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548 lines
19 KiB
C
548 lines
19 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/param.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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#include <stdlib.h>
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#include "test-utils.h"
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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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volatile long double _vx = (x), _vy = (y), _vz = (z); \
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ATF_CHECK(feclearexcept(FE_ALL_EXCEPT) == 0); \
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CHECK_FPEQUAL((func)(_vx, _vy, _vz), (result)); \
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CHECK_FP_EXCEPTIONS_MSG(excepts, exceptmask, "for %s(%s)", \
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#func, #x); \
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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, (double)(x), (double)(y), (double)(z), \
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(double)(result), (exceptmask), (excepts)); \
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test(fmaf, (float)(x), (float)(y), (float)(z), \
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(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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* This is needed because clang constant-folds fma in ways that are incorrect
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* in rounding modes other than FE_TONEAREST.
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*/
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static volatile double one = 1.0;
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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(-one, one, one, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
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testall(one, -one, one, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
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testall(-one, -one, -one, 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, one, one, 0x1.0p-100, 1.0 + FLT_EPSILON,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, one, one, 0x1.0p-200, 1.0 + DBL_EPSILON,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, one, one, 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, one, 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, -one, one, -0x1.0p-100, -(1.0 + FLT_EPSILON),
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, -one, one, -0x1.0p-200, -(1.0 + DBL_EPSILON),
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, -one, one, -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, -one, -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, one, one, -0x1.0p-100, 1.0 - FLT_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, one, one, -0x1.0p-200, 1.0 - DBL_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, one, one, -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, one, -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, -one, one, 0x1.0p-100, -1.0 + FLT_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fma, -one, one, 0x1.0p-200, -1.0 + DBL_EPSILON / 2,
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ALL_STD_EXCEPT, FE_INEXACT);
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test(fmal, -one, one, 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, one, 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,
|
|
0x1.d87da3aafc60ep70, 0x1.d87da3aafda40p70,
|
|
0x1.d87da3aafda40p70, 0x1.d87da3aafda3fp70,
|
|
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
|
|
|
|
/* ilogb(x*y) - ilogb(z) = 0 */
|
|
testrnd(fmaf, 0x1.31ad02p+100, 0x1.2fbf7ap-42, -0x1.c3e106p+58,
|
|
-0x1.64c27cp+56, -0x1.64c27ap+56, -0x1.64c27cp+56,
|
|
-0x1.64c27ap+56, ALL_STD_EXCEPT, FE_INEXACT);
|
|
testrnd(fma, 0x1.31ad012ede8aap+100, 0x1.2fbf79c839067p-42,
|
|
-0x1.c3e106929056ep+58, -0x1.64c282b970a5fp+56,
|
|
-0x1.64c282b970a5ep+56, -0x1.64c282b970a5fp+56,
|
|
-0x1.64c282b970a5ep+56, ALL_STD_EXCEPT, FE_INEXACT);
|
|
#if LDBL_MANT_DIG == 113
|
|
testrnd(fmal, 0x1.31ad012ede8aa282fa1c19376d16p+100L,
|
|
0x1.2fbf79c839066f0f5c68f6d2e814p-42L,
|
|
-0x1.c3e106929056ec19de72bfe64215p+58L,
|
|
-0x1.64c282b970a612598fc025ca8cddp+56L,
|
|
-0x1.64c282b970a612598fc025ca8cddp+56L,
|
|
-0x1.64c282b970a612598fc025ca8cdep+56L,
|
|
-0x1.64c282b970a612598fc025ca8cddp+56L,
|
|
ALL_STD_EXCEPT, FE_INEXACT);
|
|
#elif LDBL_MANT_DIG == 64
|
|
testrnd(fmal, 0x1.31ad012ede8aa4eap+100L, 0x1.2fbf79c839066aeap-42L,
|
|
-0x1.c3e106929056e61p+58L, -0x1.64c282b970a60298p+56L,
|
|
-0x1.64c282b970a60298p+56L, -0x1.64c282b970a6029ap+56L,
|
|
-0x1.64c282b970a60298p+56L, ALL_STD_EXCEPT, FE_INEXACT);
|
|
#elif LDBL_MANT_DIG == 53
|
|
testrnd(fmal, 0x1.31ad012ede8aap+100L, 0x1.2fbf79c839067p-42L,
|
|
-0x1.c3e106929056ep+58L, -0x1.64c282b970a5fp+56L,
|
|
-0x1.64c282b970a5ep+56L, -0x1.64c282b970a5fp+56L,
|
|
-0x1.64c282b970a5ep+56L, ALL_STD_EXCEPT, FE_INEXACT);
|
|
#endif
|
|
|
|
/* x*y (rounded) ~= -z */
|
|
/* XXX spurious inexact exceptions */
|
|
testrnd(fmaf, 0x1.bbffeep-30, -0x1.1d164cp-74, 0x1.ee7296p-104,
|
|
-0x1.c46ea8p-128, -0x1.c46ea8p-128, -0x1.c46ea8p-128,
|
|
-0x1.c46ea8p-128, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
|
|
testrnd(fma, 0x1.bbffeea6fc7d6p-30, 0x1.1d164c6cbf078p-74,
|
|
-0x1.ee72993aff948p-104, -0x1.71f72ac7d9d8p-159,
|
|
-0x1.71f72ac7d9d8p-159, -0x1.71f72ac7d9d8p-159,
|
|
-0x1.71f72ac7d9d8p-159, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
|
|
#if LDBL_MANT_DIG == 113
|
|
testrnd(fmal, 0x1.bbffeea6fc7d65927d147f437675p-30L,
|
|
0x1.1d164c6cbf078b7a22607d1cd6a2p-74L,
|
|
-0x1.ee72993aff94973876031bec0944p-104L,
|
|
0x1.64e086175b3a2adc36e607058814p-217L,
|
|
0x1.64e086175b3a2adc36e607058814p-217L,
|
|
0x1.64e086175b3a2adc36e607058814p-217L,
|
|
0x1.64e086175b3a2adc36e607058814p-217L,
|
|
ALL_STD_EXCEPT & ~FE_INEXACT, 0);
|
|
#elif LDBL_MANT_DIG == 64
|
|
testrnd(fmal, 0x1.bbffeea6fc7d6592p-30L, 0x1.1d164c6cbf078b7ap-74L,
|
|
-0x1.ee72993aff949736p-104L, 0x1.af190e7a1ee6ad94p-168L,
|
|
0x1.af190e7a1ee6ad94p-168L, 0x1.af190e7a1ee6ad94p-168L,
|
|
0x1.af190e7a1ee6ad94p-168L, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
|
|
#elif LDBL_MANT_DIG == 53
|
|
testrnd(fmal, 0x1.bbffeea6fc7d6p-30L, 0x1.1d164c6cbf078p-74L,
|
|
-0x1.ee72993aff948p-104L, -0x1.71f72ac7d9d8p-159L,
|
|
-0x1.71f72ac7d9d8p-159L, -0x1.71f72ac7d9d8p-159L,
|
|
-0x1.71f72ac7d9d8p-159L, ALL_STD_EXCEPT & ~FE_INEXACT, 0);
|
|
#endif
|
|
}
|
|
|
|
static void
|
|
test_double_rounding(void)
|
|
{
|
|
|
|
/*
|
|
* a = 0x1.8000000000001p0
|
|
* b = 0x1.8000000000001p0
|
|
* c = -0x0.0000000000000000000000000080...1p+1
|
|
* a * b = 0x1.2000000000001800000000000080p+1
|
|
*
|
|
* The correct behavior is to round DOWN to 0x1.2000000000001p+1 in
|
|
* round-to-nearest mode. An implementation that computes a*b+c in
|
|
* double+double precision, however, will get 0x1.20000000000018p+1,
|
|
* and then round UP.
|
|
*/
|
|
fesetround(FE_TONEAREST);
|
|
test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
|
|
-0x1.0000000000001p-104, 0x1.2000000000001p+1,
|
|
ALL_STD_EXCEPT, FE_INEXACT);
|
|
fesetround(FE_DOWNWARD);
|
|
test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
|
|
-0x1.0000000000001p-104, 0x1.2000000000001p+1,
|
|
ALL_STD_EXCEPT, FE_INEXACT);
|
|
fesetround(FE_UPWARD);
|
|
test(fma, 0x1.8000000000001p0, 0x1.8000000000001p0,
|
|
-0x1.0000000000001p-104, 0x1.2000000000002p+1,
|
|
ALL_STD_EXCEPT, FE_INEXACT);
|
|
|
|
fesetround(FE_TONEAREST);
|
|
test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1,
|
|
ALL_STD_EXCEPT, FE_INEXACT);
|
|
fesetround(FE_DOWNWARD);
|
|
test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200002p+1,
|
|
ALL_STD_EXCEPT, FE_INEXACT);
|
|
fesetround(FE_UPWARD);
|
|
test(fmaf, 0x1.800002p+0, 0x1.800002p+0, -0x1.000002p-46, 0x1.200004p+1,
|
|
ALL_STD_EXCEPT, FE_INEXACT);
|
|
|
|
fesetround(FE_TONEAREST);
|
|
#if LDBL_MANT_DIG == 64
|
|
test(fmal, 0x1.4p+0L, 0x1.0000000000000004p+0L, 0x1p-128L,
|
|
0x1.4000000000000006p+0L, ALL_STD_EXCEPT, FE_INEXACT);
|
|
#elif LDBL_MANT_DIG == 113
|
|
test(fmal, 0x1.8000000000000000000000000001p+0L,
|
|
0x1.8000000000000000000000000001p+0L,
|
|
-0x1.0000000000000000000000000001p-224L,
|
|
0x1.2000000000000000000000000001p+1L, ALL_STD_EXCEPT, FE_INEXACT);
|
|
#endif
|
|
|
|
}
|
|
|
|
static const int rmodes[] = {
|
|
FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO
|
|
};
|
|
|
|
ATF_TC_WITHOUT_HEAD(zeroes);
|
|
ATF_TC_BODY(zeroes, tc)
|
|
{
|
|
for (size_t i = 0; i < nitems(rmodes); i++) {
|
|
printf("rmode = %d\n", rmodes[i]);
|
|
fesetround(rmodes[i]);
|
|
test_zeroes();
|
|
}
|
|
}
|
|
|
|
ATF_TC_WITHOUT_HEAD(infinities);
|
|
ATF_TC_BODY(infinities, tc)
|
|
{
|
|
for (size_t i = 0; i < nitems(rmodes); i++) {
|
|
printf("rmode = %d\n", rmodes[i]);
|
|
fesetround(rmodes[i]);
|
|
test_infinities();
|
|
}
|
|
}
|
|
|
|
ATF_TC_WITHOUT_HEAD(nans);
|
|
ATF_TC_BODY(nans, tc)
|
|
{
|
|
fesetround(FE_TONEAREST);
|
|
test_nans();
|
|
}
|
|
|
|
|
|
ATF_TC_WITHOUT_HEAD(small_z);
|
|
ATF_TC_BODY(small_z, tc)
|
|
{
|
|
for (size_t i = 0; i < nitems(rmodes); i++) {
|
|
printf("rmode = %d\n", rmodes[i]);
|
|
fesetround(rmodes[i]);
|
|
test_small_z();
|
|
}
|
|
}
|
|
|
|
|
|
ATF_TC_WITHOUT_HEAD(big_z);
|
|
ATF_TC_BODY(big_z, tc)
|
|
{
|
|
for (size_t i = 0; i < nitems(rmodes); i++) {
|
|
printf("rmode = %d\n", rmodes[i]);
|
|
fesetround(rmodes[i]);
|
|
test_big_z();
|
|
}
|
|
}
|
|
|
|
ATF_TC_WITHOUT_HEAD(accuracy);
|
|
ATF_TC_BODY(accuracy, tc)
|
|
{
|
|
fesetround(FE_TONEAREST);
|
|
test_accuracy();
|
|
}
|
|
|
|
ATF_TC_WITHOUT_HEAD(double_rounding);
|
|
ATF_TC_BODY(double_rounding, tc) {
|
|
test_double_rounding();
|
|
}
|
|
|
|
ATF_TP_ADD_TCS(tp)
|
|
{
|
|
ATF_TP_ADD_TC(tp, zeroes);
|
|
ATF_TP_ADD_TC(tp, infinities);
|
|
ATF_TP_ADD_TC(tp, nans);
|
|
ATF_TP_ADD_TC(tp, small_z);
|
|
ATF_TP_ADD_TC(tp, big_z);
|
|
ATF_TP_ADD_TC(tp, accuracy);
|
|
ATF_TP_ADD_TC(tp, double_rounding);
|
|
/*
|
|
* TODO:
|
|
* - Tests for subnormals
|
|
* - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact)
|
|
*/
|
|
return (atf_no_error());
|
|
}
|