xref: /llvm-project/llvm/unittests/Support/MathExtrasTest.cpp (revision d59a196b8cb8bb59e38ab2bd93b3454141e33bc9)
1 //===- unittests/Support/MathExtrasTest.cpp - math utils tests ------------===//
2 //
3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4 // See https://llvm.org/LICENSE.txt for license information.
5 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6 //
7 //===----------------------------------------------------------------------===//
8 
9 #include "llvm/Support/MathExtras.h"
10 #include "gtest/gtest.h"
11 
12 using namespace llvm;
13 
14 namespace {
15 
16 TEST(MathExtras, countTrailingZeros) {
17   uint8_t Z8 = 0;
18   uint16_t Z16 = 0;
19   uint32_t Z32 = 0;
20   uint64_t Z64 = 0;
21   EXPECT_EQ(8u, countTrailingZeros(Z8));
22   EXPECT_EQ(16u, countTrailingZeros(Z16));
23   EXPECT_EQ(32u, countTrailingZeros(Z32));
24   EXPECT_EQ(64u, countTrailingZeros(Z64));
25 
26   uint8_t NZ8 = 42;
27   uint16_t NZ16 = 42;
28   uint32_t NZ32 = 42;
29   uint64_t NZ64 = 42;
30   EXPECT_EQ(1u, countTrailingZeros(NZ8));
31   EXPECT_EQ(1u, countTrailingZeros(NZ16));
32   EXPECT_EQ(1u, countTrailingZeros(NZ32));
33   EXPECT_EQ(1u, countTrailingZeros(NZ64));
34 }
35 
36 TEST(MathExtras, countLeadingZeros) {
37   uint8_t Z8 = 0;
38   uint16_t Z16 = 0;
39   uint32_t Z32 = 0;
40   uint64_t Z64 = 0;
41   EXPECT_EQ(8u, countLeadingZeros(Z8));
42   EXPECT_EQ(16u, countLeadingZeros(Z16));
43   EXPECT_EQ(32u, countLeadingZeros(Z32));
44   EXPECT_EQ(64u, countLeadingZeros(Z64));
45 
46   uint8_t NZ8 = 42;
47   uint16_t NZ16 = 42;
48   uint32_t NZ32 = 42;
49   uint64_t NZ64 = 42;
50   EXPECT_EQ(2u, countLeadingZeros(NZ8));
51   EXPECT_EQ(10u, countLeadingZeros(NZ16));
52   EXPECT_EQ(26u, countLeadingZeros(NZ32));
53   EXPECT_EQ(58u, countLeadingZeros(NZ64));
54 
55   EXPECT_EQ(8u, countLeadingZeros(0x00F000FFu));
56   EXPECT_EQ(8u, countLeadingZeros(0x00F12345u));
57   for (unsigned i = 0; i <= 30; ++i) {
58     EXPECT_EQ(31 - i, countLeadingZeros(1u << i));
59   }
60 
61   EXPECT_EQ(8u, countLeadingZeros(0x00F1234500F12345ULL));
62   EXPECT_EQ(1u, countLeadingZeros(1ULL << 62));
63   for (unsigned i = 0; i <= 62; ++i) {
64     EXPECT_EQ(63 - i, countLeadingZeros(1ULL << i));
65   }
66 }
67 
68 TEST(MathExtras, onesMask) {
69   EXPECT_EQ(0U, maskLeadingOnes<uint8_t>(0));
70   EXPECT_EQ(0U, maskTrailingOnes<uint8_t>(0));
71   EXPECT_EQ(0U, maskLeadingOnes<uint16_t>(0));
72   EXPECT_EQ(0U, maskTrailingOnes<uint16_t>(0));
73   EXPECT_EQ(0U, maskLeadingOnes<uint32_t>(0));
74   EXPECT_EQ(0U, maskTrailingOnes<uint32_t>(0));
75   EXPECT_EQ(0U, maskLeadingOnes<uint64_t>(0));
76   EXPECT_EQ(0U, maskTrailingOnes<uint64_t>(0));
77 
78   EXPECT_EQ(0x00000003U, maskTrailingOnes<uint32_t>(2U));
79   EXPECT_EQ(0xC0000000U, maskLeadingOnes<uint32_t>(2U));
80 
81   EXPECT_EQ(0x000007FFU, maskTrailingOnes<uint32_t>(11U));
82   EXPECT_EQ(0xFFE00000U, maskLeadingOnes<uint32_t>(11U));
83 
84   EXPECT_EQ(0xFFFFFFFFU, maskTrailingOnes<uint32_t>(32U));
85   EXPECT_EQ(0xFFFFFFFFU, maskLeadingOnes<uint32_t>(32U));
86   EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, maskTrailingOnes<uint64_t>(64U));
87   EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, maskLeadingOnes<uint64_t>(64U));
88 
89   EXPECT_EQ(0x0000FFFFFFFFFFFFULL, maskTrailingOnes<uint64_t>(48U));
90   EXPECT_EQ(0xFFFFFFFFFFFF0000ULL, maskLeadingOnes<uint64_t>(48U));
91 }
92 
93 TEST(MathExtras, findFirstSet) {
94   uint8_t Z8 = 0;
95   uint16_t Z16 = 0;
96   uint32_t Z32 = 0;
97   uint64_t Z64 = 0;
98   EXPECT_EQ(0xFFULL, findFirstSet(Z8));
99   EXPECT_EQ(0xFFFFULL, findFirstSet(Z16));
100   EXPECT_EQ(0xFFFFFFFFULL, findFirstSet(Z32));
101   EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, findFirstSet(Z64));
102 
103   uint8_t NZ8 = 42;
104   uint16_t NZ16 = 42;
105   uint32_t NZ32 = 42;
106   uint64_t NZ64 = 42;
107   EXPECT_EQ(1u, findFirstSet(NZ8));
108   EXPECT_EQ(1u, findFirstSet(NZ16));
109   EXPECT_EQ(1u, findFirstSet(NZ32));
110   EXPECT_EQ(1u, findFirstSet(NZ64));
111 }
112 
113 TEST(MathExtras, findLastSet) {
114   uint8_t Z8 = 0;
115   uint16_t Z16 = 0;
116   uint32_t Z32 = 0;
117   uint64_t Z64 = 0;
118   EXPECT_EQ(0xFFULL, findLastSet(Z8));
119   EXPECT_EQ(0xFFFFULL, findLastSet(Z16));
120   EXPECT_EQ(0xFFFFFFFFULL, findLastSet(Z32));
121   EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, findLastSet(Z64));
122 
123   uint8_t NZ8 = 42;
124   uint16_t NZ16 = 42;
125   uint32_t NZ32 = 42;
126   uint64_t NZ64 = 42;
127   EXPECT_EQ(5u, findLastSet(NZ8));
128   EXPECT_EQ(5u, findLastSet(NZ16));
129   EXPECT_EQ(5u, findLastSet(NZ32));
130   EXPECT_EQ(5u, findLastSet(NZ64));
131 }
132 
133 TEST(MathExtras, isIntN) {
134   EXPECT_TRUE(isIntN(16, 32767));
135   EXPECT_FALSE(isIntN(16, 32768));
136 }
137 
138 TEST(MathExtras, isUIntN) {
139   EXPECT_TRUE(isUIntN(16, 65535));
140   EXPECT_FALSE(isUIntN(16, 65536));
141   EXPECT_TRUE(isUIntN(1, 0));
142   EXPECT_TRUE(isUIntN(6, 63));
143 }
144 
145 TEST(MathExtras, maxIntN) {
146   EXPECT_EQ(32767, maxIntN(16));
147   EXPECT_EQ(2147483647, maxIntN(32));
148   EXPECT_EQ(std::numeric_limits<int32_t>::max(), maxIntN(32));
149   EXPECT_EQ(std::numeric_limits<int64_t>::max(), maxIntN(64));
150 }
151 
152 TEST(MathExtras, minIntN) {
153   EXPECT_EQ(-32768LL, minIntN(16));
154   EXPECT_EQ(-64LL, minIntN(7));
155   EXPECT_EQ(std::numeric_limits<int32_t>::min(), minIntN(32));
156   EXPECT_EQ(std::numeric_limits<int64_t>::min(), minIntN(64));
157 }
158 
159 TEST(MathExtras, maxUIntN) {
160   EXPECT_EQ(0xffffULL, maxUIntN(16));
161   EXPECT_EQ(0xffffffffULL, maxUIntN(32));
162   EXPECT_EQ(0xffffffffffffffffULL, maxUIntN(64));
163   EXPECT_EQ(1ULL, maxUIntN(1));
164   EXPECT_EQ(0x0fULL, maxUIntN(4));
165 }
166 
167 TEST(MathExtras, reverseBits) {
168   uint8_t NZ8 = 42;
169   uint16_t NZ16 = 42;
170   uint32_t NZ32 = 42;
171   uint64_t NZ64 = 42;
172   EXPECT_EQ(0x54ULL, reverseBits(NZ8));
173   EXPECT_EQ(0x5400ULL, reverseBits(NZ16));
174   EXPECT_EQ(0x54000000ULL, reverseBits(NZ32));
175   EXPECT_EQ(0x5400000000000000ULL, reverseBits(NZ64));
176 }
177 
178 TEST(MathExtras, isShiftedMask_32) {
179   EXPECT_FALSE(isShiftedMask_32(0x01010101));
180   EXPECT_TRUE(isShiftedMask_32(0xf0000000));
181   EXPECT_TRUE(isShiftedMask_32(0xffff0000));
182   EXPECT_TRUE(isShiftedMask_32(0xff << 1));
183 
184   unsigned MaskIdx, MaskLen;
185   EXPECT_FALSE(isShiftedMask_32(0x01010101, MaskIdx, MaskLen));
186   EXPECT_TRUE(isShiftedMask_32(0xf0000000, MaskIdx, MaskLen));
187   EXPECT_EQ(28, (int)MaskIdx);
188   EXPECT_EQ(4, (int)MaskLen);
189   EXPECT_TRUE(isShiftedMask_32(0xffff0000, MaskIdx, MaskLen));
190   EXPECT_EQ(16, (int)MaskIdx);
191   EXPECT_EQ(16, (int)MaskLen);
192   EXPECT_TRUE(isShiftedMask_32(0xff << 1, MaskIdx, MaskLen));
193   EXPECT_EQ(1, (int)MaskIdx);
194   EXPECT_EQ(8, (int)MaskLen);
195 }
196 
197 TEST(MathExtras, isShiftedMask_64) {
198   EXPECT_FALSE(isShiftedMask_64(0x0101010101010101ull));
199   EXPECT_TRUE(isShiftedMask_64(0xf000000000000000ull));
200   EXPECT_TRUE(isShiftedMask_64(0xffff000000000000ull));
201   EXPECT_TRUE(isShiftedMask_64(0xffull << 55));
202 
203   unsigned MaskIdx, MaskLen;
204   EXPECT_FALSE(isShiftedMask_64(0x0101010101010101ull, MaskIdx, MaskLen));
205   EXPECT_TRUE(isShiftedMask_64(0xf000000000000000ull, MaskIdx, MaskLen));
206   EXPECT_EQ(60, (int)MaskIdx);
207   EXPECT_EQ(4, (int)MaskLen);
208   EXPECT_TRUE(isShiftedMask_64(0xffff000000000000ull, MaskIdx, MaskLen));
209   EXPECT_EQ(48, (int)MaskIdx);
210   EXPECT_EQ(16, (int)MaskLen);
211   EXPECT_TRUE(isShiftedMask_64(0xffull << 55, MaskIdx, MaskLen));
212   EXPECT_EQ(55, (int)MaskIdx);
213   EXPECT_EQ(8, (int)MaskLen);
214 }
215 
216 TEST(MathExtras, isPowerOf2_32) {
217   EXPECT_FALSE(isPowerOf2_32(0));
218   EXPECT_TRUE(isPowerOf2_32(1 << 6));
219   EXPECT_TRUE(isPowerOf2_32(1 << 12));
220   EXPECT_FALSE(isPowerOf2_32((1 << 19) + 3));
221   EXPECT_FALSE(isPowerOf2_32(0xABCDEF0));
222 }
223 
224 TEST(MathExtras, isPowerOf2_64) {
225   EXPECT_FALSE(isPowerOf2_64(0));
226   EXPECT_TRUE(isPowerOf2_64(1LL << 46));
227   EXPECT_TRUE(isPowerOf2_64(1LL << 12));
228   EXPECT_FALSE(isPowerOf2_64((1LL << 53) + 3));
229   EXPECT_FALSE(isPowerOf2_64(0xABCDEF0ABCDEF0LL));
230 }
231 
232 TEST(MathExtras, PowerOf2Ceil) {
233   EXPECT_EQ(0U, PowerOf2Ceil(0U));
234   EXPECT_EQ(8U, PowerOf2Ceil(8U));
235   EXPECT_EQ(8U, PowerOf2Ceil(7U));
236 }
237 
238 TEST(MathExtras, PowerOf2Floor) {
239   EXPECT_EQ(0U, PowerOf2Floor(0U));
240   EXPECT_EQ(8U, PowerOf2Floor(8U));
241   EXPECT_EQ(4U, PowerOf2Floor(7U));
242 }
243 
244 TEST(MathExtras, CTLog2) {
245   EXPECT_EQ(CTLog2<1ULL << 0>(), 0U);
246   EXPECT_EQ(CTLog2<1ULL << 1>(), 1U);
247   EXPECT_EQ(CTLog2<1ULL << 2>(), 2U);
248   EXPECT_EQ(CTLog2<1ULL << 3>(), 3U);
249   EXPECT_EQ(CTLog2<1ULL << 4>(), 4U);
250   EXPECT_EQ(CTLog2<1ULL << 5>(), 5U);
251   EXPECT_EQ(CTLog2<1ULL << 6>(), 6U);
252   EXPECT_EQ(CTLog2<1ULL << 7>(), 7U);
253   EXPECT_EQ(CTLog2<1ULL << 8>(), 8U);
254   EXPECT_EQ(CTLog2<1ULL << 9>(), 9U);
255   EXPECT_EQ(CTLog2<1ULL << 10>(), 10U);
256   EXPECT_EQ(CTLog2<1ULL << 11>(), 11U);
257   EXPECT_EQ(CTLog2<1ULL << 12>(), 12U);
258   EXPECT_EQ(CTLog2<1ULL << 13>(), 13U);
259   EXPECT_EQ(CTLog2<1ULL << 14>(), 14U);
260   EXPECT_EQ(CTLog2<1ULL << 15>(), 15U);
261 }
262 
263 TEST(MathExtras, countLeadingOnes) {
264   for (int i = 30; i >= 0; --i) {
265     // Start with all ones and unset some bit.
266     EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i)));
267   }
268   for (int i = 62; i >= 0; --i) {
269     // Start with all ones and unset some bit.
270     EXPECT_EQ(63u - i, countLeadingOnes(0xFFFFFFFFFFFFFFFFULL ^ (1LL << i)));
271   }
272   for (int i = 30; i >= 0; --i) {
273     // Start with all ones and unset some bit.
274     EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i)));
275   }
276 }
277 
278 TEST(MathExtras, FloatBits) {
279   static const float kValue = 5632.34f;
280   EXPECT_FLOAT_EQ(kValue, BitsToFloat(FloatToBits(kValue)));
281 }
282 
283 TEST(MathExtras, DoubleBits) {
284   static const double kValue = 87987234.983498;
285   EXPECT_DOUBLE_EQ(kValue, BitsToDouble(DoubleToBits(kValue)));
286 }
287 
288 TEST(MathExtras, MinAlign) {
289   EXPECT_EQ(1u, MinAlign(2, 3));
290   EXPECT_EQ(2u, MinAlign(2, 4));
291   EXPECT_EQ(1u, MinAlign(17, 64));
292   EXPECT_EQ(256u, MinAlign(256, 512));
293 }
294 
295 TEST(MathExtras, NextPowerOf2) {
296   EXPECT_EQ(4u, NextPowerOf2(3));
297   EXPECT_EQ(16u, NextPowerOf2(15));
298   EXPECT_EQ(256u, NextPowerOf2(128));
299 }
300 
301 TEST(MathExtras, alignTo) {
302   EXPECT_EQ(8u, alignTo(5, 8));
303   EXPECT_EQ(24u, alignTo(17, 8));
304   EXPECT_EQ(0u, alignTo(~0LL, 8));
305 
306   EXPECT_EQ(7u, alignTo(5, 8, 7));
307   EXPECT_EQ(17u, alignTo(17, 8, 1));
308   EXPECT_EQ(3u, alignTo(~0LL, 8, 3));
309   EXPECT_EQ(552u, alignTo(321, 255, 42));
310 }
311 
312 template <typename T> void SaturatingAddTestHelper() {
313   const T Max = std::numeric_limits<T>::max();
314   bool ResultOverflowed;
315 
316   EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2)));
317   EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2), &ResultOverflowed));
318   EXPECT_FALSE(ResultOverflowed);
319 
320   EXPECT_EQ(Max, SaturatingAdd(Max, T(1)));
321   EXPECT_EQ(Max, SaturatingAdd(Max, T(1), &ResultOverflowed));
322   EXPECT_TRUE(ResultOverflowed);
323 
324   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1)));
325   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1), &ResultOverflowed));
326   EXPECT_FALSE(ResultOverflowed);
327 
328   EXPECT_EQ(Max, SaturatingAdd(T(1), Max));
329   EXPECT_EQ(Max, SaturatingAdd(T(1), Max, &ResultOverflowed));
330   EXPECT_TRUE(ResultOverflowed);
331 
332   EXPECT_EQ(Max, SaturatingAdd(Max, Max));
333   EXPECT_EQ(Max, SaturatingAdd(Max, Max, &ResultOverflowed));
334   EXPECT_TRUE(ResultOverflowed);
335 
336   EXPECT_EQ(T(6), SaturatingAdd(T(1), T(2), T(3)));
337   EXPECT_EQ(T(6), SaturatingAdd(T(1), T(2), T(3), &ResultOverflowed));
338   EXPECT_FALSE(ResultOverflowed);
339 
340   EXPECT_EQ(T(10), SaturatingAdd(T(1), T(2), T(3), T(4)));
341   EXPECT_EQ(T(10), SaturatingAdd(T(1), T(2), T(3), T(4), &ResultOverflowed));
342   EXPECT_FALSE(ResultOverflowed);
343 
344   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(0)));
345   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(0), &ResultOverflowed));
346   EXPECT_FALSE(ResultOverflowed);
347 
348   EXPECT_EQ(Max, SaturatingAdd(T(0), T(0), Max));
349   EXPECT_EQ(Max, SaturatingAdd(T(0), T(0), Max, &ResultOverflowed));
350   EXPECT_FALSE(ResultOverflowed);
351 
352   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(1)));
353   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(1), &ResultOverflowed));
354   EXPECT_TRUE(ResultOverflowed);
355 
356   EXPECT_EQ(Max, SaturatingAdd(T(0), T(1), Max));
357   EXPECT_EQ(Max, SaturatingAdd(T(0), T(1), Max, &ResultOverflowed));
358   EXPECT_TRUE(ResultOverflowed);
359 
360   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 2), T(1)));
361   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 2), T(1), &ResultOverflowed));
362   EXPECT_FALSE(ResultOverflowed);
363 
364   EXPECT_EQ(Max, SaturatingAdd(T(1), T(1), T(Max - 2)));
365   EXPECT_EQ(Max, SaturatingAdd(T(1), T(1), T(Max - 2), &ResultOverflowed));
366   EXPECT_FALSE(ResultOverflowed);
367 
368   EXPECT_EQ(Max, SaturatingAdd(Max, Max, Max));
369   EXPECT_EQ(Max, SaturatingAdd(Max, Max, Max, &ResultOverflowed));
370   EXPECT_TRUE(ResultOverflowed);
371 }
372 
373 TEST(MathExtras, SaturatingAdd) {
374   SaturatingAddTestHelper<uint8_t>();
375   SaturatingAddTestHelper<uint16_t>();
376   SaturatingAddTestHelper<uint32_t>();
377   SaturatingAddTestHelper<uint64_t>();
378 }
379 
380 template<typename T>
381 void SaturatingMultiplyTestHelper()
382 {
383   const T Max = std::numeric_limits<T>::max();
384   bool ResultOverflowed;
385 
386   // Test basic multiplication.
387   EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3)));
388   EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3), &ResultOverflowed));
389   EXPECT_FALSE(ResultOverflowed);
390 
391   EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2)));
392   EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2), &ResultOverflowed));
393   EXPECT_FALSE(ResultOverflowed);
394 
395   // Test multiplication by zero.
396   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0)));
397   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0), &ResultOverflowed));
398   EXPECT_FALSE(ResultOverflowed);
399 
400   EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0)));
401   EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0), &ResultOverflowed));
402   EXPECT_FALSE(ResultOverflowed);
403 
404   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1)));
405   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1), &ResultOverflowed));
406   EXPECT_FALSE(ResultOverflowed);
407 
408   EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0)));
409   EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0), &ResultOverflowed));
410   EXPECT_FALSE(ResultOverflowed);
411 
412   EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max));
413   EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max, &ResultOverflowed));
414   EXPECT_FALSE(ResultOverflowed);
415 
416   // Test multiplication by maximum value.
417   EXPECT_EQ(Max, SaturatingMultiply(Max, T(2)));
418   EXPECT_EQ(Max, SaturatingMultiply(Max, T(2), &ResultOverflowed));
419   EXPECT_TRUE(ResultOverflowed);
420 
421   EXPECT_EQ(Max, SaturatingMultiply(T(2), Max));
422   EXPECT_EQ(Max, SaturatingMultiply(T(2), Max, &ResultOverflowed));
423   EXPECT_TRUE(ResultOverflowed);
424 
425   EXPECT_EQ(Max, SaturatingMultiply(Max, Max));
426   EXPECT_EQ(Max, SaturatingMultiply(Max, Max, &ResultOverflowed));
427   EXPECT_TRUE(ResultOverflowed);
428 
429   // Test interesting boundary conditions for algorithm -
430   // ((1 << A) - 1) * ((1 << B) + K) for K in [-1, 0, 1]
431   // and A + B == std::numeric_limits<T>::digits.
432   // We expect overflow iff A > B and K = 1.
433   const int Digits = std::numeric_limits<T>::digits;
434   for (int A = 1, B = Digits - 1; B >= 1; ++A, --B) {
435     for (int K = -1; K <= 1; ++K) {
436       T X = (T(1) << A) - T(1);
437       T Y = (T(1) << B) + K;
438       bool OverflowExpected = A > B && K == 1;
439 
440       if(OverflowExpected) {
441         EXPECT_EQ(Max, SaturatingMultiply(X, Y));
442         EXPECT_EQ(Max, SaturatingMultiply(X, Y, &ResultOverflowed));
443         EXPECT_TRUE(ResultOverflowed);
444       } else {
445         EXPECT_EQ(X * Y, SaturatingMultiply(X, Y));
446         EXPECT_EQ(X * Y, SaturatingMultiply(X, Y, &ResultOverflowed));
447         EXPECT_FALSE(ResultOverflowed);
448       }
449     }
450   }
451 }
452 
453 TEST(MathExtras, SaturatingMultiply) {
454   SaturatingMultiplyTestHelper<uint8_t>();
455   SaturatingMultiplyTestHelper<uint16_t>();
456   SaturatingMultiplyTestHelper<uint32_t>();
457   SaturatingMultiplyTestHelper<uint64_t>();
458 }
459 
460 template<typename T>
461 void SaturatingMultiplyAddTestHelper()
462 {
463   const T Max = std::numeric_limits<T>::max();
464   bool ResultOverflowed;
465 
466   // Test basic multiply-add.
467   EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10)));
468   EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10), &ResultOverflowed));
469   EXPECT_FALSE(ResultOverflowed);
470 
471   // Test multiply overflows, add doesn't overflow
472   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(0), &ResultOverflowed));
473   EXPECT_TRUE(ResultOverflowed);
474 
475   // Test multiply doesn't overflow, add overflows
476   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
477   EXPECT_TRUE(ResultOverflowed);
478 
479   // Test multiply-add with Max as operand
480   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
481   EXPECT_TRUE(ResultOverflowed);
482 
483   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), Max, T(1), &ResultOverflowed));
484   EXPECT_TRUE(ResultOverflowed);
485 
486   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(1), &ResultOverflowed));
487   EXPECT_TRUE(ResultOverflowed);
488 
489   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, Max, &ResultOverflowed));
490   EXPECT_TRUE(ResultOverflowed);
491 
492   // Test multiply-add with 0 as operand
493   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(1), T(0), &ResultOverflowed));
494   EXPECT_FALSE(ResultOverflowed);
495 
496   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(0), T(1), &ResultOverflowed));
497   EXPECT_FALSE(ResultOverflowed);
498 
499   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(0), T(0), T(1), &ResultOverflowed));
500   EXPECT_FALSE(ResultOverflowed);
501 
502   EXPECT_EQ(T(0), SaturatingMultiplyAdd(T(0), T(0), T(0), &ResultOverflowed));
503   EXPECT_FALSE(ResultOverflowed);
504 
505 }
506 
507 TEST(MathExtras, SaturatingMultiplyAdd) {
508   SaturatingMultiplyAddTestHelper<uint8_t>();
509   SaturatingMultiplyAddTestHelper<uint16_t>();
510   SaturatingMultiplyAddTestHelper<uint32_t>();
511   SaturatingMultiplyAddTestHelper<uint64_t>();
512 }
513 
514 TEST(MathExtras, IsShiftedUInt) {
515   EXPECT_TRUE((isShiftedUInt<1, 0>(0)));
516   EXPECT_TRUE((isShiftedUInt<1, 0>(1)));
517   EXPECT_FALSE((isShiftedUInt<1, 0>(2)));
518   EXPECT_FALSE((isShiftedUInt<1, 0>(3)));
519   EXPECT_FALSE((isShiftedUInt<1, 0>(0x8000000000000000)));
520   EXPECT_TRUE((isShiftedUInt<1, 63>(0x8000000000000000)));
521   EXPECT_TRUE((isShiftedUInt<2, 62>(0xC000000000000000)));
522   EXPECT_FALSE((isShiftedUInt<2, 62>(0xE000000000000000)));
523 
524   // 0x201 is ten bits long and has a 1 in the MSB and LSB.
525   EXPECT_TRUE((isShiftedUInt<10, 5>(uint64_t(0x201) << 5)));
526   EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 4)));
527   EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 6)));
528 }
529 
530 TEST(MathExtras, IsShiftedInt) {
531   EXPECT_TRUE((isShiftedInt<1, 0>(0)));
532   EXPECT_TRUE((isShiftedInt<1, 0>(-1)));
533   EXPECT_FALSE((isShiftedInt<1, 0>(2)));
534   EXPECT_FALSE((isShiftedInt<1, 0>(3)));
535   EXPECT_FALSE((isShiftedInt<1, 0>(0x8000000000000000)));
536   EXPECT_TRUE((isShiftedInt<1, 63>(0x8000000000000000)));
537   EXPECT_TRUE((isShiftedInt<2, 62>(0xC000000000000000)));
538   EXPECT_FALSE((isShiftedInt<2, 62>(0xE000000000000000)));
539 
540   // 0x201 is ten bits long and has a 1 in the MSB and LSB.
541   EXPECT_TRUE((isShiftedInt<11, 5>(int64_t(0x201) << 5)));
542   EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 3)));
543   EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 6)));
544   EXPECT_TRUE((isShiftedInt<11, 5>(-(int64_t(0x201) << 5))));
545   EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 3))));
546   EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 6))));
547 
548   EXPECT_TRUE((isShiftedInt<6, 10>(-(int64_t(1) << 15))));
549   EXPECT_FALSE((isShiftedInt<6, 10>(int64_t(1) << 15)));
550 }
551 
552 template <typename T>
553 class OverflowTest : public ::testing::Test { };
554 
555 using OverflowTestTypes = ::testing::Types<signed char, short, int, long,
556                                            long long>;
557 
558 TYPED_TEST_SUITE(OverflowTest, OverflowTestTypes, );
559 
560 TYPED_TEST(OverflowTest, AddNoOverflow) {
561   TypeParam Result;
562   EXPECT_FALSE(AddOverflow<TypeParam>(1, 2, Result));
563   EXPECT_EQ(Result, TypeParam(3));
564 }
565 
566 TYPED_TEST(OverflowTest, AddOverflowToNegative) {
567   TypeParam Result;
568   auto MaxValue = std::numeric_limits<TypeParam>::max();
569   EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, MaxValue, Result));
570   EXPECT_EQ(Result, TypeParam(-2));
571 }
572 
573 TYPED_TEST(OverflowTest, AddOverflowToMin) {
574   TypeParam Result;
575   auto MaxValue = std::numeric_limits<TypeParam>::max();
576   EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, TypeParam(1), Result));
577   EXPECT_EQ(Result, std::numeric_limits<TypeParam>::min());
578 }
579 
580 TYPED_TEST(OverflowTest, AddOverflowToZero) {
581   TypeParam Result;
582   auto MinValue = std::numeric_limits<TypeParam>::min();
583   EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, MinValue, Result));
584   EXPECT_EQ(Result, TypeParam(0));
585 }
586 
587 TYPED_TEST(OverflowTest, AddOverflowToMax) {
588   TypeParam Result;
589   auto MinValue = std::numeric_limits<TypeParam>::min();
590   EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, TypeParam(-1), Result));
591   EXPECT_EQ(Result, std::numeric_limits<TypeParam>::max());
592 }
593 
594 TYPED_TEST(OverflowTest, SubNoOverflow) {
595   TypeParam Result;
596   EXPECT_FALSE(SubOverflow<TypeParam>(1, 2, Result));
597   EXPECT_EQ(Result, TypeParam(-1));
598 }
599 
600 TYPED_TEST(OverflowTest, SubOverflowToMax) {
601   TypeParam Result;
602   auto MinValue = std::numeric_limits<TypeParam>::min();
603   EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
604   EXPECT_EQ(Result, MinValue);
605 }
606 
607 TYPED_TEST(OverflowTest, SubOverflowToMin) {
608   TypeParam Result;
609   auto MinValue = std::numeric_limits<TypeParam>::min();
610   EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
611   EXPECT_EQ(Result, MinValue);
612 }
613 
614 TYPED_TEST(OverflowTest, SubOverflowToNegative) {
615   TypeParam Result;
616   auto MaxValue = std::numeric_limits<TypeParam>::max();
617   auto MinValue = std::numeric_limits<TypeParam>::min();
618   EXPECT_TRUE(SubOverflow<TypeParam>(MaxValue, MinValue, Result));
619   EXPECT_EQ(Result, TypeParam(-1));
620 }
621 
622 TYPED_TEST(OverflowTest, SubOverflowToPositive) {
623   TypeParam Result;
624   auto MaxValue = std::numeric_limits<TypeParam>::max();
625   auto MinValue = std::numeric_limits<TypeParam>::min();
626   EXPECT_TRUE(SubOverflow<TypeParam>(MinValue, MaxValue, Result));
627   EXPECT_EQ(Result, TypeParam(1));
628 }
629 
630 TYPED_TEST(OverflowTest, MulNoOverflow) {
631   TypeParam Result;
632   EXPECT_FALSE(MulOverflow<TypeParam>(1, 2, Result));
633   EXPECT_EQ(Result, 2);
634   EXPECT_FALSE(MulOverflow<TypeParam>(-1, 3, Result));
635   EXPECT_EQ(Result, -3);
636   EXPECT_FALSE(MulOverflow<TypeParam>(4, -2, Result));
637   EXPECT_EQ(Result, -8);
638   EXPECT_FALSE(MulOverflow<TypeParam>(-6, -5, Result));
639   EXPECT_EQ(Result, 30);
640 }
641 
642 TYPED_TEST(OverflowTest, MulNoOverflowToMax) {
643   TypeParam Result;
644   auto MaxValue = std::numeric_limits<TypeParam>::max();
645   auto MinValue = std::numeric_limits<TypeParam>::min();
646   EXPECT_FALSE(MulOverflow<TypeParam>(MinValue + 1, -1, Result));
647   EXPECT_EQ(Result, MaxValue);
648 }
649 
650 TYPED_TEST(OverflowTest, MulOverflowToMin) {
651   TypeParam Result;
652   auto MinValue = std::numeric_limits<TypeParam>::min();
653   EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, -1, Result));
654   EXPECT_EQ(Result, MinValue);
655 }
656 
657 TYPED_TEST(OverflowTest, MulOverflowMax) {
658   TypeParam Result;
659   auto MinValue = std::numeric_limits<TypeParam>::min();
660   auto MaxValue = std::numeric_limits<TypeParam>::max();
661   EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, MinValue, Result));
662   EXPECT_EQ(Result, 0);
663   EXPECT_TRUE(MulOverflow<TypeParam>(MaxValue, MaxValue, Result));
664   EXPECT_EQ(Result, 1);
665 }
666 
667 TYPED_TEST(OverflowTest, MulResultZero) {
668   TypeParam Result;
669   EXPECT_FALSE(MulOverflow<TypeParam>(4, 0, Result));
670   EXPECT_EQ(Result, TypeParam(0));
671   EXPECT_FALSE(MulOverflow<TypeParam>(-5, 0, Result));
672   EXPECT_EQ(Result, TypeParam(0));
673   EXPECT_FALSE(MulOverflow<TypeParam>(0, 5, Result));
674   EXPECT_EQ(Result, TypeParam(0));
675   EXPECT_FALSE(MulOverflow<TypeParam>(0, -5, Result));
676   EXPECT_EQ(Result, TypeParam(0));
677 }
678 
679 } // namespace
680