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 
185 TEST(MathExtras, isShiftedMask_64) {
186   EXPECT_FALSE(isShiftedMask_64(0x0101010101010101ull));
187   EXPECT_TRUE(isShiftedMask_64(0xf000000000000000ull));
188   EXPECT_TRUE(isShiftedMask_64(0xffff000000000000ull));
189   EXPECT_TRUE(isShiftedMask_64(0xffull << 55));
190 }
191 
192 TEST(MathExtras, isPowerOf2_32) {
193   EXPECT_FALSE(isPowerOf2_32(0));
194   EXPECT_TRUE(isPowerOf2_32(1 << 6));
195   EXPECT_TRUE(isPowerOf2_32(1 << 12));
196   EXPECT_FALSE(isPowerOf2_32((1 << 19) + 3));
197   EXPECT_FALSE(isPowerOf2_32(0xABCDEF0));
198 }
199 
200 TEST(MathExtras, isPowerOf2_64) {
201   EXPECT_FALSE(isPowerOf2_64(0));
202   EXPECT_TRUE(isPowerOf2_64(1LL << 46));
203   EXPECT_TRUE(isPowerOf2_64(1LL << 12));
204   EXPECT_FALSE(isPowerOf2_64((1LL << 53) + 3));
205   EXPECT_FALSE(isPowerOf2_64(0xABCDEF0ABCDEF0LL));
206 }
207 
208 TEST(MathExtras, PowerOf2Ceil) {
209   EXPECT_EQ(0U, PowerOf2Ceil(0U));
210   EXPECT_EQ(8U, PowerOf2Ceil(8U));
211   EXPECT_EQ(8U, PowerOf2Ceil(7U));
212 }
213 
214 TEST(MathExtras, PowerOf2Floor) {
215   EXPECT_EQ(0U, PowerOf2Floor(0U));
216   EXPECT_EQ(8U, PowerOf2Floor(8U));
217   EXPECT_EQ(4U, PowerOf2Floor(7U));
218 }
219 
220 TEST(MathExtras, CTLog2) {
221   EXPECT_EQ(CTLog2<1ULL << 0>(), 0U);
222   EXPECT_EQ(CTLog2<1ULL << 1>(), 1U);
223   EXPECT_EQ(CTLog2<1ULL << 2>(), 2U);
224   EXPECT_EQ(CTLog2<1ULL << 3>(), 3U);
225   EXPECT_EQ(CTLog2<1ULL << 4>(), 4U);
226   EXPECT_EQ(CTLog2<1ULL << 5>(), 5U);
227   EXPECT_EQ(CTLog2<1ULL << 6>(), 6U);
228   EXPECT_EQ(CTLog2<1ULL << 7>(), 7U);
229   EXPECT_EQ(CTLog2<1ULL << 8>(), 8U);
230   EXPECT_EQ(CTLog2<1ULL << 9>(), 9U);
231   EXPECT_EQ(CTLog2<1ULL << 10>(), 10U);
232   EXPECT_EQ(CTLog2<1ULL << 11>(), 11U);
233   EXPECT_EQ(CTLog2<1ULL << 12>(), 12U);
234   EXPECT_EQ(CTLog2<1ULL << 13>(), 13U);
235   EXPECT_EQ(CTLog2<1ULL << 14>(), 14U);
236   EXPECT_EQ(CTLog2<1ULL << 15>(), 15U);
237 }
238 
239 TEST(MathExtras, countLeadingOnes) {
240   for (int i = 30; i >= 0; --i) {
241     // Start with all ones and unset some bit.
242     EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i)));
243   }
244   for (int i = 62; i >= 0; --i) {
245     // Start with all ones and unset some bit.
246     EXPECT_EQ(63u - i, countLeadingOnes(0xFFFFFFFFFFFFFFFFULL ^ (1LL << i)));
247   }
248   for (int i = 30; i >= 0; --i) {
249     // Start with all ones and unset some bit.
250     EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i)));
251   }
252 }
253 
254 TEST(MathExtras, FloatBits) {
255   static const float kValue = 5632.34f;
256   EXPECT_FLOAT_EQ(kValue, BitsToFloat(FloatToBits(kValue)));
257 }
258 
259 TEST(MathExtras, DoubleBits) {
260   static const double kValue = 87987234.983498;
261   EXPECT_DOUBLE_EQ(kValue, BitsToDouble(DoubleToBits(kValue)));
262 }
263 
264 TEST(MathExtras, MinAlign) {
265   EXPECT_EQ(1u, MinAlign(2, 3));
266   EXPECT_EQ(2u, MinAlign(2, 4));
267   EXPECT_EQ(1u, MinAlign(17, 64));
268   EXPECT_EQ(256u, MinAlign(256, 512));
269 }
270 
271 TEST(MathExtras, NextPowerOf2) {
272   EXPECT_EQ(4u, NextPowerOf2(3));
273   EXPECT_EQ(16u, NextPowerOf2(15));
274   EXPECT_EQ(256u, NextPowerOf2(128));
275 }
276 
277 TEST(MathExtras, alignTo) {
278   EXPECT_EQ(8u, alignTo(5, 8));
279   EXPECT_EQ(24u, alignTo(17, 8));
280   EXPECT_EQ(0u, alignTo(~0LL, 8));
281 
282   EXPECT_EQ(7u, alignTo(5, 8, 7));
283   EXPECT_EQ(17u, alignTo(17, 8, 1));
284   EXPECT_EQ(3u, alignTo(~0LL, 8, 3));
285   EXPECT_EQ(552u, alignTo(321, 255, 42));
286 }
287 
288 template<typename T>
289 void SaturatingAddTestHelper()
290 {
291   const T Max = std::numeric_limits<T>::max();
292   bool ResultOverflowed;
293 
294   EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2)));
295   EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2), &ResultOverflowed));
296   EXPECT_FALSE(ResultOverflowed);
297 
298   EXPECT_EQ(Max, SaturatingAdd(Max, T(1)));
299   EXPECT_EQ(Max, SaturatingAdd(Max, T(1), &ResultOverflowed));
300   EXPECT_TRUE(ResultOverflowed);
301 
302   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1)));
303   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1), &ResultOverflowed));
304   EXPECT_FALSE(ResultOverflowed);
305 
306   EXPECT_EQ(Max, SaturatingAdd(T(1), Max));
307   EXPECT_EQ(Max, SaturatingAdd(T(1), Max, &ResultOverflowed));
308   EXPECT_TRUE(ResultOverflowed);
309 
310   EXPECT_EQ(Max, SaturatingAdd(Max, Max));
311   EXPECT_EQ(Max, SaturatingAdd(Max, Max, &ResultOverflowed));
312   EXPECT_TRUE(ResultOverflowed);
313 }
314 
315 TEST(MathExtras, SaturatingAdd) {
316   SaturatingAddTestHelper<uint8_t>();
317   SaturatingAddTestHelper<uint16_t>();
318   SaturatingAddTestHelper<uint32_t>();
319   SaturatingAddTestHelper<uint64_t>();
320 }
321 
322 template<typename T>
323 void SaturatingMultiplyTestHelper()
324 {
325   const T Max = std::numeric_limits<T>::max();
326   bool ResultOverflowed;
327 
328   // Test basic multiplication.
329   EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3)));
330   EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3), &ResultOverflowed));
331   EXPECT_FALSE(ResultOverflowed);
332 
333   EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2)));
334   EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2), &ResultOverflowed));
335   EXPECT_FALSE(ResultOverflowed);
336 
337   // Test multiplication by zero.
338   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0)));
339   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0), &ResultOverflowed));
340   EXPECT_FALSE(ResultOverflowed);
341 
342   EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0)));
343   EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0), &ResultOverflowed));
344   EXPECT_FALSE(ResultOverflowed);
345 
346   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1)));
347   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1), &ResultOverflowed));
348   EXPECT_FALSE(ResultOverflowed);
349 
350   EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0)));
351   EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0), &ResultOverflowed));
352   EXPECT_FALSE(ResultOverflowed);
353 
354   EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max));
355   EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max, &ResultOverflowed));
356   EXPECT_FALSE(ResultOverflowed);
357 
358   // Test multiplication by maximum value.
359   EXPECT_EQ(Max, SaturatingMultiply(Max, T(2)));
360   EXPECT_EQ(Max, SaturatingMultiply(Max, T(2), &ResultOverflowed));
361   EXPECT_TRUE(ResultOverflowed);
362 
363   EXPECT_EQ(Max, SaturatingMultiply(T(2), Max));
364   EXPECT_EQ(Max, SaturatingMultiply(T(2), Max, &ResultOverflowed));
365   EXPECT_TRUE(ResultOverflowed);
366 
367   EXPECT_EQ(Max, SaturatingMultiply(Max, Max));
368   EXPECT_EQ(Max, SaturatingMultiply(Max, Max, &ResultOverflowed));
369   EXPECT_TRUE(ResultOverflowed);
370 
371   // Test interesting boundary conditions for algorithm -
372   // ((1 << A) - 1) * ((1 << B) + K) for K in [-1, 0, 1]
373   // and A + B == std::numeric_limits<T>::digits.
374   // We expect overflow iff A > B and K = 1.
375   const int Digits = std::numeric_limits<T>::digits;
376   for (int A = 1, B = Digits - 1; B >= 1; ++A, --B) {
377     for (int K = -1; K <= 1; ++K) {
378       T X = (T(1) << A) - T(1);
379       T Y = (T(1) << B) + K;
380       bool OverflowExpected = A > B && K == 1;
381 
382       if(OverflowExpected) {
383         EXPECT_EQ(Max, SaturatingMultiply(X, Y));
384         EXPECT_EQ(Max, SaturatingMultiply(X, Y, &ResultOverflowed));
385         EXPECT_TRUE(ResultOverflowed);
386       } else {
387         EXPECT_EQ(X * Y, SaturatingMultiply(X, Y));
388         EXPECT_EQ(X * Y, SaturatingMultiply(X, Y, &ResultOverflowed));
389         EXPECT_FALSE(ResultOverflowed);
390       }
391     }
392   }
393 }
394 
395 TEST(MathExtras, SaturatingMultiply) {
396   SaturatingMultiplyTestHelper<uint8_t>();
397   SaturatingMultiplyTestHelper<uint16_t>();
398   SaturatingMultiplyTestHelper<uint32_t>();
399   SaturatingMultiplyTestHelper<uint64_t>();
400 }
401 
402 template<typename T>
403 void SaturatingMultiplyAddTestHelper()
404 {
405   const T Max = std::numeric_limits<T>::max();
406   bool ResultOverflowed;
407 
408   // Test basic multiply-add.
409   EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10)));
410   EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10), &ResultOverflowed));
411   EXPECT_FALSE(ResultOverflowed);
412 
413   // Test multiply overflows, add doesn't overflow
414   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(0), &ResultOverflowed));
415   EXPECT_TRUE(ResultOverflowed);
416 
417   // Test multiply doesn't overflow, add overflows
418   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
419   EXPECT_TRUE(ResultOverflowed);
420 
421   // Test multiply-add with Max as operand
422   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
423   EXPECT_TRUE(ResultOverflowed);
424 
425   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), Max, T(1), &ResultOverflowed));
426   EXPECT_TRUE(ResultOverflowed);
427 
428   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(1), &ResultOverflowed));
429   EXPECT_TRUE(ResultOverflowed);
430 
431   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, Max, &ResultOverflowed));
432   EXPECT_TRUE(ResultOverflowed);
433 
434   // Test multiply-add with 0 as operand
435   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(1), T(0), &ResultOverflowed));
436   EXPECT_FALSE(ResultOverflowed);
437 
438   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(0), T(1), &ResultOverflowed));
439   EXPECT_FALSE(ResultOverflowed);
440 
441   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(0), T(0), T(1), &ResultOverflowed));
442   EXPECT_FALSE(ResultOverflowed);
443 
444   EXPECT_EQ(T(0), SaturatingMultiplyAdd(T(0), T(0), T(0), &ResultOverflowed));
445   EXPECT_FALSE(ResultOverflowed);
446 
447 }
448 
449 TEST(MathExtras, SaturatingMultiplyAdd) {
450   SaturatingMultiplyAddTestHelper<uint8_t>();
451   SaturatingMultiplyAddTestHelper<uint16_t>();
452   SaturatingMultiplyAddTestHelper<uint32_t>();
453   SaturatingMultiplyAddTestHelper<uint64_t>();
454 }
455 
456 TEST(MathExtras, IsShiftedUInt) {
457   EXPECT_TRUE((isShiftedUInt<1, 0>(0)));
458   EXPECT_TRUE((isShiftedUInt<1, 0>(1)));
459   EXPECT_FALSE((isShiftedUInt<1, 0>(2)));
460   EXPECT_FALSE((isShiftedUInt<1, 0>(3)));
461   EXPECT_FALSE((isShiftedUInt<1, 0>(0x8000000000000000)));
462   EXPECT_TRUE((isShiftedUInt<1, 63>(0x8000000000000000)));
463   EXPECT_TRUE((isShiftedUInt<2, 62>(0xC000000000000000)));
464   EXPECT_FALSE((isShiftedUInt<2, 62>(0xE000000000000000)));
465 
466   // 0x201 is ten bits long and has a 1 in the MSB and LSB.
467   EXPECT_TRUE((isShiftedUInt<10, 5>(uint64_t(0x201) << 5)));
468   EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 4)));
469   EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 6)));
470 }
471 
472 TEST(MathExtras, IsShiftedInt) {
473   EXPECT_TRUE((isShiftedInt<1, 0>(0)));
474   EXPECT_TRUE((isShiftedInt<1, 0>(-1)));
475   EXPECT_FALSE((isShiftedInt<1, 0>(2)));
476   EXPECT_FALSE((isShiftedInt<1, 0>(3)));
477   EXPECT_FALSE((isShiftedInt<1, 0>(0x8000000000000000)));
478   EXPECT_TRUE((isShiftedInt<1, 63>(0x8000000000000000)));
479   EXPECT_TRUE((isShiftedInt<2, 62>(0xC000000000000000)));
480   EXPECT_FALSE((isShiftedInt<2, 62>(0xE000000000000000)));
481 
482   // 0x201 is ten bits long and has a 1 in the MSB and LSB.
483   EXPECT_TRUE((isShiftedInt<11, 5>(int64_t(0x201) << 5)));
484   EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 3)));
485   EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 6)));
486   EXPECT_TRUE((isShiftedInt<11, 5>(-(int64_t(0x201) << 5))));
487   EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 3))));
488   EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 6))));
489 
490   EXPECT_TRUE((isShiftedInt<6, 10>(-(int64_t(1) << 15))));
491   EXPECT_FALSE((isShiftedInt<6, 10>(int64_t(1) << 15)));
492 }
493 
494 template <typename T>
495 class OverflowTest : public ::testing::Test { };
496 
497 using OverflowTestTypes = ::testing::Types<signed char, short, int, long,
498                                            long long>;
499 
500 TYPED_TEST_SUITE(OverflowTest, OverflowTestTypes, );
501 
502 TYPED_TEST(OverflowTest, AddNoOverflow) {
503   TypeParam Result;
504   EXPECT_FALSE(AddOverflow<TypeParam>(1, 2, Result));
505   EXPECT_EQ(Result, TypeParam(3));
506 }
507 
508 TYPED_TEST(OverflowTest, AddOverflowToNegative) {
509   TypeParam Result;
510   auto MaxValue = std::numeric_limits<TypeParam>::max();
511   EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, MaxValue, Result));
512   EXPECT_EQ(Result, TypeParam(-2));
513 }
514 
515 TYPED_TEST(OverflowTest, AddOverflowToMin) {
516   TypeParam Result;
517   auto MaxValue = std::numeric_limits<TypeParam>::max();
518   EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, TypeParam(1), Result));
519   EXPECT_EQ(Result, std::numeric_limits<TypeParam>::min());
520 }
521 
522 TYPED_TEST(OverflowTest, AddOverflowToZero) {
523   TypeParam Result;
524   auto MinValue = std::numeric_limits<TypeParam>::min();
525   EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, MinValue, Result));
526   EXPECT_EQ(Result, TypeParam(0));
527 }
528 
529 TYPED_TEST(OverflowTest, AddOverflowToMax) {
530   TypeParam Result;
531   auto MinValue = std::numeric_limits<TypeParam>::min();
532   EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, TypeParam(-1), Result));
533   EXPECT_EQ(Result, std::numeric_limits<TypeParam>::max());
534 }
535 
536 TYPED_TEST(OverflowTest, SubNoOverflow) {
537   TypeParam Result;
538   EXPECT_FALSE(SubOverflow<TypeParam>(1, 2, Result));
539   EXPECT_EQ(Result, TypeParam(-1));
540 }
541 
542 TYPED_TEST(OverflowTest, SubOverflowToMax) {
543   TypeParam Result;
544   auto MinValue = std::numeric_limits<TypeParam>::min();
545   EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
546   EXPECT_EQ(Result, MinValue);
547 }
548 
549 TYPED_TEST(OverflowTest, SubOverflowToMin) {
550   TypeParam Result;
551   auto MinValue = std::numeric_limits<TypeParam>::min();
552   EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
553   EXPECT_EQ(Result, MinValue);
554 }
555 
556 TYPED_TEST(OverflowTest, SubOverflowToNegative) {
557   TypeParam Result;
558   auto MaxValue = std::numeric_limits<TypeParam>::max();
559   auto MinValue = std::numeric_limits<TypeParam>::min();
560   EXPECT_TRUE(SubOverflow<TypeParam>(MaxValue, MinValue, Result));
561   EXPECT_EQ(Result, TypeParam(-1));
562 }
563 
564 TYPED_TEST(OverflowTest, SubOverflowToPositive) {
565   TypeParam Result;
566   auto MaxValue = std::numeric_limits<TypeParam>::max();
567   auto MinValue = std::numeric_limits<TypeParam>::min();
568   EXPECT_TRUE(SubOverflow<TypeParam>(MinValue, MaxValue, Result));
569   EXPECT_EQ(Result, TypeParam(1));
570 }
571 
572 TYPED_TEST(OverflowTest, MulNoOverflow) {
573   TypeParam Result;
574   EXPECT_FALSE(MulOverflow<TypeParam>(1, 2, Result));
575   EXPECT_EQ(Result, 2);
576   EXPECT_FALSE(MulOverflow<TypeParam>(-1, 3, Result));
577   EXPECT_EQ(Result, -3);
578   EXPECT_FALSE(MulOverflow<TypeParam>(4, -2, Result));
579   EXPECT_EQ(Result, -8);
580   EXPECT_FALSE(MulOverflow<TypeParam>(-6, -5, Result));
581   EXPECT_EQ(Result, 30);
582 }
583 
584 TYPED_TEST(OverflowTest, MulNoOverflowToMax) {
585   TypeParam Result;
586   auto MaxValue = std::numeric_limits<TypeParam>::max();
587   auto MinValue = std::numeric_limits<TypeParam>::min();
588   EXPECT_FALSE(MulOverflow<TypeParam>(MinValue + 1, -1, Result));
589   EXPECT_EQ(Result, MaxValue);
590 }
591 
592 TYPED_TEST(OverflowTest, MulOverflowToMin) {
593   TypeParam Result;
594   auto MinValue = std::numeric_limits<TypeParam>::min();
595   EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, -1, Result));
596   EXPECT_EQ(Result, MinValue);
597 }
598 
599 TYPED_TEST(OverflowTest, MulOverflowMax) {
600   TypeParam Result;
601   auto MinValue = std::numeric_limits<TypeParam>::min();
602   auto MaxValue = std::numeric_limits<TypeParam>::max();
603   EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, MinValue, Result));
604   EXPECT_EQ(Result, 0);
605   EXPECT_TRUE(MulOverflow<TypeParam>(MaxValue, MaxValue, Result));
606   EXPECT_EQ(Result, 1);
607 }
608 
609 TYPED_TEST(OverflowTest, MulResultZero) {
610   TypeParam Result;
611   EXPECT_FALSE(MulOverflow<TypeParam>(4, 0, Result));
612   EXPECT_EQ(Result, TypeParam(0));
613   EXPECT_FALSE(MulOverflow<TypeParam>(-5, 0, Result));
614   EXPECT_EQ(Result, TypeParam(0));
615   EXPECT_FALSE(MulOverflow<TypeParam>(0, 5, Result));
616   EXPECT_EQ(Result, TypeParam(0));
617   EXPECT_FALSE(MulOverflow<TypeParam>(0, -5, Result));
618   EXPECT_EQ(Result, TypeParam(0));
619 }
620 
621 } // namespace
622