415 lines
14 KiB
C
415 lines
14 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 fma{,f,l}().
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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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#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. 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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#define test(func, x, y, z, result, exceptmask, excepts) do { \
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assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
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assert(fpequal((func)((x), (y), (z)), (result))); \
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assert(((func), fetestexcept(exceptmask) == (excepts))); \
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} while (0)
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#define testall(x, y, z, result, exceptmask, excepts) do { \
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test(fma, (x), (y), (z), (double)(result), (exceptmask), (excepts)); \
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test(fmaf, (x), (y), (z), (float)(result), (exceptmask), (excepts)); \
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test(fmal, (x), (y), (z), (result), (exceptmask), (excepts)); \
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} while (0)
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/* Test in all rounding modes. */
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#define testrnd(func, x, y, z, rn, ru, rd, rz, exceptmask, excepts) do { \
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fesetround(FE_TONEAREST); \
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test((func), (x), (y), (z), (rn), (exceptmask), (excepts)); \
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fesetround(FE_UPWARD); \
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test((func), (x), (y), (z), (ru), (exceptmask), (excepts)); \
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fesetround(FE_DOWNWARD); \
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test((func), (x), (y), (z), (rd), (exceptmask), (excepts)); \
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fesetround(FE_TOWARDZERO); \
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test((func), (x), (y), (z), (rz), (exceptmask), (excepts)); \
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} while (0)
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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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*/
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int
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fpequal(long double x, long double y)
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{
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return ((x == y && !signbit(x) == !signbit(y))
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|| (isnan(x) && isnan(y)));
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}
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static void
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test_zeroes(void)
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{
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const int rd = (fegetround() == FE_DOWNWARD);
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testall(0.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
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testall(1.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
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testall(0.0, 1.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
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testall(0.0, 0.0, 1.0, 1.0, ALL_STD_EXCEPT, 0);
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testall(-0.0, 0.0, 0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
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testall(0.0, -0.0, 0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
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testall(-0.0, -0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
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testall(0.0, 0.0, -0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
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testall(-0.0, -0.0, -0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
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testall(-0.0, 0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0);
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testall(0.0, -0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0);
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testall(-1.0, 1.0, 1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
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testall(1.0, -1.0, 1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
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testall(-1.0, -1.0, -1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
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switch (fegetround()) {
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case FE_TONEAREST:
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case FE_TOWARDZERO:
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test(fmaf, -FLT_MIN, FLT_MIN, 0.0, -0.0,
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ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
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test(fma, -DBL_MIN, DBL_MIN, 0.0, -0.0,
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ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
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test(fmal, -LDBL_MIN, LDBL_MIN, 0.0, -0.0,
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ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
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}
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}
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static void
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test_infinities(void)
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{
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testall(INFINITY, 1.0, -1.0, INFINITY, ALL_STD_EXCEPT, 0);
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testall(-1.0, INFINITY, 0.0, -INFINITY, ALL_STD_EXCEPT, 0);
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testall(0.0, 0.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
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testall(1.0, 1.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
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testall(1.0, 1.0, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
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testall(INFINITY, -INFINITY, 1.0, -INFINITY, ALL_STD_EXCEPT, 0);
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testall(INFINITY, INFINITY, 1.0, INFINITY, ALL_STD_EXCEPT, 0);
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testall(-INFINITY, -INFINITY, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
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testall(0.0, INFINITY, 1.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
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testall(INFINITY, 0.0, -0.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
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/* The invalid exception is optional in this case. */
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testall(INFINITY, 0.0, NAN, NAN, ALL_STD_EXCEPT & ~FE_INVALID, 0);
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testall(INFINITY, INFINITY, -INFINITY, NAN,
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ALL_STD_EXCEPT, FE_INVALID);
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testall(-INFINITY, INFINITY, INFINITY, NAN,
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ALL_STD_EXCEPT, FE_INVALID);
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testall(INFINITY, -1.0, INFINITY, NAN,
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ALL_STD_EXCEPT, FE_INVALID);
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test(fmaf, FLT_MAX, FLT_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
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test(fma, DBL_MAX, DBL_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
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test(fmal, LDBL_MAX, LDBL_MAX, -INFINITY, -INFINITY,
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ALL_STD_EXCEPT, 0);
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test(fmaf, FLT_MAX, -FLT_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
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test(fma, DBL_MAX, -DBL_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
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test(fmal, LDBL_MAX, -LDBL_MAX, INFINITY, INFINITY,
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ALL_STD_EXCEPT, 0);
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}
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static void
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test_nans(void)
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{
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testall(NAN, 0.0, 0.0, NAN, ALL_STD_EXCEPT, 0);
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testall(1.0, NAN, 1.0, NAN, ALL_STD_EXCEPT, 0);
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testall(1.0, -1.0, NAN, NAN, ALL_STD_EXCEPT, 0);
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testall(0.0, 0.0, NAN, NAN, ALL_STD_EXCEPT, 0);
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testall(NAN, NAN, NAN, NAN, ALL_STD_EXCEPT, 0);
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/* x*y should not raise an inexact/overflow/underflow if z is NaN. */
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testall(M_PI, M_PI, NAN, NAN, ALL_STD_EXCEPT, 0);
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test(fmaf, FLT_MIN, FLT_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
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test(fma, DBL_MIN, DBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
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test(fmal, LDBL_MIN, LDBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
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test(fmaf, FLT_MAX, FLT_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
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test(fma, DBL_MAX, DBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
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test(fmal, LDBL_MAX, LDBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
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}
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/*
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* Tests for cases where z is very small compared to x*y.
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*/
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static void
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test_small_z(void)
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{
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/* x*y positive, z positive */
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if (fegetround() == FE_UPWARD) {
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test(fmaf, 1.0, 1.0, 0x1.0p-100, 1.0 + FLT_EPSILON,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, 1.0, 1.0, 0x1.0p-200, 1.0 + DBL_EPSILON,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, 1.0, 1.0, 0x1.0p-200, 1.0 + LDBL_EPSILON,
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ALL_STD_EXCEPT, FE_INEXACT);
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} else {
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testall(0x1.0p100, 1.0, 0x1.0p-100, 0x1.0p100,
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ALL_STD_EXCEPT, FE_INEXACT);
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}
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/* x*y negative, z negative */
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if (fegetround() == FE_DOWNWARD) {
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test(fmaf, -1.0, 1.0, -0x1.0p-100, -(1.0 + FLT_EPSILON),
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, -1.0, 1.0, -0x1.0p-200, -(1.0 + DBL_EPSILON),
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, -1.0, 1.0, -0x1.0p-200, -(1.0 + LDBL_EPSILON),
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ALL_STD_EXCEPT, FE_INEXACT);
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} else {
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testall(0x1.0p100, -1.0, -0x1.0p-100, -0x1.0p100,
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ALL_STD_EXCEPT, FE_INEXACT);
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}
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/* x*y positive, z negative */
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if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
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test(fmaf, 1.0, 1.0, -0x1.0p-100, 1.0 - FLT_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, 1.0, 1.0, -0x1.0p-200, 1.0 - DBL_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, 1.0, 1.0, -0x1.0p-200, 1.0 - LDBL_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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} else {
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testall(0x1.0p100, 1.0, -0x1.0p-100, 0x1.0p100,
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ALL_STD_EXCEPT, FE_INEXACT);
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}
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/* x*y negative, z positive */
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if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
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test(fmaf, -1.0, 1.0, 0x1.0p-100, -1.0 + FLT_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, -1.0, 1.0, 0x1.0p-200, -1.0 + DBL_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, -1.0, 1.0, 0x1.0p-200, -1.0 + LDBL_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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} else {
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testall(-0x1.0p100, 1.0, 0x1.0p-100, -0x1.0p100,
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ALL_STD_EXCEPT, FE_INEXACT);
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}
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}
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/*
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* Tests for cases where z is very large compared to x*y.
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*/
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static void
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test_big_z(void)
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{
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/* z positive, x*y positive */
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if (fegetround() == FE_UPWARD) {
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test(fmaf, 0x1.0p-50, 0x1.0p-50, 1.0, 1.0 + FLT_EPSILON,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + DBL_EPSILON,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + LDBL_EPSILON,
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ALL_STD_EXCEPT, FE_INEXACT);
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} else {
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testall(-0x1.0p-50, -0x1.0p-50, 0x1.0p100, 0x1.0p100,
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ALL_STD_EXCEPT, FE_INEXACT);
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}
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/* z negative, x*y negative */
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if (fegetround() == FE_DOWNWARD) {
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test(fmaf, -0x1.0p-50, 0x1.0p-50, -1.0, -(1.0 + FLT_EPSILON),
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + DBL_EPSILON),
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + LDBL_EPSILON),
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ALL_STD_EXCEPT, FE_INEXACT);
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} else {
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testall(0x1.0p-50, -0x1.0p-50, -0x1.0p100, -0x1.0p100,
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ALL_STD_EXCEPT, FE_INEXACT);
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}
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/* z negative, x*y positive */
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if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
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test(fmaf, -0x1.0p-50, -0x1.0p-50, -1.0,
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-1.0 + FLT_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, -0x1.0p-100, -0x1.0p-100, -1.0,
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-1.0 + DBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, -0x1.0p-100, -0x1.0p-100, -1.0,
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-1.0 + LDBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
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} else {
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testall(0x1.0p-50, 0x1.0p-50, -0x1.0p100, -0x1.0p100,
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ALL_STD_EXCEPT, FE_INEXACT);
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}
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/* z positive, x*y negative */
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if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
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test(fmaf, 0x1.0p-50, -0x1.0p-50, 1.0, 1.0 - FLT_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - DBL_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - LDBL_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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} else {
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testall(-0x1.0p-50, 0x1.0p-50, 0x1.0p100, 0x1.0p100,
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ALL_STD_EXCEPT, FE_INEXACT);
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}
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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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/* ilogb(x*y) - ilogb(z) = 20 */
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testrnd(fmaf, -0x1.c139d8p-51, -0x1.600e7ap32, 0x1.26558cp-38,
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0x1.34e48ap-18, 0x1.34e48cp-18, 0x1.34e48ap-18, 0x1.34e48ap-18,
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ALL_STD_EXCEPT, FE_INEXACT);
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testrnd(fma, -0x1.c139d7b84f1a3p-51, -0x1.600e7a2a16484p32,
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0x1.26558cac31580p-38, 0x1.34e48a78aae97p-18,
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0x1.34e48a78aae97p-18, 0x1.34e48a78aae96p-18,
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0x1.34e48a78aae96p-18, ALL_STD_EXCEPT, FE_INEXACT);
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#if LDBL_MANT_DIG == 113
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testrnd(fmal, -0x1.c139d7b84f1a3079263afcc5bae3p-51L,
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-0x1.600e7a2a164840edbe2e7d301a72p32L,
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0x1.26558cac315807eb07e448042101p-38L,
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0x1.34e48a78aae96c76ed36077dd387p-18L,
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0x1.34e48a78aae96c76ed36077dd388p-18L,
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0x1.34e48a78aae96c76ed36077dd387p-18L,
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0x1.34e48a78aae96c76ed36077dd387p-18L,
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ALL_STD_EXCEPT, FE_INEXACT);
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#elif LDBL_MANT_DIG == 64
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testrnd(fmal, -0x1.c139d7b84f1a307ap-51L, -0x1.600e7a2a164840eep32L,
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0x1.26558cac315807ecp-38L, 0x1.34e48a78aae96c78p-18L,
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0x1.34e48a78aae96c78p-18L, 0x1.34e48a78aae96c76p-18L,
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0x1.34e48a78aae96c76p-18L, ALL_STD_EXCEPT, FE_INEXACT);
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#elif LDBL_MANT_DIG == 53
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testrnd(fmal, -0x1.c139d7b84f1a3p-51L, -0x1.600e7a2a16484p32L,
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0x1.26558cac31580p-38L, 0x1.34e48a78aae97p-18L,
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0x1.34e48a78aae97p-18L, 0x1.34e48a78aae96p-18L,
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0x1.34e48a78aae96p-18L, ALL_STD_EXCEPT, FE_INEXACT);
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#endif
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/* ilogb(x*y) - ilogb(z) = -40 */
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testrnd(fmaf, 0x1.98210ap53, 0x1.9556acp-24, 0x1.d87da4p70,
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0x1.d87da4p70, 0x1.d87da6p70, 0x1.d87da4p70, 0x1.d87da4p70,
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ALL_STD_EXCEPT, FE_INEXACT);
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testrnd(fma, 0x1.98210ac83fe2bp53, 0x1.9556ac1475f0fp-24,
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0x1.d87da3aafc60ep70, 0x1.d87da3aafda40p70,
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0x1.d87da3aafda40p70, 0x1.d87da3aafda3fp70,
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0x1.d87da3aafda3fp70, ALL_STD_EXCEPT, FE_INEXACT);
|
|
#if LDBL_MANT_DIG == 113
|
|
testrnd(fmal, 0x1.98210ac83fe2a8f65b6278b74cebp53L,
|
|
0x1.9556ac1475f0f28968b61d0de65ap-24L,
|
|
0x1.d87da3aafc60d830aa4c6d73b749p70L,
|
|
0x1.d87da3aafda3f36a69eb86488224p70L,
|
|
0x1.d87da3aafda3f36a69eb86488225p70L,
|
|
0x1.d87da3aafda3f36a69eb86488224p70L,
|
|
0x1.d87da3aafda3f36a69eb86488224p70L,
|
|
ALL_STD_EXCEPT, FE_INEXACT);
|
|
#elif LDBL_MANT_DIG == 64
|
|
testrnd(fmal, 0x1.98210ac83fe2a8f6p53L, 0x1.9556ac1475f0f28ap-24L,
|
|
0x1.d87da3aafc60d83p70L, 0x1.d87da3aafda3f36ap70L,
|
|
0x1.d87da3aafda3f36ap70L, 0x1.d87da3aafda3f368p70L,
|
|
0x1.d87da3aafda3f368p70L, ALL_STD_EXCEPT, FE_INEXACT);
|
|
#elif LDBL_MANT_DIG == 53
|
|
testrnd(fmal, 0x1.98210ac83fe2bp53L, 0x1.9556ac1475f0fp-24L,
|
|
0x1.d87da3aafc60ep70L, 0x1.d87da3aafda40p70L,
|
|
0x1.d87da3aafda40p70L, 0x1.d87da3aafda3fp70L,
|
|
0x1.d87da3aafda3fp70L, ALL_STD_EXCEPT, FE_INEXACT);
|
|
#endif
|
|
}
|
|
|
|
int
|
|
main(int argc, char *argv[])
|
|
{
|
|
int rmodes[] = { FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO };
|
|
int i;
|
|
|
|
printf("1..18\n");
|
|
|
|
for (i = 0; i < 4; i++) {
|
|
fesetround(rmodes[i]);
|
|
test_zeroes();
|
|
printf("ok %d - fma zeroes\n", i + 1);
|
|
}
|
|
|
|
for (i = 0; i < 4; i++) {
|
|
fesetround(rmodes[i]);
|
|
test_infinities();
|
|
printf("ok %d - fma infinities\n", i + 5);
|
|
}
|
|
|
|
fesetround(FE_TONEAREST);
|
|
test_nans();
|
|
printf("ok 9 - fma NaNs\n");
|
|
|
|
for (i = 0; i < 4; i++) {
|
|
fesetround(rmodes[i]);
|
|
test_small_z();
|
|
printf("ok %d - fma small z\n", i + 10);
|
|
}
|
|
|
|
for (i = 0; i < 4; i++) {
|
|
fesetround(rmodes[i]);
|
|
test_big_z();
|
|
printf("ok %d - fma big z\n", i + 14);
|
|
}
|
|
|
|
fesetround(FE_TONEAREST);
|
|
test_accuracy();
|
|
printf("ok 18 - fma accuracy\n");
|
|
|
|
/*
|
|
* TODO:
|
|
* - Tests for subnormals
|
|
* - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact)
|
|
*/
|
|
|
|
return (0);
|
|
}
|