xref: /llvm-project/llvm/unittests/Support/MathExtrasTest.cpp (revision bfd95a003139a8f930874b2234c3cab545d504a1)
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 #include <limits>
12 
13 using namespace llvm;
14 
15 namespace {
16 
17 TEST(MathExtras, onesMask) {
18   EXPECT_EQ(0U, maskLeadingOnes<uint8_t>(0));
19   EXPECT_EQ(0U, maskTrailingOnes<uint8_t>(0));
20   EXPECT_EQ(0U, maskLeadingOnes<uint16_t>(0));
21   EXPECT_EQ(0U, maskTrailingOnes<uint16_t>(0));
22   EXPECT_EQ(0U, maskLeadingOnes<uint32_t>(0));
23   EXPECT_EQ(0U, maskTrailingOnes<uint32_t>(0));
24   EXPECT_EQ(0U, maskLeadingOnes<uint64_t>(0));
25   EXPECT_EQ(0U, maskTrailingOnes<uint64_t>(0));
26 
27   EXPECT_EQ(0x00000003U, maskTrailingOnes<uint32_t>(2U));
28   EXPECT_EQ(0xC0000000U, maskLeadingOnes<uint32_t>(2U));
29 
30   EXPECT_EQ(0x000007FFU, maskTrailingOnes<uint32_t>(11U));
31   EXPECT_EQ(0xFFE00000U, maskLeadingOnes<uint32_t>(11U));
32 
33   EXPECT_EQ(0xFFFFFFFFU, maskTrailingOnes<uint32_t>(32U));
34   EXPECT_EQ(0xFFFFFFFFU, maskLeadingOnes<uint32_t>(32U));
35   EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, maskTrailingOnes<uint64_t>(64U));
36   EXPECT_EQ(0xFFFFFFFFFFFFFFFFULL, maskLeadingOnes<uint64_t>(64U));
37 
38   EXPECT_EQ(0x0000FFFFFFFFFFFFULL, maskTrailingOnes<uint64_t>(48U));
39   EXPECT_EQ(0xFFFFFFFFFFFF0000ULL, maskLeadingOnes<uint64_t>(48U));
40 }
41 
42 TEST(MathExtras, isIntN) {
43   EXPECT_TRUE(isIntN(16, 32767));
44   EXPECT_FALSE(isIntN(16, 32768));
45   EXPECT_TRUE(isIntN(0, 0));
46   EXPECT_FALSE(isIntN(0, 1));
47   EXPECT_FALSE(isIntN(0, -1));
48 }
49 
50 TEST(MathExtras, isUIntN) {
51   EXPECT_TRUE(isUIntN(16, 65535));
52   EXPECT_FALSE(isUIntN(16, 65536));
53   EXPECT_TRUE(isUIntN(1, 0));
54   EXPECT_TRUE(isUIntN(6, 63));
55   EXPECT_TRUE(isUIntN(0, 0));
56   EXPECT_FALSE(isUIntN(0, 1));
57 }
58 
59 TEST(MathExtras, maxIntN) {
60   EXPECT_EQ(32767, maxIntN(16));
61   EXPECT_EQ(2147483647, maxIntN(32));
62   EXPECT_EQ(std::numeric_limits<int32_t>::max(), maxIntN(32));
63   EXPECT_EQ(std::numeric_limits<int64_t>::max(), maxIntN(64));
64   EXPECT_EQ(0, maxIntN(0));
65 }
66 
67 TEST(MathExtras, minIntN) {
68   EXPECT_EQ(-32768LL, minIntN(16));
69   EXPECT_EQ(-64LL, minIntN(7));
70   EXPECT_EQ(std::numeric_limits<int32_t>::min(), minIntN(32));
71   EXPECT_EQ(std::numeric_limits<int64_t>::min(), minIntN(64));
72   EXPECT_EQ(0, minIntN(0));
73 }
74 
75 TEST(MathExtras, maxUIntN) {
76   EXPECT_EQ(0xffffULL, maxUIntN(16));
77   EXPECT_EQ(0xffffffffULL, maxUIntN(32));
78   EXPECT_EQ(0xffffffffffffffffULL, maxUIntN(64));
79   EXPECT_EQ(1ULL, maxUIntN(1));
80   EXPECT_EQ(0x0fULL, maxUIntN(4));
81   EXPECT_EQ(0ULL, maxUIntN(0));
82 }
83 
84 TEST(MathExtras, reverseBits) {
85   uint8_t NZ8 = 42;
86   uint16_t NZ16 = 42;
87   uint32_t NZ32 = 42;
88   uint64_t NZ64 = 42;
89   EXPECT_EQ(0x54ULL, reverseBits(NZ8));
90   EXPECT_EQ(0x5400ULL, reverseBits(NZ16));
91   EXPECT_EQ(0x54000000ULL, reverseBits(NZ32));
92   EXPECT_EQ(0x5400000000000000ULL, reverseBits(NZ64));
93 }
94 
95 TEST(MathExtras, isShiftedMask_32) {
96   EXPECT_FALSE(isShiftedMask_32(0x01010101));
97   EXPECT_TRUE(isShiftedMask_32(0xf0000000));
98   EXPECT_TRUE(isShiftedMask_32(0xffff0000));
99   EXPECT_TRUE(isShiftedMask_32(0xff << 1));
100 
101   unsigned MaskIdx, MaskLen;
102   EXPECT_FALSE(isShiftedMask_32(0x01010101, MaskIdx, MaskLen));
103   EXPECT_TRUE(isShiftedMask_32(0xf0000000, MaskIdx, MaskLen));
104   EXPECT_EQ(28, (int)MaskIdx);
105   EXPECT_EQ(4, (int)MaskLen);
106   EXPECT_TRUE(isShiftedMask_32(0xffff0000, MaskIdx, MaskLen));
107   EXPECT_EQ(16, (int)MaskIdx);
108   EXPECT_EQ(16, (int)MaskLen);
109   EXPECT_TRUE(isShiftedMask_32(0xff << 1, MaskIdx, MaskLen));
110   EXPECT_EQ(1, (int)MaskIdx);
111   EXPECT_EQ(8, (int)MaskLen);
112 }
113 
114 TEST(MathExtras, isShiftedMask_64) {
115   EXPECT_FALSE(isShiftedMask_64(0x0101010101010101ull));
116   EXPECT_TRUE(isShiftedMask_64(0xf000000000000000ull));
117   EXPECT_TRUE(isShiftedMask_64(0xffff000000000000ull));
118   EXPECT_TRUE(isShiftedMask_64(0xffull << 55));
119 
120   unsigned MaskIdx, MaskLen;
121   EXPECT_FALSE(isShiftedMask_64(0x0101010101010101ull, MaskIdx, MaskLen));
122   EXPECT_TRUE(isShiftedMask_64(0xf000000000000000ull, MaskIdx, MaskLen));
123   EXPECT_EQ(60, (int)MaskIdx);
124   EXPECT_EQ(4, (int)MaskLen);
125   EXPECT_TRUE(isShiftedMask_64(0xffff000000000000ull, MaskIdx, MaskLen));
126   EXPECT_EQ(48, (int)MaskIdx);
127   EXPECT_EQ(16, (int)MaskLen);
128   EXPECT_TRUE(isShiftedMask_64(0xffull << 55, MaskIdx, MaskLen));
129   EXPECT_EQ(55, (int)MaskIdx);
130   EXPECT_EQ(8, (int)MaskLen);
131 }
132 
133 TEST(MathExtras, isPowerOf2_32) {
134   EXPECT_FALSE(isPowerOf2_32(0));
135   EXPECT_TRUE(isPowerOf2_32(1 << 6));
136   EXPECT_TRUE(isPowerOf2_32(1 << 12));
137   EXPECT_FALSE(isPowerOf2_32((1 << 19) + 3));
138   EXPECT_FALSE(isPowerOf2_32(0xABCDEF0));
139 }
140 
141 TEST(MathExtras, isPowerOf2_64) {
142   EXPECT_FALSE(isPowerOf2_64(0));
143   EXPECT_TRUE(isPowerOf2_64(1LL << 46));
144   EXPECT_TRUE(isPowerOf2_64(1LL << 12));
145   EXPECT_FALSE(isPowerOf2_64((1LL << 53) + 3));
146   EXPECT_FALSE(isPowerOf2_64(0xABCDEF0ABCDEF0LL));
147 }
148 
149 TEST(MathExtras, PowerOf2Ceil) {
150   EXPECT_EQ(0U, PowerOf2Ceil(0U));
151   EXPECT_EQ(8U, PowerOf2Ceil(8U));
152   EXPECT_EQ(8U, PowerOf2Ceil(7U));
153 }
154 
155 TEST(MathExtras, CTLog2) {
156   EXPECT_EQ(CTLog2<1ULL << 0>(), 0U);
157   EXPECT_EQ(CTLog2<1ULL << 1>(), 1U);
158   EXPECT_EQ(CTLog2<1ULL << 2>(), 2U);
159   EXPECT_EQ(CTLog2<1ULL << 3>(), 3U);
160   EXPECT_EQ(CTLog2<1ULL << 4>(), 4U);
161   EXPECT_EQ(CTLog2<1ULL << 5>(), 5U);
162   EXPECT_EQ(CTLog2<1ULL << 6>(), 6U);
163   EXPECT_EQ(CTLog2<1ULL << 7>(), 7U);
164   EXPECT_EQ(CTLog2<1ULL << 8>(), 8U);
165   EXPECT_EQ(CTLog2<1ULL << 9>(), 9U);
166   EXPECT_EQ(CTLog2<1ULL << 10>(), 10U);
167   EXPECT_EQ(CTLog2<1ULL << 11>(), 11U);
168   EXPECT_EQ(CTLog2<1ULL << 12>(), 12U);
169   EXPECT_EQ(CTLog2<1ULL << 13>(), 13U);
170   EXPECT_EQ(CTLog2<1ULL << 14>(), 14U);
171   EXPECT_EQ(CTLog2<1ULL << 15>(), 15U);
172 }
173 
174 TEST(MathExtras, MinAlign) {
175   EXPECT_EQ(1u, MinAlign(2, 3));
176   EXPECT_EQ(2u, MinAlign(2, 4));
177   EXPECT_EQ(1u, MinAlign(17, 64));
178   EXPECT_EQ(256u, MinAlign(256, 512));
179   EXPECT_EQ(2u, MinAlign(0, 2));
180 }
181 
182 TEST(MathExtras, NextPowerOf2) {
183   EXPECT_EQ(4u, NextPowerOf2(3));
184   EXPECT_EQ(16u, NextPowerOf2(15));
185   EXPECT_EQ(256u, NextPowerOf2(128));
186 }
187 
188 TEST(MathExtras, AlignTo) {
189   EXPECT_EQ(8u, alignTo(5, 8));
190   EXPECT_EQ(24u, alignTo(17, 8));
191   EXPECT_EQ(0u, alignTo(~0LL, 8));
192   EXPECT_EQ(static_cast<uint64_t>(std::numeric_limits<uint32_t>::max()) + 1,
193             alignTo(std::numeric_limits<uint32_t>::max(), 2));
194 
195   EXPECT_EQ(7u, alignTo(5, 8, 7));
196   EXPECT_EQ(17u, alignTo(17, 8, 1));
197   EXPECT_EQ(3u, alignTo(~0LL, 8, 3));
198   EXPECT_EQ(552u, alignTo(321, 255, 42));
199   EXPECT_EQ(std::numeric_limits<uint32_t>::max(),
200             alignTo(std::numeric_limits<uint32_t>::max(), 2, 1));
201 }
202 
203 TEST(MathExtras, AlignToPowerOf2) {
204   EXPECT_EQ(8u, alignToPowerOf2(5, 8));
205   EXPECT_EQ(24u, alignToPowerOf2(17, 8));
206   EXPECT_EQ(0u, alignToPowerOf2(~0LL, 8));
207   EXPECT_EQ(static_cast<uint64_t>(std::numeric_limits<uint32_t>::max()) + 1,
208             alignToPowerOf2(std::numeric_limits<uint32_t>::max(), 2));
209 }
210 
211 TEST(MathExtras, AlignDown) {
212   EXPECT_EQ(0u, alignDown(5, 8));
213   EXPECT_EQ(16u, alignDown(17, 8));
214   EXPECT_EQ(std::numeric_limits<uint32_t>::max() - 1,
215             alignDown(std::numeric_limits<uint32_t>::max(), 2));
216 }
217 
218 template <typename T> void SaturatingAddTestHelper() {
219   const T Max = std::numeric_limits<T>::max();
220   bool ResultOverflowed;
221 
222   EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2)));
223   EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2), &ResultOverflowed));
224   EXPECT_FALSE(ResultOverflowed);
225 
226   EXPECT_EQ(Max, SaturatingAdd(Max, T(1)));
227   EXPECT_EQ(Max, SaturatingAdd(Max, T(1), &ResultOverflowed));
228   EXPECT_TRUE(ResultOverflowed);
229 
230   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1)));
231   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1), &ResultOverflowed));
232   EXPECT_FALSE(ResultOverflowed);
233 
234   EXPECT_EQ(Max, SaturatingAdd(T(1), Max));
235   EXPECT_EQ(Max, SaturatingAdd(T(1), Max, &ResultOverflowed));
236   EXPECT_TRUE(ResultOverflowed);
237 
238   EXPECT_EQ(Max, SaturatingAdd(Max, Max));
239   EXPECT_EQ(Max, SaturatingAdd(Max, Max, &ResultOverflowed));
240   EXPECT_TRUE(ResultOverflowed);
241 
242   EXPECT_EQ(T(6), SaturatingAdd(T(1), T(2), T(3)));
243   EXPECT_EQ(T(6), SaturatingAdd(T(1), T(2), T(3), &ResultOverflowed));
244   EXPECT_FALSE(ResultOverflowed);
245 
246   EXPECT_EQ(T(10), SaturatingAdd(T(1), T(2), T(3), T(4)));
247   EXPECT_EQ(T(10), SaturatingAdd(T(1), T(2), T(3), T(4), &ResultOverflowed));
248   EXPECT_FALSE(ResultOverflowed);
249 
250   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(0)));
251   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(0), &ResultOverflowed));
252   EXPECT_FALSE(ResultOverflowed);
253 
254   EXPECT_EQ(Max, SaturatingAdd(T(0), T(0), Max));
255   EXPECT_EQ(Max, SaturatingAdd(T(0), T(0), Max, &ResultOverflowed));
256   EXPECT_FALSE(ResultOverflowed);
257 
258   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(1)));
259   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(1), &ResultOverflowed));
260   EXPECT_TRUE(ResultOverflowed);
261 
262   EXPECT_EQ(Max, SaturatingAdd(T(0), T(1), Max));
263   EXPECT_EQ(Max, SaturatingAdd(T(0), T(1), Max, &ResultOverflowed));
264   EXPECT_TRUE(ResultOverflowed);
265 
266   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 2), T(1)));
267   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 2), T(1), &ResultOverflowed));
268   EXPECT_FALSE(ResultOverflowed);
269 
270   EXPECT_EQ(Max, SaturatingAdd(T(1), T(1), T(Max - 2)));
271   EXPECT_EQ(Max, SaturatingAdd(T(1), T(1), T(Max - 2), &ResultOverflowed));
272   EXPECT_FALSE(ResultOverflowed);
273 
274   EXPECT_EQ(Max, SaturatingAdd(Max, Max, Max));
275   EXPECT_EQ(Max, SaturatingAdd(Max, Max, Max, &ResultOverflowed));
276   EXPECT_TRUE(ResultOverflowed);
277 }
278 
279 TEST(MathExtras, SaturatingAdd) {
280   SaturatingAddTestHelper<uint8_t>();
281   SaturatingAddTestHelper<uint16_t>();
282   SaturatingAddTestHelper<uint32_t>();
283   SaturatingAddTestHelper<uint64_t>();
284 }
285 
286 template<typename T>
287 void SaturatingMultiplyTestHelper()
288 {
289   const T Max = std::numeric_limits<T>::max();
290   bool ResultOverflowed;
291 
292   // Test basic multiplication.
293   EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3)));
294   EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3), &ResultOverflowed));
295   EXPECT_FALSE(ResultOverflowed);
296 
297   EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2)));
298   EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2), &ResultOverflowed));
299   EXPECT_FALSE(ResultOverflowed);
300 
301   // Test multiplication by zero.
302   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0)));
303   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0), &ResultOverflowed));
304   EXPECT_FALSE(ResultOverflowed);
305 
306   EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0)));
307   EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0), &ResultOverflowed));
308   EXPECT_FALSE(ResultOverflowed);
309 
310   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1)));
311   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1), &ResultOverflowed));
312   EXPECT_FALSE(ResultOverflowed);
313 
314   EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0)));
315   EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0), &ResultOverflowed));
316   EXPECT_FALSE(ResultOverflowed);
317 
318   EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max));
319   EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max, &ResultOverflowed));
320   EXPECT_FALSE(ResultOverflowed);
321 
322   // Test multiplication by maximum value.
323   EXPECT_EQ(Max, SaturatingMultiply(Max, T(2)));
324   EXPECT_EQ(Max, SaturatingMultiply(Max, T(2), &ResultOverflowed));
325   EXPECT_TRUE(ResultOverflowed);
326 
327   EXPECT_EQ(Max, SaturatingMultiply(T(2), Max));
328   EXPECT_EQ(Max, SaturatingMultiply(T(2), Max, &ResultOverflowed));
329   EXPECT_TRUE(ResultOverflowed);
330 
331   EXPECT_EQ(Max, SaturatingMultiply(Max, Max));
332   EXPECT_EQ(Max, SaturatingMultiply(Max, Max, &ResultOverflowed));
333   EXPECT_TRUE(ResultOverflowed);
334 
335   // Test interesting boundary conditions for algorithm -
336   // ((1 << A) - 1) * ((1 << B) + K) for K in [-1, 0, 1]
337   // and A + B == std::numeric_limits<T>::digits.
338   // We expect overflow iff A > B and K = 1.
339   const int Digits = std::numeric_limits<T>::digits;
340   for (int A = 1, B = Digits - 1; B >= 1; ++A, --B) {
341     for (int K = -1; K <= 1; ++K) {
342       T X = (T(1) << A) - T(1);
343       T Y = (T(1) << B) + K;
344       bool OverflowExpected = A > B && K == 1;
345 
346       if(OverflowExpected) {
347         EXPECT_EQ(Max, SaturatingMultiply(X, Y));
348         EXPECT_EQ(Max, SaturatingMultiply(X, Y, &ResultOverflowed));
349         EXPECT_TRUE(ResultOverflowed);
350       } else {
351         EXPECT_EQ(X * Y, SaturatingMultiply(X, Y));
352         EXPECT_EQ(X * Y, SaturatingMultiply(X, Y, &ResultOverflowed));
353         EXPECT_FALSE(ResultOverflowed);
354       }
355     }
356   }
357 }
358 
359 TEST(MathExtras, SaturatingMultiply) {
360   SaturatingMultiplyTestHelper<uint8_t>();
361   SaturatingMultiplyTestHelper<uint16_t>();
362   SaturatingMultiplyTestHelper<uint32_t>();
363   SaturatingMultiplyTestHelper<uint64_t>();
364 }
365 
366 template<typename T>
367 void SaturatingMultiplyAddTestHelper()
368 {
369   const T Max = std::numeric_limits<T>::max();
370   bool ResultOverflowed;
371 
372   // Test basic multiply-add.
373   EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10)));
374   EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10), &ResultOverflowed));
375   EXPECT_FALSE(ResultOverflowed);
376 
377   // Test multiply overflows, add doesn't overflow
378   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(0), &ResultOverflowed));
379   EXPECT_TRUE(ResultOverflowed);
380 
381   // Test multiply doesn't overflow, add overflows
382   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
383   EXPECT_TRUE(ResultOverflowed);
384 
385   // Test multiply-add with Max as operand
386   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
387   EXPECT_TRUE(ResultOverflowed);
388 
389   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), Max, T(1), &ResultOverflowed));
390   EXPECT_TRUE(ResultOverflowed);
391 
392   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(1), &ResultOverflowed));
393   EXPECT_TRUE(ResultOverflowed);
394 
395   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, Max, &ResultOverflowed));
396   EXPECT_TRUE(ResultOverflowed);
397 
398   // Test multiply-add with 0 as operand
399   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(1), T(0), &ResultOverflowed));
400   EXPECT_FALSE(ResultOverflowed);
401 
402   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(0), T(1), &ResultOverflowed));
403   EXPECT_FALSE(ResultOverflowed);
404 
405   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(0), T(0), T(1), &ResultOverflowed));
406   EXPECT_FALSE(ResultOverflowed);
407 
408   EXPECT_EQ(T(0), SaturatingMultiplyAdd(T(0), T(0), T(0), &ResultOverflowed));
409   EXPECT_FALSE(ResultOverflowed);
410 
411 }
412 
413 TEST(MathExtras, SaturatingMultiplyAdd) {
414   SaturatingMultiplyAddTestHelper<uint8_t>();
415   SaturatingMultiplyAddTestHelper<uint16_t>();
416   SaturatingMultiplyAddTestHelper<uint32_t>();
417   SaturatingMultiplyAddTestHelper<uint64_t>();
418 }
419 
420 TEST(MathExtras, IsShiftedUInt) {
421   EXPECT_TRUE((isShiftedUInt<1, 0>(0)));
422   EXPECT_TRUE((isShiftedUInt<1, 0>(1)));
423   EXPECT_FALSE((isShiftedUInt<1, 0>(2)));
424   EXPECT_FALSE((isShiftedUInt<1, 0>(3)));
425   EXPECT_FALSE((isShiftedUInt<1, 0>(0x8000000000000000)));
426   EXPECT_TRUE((isShiftedUInt<1, 63>(0x8000000000000000)));
427   EXPECT_TRUE((isShiftedUInt<2, 62>(0xC000000000000000)));
428   EXPECT_FALSE((isShiftedUInt<2, 62>(0xE000000000000000)));
429 
430   // 0x201 is ten bits long and has a 1 in the MSB and LSB.
431   EXPECT_TRUE((isShiftedUInt<10, 5>(uint64_t(0x201) << 5)));
432   EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 4)));
433   EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 6)));
434 }
435 
436 TEST(MathExtras, IsShiftedInt) {
437   EXPECT_TRUE((isShiftedInt<1, 0>(0)));
438   EXPECT_TRUE((isShiftedInt<1, 0>(-1)));
439   EXPECT_FALSE((isShiftedInt<1, 0>(2)));
440   EXPECT_FALSE((isShiftedInt<1, 0>(3)));
441   EXPECT_FALSE((isShiftedInt<1, 0>(0x8000000000000000)));
442   EXPECT_TRUE((isShiftedInt<1, 63>(0x8000000000000000)));
443   EXPECT_TRUE((isShiftedInt<2, 62>(0xC000000000000000)));
444   EXPECT_FALSE((isShiftedInt<2, 62>(0xE000000000000000)));
445 
446   // 0x201 is ten bits long and has a 1 in the MSB and LSB.
447   EXPECT_TRUE((isShiftedInt<11, 5>(int64_t(0x201) << 5)));
448   EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 3)));
449   EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 6)));
450   EXPECT_TRUE((isShiftedInt<11, 5>(-(int64_t(0x201) << 5))));
451   EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 3))));
452   EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 6))));
453 
454   EXPECT_TRUE((isShiftedInt<6, 10>(-(int64_t(1) << 15))));
455   EXPECT_FALSE((isShiftedInt<6, 10>(int64_t(1) << 15)));
456 }
457 
458 TEST(MathExtras, DivideNearest) {
459   EXPECT_EQ(divideNearest(14, 3), 5u);
460   EXPECT_EQ(divideNearest(15, 3), 5u);
461   EXPECT_EQ(divideNearest(0, 3), 0u);
462   EXPECT_EQ(divideNearest(5, 4), 1u);
463   EXPECT_EQ(divideNearest(6, 4), 2u);
464   EXPECT_EQ(divideNearest(3, 1), 3u);
465   EXPECT_EQ(divideNearest(3, 6), 1u);
466   EXPECT_EQ(divideNearest(3, 7), 0u);
467   EXPECT_EQ(divideNearest(std::numeric_limits<uint32_t>::max(), 2),
468             std::numeric_limits<uint32_t>::max() / 2 + 1);
469   EXPECT_EQ(divideNearest(std::numeric_limits<uint64_t>::max(), 2),
470             std::numeric_limits<uint64_t>::max() / 2 + 1);
471   EXPECT_EQ(divideNearest(std::numeric_limits<uint64_t>::max(), 1),
472             std::numeric_limits<uint64_t>::max());
473   EXPECT_EQ(divideNearest(std::numeric_limits<uint64_t>::max() - 1,
474                           std::numeric_limits<uint64_t>::max()),
475             1u);
476 }
477 
478 TEST(MathExtras, DivideCeil) {
479   EXPECT_EQ(divideCeil(14, 3), 5u);
480   EXPECT_EQ(divideCeil(15, 3), 5u);
481   EXPECT_EQ(divideCeil(0, 3), 0u);
482   EXPECT_EQ(divideCeil(5, 4), 2u);
483   EXPECT_EQ(divideCeil(6, 4), 2u);
484   EXPECT_EQ(divideCeil(3, 1), 3u);
485   EXPECT_EQ(divideCeil(3, 6), 1u);
486   EXPECT_EQ(divideCeil(3, 7), 1u);
487   EXPECT_EQ(divideCeil(std::numeric_limits<uint32_t>::max(), 2),
488             std::numeric_limits<uint32_t>::max() / 2 + 1);
489   EXPECT_EQ(divideCeil(std::numeric_limits<uint64_t>::max(), 2),
490             std::numeric_limits<uint64_t>::max() / 2 + 1);
491   EXPECT_EQ(divideCeil(std::numeric_limits<uint64_t>::max(), 1),
492             std::numeric_limits<uint64_t>::max());
493 
494   EXPECT_EQ(divideCeilSigned(14, 3), 5);
495   EXPECT_EQ(divideCeilSigned(15, 3), 5);
496   EXPECT_EQ(divideCeilSigned(14, -3), -4);
497   EXPECT_EQ(divideCeilSigned(-14, -3), 5);
498   EXPECT_EQ(divideCeilSigned(-14, 3), -4);
499   EXPECT_EQ(divideCeilSigned(-15, 3), -5);
500   EXPECT_EQ(divideCeilSigned(0, 3), 0);
501   EXPECT_EQ(divideCeilSigned(0, -3), 0);
502   EXPECT_EQ(divideCeilSigned(std::numeric_limits<int32_t>::max(), 2),
503             std::numeric_limits<int32_t>::max() / 2 + 1);
504   EXPECT_EQ(divideCeilSigned(std::numeric_limits<int64_t>::max(), 2),
505             std::numeric_limits<int64_t>::max() / 2 + 1);
506   EXPECT_EQ(divideCeilSigned(std::numeric_limits<int32_t>::max(), -2),
507             std::numeric_limits<int32_t>::min() / 2 + 1);
508   EXPECT_EQ(divideCeilSigned(std::numeric_limits<int64_t>::max(), -2),
509             std::numeric_limits<int64_t>::min() / 2 + 1);
510   EXPECT_EQ(divideCeilSigned(std::numeric_limits<int64_t>::min(), 1),
511             std::numeric_limits<int64_t>::min());
512 }
513 
514 TEST(MathExtras, DivideFloorSigned) {
515   EXPECT_EQ(divideFloorSigned(14, 3), 4);
516   EXPECT_EQ(divideFloorSigned(15, 3), 5);
517   EXPECT_EQ(divideFloorSigned(14, -3), -5);
518   EXPECT_EQ(divideFloorSigned(-14, -3), 4);
519   EXPECT_EQ(divideFloorSigned(-14, 3), -5);
520   EXPECT_EQ(divideFloorSigned(-15, 3), -5);
521   EXPECT_EQ(divideFloorSigned(0, 3), 0);
522   EXPECT_EQ(divideFloorSigned(0, -3), 0);
523   EXPECT_EQ(divideFloorSigned(std::numeric_limits<int32_t>::max(), 2),
524             std::numeric_limits<int32_t>::max() / 2);
525   EXPECT_EQ(divideFloorSigned(std::numeric_limits<int64_t>::max(), 2),
526             std::numeric_limits<int64_t>::max() / 2);
527   EXPECT_EQ(divideFloorSigned(std::numeric_limits<int32_t>::max(), -2),
528             std::numeric_limits<int32_t>::min() / 2);
529   EXPECT_EQ(divideFloorSigned(std::numeric_limits<int64_t>::max(), -2),
530             std::numeric_limits<int64_t>::min() / 2);
531   EXPECT_EQ(divideFloorSigned(std::numeric_limits<int64_t>::min(), 1),
532             std::numeric_limits<int64_t>::min());
533 }
534 
535 TEST(MathExtras, Mod) {
536   EXPECT_EQ(mod(1, 14), 1);
537   EXPECT_EQ(mod(-1, 14), 13);
538   EXPECT_EQ(mod(14, 3), 2);
539   EXPECT_EQ(mod(15, 3), 0);
540   EXPECT_EQ(mod(-14, 3), 1);
541   EXPECT_EQ(mod(-15, 3), 0);
542   EXPECT_EQ(mod(0, 3), 0);
543 }
544 
545 template <typename T> class OverflowTest : public ::testing::Test {};
546 
547 using OverflowTestTypes = ::testing::Types<signed char, short, int, long,
548                                            long long>;
549 
550 TYPED_TEST_SUITE(OverflowTest, OverflowTestTypes, );
551 
552 TYPED_TEST(OverflowTest, AddNoOverflow) {
553   TypeParam Result;
554   EXPECT_FALSE(AddOverflow<TypeParam>(1, 2, Result));
555   EXPECT_EQ(Result, TypeParam(3));
556 }
557 
558 TYPED_TEST(OverflowTest, AddOverflowToNegative) {
559   TypeParam Result;
560   auto MaxValue = std::numeric_limits<TypeParam>::max();
561   EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, MaxValue, Result));
562   EXPECT_EQ(Result, TypeParam(-2));
563 }
564 
565 TYPED_TEST(OverflowTest, AddOverflowToMin) {
566   TypeParam Result;
567   auto MaxValue = std::numeric_limits<TypeParam>::max();
568   EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, TypeParam(1), Result));
569   EXPECT_EQ(Result, std::numeric_limits<TypeParam>::min());
570 }
571 
572 TYPED_TEST(OverflowTest, AddOverflowToZero) {
573   TypeParam Result;
574   auto MinValue = std::numeric_limits<TypeParam>::min();
575   EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, MinValue, Result));
576   EXPECT_EQ(Result, TypeParam(0));
577 }
578 
579 TYPED_TEST(OverflowTest, AddOverflowToMax) {
580   TypeParam Result;
581   auto MinValue = std::numeric_limits<TypeParam>::min();
582   EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, TypeParam(-1), Result));
583   EXPECT_EQ(Result, std::numeric_limits<TypeParam>::max());
584 }
585 
586 TYPED_TEST(OverflowTest, SubNoOverflow) {
587   TypeParam Result;
588   EXPECT_FALSE(SubOverflow<TypeParam>(1, 2, Result));
589   EXPECT_EQ(Result, TypeParam(-1));
590 }
591 
592 TYPED_TEST(OverflowTest, SubOverflowToMax) {
593   TypeParam Result;
594   auto MinValue = std::numeric_limits<TypeParam>::min();
595   EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
596   EXPECT_EQ(Result, MinValue);
597 }
598 
599 TYPED_TEST(OverflowTest, SubOverflowToMin) {
600   TypeParam Result;
601   auto MinValue = std::numeric_limits<TypeParam>::min();
602   EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
603   EXPECT_EQ(Result, MinValue);
604 }
605 
606 TYPED_TEST(OverflowTest, SubOverflowToNegative) {
607   TypeParam Result;
608   auto MaxValue = std::numeric_limits<TypeParam>::max();
609   auto MinValue = std::numeric_limits<TypeParam>::min();
610   EXPECT_TRUE(SubOverflow<TypeParam>(MaxValue, MinValue, Result));
611   EXPECT_EQ(Result, TypeParam(-1));
612 }
613 
614 TYPED_TEST(OverflowTest, SubOverflowToPositive) {
615   TypeParam Result;
616   auto MaxValue = std::numeric_limits<TypeParam>::max();
617   auto MinValue = std::numeric_limits<TypeParam>::min();
618   EXPECT_TRUE(SubOverflow<TypeParam>(MinValue, MaxValue, Result));
619   EXPECT_EQ(Result, TypeParam(1));
620 }
621 
622 TYPED_TEST(OverflowTest, MulNoOverflow) {
623   TypeParam Result;
624   EXPECT_FALSE(MulOverflow<TypeParam>(1, 2, Result));
625   EXPECT_EQ(Result, 2);
626   EXPECT_FALSE(MulOverflow<TypeParam>(-1, 3, Result));
627   EXPECT_EQ(Result, -3);
628   EXPECT_FALSE(MulOverflow<TypeParam>(4, -2, Result));
629   EXPECT_EQ(Result, -8);
630   EXPECT_FALSE(MulOverflow<TypeParam>(-6, -5, Result));
631   EXPECT_EQ(Result, 30);
632 }
633 
634 TYPED_TEST(OverflowTest, MulNoOverflowToMax) {
635   TypeParam Result;
636   auto MaxValue = std::numeric_limits<TypeParam>::max();
637   auto MinValue = std::numeric_limits<TypeParam>::min();
638   EXPECT_FALSE(MulOverflow<TypeParam>(MinValue + 1, -1, Result));
639   EXPECT_EQ(Result, MaxValue);
640 }
641 
642 TYPED_TEST(OverflowTest, MulOverflowToMin) {
643   TypeParam Result;
644   auto MinValue = std::numeric_limits<TypeParam>::min();
645   EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, -1, Result));
646   EXPECT_EQ(Result, MinValue);
647 }
648 
649 TYPED_TEST(OverflowTest, MulOverflowMax) {
650   TypeParam Result;
651   auto MinValue = std::numeric_limits<TypeParam>::min();
652   auto MaxValue = std::numeric_limits<TypeParam>::max();
653   EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, MinValue, Result));
654   EXPECT_EQ(Result, 0);
655   EXPECT_TRUE(MulOverflow<TypeParam>(MaxValue, MaxValue, Result));
656   EXPECT_EQ(Result, 1);
657 }
658 
659 TYPED_TEST(OverflowTest, MulResultZero) {
660   TypeParam Result;
661   EXPECT_FALSE(MulOverflow<TypeParam>(4, 0, Result));
662   EXPECT_EQ(Result, TypeParam(0));
663   EXPECT_FALSE(MulOverflow<TypeParam>(-5, 0, Result));
664   EXPECT_EQ(Result, TypeParam(0));
665   EXPECT_FALSE(MulOverflow<TypeParam>(0, 5, Result));
666   EXPECT_EQ(Result, TypeParam(0));
667   EXPECT_FALSE(MulOverflow<TypeParam>(0, -5, Result));
668   EXPECT_EQ(Result, TypeParam(0));
669 }
670 } // namespace
671