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, isPowerOf2_32) {
179   EXPECT_FALSE(isPowerOf2_32(0));
180   EXPECT_TRUE(isPowerOf2_32(1 << 6));
181   EXPECT_TRUE(isPowerOf2_32(1 << 12));
182   EXPECT_FALSE(isPowerOf2_32((1 << 19) + 3));
183   EXPECT_FALSE(isPowerOf2_32(0xABCDEF0));
184 }
185 
186 TEST(MathExtras, isPowerOf2_64) {
187   EXPECT_FALSE(isPowerOf2_64(0));
188   EXPECT_TRUE(isPowerOf2_64(1LL << 46));
189   EXPECT_TRUE(isPowerOf2_64(1LL << 12));
190   EXPECT_FALSE(isPowerOf2_64((1LL << 53) + 3));
191   EXPECT_FALSE(isPowerOf2_64(0xABCDEF0ABCDEF0LL));
192 }
193 
194 TEST(MathExtras, PowerOf2Ceil) {
195   EXPECT_EQ(0U, PowerOf2Ceil(0U));
196   EXPECT_EQ(8U, PowerOf2Ceil(8U));
197   EXPECT_EQ(8U, PowerOf2Ceil(7U));
198 }
199 
200 TEST(MathExtras, PowerOf2Floor) {
201   EXPECT_EQ(0U, PowerOf2Floor(0U));
202   EXPECT_EQ(8U, PowerOf2Floor(8U));
203   EXPECT_EQ(4U, PowerOf2Floor(7U));
204 }
205 
206 TEST(MathExtras, CTLog2) {
207   EXPECT_EQ(CTLog2<1ULL << 0>(), 0U);
208   EXPECT_EQ(CTLog2<1ULL << 1>(), 1U);
209   EXPECT_EQ(CTLog2<1ULL << 2>(), 2U);
210   EXPECT_EQ(CTLog2<1ULL << 3>(), 3U);
211   EXPECT_EQ(CTLog2<1ULL << 4>(), 4U);
212   EXPECT_EQ(CTLog2<1ULL << 5>(), 5U);
213   EXPECT_EQ(CTLog2<1ULL << 6>(), 6U);
214   EXPECT_EQ(CTLog2<1ULL << 7>(), 7U);
215   EXPECT_EQ(CTLog2<1ULL << 8>(), 8U);
216   EXPECT_EQ(CTLog2<1ULL << 9>(), 9U);
217   EXPECT_EQ(CTLog2<1ULL << 10>(), 10U);
218   EXPECT_EQ(CTLog2<1ULL << 11>(), 11U);
219   EXPECT_EQ(CTLog2<1ULL << 12>(), 12U);
220   EXPECT_EQ(CTLog2<1ULL << 13>(), 13U);
221   EXPECT_EQ(CTLog2<1ULL << 14>(), 14U);
222   EXPECT_EQ(CTLog2<1ULL << 15>(), 15U);
223 }
224 
225 TEST(MathExtras, ByteSwap_32) {
226   EXPECT_EQ(0x44332211u, ByteSwap_32(0x11223344));
227   EXPECT_EQ(0xDDCCBBAAu, ByteSwap_32(0xAABBCCDD));
228 }
229 
230 TEST(MathExtras, ByteSwap_64) {
231   EXPECT_EQ(0x8877665544332211ULL, ByteSwap_64(0x1122334455667788LL));
232   EXPECT_EQ(0x1100FFEEDDCCBBAAULL, ByteSwap_64(0xAABBCCDDEEFF0011LL));
233 }
234 
235 TEST(MathExtras, countLeadingOnes) {
236   for (int i = 30; i >= 0; --i) {
237     // Start with all ones and unset some bit.
238     EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i)));
239   }
240   for (int i = 62; i >= 0; --i) {
241     // Start with all ones and unset some bit.
242     EXPECT_EQ(63u - i, countLeadingOnes(0xFFFFFFFFFFFFFFFFULL ^ (1LL << i)));
243   }
244   for (int i = 30; i >= 0; --i) {
245     // Start with all ones and unset some bit.
246     EXPECT_EQ(31u - i, countLeadingOnes(0xFFFFFFFF ^ (1 << i)));
247   }
248 }
249 
250 TEST(MathExtras, FloatBits) {
251   static const float kValue = 5632.34f;
252   EXPECT_FLOAT_EQ(kValue, BitsToFloat(FloatToBits(kValue)));
253 }
254 
255 TEST(MathExtras, DoubleBits) {
256   static const double kValue = 87987234.983498;
257   EXPECT_DOUBLE_EQ(kValue, BitsToDouble(DoubleToBits(kValue)));
258 }
259 
260 TEST(MathExtras, MinAlign) {
261   EXPECT_EQ(1u, MinAlign(2, 3));
262   EXPECT_EQ(2u, MinAlign(2, 4));
263   EXPECT_EQ(1u, MinAlign(17, 64));
264   EXPECT_EQ(256u, MinAlign(256, 512));
265 }
266 
267 TEST(MathExtras, NextPowerOf2) {
268   EXPECT_EQ(4u, NextPowerOf2(3));
269   EXPECT_EQ(16u, NextPowerOf2(15));
270   EXPECT_EQ(256u, NextPowerOf2(128));
271 }
272 
273 TEST(MathExtras, alignTo) {
274   EXPECT_EQ(8u, alignTo(5, 8));
275   EXPECT_EQ(24u, alignTo(17, 8));
276   EXPECT_EQ(0u, alignTo(~0LL, 8));
277 
278   EXPECT_EQ(7u, alignTo(5, 8, 7));
279   EXPECT_EQ(17u, alignTo(17, 8, 1));
280   EXPECT_EQ(3u, alignTo(~0LL, 8, 3));
281   EXPECT_EQ(552u, alignTo(321, 255, 42));
282 }
283 
284 template<typename T>
285 void SaturatingAddTestHelper()
286 {
287   const T Max = std::numeric_limits<T>::max();
288   bool ResultOverflowed;
289 
290   EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2)));
291   EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2), &ResultOverflowed));
292   EXPECT_FALSE(ResultOverflowed);
293 
294   EXPECT_EQ(Max, SaturatingAdd(Max, T(1)));
295   EXPECT_EQ(Max, SaturatingAdd(Max, T(1), &ResultOverflowed));
296   EXPECT_TRUE(ResultOverflowed);
297 
298   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1)));
299   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1), &ResultOverflowed));
300   EXPECT_FALSE(ResultOverflowed);
301 
302   EXPECT_EQ(Max, SaturatingAdd(T(1), Max));
303   EXPECT_EQ(Max, SaturatingAdd(T(1), Max, &ResultOverflowed));
304   EXPECT_TRUE(ResultOverflowed);
305 
306   EXPECT_EQ(Max, SaturatingAdd(Max, Max));
307   EXPECT_EQ(Max, SaturatingAdd(Max, Max, &ResultOverflowed));
308   EXPECT_TRUE(ResultOverflowed);
309 }
310 
311 TEST(MathExtras, SaturatingAdd) {
312   SaturatingAddTestHelper<uint8_t>();
313   SaturatingAddTestHelper<uint16_t>();
314   SaturatingAddTestHelper<uint32_t>();
315   SaturatingAddTestHelper<uint64_t>();
316 }
317 
318 template<typename T>
319 void SaturatingMultiplyTestHelper()
320 {
321   const T Max = std::numeric_limits<T>::max();
322   bool ResultOverflowed;
323 
324   // Test basic multiplication.
325   EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3)));
326   EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3), &ResultOverflowed));
327   EXPECT_FALSE(ResultOverflowed);
328 
329   EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2)));
330   EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2), &ResultOverflowed));
331   EXPECT_FALSE(ResultOverflowed);
332 
333   // Test multiplication by zero.
334   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0)));
335   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0), &ResultOverflowed));
336   EXPECT_FALSE(ResultOverflowed);
337 
338   EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0)));
339   EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0), &ResultOverflowed));
340   EXPECT_FALSE(ResultOverflowed);
341 
342   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1)));
343   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1), &ResultOverflowed));
344   EXPECT_FALSE(ResultOverflowed);
345 
346   EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0)));
347   EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0), &ResultOverflowed));
348   EXPECT_FALSE(ResultOverflowed);
349 
350   EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max));
351   EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max, &ResultOverflowed));
352   EXPECT_FALSE(ResultOverflowed);
353 
354   // Test multiplication by maximum value.
355   EXPECT_EQ(Max, SaturatingMultiply(Max, T(2)));
356   EXPECT_EQ(Max, SaturatingMultiply(Max, T(2), &ResultOverflowed));
357   EXPECT_TRUE(ResultOverflowed);
358 
359   EXPECT_EQ(Max, SaturatingMultiply(T(2), Max));
360   EXPECT_EQ(Max, SaturatingMultiply(T(2), Max, &ResultOverflowed));
361   EXPECT_TRUE(ResultOverflowed);
362 
363   EXPECT_EQ(Max, SaturatingMultiply(Max, Max));
364   EXPECT_EQ(Max, SaturatingMultiply(Max, Max, &ResultOverflowed));
365   EXPECT_TRUE(ResultOverflowed);
366 
367   // Test interesting boundary conditions for algorithm -
368   // ((1 << A) - 1) * ((1 << B) + K) for K in [-1, 0, 1]
369   // and A + B == std::numeric_limits<T>::digits.
370   // We expect overflow iff A > B and K = 1.
371   const int Digits = std::numeric_limits<T>::digits;
372   for (int A = 1, B = Digits - 1; B >= 1; ++A, --B) {
373     for (int K = -1; K <= 1; ++K) {
374       T X = (T(1) << A) - T(1);
375       T Y = (T(1) << B) + K;
376       bool OverflowExpected = A > B && K == 1;
377 
378       if(OverflowExpected) {
379         EXPECT_EQ(Max, SaturatingMultiply(X, Y));
380         EXPECT_EQ(Max, SaturatingMultiply(X, Y, &ResultOverflowed));
381         EXPECT_TRUE(ResultOverflowed);
382       } else {
383         EXPECT_EQ(X * Y, SaturatingMultiply(X, Y));
384         EXPECT_EQ(X * Y, SaturatingMultiply(X, Y, &ResultOverflowed));
385         EXPECT_FALSE(ResultOverflowed);
386       }
387     }
388   }
389 }
390 
391 TEST(MathExtras, SaturatingMultiply) {
392   SaturatingMultiplyTestHelper<uint8_t>();
393   SaturatingMultiplyTestHelper<uint16_t>();
394   SaturatingMultiplyTestHelper<uint32_t>();
395   SaturatingMultiplyTestHelper<uint64_t>();
396 }
397 
398 template<typename T>
399 void SaturatingMultiplyAddTestHelper()
400 {
401   const T Max = std::numeric_limits<T>::max();
402   bool ResultOverflowed;
403 
404   // Test basic multiply-add.
405   EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10)));
406   EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10), &ResultOverflowed));
407   EXPECT_FALSE(ResultOverflowed);
408 
409   // Test multiply overflows, add doesn't overflow
410   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(0), &ResultOverflowed));
411   EXPECT_TRUE(ResultOverflowed);
412 
413   // Test multiply doesn't overflow, add overflows
414   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
415   EXPECT_TRUE(ResultOverflowed);
416 
417   // Test multiply-add with Max as operand
418   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
419   EXPECT_TRUE(ResultOverflowed);
420 
421   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), Max, T(1), &ResultOverflowed));
422   EXPECT_TRUE(ResultOverflowed);
423 
424   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(1), &ResultOverflowed));
425   EXPECT_TRUE(ResultOverflowed);
426 
427   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, Max, &ResultOverflowed));
428   EXPECT_TRUE(ResultOverflowed);
429 
430   // Test multiply-add with 0 as operand
431   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(1), T(0), &ResultOverflowed));
432   EXPECT_FALSE(ResultOverflowed);
433 
434   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(0), T(1), &ResultOverflowed));
435   EXPECT_FALSE(ResultOverflowed);
436 
437   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(0), T(0), T(1), &ResultOverflowed));
438   EXPECT_FALSE(ResultOverflowed);
439 
440   EXPECT_EQ(T(0), SaturatingMultiplyAdd(T(0), T(0), T(0), &ResultOverflowed));
441   EXPECT_FALSE(ResultOverflowed);
442 
443 }
444 
445 TEST(MathExtras, SaturatingMultiplyAdd) {
446   SaturatingMultiplyAddTestHelper<uint8_t>();
447   SaturatingMultiplyAddTestHelper<uint16_t>();
448   SaturatingMultiplyAddTestHelper<uint32_t>();
449   SaturatingMultiplyAddTestHelper<uint64_t>();
450 }
451 
452 TEST(MathExtras, IsShiftedUInt) {
453   EXPECT_TRUE((isShiftedUInt<1, 0>(0)));
454   EXPECT_TRUE((isShiftedUInt<1, 0>(1)));
455   EXPECT_FALSE((isShiftedUInt<1, 0>(2)));
456   EXPECT_FALSE((isShiftedUInt<1, 0>(3)));
457   EXPECT_FALSE((isShiftedUInt<1, 0>(0x8000000000000000)));
458   EXPECT_TRUE((isShiftedUInt<1, 63>(0x8000000000000000)));
459   EXPECT_TRUE((isShiftedUInt<2, 62>(0xC000000000000000)));
460   EXPECT_FALSE((isShiftedUInt<2, 62>(0xE000000000000000)));
461 
462   // 0x201 is ten bits long and has a 1 in the MSB and LSB.
463   EXPECT_TRUE((isShiftedUInt<10, 5>(uint64_t(0x201) << 5)));
464   EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 4)));
465   EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 6)));
466 }
467 
468 TEST(MathExtras, IsShiftedInt) {
469   EXPECT_TRUE((isShiftedInt<1, 0>(0)));
470   EXPECT_TRUE((isShiftedInt<1, 0>(-1)));
471   EXPECT_FALSE((isShiftedInt<1, 0>(2)));
472   EXPECT_FALSE((isShiftedInt<1, 0>(3)));
473   EXPECT_FALSE((isShiftedInt<1, 0>(0x8000000000000000)));
474   EXPECT_TRUE((isShiftedInt<1, 63>(0x8000000000000000)));
475   EXPECT_TRUE((isShiftedInt<2, 62>(0xC000000000000000)));
476   EXPECT_FALSE((isShiftedInt<2, 62>(0xE000000000000000)));
477 
478   // 0x201 is ten bits long and has a 1 in the MSB and LSB.
479   EXPECT_TRUE((isShiftedInt<11, 5>(int64_t(0x201) << 5)));
480   EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 3)));
481   EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 6)));
482   EXPECT_TRUE((isShiftedInt<11, 5>(-(int64_t(0x201) << 5))));
483   EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 3))));
484   EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 6))));
485 
486   EXPECT_TRUE((isShiftedInt<6, 10>(-(int64_t(1) << 15))));
487   EXPECT_FALSE((isShiftedInt<6, 10>(int64_t(1) << 15)));
488 }
489 
490 template <typename T>
491 class OverflowTest : public ::testing::Test { };
492 
493 using OverflowTestTypes = ::testing::Types<signed char, short, int, long,
494                                            long long>;
495 
496 TYPED_TEST_CASE(OverflowTest, OverflowTestTypes);
497 
498 TYPED_TEST(OverflowTest, AddNoOverflow) {
499   TypeParam Result;
500   EXPECT_FALSE(AddOverflow<TypeParam>(1, 2, Result));
501   EXPECT_EQ(Result, TypeParam(3));
502 }
503 
504 TYPED_TEST(OverflowTest, AddOverflowToNegative) {
505   TypeParam Result;
506   auto MaxValue = std::numeric_limits<TypeParam>::max();
507   EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, MaxValue, Result));
508   EXPECT_EQ(Result, TypeParam(-2));
509 }
510 
511 TYPED_TEST(OverflowTest, AddOverflowToMin) {
512   TypeParam Result;
513   auto MaxValue = std::numeric_limits<TypeParam>::max();
514   EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, TypeParam(1), Result));
515   EXPECT_EQ(Result, std::numeric_limits<TypeParam>::min());
516 }
517 
518 TYPED_TEST(OverflowTest, AddOverflowToZero) {
519   TypeParam Result;
520   auto MinValue = std::numeric_limits<TypeParam>::min();
521   EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, MinValue, Result));
522   EXPECT_EQ(Result, TypeParam(0));
523 }
524 
525 TYPED_TEST(OverflowTest, AddOverflowToMax) {
526   TypeParam Result;
527   auto MinValue = std::numeric_limits<TypeParam>::min();
528   EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, TypeParam(-1), Result));
529   EXPECT_EQ(Result, std::numeric_limits<TypeParam>::max());
530 }
531 
532 TYPED_TEST(OverflowTest, SubNoOverflow) {
533   TypeParam Result;
534   EXPECT_FALSE(SubOverflow<TypeParam>(1, 2, Result));
535   EXPECT_EQ(Result, TypeParam(-1));
536 }
537 
538 TYPED_TEST(OverflowTest, SubOverflowToMax) {
539   TypeParam Result;
540   auto MinValue = std::numeric_limits<TypeParam>::min();
541   EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
542   EXPECT_EQ(Result, MinValue);
543 }
544 
545 TYPED_TEST(OverflowTest, SubOverflowToMin) {
546   TypeParam Result;
547   auto MinValue = std::numeric_limits<TypeParam>::min();
548   EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
549   EXPECT_EQ(Result, MinValue);
550 }
551 
552 TYPED_TEST(OverflowTest, SubOverflowToNegative) {
553   TypeParam Result;
554   auto MaxValue = std::numeric_limits<TypeParam>::max();
555   auto MinValue = std::numeric_limits<TypeParam>::min();
556   EXPECT_TRUE(SubOverflow<TypeParam>(MaxValue, MinValue, Result));
557   EXPECT_EQ(Result, TypeParam(-1));
558 }
559 
560 TYPED_TEST(OverflowTest, SubOverflowToPositive) {
561   TypeParam Result;
562   auto MaxValue = std::numeric_limits<TypeParam>::max();
563   auto MinValue = std::numeric_limits<TypeParam>::min();
564   EXPECT_TRUE(SubOverflow<TypeParam>(MinValue, MaxValue, Result));
565   EXPECT_EQ(Result, TypeParam(1));
566 }
567 
568 TYPED_TEST(OverflowTest, MulNoOverflow) {
569   TypeParam Result;
570   EXPECT_FALSE(MulOverflow<TypeParam>(1, 2, Result));
571   EXPECT_EQ(Result, 2);
572   EXPECT_FALSE(MulOverflow<TypeParam>(-1, 3, Result));
573   EXPECT_EQ(Result, -3);
574   EXPECT_FALSE(MulOverflow<TypeParam>(4, -2, Result));
575   EXPECT_EQ(Result, -8);
576   EXPECT_FALSE(MulOverflow<TypeParam>(-6, -5, Result));
577   EXPECT_EQ(Result, 30);
578 }
579 
580 TYPED_TEST(OverflowTest, MulNoOverflowToMax) {
581   TypeParam Result;
582   auto MaxValue = std::numeric_limits<TypeParam>::max();
583   auto MinValue = std::numeric_limits<TypeParam>::min();
584   EXPECT_FALSE(MulOverflow<TypeParam>(MinValue + 1, -1, Result));
585   EXPECT_EQ(Result, MaxValue);
586 }
587 
588 TYPED_TEST(OverflowTest, MulOverflowToMin) {
589   TypeParam Result;
590   auto MinValue = std::numeric_limits<TypeParam>::min();
591   EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, -1, Result));
592   EXPECT_EQ(Result, MinValue);
593 }
594 
595 TYPED_TEST(OverflowTest, MulOverflowMax) {
596   TypeParam Result;
597   auto MinValue = std::numeric_limits<TypeParam>::min();
598   auto MaxValue = std::numeric_limits<TypeParam>::max();
599   EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, MinValue, Result));
600   EXPECT_EQ(Result, 0);
601   EXPECT_TRUE(MulOverflow<TypeParam>(MaxValue, MaxValue, Result));
602   EXPECT_EQ(Result, 1);
603 }
604 
605 TYPED_TEST(OverflowTest, MulResultZero) {
606   TypeParam Result;
607   EXPECT_FALSE(MulOverflow<TypeParam>(4, 0, Result));
608   EXPECT_EQ(Result, TypeParam(0));
609   EXPECT_FALSE(MulOverflow<TypeParam>(-5, 0, Result));
610   EXPECT_EQ(Result, TypeParam(0));
611   EXPECT_FALSE(MulOverflow<TypeParam>(0, 5, Result));
612   EXPECT_EQ(Result, TypeParam(0));
613   EXPECT_FALSE(MulOverflow<TypeParam>(0, -5, Result));
614   EXPECT_EQ(Result, TypeParam(0));
615 }
616 
617 } // namespace
618