1 /*-
2 * Copyright (c) 2005 David Schultz <das@FreeBSD.org>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
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.
13 *
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
24 * SUCH DAMAGE.
25 */
26
27 /*
28 * Test the correctness of nextafter{,f,l} and nexttoward{,f,l}.
29 */
30
31 #include <sys/cdefs.h>
32 #include <fenv.h>
33 #include <float.h>
34 #include <math.h>
35 #include <stdio.h>
36 #include <stdlib.h>
37
38 #ifdef __i386__
39 #include <ieeefp.h>
40 #endif
41
42 #include "test-utils.h"
43
44 #define test(exp, ans, ex) do { \
45 double __ans = (ans); \
46 feclearexcept(ALL_STD_EXCEPT); \
47 _testl(#exp, __LINE__, (exp), __ans, (ex)); \
48 } while (0)
49 #define testf(exp, ans, ex) do { \
50 float __ans = (ans); \
51 feclearexcept(ALL_STD_EXCEPT); \
52 _testl(#exp, __LINE__, (exp), __ans, (ex)); \
53 } while (0)
54 #define testl(exp, ans, ex) do { \
55 long double __ans = (ans); \
56 feclearexcept(ALL_STD_EXCEPT); \
57 _testl(#exp, __LINE__, (exp), __ans, (ex)); \
58 } while (0)
59 #define testboth(arg1, arg2, ans, ex, prec) do { \
60 test##prec(nextafter##prec((arg1), (arg2)), (ans), (ex)); \
61 test##prec(nexttoward##prec((arg1), (arg2)), (ans), (ex)); \
62 } while (0)
63 #define testall(arg1, arg2, ans, ex) do { \
64 testboth((arg1), (arg2), (ans), (ex), ); \
65 testboth((arg1), (arg2), (ans), (ex), f); \
66 testboth((arg1), (arg2), (ans), (ex), l); \
67 } while (0)
68
69 static void _testl(const char *, int, long double, long double, int);
70 static double idd(double);
71 static float idf(float);
72
73 static const int ex_under = FE_UNDERFLOW | FE_INEXACT; /* shorthand */
74 static const int ex_over = FE_OVERFLOW | FE_INEXACT;
75 static const long double ldbl_eps = LDBL_EPSILON;
76
77
78
79 ATF_TC_WITHOUT_HEAD(zeros);
ATF_TC_BODY(zeros,tc)80 ATF_TC_BODY(zeros, tc)
81 {
82 long double ldbl_small;
83
84 #ifdef __i386__
85 fpsetprec(FP_PE);
86 #endif
87 /*
88 * We can't use a compile-time constant here because gcc on
89 * FreeBSD/i386 assumes long doubles are truncated to the
90 * double format.
91 */
92 ldbl_small = ldexpl(1.0, LDBL_MIN_EXP - LDBL_MANT_DIG);
93
94 /*
95 * Special cases involving zeroes.
96 */
97 #define ztest(prec) \
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)
102
103 ztest();
104 ztest(f);
105 ztest(l);
106 #undef ztest
107
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)
113
114 stest(nextafter, 0x1p-1074, );
115 stest(nextafterf, 0x1p-149f, f);
116 stest(nextafterl, ldbl_small, l);
117 stest(nexttoward, 0x1p-1074, );
118 stest(nexttowardf, 0x1p-149f, f);
119 stest(nexttowardl, ldbl_small, l);
120 #undef stest
121 }
122
123 ATF_TC_WITHOUT_HEAD(eq_and_nan);
ATF_TC_BODY(eq_and_nan,tc)124 ATF_TC_BODY(eq_and_nan, tc)
125 {
126 /*
127 * `x == y' and NaN tests
128 */
129 testall(42.0, 42.0, 42.0, 0);
130 testall(-42.0, -42.0, -42.0, 0);
131 testall(INFINITY, INFINITY, INFINITY, 0);
132 testall(-INFINITY, -INFINITY, -INFINITY, 0);
133 testall(NAN, 42.0, NAN, 0);
134 testall(42.0, NAN, NAN, 0);
135 testall(NAN, NAN, NAN, 0);
136 }
137
138 ATF_TC_WITHOUT_HEAD(ordinary);
ATF_TC_BODY(ordinary,tc)139 ATF_TC_BODY(ordinary, tc)
140 {
141 /*
142 * Tests where x is an ordinary normalized number
143 */
144 testboth(1.0, 2.0, 1.0 + DBL_EPSILON, 0, );
145 testboth(1.0, -INFINITY, 1.0 - DBL_EPSILON / 2, 0, );
146 testboth(1.0, 2.0, 1.0 + FLT_EPSILON, 0, f);
147 testboth(1.0, -INFINITY, 1.0 - FLT_EPSILON / 2, 0, f);
148 testboth(1.0, 2.0, 1.0 + ldbl_eps, 0, l);
149 testboth(1.0, -INFINITY, 1.0 - ldbl_eps / 2, 0, l);
150
151 testboth(-1.0, 2.0, -1.0 + DBL_EPSILON / 2, 0, );
152 testboth(-1.0, -INFINITY, -1.0 - DBL_EPSILON, 0, );
153 testboth(-1.0, 2.0, -1.0 + FLT_EPSILON / 2, 0, f);
154 testboth(-1.0, -INFINITY, -1.0 - FLT_EPSILON, 0, f);
155 testboth(-1.0, 2.0, -1.0 + ldbl_eps / 2, 0, l);
156 testboth(-1.0, -INFINITY, -1.0 - ldbl_eps, 0, l);
157
158 /* Cases where nextafter(...) != nexttoward(...) */
159 test(nexttoward(1.0, 1.0 + ldbl_eps), 1.0 + DBL_EPSILON, 0);
160 testf(nexttowardf(1.0, 1.0 + ldbl_eps), 1.0 + FLT_EPSILON, 0);
161 testl(nexttowardl(1.0, 1.0 + ldbl_eps), 1.0 + ldbl_eps, 0);
162 }
163
164 ATF_TC_WITHOUT_HEAD(boundaries);
ATF_TC_BODY(boundaries,tc)165 ATF_TC_BODY(boundaries, tc)
166 {
167 /*
168 * Tests at word boundaries, normalization boundaries, etc.
169 */
170 testboth(0x1.87654ffffffffp+0, INFINITY, 0x1.87655p+0, 0, );
171 testboth(0x1.87655p+0, -INFINITY, 0x1.87654ffffffffp+0, 0, );
172 testboth(0x1.fffffffffffffp+0, INFINITY, 0x1p1, 0, );
173 testboth(0x1p1, -INFINITY, 0x1.fffffffffffffp+0, 0, );
174 testboth(0x0.fffffffffffffp-1022, INFINITY, 0x1p-1022, 0, );
175 testboth(0x1p-1022, -INFINITY, 0x0.fffffffffffffp-1022, ex_under, );
176
177 testboth(0x1.fffffep0f, INFINITY, 0x1p1, 0, f);
178 testboth(0x1p1, -INFINITY, 0x1.fffffep0f, 0, f);
179 testboth(0x0.fffffep-126f, INFINITY, 0x1p-126f, 0, f);
180 testboth(0x1p-126f, -INFINITY, 0x0.fffffep-126f, ex_under, f);
181
182 #if LDBL_MANT_DIG == 53
183 testboth(0x1.87654ffffffffp+0L, INFINITY, 0x1.87655p+0L, 0, l);
184 testboth(0x1.87655p+0L, -INFINITY, 0x1.87654ffffffffp+0L, 0, l);
185 testboth(0x1.fffffffffffffp+0L, INFINITY, 0x1p1L, 0, l);
186 testboth(0x1p1L, -INFINITY, 0x1.fffffffffffffp+0L, 0, l);
187 testboth(0x0.fffffffffffffp-1022L, INFINITY, 0x1p-1022L, 0, l);
188 testboth(0x1p-1022L, -INFINITY, 0x0.fffffffffffffp-1022L, ex_under, l);
189 #elif LDBL_MANT_DIG == 64 && !defined(__i386)
190 testboth(0x1.87654321fffffffep+0L, INFINITY, 0x1.87654322p+0L, 0, l);
191 testboth(0x1.87654322p+0L, -INFINITY, 0x1.87654321fffffffep+0L, 0, l);
192 testboth(0x1.fffffffffffffffep0L, INFINITY, 0x1p1L, 0, l);
193 testboth(0x1p1L, -INFINITY, 0x1.fffffffffffffffep0L, 0, l);
194 testboth(0x0.fffffffffffffffep-16382L, INFINITY, 0x1p-16382L, 0, l);
195 testboth(0x1p-16382L, -INFINITY,
196 0x0.fffffffffffffffep-16382L, ex_under, l);
197 #elif LDBL_MANT_DIG == 113
198 testboth(0x1.876543210987ffffffffffffffffp+0L, INFINITY,
199 0x1.876543210988p+0, 0, l);
200 testboth(0x1.876543210988p+0L, -INFINITY,
201 0x1.876543210987ffffffffffffffffp+0L, 0, l);
202 testboth(0x1.ffffffffffffffffffffffffffffp0L, INFINITY, 0x1p1L, 0, l);
203 testboth(0x1p1L, -INFINITY, 0x1.ffffffffffffffffffffffffffffp0L, 0, l);
204 testboth(0x0.ffffffffffffffffffffffffffffp-16382L, INFINITY,
205 0x1p-16382L, 0, l);
206 testboth(0x1p-16382L, -INFINITY,
207 0x0.ffffffffffffffffffffffffffffp-16382L, ex_under, l);
208 #endif
209 }
210
211 ATF_TC_WITHOUT_HEAD(overflow);
ATF_TC_BODY(overflow,tc)212 ATF_TC_BODY(overflow, tc)
213 {
214 long double ldbl_max;
215 /*
216 * We can't use a compile-time constant here because gcc on
217 * FreeBSD/i386 assumes long doubles are truncated to the
218 * double format.
219 */
220 ldbl_max = ldexpl(1.0 - ldbl_eps / 2, LDBL_MAX_EXP);
221
222 /*
223 * Overflow tests
224 */
225 test(idd(nextafter(DBL_MAX, INFINITY)), INFINITY, ex_over);
226 test(idd(nextafter(INFINITY, 0.0)), DBL_MAX, 0);
227 test(idd(nexttoward(DBL_MAX, DBL_MAX * 2.0L)), INFINITY, ex_over);
228 #if LDBL_MANT_DIG > 53
229 test(idd(nexttoward(INFINITY, DBL_MAX * 2.0L)), DBL_MAX, 0);
230 #endif
231
232 testf(idf(nextafterf(FLT_MAX, INFINITY)), INFINITY, ex_over);
233 testf(idf(nextafterf(INFINITY, 0.0)), FLT_MAX, 0);
234 testf(idf(nexttowardf(FLT_MAX, FLT_MAX * 2.0)), INFINITY, ex_over);
235 testf(idf(nexttowardf(INFINITY, FLT_MAX * 2.0)), FLT_MAX, 0);
236
237 testboth(ldbl_max, INFINITY, INFINITY, ex_over, l);
238 testboth(INFINITY, 0.0, ldbl_max, 0, l);
239 }
240
241 static void
_testl(const char * exp,int line,long double actual,long double expected,int except)242 _testl(const char *exp, int line, long double actual, long double expected,
243 int except)
244 {
245 int actual_except;
246
247 actual_except = fetestexcept(ALL_STD_EXCEPT);
248 if (!fpequal_cs(actual, expected, true)) {
249 atf_tc_fail_check(__FILE__, line,
250 "%s returned %La, expecting %La\n", exp, actual, expected);
251 }
252 if (actual_except != except) {
253 atf_tc_fail_check(__FILE__, line,
254 "%s raised 0x%x, expecting 0x%x\n", exp, actual_except,
255 except);
256 }
257 }
258
259 /*
260 * The idd() and idf() routines ensure that doubles and floats are
261 * converted to their respective types instead of stored in the FPU
262 * with extra precision.
263 */
264 static double
idd(double x)265 idd(double x)
266 {
267 return (x);
268 }
269
270 static float
idf(float x)271 idf(float x)
272 {
273 return (x);
274 }
275
ATF_TP_ADD_TCS(tp)276 ATF_TP_ADD_TCS(tp)
277 {
278 ATF_TP_ADD_TC(tp, zeros);
279 ATF_TP_ADD_TC(tp, ordinary);
280 ATF_TP_ADD_TC(tp, eq_and_nan);
281 ATF_TP_ADD_TC(tp, boundaries);
282 ATF_TP_ADD_TC(tp, overflow);
283
284 return (atf_no_error());
285 }
286