xref: /llvm-project/llvm/unittests/Support/MathExtrasTest.cpp (revision f1eed011b4b28aecd07170f9b26cc0efb45904ee)
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(8u, alignTo(5ULL, 8ULL));
193 
194   EXPECT_EQ(8u, alignTo<8>(5));
195   EXPECT_EQ(24u, alignTo<8>(17));
196   EXPECT_EQ(0u, alignTo<8>(~0LL));
197   EXPECT_EQ(254u,
198             alignTo<static_cast<uint8_t>(127)>(static_cast<uint8_t>(200)));
199 
200   EXPECT_EQ(7u, alignTo(5, 8, 7));
201   EXPECT_EQ(17u, alignTo(17, 8, 1));
202   EXPECT_EQ(3u, alignTo(~0LL, 8, 3));
203   EXPECT_EQ(552u, alignTo(321, 255, 42));
204   EXPECT_EQ(std::numeric_limits<uint32_t>::max(),
205             alignTo(std::numeric_limits<uint32_t>::max(), 2, 1));
206 
207   // Overflow.
208   EXPECT_EQ(0u, alignTo(static_cast<uint8_t>(200), static_cast<uint8_t>(128)));
209   EXPECT_EQ(0u, alignTo<static_cast<uint8_t>(128)>(static_cast<uint8_t>(200)));
210   EXPECT_EQ(0u, alignTo(static_cast<uint8_t>(200), static_cast<uint8_t>(128),
211                         static_cast<uint8_t>(0)));
212   EXPECT_EQ(0u, alignTo(std::numeric_limits<uint32_t>::max(), 2));
213 }
214 
215 TEST(MathExtras, AlignToPowerOf2) {
216   EXPECT_EQ(0u, alignToPowerOf2(0u, 8));
217   EXPECT_EQ(8u, alignToPowerOf2(5, 8));
218   EXPECT_EQ(24u, alignToPowerOf2(17, 8));
219   EXPECT_EQ(0u, alignToPowerOf2(~0LL, 8));
220   EXPECT_EQ(240u, alignToPowerOf2(240, 16));
221   EXPECT_EQ(static_cast<uint64_t>(std::numeric_limits<uint32_t>::max()) + 1,
222             alignToPowerOf2(std::numeric_limits<uint32_t>::max(), 2));
223 }
224 
225 TEST(MathExtras, AlignDown) {
226   EXPECT_EQ(0u, alignDown(5, 8));
227   EXPECT_EQ(16u, alignDown(17, 8));
228   EXPECT_EQ(std::numeric_limits<uint32_t>::max() - 1,
229             alignDown(std::numeric_limits<uint32_t>::max(), 2));
230 }
231 
232 template <typename T> void SaturatingAddTestHelper() {
233   const T Max = std::numeric_limits<T>::max();
234   bool ResultOverflowed;
235 
236   EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2)));
237   EXPECT_EQ(T(3), SaturatingAdd(T(1), T(2), &ResultOverflowed));
238   EXPECT_FALSE(ResultOverflowed);
239 
240   EXPECT_EQ(Max, SaturatingAdd(Max, T(1)));
241   EXPECT_EQ(Max, SaturatingAdd(Max, T(1), &ResultOverflowed));
242   EXPECT_TRUE(ResultOverflowed);
243 
244   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1)));
245   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 1), &ResultOverflowed));
246   EXPECT_FALSE(ResultOverflowed);
247 
248   EXPECT_EQ(Max, SaturatingAdd(T(1), Max));
249   EXPECT_EQ(Max, SaturatingAdd(T(1), Max, &ResultOverflowed));
250   EXPECT_TRUE(ResultOverflowed);
251 
252   EXPECT_EQ(Max, SaturatingAdd(Max, Max));
253   EXPECT_EQ(Max, SaturatingAdd(Max, Max, &ResultOverflowed));
254   EXPECT_TRUE(ResultOverflowed);
255 
256   EXPECT_EQ(T(6), SaturatingAdd(T(1), T(2), T(3)));
257   EXPECT_EQ(T(6), SaturatingAdd(T(1), T(2), T(3), &ResultOverflowed));
258   EXPECT_FALSE(ResultOverflowed);
259 
260   EXPECT_EQ(T(10), SaturatingAdd(T(1), T(2), T(3), T(4)));
261   EXPECT_EQ(T(10), SaturatingAdd(T(1), T(2), T(3), T(4), &ResultOverflowed));
262   EXPECT_FALSE(ResultOverflowed);
263 
264   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(0)));
265   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(0), &ResultOverflowed));
266   EXPECT_FALSE(ResultOverflowed);
267 
268   EXPECT_EQ(Max, SaturatingAdd(T(0), T(0), Max));
269   EXPECT_EQ(Max, SaturatingAdd(T(0), T(0), Max, &ResultOverflowed));
270   EXPECT_FALSE(ResultOverflowed);
271 
272   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(1)));
273   EXPECT_EQ(Max, SaturatingAdd(Max, T(0), T(1), &ResultOverflowed));
274   EXPECT_TRUE(ResultOverflowed);
275 
276   EXPECT_EQ(Max, SaturatingAdd(T(0), T(1), Max));
277   EXPECT_EQ(Max, SaturatingAdd(T(0), T(1), Max, &ResultOverflowed));
278   EXPECT_TRUE(ResultOverflowed);
279 
280   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 2), T(1)));
281   EXPECT_EQ(Max, SaturatingAdd(T(1), T(Max - 2), T(1), &ResultOverflowed));
282   EXPECT_FALSE(ResultOverflowed);
283 
284   EXPECT_EQ(Max, SaturatingAdd(T(1), T(1), T(Max - 2)));
285   EXPECT_EQ(Max, SaturatingAdd(T(1), T(1), T(Max - 2), &ResultOverflowed));
286   EXPECT_FALSE(ResultOverflowed);
287 
288   EXPECT_EQ(Max, SaturatingAdd(Max, Max, Max));
289   EXPECT_EQ(Max, SaturatingAdd(Max, Max, Max, &ResultOverflowed));
290   EXPECT_TRUE(ResultOverflowed);
291 }
292 
293 TEST(MathExtras, SaturatingAdd) {
294   SaturatingAddTestHelper<uint8_t>();
295   SaturatingAddTestHelper<uint16_t>();
296   SaturatingAddTestHelper<uint32_t>();
297   SaturatingAddTestHelper<uint64_t>();
298 }
299 
300 template<typename T>
301 void SaturatingMultiplyTestHelper()
302 {
303   const T Max = std::numeric_limits<T>::max();
304   bool ResultOverflowed;
305 
306   // Test basic multiplication.
307   EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3)));
308   EXPECT_EQ(T(6), SaturatingMultiply(T(2), T(3), &ResultOverflowed));
309   EXPECT_FALSE(ResultOverflowed);
310 
311   EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2)));
312   EXPECT_EQ(T(6), SaturatingMultiply(T(3), T(2), &ResultOverflowed));
313   EXPECT_FALSE(ResultOverflowed);
314 
315   // Test multiplication by zero.
316   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0)));
317   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(0), &ResultOverflowed));
318   EXPECT_FALSE(ResultOverflowed);
319 
320   EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0)));
321   EXPECT_EQ(T(0), SaturatingMultiply(T(1), T(0), &ResultOverflowed));
322   EXPECT_FALSE(ResultOverflowed);
323 
324   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1)));
325   EXPECT_EQ(T(0), SaturatingMultiply(T(0), T(1), &ResultOverflowed));
326   EXPECT_FALSE(ResultOverflowed);
327 
328   EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0)));
329   EXPECT_EQ(T(0), SaturatingMultiply(Max, T(0), &ResultOverflowed));
330   EXPECT_FALSE(ResultOverflowed);
331 
332   EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max));
333   EXPECT_EQ(T(0), SaturatingMultiply(T(0), Max, &ResultOverflowed));
334   EXPECT_FALSE(ResultOverflowed);
335 
336   // Test multiplication by maximum value.
337   EXPECT_EQ(Max, SaturatingMultiply(Max, T(2)));
338   EXPECT_EQ(Max, SaturatingMultiply(Max, T(2), &ResultOverflowed));
339   EXPECT_TRUE(ResultOverflowed);
340 
341   EXPECT_EQ(Max, SaturatingMultiply(T(2), Max));
342   EXPECT_EQ(Max, SaturatingMultiply(T(2), Max, &ResultOverflowed));
343   EXPECT_TRUE(ResultOverflowed);
344 
345   EXPECT_EQ(Max, SaturatingMultiply(Max, Max));
346   EXPECT_EQ(Max, SaturatingMultiply(Max, Max, &ResultOverflowed));
347   EXPECT_TRUE(ResultOverflowed);
348 
349   // Test interesting boundary conditions for algorithm -
350   // ((1 << A) - 1) * ((1 << B) + K) for K in [-1, 0, 1]
351   // and A + B == std::numeric_limits<T>::digits.
352   // We expect overflow iff A > B and K = 1.
353   const int Digits = std::numeric_limits<T>::digits;
354   for (int A = 1, B = Digits - 1; B >= 1; ++A, --B) {
355     for (int K = -1; K <= 1; ++K) {
356       T X = (T(1) << A) - T(1);
357       T Y = (T(1) << B) + K;
358       bool OverflowExpected = A > B && K == 1;
359 
360       if(OverflowExpected) {
361         EXPECT_EQ(Max, SaturatingMultiply(X, Y));
362         EXPECT_EQ(Max, SaturatingMultiply(X, Y, &ResultOverflowed));
363         EXPECT_TRUE(ResultOverflowed);
364       } else {
365         EXPECT_EQ(X * Y, SaturatingMultiply(X, Y));
366         EXPECT_EQ(X * Y, SaturatingMultiply(X, Y, &ResultOverflowed));
367         EXPECT_FALSE(ResultOverflowed);
368       }
369     }
370   }
371 }
372 
373 TEST(MathExtras, SaturatingMultiply) {
374   SaturatingMultiplyTestHelper<uint8_t>();
375   SaturatingMultiplyTestHelper<uint16_t>();
376   SaturatingMultiplyTestHelper<uint32_t>();
377   SaturatingMultiplyTestHelper<uint64_t>();
378 }
379 
380 template<typename T>
381 void SaturatingMultiplyAddTestHelper()
382 {
383   const T Max = std::numeric_limits<T>::max();
384   bool ResultOverflowed;
385 
386   // Test basic multiply-add.
387   EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10)));
388   EXPECT_EQ(T(16), SaturatingMultiplyAdd(T(2), T(3), T(10), &ResultOverflowed));
389   EXPECT_FALSE(ResultOverflowed);
390 
391   // Test multiply overflows, add doesn't overflow
392   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(0), &ResultOverflowed));
393   EXPECT_TRUE(ResultOverflowed);
394 
395   // Test multiply doesn't overflow, add overflows
396   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
397   EXPECT_TRUE(ResultOverflowed);
398 
399   // Test multiply-add with Max as operand
400   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), T(1), Max, &ResultOverflowed));
401   EXPECT_TRUE(ResultOverflowed);
402 
403   EXPECT_EQ(Max, SaturatingMultiplyAdd(T(1), Max, T(1), &ResultOverflowed));
404   EXPECT_TRUE(ResultOverflowed);
405 
406   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, T(1), &ResultOverflowed));
407   EXPECT_TRUE(ResultOverflowed);
408 
409   EXPECT_EQ(Max, SaturatingMultiplyAdd(Max, Max, Max, &ResultOverflowed));
410   EXPECT_TRUE(ResultOverflowed);
411 
412   // Test multiply-add with 0 as operand
413   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(1), T(0), &ResultOverflowed));
414   EXPECT_FALSE(ResultOverflowed);
415 
416   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(1), T(0), T(1), &ResultOverflowed));
417   EXPECT_FALSE(ResultOverflowed);
418 
419   EXPECT_EQ(T(1), SaturatingMultiplyAdd(T(0), T(0), T(1), &ResultOverflowed));
420   EXPECT_FALSE(ResultOverflowed);
421 
422   EXPECT_EQ(T(0), SaturatingMultiplyAdd(T(0), T(0), T(0), &ResultOverflowed));
423   EXPECT_FALSE(ResultOverflowed);
424 
425 }
426 
427 TEST(MathExtras, SaturatingMultiplyAdd) {
428   SaturatingMultiplyAddTestHelper<uint8_t>();
429   SaturatingMultiplyAddTestHelper<uint16_t>();
430   SaturatingMultiplyAddTestHelper<uint32_t>();
431   SaturatingMultiplyAddTestHelper<uint64_t>();
432 }
433 
434 TEST(MathExtras, IsShiftedUInt) {
435   EXPECT_TRUE((isShiftedUInt<1, 0>(0)));
436   EXPECT_TRUE((isShiftedUInt<1, 0>(1)));
437   EXPECT_FALSE((isShiftedUInt<1, 0>(2)));
438   EXPECT_FALSE((isShiftedUInt<1, 0>(3)));
439   EXPECT_FALSE((isShiftedUInt<1, 0>(0x8000000000000000)));
440   EXPECT_TRUE((isShiftedUInt<1, 63>(0x8000000000000000)));
441   EXPECT_TRUE((isShiftedUInt<2, 62>(0xC000000000000000)));
442   EXPECT_FALSE((isShiftedUInt<2, 62>(0xE000000000000000)));
443 
444   // 0x201 is ten bits long and has a 1 in the MSB and LSB.
445   EXPECT_TRUE((isShiftedUInt<10, 5>(uint64_t(0x201) << 5)));
446   EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 4)));
447   EXPECT_FALSE((isShiftedUInt<10, 5>(uint64_t(0x201) << 6)));
448 }
449 
450 TEST(MathExtras, IsShiftedInt) {
451   EXPECT_TRUE((isShiftedInt<1, 0>(0)));
452   EXPECT_TRUE((isShiftedInt<1, 0>(-1)));
453   EXPECT_FALSE((isShiftedInt<1, 0>(2)));
454   EXPECT_FALSE((isShiftedInt<1, 0>(3)));
455   EXPECT_FALSE((isShiftedInt<1, 0>(0x8000000000000000)));
456   EXPECT_TRUE((isShiftedInt<1, 63>(0x8000000000000000)));
457   EXPECT_TRUE((isShiftedInt<2, 62>(0xC000000000000000)));
458   EXPECT_FALSE((isShiftedInt<2, 62>(0xE000000000000000)));
459 
460   // 0x201 is ten bits long and has a 1 in the MSB and LSB.
461   EXPECT_TRUE((isShiftedInt<11, 5>(int64_t(0x201) << 5)));
462   EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 3)));
463   EXPECT_FALSE((isShiftedInt<11, 5>(int64_t(0x201) << 6)));
464   EXPECT_TRUE((isShiftedInt<11, 5>(-(int64_t(0x201) << 5))));
465   EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 3))));
466   EXPECT_FALSE((isShiftedInt<11, 5>(-(int64_t(0x201) << 6))));
467 
468   EXPECT_TRUE((isShiftedInt<6, 10>(-(int64_t(1) << 15))));
469   EXPECT_FALSE((isShiftedInt<6, 10>(int64_t(1) << 15)));
470 }
471 
472 TEST(MathExtras, DivideNearest) {
473   EXPECT_EQ(divideNearest(14, 3), 5u);
474   EXPECT_EQ(divideNearest(15, 3), 5u);
475   EXPECT_EQ(divideNearest(0, 3), 0u);
476   EXPECT_EQ(divideNearest(5, 4), 1u);
477   EXPECT_EQ(divideNearest(6, 4), 2u);
478   EXPECT_EQ(divideNearest(3, 1), 3u);
479   EXPECT_EQ(divideNearest(3, 6), 1u);
480   EXPECT_EQ(divideNearest(3, 7), 0u);
481   EXPECT_EQ(divideNearest(std::numeric_limits<uint32_t>::max(), 2),
482             std::numeric_limits<uint32_t>::max() / 2 + 1);
483   EXPECT_EQ(divideNearest(std::numeric_limits<uint64_t>::max(), 2),
484             std::numeric_limits<uint64_t>::max() / 2 + 1);
485   EXPECT_EQ(divideNearest(std::numeric_limits<uint64_t>::max(), 1),
486             std::numeric_limits<uint64_t>::max());
487   EXPECT_EQ(divideNearest(std::numeric_limits<uint64_t>::max() - 1,
488                           std::numeric_limits<uint64_t>::max()),
489             1u);
490 }
491 
492 TEST(MathExtras, DivideCeil) {
493   EXPECT_EQ(divideCeil(14, 3), 5u);
494   EXPECT_EQ(divideCeil(15, 3), 5u);
495   EXPECT_EQ(divideCeil(0, 3), 0u);
496   EXPECT_EQ(divideCeil(5, 4), 2u);
497   EXPECT_EQ(divideCeil(6, 4), 2u);
498   EXPECT_EQ(divideCeil(3, 1), 3u);
499   EXPECT_EQ(divideCeil(3, 6), 1u);
500   EXPECT_EQ(divideCeil(3, 7), 1u);
501   EXPECT_EQ(divideCeil(std::numeric_limits<uint32_t>::max(), 2),
502             std::numeric_limits<uint32_t>::max() / 2 + 1);
503   EXPECT_EQ(divideCeil(std::numeric_limits<uint64_t>::max(), 2),
504             std::numeric_limits<uint64_t>::max() / 2 + 1);
505   EXPECT_EQ(divideCeil(std::numeric_limits<uint64_t>::max(), 1),
506             std::numeric_limits<uint64_t>::max());
507 
508   EXPECT_EQ(divideCeilSigned(14, 3), 5);
509   EXPECT_EQ(divideCeilSigned(15, 3), 5);
510   EXPECT_EQ(divideCeilSigned(14, -3), -4);
511   EXPECT_EQ(divideCeilSigned(-14, -3), 5);
512   EXPECT_EQ(divideCeilSigned(-14, 3), -4);
513   EXPECT_EQ(divideCeilSigned(-15, 3), -5);
514   EXPECT_EQ(divideCeilSigned(0, 3), 0);
515   EXPECT_EQ(divideCeilSigned(0, -3), 0);
516   EXPECT_EQ(divideCeilSigned(std::numeric_limits<int32_t>::max(), 2),
517             std::numeric_limits<int32_t>::max() / 2 + 1);
518   EXPECT_EQ(divideCeilSigned(std::numeric_limits<int64_t>::max(), 2),
519             std::numeric_limits<int64_t>::max() / 2 + 1);
520   EXPECT_EQ(divideCeilSigned(std::numeric_limits<int32_t>::max(), -2),
521             std::numeric_limits<int32_t>::min() / 2 + 1);
522   EXPECT_EQ(divideCeilSigned(std::numeric_limits<int64_t>::max(), -2),
523             std::numeric_limits<int64_t>::min() / 2 + 1);
524   EXPECT_EQ(divideCeilSigned(std::numeric_limits<int64_t>::min(), 1),
525             std::numeric_limits<int64_t>::min());
526 
527   // Overflow.
528   EXPECT_TRUE(
529       divideSignedWouldOverflow(std::numeric_limits<int8_t>::min(), -1));
530   EXPECT_TRUE(
531       divideSignedWouldOverflow(std::numeric_limits<int64_t>::min(), -1));
532 }
533 
534 TEST(MathExtras, DivideFloorSigned) {
535   EXPECT_EQ(divideFloorSigned(14, 3), 4);
536   EXPECT_EQ(divideFloorSigned(15, 3), 5);
537   EXPECT_EQ(divideFloorSigned(14, -3), -5);
538   EXPECT_EQ(divideFloorSigned(-14, -3), 4);
539   EXPECT_EQ(divideFloorSigned(-14, 3), -5);
540   EXPECT_EQ(divideFloorSigned(-15, 3), -5);
541   EXPECT_EQ(divideFloorSigned(0, 3), 0);
542   EXPECT_EQ(divideFloorSigned(0, -3), 0);
543   EXPECT_EQ(divideFloorSigned(std::numeric_limits<int32_t>::max(), 2),
544             std::numeric_limits<int32_t>::max() / 2);
545   EXPECT_EQ(divideFloorSigned(std::numeric_limits<int64_t>::max(), 2),
546             std::numeric_limits<int64_t>::max() / 2);
547   EXPECT_EQ(divideFloorSigned(std::numeric_limits<int32_t>::max(), -2),
548             std::numeric_limits<int32_t>::min() / 2);
549   EXPECT_EQ(divideFloorSigned(std::numeric_limits<int64_t>::max(), -2),
550             std::numeric_limits<int64_t>::min() / 2);
551   EXPECT_EQ(divideFloorSigned(std::numeric_limits<int64_t>::min(), 1),
552             std::numeric_limits<int64_t>::min());
553 
554   // Same overflow condition, divideSignedWouldOverflow, applies.
555 }
556 
557 TEST(MathExtras, Mod) {
558   EXPECT_EQ(mod(1, 14), 1);
559   EXPECT_EQ(mod(-1, 14), 13);
560   EXPECT_EQ(mod(14, 3), 2);
561   EXPECT_EQ(mod(15, 3), 0);
562   EXPECT_EQ(mod(-14, 3), 1);
563   EXPECT_EQ(mod(-15, 3), 0);
564   EXPECT_EQ(mod(0, 3), 0);
565 }
566 
567 template <typename T> class OverflowTest : public ::testing::Test {};
568 
569 using OverflowTestTypes = ::testing::Types<signed char, short, int, long,
570                                            long long>;
571 
572 TYPED_TEST_SUITE(OverflowTest, OverflowTestTypes, );
573 
574 TYPED_TEST(OverflowTest, AddNoOverflow) {
575   TypeParam Result;
576   EXPECT_FALSE(AddOverflow<TypeParam>(1, 2, Result));
577   EXPECT_EQ(Result, TypeParam(3));
578 }
579 
580 TYPED_TEST(OverflowTest, AddOverflowToNegative) {
581   TypeParam Result;
582   auto MaxValue = std::numeric_limits<TypeParam>::max();
583   EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, MaxValue, Result));
584   EXPECT_EQ(Result, TypeParam(-2));
585 }
586 
587 TYPED_TEST(OverflowTest, AddOverflowToMin) {
588   TypeParam Result;
589   auto MaxValue = std::numeric_limits<TypeParam>::max();
590   EXPECT_TRUE(AddOverflow<TypeParam>(MaxValue, TypeParam(1), Result));
591   EXPECT_EQ(Result, std::numeric_limits<TypeParam>::min());
592 }
593 
594 TYPED_TEST(OverflowTest, AddOverflowToZero) {
595   TypeParam Result;
596   auto MinValue = std::numeric_limits<TypeParam>::min();
597   EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, MinValue, Result));
598   EXPECT_EQ(Result, TypeParam(0));
599 }
600 
601 TYPED_TEST(OverflowTest, AddOverflowToMax) {
602   TypeParam Result;
603   auto MinValue = std::numeric_limits<TypeParam>::min();
604   EXPECT_TRUE(AddOverflow<TypeParam>(MinValue, TypeParam(-1), Result));
605   EXPECT_EQ(Result, std::numeric_limits<TypeParam>::max());
606 }
607 
608 TYPED_TEST(OverflowTest, SubNoOverflow) {
609   TypeParam Result;
610   EXPECT_FALSE(SubOverflow<TypeParam>(1, 2, Result));
611   EXPECT_EQ(Result, TypeParam(-1));
612 }
613 
614 TYPED_TEST(OverflowTest, SubOverflowToMax) {
615   TypeParam Result;
616   auto MinValue = std::numeric_limits<TypeParam>::min();
617   EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
618   EXPECT_EQ(Result, MinValue);
619 }
620 
621 TYPED_TEST(OverflowTest, SubOverflowToMin) {
622   TypeParam Result;
623   auto MinValue = std::numeric_limits<TypeParam>::min();
624   EXPECT_TRUE(SubOverflow<TypeParam>(0, MinValue, Result));
625   EXPECT_EQ(Result, MinValue);
626 }
627 
628 TYPED_TEST(OverflowTest, SubOverflowToNegative) {
629   TypeParam Result;
630   auto MaxValue = std::numeric_limits<TypeParam>::max();
631   auto MinValue = std::numeric_limits<TypeParam>::min();
632   EXPECT_TRUE(SubOverflow<TypeParam>(MaxValue, MinValue, Result));
633   EXPECT_EQ(Result, TypeParam(-1));
634 }
635 
636 TYPED_TEST(OverflowTest, SubOverflowToPositive) {
637   TypeParam Result;
638   auto MaxValue = std::numeric_limits<TypeParam>::max();
639   auto MinValue = std::numeric_limits<TypeParam>::min();
640   EXPECT_TRUE(SubOverflow<TypeParam>(MinValue, MaxValue, Result));
641   EXPECT_EQ(Result, TypeParam(1));
642 }
643 
644 TYPED_TEST(OverflowTest, MulNoOverflow) {
645   TypeParam Result;
646   EXPECT_FALSE(MulOverflow<TypeParam>(1, 2, Result));
647   EXPECT_EQ(Result, 2);
648   EXPECT_FALSE(MulOverflow<TypeParam>(-1, 3, Result));
649   EXPECT_EQ(Result, -3);
650   EXPECT_FALSE(MulOverflow<TypeParam>(4, -2, Result));
651   EXPECT_EQ(Result, -8);
652   EXPECT_FALSE(MulOverflow<TypeParam>(-6, -5, Result));
653   EXPECT_EQ(Result, 30);
654 }
655 
656 TYPED_TEST(OverflowTest, MulNoOverflowToMax) {
657   TypeParam Result;
658   auto MaxValue = std::numeric_limits<TypeParam>::max();
659   auto MinValue = std::numeric_limits<TypeParam>::min();
660   EXPECT_FALSE(MulOverflow<TypeParam>(MinValue + 1, -1, Result));
661   EXPECT_EQ(Result, MaxValue);
662 }
663 
664 TYPED_TEST(OverflowTest, MulOverflowToMin) {
665   TypeParam Result;
666   auto MinValue = std::numeric_limits<TypeParam>::min();
667   EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, -1, Result));
668   EXPECT_EQ(Result, MinValue);
669 }
670 
671 TYPED_TEST(OverflowTest, MulOverflowMax) {
672   TypeParam Result;
673   auto MinValue = std::numeric_limits<TypeParam>::min();
674   auto MaxValue = std::numeric_limits<TypeParam>::max();
675   EXPECT_TRUE(MulOverflow<TypeParam>(MinValue, MinValue, Result));
676   EXPECT_EQ(Result, 0);
677   EXPECT_TRUE(MulOverflow<TypeParam>(MaxValue, MaxValue, Result));
678   EXPECT_EQ(Result, 1);
679 }
680 
681 TYPED_TEST(OverflowTest, MulResultZero) {
682   TypeParam Result;
683   EXPECT_FALSE(MulOverflow<TypeParam>(4, 0, Result));
684   EXPECT_EQ(Result, TypeParam(0));
685   EXPECT_FALSE(MulOverflow<TypeParam>(-5, 0, Result));
686   EXPECT_EQ(Result, TypeParam(0));
687   EXPECT_FALSE(MulOverflow<TypeParam>(0, 5, Result));
688   EXPECT_EQ(Result, TypeParam(0));
689   EXPECT_FALSE(MulOverflow<TypeParam>(0, -5, Result));
690   EXPECT_EQ(Result, TypeParam(0));
691 }
692 } // namespace
693