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assert((func, fetestexcept(ALL_STD_EXCEPT) == (excepts))); \
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} while (0)
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#define test2(func, y, x, result, excepts) \
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test2_tol(func, (y), (x), (result), 0, (excepts))
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#define testall2_tol(prefix, y, x, result, tol, excepts) do { \
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test2_tol(prefix, (double)(y), (double)(x), (double)(result), \
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(tol) * ldexp(1.0, 1 - DBL_MANT_DIG), (excepts)); \
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test2_tol(prefix##f, (float)(y), (float)(x), (float)(result), \
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(tol) * ldexpf(1.0, 1 - FLT_MANT_DIG), (excepts)); \
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test2_tol(prefix##l, (y), (x), (result), \
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(tol) * ldexpl(1.0, 1 - LDBL_MANT_DIG), (excepts)); \
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} while (0)
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#define testall2(prefix, y, x, result, excepts) \
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testall2_tol(prefix, (y), (x), (result), 0, (excepts))
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long double
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pi = 3.14159265358979323846264338327950280e+00L,
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pio3 = 1.04719755119659774615421446109316766e+00L,
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c3pi = 9.42477796076937971538793014983850839e+00L,
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c5pi = 1.57079632679489661923132169163975140e+01L,
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c7pi = 2.19911485751285526692385036829565196e+01L,
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c5pio3 = 5.23598775598298873077107230546583851e+00L,
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sqrt2m1 = 4.14213562373095048801688724209698081e-01L;
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/*
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* Determine whether x and y are equal to within a relative error of tol,
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* with two special rules:
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* +0.0 != -0.0
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* NaN == NaN
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*/
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int
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fpequal(long double x, long double y, long double tol)
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{
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fenv_t env;
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int ret;
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if (isnan(x) && isnan(y))
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return (1);
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if (!signbit(x) != !signbit(y))
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return (0);
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if (x == y)
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return (1);
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if (tol == 0)
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return (0);
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/* Hard case: need to check the tolerance. */
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feholdexcept(&env);
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ret = fabsl(x - y) <= fabsl(y * tol);
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fesetenv(&env);
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return (ret);
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}
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/*
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* Test special case inputs in asin(), acos() and atan(): signed
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* zeroes, infinities, and NaNs.
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*/
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static void
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test_special(void)
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{
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testall(asin, 0.0, 0.0, 0);
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testall(acos, 0.0, pi / 2, FE_INEXACT);
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testall(atan, 0.0, 0.0, 0);
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testall(asin, -0.0, -0.0, 0);
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testall(acos, -0.0, pi / 2, FE_INEXACT);
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testall(atan, -0.0, -0.0, 0);
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testall(asin, INFINITY, NAN, FE_INVALID);
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testall(acos, INFINITY, NAN, FE_INVALID);
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testall(atan, INFINITY, pi / 2, FE_INEXACT);
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testall(asin, -INFINITY, NAN, FE_INVALID);
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testall(acos, -INFINITY, NAN, FE_INVALID);
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testall(atan, -INFINITY, -pi / 2, FE_INEXACT);
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testall(asin, NAN, NAN, 0);
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testall(acos, NAN, NAN, 0);
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testall(atan, NAN, NAN, 0);
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}
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/*
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* Test special case inputs in atan2(), where the exact value of y/x is
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* zero or non-finite.
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*/
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static void
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test_special_atan2(void)
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{
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long double z;
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int e;
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testall2(atan2, 0.0, -0.0, pi, FE_INEXACT);
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testall2(atan2, -0.0, -0.0, -pi, FE_INEXACT);
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testall2(atan2, 0.0, 0.0, 0.0, 0);
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testall2(atan2, -0.0, 0.0, -0.0, 0);
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testall2(atan2, INFINITY, -INFINITY, c3pi / 4, FE_INEXACT);
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testall2(atan2, -INFINITY, -INFINITY, -c3pi / 4, FE_INEXACT);
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testall2(atan2, INFINITY, INFINITY, pi / 4, FE_INEXACT);
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testall2(atan2, -INFINITY, INFINITY, -pi / 4, FE_INEXACT);
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/* Tests with one input in the range (0, Inf]. */
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z = 1.23456789L;
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for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP; e++) {
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test2(atan2f, 0.0, ldexpf(z, e), 0.0, 0);
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test2(atan2f, -0.0, ldexpf(z, e), -0.0, 0);
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test2(atan2f, 0.0, ldexpf(-z, e), (float)pi, FE_INEXACT);
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test2(atan2f, -0.0, ldexpf(-z, e), (float)-pi, FE_INEXACT);
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test2(atan2f, ldexpf(z, e), 0.0, (float)pi / 2, FE_INEXACT);
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test2(atan2f, ldexpf(z, e), -0.0, (float)pi / 2, FE_INEXACT);
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test2(atan2f, ldexpf(-z, e), 0.0, (float)-pi / 2, FE_INEXACT);
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test2(atan2f, ldexpf(-z, e), -0.0, (float)-pi / 2, FE_INEXACT);
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}
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for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP; e++) {
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test2(atan2, 0.0, ldexp(z, e), 0.0, 0);
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test2(atan2, -0.0, ldexp(z, e), -0.0, 0);
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test2(atan2, 0.0, ldexp(-z, e), (double)pi, FE_INEXACT);
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test2(atan2, -0.0, ldexp(-z, e), (double)-pi, FE_INEXACT);
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test2(atan2, ldexp(z, e), 0.0, (double)pi / 2, FE_INEXACT);
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test2(atan2, ldexp(z, e), -0.0, (double)pi / 2, FE_INEXACT);
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test2(atan2, ldexp(-z, e), 0.0, (double)-pi / 2, FE_INEXACT);
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test2(atan2, ldexp(-z, e), -0.0, (double)-pi / 2, FE_INEXACT);
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}
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for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP; e++) {
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test2(atan2l, 0.0, ldexpl(z, e), 0.0, 0);
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test2(atan2l, -0.0, ldexpl(z, e), -0.0, 0);
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test2(atan2l, 0.0, ldexpl(-z, e), pi, FE_INEXACT);
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test2(atan2l, -0.0, ldexpl(-z, e), -pi, FE_INEXACT);
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test2(atan2l, ldexpl(z, e), 0.0, pi / 2, FE_INEXACT);
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test2(atan2l, ldexpl(z, e), -0.0, pi / 2, FE_INEXACT);
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test2(atan2l, ldexpl(-z, e), 0.0, -pi / 2, FE_INEXACT);
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test2(atan2l, ldexpl(-z, e), -0.0, -pi / 2, FE_INEXACT);
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}
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/* Tests with one input in the range (0, Inf). */
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for (e = FLT_MIN_EXP - FLT_MANT_DIG; e <= FLT_MAX_EXP - 1; e++) {
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test2(atan2f, ldexpf(z, e), INFINITY, 0.0, 0);
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test2(atan2f, ldexpf(-z,e), INFINITY, -0.0, 0);
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test2(atan2f, ldexpf(z, e), -INFINITY, (float)pi, FE_INEXACT);
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test2(atan2f, ldexpf(-z,e), -INFINITY, (float)-pi, FE_INEXACT);
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test2(atan2f, INFINITY, ldexpf(z,e), (float)pi/2, FE_INEXACT);
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test2(atan2f, INFINITY, ldexpf(-z,e), (float)pi/2, FE_INEXACT);
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test2(atan2f, -INFINITY, ldexpf(z,e), (float)-pi/2,FE_INEXACT);
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test2(atan2f, -INFINITY, ldexpf(-z,e),(float)-pi/2,FE_INEXACT);
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}
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for (e = DBL_MIN_EXP - DBL_MANT_DIG; e <= DBL_MAX_EXP - 1; e++) {
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test2(atan2, ldexp(z, e), INFINITY, 0.0, 0);
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test2(atan2, ldexp(-z,e), INFINITY, -0.0, 0);
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test2(atan2, ldexp(z, e), -INFINITY, (double)pi, FE_INEXACT);
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test2(atan2, ldexp(-z,e), -INFINITY, (double)-pi, FE_INEXACT);
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test2(atan2, INFINITY, ldexp(z,e), (double)pi/2, FE_INEXACT);
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test2(atan2, INFINITY, ldexp(-z,e), (double)pi/2, FE_INEXACT);
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test2(atan2, -INFINITY, ldexp(z,e), (double)-pi/2,FE_INEXACT);
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test2(atan2, -INFINITY, ldexp(-z,e),(double)-pi/2,FE_INEXACT);
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}
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for (e = LDBL_MIN_EXP - LDBL_MANT_DIG; e <= LDBL_MAX_EXP - 1; e++) {
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test2(atan2l, ldexpl(z, e), INFINITY, 0.0, 0);
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test2(atan2l, ldexpl(-z,e), INFINITY, -0.0, 0);
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test2(atan2l, ldexpl(z, e), -INFINITY, pi, FE_INEXACT);
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test2(atan2l, ldexpl(-z,e), -INFINITY, -pi, FE_INEXACT);
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test2(atan2l, INFINITY, ldexpl(z, e), pi / 2, FE_INEXACT);
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test2(atan2l, INFINITY, ldexpl(-z, e), pi / 2, FE_INEXACT);
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test2(atan2l, -INFINITY, ldexpl(z, e), -pi / 2, FE_INEXACT);
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test2(atan2l, -INFINITY, ldexpl(-z, e), -pi / 2, FE_INEXACT);
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}
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}
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/*
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* Test various inputs to asin(), acos() and atan() and verify that the
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* results are accurate to within 1 ulp.
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*/
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static void
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test_accuracy(void)
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{
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/* We expect correctly rounded results for these basic cases. */
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testall(asin, 1.0, pi / 2, FE_INEXACT);
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testall(acos, 1.0, 0, 0);
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testall(atan, 1.0, pi / 4, FE_INEXACT);
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testall(asin, -1.0, -pi / 2, FE_INEXACT);
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testall(acos, -1.0, pi, FE_INEXACT);
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testall(atan, -1.0, -pi / 4, FE_INEXACT);
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/*
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* Here we expect answers to be within 1 ulp, although inexactness
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* in the input, combined with double rounding, could cause larger
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* errors.
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*/
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testall_tol(asin, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT);
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testall_tol(acos, sqrtl(2) / 2, pi / 4, 1, FE_INEXACT);
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testall_tol(asin, -sqrtl(2) / 2, -pi / 4, 1, FE_INEXACT);
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testall_tol(acos, -sqrtl(2) / 2, c3pi / 4, 1, FE_INEXACT);
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testall_tol(asin, sqrtl(3) / 2, pio3, 1, FE_INEXACT);
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testall_tol(acos, sqrtl(3) / 2, pio3 / 2, 1, FE_INEXACT);
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testall_tol(atan, sqrtl(3), pio3, 1, FE_INEXACT);
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testall_tol(asin, -sqrtl(3) / 2, -pio3, 1, FE_INEXACT);
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testall_tol(acos, -sqrtl(3) / 2, c5pio3 / 2, 1, FE_INEXACT);
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testall_tol(atan, -sqrtl(3), -pio3, 1, FE_INEXACT);
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testall_tol(atan, sqrt2m1, pi / 8, 1, FE_INEXACT);
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testall_tol(atan, -sqrt2m1, -pi / 8, 1, FE_INEXACT);
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}
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/*
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* Test inputs to atan2() where x is a power of 2. These are easy cases
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* because y/x is exact.
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*/
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static void
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test_p2x_atan2(void)
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{
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testall2(atan2, 1.0, 1.0, pi / 4, FE_INEXACT);
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testall2(atan2, 1.0, -1.0, c3pi / 4, FE_INEXACT);
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testall2(atan2, -1.0, 1.0, -pi / 4, FE_INEXACT);
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testall2(atan2, -1.0, -1.0, -c3pi / 4, FE_INEXACT);
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testall2_tol(atan2, sqrt2m1 * 2, 2.0, pi / 8, 1, FE_INEXACT);
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testall2_tol(atan2, sqrt2m1 * 2, -2.0, c7pi / 8, 1, FE_INEXACT);
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testall2_tol(atan2, -sqrt2m1 * 2, 2.0, -pi / 8, 1, FE_INEXACT);
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testall2_tol(atan2, -sqrt2m1 * 2, -2.0, -c7pi / 8, 1, FE_INEXACT);
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testall2_tol(atan2, sqrtl(3) * 0.5, 0.5, pio3, 1, FE_INEXACT);
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testall2_tol(atan2, sqrtl(3) * 0.5, -0.5, pio3 * 2, 1, FE_INEXACT);
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testall2_tol(atan2, -sqrtl(3) * 0.5, 0.5, -pio3, 1, FE_INEXACT);
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testall2_tol(atan2, -sqrtl(3) * 0.5, -0.5, -pio3 * 2, 1, FE_INEXACT);
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}
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/*
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* Test inputs very close to 0.
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*/
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static void
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test_tiny(void)
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{
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float tiny = 0x1.23456p-120f;
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testall(asin, tiny, tiny, FE_INEXACT);
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testall(acos, tiny, pi / 2, FE_INEXACT);
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testall(atan, tiny, tiny, FE_INEXACT);
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testall(asin, -tiny, -tiny, FE_INEXACT);
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testall(acos, -tiny, pi / 2, FE_INEXACT);
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testall(atan, -tiny, -tiny, FE_INEXACT);
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/* Test inputs to atan2() that would cause y/x to underflow. */
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test2(atan2f, 0x1.0p-100, 0x1.0p100, 0.0, FE_INEXACT | FE_UNDERFLOW);
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test2(atan2, 0x1.0p-1000, 0x1.0p1000, 0.0, FE_INEXACT | FE_UNDERFLOW);
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test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP),
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ldexpl(1.0, LDBL_MAX_EXP - 100), 0.0, FE_INEXACT | FE_UNDERFLOW);
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test2(atan2f, -0x1.0p-100, 0x1.0p100, -0.0, FE_INEXACT | FE_UNDERFLOW);
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test2(atan2, -0x1.0p-1000, 0x1.0p1000, -0.0, FE_INEXACT | FE_UNDERFLOW);
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test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP),
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ldexpl(1.0, LDBL_MAX_EXP - 100), -0.0, FE_INEXACT | FE_UNDERFLOW);
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test2(atan2f, 0x1.0p-100, -0x1.0p100, (float)pi, FE_INEXACT);
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test2(atan2, 0x1.0p-1000, -0x1.0p1000, (double)pi, FE_INEXACT);
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test2(atan2l, ldexpl(1.0, 100 - LDBL_MAX_EXP),
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-ldexpl(1.0, LDBL_MAX_EXP - 100), pi, FE_INEXACT);
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test2(atan2f, -0x1.0p-100, -0x1.0p100, (float)-pi, FE_INEXACT);
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test2(atan2, -0x1.0p-1000, -0x1.0p1000, (double)-pi, FE_INEXACT);
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test2(atan2l, -ldexpl(1.0, 100 - LDBL_MAX_EXP),
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-ldexpl(1.0, LDBL_MAX_EXP - 100), -pi, FE_INEXACT);
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}
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/*
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* Test very large inputs to atan().
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*/
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static void
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test_atan_huge(void)
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{
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float huge = 0x1.23456p120;
|
|
|
|
testall(atan, huge, pi / 2, FE_INEXACT);
|
|
testall(atan, -huge, -pi / 2, FE_INEXACT);
|
|
|
|
/* Test inputs to atan2() that would cause y/x to overflow. */
|
|
test2(atan2f, 0x1.0p100, 0x1.0p-100, (float)pi / 2, FE_INEXACT);
|
|
test2(atan2, 0x1.0p1000, 0x1.0p-1000, (double)pi / 2, FE_INEXACT);
|
|
test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100),
|
|
ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT);
|
|
test2(atan2f, -0x1.0p100, 0x1.0p-100, (float)-pi / 2, FE_INEXACT);
|
|
test2(atan2, -0x1.0p1000, 0x1.0p-1000, (double)-pi / 2, FE_INEXACT);
|
|
test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100),
|
|
ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT);
|
|
|
|
test2(atan2f, 0x1.0p100, -0x1.0p-100, (float)pi / 2, FE_INEXACT);
|
|
test2(atan2, 0x1.0p1000, -0x1.0p-1000, (double)pi / 2, FE_INEXACT);
|
|
test2(atan2l, ldexpl(1.0, LDBL_MAX_EXP - 100),
|
|
-ldexpl(1.0, 100 - LDBL_MAX_EXP), pi / 2, FE_INEXACT);
|
|
test2(atan2f, -0x1.0p100, -0x1.0p-100, (float)-pi / 2, FE_INEXACT);
|
|
test2(atan2, -0x1.0p1000, -0x1.0p-1000, (double)-pi / 2, FE_INEXACT);
|
|
test2(atan2l, -ldexpl(1.0, LDBL_MAX_EXP - 100),
|
|
-ldexpl(1.0, 100 - LDBL_MAX_EXP), -pi / 2, FE_INEXACT);
|
|
}
|
|
|
|
/*
|
|
* Test that sin(asin(x)) == x, and similarly for acos() and atan().
|
|
* You need to have a working sinl(), cosl(), and tanl() for these
|
|
* tests to pass.
|
|
*/
|
|
static long double
|
|
sinasinf(float x)
|
|
{
|
|
|
|
return (sinl(asinf(x)));
|
|
}
|
|
|
|
static long double
|
|
sinasin(double x)
|
|
{
|
|
|
|
return (sinl(asin(x)));
|
|
}
|
|
|
|
static long double
|
|
sinasinl(long double x)
|
|
{
|
|
|
|
return (sinl(asinl(x)));
|
|
}
|
|
|
|
static long double
|
|
cosacosf(float x)
|
|
{
|
|
|
|
return (cosl(acosf(x)));
|
|
}
|
|
|
|
static long double
|
|
cosacos(double x)
|
|
{
|
|
|
|
return (cosl(acos(x)));
|
|
}
|
|
|
|
static long double
|
|
cosacosl(long double x)
|
|
{
|
|
|
|
return (cosl(acosl(x)));
|
|
}
|
|
|
|
static long double
|
|
tanatanf(float x)
|
|
{
|
|
|
|
return (tanl(atanf(x)));
|
|
}
|
|
|
|
static long double
|
|
tanatan(double x)
|
|
{
|
|
|
|
return (tanl(atan(x)));
|
|
}
|
|
|
|
static long double
|
|
tanatanl(long double x)
|
|
{
|
|
|
|
return (tanl(atanl(x)));
|
|
}
|
|
|
|
static void
|
|
test_inverse(void)
|
|
{
|
|
float i;
|
|
|
|
for (i = -1; i <= 1; i += 0x1.0p-12f) {
|
|
testall_tol(sinasin, i, i, 2, i == 0 ? 0 : FE_INEXACT);
|
|
/* The relative error for cosacos is very large near x=0. */
|
|
if (fabsf(i) > 0x1.0p-4f)
|
|
testall_tol(cosacos, i, i, 16, i == 1 ? 0 : FE_INEXACT);
|
|
testall_tol(tanatan, i, i, 2, i == 0 ? 0 : FE_INEXACT);
|
|
}
|
|
}
|
|
|
|
int
|
|
main(int argc, char *argv[])
|
|
{
|
|
|
|
printf("1..7\n");
|
|
|
|
test_special();
|
|
printf("ok 1 - special\n");
|
|
|
|
test_special_atan2();
|
|
printf("ok 2 - atan2 special\n");
|
|
|
|
test_accuracy();
|
|
printf("ok 3 - accuracy\n");
|
|
|
|
test_p2x_atan2();
|
|
printf("ok 4 - atan2 p2x\n");
|
|
|
|
test_tiny();
|
|
printf("ok 5 - tiny inputs\n");
|
|
|
|
test_atan_huge();
|
|
printf("ok 6 - atan huge inputs\n");
|
|
|
|
test_inverse();
|
|
printf("ok 7 - inverse\n");
|
|
|
|
return (0);
|
|
}
|