1//===-- A class to manipulate wide integers. --------------------*- C++ -*-===//
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#ifndef LLVM_LIBC_SRC___SUPPORT_BIG_INT_H
10#define LLVM_LIBC_SRC___SUPPORT_BIG_INT_H
11
12#include "src/__support/CPP/array.h"
13#include "src/__support/CPP/bit.h" // countl_zero
14#include "src/__support/CPP/limits.h"
15#include "src/__support/CPP/optional.h"
16#include "src/__support/CPP/type_traits.h"
17#include "src/__support/macros/attributes.h" // LIBC_INLINE
18#include "src/__support/macros/config.h"
19#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
20#include "src/__support/macros/properties/compiler.h" // LIBC_COMPILER_IS_CLANG
21#include "src/__support/macros/properties/types.h" // LIBC_TYPES_HAS_INT128, LIBC_TYPES_HAS_INT64
22#include "src/__support/math_extras.h" // add_with_carry, sub_with_borrow
23#include "src/__support/number_pair.h"
24
25#include <stddef.h> // For size_t
26#include <stdint.h>
27
28namespace LIBC_NAMESPACE_DECL {
29
30namespace multiword {
31
32// A type trait mapping unsigned integers to their half-width unsigned
33// counterparts.
34template <typename T> struct half_width;
35template <> struct half_width<uint16_t> : cpp::type_identity<uint8_t> {};
36template <> struct half_width<uint32_t> : cpp::type_identity<uint16_t> {};
37#ifdef LIBC_TYPES_HAS_INT64
38template <> struct half_width<uint64_t> : cpp::type_identity<uint32_t> {};
39#ifdef LIBC_TYPES_HAS_INT128
40template <> struct half_width<__uint128_t> : cpp::type_identity<uint64_t> {};
41#endif // LIBC_TYPES_HAS_INT128
42#endif // LIBC_TYPES_HAS_INT64
43template <typename T> using half_width_t = typename half_width<T>::type;
44
45// An array of two elements that can be used in multiword operations.
46template <typename T> struct DoubleWide final : cpp::array<T, 2> {
47 using UP = cpp::array<T, 2>;
48 using UP::UP;
49 LIBC_INLINE constexpr DoubleWide(T lo, T hi) : UP({lo, hi}) {}
50};
51
52// Converts an unsigned value into a DoubleWide<half_width_t<T>>.
53template <typename T> LIBC_INLINE constexpr auto split(T value) {
54 static_assert(cpp::is_unsigned_v<T>);
55 using half_type = half_width_t<T>;
56 return DoubleWide<half_type>(
57 half_type(value),
58 half_type(value >> cpp::numeric_limits<half_type>::digits));
59}
60
61// The low part of a DoubleWide value.
62template <typename T> LIBC_INLINE constexpr T lo(const DoubleWide<T> &value) {
63 return value[0];
64}
65// The high part of a DoubleWide value.
66template <typename T> LIBC_INLINE constexpr T hi(const DoubleWide<T> &value) {
67 return value[1];
68}
69// The low part of an unsigned value.
70template <typename T> LIBC_INLINE constexpr half_width_t<T> lo(T value) {
71 return lo(split(value));
72}
73// The high part of an unsigned value.
74template <typename T> LIBC_INLINE constexpr half_width_t<T> hi(T value) {
75 return hi(split(value));
76}
77
78// Returns 'a' times 'b' in a DoubleWide<word>. Cannot overflow by construction.
79template <typename word>
80LIBC_INLINE constexpr DoubleWide<word> mul2(word a, word b) {
81 if constexpr (cpp::is_same_v<word, uint8_t>) {
82 return split<uint16_t>(value: uint16_t(a) * uint16_t(b));
83 } else if constexpr (cpp::is_same_v<word, uint16_t>) {
84 return split<uint32_t>(value: uint32_t(a) * uint32_t(b));
85 }
86#ifdef LIBC_TYPES_HAS_INT64
87 else if constexpr (cpp::is_same_v<word, uint32_t>) {
88 return split<uint64_t>(value: uint64_t(a) * uint64_t(b));
89 }
90#endif
91#ifdef LIBC_TYPES_HAS_INT128
92 else if constexpr (cpp::is_same_v<word, uint64_t>) {
93 return split<__uint128_t>(value: __uint128_t(a) * __uint128_t(b));
94 }
95#endif
96 else {
97 using half_word = half_width_t<word>;
98 const auto shiftl = [](word value) -> word {
99 return value << cpp::numeric_limits<half_word>::digits;
100 };
101 const auto shiftr = [](word value) -> word {
102 return value >> cpp::numeric_limits<half_word>::digits;
103 };
104 // Here we do a one digit multiplication where 'a' and 'b' are of type
105 // word. We split 'a' and 'b' into half words and perform the classic long
106 // multiplication with 'a' and 'b' being two-digit numbers.
107
108 // a a_hi a_lo
109 // x b => x b_hi b_lo
110 // ---- -----------
111 // c result
112 // We convert 'lo' and 'hi' from 'half_word' to 'word' so multiplication
113 // doesn't overflow.
114 const word a_lo = lo(a);
115 const word b_lo = lo(b);
116 const word a_hi = hi(a);
117 const word b_hi = hi(b);
118 const word step1 = b_lo * a_lo; // no overflow;
119 const word step2 = b_lo * a_hi; // no overflow;
120 const word step3 = b_hi * a_lo; // no overflow;
121 const word step4 = b_hi * a_hi; // no overflow;
122 word lo_digit = step1;
123 word hi_digit = step4;
124 const word no_carry = 0;
125 word carry;
126 word _; // unused carry variable.
127 lo_digit = add_with_carry<word>(lo_digit, shiftl(step2), no_carry, carry);
128 hi_digit = add_with_carry<word>(hi_digit, shiftr(step2), carry, _);
129 lo_digit = add_with_carry<word>(lo_digit, shiftl(step3), no_carry, carry);
130 hi_digit = add_with_carry<word>(hi_digit, shiftr(step3), carry, _);
131 return DoubleWide<word>(lo_digit, hi_digit);
132 }
133}
134
135// In-place 'dst op= rhs' with operation with carry propagation. Returns carry.
136template <typename Function, typename word, size_t N, size_t M>
137LIBC_INLINE constexpr word inplace_binop(Function op_with_carry,
138 cpp::array<word, N> &dst,
139 const cpp::array<word, M> &rhs) {
140 static_assert(N >= M);
141 word carry_out = 0;
142 for (size_t i = 0; i < N; ++i) {
143 const bool has_rhs_value = i < M;
144 const word rhs_value = has_rhs_value ? rhs[i] : 0;
145 const word carry_in = carry_out;
146 dst[i] = op_with_carry(dst[i], rhs_value, carry_in, carry_out);
147 // stop early when rhs is over and no carry is to be propagated.
148 if (!has_rhs_value && carry_out == 0)
149 break;
150 }
151 return carry_out;
152}
153
154// In-place addition. Returns carry.
155template <typename word, size_t N, size_t M>
156LIBC_INLINE constexpr word add_with_carry(cpp::array<word, N> &dst,
157 const cpp::array<word, M> &rhs) {
158 return inplace_binop(LIBC_NAMESPACE::add_with_carry<word>, dst, rhs);
159}
160
161// In-place subtraction. Returns borrow.
162template <typename word, size_t N, size_t M>
163LIBC_INLINE constexpr word sub_with_borrow(cpp::array<word, N> &dst,
164 const cpp::array<word, M> &rhs) {
165 return inplace_binop(LIBC_NAMESPACE::sub_with_borrow<word>, dst, rhs);
166}
167
168// In-place multiply-add. Returns carry.
169// i.e., 'dst += b * c'
170template <typename word, size_t N>
171LIBC_INLINE constexpr word mul_add_with_carry(cpp::array<word, N> &dst, word b,
172 word c) {
173 return add_with_carry(dst, mul2(b, c));
174}
175
176// An array of two elements serving as an accumulator during multiword
177// computations.
178template <typename T> struct Accumulator final : cpp::array<T, 2> {
179 using UP = cpp::array<T, 2>;
180 LIBC_INLINE constexpr Accumulator() : UP({0, 0}) {}
181 LIBC_INLINE constexpr T advance(T carry_in) {
182 auto result = UP::front();
183 UP::front() = UP::back();
184 UP::back() = carry_in;
185 return result;
186 }
187 LIBC_INLINE constexpr T sum() const { return UP::front(); }
188 LIBC_INLINE constexpr T carry() const { return UP::back(); }
189};
190
191// In-place multiplication by a single word. Returns carry.
192template <typename word, size_t N>
193LIBC_INLINE constexpr word scalar_multiply_with_carry(cpp::array<word, N> &dst,
194 word x) {
195 Accumulator<word> acc;
196 for (auto &val : dst) {
197 const word carry = mul_add_with_carry(acc, val, x);
198 val = acc.advance(carry);
199 }
200 return acc.carry();
201}
202
203// Multiplication of 'lhs' by 'rhs' into 'dst'. Returns carry.
204// This function is safe to use for signed numbers.
205// https://stackoverflow.com/a/20793834
206// https://pages.cs.wisc.edu/%7Emarkhill/cs354/Fall2008/beyond354/int.mult.html
207template <typename word, size_t O, size_t M, size_t N>
208LIBC_INLINE constexpr word multiply_with_carry(cpp::array<word, O> &dst,
209 const cpp::array<word, M> &lhs,
210 const cpp::array<word, N> &rhs) {
211 static_assert(O >= M + N);
212 Accumulator<word> acc;
213 for (size_t i = 0; i < O; ++i) {
214 const size_t lower_idx = i < N ? 0 : i - N + 1;
215 const size_t upper_idx = i < M ? i : M - 1;
216 word carry = 0;
217 for (size_t j = lower_idx; j <= upper_idx; ++j)
218 carry += mul_add_with_carry(acc, lhs[j], rhs[i - j]);
219 dst[i] = acc.advance(carry);
220 }
221 return acc.carry();
222}
223
224template <typename word, size_t N>
225LIBC_INLINE constexpr void quick_mul_hi(cpp::array<word, N> &dst,
226 const cpp::array<word, N> &lhs,
227 const cpp::array<word, N> &rhs) {
228 Accumulator<word> acc;
229 word carry = 0;
230 // First round of accumulation for those at N - 1 in the full product.
231 for (size_t i = 0; i < N; ++i)
232 carry += mul_add_with_carry(acc, lhs[i], rhs[N - 1 - i]);
233 for (size_t i = N; i < 2 * N - 1; ++i) {
234 acc.advance(carry);
235 carry = 0;
236 for (size_t j = i - N + 1; j < N; ++j)
237 carry += mul_add_with_carry(acc, lhs[j], rhs[i - j]);
238 dst[i - N] = acc.sum();
239 }
240 dst.back() = acc.carry();
241}
242
243template <typename word, size_t N>
244LIBC_INLINE constexpr bool is_negative(const cpp::array<word, N> &array) {
245 using signed_word = cpp::make_signed_t<word>;
246 return cpp::bit_cast<signed_word>(array.back()) < 0;
247}
248
249// An enum for the shift function below.
250enum Direction { LEFT, RIGHT };
251
252// A bitwise shift on an array of elements.
253// 'offset' must be less than TOTAL_BITS (i.e., sizeof(word) * CHAR_BIT * N)
254// otherwise the behavior is undefined.
255template <Direction direction, bool is_signed, typename word, size_t N>
256LIBC_INLINE constexpr cpp::array<word, N> shift(cpp::array<word, N> array,
257 size_t offset) {
258 static_assert(direction == LEFT || direction == RIGHT);
259 constexpr size_t WORD_BITS = cpp::numeric_limits<word>::digits;
260#ifdef LIBC_TYPES_HAS_INT128
261 constexpr size_t TOTAL_BITS = N * WORD_BITS;
262 if constexpr (TOTAL_BITS == 128) {
263 using type = cpp::conditional_t<is_signed, __int128_t, __uint128_t>;
264 auto tmp = cpp::bit_cast<type>(array);
265 if constexpr (direction == LEFT)
266 tmp <<= offset;
267 else
268 tmp >>= offset;
269 return cpp::bit_cast<cpp::array<word, N>>(tmp);
270 }
271#endif
272 if (LIBC_UNLIKELY(offset == 0))
273 return array;
274 const bool is_neg = is_signed && is_negative(array);
275 constexpr auto at = [](size_t index) -> int {
276 // reverse iteration when direction == LEFT.
277 if constexpr (direction == LEFT)
278 return int(N) - int(index) - 1;
279 return int(index);
280 };
281 const auto safe_get_at = [&](size_t index) -> word {
282 // return appropriate value when accessing out of bound elements.
283 const int i = at(index);
284 if (i < 0)
285 return 0;
286 if (i >= int(N))
287 return is_neg ? cpp::numeric_limits<word>::max() : 0;
288 return array[static_cast<unsigned>(i)];
289 };
290 const size_t index_offset = offset / WORD_BITS;
291 const size_t bit_offset = offset % WORD_BITS;
292#ifdef LIBC_COMPILER_IS_CLANG
293 __builtin_assume(index_offset < N);
294#endif
295 cpp::array<word, N> out = {};
296 for (size_t index = 0; index < N; ++index) {
297 const word part1 = safe_get_at(index + index_offset);
298 const word part2 = safe_get_at(index + index_offset + 1);
299 word &dst = out[static_cast<unsigned>(at(index))];
300 if (bit_offset == 0)
301 dst = part1; // no crosstalk between parts.
302 else if constexpr (direction == LEFT)
303 dst = static_cast<word>((part1 << bit_offset) |
304 (part2 >> (WORD_BITS - bit_offset)));
305 else
306 dst = static_cast<word>((part1 >> bit_offset) |
307 (part2 << (WORD_BITS - bit_offset)));
308 }
309 return out;
310}
311
312#define DECLARE_COUNTBIT(NAME, INDEX_EXPR) \
313 template <typename word, size_t N> \
314 LIBC_INLINE constexpr int NAME(const cpp::array<word, N> &val) { \
315 int bit_count = 0; \
316 for (size_t i = 0; i < N; ++i) { \
317 const int word_count = cpp::NAME<word>(val[INDEX_EXPR]); \
318 bit_count += word_count; \
319 if (word_count != cpp::numeric_limits<word>::digits) \
320 break; \
321 } \
322 return bit_count; \
323 }
324
325DECLARE_COUNTBIT(countr_zero, i) // iterating forward
326DECLARE_COUNTBIT(countr_one, i) // iterating forward
327DECLARE_COUNTBIT(countl_zero, N - i - 1) // iterating backward
328DECLARE_COUNTBIT(countl_one, N - i - 1) // iterating backward
329
330} // namespace multiword
331
332template <size_t Bits, bool Signed, typename WordType = uint64_t>
333struct BigInt {
334private:
335 static_assert(cpp::is_integral_v<WordType> && cpp::is_unsigned_v<WordType>,
336 "WordType must be unsigned integer.");
337
338 struct Division {
339 BigInt quotient;
340 BigInt remainder;
341 };
342
343public:
344 using word_type = WordType;
345 using unsigned_type = BigInt<Bits, false, word_type>;
346 using signed_type = BigInt<Bits, true, word_type>;
347
348 LIBC_INLINE_VAR static constexpr bool SIGNED = Signed;
349 LIBC_INLINE_VAR static constexpr size_t BITS = Bits;
350 LIBC_INLINE_VAR
351 static constexpr size_t WORD_SIZE = sizeof(WordType) * CHAR_BIT;
352
353 static_assert(Bits > 0 && Bits % WORD_SIZE == 0,
354 "Number of bits in BigInt should be a multiple of WORD_SIZE.");
355
356 LIBC_INLINE_VAR static constexpr size_t WORD_COUNT = Bits / WORD_SIZE;
357
358 cpp::array<WordType, WORD_COUNT> val{}; // zero initialized.
359
360 LIBC_INLINE constexpr BigInt() = default;
361
362 LIBC_INLINE constexpr BigInt(const BigInt &other) = default;
363
364 template <size_t OtherBits, bool OtherSigned, typename OtherWordType>
365 LIBC_INLINE constexpr BigInt(
366 const BigInt<OtherBits, OtherSigned, OtherWordType> &other) {
367 using BigIntOther = BigInt<OtherBits, OtherSigned, OtherWordType>;
368 const bool should_sign_extend = Signed && other.is_neg();
369
370 static_assert(!(Bits == OtherBits && WORD_SIZE != BigIntOther::WORD_SIZE) &&
371 "This is currently untested for casting between bigints with "
372 "the same bit width but different word sizes.");
373
374 if constexpr (BigIntOther::WORD_SIZE < WORD_SIZE) {
375 // OtherWordType is smaller
376 constexpr size_t WORD_SIZE_RATIO = WORD_SIZE / BigIntOther::WORD_SIZE;
377 static_assert(
378 (WORD_SIZE % BigIntOther::WORD_SIZE) == 0 &&
379 "Word types must be multiples of each other for correct conversion.");
380 if constexpr (OtherBits >= Bits) { // truncate
381 // for each big word
382 for (size_t i = 0; i < WORD_COUNT; ++i) {
383 WordType cur_word = 0;
384 // combine WORD_SIZE_RATIO small words into a big word
385 for (size_t j = 0; j < WORD_SIZE_RATIO; ++j)
386 cur_word |= static_cast<WordType>(other[(i * WORD_SIZE_RATIO) + j])
387 << (BigIntOther::WORD_SIZE * j);
388
389 val[i] = cur_word;
390 }
391 } else { // zero or sign extend
392 size_t i = 0;
393 WordType cur_word = 0;
394 // for each small word
395 for (; i < BigIntOther::WORD_COUNT; ++i) {
396 // combine WORD_SIZE_RATIO small words into a big word
397 cur_word |= static_cast<WordType>(other[i])
398 << (BigIntOther::WORD_SIZE * (i % WORD_SIZE_RATIO));
399 // if we've completed a big word, copy it into place and reset
400 if ((i % WORD_SIZE_RATIO) == WORD_SIZE_RATIO - 1) {
401 val[i / WORD_SIZE_RATIO] = cur_word;
402 cur_word = 0;
403 }
404 }
405 // Pretend there are extra words of the correct sign extension as needed
406
407 const WordType extension_bits =
408 should_sign_extend ? cpp::numeric_limits<WordType>::max()
409 : cpp::numeric_limits<WordType>::min();
410 if ((i % WORD_SIZE_RATIO) != 0) {
411 cur_word |= static_cast<WordType>(extension_bits)
412 << (BigIntOther::WORD_SIZE * (i % WORD_SIZE_RATIO));
413 }
414 // Copy the last word into place.
415 val[(i / WORD_SIZE_RATIO)] = cur_word;
416 extend(index: (i / WORD_SIZE_RATIO) + 1, is_neg: should_sign_extend);
417 }
418 } else if constexpr (BigIntOther::WORD_SIZE == WORD_SIZE) {
419 if constexpr (OtherBits >= Bits) { // truncate
420 for (size_t i = 0; i < WORD_COUNT; ++i)
421 val[i] = other[i];
422 } else { // zero or sign extend
423 size_t i = 0;
424 for (; i < BigIntOther::WORD_COUNT; ++i)
425 val[i] = other[i];
426 extend(index: i, is_neg: should_sign_extend);
427 }
428 } else {
429 // OtherWordType is bigger.
430 constexpr size_t WORD_SIZE_RATIO = BigIntOther::WORD_SIZE / WORD_SIZE;
431 static_assert(
432 (BigIntOther::WORD_SIZE % WORD_SIZE) == 0 &&
433 "Word types must be multiples of each other for correct conversion.");
434 if constexpr (OtherBits >= Bits) { // truncate
435 // for each small word
436 for (size_t i = 0; i < WORD_COUNT; ++i) {
437 // split each big word into WORD_SIZE_RATIO small words
438 val[i] = static_cast<WordType>(other[i / WORD_SIZE_RATIO] >>
439 ((i % WORD_SIZE_RATIO) * WORD_SIZE));
440 }
441 } else { // zero or sign extend
442 size_t i = 0;
443 // for each big word
444 for (; i < BigIntOther::WORD_COUNT; ++i) {
445 // split each big word into WORD_SIZE_RATIO small words
446 for (size_t j = 0; j < WORD_SIZE_RATIO; ++j)
447 val[(i * WORD_SIZE_RATIO) + j] =
448 static_cast<WordType>(other[i] >> (j * WORD_SIZE));
449 }
450 extend(index: i * WORD_SIZE_RATIO, is_neg: should_sign_extend);
451 }
452 }
453 }
454
455 // Construct a BigInt from a C array.
456 template <size_t N> LIBC_INLINE constexpr BigInt(const WordType (&nums)[N]) {
457 static_assert(N == WORD_COUNT);
458 for (size_t i = 0; i < WORD_COUNT; ++i)
459 val[i] = nums[i];
460 }
461
462 LIBC_INLINE constexpr explicit BigInt(
463 const cpp::array<WordType, WORD_COUNT> &words) {
464 val = words;
465 }
466
467 // Initialize the first word to |v| and the rest to 0.
468 template <typename T, typename = cpp::enable_if_t<cpp::is_integral_v<T>>>
469 LIBC_INLINE constexpr BigInt(T v) {
470 constexpr size_t T_SIZE = sizeof(T) * CHAR_BIT;
471 const bool is_neg = v < 0;
472 for (size_t i = 0; i < WORD_COUNT; ++i) {
473 if (v == 0) {
474 extend(index: i, is_neg);
475 return;
476 }
477 val[i] = static_cast<WordType>(v);
478 if constexpr (T_SIZE > WORD_SIZE)
479 v >>= WORD_SIZE;
480 else
481 v = 0;
482 }
483 }
484 LIBC_INLINE constexpr BigInt &operator=(const BigInt &other) = default;
485
486 // constants
487 LIBC_INLINE static constexpr BigInt zero() { return BigInt(); }
488 LIBC_INLINE static constexpr BigInt one() { return BigInt(1); }
489 LIBC_INLINE static constexpr BigInt all_ones() { return ~zero(); }
490 LIBC_INLINE static constexpr BigInt min() {
491 BigInt out;
492 if constexpr (SIGNED)
493 out.set_msb();
494 return out;
495 }
496 LIBC_INLINE static constexpr BigInt max() {
497 BigInt out = all_ones();
498 if constexpr (SIGNED)
499 out.clear_msb();
500 return out;
501 }
502
503 // TODO: Reuse the Sign type.
504 LIBC_INLINE constexpr bool is_neg() const { return SIGNED && get_msb(); }
505
506 template <size_t OtherBits, bool OtherSigned, typename OtherWordType>
507 LIBC_INLINE constexpr explicit
508 operator BigInt<OtherBits, OtherSigned, OtherWordType>() const {
509 return BigInt<OtherBits, OtherSigned, OtherWordType>(this);
510 }
511
512 template <typename T> LIBC_INLINE constexpr explicit operator T() const {
513 return to<T>();
514 }
515
516 template <typename T>
517 LIBC_INLINE constexpr cpp::enable_if_t<
518 cpp::is_integral_v<T> && !cpp::is_same_v<T, bool>, T>
519 to() const {
520 constexpr size_t T_SIZE = sizeof(T) * CHAR_BIT;
521 T lo = static_cast<T>(val[0]);
522 if constexpr (T_SIZE <= WORD_SIZE)
523 return lo;
524 constexpr size_t MAX_COUNT =
525 T_SIZE > Bits ? WORD_COUNT : T_SIZE / WORD_SIZE;
526 for (size_t i = 1; i < MAX_COUNT; ++i)
527 lo += static_cast<T>(static_cast<T>(val[i]) << (WORD_SIZE * i));
528 if constexpr (Signed && (T_SIZE > Bits)) {
529 // Extend sign for negative numbers.
530 constexpr T MASK = (~T(0) << Bits);
531 if (is_neg())
532 lo |= MASK;
533 }
534 return lo;
535 }
536
537 LIBC_INLINE constexpr explicit operator bool() const { return !is_zero(); }
538
539 LIBC_INLINE constexpr bool is_zero() const {
540 for (auto part : val)
541 if (part != 0)
542 return false;
543 return true;
544 }
545
546 // Add 'rhs' to this number and store the result in this number.
547 // Returns the carry value produced by the addition operation.
548 LIBC_INLINE constexpr WordType add_overflow(const BigInt &rhs) {
549 return multiword::add_with_carry(val, rhs.val);
550 }
551
552 LIBC_INLINE constexpr BigInt operator+(const BigInt &other) const {
553 BigInt result = *this;
554 result.add_overflow(other);
555 return result;
556 }
557
558 // This will only apply when initializing a variable from constant values, so
559 // it will always use the constexpr version of add_with_carry.
560 LIBC_INLINE constexpr BigInt operator+(BigInt &&other) const {
561 // We use addition commutativity to reuse 'other' and prevent allocation.
562 other.add_overflow(*this); // Returned carry value is ignored.
563 return other;
564 }
565
566 LIBC_INLINE constexpr BigInt &operator+=(const BigInt &other) {
567 add_overflow(rhs: other); // Returned carry value is ignored.
568 return *this;
569 }
570
571 // Subtract 'rhs' to this number and store the result in this number.
572 // Returns the carry value produced by the subtraction operation.
573 LIBC_INLINE constexpr WordType sub_overflow(const BigInt &rhs) {
574 return multiword::sub_with_borrow(val, rhs.val);
575 }
576
577 LIBC_INLINE constexpr BigInt operator-(const BigInt &other) const {
578 BigInt result = *this;
579 result.sub_overflow(other); // Returned carry value is ignored.
580 return result;
581 }
582
583 LIBC_INLINE constexpr BigInt operator-(BigInt &&other) const {
584 BigInt result = *this;
585 result.sub_overflow(other); // Returned carry value is ignored.
586 return result;
587 }
588
589 LIBC_INLINE constexpr BigInt &operator-=(const BigInt &other) {
590 // TODO(lntue): Set overflow flag / errno when carry is true.
591 sub_overflow(rhs: other); // Returned carry value is ignored.
592 return *this;
593 }
594
595 // Multiply this number with x and store the result in this number.
596 LIBC_INLINE constexpr WordType mul(WordType x) {
597 return multiword::scalar_multiply_with_carry(val, x);
598 }
599
600 // Return the full product.
601 template <size_t OtherBits>
602 LIBC_INLINE constexpr auto
603 ful_mul(const BigInt<OtherBits, Signed, WordType> &other) const {
604 BigInt<Bits + OtherBits, Signed, WordType> result;
605 multiword::multiply_with_carry(result.val, val, other.val);
606 return result;
607 }
608
609 LIBC_INLINE constexpr BigInt operator*(const BigInt &other) const {
610 // Perform full mul and truncate.
611 return BigInt(ful_mul(other));
612 }
613
614 // Fast hi part of the full product. The normal product `operator*` returns
615 // `Bits` least significant bits of the full product, while this function will
616 // approximate `Bits` most significant bits of the full product with errors
617 // bounded by:
618 // 0 <= (a.full_mul(b) >> Bits) - a.quick_mul_hi(b)) <= WORD_COUNT - 1.
619 //
620 // An example usage of this is to quickly (but less accurately) compute the
621 // product of (normalized) mantissas of floating point numbers:
622 // (mant_1, mant_2) -> quick_mul_hi -> normalize leading bit
623 // is much more efficient than:
624 // (mant_1, mant_2) -> ful_mul -> normalize leading bit
625 // -> convert back to same Bits width by shifting/rounding,
626 // especially for higher precisions.
627 //
628 // Performance summary:
629 // Number of 64-bit x 64-bit -> 128-bit multiplications performed.
630 // Bits WORD_COUNT ful_mul quick_mul_hi Error bound
631 // 128 2 4 3 1
632 // 196 3 9 6 2
633 // 256 4 16 10 3
634 // 512 8 64 36 7
635 LIBC_INLINE constexpr BigInt quick_mul_hi(const BigInt &other) const {
636 BigInt result;
637 multiword::quick_mul_hi(result.val, val, other.val);
638 return result;
639 }
640
641 // BigInt(x).pow_n(n) computes x ^ n.
642 // Note 0 ^ 0 == 1.
643 LIBC_INLINE constexpr void pow_n(uint64_t power) {
644 static_assert(!Signed);
645 BigInt result = one();
646 BigInt cur_power = *this;
647 while (power > 0) {
648 if ((power % 2) > 0)
649 result *= cur_power;
650 power >>= 1;
651 cur_power *= cur_power;
652 }
653 *this = result;
654 }
655
656 // Performs inplace signed / unsigned division. Returns remainder if not
657 // dividing by zero.
658 // For signed numbers it behaves like C++ signed integer division.
659 // That is by truncating the fractionnal part
660 // https://stackoverflow.com/a/3602857
661 LIBC_INLINE constexpr cpp::optional<BigInt> div(const BigInt &divider) {
662 if (LIBC_UNLIKELY(divider.is_zero()))
663 return cpp::nullopt;
664 if (LIBC_UNLIKELY(divider == BigInt::one()))
665 return BigInt::zero();
666 Division result;
667 if constexpr (SIGNED)
668 result = divide_signed(dividend: *this, divider);
669 else
670 result = divide_unsigned(dividend: *this, divider);
671 *this = result.quotient;
672 return result.remainder;
673 }
674
675 // Efficiently perform BigInt / (x * 2^e), where x is a half-word-size
676 // unsigned integer, and return the remainder. The main idea is as follow:
677 // Let q = y / (x * 2^e) be the quotient, and
678 // r = y % (x * 2^e) be the remainder.
679 // First, notice that:
680 // r % (2^e) = y % (2^e),
681 // so we just need to focus on all the bits of y that is >= 2^e.
682 // To speed up the shift-and-add steps, we only use x as the divisor, and
683 // performing 32-bit shiftings instead of bit-by-bit shiftings.
684 // Since the remainder of each division step < x < 2^(WORD_SIZE / 2), the
685 // computation of each step is now properly contained within WordType.
686 // And finally we perform some extra alignment steps for the remaining bits.
687 LIBC_INLINE constexpr cpp::optional<BigInt>
688 div_uint_half_times_pow_2(multiword::half_width_t<WordType> x, size_t e) {
689 BigInt remainder;
690 if (x == 0)
691 return cpp::nullopt;
692 if (e >= Bits) {
693 remainder = *this;
694 *this = BigInt<Bits, false, WordType>();
695 return remainder;
696 }
697 BigInt quotient;
698 WordType x_word = static_cast<WordType>(x);
699 constexpr size_t LOG2_WORD_SIZE =
700 static_cast<size_t>(cpp::bit_width(value: WORD_SIZE) - 1);
701 constexpr size_t HALF_WORD_SIZE = WORD_SIZE >> 1;
702 constexpr WordType HALF_MASK = ((WordType(1) << HALF_WORD_SIZE) - 1);
703 // lower = smallest multiple of WORD_SIZE that is >= e.
704 size_t lower = ((e >> LOG2_WORD_SIZE) + ((e & (WORD_SIZE - 1)) != 0))
705 << LOG2_WORD_SIZE;
706 // lower_pos is the index of the closest WORD_SIZE-bit chunk >= 2^e.
707 size_t lower_pos = lower / WORD_SIZE;
708 // Keep track of current remainder mod x * 2^(32*i)
709 WordType rem = 0;
710 // pos is the index of the current 64-bit chunk that we are processing.
711 size_t pos = WORD_COUNT;
712
713 // TODO: look into if constexpr(Bits > 256) skip leading zeroes.
714
715 for (size_t q_pos = WORD_COUNT - lower_pos; q_pos > 0; --q_pos) {
716 // q_pos is 1 + the index of the current WORD_SIZE-bit chunk of the
717 // quotient being processed. Performing the division / modulus with
718 // divisor:
719 // x * 2^(WORD_SIZE*q_pos - WORD_SIZE/2),
720 // i.e. using the upper (WORD_SIZE/2)-bit of the current WORD_SIZE-bit
721 // chunk.
722 rem <<= HALF_WORD_SIZE;
723 rem += val[--pos] >> HALF_WORD_SIZE;
724 WordType q_tmp = rem / x_word;
725 rem %= x_word;
726
727 // Performing the division / modulus with divisor:
728 // x * 2^(WORD_SIZE*(q_pos - 1)),
729 // i.e. using the lower (WORD_SIZE/2)-bit of the current WORD_SIZE-bit
730 // chunk.
731 rem <<= HALF_WORD_SIZE;
732 rem += val[pos] & HALF_MASK;
733 quotient.val[q_pos - 1] = (q_tmp << HALF_WORD_SIZE) + rem / x_word;
734 rem %= x_word;
735 }
736
737 // So far, what we have is:
738 // quotient = y / (x * 2^lower), and
739 // rem = (y % (x * 2^lower)) / 2^lower.
740 // If (lower > e), we will need to perform an extra adjustment of the
741 // quotient and remainder, namely:
742 // y / (x * 2^e) = [ y / (x * 2^lower) ] * 2^(lower - e) +
743 // + (rem * 2^(lower - e)) / x
744 // (y % (x * 2^e)) / 2^e = (rem * 2^(lower - e)) % x
745 size_t last_shift = lower - e;
746
747 if (last_shift > 0) {
748 // quotient * 2^(lower - e)
749 quotient <<= last_shift;
750 WordType q_tmp = 0;
751 WordType d = val[--pos];
752 if (last_shift >= HALF_WORD_SIZE) {
753 // The shifting (rem * 2^(lower - e)) might overflow WordTyoe, so we
754 // perform a HALF_WORD_SIZE-bit shift first.
755 rem <<= HALF_WORD_SIZE;
756 rem += d >> HALF_WORD_SIZE;
757 d &= HALF_MASK;
758 q_tmp = rem / x_word;
759 rem %= x_word;
760 last_shift -= HALF_WORD_SIZE;
761 } else {
762 // Only use the upper HALF_WORD_SIZE-bit of the current WORD_SIZE-bit
763 // chunk.
764 d >>= HALF_WORD_SIZE;
765 }
766
767 if (last_shift > 0) {
768 rem <<= HALF_WORD_SIZE;
769 rem += d;
770 q_tmp <<= last_shift;
771 x_word <<= HALF_WORD_SIZE - last_shift;
772 q_tmp += rem / x_word;
773 rem %= x_word;
774 }
775
776 quotient.val[0] += q_tmp;
777
778 if (lower - e <= HALF_WORD_SIZE) {
779 // The remainder rem * 2^(lower - e) might overflow to the higher
780 // WORD_SIZE-bit chunk.
781 if (pos < WORD_COUNT - 1) {
782 remainder[pos + 1] = rem >> HALF_WORD_SIZE;
783 }
784 remainder[pos] = (rem << HALF_WORD_SIZE) + (val[pos] & HALF_MASK);
785 } else {
786 remainder[pos] = rem;
787 }
788
789 } else {
790 remainder[pos] = rem;
791 }
792
793 // Set the remaining lower bits of the remainder.
794 for (; pos > 0; --pos) {
795 remainder[pos - 1] = val[pos - 1];
796 }
797
798 *this = quotient;
799 return remainder;
800 }
801
802 LIBC_INLINE constexpr BigInt operator/(const BigInt &other) const {
803 BigInt result(*this);
804 result.div(other);
805 return result;
806 }
807
808 LIBC_INLINE constexpr BigInt &operator/=(const BigInt &other) {
809 div(divider: other);
810 return *this;
811 }
812
813 LIBC_INLINE constexpr BigInt operator%(const BigInt &other) const {
814 BigInt result(*this);
815 return *result.div(other);
816 }
817
818 LIBC_INLINE constexpr BigInt operator%=(const BigInt &other) {
819 *this = *this % other;
820 return *this;
821 }
822
823 LIBC_INLINE constexpr BigInt &operator*=(const BigInt &other) {
824 *this = *this * other;
825 return *this;
826 }
827
828 LIBC_INLINE constexpr BigInt &operator<<=(size_t s) {
829 val = multiword::shift<multiword::LEFT, SIGNED>(val, s);
830 return *this;
831 }
832
833 LIBC_INLINE constexpr BigInt operator<<(size_t s) const {
834 return BigInt(multiword::shift<multiword::LEFT, SIGNED>(val, s));
835 }
836
837 LIBC_INLINE constexpr BigInt &operator>>=(size_t s) {
838 val = multiword::shift<multiword::RIGHT, SIGNED>(val, s);
839 return *this;
840 }
841
842 LIBC_INLINE constexpr BigInt operator>>(size_t s) const {
843 return BigInt(multiword::shift<multiword::RIGHT, SIGNED>(val, s));
844 }
845
846#define DEFINE_BINOP(OP) \
847 LIBC_INLINE friend constexpr BigInt operator OP(const BigInt &lhs, \
848 const BigInt &rhs) { \
849 BigInt result; \
850 for (size_t i = 0; i < WORD_COUNT; ++i) \
851 result[i] = lhs[i] OP rhs[i]; \
852 return result; \
853 } \
854 LIBC_INLINE friend constexpr BigInt operator OP##=(BigInt &lhs, \
855 const BigInt &rhs) { \
856 for (size_t i = 0; i < WORD_COUNT; ++i) \
857 lhs[i] OP## = rhs[i]; \
858 return lhs; \
859 }
860
861 DEFINE_BINOP(&) // & and &=
862 DEFINE_BINOP(|) // | and |=
863 DEFINE_BINOP(^) // ^ and ^=
864#undef DEFINE_BINOP
865
866 LIBC_INLINE constexpr BigInt operator~() const {
867 BigInt result;
868 for (size_t i = 0; i < WORD_COUNT; ++i)
869 result[i] = static_cast<WordType>(~val[i]);
870 return result;
871 }
872
873 LIBC_INLINE constexpr BigInt operator-() const {
874 BigInt result(*this);
875 result.negate();
876 return result;
877 }
878
879 LIBC_INLINE friend constexpr bool operator==(const BigInt &lhs,
880 const BigInt &rhs) {
881 for (size_t i = 0; i < WORD_COUNT; ++i)
882 if (lhs.val[i] != rhs.val[i])
883 return false;
884 return true;
885 }
886
887 LIBC_INLINE friend constexpr bool operator!=(const BigInt &lhs,
888 const BigInt &rhs) {
889 return !(lhs == rhs);
890 }
891
892 LIBC_INLINE friend constexpr bool operator>(const BigInt &lhs,
893 const BigInt &rhs) {
894 return cmp(lhs, rhs) > 0;
895 }
896 LIBC_INLINE friend constexpr bool operator>=(const BigInt &lhs,
897 const BigInt &rhs) {
898 return cmp(lhs, rhs) >= 0;
899 }
900 LIBC_INLINE friend constexpr bool operator<(const BigInt &lhs,
901 const BigInt &rhs) {
902 return cmp(lhs, rhs) < 0;
903 }
904 LIBC_INLINE friend constexpr bool operator<=(const BigInt &lhs,
905 const BigInt &rhs) {
906 return cmp(lhs, rhs) <= 0;
907 }
908
909 LIBC_INLINE constexpr BigInt &operator++() {
910 increment();
911 return *this;
912 }
913
914 LIBC_INLINE constexpr BigInt operator++(int) {
915 BigInt oldval(*this);
916 increment();
917 return oldval;
918 }
919
920 LIBC_INLINE constexpr BigInt &operator--() {
921 decrement();
922 return *this;
923 }
924
925 LIBC_INLINE constexpr BigInt operator--(int) {
926 BigInt oldval(*this);
927 decrement();
928 return oldval;
929 }
930
931 // Return the i-th word of the number.
932 LIBC_INLINE constexpr const WordType &operator[](size_t i) const {
933 return val[i];
934 }
935
936 // Return the i-th word of the number.
937 LIBC_INLINE constexpr WordType &operator[](size_t i) { return val[i]; }
938
939 // Return the i-th bit of the number.
940 LIBC_INLINE constexpr bool get_bit(size_t i) const {
941 const size_t word_index = i / WORD_SIZE;
942 return 1 & (val[word_index] >> (i % WORD_SIZE));
943 }
944
945 // Set the i-th bit of the number.
946 LIBC_INLINE constexpr void set_bit(size_t i) {
947 const size_t word_index = i / WORD_SIZE;
948 val[word_index] |= WordType(1) << (i % WORD_SIZE);
949 }
950
951private:
952 LIBC_INLINE friend constexpr int cmp(const BigInt &lhs, const BigInt &rhs) {
953 constexpr auto compare = [](WordType a, WordType b) {
954 return a == b ? 0 : a > b ? 1 : -1;
955 };
956 if constexpr (Signed) {
957 const bool lhs_is_neg = lhs.is_neg();
958 const bool rhs_is_neg = rhs.is_neg();
959 if (lhs_is_neg != rhs_is_neg)
960 return rhs_is_neg ? 1 : -1;
961 }
962 for (size_t i = WORD_COUNT; i-- > 0;)
963 if (auto cmp = compare(lhs[i], rhs[i]); cmp != 0)
964 return cmp;
965 return 0;
966 }
967
968 LIBC_INLINE constexpr void bitwise_not() {
969 for (auto &part : val)
970 part = static_cast<WordType>(~part);
971 }
972
973 LIBC_INLINE constexpr void negate() {
974 bitwise_not();
975 increment();
976 }
977
978 LIBC_INLINE constexpr void increment() {
979 multiword::add_with_carry(val, cpp::array<WordType, 1>{1});
980 }
981
982 LIBC_INLINE constexpr void decrement() {
983 multiword::sub_with_borrow(val, cpp::array<WordType, 1>{1});
984 }
985
986 LIBC_INLINE constexpr void extend(size_t index, bool is_neg) {
987 const WordType value = is_neg ? cpp::numeric_limits<WordType>::max()
988 : cpp::numeric_limits<WordType>::min();
989 for (size_t i = index; i < WORD_COUNT; ++i)
990 val[i] = value;
991 }
992
993 LIBC_INLINE constexpr bool get_msb() const {
994 return val.back() >> (WORD_SIZE - 1);
995 }
996
997 LIBC_INLINE constexpr void set_msb() {
998 val.back() |= mask_leading_ones<WordType, 1>();
999 }
1000
1001 LIBC_INLINE constexpr void clear_msb() {
1002 val.back() &= mask_trailing_ones<WordType, WORD_SIZE - 1>();
1003 }
1004 LIBC_INLINE constexpr static Division divide_unsigned(const BigInt &dividend,
1005 const BigInt &divider) {
1006 BigInt remainder = dividend;
1007 BigInt quotient;
1008 if (remainder >= divider) {
1009 BigInt subtractor = divider;
1010 int cur_bit = multiword::countl_zero(subtractor.val) -
1011 multiword::countl_zero(remainder.val);
1012 subtractor <<= static_cast<size_t>(cur_bit);
1013 for (; cur_bit >= 0 && remainder > 0; --cur_bit, subtractor >>= 1) {
1014 if (remainder < subtractor)
1015 continue;
1016 remainder -= subtractor;
1017 quotient.set_bit(static_cast<size_t>(cur_bit));
1018 }
1019 }
1020 return Division{quotient, remainder};
1021 }
1022
1023 LIBC_INLINE constexpr static Division divide_signed(const BigInt &dividend,
1024 const BigInt &divider) {
1025 // Special case because it is not possible to negate the min value of a
1026 // signed integer.
1027 if (dividend == min() && divider == min())
1028 return Division{one(), zero()};
1029 // 1. Convert the dividend and divisor to unsigned representation.
1030 unsigned_type udividend(dividend);
1031 unsigned_type udivider(divider);
1032 // 2. Negate the dividend if it's negative, and similarly for the divisor.
1033 const bool dividend_is_neg = dividend.is_neg();
1034 const bool divider_is_neg = divider.is_neg();
1035 if (dividend_is_neg)
1036 udividend.negate();
1037 if (divider_is_neg)
1038 udivider.negate();
1039 // 3. Use unsigned multiword division algorithm.
1040 const auto unsigned_result = divide_unsigned(dividend: udividend, divider: udivider);
1041 // 4. Convert the quotient and remainder to signed representation.
1042 Division result;
1043 result.quotient = signed_type(unsigned_result.quotient);
1044 result.remainder = signed_type(unsigned_result.remainder);
1045 // 5. Negate the quotient if the dividend and divisor had opposite signs.
1046 if (dividend_is_neg != divider_is_neg)
1047 result.quotient.negate();
1048 // 6. Negate the remainder if the dividend was negative.
1049 if (dividend_is_neg)
1050 result.remainder.negate();
1051 return result;
1052 }
1053
1054 friend signed_type;
1055 friend unsigned_type;
1056};
1057
1058namespace internal {
1059// We default BigInt's WordType to 'uint64_t' or 'uint32_t' depending on type
1060// availability.
1061template <size_t Bits>
1062struct WordTypeSelector : cpp::type_identity<
1063#ifdef LIBC_TYPES_HAS_INT64
1064 uint64_t
1065#else
1066 uint32_t
1067#endif // LIBC_TYPES_HAS_INT64
1068 > {
1069};
1070// Except if we request 16 or 32 bits explicitly.
1071template <> struct WordTypeSelector<16> : cpp::type_identity<uint16_t> {};
1072template <> struct WordTypeSelector<32> : cpp::type_identity<uint32_t> {};
1073template <> struct WordTypeSelector<96> : cpp::type_identity<uint32_t> {};
1074
1075template <size_t Bits>
1076using WordTypeSelectorT = typename WordTypeSelector<Bits>::type;
1077} // namespace internal
1078
1079template <size_t Bits>
1080using UInt = BigInt<Bits, false, internal::WordTypeSelectorT<Bits>>;
1081
1082template <size_t Bits>
1083using Int = BigInt<Bits, true, internal::WordTypeSelectorT<Bits>>;
1084
1085// Provides limits of BigInt.
1086template <size_t Bits, bool Signed, typename T>
1087struct cpp::numeric_limits<BigInt<Bits, Signed, T>> {
1088 LIBC_INLINE static constexpr BigInt<Bits, Signed, T> max() {
1089 return BigInt<Bits, Signed, T>::max();
1090 }
1091 LIBC_INLINE static constexpr BigInt<Bits, Signed, T> min() {
1092 return BigInt<Bits, Signed, T>::min();
1093 }
1094 // Meant to match std::numeric_limits interface.
1095 // NOLINTNEXTLINE(readability-identifier-naming)
1096 LIBC_INLINE_VAR static constexpr int digits = Bits - Signed;
1097};
1098
1099// type traits to determine whether a T is a BigInt.
1100template <typename T> struct is_big_int : cpp::false_type {};
1101
1102template <size_t Bits, bool Signed, typename T>
1103struct is_big_int<BigInt<Bits, Signed, T>> : cpp::true_type {};
1104
1105template <class T>
1106LIBC_INLINE_VAR constexpr bool is_big_int_v = is_big_int<T>::value;
1107
1108// extensions of type traits to include BigInt
1109
1110// is_integral_or_big_int
1111template <typename T>
1112struct is_integral_or_big_int
1113 : cpp::bool_constant<(cpp::is_integral_v<T> || is_big_int_v<T>)> {};
1114
1115template <typename T>
1116LIBC_INLINE_VAR constexpr bool is_integral_or_big_int_v =
1117 is_integral_or_big_int<T>::value;
1118
1119// make_big_int_unsigned
1120template <typename T> struct make_big_int_unsigned;
1121
1122template <size_t Bits, bool Signed, typename T>
1123struct make_big_int_unsigned<BigInt<Bits, Signed, T>>
1124 : cpp::type_identity<BigInt<Bits, false, T>> {};
1125
1126template <typename T>
1127using make_big_int_unsigned_t = typename make_big_int_unsigned<T>::type;
1128
1129// make_big_int_signed
1130template <typename T> struct make_big_int_signed;
1131
1132template <size_t Bits, bool Signed, typename T>
1133struct make_big_int_signed<BigInt<Bits, Signed, T>>
1134 : cpp::type_identity<BigInt<Bits, true, T>> {};
1135
1136template <typename T>
1137using make_big_int_signed_t = typename make_big_int_signed<T>::type;
1138
1139// make_integral_or_big_int_unsigned
1140template <typename T, class = void> struct make_integral_or_big_int_unsigned;
1141
1142template <typename T>
1143struct make_integral_or_big_int_unsigned<
1144 T, cpp::enable_if_t<cpp::is_integral_v<T>>> : cpp::make_unsigned<T> {};
1145
1146template <typename T>
1147struct make_integral_or_big_int_unsigned<T, cpp::enable_if_t<is_big_int_v<T>>>
1148 : make_big_int_unsigned<T> {};
1149
1150template <typename T>
1151using make_integral_or_big_int_unsigned_t =
1152 typename make_integral_or_big_int_unsigned<T>::type;
1153
1154// make_integral_or_big_int_signed
1155template <typename T, class = void> struct make_integral_or_big_int_signed;
1156
1157template <typename T>
1158struct make_integral_or_big_int_signed<T,
1159 cpp::enable_if_t<cpp::is_integral_v<T>>>
1160 : cpp::make_signed<T> {};
1161
1162template <typename T>
1163struct make_integral_or_big_int_signed<T, cpp::enable_if_t<is_big_int_v<T>>>
1164 : make_big_int_signed<T> {};
1165
1166template <typename T>
1167using make_integral_or_big_int_signed_t =
1168 typename make_integral_or_big_int_signed<T>::type;
1169
1170// is_unsigned_integral_or_big_int
1171template <typename T>
1172struct is_unsigned_integral_or_big_int
1173 : cpp::bool_constant<
1174 cpp::is_same_v<T, make_integral_or_big_int_unsigned_t<T>>> {};
1175
1176template <typename T>
1177// Meant to look like <type_traits> helper variable templates.
1178// NOLINTNEXTLINE(readability-identifier-naming)
1179LIBC_INLINE_VAR constexpr bool is_unsigned_integral_or_big_int_v =
1180 is_unsigned_integral_or_big_int<T>::value;
1181
1182namespace cpp {
1183
1184// Specialization of cpp::bit_cast ('bit.h') from T to BigInt.
1185template <typename To, typename From>
1186LIBC_INLINE constexpr cpp::enable_if_t<
1187 (sizeof(To) == sizeof(From)) && cpp::is_trivially_copyable<To>::value &&
1188 cpp::is_trivially_copyable<From>::value && is_big_int<To>::value,
1189 To>
1190bit_cast(const From &from) {
1191 To out;
1192 using Storage = decltype(out.val);
1193 out.val = cpp::bit_cast<Storage>(from);
1194 return out;
1195}
1196
1197// Specialization of cpp::bit_cast ('bit.h') from BigInt to T.
1198template <typename To, size_t Bits>
1199LIBC_INLINE constexpr cpp::enable_if_t<
1200 sizeof(To) == sizeof(UInt<Bits>) &&
1201 cpp::is_trivially_constructible<To>::value &&
1202 cpp::is_trivially_copyable<To>::value &&
1203 cpp::is_trivially_copyable<UInt<Bits>>::value,
1204 To>
1205bit_cast(const UInt<Bits> &from) {
1206 return cpp::bit_cast<To>(from.val);
1207}
1208
1209// Specialization of cpp::popcount ('bit.h') for BigInt.
1210template <typename T>
1211[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1212popcount(T value) {
1213 int bits = 0;
1214 for (auto word : value.val)
1215 if (word)
1216 bits += popcount(word);
1217 return bits;
1218}
1219
1220// Specialization of cpp::has_single_bit ('bit.h') for BigInt.
1221template <typename T>
1222[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, bool>
1223has_single_bit(T value) {
1224 int bits = 0;
1225 for (auto word : value.val) {
1226 if (word == 0)
1227 continue;
1228 bits += popcount(word);
1229 if (bits > 1)
1230 return false;
1231 }
1232 return bits == 1;
1233}
1234
1235// Specialization of cpp::countr_zero ('bit.h') for BigInt.
1236template <typename T>
1237[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1238countr_zero(const T &value) {
1239 return multiword::countr_zero(value.val);
1240}
1241
1242// Specialization of cpp::countl_zero ('bit.h') for BigInt.
1243template <typename T>
1244[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1245countl_zero(const T &value) {
1246 return multiword::countl_zero(value.val);
1247}
1248
1249// Specialization of cpp::countl_one ('bit.h') for BigInt.
1250template <typename T>
1251[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1252countl_one(T value) {
1253 return multiword::countl_one(value.val);
1254}
1255
1256// Specialization of cpp::countr_one ('bit.h') for BigInt.
1257template <typename T>
1258[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1259countr_one(T value) {
1260 return multiword::countr_one(value.val);
1261}
1262
1263// Specialization of cpp::bit_width ('bit.h') for BigInt.
1264template <typename T>
1265[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1266bit_width(T value) {
1267 return cpp::numeric_limits<T>::digits - cpp::countl_zero(value);
1268}
1269
1270// Forward-declare rotr so that rotl can use it.
1271template <typename T>
1272[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
1273rotr(T value, int rotate);
1274
1275// Specialization of cpp::rotl ('bit.h') for BigInt.
1276template <typename T>
1277[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
1278rotl(T value, int rotate) {
1279 constexpr int N = cpp::numeric_limits<T>::digits;
1280 rotate = rotate % N;
1281 if (!rotate)
1282 return value;
1283 if (rotate < 0)
1284 return cpp::rotr<T>(value, -rotate);
1285 return (value << static_cast<size_t>(rotate)) |
1286 (value >> (N - static_cast<size_t>(rotate)));
1287}
1288
1289// Specialization of cpp::rotr ('bit.h') for BigInt.
1290template <typename T>
1291[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
1292rotr(T value, int rotate) {
1293 constexpr int N = cpp::numeric_limits<T>::digits;
1294 rotate = rotate % N;
1295 if (!rotate)
1296 return value;
1297 if (rotate < 0)
1298 return cpp::rotl<T>(value, -rotate);
1299 return (value >> static_cast<size_t>(rotate)) |
1300 (value << (N - static_cast<size_t>(rotate)));
1301}
1302
1303} // namespace cpp
1304
1305// Specialization of mask_trailing_ones ('math_extras.h') for BigInt.
1306template <typename T, size_t count>
1307LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
1308mask_trailing_ones() {
1309 static_assert(!T::SIGNED && count <= T::BITS);
1310 if (count == T::BITS)
1311 return T::all_ones();
1312 constexpr size_t QUOTIENT = count / T::WORD_SIZE;
1313 constexpr size_t REMAINDER = count % T::WORD_SIZE;
1314 T out; // zero initialized
1315 for (size_t i = 0; i <= QUOTIENT; ++i)
1316 out[i] = i < QUOTIENT
1317 ? cpp::numeric_limits<typename T::word_type>::max()
1318 : mask_trailing_ones<typename T::word_type, REMAINDER>();
1319 return out;
1320}
1321
1322// Specialization of mask_leading_ones ('math_extras.h') for BigInt.
1323template <typename T, size_t count>
1324LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T> mask_leading_ones() {
1325 static_assert(!T::SIGNED && count <= T::BITS);
1326 if (count == T::BITS)
1327 return T::all_ones();
1328 constexpr size_t QUOTIENT = (T::BITS - count - 1U) / T::WORD_SIZE;
1329 constexpr size_t REMAINDER = count % T::WORD_SIZE;
1330 T out; // zero initialized
1331 for (size_t i = QUOTIENT; i < T::WORD_COUNT; ++i)
1332 out[i] = i > QUOTIENT
1333 ? cpp::numeric_limits<typename T::word_type>::max()
1334 : mask_leading_ones<typename T::word_type, REMAINDER>();
1335 return out;
1336}
1337
1338// Specialization of mask_trailing_zeros ('math_extras.h') for BigInt.
1339template <typename T, size_t count>
1340LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
1341mask_trailing_zeros() {
1342 return mask_leading_ones<T, T::BITS - count>();
1343}
1344
1345// Specialization of mask_leading_zeros ('math_extras.h') for BigInt.
1346template <typename T, size_t count>
1347LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
1348mask_leading_zeros() {
1349 return mask_trailing_ones<T, T::BITS - count>();
1350}
1351
1352// Specialization of count_zeros ('math_extras.h') for BigInt.
1353template <typename T>
1354[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1355count_zeros(T value) {
1356 return cpp::popcount(~value);
1357}
1358
1359// Specialization of first_leading_zero ('math_extras.h') for BigInt.
1360template <typename T>
1361[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1362first_leading_zero(T value) {
1363 return value == cpp::numeric_limits<T>::max() ? 0
1364 : cpp::countl_one(value) + 1;
1365}
1366
1367// Specialization of first_leading_one ('math_extras.h') for BigInt.
1368template <typename T>
1369[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1370first_leading_one(T value) {
1371 return first_leading_zero(~value);
1372}
1373
1374// Specialization of first_trailing_zero ('math_extras.h') for BigInt.
1375template <typename T>
1376[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1377first_trailing_zero(T value) {
1378 return value == cpp::numeric_limits<T>::max() ? 0
1379 : cpp::countr_zero(~value) + 1;
1380}
1381
1382// Specialization of first_trailing_one ('math_extras.h') for BigInt.
1383template <typename T>
1384[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
1385first_trailing_one(T value) {
1386 return value == 0 ? 0 : cpp::countr_zero(value) + 1;
1387}
1388
1389} // namespace LIBC_NAMESPACE_DECL
1390
1391#endif // LLVM_LIBC_SRC___SUPPORT_BIG_INT_H
1392