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| Current File : //usr/src/tools/regression/lib/msun/test-fma.c |
/*-
* Copyright (c) 2008 David Schultz <das@FreeBSD.org>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
/*
* Tests for fma{,f,l}().
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD: release/9.1.0/tools/regression/lib/msun/test-fma.c 216222 2010-12-06 00:02:49Z das $");
#include <assert.h>
#include <fenv.h>
#include <float.h>
#include <math.h>
#include <stdio.h>
#define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \
FE_OVERFLOW | FE_UNDERFLOW)
#pragma STDC FENV_ACCESS ON
/*
* Test that a function returns the correct value and sets the
* exception flags correctly. The exceptmask specifies which
* exceptions we should check. We need to be lenient for several
* reasons, but mainly because on some architectures it's impossible
* to raise FE_OVERFLOW without raising FE_INEXACT.
*
* These are macros instead of functions so that assert provides more
* meaningful error messages.
*/
#define test(func, x, y, z, result, exceptmask, excepts) do { \
assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
assert(fpequal((func)((x), (y), (z)), (result))); \
assert(((func), fetestexcept(exceptmask) == (excepts))); \
} while (0)
#define testall(x, y, z, result, exceptmask, excepts) do { \
test(fma, (x), (y), (z), (double)(result), (exceptmask), (excepts)); \
test(fmaf, (x), (y), (z), (float)(result), (exceptmask), (excepts)); \
test(fmal, (x), (y), (z), (result), (exceptmask), (excepts)); \
} while (0)
/* Test in all rounding modes. */
#define testrnd(func, x, y, z, rn, ru, rd, rz, exceptmask, excepts) do { \
fesetround(FE_TONEAREST); \
test((func), (x), (y), (z), (rn), (exceptmask), (excepts)); \
fesetround(FE_UPWARD); \
test((func), (x), (y), (z), (ru), (exceptmask), (excepts)); \
fesetround(FE_DOWNWARD); \
test((func), (x), (y), (z), (rd), (exceptmask), (excepts)); \
fesetround(FE_TOWARDZERO); \
test((func), (x), (y), (z), (rz), (exceptmask), (excepts)); \
} while (0)
/*
* Determine whether x and y are equal, with two special rules:
* +0.0 != -0.0
* NaN == NaN
*/
int
fpequal(long double x, long double y)
{
return ((x == y && !signbit(x) == !signbit(y))
|| (isnan(x) && isnan(y)));
}
static void
test_zeroes(void)
{
const int rd = (fegetround() == FE_DOWNWARD);
testall(0.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
testall(1.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
testall(0.0, 1.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
testall(0.0, 0.0, 1.0, 1.0, ALL_STD_EXCEPT, 0);
testall(-0.0, 0.0, 0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
testall(0.0, -0.0, 0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
testall(-0.0, -0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
testall(0.0, 0.0, -0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
testall(-0.0, -0.0, -0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
testall(-0.0, 0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0);
testall(0.0, -0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0);
testall(-1.0, 1.0, 1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
testall(1.0, -1.0, 1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
testall(-1.0, -1.0, -1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
switch (fegetround()) {
case FE_TONEAREST:
case FE_TOWARDZERO:
test(fmaf, -FLT_MIN, FLT_MIN, 0.0, -0.0,
ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
test(fma, -DBL_MIN, DBL_MIN, 0.0, -0.0,
ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
test(fmal, -LDBL_MIN, LDBL_MIN, 0.0, -0.0,
ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
}
}
static void
test_infinities(void)
{
testall(INFINITY, 1.0, -1.0, INFINITY, ALL_STD_EXCEPT, 0);
testall(-1.0, INFINITY, 0.0, -INFINITY, ALL_STD_EXCEPT, 0);
testall(0.0, 0.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
testall(1.0, 1.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
testall(1.0, 1.0, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
testall(INFINITY, -INFINITY, 1.0, -INFINITY, ALL_STD_EXCEPT, 0);
testall(INFINITY, INFINITY, 1.0, INFINITY, ALL_STD_EXCEPT, 0);
testall(-INFINITY, -INFINITY, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
testall(0.0, INFINITY, 1.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
testall(INFINITY, 0.0, -0.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
/* The invalid exception is optional in this case. */
testall(INFINITY, 0.0, NAN, NAN, ALL_STD_EXCEPT & ~FE_INVALID, 0);
testall(INFINITY, INFINITY, -INFINITY, NAN,
ALL_STD_EXCEPT, FE_INVALID);
testall(-INFINITY, INFINITY, INFINITY, NAN,
ALL_STD_EXCEPT, FE_INVALID);
testall(INFINITY, -1.0, INFINITY, NAN,
ALL_STD_EXCEPT, FE_INVALID);
test(fmaf, FLT_MAX, FLT_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
test(fma, DBL_MAX, DBL_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
test(fmal, LDBL_MAX, LDBL_MAX, -INFINITY, -INFINITY,
ALL_STD_EXCEPT, 0);
test(fmaf, FLT_MAX, -FLT_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
test(fma, DBL_MAX, -DBL_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
test(fmal, LDBL_MAX, -LDBL_MAX, INFINITY, INFINITY,
ALL_STD_EXCEPT, 0);
}
static void
test_nans(void)
{
testall(NAN, 0.0, 0.0, NAN, ALL_STD_EXCEPT, 0);
testall(1.0, NAN, 1.0, NAN, ALL_STD_EXCEPT, 0);
testall(1.0, -1.0, NAN, NAN, ALL_STD_EXCEPT, 0);
testall(0.0, 0.0, NAN, NAN, ALL_STD_EXCEPT, 0);
testall(NAN, NAN, NAN, NAN, ALL_STD_EXCEPT, 0);
/* x*y should not raise an inexact/overflow/underflow if z is NaN. */
testall(M_PI, M_PI, NAN, NAN, ALL_STD_EXCEPT, 0);
test(fmaf, FLT_MIN, FLT_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
test(fma, DBL_MIN, DBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
test(fmal, LDBL_MIN, LDBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
test(fmaf, FLT_MAX, FLT_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
test(fma, DBL_MAX, DBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
test(fmal, LDBL_MAX, LDBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
}
/*
* Tests for cases where z is very small compared to x*y.
*/
static void
test_small_z(void)
{
/* x*y positive, z positive */
if (fegetround() == FE_UPWARD) {
test(fmaf, 1.0, 1.0, 0x1.0p-100, 1.0 + FLT_EPSILON,
ALL_STD_EXCEPT, FE_INEXACT);
test(fma, 1.0, 1.0, 0x1.0p-200, 1.0 + DBL_EPSILON,
ALL_STD_EXCEPT, FE_INEXACT);
test(fmal, 1.0, 1.0, 0x1.0p-200, 1.0 + LDBL_EPSILON,
ALL_STD_EXCEPT, FE_INEXACT);
} else {
testall(0x1.0p100, 1.0, 0x1.0p-100, 0x1.0p100,
ALL_STD_EXCEPT, FE_INEXACT);
}
/* x*y negative, z negative */
if (fegetround() == FE_DOWNWARD) {
test(fmaf, -1.0, 1.0, -0x1.0p-100, -(1.0 + FLT_EPSILON),
ALL_STD_EXCEPT, FE_INEXACT);
test(fma, -1.0, 1.0, -0x1.0p-200, -(1.0 + DBL_EPSILON),
ALL_STD_EXCEPT, FE_INEXACT);
test(fmal, -1.0, 1.0, -0x1.0p-200, -(1.0 + LDBL_EPSILON),
ALL_STD_EXCEPT, FE_INEXACT);
} else {
testall(0x1.0p100, -1.0, -0x1.0p-100, -0x1.0p100,
ALL_STD_EXCEPT, FE_INEXACT);
}
/* x*y positive, z negative */
if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
test(fmaf, 1.0, 1.0, -0x1.0p-100, 1.0 - FLT_EPSILON / 2,
ALL_STD_EXCEPT, FE_INEXACT);
test(fma, 1.0, 1.0, -0x1.0p-200, 1.0 - DBL_EPSILON / 2,
ALL_STD_EXCEPT, FE_INEXACT);
test(fmal, 1.0, 1.0, -0x1.0p-200, 1.0 - LDBL_EPSILON / 2,
ALL_STD_EXCEPT, FE_INEXACT);
} else {
testall(0x1.0p100, 1.0, -0x1.0p-100, 0x1.0p100,
ALL_STD_EXCEPT, FE_INEXACT);
}
/* x*y negative, z positive */
if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
test(fmaf, -1.0, 1.0, 0x1.0p-100, -1.0 + FLT_EPSILON / 2,
ALL_STD_EXCEPT, FE_INEXACT);
test(fma, -1.0, 1.0, 0x1.0p-200, -1.0 + DBL_EPSILON / 2,
ALL_STD_EXCEPT, FE_INEXACT);
test(fmal, -1.0, 1.0, 0x1.0p-200, -1.0 + LDBL_EPSILON / 2,
ALL_STD_EXCEPT, FE_INEXACT);
} else {
testall(-0x1.0p100, 1.0, 0x1.0p-100, -0x1.0p100,
ALL_STD_EXCEPT, FE_INEXACT);
}
}
/*
* Tests for cases where z is very large compared to x*y.
*/
static void
test_big_z(void)
{
/* z positive, x*y positive */
if (fegetround() == FE_UPWARD) {
test(fmaf, 0x1.0p-50, 0x1.0p-50, 1.0, 1.0 + FLT_EPSILON,
ALL_STD_EXCEPT, FE_INEXACT);
test(fma, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + DBL_EPSILON,
ALL_STD_EXCEPT, FE_INEXACT);
test(fmal, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + LDBL_EPSILON,
ALL_STD_EXCEPT, FE_INEXACT);
} else {
testall(-0x1.0p-50, -0x1.0p-50, 0x1.0p100, 0x1.0p100,
ALL_STD_EXCEPT, FE_INEXACT);
}
/* z negative, x*y negative */
if (fegetround() == FE_DOWNWARD) {
test(fmaf, -0x1.0p-50, 0x1.0p-50, -1.0, -(1.0 + FLT_EPSILON),
ALL_STD_EXCEPT, FE_INEXACT);
test(fma, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + DBL_EPSILON),
ALL_STD_EXCEPT, FE_INEXACT);
test(fmal, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + LDBL_EPSILON),
ALL_STD_EXCEPT, FE_INEXACT);
} else {
testall(0x1.0p-50, -0x1.0p-50, -0x1.0p100, -0x1.0p100,
ALL_STD_EXCEPT, FE_INEXACT);
}
/* z negative, x*y positive */
if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
test(fmaf, -0x1.0p-50, -0x1.0p-50, -1.0,
-1.0 + FLT_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
test(fma, -0x1.0p-100, -0x1.0p-100, -1.0,
-1.0 + DBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
test(fmal, -0x1.0p-100, -0x1.0p-100, -1.0,
-1.0 + LDBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
} else {
testall(0x1.0p-50, 0x1.0p-50, -0x1.0p100, -0x1.0p100,
ALL_STD_EXCEPT, FE_INEXACT);
}
/* z positive, x*y negative */
if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
test(fmaf, 0x1.0p-50, -0x1.0p-50, 1.0, 1.0 - FLT_EPSILON / 2,
ALL_STD_EXCEPT, FE_INEXACT);
test(fma, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - DBL_EPSILON / 2,
ALL_STD_EXCEPT, FE_INEXACT);
test(fmal, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - LDBL_EPSILON / 2,
ALL_STD_EXCEPT, FE_INEXACT);
} else {
testall(-0x1.0p-50, 0x1.0p-50, 0x1.0p100, 0x1.0p100,
ALL_STD_EXCEPT, FE_INEXACT);
}
}
static void
test_accuracy(void)
{
/* ilogb(x*y) - ilogb(z) = 20 */
testrnd(fmaf, -0x1.c139d8p-51, -0x1.600e7ap32, 0x1.26558cp-38,
0x1.34e48ap-18, 0x1.34e48cp-18, 0x1.34e48ap-18, 0x1.34e48ap-18,
ALL_STD_EXCEPT, FE_INEXACT);
testrnd(fma, -0x1.c139d7b84f1a3p-51, -0x1.600e7a2a16484p32,
0x1.26558cac31580p-38, 0x1.34e48a78aae97p-18,
0x1.34e48a78aae97p-18, 0x1.34e48a78aae96p-18,
0x1.34e48a78aae96p-18, ALL_STD_EXCEPT, FE_INEXACT);
#if LDBL_MANT_DIG == 113
testrnd(fmal, -0x1.c139d7b84f1a3079263afcc5bae3p-51L,
-0x1.600e7a2a164840edbe2e7d301a72p32L,
0x1.26558cac315807eb07e448042101p-38L,
0x1.34e48a78aae96c76ed36077dd387p-18L,
0x1.34e48a78aae96c76ed36077dd388p-18L,
0x1.34e48a78aae96c76ed36077dd387p-18L,
0x1.34e48a78aae96c76ed36077dd387p-18L,
ALL_STD_EXCEPT, FE_INEXACT);
#elif LDBL_MANT_DIG == 64
testrnd(fmal, -0x1.c139d7b84f1a307ap-51L, -0x1.600e7a2a164840eep32L,
0x1.26558cac315807ecp-38L, 0x1.34e48a78aae96c78p-18L,
0x1.34e48a78aae96c78p-18L, 0x1.34e48a78aae96c76p-18L,
0x1.34e48a78aae96c76p-18L, ALL_STD_EXCEPT, FE_INEXACT);
#elif LDBL_MANT_DIG == 53
testrnd(fmal, -0x1.c139d7b84f1a3p-51L, -0x1.600e7a2a16484p32L,
0x1.26558cac31580p-38L, 0x1.34e48a78aae97p-18L,
0x1.34e48a78aae97p-18L, 0x1.34e48a78aae96p-18L,
0x1.34e48a78aae96p-18L, ALL_STD_EXCEPT, FE_INEXACT);
#endif
/* ilogb(x*y) - ilogb(z) = -40 */
testrnd(fmaf, 0x1.98210ap53, 0x1.9556acp-24, 0x1.d87da4p70,
0x1.d87da4p70, 0x1.d87da6p70, 0x1.d87da4p70, 0x1.d87da4p70,
ALL_STD_EXCEPT, FE_INEXACT);
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
}
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);
}