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Basic tests for complex inverse trig and hyperbolic functions.
This commit is contained in:
David Schultz
parent
5faf6ff4cc
commit
659a67c641
2 changed files with 444 additions and 1 deletions
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@ -2,7 +2,8 @@
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TESTS= test-cexp test-conj test-csqrt test-ctrig \
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test-exponential test-fenv test-fma \
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test-fmaxmin test-ilogb test-invtrig test-logarithm test-lrint \
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test-fmaxmin test-ilogb test-invtrig test-invctrig \
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test-logarithm test-lrint \
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test-lround test-nan test-nearbyint test-next test-rem test-trig
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CFLAGS+= -O0 -lm
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442
tools/regression/lib/msun/test-invctrig.c
Normal file
442
tools/regression/lib/msun/test-invctrig.c
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@ -0,0 +1,442 @@
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/*-
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* Copyright (c) 2008-2013 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 casin[h](), cacos[h](), and catan[h]().
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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 <complex.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 OPT_INVALID (ALL_STD_EXCEPT & ~FE_INVALID)
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#define OPT_INEXACT (ALL_STD_EXCEPT & ~FE_INEXACT)
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#define FLT_ULP() ldexpl(1.0, 1 - FLT_MANT_DIG)
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#define DBL_ULP() ldexpl(1.0, 1 - DBL_MANT_DIG)
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#define LDBL_ULP() ldexpl(1.0, 1 - LDBL_MANT_DIG)
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#pragma STDC FENV_ACCESS ON
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#pragma STDC CX_LIMITED_RANGE OFF
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/* Flags that determine whether to check the signs of the result. */
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#define CS_REAL 1
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#define CS_IMAG 2
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#define CS_BOTH (CS_REAL | CS_IMAG)
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#ifdef DEBUG
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#define debug(...) printf(__VA_ARGS__)
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#else
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#define debug(...) (void)0
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#endif
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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. The exceptmask specifies which
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* exceptions we should check. We need to be lenient for several
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* reasons, but mainly because on some architectures it's impossible
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* to raise FE_OVERFLOW without raising FE_INEXACT.
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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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* XXX The volatile here is to avoid gcc's bogus constant folding and work
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* around the lack of support for the FENV_ACCESS pragma.
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*/
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#define test_p(func, z, result, exceptmask, excepts, checksign) do { \
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volatile long double complex _d = z; \
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debug(" testing %s(%Lg + %Lg I) == %Lg + %Lg I\n", #func, \
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creall(_d), cimagl(_d), creall(result), cimagl(result)); \
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assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
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assert(cfpequal((func)(_d), (result), (checksign))); \
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assert(((func), fetestexcept(exceptmask) == (excepts))); \
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} while (0)
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/*
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* Test within a given tolerance. The tolerance indicates relative error
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* in ulps.
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*/
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#define test_p_tol(func, z, result, tol) do { \
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volatile long double complex _d = z; \
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debug(" testing %s(%Lg + %Lg I) ~= %Lg + %Lg I\n", #func, \
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creall(_d), cimagl(_d), creall(result), cimagl(result)); \
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assert(cfpequal_tol((func)(_d), (result), (tol))); \
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} while (0)
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/* These wrappers apply the identities f(conj(z)) = conj(f(z)). */
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#define test(func, z, result, exceptmask, excepts, checksign) do { \
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test_p(func, z, result, exceptmask, excepts, checksign); \
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test_p(func, conjl(z), conjl(result), exceptmask, excepts, checksign); \
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} while (0)
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#define test_tol(func, z, result, tol) do { \
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test_p_tol(func, z, result, tol); \
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test_p_tol(func, conjl(z), conjl(result), tol); \
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} while (0)
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/* Test the given function in all precisions. */
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#define testall(func, x, result, exceptmask, excepts, checksign) do { \
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test(func, x, result, exceptmask, excepts, checksign); \
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test(func##f, x, result, exceptmask, excepts, checksign); \
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} while (0)
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#define testall_odd(func, x, result, exceptmask, excepts, checksign) do { \
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testall(func, x, result, exceptmask, excepts, checksign); \
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testall(func, -(x), -result, exceptmask, excepts, checksign); \
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} while (0)
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#define testall_even(func, x, result, exceptmask, excepts, checksign) do { \
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testall(func, x, result, exceptmask, excepts, checksign); \
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testall(func, -(x), result, exceptmask, excepts, checksign); \
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} while (0)
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/*
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* Test the given function in all precisions, within a given tolerance.
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* The tolerance is specified in ulps.
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*/
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#define testall_tol(func, x, result, tol) do { \
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test_tol(func, x, result, (tol) * DBL_ULP()); \
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test_tol(func##f, x, result, (tol) * FLT_ULP()); \
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} while (0)
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#define testall_odd_tol(func, x, result, tol) do { \
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testall_tol(func, x, result, tol); \
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testall_tol(func, -(x), -result, tol); \
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} while (0)
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#define testall_even_tol(func, x, result, tol) do { \
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testall_tol(func, x, result, tol); \
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testall_tol(func, -(x), result, tol); \
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} while (0)
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static const long double
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pi = 3.14159265358979323846264338327950280L,
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c3pi = 9.42477796076937971538793014983850839L;
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/*
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* Determine whether x and y are equal, with two special rules:
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* +0.0 != -0.0
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* NaN == NaN
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* If checksign is 0, we compare the absolute values instead.
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*/
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static int
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fpequal(long double x, long double y, int checksign)
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{
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if (isnan(x) && isnan(y))
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return (1);
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if (checksign)
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return (x == y && !signbit(x) == !signbit(y));
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else
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return (fabsl(x) == fabsl(y));
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}
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static int
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fpequal_tol(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 || y == 0.0)
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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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static int
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cfpequal(long double complex x, long double complex y, int checksign)
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{
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return (fpequal(creal(x), creal(y), checksign & CS_REAL)
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&& fpequal(cimag(x), cimag(y), checksign & CS_IMAG));
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}
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static int
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cfpequal_tol(long double complex x, long double complex y, long double tol)
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{
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return (fpequal_tol(creal(x), creal(y), tol)
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&& fpequal_tol(cimag(x), cimag(y), tol));
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}
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/* Tests for 0 */
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void
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test_zero(void)
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{
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long double complex zero = CMPLXL(0.0, 0.0);
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testall_tol(cacosh, zero, CMPLXL(0.0, pi / 2), 1);
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testall_tol(cacosh, -zero, CMPLXL(0.0, -pi / 2), 1);
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testall_tol(cacos, zero, CMPLXL(pi / 2, -0.0), 1);
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testall_tol(cacos, -zero, CMPLXL(pi / 2, 0.0), 1);
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testall_odd(casinh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
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testall_odd(casin, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
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testall_odd(catanh, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
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testall_odd(catan, zero, zero, ALL_STD_EXCEPT, 0, CS_BOTH);
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}
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/*
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* Tests for NaN inputs.
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*/
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void
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test_nan()
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{
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long double complex nan_nan = CMPLXL(NAN, NAN);
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long double complex z;
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/*
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* IN CACOSH CACOS CASINH CATANH
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* NaN,NaN NaN,NaN NaN,NaN NaN,NaN NaN,NaN
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* finite,NaN NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN*
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* NaN,finite NaN,NaN* NaN,NaN* NaN,NaN* NaN,NaN*
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* NaN,Inf Inf,NaN NaN,-Inf ?Inf,NaN ?0,pi/2
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* +-Inf,NaN Inf,NaN NaN,?Inf +-Inf,NaN +-0,NaN
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* +-0,NaN NaN,NaN* pi/2,NaN NaN,NaN* +-0,NaN
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* NaN,0 NaN,NaN* NaN,NaN* NaN,0 NaN,NaN*
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*
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* * = raise invalid
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*/
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z = nan_nan;
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testall(cacosh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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testall(cacos, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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testall(casinh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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testall(casin, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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testall(catanh, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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testall(catan, z, nan_nan, ALL_STD_EXCEPT, 0, 0);
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z = CMPLXL(0.5, NAN);
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testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
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testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
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testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
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z = CMPLXL(NAN, 0.5);
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testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
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testall(casinh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
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testall(catanh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(catan, z, nan_nan, OPT_INVALID, 0, 0);
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z = CMPLXL(NAN, INFINITY);
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testall(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
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testall(cacosh, -z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
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testall(cacos, z, CMPLXL(NAN, -INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
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testall(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0, 0);
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testall(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, CS_IMAG);
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testall_tol(catanh, z, CMPLXL(0.0, pi / 2), 1);
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testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, CS_IMAG);
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z = CMPLXL(INFINITY, NAN);
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testall_even(cacosh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
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CS_REAL);
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testall_even(cacos, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
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testall_odd(casinh, z, CMPLXL(INFINITY, NAN), ALL_STD_EXCEPT, 0,
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CS_REAL);
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testall_odd(casin, z, CMPLXL(NAN, INFINITY), ALL_STD_EXCEPT, 0, 0);
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testall_odd(catanh, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
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testall_odd_tol(catan, z, CMPLXL(pi / 2, 0.0), 1);
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z = CMPLXL(0.0, NAN);
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/* XXX We allow a spurious inexact exception here. */
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testall_even(cacosh, z, nan_nan, OPT_INVALID & ~FE_INEXACT, 0, 0);
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testall_even_tol(cacos, z, CMPLXL(pi / 2, NAN), 1);
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testall_odd(casinh, z, nan_nan, OPT_INVALID, 0, 0);
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testall_odd(casin, z, CMPLXL(0.0, NAN), ALL_STD_EXCEPT, 0, CS_REAL);
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testall_odd(catanh, z, CMPLXL(0.0, NAN), OPT_INVALID, 0, CS_REAL);
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testall_odd(catan, z, nan_nan, OPT_INVALID, 0, 0);
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z = CMPLXL(NAN, 0.0);
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testall(cacosh, z, nan_nan, OPT_INVALID, 0, 0);
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testall(cacos, z, nan_nan, OPT_INVALID, 0, 0);
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testall(casinh, z, CMPLXL(NAN, 0), ALL_STD_EXCEPT, 0, CS_IMAG);
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testall(casin, z, nan_nan, OPT_INVALID, 0, 0);
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testall(catanh, z, nan_nan, OPT_INVALID, 0, CS_IMAG);
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testall(catan, z, CMPLXL(NAN, 0.0), ALL_STD_EXCEPT, 0, 0);
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}
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void
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test_inf(void)
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{
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long double complex z;
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/*
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* IN CACOSH CACOS CASINH CATANH
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* Inf,Inf Inf,pi/4 pi/4,-Inf Inf,pi/4 0,pi/2
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* -Inf,Inf Inf,3pi/4 3pi/4,-Inf --- ---
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* Inf,finite Inf,0 0,-Inf Inf,0 0,pi/2
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* -Inf,finite Inf,pi pi,-Inf --- ---
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* finite,Inf Inf,pi/2 pi/2,-Inf Inf,pi/2 0,pi/2
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*/
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z = CMPLXL(INFINITY, INFINITY);
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testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 4), 1);
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testall_tol(cacosh, -z, CMPLXL(INFINITY, -c3pi / 4), 1);
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testall_tol(cacos, z, CMPLXL(pi / 4, -INFINITY), 1);
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testall_tol(cacos, -z, CMPLXL(c3pi / 4, INFINITY), 1);
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testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 4), 1);
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testall_odd_tol(casin, z, CMPLXL(pi / 4, INFINITY), 1);
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testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
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testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
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z = CMPLXL(INFINITY, 0.5);
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/* XXX We allow a spurious inexact exception here. */
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testall(cacosh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
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testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi), 1);
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testall(cacos, z, CMPLXL(0, -INFINITY), OPT_INEXACT, 0, CS_BOTH);
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testall_tol(cacos, -z, CMPLXL(pi, INFINITY), 1);
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testall_odd(casinh, z, CMPLXL(INFINITY, 0), OPT_INEXACT, 0, CS_BOTH);
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testall_odd_tol(casin, z, CMPLXL(pi / 2, INFINITY), 1);
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testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
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testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
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z = CMPLXL(0.5, INFINITY);
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testall_tol(cacosh, z, CMPLXL(INFINITY, pi / 2), 1);
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testall_tol(cacosh, -z, CMPLXL(INFINITY, -pi / 2), 1);
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testall_tol(cacos, z, CMPLXL(pi / 2, -INFINITY), 1);
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testall_tol(cacos, -z, CMPLXL(pi / 2, INFINITY), 1);
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testall_odd_tol(casinh, z, CMPLXL(INFINITY, pi / 2), 1);
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/* XXX We allow a spurious inexact exception here. */
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testall_odd(casin, z, CMPLXL(0.0, INFINITY), OPT_INEXACT, 0, CS_BOTH);
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testall_odd_tol(catanh, z, CMPLXL(0, pi / 2), 1);
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testall_odd_tol(catan, z, CMPLXL(pi / 2, 0), 1);
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}
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/* Tests along the real and imaginary axes. */
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void
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test_axes(void)
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{
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static const long double nums[] = {
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-2, -1, -0.5, 0.5, 1, 2
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};
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long double complex z;
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int i;
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for (i = 0; i < sizeof(nums) / sizeof(nums[0]); i++) {
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/* Real axis */
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z = CMPLXL(nums[i], 0.0);
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if (fabs(nums[i]) <= 1) {
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testall_tol(cacosh, z, CMPLXL(0.0, acos(nums[i])), 1);
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testall_tol(cacos, z, CMPLXL(acosl(nums[i]), -0.0), 1);
|
||||
testall_tol(casin, z, CMPLXL(asinl(nums[i]), 0.0), 1);
|
||||
testall_tol(catanh, z, CMPLXL(atanh(nums[i]), 0.0), 1);
|
||||
} else {
|
||||
testall_tol(cacosh, z,
|
||||
CMPLXL(acosh(fabs(nums[i])),
|
||||
(nums[i] < 0) ? pi : 0), 1);
|
||||
testall_tol(cacos, z,
|
||||
CMPLXL((nums[i] < 0) ? pi : 0,
|
||||
-acosh(fabs(nums[i]))), 1);
|
||||
testall_tol(casin, z,
|
||||
CMPLXL(copysign(pi / 2, nums[i]),
|
||||
acosh(fabs(nums[i]))), 1);
|
||||
testall_tol(catanh, z,
|
||||
CMPLXL(atanh(1 / nums[i]), pi / 2), 1);
|
||||
}
|
||||
testall_tol(casinh, z, CMPLXL(asinh(nums[i]), 0.0), 1);
|
||||
testall_tol(catan, z, CMPLXL(atan(nums[i]), 0), 1);
|
||||
|
||||
/* TODO: Test the imaginary axis. */
|
||||
}
|
||||
}
|
||||
|
||||
void
|
||||
test_small(void)
|
||||
{
|
||||
/*
|
||||
* z = 0.75 + i 0.25
|
||||
* acos(z) = Pi/4 - i ln(2)/2
|
||||
* asin(z) = Pi/4 + i ln(2)/2
|
||||
* atan(z) = atan(4)/2 + i ln(17/9)/4
|
||||
*/
|
||||
static const struct {
|
||||
complex long double z;
|
||||
complex long double acos_z;
|
||||
complex long double asin_z;
|
||||
complex long double atan_z;
|
||||
} tests[] = {
|
||||
{ CMPLXL(0.75L, 0.25L),
|
||||
CMPLXL(pi / 4, -0.34657359027997265470861606072908828L),
|
||||
CMPLXL(pi / 4, 0.34657359027997265470861606072908828L),
|
||||
CMPLXL(0.66290883183401623252961960521423782L,
|
||||
0.15899719167999917436476103600701878L) },
|
||||
};
|
||||
int i;
|
||||
|
||||
for (i = 0; i < sizeof(tests) / sizeof(tests[0]); i++) {
|
||||
testall_tol(cacos, tests[i].z, tests[i].acos_z, 2);
|
||||
testall_odd_tol(casin, tests[i].z, tests[i].asin_z, 2);
|
||||
testall_odd_tol(catan, tests[i].z, tests[i].atan_z, 2);
|
||||
}
|
||||
}
|
||||
|
||||
/* Test inputs that might cause overflow in a sloppy implementation. */
|
||||
void
|
||||
test_large(void)
|
||||
{
|
||||
|
||||
/* TODO: Write these tests */
|
||||
}
|
||||
|
||||
int
|
||||
main(int argc, char *argv[])
|
||||
{
|
||||
|
||||
printf("1..6\n");
|
||||
|
||||
test_zero();
|
||||
printf("ok 1 - invctrig zero\n");
|
||||
|
||||
test_nan();
|
||||
printf("ok 2 - invctrig nan\n");
|
||||
|
||||
test_inf();
|
||||
printf("ok 3 - invctrig inf\n");
|
||||
|
||||
test_axes();
|
||||
printf("ok 4 - invctrig axes\n");
|
||||
|
||||
test_small();
|
||||
printf("ok 5 - invctrig small\n");
|
||||
|
||||
test_large();
|
||||
printf("ok 6 - invctrig large\n");
|
||||
|
||||
return (0);
|
||||
}
|
||||
Loading…
Reference in a new issue