2 * Copyright (c) 2005 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 * Test the correctness of nextafter{,f,l} and nexttoward{,f,l}.
31 #include <sys/cdefs.h>
32 __FBSDID("$FreeBSD$");
44 #define ALL_STD_EXCEPT (FE_DIVBYZERO | FE_INEXACT | FE_INVALID |\
45 FE_OVERFLOW | FE_UNDERFLOW)
46 #define test(exp, ans, ex) do { \
47 double __ans = (ans); \
48 feclearexcept(ALL_STD_EXCEPT); \
49 _testl(#exp, __LINE__, (exp), __ans, (ex)); \
51 #define testf(exp, ans, ex) do { \
52 float __ans = (ans); \
53 feclearexcept(ALL_STD_EXCEPT); \
54 _testl(#exp, __LINE__, (exp), __ans, (ex)); \
56 #define testl(exp, ans, ex) do { \
57 long double __ans = (ans); \
58 feclearexcept(ALL_STD_EXCEPT); \
59 _testl(#exp, __LINE__, (exp), __ans, (ex)); \
61 #define testboth(arg1, arg2, ans, ex, prec) do { \
62 test##prec(nextafter##prec((arg1), (arg2)), (ans), (ex)); \
63 test##prec(nexttoward##prec((arg1), (arg2)), (ans), (ex)); \
65 #define testall(arg1, arg2, ans, ex) do { \
66 testboth((arg1), (arg2), (ans), (ex), ); \
67 testboth((arg1), (arg2), (ans), (ex), f); \
68 testboth((arg1), (arg2), (ans), (ex), l); \
71 static void _testl(const char *, int, long double, long double, int);
72 static double idd(double);
73 static float idf(float);
76 main(int argc, char *argv[])
78 static const int ex_under = FE_UNDERFLOW | FE_INEXACT; /* shorthand */
79 static const int ex_over = FE_OVERFLOW | FE_INEXACT;
88 * We can't use a compile-time constant here because gcc on
89 * FreeBSD/i386 assumes long doubles are truncated to the
92 ldbl_eps = ldexpl(1.0, LDBL_MIN_EXP - LDBL_MANT_DIG);
95 * Special cases involving zeroes.
98 test##prec(copysign##prec(1.0, nextafter##prec(0.0, -0.0)), -1.0, 0); \
99 test##prec(copysign##prec(1.0, nextafter##prec(-0.0, 0.0)), 1.0, 0); \
100 test##prec(copysign##prec(1.0, nexttoward##prec(0.0, -0.0)), -1.0, 0);\
101 test##prec(copysign##prec(1.0, nexttoward##prec(-0.0, 0.0)), 1.0, 0)
108 #define stest(next, eps, prec) \
109 test##prec(next(-0.0, 42.0), eps, ex_under); \
110 test##prec(next(0.0, -42.0), -eps, ex_under); \
111 test##prec(next(0.0, INFINITY), eps, ex_under); \
112 test##prec(next(-0.0, -INFINITY), -eps, ex_under)
114 stest(nextafter, 0x1p-1074, );
115 stest(nextafterf, 0x1p-149f, f);
116 stest(nextafterl, ldbl_eps, l);
117 stest(nexttoward, 0x1p-1074, );
118 stest(nexttowardf, 0x1p-149f, f);
119 stest(nexttowardl, ldbl_eps, l);
122 printf("ok 1 - next\n");
125 * `x == y' and NaN tests
127 testall(42.0, 42.0, 42.0, 0);
128 testall(-42.0, -42.0, -42.0, 0);
129 testall(INFINITY, INFINITY, INFINITY, 0);
130 testall(-INFINITY, -INFINITY, -INFINITY, 0);
131 testall(NAN, 42.0, NAN, 0);
132 testall(42.0, NAN, NAN, 0);
133 testall(NAN, NAN, NAN, 0);
135 printf("ok 2 - next\n");
138 * Tests where x is an ordinary normalized number
140 testboth(1.0, 2.0, 1.0 + DBL_EPSILON, 0, );
141 testboth(1.0, -INFINITY, 1.0 - DBL_EPSILON/2, 0, );
142 testboth(1.0, 2.0, 1.0 + FLT_EPSILON, 0, f);
143 testboth(1.0, -INFINITY, 1.0 - FLT_EPSILON/2, 0, f);
144 testboth(1.0, 2.0, 1.0 + LDBL_EPSILON, 0, l);
145 testboth(1.0, -INFINITY, 1.0 - LDBL_EPSILON/2, 0, l);
147 testboth(-1.0, 2.0, -1.0 + DBL_EPSILON/2, 0, );
148 testboth(-1.0, -INFINITY, -1.0 - DBL_EPSILON, 0, );
149 testboth(-1.0, 2.0, -1.0 + FLT_EPSILON/2, 0, f);
150 testboth(-1.0, -INFINITY, -1.0 - FLT_EPSILON, 0, f);
151 testboth(-1.0, 2.0, -1.0 + LDBL_EPSILON/2, 0, l);
152 testboth(-1.0, -INFINITY, -1.0 - LDBL_EPSILON, 0, l);
154 /* Cases where nextafter(...) != nexttoward(...) */
155 test(nexttoward(1.0, 1.0 + LDBL_EPSILON), 1.0 + DBL_EPSILON, 0);
156 testf(nexttowardf(1.0, 1.0 + LDBL_EPSILON), 1.0 + FLT_EPSILON, 0);
157 testl(nexttowardl(1.0, 1.0 + LDBL_EPSILON), 1.0 + LDBL_EPSILON, 0);
159 printf("ok 3 - next\n");
162 * Tests at word boundaries, normalization boundaries, etc.
164 testboth(0x1.87654ffffffffp+0, INFINITY, 0x1.87655p+0, 0, );
165 testboth(0x1.87655p+0, -INFINITY, 0x1.87654ffffffffp+0, 0, );
166 testboth(0x1.fffffffffffffp+0, INFINITY, 0x1p1, 0, );
167 testboth(0x1p1, -INFINITY, 0x1.fffffffffffffp+0, 0, );
168 testboth(0x0.fffffffffffffp-1022, INFINITY, 0x1p-1022, 0, );
169 testboth(0x1p-1022, -INFINITY, 0x0.fffffffffffffp-1022, ex_under, );
171 testboth(0x1.fffffep0f, INFINITY, 0x1p1, 0, f);
172 testboth(0x1p1, -INFINITY, 0x1.fffffep0f, 0, f);
173 testboth(0x0.fffffep-126f, INFINITY, 0x1p-126f, 0, f);
174 testboth(0x1p-126f, -INFINITY, 0x0.fffffep-126f, ex_under, f);
176 #if LDBL_MANT_DIG == 53
177 testboth(0x1.87654ffffffffp+0L, INFINITY, 0x1.87655p+0L, 0, l);
178 testboth(0x1.87655p+0L, -INFINITY, 0x1.87654ffffffffp+0L, 0, l);
179 testboth(0x1.fffffffffffffp+0L, INFINITY, 0x1p1L, 0, l);
180 testboth(0x1p1L, -INFINITY, 0x1.fffffffffffffp+0L, 0, l);
181 testboth(0x0.fffffffffffffp-1022L, INFINITY, 0x1p-1022L, 0, l);
182 testboth(0x1p-1022L, -INFINITY, 0x0.fffffffffffffp-1022L, ex_under, l);
183 #elif LDBL_MANT_DIG == 64
184 testboth(0x1.87654321fffffffep+0L, INFINITY, 0x1.87654322p+0L, 0, l);
185 testboth(0x1.87654322p+0L, -INFINITY, 0x1.87654321fffffffep+0L, 0, l);
186 testboth(0x1.fffffffffffffffep0L, INFINITY, 0x1p1L, 0, l);
187 testboth(0x1p1L, -INFINITY, 0x1.fffffffffffffffep0L, 0, l);
188 testboth(0x0.fffffffffffffffep-16382L, INFINITY, 0x1p-16382L, 0, l);
189 testboth(0x1p-16382L, -INFINITY,
190 0x0.fffffffffffffffep-16382L, ex_under, l);
191 #elif LDBL_MANT_DIG == 113
192 testboth(0x1.876543210987ffffffffffffffffp+0L, INFINITY,
193 0x1.876543210988p+0, 0, l);
194 testboth(0x1.876543210988p+0L, -INFINITY,
195 0x1.876543210987ffffffffffffffffp+0L, 0, l);
196 testboth(0x1.ffffffffffffffffffffffffffffp0L, INFINITY, 0x1p1L, 0, l);
197 testboth(0x1p1L, -INFINITY, 0x1.ffffffffffffffffffffffffffffp0L, 0, l);
198 testboth(0x0.ffffffffffffffffffffffffffffp-16382L, INFINITY,
200 testboth(0x1p-16382L, -INFINITY,
201 0x0.ffffffffffffffffffffffffffffp-16382L, ex_under, l);
204 printf("ok 4 - next\n");
209 test(idd(nextafter(DBL_MAX, INFINITY)), INFINITY, ex_over);
210 test(idd(nextafter(INFINITY, 0.0)), DBL_MAX, 0);
211 test(idd(nexttoward(DBL_MAX, DBL_MAX * 2.0L)), INFINITY, ex_over);
212 test(idd(nexttoward(INFINITY, DBL_MAX * 2.0L)), DBL_MAX, 0);
214 testf(idf(nextafterf(FLT_MAX, INFINITY)), INFINITY, ex_over);
215 testf(idf(nextafterf(INFINITY, 0.0)), FLT_MAX, 0);
216 testf(idf(nexttowardf(FLT_MAX, FLT_MAX * 2.0)), INFINITY, ex_over);
217 testf(idf(nexttowardf(INFINITY, FLT_MAX * 2.0)), FLT_MAX, 0);
219 testboth(LDBL_MAX, INFINITY, INFINITY, ex_over, l);
220 testboth(INFINITY, 0.0, LDBL_MAX, 0, l);
222 printf("ok 5 - next\n");
228 _testl(const char *exp, int line, long double actual, long double expected,
233 actual_except = fetestexcept(ALL_STD_EXCEPT);
234 if (actual != expected && !(isnan(actual) && isnan(expected))) {
235 fprintf(stderr, "%d: %s returned %La, expecting %La\n",
236 line, exp, actual, expected);
239 if (actual_except != except) {
240 fprintf(stderr, "%d: %s raised 0x%x, expecting 0x%x\n",
241 line, exp, actual_except, except);
247 * The idd() and idf() routines ensure that doubles and floats are
248 * converted to their respective types instead of stored in the FPU
249 * with extra precision.