1 // Copyright 2017 The Chromium Authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style license that can be
3 // found in the LICENSE file.
4
5 #ifndef THIRD_PARTY_BASE_NUMERICS_CHECKED_MATH_IMPL_H_
6 #define THIRD_PARTY_BASE_NUMERICS_CHECKED_MATH_IMPL_H_
7
8 #include <stddef.h>
9 #include <stdint.h>
10
11 #include <climits>
12 #include <cmath>
13 #include <cstdlib>
14 #include <limits>
15 #include <type_traits>
16
17 #include "third_party/base/numerics/safe_conversions.h"
18 #include "third_party/base/numerics/safe_math_shared_impl.h"
19
20 namespace pdfium {
21 namespace base {
22 namespace internal {
23
24 template <typename T>
CheckedAddImpl(T x,T y,T * result)25 constexpr bool CheckedAddImpl(T x, T y, T* result) {
26 static_assert(std::is_integral<T>::value, "Type must be integral");
27 // Since the value of x+y is undefined if we have a signed type, we compute
28 // it using the unsigned type of the same size.
29 using UnsignedDst = typename std::make_unsigned<T>::type;
30 using SignedDst = typename std::make_signed<T>::type;
31 const UnsignedDst ux = static_cast<UnsignedDst>(x);
32 const UnsignedDst uy = static_cast<UnsignedDst>(y);
33 const UnsignedDst uresult = static_cast<UnsignedDst>(ux + uy);
34 // Addition is valid if the sign of (x + y) is equal to either that of x or
35 // that of y.
36 if (std::is_signed<T>::value
37 ? static_cast<SignedDst>((uresult ^ ux) & (uresult ^ uy)) < 0
38 : uresult < uy) // Unsigned is either valid or underflow.
39 return false;
40 *result = static_cast<T>(uresult);
41 return true;
42 }
43
44 template <typename T, typename U, class Enable = void>
45 struct CheckedAddOp {};
46
47 template <typename T, typename U>
48 struct CheckedAddOp<T,
49 U,
50 typename std::enable_if<std::is_integral<T>::value &&
51 std::is_integral<U>::value>::type> {
52 using result_type = typename MaxExponentPromotion<T, U>::type;
53 template <typename V>
54 static constexpr bool Do(T x, U y, V* result) {
55 if constexpr (CheckedAddFastOp<T, U>::is_supported)
56 return CheckedAddFastOp<T, U>::Do(x, y, result);
57
58 // Double the underlying type up to a full machine word.
59 using FastPromotion = typename FastIntegerArithmeticPromotion<T, U>::type;
60 using Promotion =
61 typename std::conditional<(IntegerBitsPlusSign<FastPromotion>::value >
62 IntegerBitsPlusSign<intptr_t>::value),
63 typename BigEnoughPromotion<T, U>::type,
64 FastPromotion>::type;
65 // Fail if either operand is out of range for the promoted type.
66 // TODO(jschuh): This could be made to work for a broader range of values.
67 if (BASE_NUMERICS_UNLIKELY(!IsValueInRangeForNumericType<Promotion>(x) ||
68 !IsValueInRangeForNumericType<Promotion>(y))) {
69 return false;
70 }
71
72 Promotion presult = {};
73 bool is_valid = true;
74 if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
75 presult = static_cast<Promotion>(x) + static_cast<Promotion>(y);
76 } else {
77 is_valid = CheckedAddImpl(static_cast<Promotion>(x),
78 static_cast<Promotion>(y), &presult);
79 }
80 if (!is_valid || !IsValueInRangeForNumericType<V>(presult))
81 return false;
82 *result = static_cast<V>(presult);
83 return true;
84 }
85 };
86
87 template <typename T>
88 constexpr bool CheckedSubImpl(T x, T y, T* result) {
89 static_assert(std::is_integral<T>::value, "Type must be integral");
90 // Since the value of x+y is undefined if we have a signed type, we compute
91 // it using the unsigned type of the same size.
92 using UnsignedDst = typename std::make_unsigned<T>::type;
93 using SignedDst = typename std::make_signed<T>::type;
94 const UnsignedDst ux = static_cast<UnsignedDst>(x);
95 const UnsignedDst uy = static_cast<UnsignedDst>(y);
96 const UnsignedDst uresult = static_cast<UnsignedDst>(ux - uy);
97 // Subtraction is valid if either x and y have same sign, or (x-y) and x have
98 // the same sign.
99 if (std::is_signed<T>::value
100 ? static_cast<SignedDst>((uresult ^ ux) & (ux ^ uy)) < 0
101 : x < y)
102 return false;
103 *result = static_cast<T>(uresult);
104 return true;
105 }
106
107 template <typename T, typename U, class Enable = void>
108 struct CheckedSubOp {};
109
110 template <typename T, typename U>
111 struct CheckedSubOp<T,
112 U,
113 typename std::enable_if<std::is_integral<T>::value &&
114 std::is_integral<U>::value>::type> {
115 using result_type = typename MaxExponentPromotion<T, U>::type;
116 template <typename V>
117 static constexpr bool Do(T x, U y, V* result) {
118 if constexpr (CheckedSubFastOp<T, U>::is_supported)
119 return CheckedSubFastOp<T, U>::Do(x, y, result);
120
121 // Double the underlying type up to a full machine word.
122 using FastPromotion = typename FastIntegerArithmeticPromotion<T, U>::type;
123 using Promotion =
124 typename std::conditional<(IntegerBitsPlusSign<FastPromotion>::value >
125 IntegerBitsPlusSign<intptr_t>::value),
126 typename BigEnoughPromotion<T, U>::type,
127 FastPromotion>::type;
128 // Fail if either operand is out of range for the promoted type.
129 // TODO(jschuh): This could be made to work for a broader range of values.
130 if (BASE_NUMERICS_UNLIKELY(!IsValueInRangeForNumericType<Promotion>(x) ||
131 !IsValueInRangeForNumericType<Promotion>(y))) {
132 return false;
133 }
134
135 Promotion presult = {};
136 bool is_valid = true;
137 if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
138 presult = static_cast<Promotion>(x) - static_cast<Promotion>(y);
139 } else {
140 is_valid = CheckedSubImpl(static_cast<Promotion>(x),
141 static_cast<Promotion>(y), &presult);
142 }
143 if (!is_valid || !IsValueInRangeForNumericType<V>(presult))
144 return false;
145 *result = static_cast<V>(presult);
146 return true;
147 }
148 };
149
150 template <typename T>
151 constexpr bool CheckedMulImpl(T x, T y, T* result) {
152 static_assert(std::is_integral<T>::value, "Type must be integral");
153 // Since the value of x*y is potentially undefined if we have a signed type,
154 // we compute it using the unsigned type of the same size.
155 using UnsignedDst = typename std::make_unsigned<T>::type;
156 using SignedDst = typename std::make_signed<T>::type;
157 const UnsignedDst ux = SafeUnsignedAbs(x);
158 const UnsignedDst uy = SafeUnsignedAbs(y);
159 const UnsignedDst uresult = static_cast<UnsignedDst>(ux * uy);
160 const bool is_negative =
161 std::is_signed<T>::value && static_cast<SignedDst>(x ^ y) < 0;
162 // We have a fast out for unsigned identity or zero on the second operand.
163 // After that it's an unsigned overflow check on the absolute value, with
164 // a +1 bound for a negative result.
165 if (uy > UnsignedDst(!std::is_signed<T>::value || is_negative) &&
166 ux > (std::numeric_limits<T>::max() + UnsignedDst(is_negative)) / uy)
167 return false;
168 *result = static_cast<T>(is_negative ? 0 - uresult : uresult);
169 return true;
170 }
171
172 template <typename T, typename U, class Enable = void>
173 struct CheckedMulOp {};
174
175 template <typename T, typename U>
176 struct CheckedMulOp<T,
177 U,
178 typename std::enable_if<std::is_integral<T>::value &&
179 std::is_integral<U>::value>::type> {
180 using result_type = typename MaxExponentPromotion<T, U>::type;
181 template <typename V>
182 static constexpr bool Do(T x, U y, V* result) {
183 if constexpr (CheckedMulFastOp<T, U>::is_supported)
184 return CheckedMulFastOp<T, U>::Do(x, y, result);
185
186 using Promotion = typename FastIntegerArithmeticPromotion<T, U>::type;
187 // Verify the destination type can hold the result (always true for 0).
188 if (BASE_NUMERICS_UNLIKELY((!IsValueInRangeForNumericType<Promotion>(x) ||
189 !IsValueInRangeForNumericType<Promotion>(y)) &&
190 x && y)) {
191 return false;
192 }
193
194 Promotion presult = {};
195 bool is_valid = true;
196 if (CheckedMulFastOp<Promotion, Promotion>::is_supported) {
197 // The fast op may be available with the promoted type.
198 // The casts here are safe because of the "value in range" conditional
199 // above.
200 is_valid = CheckedMulFastOp<Promotion, Promotion>::Do(
201 static_cast<Promotion>(x), static_cast<Promotion>(y), &presult);
202 } else if (IsIntegerArithmeticSafe<Promotion, T, U>::value) {
203 presult = static_cast<Promotion>(x) * static_cast<Promotion>(y);
204 } else {
205 is_valid = CheckedMulImpl(static_cast<Promotion>(x),
206 static_cast<Promotion>(y), &presult);
207 }
208 if (!is_valid || !IsValueInRangeForNumericType<V>(presult))
209 return false;
210 *result = static_cast<V>(presult);
211 return true;
212 }
213 };
214
215 // Division just requires a check for a zero denominator or an invalid negation
216 // on signed min/-1.
217 template <typename T, typename U, class Enable = void>
218 struct CheckedDivOp {};
219
220 template <typename T, typename U>
221 struct CheckedDivOp<T,
222 U,
223 typename std::enable_if<std::is_integral<T>::value &&
224 std::is_integral<U>::value>::type> {
225 using result_type = typename MaxExponentPromotion<T, U>::type;
226 template <typename V>
227 static constexpr bool Do(T x, U y, V* result) {
228 if (BASE_NUMERICS_UNLIKELY(!y))
229 return false;
230
231 // The overflow check can be compiled away if we don't have the exact
232 // combination of types needed to trigger this case.
233 using Promotion = typename BigEnoughPromotion<T, U>::type;
234 if (BASE_NUMERICS_UNLIKELY(
235 (std::is_signed<T>::value && std::is_signed<U>::value &&
236 IsTypeInRangeForNumericType<T, Promotion>::value &&
237 static_cast<Promotion>(x) ==
238 std::numeric_limits<Promotion>::lowest() &&
239 y == static_cast<U>(-1)))) {
240 return false;
241 }
242
243 // This branch always compiles away if the above branch wasn't removed.
244 if (BASE_NUMERICS_UNLIKELY((!IsValueInRangeForNumericType<Promotion>(x) ||
245 !IsValueInRangeForNumericType<Promotion>(y)) &&
246 x)) {
247 return false;
248 }
249
250 const Promotion presult = Promotion(x) / Promotion(y);
251 if (!IsValueInRangeForNumericType<V>(presult))
252 return false;
253 *result = static_cast<V>(presult);
254 return true;
255 }
256 };
257
258 template <typename T, typename U, class Enable = void>
259 struct CheckedModOp {};
260
261 template <typename T, typename U>
262 struct CheckedModOp<T,
263 U,
264 typename std::enable_if<std::is_integral<T>::value &&
265 std::is_integral<U>::value>::type> {
266 using result_type = typename MaxExponentPromotion<T, U>::type;
267 template <typename V>
268 static constexpr bool Do(T x, U y, V* result) {
269 if (BASE_NUMERICS_UNLIKELY(!y))
270 return false;
271
272 using Promotion = typename BigEnoughPromotion<T, U>::type;
273 if (BASE_NUMERICS_UNLIKELY(
274 (std::is_signed<T>::value && std::is_signed<U>::value &&
275 IsTypeInRangeForNumericType<T, Promotion>::value &&
276 static_cast<Promotion>(x) ==
277 std::numeric_limits<Promotion>::lowest() &&
278 y == static_cast<U>(-1)))) {
279 *result = 0;
280 return true;
281 }
282
283 const Promotion presult =
284 static_cast<Promotion>(x) % static_cast<Promotion>(y);
285 if (!IsValueInRangeForNumericType<V>(presult))
286 return false;
287 *result = static_cast<Promotion>(presult);
288 return true;
289 }
290 };
291
292 template <typename T, typename U, class Enable = void>
293 struct CheckedLshOp {};
294
295 // Left shift. Shifts less than 0 or greater than or equal to the number
296 // of bits in the promoted type are undefined. Shifts of negative values
297 // are undefined. Otherwise it is defined when the result fits.
298 template <typename T, typename U>
299 struct CheckedLshOp<T,
300 U,
301 typename std::enable_if<std::is_integral<T>::value &&
302 std::is_integral<U>::value>::type> {
303 using result_type = T;
304 template <typename V>
305 static constexpr bool Do(T x, U shift, V* result) {
306 // Disallow negative numbers and verify the shift is in bounds.
307 if (BASE_NUMERICS_LIKELY(!IsValueNegative(x) &&
308 as_unsigned(shift) <
309 as_unsigned(std::numeric_limits<T>::digits))) {
310 // Shift as unsigned to avoid undefined behavior.
311 *result = static_cast<V>(as_unsigned(x) << shift);
312 // If the shift can be reversed, we know it was valid.
313 return *result >> shift == x;
314 }
315
316 // Handle the legal corner-case of a full-width signed shift of zero.
317 if (!std::is_signed<T>::value || x ||
318 as_unsigned(shift) != as_unsigned(std::numeric_limits<T>::digits))
319 return false;
320 *result = 0;
321 return true;
322 }
323 };
324
325 template <typename T, typename U, class Enable = void>
326 struct CheckedRshOp {};
327
328 // Right shift. Shifts less than 0 or greater than or equal to the number
329 // of bits in the promoted type are undefined. Otherwise, it is always defined,
330 // but a right shift of a negative value is implementation-dependent.
331 template <typename T, typename U>
332 struct CheckedRshOp<T,
333 U,
334 typename std::enable_if<std::is_integral<T>::value &&
335 std::is_integral<U>::value>::type> {
336 using result_type = T;
337 template <typename V>
338 static constexpr bool Do(T x, U shift, V* result) {
339 // Use sign conversion to push negative values out of range.
340 if (BASE_NUMERICS_UNLIKELY(as_unsigned(shift) >=
341 IntegerBitsPlusSign<T>::value)) {
342 return false;
343 }
344
345 const T tmp = x >> shift;
346 if (!IsValueInRangeForNumericType<V>(tmp))
347 return false;
348 *result = static_cast<V>(tmp);
349 return true;
350 }
351 };
352
353 template <typename T, typename U, class Enable = void>
354 struct CheckedAndOp {};
355
356 // For simplicity we support only unsigned integer results.
357 template <typename T, typename U>
358 struct CheckedAndOp<T,
359 U,
360 typename std::enable_if<std::is_integral<T>::value &&
361 std::is_integral<U>::value>::type> {
362 using result_type = typename std::make_unsigned<
363 typename MaxExponentPromotion<T, U>::type>::type;
364 template <typename V>
365 static constexpr bool Do(T x, U y, V* result) {
366 const result_type tmp =
367 static_cast<result_type>(x) & static_cast<result_type>(y);
368 if (!IsValueInRangeForNumericType<V>(tmp))
369 return false;
370 *result = static_cast<V>(tmp);
371 return true;
372 }
373 };
374
375 template <typename T, typename U, class Enable = void>
376 struct CheckedOrOp {};
377
378 // For simplicity we support only unsigned integers.
379 template <typename T, typename U>
380 struct CheckedOrOp<T,
381 U,
382 typename std::enable_if<std::is_integral<T>::value &&
383 std::is_integral<U>::value>::type> {
384 using result_type = typename std::make_unsigned<
385 typename MaxExponentPromotion<T, U>::type>::type;
386 template <typename V>
387 static constexpr bool Do(T x, U y, V* result) {
388 const result_type tmp =
389 static_cast<result_type>(x) | static_cast<result_type>(y);
390 if (!IsValueInRangeForNumericType<V>(tmp))
391 return false;
392 *result = static_cast<V>(tmp);
393 return true;
394 }
395 };
396
397 template <typename T, typename U, class Enable = void>
398 struct CheckedXorOp {};
399
400 // For simplicity we support only unsigned integers.
401 template <typename T, typename U>
402 struct CheckedXorOp<T,
403 U,
404 typename std::enable_if<std::is_integral<T>::value &&
405 std::is_integral<U>::value>::type> {
406 using result_type = typename std::make_unsigned<
407 typename MaxExponentPromotion<T, U>::type>::type;
408 template <typename V>
409 static constexpr bool Do(T x, U y, V* result) {
410 const result_type tmp =
411 static_cast<result_type>(x) ^ static_cast<result_type>(y);
412 if (!IsValueInRangeForNumericType<V>(tmp))
413 return false;
414 *result = static_cast<V>(tmp);
415 return true;
416 }
417 };
418
419 // Max doesn't really need to be implemented this way because it can't fail,
420 // but it makes the code much cleaner to use the MathOp wrappers.
421 template <typename T, typename U, class Enable = void>
422 struct CheckedMaxOp {};
423
424 template <typename T, typename U>
425 struct CheckedMaxOp<
426 T,
427 U,
428 typename std::enable_if<std::is_arithmetic<T>::value &&
429 std::is_arithmetic<U>::value>::type> {
430 using result_type = typename MaxExponentPromotion<T, U>::type;
431 template <typename V>
432 static constexpr bool Do(T x, U y, V* result) {
433 const result_type tmp = IsGreater<T, U>::Test(x, y)
434 ? static_cast<result_type>(x)
435 : static_cast<result_type>(y);
436 if (!IsValueInRangeForNumericType<V>(tmp))
437 return false;
438 *result = static_cast<V>(tmp);
439 return true;
440 }
441 };
442
443 // Min doesn't really need to be implemented this way because it can't fail,
444 // but it makes the code much cleaner to use the MathOp wrappers.
445 template <typename T, typename U, class Enable = void>
446 struct CheckedMinOp {};
447
448 template <typename T, typename U>
449 struct CheckedMinOp<
450 T,
451 U,
452 typename std::enable_if<std::is_arithmetic<T>::value &&
453 std::is_arithmetic<U>::value>::type> {
454 using result_type = typename LowestValuePromotion<T, U>::type;
455 template <typename V>
456 static constexpr bool Do(T x, U y, V* result) {
457 const result_type tmp = IsLess<T, U>::Test(x, y)
458 ? static_cast<result_type>(x)
459 : static_cast<result_type>(y);
460 if (!IsValueInRangeForNumericType<V>(tmp))
461 return false;
462 *result = static_cast<V>(tmp);
463 return true;
464 }
465 };
466
467 // This is just boilerplate that wraps the standard floating point arithmetic.
468 // A macro isn't the nicest solution, but it beats rewriting these repeatedly.
469 #define BASE_FLOAT_ARITHMETIC_OPS(NAME, OP) \
470 template <typename T, typename U> \
471 struct Checked##NAME##Op< \
472 T, U, \
473 typename std::enable_if<std::is_floating_point<T>::value || \
474 std::is_floating_point<U>::value>::type> { \
475 using result_type = typename MaxExponentPromotion<T, U>::type; \
476 template <typename V> \
477 static constexpr bool Do(T x, U y, V* result) { \
478 using Promotion = typename MaxExponentPromotion<T, U>::type; \
479 const Promotion presult = x OP y; \
480 if (!IsValueInRangeForNumericType<V>(presult)) \
481 return false; \
482 *result = static_cast<V>(presult); \
483 return true; \
484 } \
485 };
486
487 BASE_FLOAT_ARITHMETIC_OPS(Add, +)
488 BASE_FLOAT_ARITHMETIC_OPS(Sub, -)
489 BASE_FLOAT_ARITHMETIC_OPS(Mul, *)
490 BASE_FLOAT_ARITHMETIC_OPS(Div, /)
491
492 #undef BASE_FLOAT_ARITHMETIC_OPS
493
494 // Floats carry around their validity state with them, but integers do not. So,
495 // we wrap the underlying value in a specialization in order to hide that detail
496 // and expose an interface via accessors.
497 enum NumericRepresentation {
498 NUMERIC_INTEGER,
499 NUMERIC_FLOATING,
500 NUMERIC_UNKNOWN
501 };
502
503 template <typename NumericType>
504 struct GetNumericRepresentation {
505 static const NumericRepresentation value =
506 std::is_integral<NumericType>::value
507 ? NUMERIC_INTEGER
508 : (std::is_floating_point<NumericType>::value ? NUMERIC_FLOATING
509 : NUMERIC_UNKNOWN);
510 };
511
512 template <typename T,
513 NumericRepresentation type = GetNumericRepresentation<T>::value>
514 class CheckedNumericState {};
515
516 // Integrals require quite a bit of additional housekeeping to manage state.
517 template <typename T>
518 class CheckedNumericState<T, NUMERIC_INTEGER> {
519 public:
520 template <typename Src = int>
521 constexpr explicit CheckedNumericState(Src value = 0, bool is_valid = true)
522 : is_valid_(is_valid && IsValueInRangeForNumericType<T>(value)),
523 value_(WellDefinedConversionOrZero(value, is_valid_)) {
524 static_assert(std::is_arithmetic<Src>::value, "Argument must be numeric.");
525 }
526
527 template <typename Src>
528 constexpr CheckedNumericState(const CheckedNumericState<Src>& rhs)
529 : CheckedNumericState(rhs.value(), rhs.is_valid()) {}
530
531 constexpr bool is_valid() const { return is_valid_; }
532
533 constexpr T value() const { return value_; }
534
535 private:
536 // Ensures that a type conversion does not trigger undefined behavior.
537 template <typename Src>
538 static constexpr T WellDefinedConversionOrZero(Src value, bool is_valid) {
539 using SrcType = typename internal::UnderlyingType<Src>::type;
540 return (std::is_integral<SrcType>::value || is_valid)
541 ? static_cast<T>(value)
542 : 0;
543 }
544
545 // is_valid_ precedes value_ because member initializers in the constructors
546 // are evaluated in field order, and is_valid_ must be read when initializing
547 // value_.
548 bool is_valid_;
549 T value_;
550 };
551
552 // Floating points maintain their own validity, but need translation wrappers.
553 template <typename T>
554 class CheckedNumericState<T, NUMERIC_FLOATING> {
555 public:
556 template <typename Src = double>
557 constexpr explicit CheckedNumericState(Src value = 0.0, bool is_valid = true)
558 : value_(WellDefinedConversionOrNaN(
559 value,
560 is_valid && IsValueInRangeForNumericType<T>(value))) {}
561
562 template <typename Src>
563 constexpr CheckedNumericState(const CheckedNumericState<Src>& rhs)
564 : CheckedNumericState(rhs.value(), rhs.is_valid()) {}
565
566 constexpr bool is_valid() const {
567 // Written this way because std::isfinite is not reliably constexpr.
568 return IsConstantEvaluated()
569 ? value_ <= std::numeric_limits<T>::max() &&
570 value_ >= std::numeric_limits<T>::lowest()
571 : std::isfinite(value_);
572 }
573
574 constexpr T value() const { return value_; }
575
576 private:
577 // Ensures that a type conversion does not trigger undefined behavior.
578 template <typename Src>
579 static constexpr T WellDefinedConversionOrNaN(Src value, bool is_valid) {
580 using SrcType = typename internal::UnderlyingType<Src>::type;
581 return (StaticDstRangeRelationToSrcRange<T, SrcType>::value ==
582 NUMERIC_RANGE_CONTAINED ||
583 is_valid)
584 ? static_cast<T>(value)
585 : std::numeric_limits<T>::quiet_NaN();
586 }
587
588 T value_;
589 };
590
591 } // namespace internal
592 } // namespace base
593 } // namespace pdfium
594
595 #endif // THIRD_PARTY_BASE_NUMERICS_CHECKED_MATH_IMPL_H_
596