2 * Copyright (c) 2008 David Schultz <das@FreeBSD.org>
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
28 * Tests for fma{,f,l}().
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
40 #define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID | \
41 FE_OVERFLOW | FE_UNDERFLOW)
43 #pragma STDC FENV_ACCESS ON
46 * Test that a function returns the correct value and sets the
47 * exception flags correctly. The exceptmask specifies which
48 * exceptions we should check. We need to be lenient for several
49 * reasons, but mainly because on some architectures it's impossible
50 * to raise FE_OVERFLOW without raising FE_INEXACT.
52 * These are macros instead of functions so that assert provides more
53 * meaningful error messages.
55 #define test(func, x, y, z, result, exceptmask, excepts) do { \
56 assert(feclearexcept(FE_ALL_EXCEPT) == 0); \
57 assert(fpequal((func)((x), (y), (z)), (result))); \
58 assert(((func), fetestexcept(exceptmask) == (excepts))); \
61 #define testall(x, y, z, result, exceptmask, excepts) do { \
62 test(fma, (x), (y), (z), (double)(result), (exceptmask), (excepts)); \
63 test(fmaf, (x), (y), (z), (float)(result), (exceptmask), (excepts)); \
64 test(fmal, (x), (y), (z), (result), (exceptmask), (excepts)); \
67 /* Test in all rounding modes. */
68 #define testrnd(func, x, y, z, rn, ru, rd, rz, exceptmask, excepts) do { \
69 fesetround(FE_TONEAREST); \
70 test((func), (x), (y), (z), (rn), (exceptmask), (excepts)); \
71 fesetround(FE_UPWARD); \
72 test((func), (x), (y), (z), (ru), (exceptmask), (excepts)); \
73 fesetround(FE_DOWNWARD); \
74 test((func), (x), (y), (z), (rd), (exceptmask), (excepts)); \
75 fesetround(FE_TOWARDZERO); \
76 test((func), (x), (y), (z), (rz), (exceptmask), (excepts)); \
80 * Determine whether x and y are equal, with two special rules:
85 fpequal(long double x, long double y)
88 return ((x == y && !signbit(x) == !signbit(y))
89 || (isnan(x) && isnan(y)));
95 const int rd = (fegetround() == FE_DOWNWARD);
97 testall(0.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
98 testall(1.0, 0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
99 testall(0.0, 1.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
100 testall(0.0, 0.0, 1.0, 1.0, ALL_STD_EXCEPT, 0);
102 testall(-0.0, 0.0, 0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
103 testall(0.0, -0.0, 0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
104 testall(-0.0, -0.0, 0.0, 0.0, ALL_STD_EXCEPT, 0);
105 testall(0.0, 0.0, -0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
106 testall(-0.0, -0.0, -0.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
108 testall(-0.0, 0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0);
109 testall(0.0, -0.0, -0.0, -0.0, ALL_STD_EXCEPT, 0);
111 testall(-1.0, 1.0, 1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
112 testall(1.0, -1.0, 1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
113 testall(-1.0, -1.0, -1.0, rd ? -0.0 : 0.0, ALL_STD_EXCEPT, 0);
115 switch (fegetround()) {
118 test(fmaf, -FLT_MIN, FLT_MIN, 0.0, -0.0,
119 ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
120 test(fma, -DBL_MIN, DBL_MIN, 0.0, -0.0,
121 ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
122 test(fmal, -LDBL_MIN, LDBL_MIN, 0.0, -0.0,
123 ALL_STD_EXCEPT, FE_INEXACT | FE_UNDERFLOW);
128 test_infinities(void)
131 testall(INFINITY, 1.0, -1.0, INFINITY, ALL_STD_EXCEPT, 0);
132 testall(-1.0, INFINITY, 0.0, -INFINITY, ALL_STD_EXCEPT, 0);
133 testall(0.0, 0.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
134 testall(1.0, 1.0, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
135 testall(1.0, 1.0, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
137 testall(INFINITY, -INFINITY, 1.0, -INFINITY, ALL_STD_EXCEPT, 0);
138 testall(INFINITY, INFINITY, 1.0, INFINITY, ALL_STD_EXCEPT, 0);
139 testall(-INFINITY, -INFINITY, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
141 testall(0.0, INFINITY, 1.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
142 testall(INFINITY, 0.0, -0.0, NAN, ALL_STD_EXCEPT, FE_INVALID);
144 /* The invalid exception is optional in this case. */
145 testall(INFINITY, 0.0, NAN, NAN, ALL_STD_EXCEPT & ~FE_INVALID, 0);
147 testall(INFINITY, INFINITY, -INFINITY, NAN,
148 ALL_STD_EXCEPT, FE_INVALID);
149 testall(-INFINITY, INFINITY, INFINITY, NAN,
150 ALL_STD_EXCEPT, FE_INVALID);
151 testall(INFINITY, -1.0, INFINITY, NAN,
152 ALL_STD_EXCEPT, FE_INVALID);
154 test(fmaf, FLT_MAX, FLT_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
155 test(fma, DBL_MAX, DBL_MAX, -INFINITY, -INFINITY, ALL_STD_EXCEPT, 0);
156 test(fmal, LDBL_MAX, LDBL_MAX, -INFINITY, -INFINITY,
158 test(fmaf, FLT_MAX, -FLT_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
159 test(fma, DBL_MAX, -DBL_MAX, INFINITY, INFINITY, ALL_STD_EXCEPT, 0);
160 test(fmal, LDBL_MAX, -LDBL_MAX, INFINITY, INFINITY,
168 testall(NAN, 0.0, 0.0, NAN, ALL_STD_EXCEPT, 0);
169 testall(1.0, NAN, 1.0, NAN, ALL_STD_EXCEPT, 0);
170 testall(1.0, -1.0, NAN, NAN, ALL_STD_EXCEPT, 0);
171 testall(0.0, 0.0, NAN, NAN, ALL_STD_EXCEPT, 0);
172 testall(NAN, NAN, NAN, NAN, ALL_STD_EXCEPT, 0);
174 /* x*y should not raise an inexact/overflow/underflow if z is NaN. */
175 testall(M_PI, M_PI, NAN, NAN, ALL_STD_EXCEPT, 0);
176 test(fmaf, FLT_MIN, FLT_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
177 test(fma, DBL_MIN, DBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
178 test(fmal, LDBL_MIN, LDBL_MIN, NAN, NAN, ALL_STD_EXCEPT, 0);
179 test(fmaf, FLT_MAX, FLT_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
180 test(fma, DBL_MAX, DBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
181 test(fmal, LDBL_MAX, LDBL_MAX, NAN, NAN, ALL_STD_EXCEPT, 0);
185 * Tests for cases where z is very small compared to x*y.
191 /* x*y positive, z positive */
192 if (fegetround() == FE_UPWARD) {
193 test(fmaf, 1.0, 1.0, 0x1.0p-100, 1.0 + FLT_EPSILON,
194 ALL_STD_EXCEPT, FE_INEXACT);
195 test(fma, 1.0, 1.0, 0x1.0p-200, 1.0 + DBL_EPSILON,
196 ALL_STD_EXCEPT, FE_INEXACT);
197 test(fmal, 1.0, 1.0, 0x1.0p-200, 1.0 + LDBL_EPSILON,
198 ALL_STD_EXCEPT, FE_INEXACT);
200 testall(0x1.0p100, 1.0, 0x1.0p-100, 0x1.0p100,
201 ALL_STD_EXCEPT, FE_INEXACT);
204 /* x*y negative, z negative */
205 if (fegetround() == FE_DOWNWARD) {
206 test(fmaf, -1.0, 1.0, -0x1.0p-100, -(1.0 + FLT_EPSILON),
207 ALL_STD_EXCEPT, FE_INEXACT);
208 test(fma, -1.0, 1.0, -0x1.0p-200, -(1.0 + DBL_EPSILON),
209 ALL_STD_EXCEPT, FE_INEXACT);
210 test(fmal, -1.0, 1.0, -0x1.0p-200, -(1.0 + LDBL_EPSILON),
211 ALL_STD_EXCEPT, FE_INEXACT);
213 testall(0x1.0p100, -1.0, -0x1.0p-100, -0x1.0p100,
214 ALL_STD_EXCEPT, FE_INEXACT);
217 /* x*y positive, z negative */
218 if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
219 test(fmaf, 1.0, 1.0, -0x1.0p-100, 1.0 - FLT_EPSILON / 2,
220 ALL_STD_EXCEPT, FE_INEXACT);
221 test(fma, 1.0, 1.0, -0x1.0p-200, 1.0 - DBL_EPSILON / 2,
222 ALL_STD_EXCEPT, FE_INEXACT);
223 test(fmal, 1.0, 1.0, -0x1.0p-200, 1.0 - LDBL_EPSILON / 2,
224 ALL_STD_EXCEPT, FE_INEXACT);
226 testall(0x1.0p100, 1.0, -0x1.0p-100, 0x1.0p100,
227 ALL_STD_EXCEPT, FE_INEXACT);
230 /* x*y negative, z positive */
231 if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
232 test(fmaf, -1.0, 1.0, 0x1.0p-100, -1.0 + FLT_EPSILON / 2,
233 ALL_STD_EXCEPT, FE_INEXACT);
234 test(fma, -1.0, 1.0, 0x1.0p-200, -1.0 + DBL_EPSILON / 2,
235 ALL_STD_EXCEPT, FE_INEXACT);
236 test(fmal, -1.0, 1.0, 0x1.0p-200, -1.0 + LDBL_EPSILON / 2,
237 ALL_STD_EXCEPT, FE_INEXACT);
239 testall(-0x1.0p100, 1.0, 0x1.0p-100, -0x1.0p100,
240 ALL_STD_EXCEPT, FE_INEXACT);
245 * Tests for cases where z is very large compared to x*y.
251 /* z positive, x*y positive */
252 if (fegetround() == FE_UPWARD) {
253 test(fmaf, 0x1.0p-50, 0x1.0p-50, 1.0, 1.0 + FLT_EPSILON,
254 ALL_STD_EXCEPT, FE_INEXACT);
255 test(fma, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + DBL_EPSILON,
256 ALL_STD_EXCEPT, FE_INEXACT);
257 test(fmal, 0x1.0p-100, 0x1.0p-100, 1.0, 1.0 + LDBL_EPSILON,
258 ALL_STD_EXCEPT, FE_INEXACT);
260 testall(-0x1.0p-50, -0x1.0p-50, 0x1.0p100, 0x1.0p100,
261 ALL_STD_EXCEPT, FE_INEXACT);
264 /* z negative, x*y negative */
265 if (fegetround() == FE_DOWNWARD) {
266 test(fmaf, -0x1.0p-50, 0x1.0p-50, -1.0, -(1.0 + FLT_EPSILON),
267 ALL_STD_EXCEPT, FE_INEXACT);
268 test(fma, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + DBL_EPSILON),
269 ALL_STD_EXCEPT, FE_INEXACT);
270 test(fmal, -0x1.0p-100, 0x1.0p-100, -1.0, -(1.0 + LDBL_EPSILON),
271 ALL_STD_EXCEPT, FE_INEXACT);
273 testall(0x1.0p-50, -0x1.0p-50, -0x1.0p100, -0x1.0p100,
274 ALL_STD_EXCEPT, FE_INEXACT);
277 /* z negative, x*y positive */
278 if (fegetround() == FE_UPWARD || fegetround() == FE_TOWARDZERO) {
279 test(fmaf, -0x1.0p-50, -0x1.0p-50, -1.0,
280 -1.0 + FLT_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
281 test(fma, -0x1.0p-100, -0x1.0p-100, -1.0,
282 -1.0 + DBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
283 test(fmal, -0x1.0p-100, -0x1.0p-100, -1.0,
284 -1.0 + LDBL_EPSILON / 2, ALL_STD_EXCEPT, FE_INEXACT);
286 testall(0x1.0p-50, 0x1.0p-50, -0x1.0p100, -0x1.0p100,
287 ALL_STD_EXCEPT, FE_INEXACT);
290 /* z positive, x*y negative */
291 if (fegetround() == FE_DOWNWARD || fegetround() == FE_TOWARDZERO) {
292 test(fmaf, 0x1.0p-50, -0x1.0p-50, 1.0, 1.0 - FLT_EPSILON / 2,
293 ALL_STD_EXCEPT, FE_INEXACT);
294 test(fma, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - DBL_EPSILON / 2,
295 ALL_STD_EXCEPT, FE_INEXACT);
296 test(fmal, 0x1.0p-100, -0x1.0p-100, 1.0, 1.0 - LDBL_EPSILON / 2,
297 ALL_STD_EXCEPT, FE_INEXACT);
299 testall(-0x1.0p-50, 0x1.0p-50, 0x1.0p100, 0x1.0p100,
300 ALL_STD_EXCEPT, FE_INEXACT);
308 /* ilogb(x*y) - ilogb(z) = 20 */
309 testrnd(fmaf, -0x1.c139d8p-51, -0x1.600e7ap32, 0x1.26558cp-38,
310 0x1.34e48ap-18, 0x1.34e48cp-18, 0x1.34e48ap-18, 0x1.34e48ap-18,
311 ALL_STD_EXCEPT, FE_INEXACT);
312 testrnd(fma, -0x1.c139d7b84f1a3p-51, -0x1.600e7a2a16484p32,
313 0x1.26558cac31580p-38, 0x1.34e48a78aae97p-18,
314 0x1.34e48a78aae97p-18, 0x1.34e48a78aae96p-18,
315 0x1.34e48a78aae96p-18, ALL_STD_EXCEPT, FE_INEXACT);
316 #if LDBL_MANT_DIG == 113
317 testrnd(fmal, -0x1.c139d7b84f1a3079263afcc5bae3p-51L,
318 -0x1.600e7a2a164840edbe2e7d301a72p32L,
319 0x1.26558cac315807eb07e448042101p-38L,
320 0x1.34e48a78aae96c76ed36077dd387p-18L,
321 0x1.34e48a78aae96c76ed36077dd388p-18L,
322 0x1.34e48a78aae96c76ed36077dd387p-18L,
323 0x1.34e48a78aae96c76ed36077dd387p-18L,
324 ALL_STD_EXCEPT, FE_INEXACT);
325 #elif LDBL_MANT_DIG == 64
326 testrnd(fmal, -0x1.c139d7b84f1a307ap-51L, -0x1.600e7a2a164840eep32L,
327 0x1.26558cac315807ecp-38L, 0x1.34e48a78aae96c78p-18L,
328 0x1.34e48a78aae96c78p-18L, 0x1.34e48a78aae96c76p-18L,
329 0x1.34e48a78aae96c76p-18L, ALL_STD_EXCEPT, FE_INEXACT);
330 #elif LDBL_MANT_DIG == 53
331 testrnd(fmal, -0x1.c139d7b84f1a3p-51L, -0x1.600e7a2a16484p32L,
332 0x1.26558cac31580p-38L, 0x1.34e48a78aae97p-18L,
333 0x1.34e48a78aae97p-18L, 0x1.34e48a78aae96p-18L,
334 0x1.34e48a78aae96p-18L, ALL_STD_EXCEPT, FE_INEXACT);
337 /* ilogb(x*y) - ilogb(z) = -40 */
338 testrnd(fmaf, 0x1.98210ap53, 0x1.9556acp-24, 0x1.d87da4p70,
339 0x1.d87da4p70, 0x1.d87da6p70, 0x1.d87da4p70, 0x1.d87da4p70,
340 ALL_STD_EXCEPT, FE_INEXACT);
341 testrnd(fma, 0x1.98210ac83fe2bp53, 0x1.9556ac1475f0fp-24,
342 0x1.d87da3aafc60ep70, 0x1.d87da3aafda40p70,
343 0x1.d87da3aafda40p70, 0x1.d87da3aafda3fp70,
344 0x1.d87da3aafda3fp70, ALL_STD_EXCEPT, FE_INEXACT);
345 #if LDBL_MANT_DIG == 113
346 testrnd(fmal, 0x1.98210ac83fe2a8f65b6278b74cebp53L,
347 0x1.9556ac1475f0f28968b61d0de65ap-24L,
348 0x1.d87da3aafc60d830aa4c6d73b749p70L,
349 0x1.d87da3aafda3f36a69eb86488224p70L,
350 0x1.d87da3aafda3f36a69eb86488225p70L,
351 0x1.d87da3aafda3f36a69eb86488224p70L,
352 0x1.d87da3aafda3f36a69eb86488224p70L,
353 ALL_STD_EXCEPT, FE_INEXACT);
354 #elif LDBL_MANT_DIG == 64
355 testrnd(fmal, 0x1.98210ac83fe2a8f6p53L, 0x1.9556ac1475f0f28ap-24L,
356 0x1.d87da3aafc60d83p70L, 0x1.d87da3aafda3f36ap70L,
357 0x1.d87da3aafda3f36ap70L, 0x1.d87da3aafda3f368p70L,
358 0x1.d87da3aafda3f368p70L, ALL_STD_EXCEPT, FE_INEXACT);
359 #elif LDBL_MANT_DIG == 53
360 testrnd(fmal, 0x1.98210ac83fe2bp53L, 0x1.9556ac1475f0fp-24L,
361 0x1.d87da3aafc60ep70L, 0x1.d87da3aafda40p70L,
362 0x1.d87da3aafda40p70L, 0x1.d87da3aafda3fp70L,
363 0x1.d87da3aafda3fp70L, ALL_STD_EXCEPT, FE_INEXACT);
368 main(int argc, char *argv[])
370 int rmodes[] = { FE_TONEAREST, FE_UPWARD, FE_DOWNWARD, FE_TOWARDZERO };
375 for (i = 0; i < 4; i++) {
376 fesetround(rmodes[i]);
378 printf("ok %d - fma zeroes\n", i + 1);
381 for (i = 0; i < 4; i++) {
382 fesetround(rmodes[i]);
384 printf("ok %d - fma infinities\n", i + 5);
387 fesetround(FE_TONEAREST);
389 printf("ok 9 - fma NaNs\n");
391 for (i = 0; i < 4; i++) {
392 fesetround(rmodes[i]);
394 printf("ok %d - fma small z\n", i + 10);
397 for (i = 0; i < 4; i++) {
398 fesetround(rmodes[i]);
400 printf("ok %d - fma big z\n", i + 14);
403 fesetround(FE_TONEAREST);
405 printf("ok 18 - fma accuracy\n");
409 * - Tests for subnormals
410 * - Cancellation tests (e.g., z = (double)x*y, but x*y is inexact)