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[ceph.git] / ceph / src / boost / libs / multiprecision / test / test_cpp_bin_float.cpp
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7c673cae
FG		 1// Copyright John Maddock 2013.
2
3// Use, modification and distribution are subject to the
4// Boost Software License, Version 1.0.
5// (See accompanying file LICENSE_1_0.txt
6// or copy at http://www.boost.org/LICENSE_1_0.txt)
7
8#ifdef _MSC_VER
92f5a8d4 9#define _SCL_SECURE_NO_WARNINGS
7c673cae
FG		 10#endif
11
12#include <boost/multiprecision/cpp_bin_float.hpp>
13#ifdef TEST_MPFR
14#include <boost/multiprecision/mpfr.hpp>
15#endif
16#include <boost/random/mersenne_twister.hpp>
17#include <boost/random/uniform_int.hpp>
18#include "libs/multiprecision/test/test.hpp"
19#include <iostream>
20#include <iomanip>
21
22template <class T>
23T generate_random()
24{
92f5a8d4 25 typedef int e_type;
7c673cae 26 static boost::random::mt19937 gen;
92f5a8d4
TL		 27 T val = gen();
28 T prev_val = -1;
29 while (val != prev_val)
7c673cae
FG		 30 {
31 val *= (gen.max)();
32 prev_val = val;
33 val += gen();
34 }
35 e_type e;
36 val = frexp(val, &e);
37
38 static boost::random::uniform_int_distribution<e_type> ui(-20, 20);
39 return ldexp(val, ui(gen));
40}
41
7c673cae
FG		 42using namespace boost::multiprecision;
43#ifdef TEST_MPFR
44typedef number<mpfr_float_backend<35> > good_type;
45#else
46typedef double good_type;
47#endif
48typedef number<cpp_bin_float<std::numeric_limits<good_type>::digits, digit_base_2>, et_off> test_type;
49
50void test_special_cases()
51{
92f5a8d4
TL		 52 test_type max_val = (std::numeric_limits<test_type>::max)();
53 test_type min_val = (std::numeric_limits<test_type>::min)();
54 test_type eps = std::numeric_limits<test_type>::epsilon();
55 test_type inf_val = (std::numeric_limits<test_type>::infinity)();
56 test_type nan_val = (std::numeric_limits<test_type>::quiet_NaN)();
57 test_type half = 0.5;
7c673cae 58 test_type one_point_5 = 1.5;
92f5a8d4 59
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FG		 60 BOOST_CHECK((boost::math::isnormal)(max_val));
61 BOOST_CHECK((boost::math::isnormal)(-max_val));
62 BOOST_CHECK((boost::math::isnormal)(min_val));
63 BOOST_CHECK((boost::math::isnormal)(-min_val));
64 BOOST_CHECK((boost::math::isinf)(inf_val));
65 BOOST_CHECK((boost::math::isinf)(-inf_val));
66 BOOST_CHECK((boost::math::isnan)(nan_val));
67 BOOST_CHECK((boost::math::isnan)(-nan_val));
68
92f5a8d4 69 if (std::numeric_limits<test_type>::has_denorm)
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FG		 70 min_val = std::numeric_limits<test_type>::denorm_min();
71
72 // Adding epsilon will increment 1.0:
73 BOOST_CHECK(test_type(1) + eps != test_type(1));
74 BOOST_CHECK(test_type(1) + eps / 2 == test_type(1));
75 // But it's not the smallest value that will do that:
76 test_type small = 1 + eps;
92f5a8d4 77 small = ldexp(small, -std::numeric_limits<test_type>::digits);
7c673cae 78 BOOST_CHECK(test_type(1) + small != test_type(1));
92f5a8d4 79 // And if we increment 1.0 first, then an even smaller
7c673cae
FG		 80 // addition will round up:
81 test_type one_next = test_type(1) + eps;
82 BOOST_CHECK(one_next + eps / 2 != one_next);
83
84 // Overflow:
85 BOOST_CHECK_EQUAL(max_val + max_val * eps, inf_val);
86 BOOST_CHECK_EQUAL(-max_val - max_val * eps, -inf_val);
87 BOOST_CHECK_EQUAL(max_val * 2, inf_val);
88 BOOST_CHECK_EQUAL(max_val * -2, -inf_val);
89 BOOST_CHECK_EQUAL(max_val / half, inf_val);
90 BOOST_CHECK_EQUAL(max_val / -half, -inf_val);
91 BOOST_CHECK_EQUAL(max_val / min_val, inf_val);
92 BOOST_CHECK_EQUAL(max_val / -min_val, -inf_val);
93 // Underflow:
94 BOOST_CHECK_EQUAL(min_val * 2 - one_point_5 * min_val, 0);
95 BOOST_CHECK_EQUAL(-min_val * 2 + one_point_5 * min_val, 0);
96 BOOST_CHECK_EQUAL(min_val / 2, 0);
97 BOOST_CHECK_EQUAL(min_val / max_val, 0);
98 BOOST_CHECK_EQUAL(min_val * half, 0);
99 BOOST_CHECK_EQUAL(min_val - min_val, 0);
100 BOOST_CHECK_EQUAL(max_val - max_val, 0);
101 BOOST_CHECK_EQUAL(-min_val + min_val, 0);
102 BOOST_CHECK_EQUAL(-max_val + max_val, 0);
103 // Things which should not over/underflow:
104 BOOST_CHECK_EQUAL((min_val * 2) / 2, min_val);
105 BOOST_CHECK_EQUAL((max_val / 2) * 2, max_val);
106 BOOST_CHECK_GE((min_val * 2.0000001) / 1.9999999999999999, min_val);
107 BOOST_CHECK_LE((max_val / 2.0000001) * 1.9999999999999999, max_val);
108 BOOST_CHECK_EQUAL(min_val * 2 - min_val, min_val);
109 BOOST_CHECK_EQUAL(max_val / 2 + max_val / 2, max_val);
110 // Things involving zero:
111 BOOST_CHECK_EQUAL(max_val + 0, max_val);
112 BOOST_CHECK_EQUAL(max_val - 0, max_val);
113 BOOST_CHECK_EQUAL(0 + max_val, max_val);
114 BOOST_CHECK_EQUAL(0 - max_val, -max_val);
115 BOOST_CHECK_EQUAL(max_val * 0, 0);
116 BOOST_CHECK_EQUAL(0 * max_val, 0);
117 BOOST_CHECK_EQUAL(max_val / 0, inf_val);
118 BOOST_CHECK_EQUAL(0 / max_val, 0);
119 BOOST_CHECK_EQUAL(-max_val / 0, -inf_val);
120 BOOST_CHECK_EQUAL(0 / -max_val, 0);
121 // Things involving infinity:
122 BOOST_CHECK_EQUAL(inf_val + 2, inf_val);
123 BOOST_CHECK_EQUAL(inf_val - 2, inf_val);
124 BOOST_CHECK_EQUAL(inf_val + -2, inf_val);
125 BOOST_CHECK_EQUAL(inf_val - -2, inf_val);
126 BOOST_CHECK_EQUAL(-inf_val + 2, -inf_val);
127 BOOST_CHECK_EQUAL(-inf_val - 2, -inf_val);
128 BOOST_CHECK_EQUAL(-inf_val + -2, -inf_val);
129 BOOST_CHECK_EQUAL(-inf_val - -2, -inf_val);
130
131 BOOST_CHECK_EQUAL(2 + inf_val, inf_val);
132 BOOST_CHECK_EQUAL(2 - inf_val, -inf_val);
133 BOOST_CHECK_EQUAL(-2 + inf_val, inf_val);
134 BOOST_CHECK_EQUAL(-2 - inf_val, -inf_val);
135 BOOST_CHECK_EQUAL(2 + (-inf_val), -inf_val);
136 BOOST_CHECK_EQUAL(2 - (-inf_val), inf_val);
137 BOOST_CHECK_EQUAL(-2 + (-inf_val), -inf_val);
138 BOOST_CHECK_EQUAL(-2 - (-inf_val), inf_val);
139
140 BOOST_CHECK_EQUAL(sqrt(inf_val), inf_val);
141 BOOST_CHECK(boost::math::isnan(sqrt(-inf_val)));
142
143 BOOST_CHECK_EQUAL(inf_val + test_type(2), inf_val);
144 BOOST_CHECK_EQUAL(inf_val - test_type(2), inf_val);
145 BOOST_CHECK_EQUAL(inf_val + test_type(-2), inf_val);
146 BOOST_CHECK_EQUAL(inf_val - test_type(-2), inf_val);
147 BOOST_CHECK_EQUAL(-inf_val + test_type(2), -inf_val);
148 BOOST_CHECK_EQUAL(-inf_val - test_type(2), -inf_val);
149 BOOST_CHECK_EQUAL(-inf_val + test_type(-2), -inf_val);
150 BOOST_CHECK_EQUAL(-inf_val - test_type(-2), -inf_val);
151
152 BOOST_CHECK_EQUAL(test_type(2) + inf_val, inf_val);
153 BOOST_CHECK_EQUAL(test_type(2) - inf_val, -inf_val);
154 BOOST_CHECK_EQUAL(test_type(-2) + inf_val, inf_val);
155 BOOST_CHECK_EQUAL(test_type(-2) - inf_val, -inf_val);
156 BOOST_CHECK_EQUAL(test_type(2) + (-inf_val), -inf_val);
157 BOOST_CHECK_EQUAL(test_type(2) - (-inf_val), inf_val);
158 BOOST_CHECK_EQUAL(test_type(-2) + (-inf_val), -inf_val);
159 BOOST_CHECK_EQUAL(test_type(-2) - (-inf_val), inf_val);
160
161 BOOST_CHECK((boost::math::isnan)(inf_val - inf_val));
162 BOOST_CHECK_EQUAL(inf_val * 2, inf_val);
163 BOOST_CHECK_EQUAL(-inf_val * 2, -inf_val);
164 BOOST_CHECK_EQUAL(inf_val * -2, -inf_val);
165 BOOST_CHECK_EQUAL(-inf_val * -2, inf_val);
166 BOOST_CHECK_EQUAL(inf_val * test_type(-2), -inf_val);
167 BOOST_CHECK_EQUAL(-inf_val * test_type(-2), inf_val);
168 BOOST_CHECK((boost::math::isnan)(inf_val * 0));
169 BOOST_CHECK((boost::math::isnan)(-inf_val * 0));
170 BOOST_CHECK_EQUAL(inf_val / 2, inf_val);
171 BOOST_CHECK_EQUAL(-inf_val / 2, -inf_val);
172 BOOST_CHECK_EQUAL(inf_val / -2, -inf_val);
173 BOOST_CHECK_EQUAL(-inf_val / -2, inf_val);
174 BOOST_CHECK_EQUAL(inf_val / test_type(-2), -inf_val);
175 BOOST_CHECK_EQUAL(-inf_val / test_type(-2), inf_val);
176 BOOST_CHECK_EQUAL(inf_val / 0, inf_val);
177 BOOST_CHECK_EQUAL(-inf_val / 0, -inf_val);
178 BOOST_CHECK((boost::math::isnan)(inf_val / inf_val));
179 BOOST_CHECK((boost::math::isnan)(-inf_val / inf_val));
180 // Things involving nan:
181 BOOST_CHECK((boost::math::isnan)(nan_val + 2));
182 BOOST_CHECK((boost::math::isnan)(nan_val - 2));
183 BOOST_CHECK((boost::math::isnan)(nan_val + 0));
184 BOOST_CHECK((boost::math::isnan)(nan_val - 0));
185 BOOST_CHECK((boost::math::isnan)(nan_val + inf_val));
186 BOOST_CHECK((boost::math::isnan)(nan_val - inf_val));
187 BOOST_CHECK((boost::math::isnan)(nan_val + nan_val));
188 BOOST_CHECK((boost::math::isnan)(nan_val - nan_val));
189 BOOST_CHECK((boost::math::isnan)(2 + nan_val));
190 BOOST_CHECK((boost::math::isnan)(2 - nan_val));
191 BOOST_CHECK((boost::math::isnan)(0 - nan_val));
192 BOOST_CHECK((boost::math::isnan)(0 - nan_val));
193 BOOST_CHECK((boost::math::isnan)(inf_val + nan_val));
194 BOOST_CHECK((boost::math::isnan)(inf_val - nan_val));
195 BOOST_CHECK((boost::math::isnan)(nan_val * 2));
196 BOOST_CHECK((boost::math::isnan)(nan_val / 2));
197 BOOST_CHECK((boost::math::isnan)(nan_val * 0));
198 BOOST_CHECK((boost::math::isnan)(nan_val / 0));
199 BOOST_CHECK((boost::math::isnan)(nan_val * inf_val));
200 BOOST_CHECK((boost::math::isnan)(nan_val / inf_val));
201 BOOST_CHECK((boost::math::isnan)(nan_val * nan_val));
202 BOOST_CHECK((boost::math::isnan)(nan_val / nan_val));
203 BOOST_CHECK((boost::math::isnan)(2 * nan_val));
204 BOOST_CHECK((boost::math::isnan)(2 / nan_val));
205 BOOST_CHECK((boost::math::isnan)(0 / nan_val));
206 BOOST_CHECK((boost::math::isnan)(0 / nan_val));
207 BOOST_CHECK((boost::math::isnan)(inf_val * nan_val));
208 BOOST_CHECK((boost::math::isnan)(inf_val / nan_val));
209 // Corner cases:
210 BOOST_CHECK_EQUAL((max_val * half) / half, max_val);
211 BOOST_CHECK_EQUAL((max_val / 2) * 2, max_val);
212 BOOST_CHECK_EQUAL((min_val / half) * half, min_val);
213 BOOST_CHECK_EQUAL((min_val * 2) / 2, min_val);
214 BOOST_CHECK_EQUAL(max_val + min_val, max_val);
215 BOOST_CHECK_EQUAL(min_val + max_val, max_val);
216 BOOST_CHECK_EQUAL(max_val - min_val, max_val);
217 BOOST_CHECK_EQUAL(min_val - max_val, -max_val);
218 // Signed zeros:
219 BOOST_CHECK(boost::math::signbit(min_val * -min_val));
220 BOOST_CHECK(boost::math::signbit(min_val * min_val) == 0);
221 BOOST_CHECK(boost::math::signbit(-min_val * -min_val) == 0);
222 BOOST_CHECK(boost::math::signbit(-min_val * min_val));
223 BOOST_CHECK(boost::math::signbit(min_val / max_val) == 0);
224 BOOST_CHECK(boost::math::signbit(min_val / -max_val));
225 BOOST_CHECK(boost::math::signbit(-min_val / -max_val) == 0);
226 BOOST_CHECK(boost::math::signbit(-min_val / max_val));
227 BOOST_CHECK(boost::math::signbit(min_val / 2) == 0);
228 BOOST_CHECK(boost::math::signbit(min_val / -2));
229 BOOST_CHECK(boost::math::signbit(-min_val / -2) == 0);
230 BOOST_CHECK(boost::math::signbit(-min_val / 2));
231 test_type neg_zero = min_val * -min_val;
92f5a8d4 232 test_type zero = 0;
7c673cae
FG		 233 // Arithmetic involving signed zero:
234 BOOST_CHECK_EQUAL(-neg_zero, 0);
235 BOOST_CHECK(!boost::math::signbit(-neg_zero));
236 BOOST_CHECK_EQUAL(neg_zero + 2, 2);
237 BOOST_CHECK_EQUAL(neg_zero + test_type(2), 2);
238 BOOST_CHECK_EQUAL(2 + neg_zero, 2);
239 BOOST_CHECK_EQUAL(test_type(2) + neg_zero, 2);
240 BOOST_CHECK_EQUAL(neg_zero + -2, -2);
241 BOOST_CHECK_EQUAL(neg_zero + test_type(-2), -2);
242 BOOST_CHECK_EQUAL(-2 + neg_zero, -2);
243 BOOST_CHECK_EQUAL(test_type(-2) + neg_zero, -2);
244 BOOST_CHECK_EQUAL(neg_zero - 2, -2);
245 BOOST_CHECK_EQUAL(neg_zero - test_type(2), -2);
246 BOOST_CHECK_EQUAL(2 - neg_zero, 2);
247 BOOST_CHECK_EQUAL(test_type(2) - neg_zero, 2);
248 BOOST_CHECK_EQUAL(neg_zero - -2, 2);
249 BOOST_CHECK_EQUAL(neg_zero - test_type(-2), 2);
250 BOOST_CHECK_EQUAL(-2 - neg_zero, -2);
251 BOOST_CHECK_EQUAL(test_type(-2) - neg_zero, -2);
252 BOOST_CHECK(!boost::math::signbit(test_type(2) + test_type(-2)));
253 BOOST_CHECK(!boost::math::signbit(test_type(2) - test_type(2)));
254 BOOST_CHECK(!boost::math::signbit(test_type(-2) - test_type(-2)));
255 BOOST_CHECK(!boost::math::signbit(test_type(-2) + test_type(2)));
256 BOOST_CHECK(!boost::math::signbit(zero + zero));
257 BOOST_CHECK(!boost::math::signbit(zero - zero));
258 BOOST_CHECK(!boost::math::signbit(neg_zero + zero));
259 BOOST_CHECK(!boost::math::signbit(zero + neg_zero));
260 BOOST_CHECK(boost::math::signbit(neg_zero + neg_zero));
261 BOOST_CHECK(boost::math::signbit(neg_zero - zero));
262 BOOST_CHECK(!boost::math::signbit(zero - neg_zero));
263 BOOST_CHECK(!boost::math::signbit(neg_zero - neg_zero));
264 small = 0.25;
265 BOOST_CHECK(!boost::math::signbit(floor(small)));
266 BOOST_CHECK(!boost::math::signbit(round(small)));
267 BOOST_CHECK(!boost::math::signbit(trunc(small)));
268 small = -small;
269 BOOST_CHECK(boost::math::signbit(ceil(small)));
270 BOOST_CHECK(boost::math::signbit(round(small)));
271 BOOST_CHECK(boost::math::signbit(trunc(small)));
272
7c673cae
FG		 273 BOOST_CHECK_EQUAL(neg_zero * 2, 0);
274 BOOST_CHECK_EQUAL(neg_zero * test_type(2), 0);
275 BOOST_CHECK_EQUAL(2 * neg_zero, 0);
276 BOOST_CHECK_EQUAL(test_type(2) * neg_zero, 0);
277 BOOST_CHECK_EQUAL(neg_zero * -2, 0);
278 BOOST_CHECK_EQUAL(neg_zero * test_type(-2), 0);
279 BOOST_CHECK_EQUAL(-2 * neg_zero, 0);
280 BOOST_CHECK_EQUAL(test_type(-2) * neg_zero, 0);
281 BOOST_CHECK(boost::math::signbit(neg_zero * 2));
282 BOOST_CHECK(boost::math::signbit(neg_zero * test_type(2)));
283 BOOST_CHECK(boost::math::signbit(2 * neg_zero));
284 BOOST_CHECK(boost::math::signbit(test_type(2) * neg_zero));
285 BOOST_CHECK(!boost::math::signbit(neg_zero * -2));
286 BOOST_CHECK(!boost::math::signbit(neg_zero * test_type(-2)));
287 BOOST_CHECK(!boost::math::signbit(-2 * neg_zero));
288 BOOST_CHECK(!boost::math::signbit(test_type(-2) * neg_zero));
289
290 BOOST_CHECK_EQUAL(neg_zero / 2, 0);
291 BOOST_CHECK_EQUAL(neg_zero / test_type(2), 0);
292 BOOST_CHECK_EQUAL(2 / neg_zero, -inf_val);
293 BOOST_CHECK_EQUAL(test_type(2) / neg_zero, -inf_val);
294 BOOST_CHECK_EQUAL(neg_zero / -2, 0);
295 BOOST_CHECK_EQUAL(neg_zero / test_type(-2), 0);
296 BOOST_CHECK_EQUAL(-2 / neg_zero, inf_val);
297 BOOST_CHECK_EQUAL(test_type(-2) / neg_zero, inf_val);
298 BOOST_CHECK(boost::math::signbit(neg_zero / 2));
299 BOOST_CHECK(boost::math::signbit(neg_zero / test_type(2)));
300 BOOST_CHECK(boost::math::signbit(2 / neg_zero));
301 BOOST_CHECK(boost::math::signbit(test_type(2) / neg_zero));
302 BOOST_CHECK(!boost::math::signbit(neg_zero / -2));
303 BOOST_CHECK(!boost::math::signbit(neg_zero / test_type(-2)));
304 BOOST_CHECK(!boost::math::signbit(-2 / neg_zero));
305 BOOST_CHECK(!boost::math::signbit(test_type(-2) / neg_zero));
306
307 BOOST_CHECK(boost::math::signbit(neg_zero.convert_to<double>()));
308 BOOST_CHECK(boost::math::signbit(neg_zero.convert_to<float>()));
309 BOOST_CHECK(boost::math::signbit(neg_zero.convert_to<long double>()));
310 BOOST_CHECK(!boost::math::signbit(zero.convert_to<double>()));
311 BOOST_CHECK(!boost::math::signbit(zero.convert_to<float>()));
312 BOOST_CHECK(!boost::math::signbit(zero.convert_to<long double>()));
313
314 // Conversions to other types of special values:
92f5a8d4 315 if (std::numeric_limits<float>::has_infinity)
7c673cae
FG		 316 {
317 BOOST_CHECK_EQUAL(inf_val.convert_to<float>(), std::numeric_limits<float>::infinity());
318 BOOST_CHECK_EQUAL((-inf_val).convert_to<float>(), -std::numeric_limits<float>::infinity());
319 }
92f5a8d4 320 if (std::numeric_limits<float>::has_quiet_NaN)
7c673cae
FG		 321 {
322 BOOST_CHECK((boost::math::isnan)(nan_val.convert_to<float>()));
323 }
92f5a8d4 324 if (std::numeric_limits<double>::has_infinity)
7c673cae
FG		 325 {
326 BOOST_CHECK_EQUAL(inf_val.convert_to<double>(), std::numeric_limits<double>::infinity());
327 BOOST_CHECK_EQUAL((-inf_val).convert_to<double>(), -std::numeric_limits<double>::infinity());
328 }
92f5a8d4 329 if (std::numeric_limits<double>::has_quiet_NaN)
7c673cae
FG		 330 {
331 BOOST_CHECK((boost::math::isnan)(nan_val.convert_to<double>()));
332 }
92f5a8d4 333 if (std::numeric_limits<long double>::has_infinity)
7c673cae
FG		 334 {
335 BOOST_CHECK_EQUAL(inf_val.convert_to<long double>(), std::numeric_limits<long double>::infinity());
336 BOOST_CHECK_EQUAL((-inf_val).convert_to<long double>(), -std::numeric_limits<long double>::infinity());
337 }
92f5a8d4 338 if (std::numeric_limits<long double>::has_quiet_NaN)
7c673cae
FG		 339 {
340 BOOST_CHECK((boost::math::isnan)(nan_val.convert_to<long double>()));
341 }
b32b8144
FG		 342 //
343 // Bug https://svn.boost.org/trac/boost/attachment/ticket/12580
344 //
345 using std::ldexp;
346 test_type a(1);
347 test_type b = ldexp(test_type(0.99), -std::numeric_limits<test_type>::digits);
348 good_type ga(1);
349 good_type gb = ldexp(good_type(0.99), -std::numeric_limits<good_type>::digits);
350 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
351 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
352 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
353 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
354
355 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
356 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
357 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
358 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
359
360 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
361 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
362 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
363 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
364
365 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
366 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
367 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
368 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
369
92f5a8d4 370 b = ldexp(test_type(0.5), -std::numeric_limits<test_type>::digits);
b32b8144
FG		 371 gb = ldexp(good_type(0.5), -std::numeric_limits<good_type>::digits);
372 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
373 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
374 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
375 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
376
377 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
378 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
379 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
380 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
381
382 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
383 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
384 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
385 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
386
387 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
388 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
389 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
390 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
391
92f5a8d4 392 b = ldexp(test_type(1), -std::numeric_limits<test_type>::digits);
b32b8144
FG		 393 gb = ldexp(good_type(1), -std::numeric_limits<good_type>::digits);
394 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
395 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
396 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
397 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
398
399 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
400 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
401 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
402 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
403
404 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
405 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
406 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
407 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
408
409 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
410 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
411 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
412 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
413
92f5a8d4 414 b = ldexp(test_type(0.50000000001), -std::numeric_limits<test_type>::digits);
b32b8144
FG		 415 gb = ldexp(good_type(0.50000000001), -std::numeric_limits<good_type>::digits);
416 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
417 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
418 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
419 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
420
421 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
422 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
423 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
424 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
425
426 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
427 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
428 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
429 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
430
431 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
432 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
433 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
434 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
435
92f5a8d4 436 a = a + ldexp(a, -20);
b32b8144
FG		 437 ga = ga + ldexp(ga, -20);
438 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
439 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
440 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
441 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
442
443 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
444 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
445 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
446 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
447
448 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
449 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
450 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
451 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
452
453 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
454 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
455 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
456 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
457
92f5a8d4 458 b = ldexp(test_type(0.5), -std::numeric_limits<test_type>::digits);
b32b8144
FG		 459 gb = ldexp(good_type(0.5), -std::numeric_limits<good_type>::digits);
460 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
461 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
462 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
463 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
464
465 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
466 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
467 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
468 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
469
470 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
471 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
472 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
473 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
474
475 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
476 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
477 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
478 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
479
92f5a8d4 480 b = ldexp(test_type(1), -std::numeric_limits<test_type>::digits);
b32b8144
FG		 481 gb = ldexp(good_type(1), -std::numeric_limits<good_type>::digits);
482 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
483 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
484 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
485 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
486
487 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
488 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
489 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
490 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
491
492 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
493 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
494 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
495 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
496
497 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
498 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
499 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
500 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
501
92f5a8d4 502 b = ldexp(test_type(0.50000000001), -std::numeric_limits<test_type>::digits);
b32b8144
FG		 503 gb = ldexp(good_type(0.50000000001), -std::numeric_limits<good_type>::digits);
504 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
505 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
506 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
507 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
508
509 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
510 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
511 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
512 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
513
514 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
515 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
516 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
517 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
518
519 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
520 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
521 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
522 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
523
92f5a8d4
TL		 524 a = 1;
525 a = boost::math::float_prior(a);
b32b8144
FG		 526 ga = 1;
527 ga = boost::math::float_prior(ga);
528 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
529 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
530 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
531 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
532
533 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
534 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
535 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
536 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
537
538 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
539 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
540 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
541 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
542
543 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
544 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
545 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
546 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
547
92f5a8d4 548 b = ldexp(test_type(0.5), -std::numeric_limits<test_type>::digits);
b32b8144
FG		 549 gb = ldexp(good_type(0.5), -std::numeric_limits<good_type>::digits);
550 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
551 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
552 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
553 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
554
555 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
556 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
557 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
558 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
559
560 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
561 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
562 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
563 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
564
565 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
566 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
567 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
568 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
569
92f5a8d4 570 b = ldexp(test_type(1), -std::numeric_limits<test_type>::digits);
b32b8144
FG		 571 gb = ldexp(good_type(1), -std::numeric_limits<good_type>::digits);
572 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
573 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
574 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
575 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
576
577 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
578 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
579 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
580 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
581
582 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
583 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
584 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
585 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
586
587 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
588 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
589 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
590 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
591
92f5a8d4 592 b = ldexp(test_type(0.50000000001), -std::numeric_limits<test_type>::digits);
b32b8144
FG		 593 gb = ldexp(good_type(0.50000000001), -std::numeric_limits<good_type>::digits);
594 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
595 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
596 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
597 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
598
599 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
600 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
601 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
602 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
20effc67
TL		 603
604 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
605 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
606 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
607 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
608
609 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
610 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
611 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
612 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
613
614 a = boost::math::float_next(test_type(1));
615 ga = boost::math::float_next(good_type(1));
616 b = ldexp(boost::math::float_prior(test_type(1)), -std::numeric_limits<test_type>::digits);
617 gb = ldexp(boost::math::float_prior(good_type(1)), -std::numeric_limits<test_type>::digits);
618 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
619 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
620 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
621 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
622
623 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
624 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
625 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
626 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
627
628 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
629 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
630 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
631 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
632
633 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
634 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
635 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
636 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
637
638 b = ldexp(b, -1);
639 gb = ldexp(gb, -1);
640 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
641 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
642 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
643 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
644
645 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
646 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
647 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
648 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
649
650 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
651 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
652 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
653 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
654
655 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
656 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
657 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
658 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
659
660 a = 1.75; // even mantissa, not a power of 2
661 ga = 1.75;
662 b = ldexp(test_type(1), -std::numeric_limits<test_type>::digits);
663 gb = ldexp(good_type(1), -std::numeric_limits<test_type>::digits);
664 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
665 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
666 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
667 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
668
669 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
670 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
671 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
672 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
673
674 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
675 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
676 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
677 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
678
679 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
680 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
681 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
682 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
683 b = ldexp(b, -1);
684 gb = ldexp(gb, -1);
685 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
686 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
687 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
688 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
689
690 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
691 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
692 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
693 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
694
695 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
696 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
697 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
698 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
699
700 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
701 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
702 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
703 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
704
705 b = ldexp(boost::math::float_prior(test_type(1)), -std::numeric_limits<test_type>::digits);
706 gb = ldexp(boost::math::float_prior(good_type(1)), -std::numeric_limits<test_type>::digits);
707 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
708 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
709 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
710 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
711
712 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
713 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
714 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
715 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
716
717 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
718 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
719 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
720 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
721
722 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
723 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
724 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
725 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
726
727 b = ldexp(b, -1);
728 gb = ldexp(gb, -1);
729 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
730 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
731 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
732 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
733
734 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
735 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
736 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
737 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
738
739 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
740 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
741 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
742 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
743
744 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
745 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
746 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
747 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
748
749 b = ldexp(test_type(0.75), -std::numeric_limits<test_type>::digits); // even mantissa not a power of 2.
750 gb = ldexp(good_type(0.75), -std::numeric_limits<test_type>::digits);
751 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
752 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
753 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
754 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
755
756 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
757 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
758 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
759 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
760
761 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
762 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
763 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
764 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
765
766 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
767 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
768 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
769 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
770
771 b = ldexp(b, -1);
772 gb = ldexp(gb, -1);
773 BOOST_CHECK_EQUAL(good_type(test_type(a - b)), good_type(ga - gb));
774 BOOST_CHECK_EQUAL(good_type(test_type(b - a)), good_type(gb - ga));
775 BOOST_CHECK_EQUAL(good_type(test_type(a + b)), good_type(ga + gb));
776 BOOST_CHECK_EQUAL(good_type(test_type(b + a)), good_type(gb + ga));
777
778 BOOST_CHECK_EQUAL(good_type(test_type(a - -b)), good_type(ga - -gb));
779 BOOST_CHECK_EQUAL(good_type(test_type(b - -a)), good_type(gb - -ga));
780 BOOST_CHECK_EQUAL(good_type(test_type(a + -b)), good_type(ga + -gb));
781 BOOST_CHECK_EQUAL(good_type(test_type(b + -a)), good_type(gb + -ga));
b32b8144
FG		 782
783 BOOST_CHECK_EQUAL(good_type(test_type(-a - b)), good_type(-ga - gb));
784 BOOST_CHECK_EQUAL(good_type(test_type(-b - a)), good_type(-gb - ga));
785 BOOST_CHECK_EQUAL(good_type(test_type(-a + b)), good_type(-ga + gb));
786 BOOST_CHECK_EQUAL(good_type(test_type(-b + a)), good_type(-gb + ga));
787
788 BOOST_CHECK_EQUAL(good_type(test_type(-a - -b)), good_type(-ga - -gb));
789 BOOST_CHECK_EQUAL(good_type(test_type(-b - -a)), good_type(-gb - -ga));
790 BOOST_CHECK_EQUAL(good_type(test_type(-a + -b)), good_type(-ga + -gb));
791 BOOST_CHECK_EQUAL(good_type(test_type(-b + -a)), good_type(-gb + -ga));
7c673cae
FG		 792}
793
794int main()
795{
796 test_special_cases();
797 unsigned error_count = 0;
92f5a8d4 798 for (unsigned i = 0; i < 100000; ++i)
7c673cae
FG		 799 {
800 good_type a = generate_random<good_type>();
801 good_type b = generate_random<good_type>();
802 test_type ta(a);
803 test_type tb(b);
804
805 BOOST_CHECK_EQUAL(test_type(a * b), ta * tb);
806 BOOST_CHECK_EQUAL(test_type(-a * b), -ta * tb);
807 BOOST_CHECK_EQUAL(test_type(a * -b), ta * -tb);
808 BOOST_CHECK_EQUAL(test_type(-a * -b), -ta * -tb);
809
810 BOOST_CHECK_EQUAL(test_type(a + b), ta + tb);
811 BOOST_CHECK_EQUAL(test_type(-a + b), -ta + tb);
812 BOOST_CHECK_EQUAL(test_type(a + -b), ta + -tb);
813 BOOST_CHECK_EQUAL(test_type(-a + -b), -ta + -tb);
814
815 BOOST_CHECK_EQUAL(test_type(a - b), ta - tb);
816 BOOST_CHECK_EQUAL(test_type(-a - b), -ta - tb);
817 BOOST_CHECK_EQUAL(test_type(a - -b), ta - -tb);
818 BOOST_CHECK_EQUAL(test_type(-a - -b), -ta - -tb);
819
820 BOOST_CHECK_EQUAL(test_type(a / b), ta / tb);
821 BOOST_CHECK_EQUAL(test_type(-a / b), -ta / tb);
822 BOOST_CHECK_EQUAL(test_type(a / -b), ta / -tb);
823 BOOST_CHECK_EQUAL(test_type(-a / -b), -ta / -tb);
824
825 BOOST_CHECK_EQUAL(test_type(sqrt(a)), sqrt(ta));
826 BOOST_CHECK_EQUAL(test_type(floor(a)), floor(ta));
827 BOOST_CHECK_EQUAL(test_type(floor(-a)), floor(-ta));
828 BOOST_CHECK_EQUAL(test_type(ceil(a)), ceil(ta));
829 BOOST_CHECK_EQUAL(test_type(ceil(-a)), ceil(-ta));
830
831#ifdef TEST_MPFR
832 //
833 // Conversions:
834 //
835 BOOST_CHECK_EQUAL(a.convert_to<double>(), ta.convert_to<double>());
836 BOOST_CHECK_EQUAL(a.convert_to<float>(), ta.convert_to<float>());
837 BOOST_CHECK_EQUAL(b.convert_to<double>(), tb.convert_to<double>());
838 BOOST_CHECK_EQUAL(b.convert_to<float>(), tb.convert_to<float>());
839#else
840 BOOST_CHECK_EQUAL(a, ta.convert_to<double>());
841 BOOST_CHECK_EQUAL(static_cast<float>(a), ta.convert_to<float>());
842 BOOST_CHECK_EQUAL(b, tb.convert_to<double>());
843 BOOST_CHECK_EQUAL(static_cast<float>(b), tb.convert_to<float>());
844#endif
845
846 static boost::random::mt19937 i_gen;
847
848 int si = i_gen();
849 BOOST_CHECK_EQUAL(test_type(a * si), ta * si);
850 BOOST_CHECK_EQUAL(test_type(-a * si), -ta * si);
851 BOOST_CHECK_EQUAL(test_type(-a * -si), -ta * -si);
852 BOOST_CHECK_EQUAL(test_type(a * -si), ta * -si);
853 unsigned ui = std::abs(si);
854 BOOST_CHECK_EQUAL(test_type(a * ui), ta * ui);
855 BOOST_CHECK_EQUAL(test_type(-a * ui), -ta * ui);
856
857 // Divide:
858 BOOST_CHECK_EQUAL(test_type(a / si), ta / si);
859 BOOST_CHECK_EQUAL(test_type(-a / si), -ta / si);
860 BOOST_CHECK_EQUAL(test_type(-a / -si), -ta / -si);
861 BOOST_CHECK_EQUAL(test_type(a / -si), ta / -si);
862 BOOST_CHECK_EQUAL(test_type(a / ui), ta / ui);
863 BOOST_CHECK_EQUAL(test_type(-a / ui), -ta / ui);
864 // Error reporting:
f67539c2 865 if ((unsigned)boost::detail::test_errors() != error_count)
7c673cae
FG		 866 {
867 error_count = boost::detail::test_errors();
868 std::cout << std::setprecision(std::numeric_limits<test_type>::max_digits10) << std::scientific;
869 std::cout << "a (mpfr) = " << a << std::endl;
870 std::cout << "a (test) = " << ta << std::endl;
871 std::cout << "b (mpfr) = " << b << std::endl;
872 std::cout << "b (test) = " << tb << std::endl;
873 std::cout << "si = " << si << std::endl;
874 std::cout << "ui = " << ui << std::endl;
875 }
876 }
877 return boost::report_errors();
878}
Ceph