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+//===-- A class to manipulate wide integers. --------------------*- C++ -*-===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_UINT_H
+#define LLVM_LIBC_SRC___SUPPORT_UINT_H
+
+#include "src/__support/CPP/array.h"
+#include "src/__support/CPP/bit.h" // countl_zero
+#include "src/__support/CPP/limits.h"
+#include "src/__support/CPP/optional.h"
+#include "src/__support/CPP/type_traits.h"
+#include "src/__support/macros/attributes.h" // LIBC_INLINE
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/macros/properties/compiler.h" // LIBC_COMPILER_IS_CLANG
+#include "src/__support/macros/properties/types.h" // LIBC_TYPES_HAS_INT128, LIBC_TYPES_HAS_INT64
+#include "src/__support/math_extras.h" // add_with_carry, sub_with_borrow
+#include "src/__support/number_pair.h"
+
+#include <stddef.h> // For size_t
+#include <stdint.h>
+
+namespace LIBC_NAMESPACE {
+
+namespace multiword {
+
+// A type trait mapping unsigned integers to their half-width unsigned
+// counterparts.
+template <typename T> struct half_width;
+template <> struct half_width<uint16_t> : cpp::type_identity<uint8_t> {};
+template <> struct half_width<uint32_t> : cpp::type_identity<uint16_t> {};
+#ifdef LIBC_TYPES_HAS_INT64
+template <> struct half_width<uint64_t> : cpp::type_identity<uint32_t> {};
+#ifdef LIBC_TYPES_HAS_INT128
+template <> struct half_width<__uint128_t> : cpp::type_identity<uint64_t> {};
+#endif // LIBC_TYPES_HAS_INT128
+#endif // LIBC_TYPES_HAS_INT64
+template <typename T> using half_width_t = typename half_width<T>::type;
+
+// An array of two elements that can be used in multiword operations.
+template <typename T> struct DoubleWide final : cpp::array<T, 2> {
+ using UP = cpp::array<T, 2>;
+ using UP::UP;
+ LIBC_INLINE constexpr DoubleWide(T lo, T hi) : UP({lo, hi}) {}
+};
+
+// Converts an unsigned value into a DoubleWide<half_width_t<T>>.
+template <typename T> LIBC_INLINE constexpr auto split(T value) {
+ static_assert(cpp::is_unsigned_v<T>);
+ using half_type = half_width_t<T>;
+ return DoubleWide<half_type>(
+ half_type(value),
+ half_type(value >> cpp::numeric_limits<half_type>::digits));
+}
+
+// The low part of a DoubleWide value.
+template <typename T> LIBC_INLINE constexpr T lo(const DoubleWide<T> &value) {
+ return value[0];
+}
+// The high part of a DoubleWide value.
+template <typename T> LIBC_INLINE constexpr T hi(const DoubleWide<T> &value) {
+ return value[1];
+}
+// The low part of an unsigned value.
+template <typename T> LIBC_INLINE constexpr half_width_t<T> lo(T value) {
+ return lo(split(value));
+}
+// The high part of an unsigned value.
+template <typename T> LIBC_INLINE constexpr half_width_t<T> hi(T value) {
+ return hi(split(value));
+}
+
+// Returns 'a' times 'b' in a DoubleWide<word>. Cannot overflow by construction.
+template <typename word>
+LIBC_INLINE constexpr DoubleWide<word> mul2(word a, word b) {
+ if constexpr (cpp::is_same_v<word, uint8_t>) {
+ return split<uint16_t>(uint16_t(a) * uint16_t(b));
+ } else if constexpr (cpp::is_same_v<word, uint16_t>) {
+ return split<uint32_t>(uint32_t(a) * uint32_t(b));
+ }
+#ifdef LIBC_TYPES_HAS_INT64
+ else if constexpr (cpp::is_same_v<word, uint32_t>) {
+ return split<uint64_t>(uint64_t(a) * uint64_t(b));
+ }
+#endif
+#ifdef LIBC_TYPES_HAS_INT128
+ else if constexpr (cpp::is_same_v<word, uint64_t>) {
+ return split<__uint128_t>(__uint128_t(a) * __uint128_t(b));
+ }
+#endif
+ else {
+ using half_word = half_width_t<word>;
+ const auto shiftl = [](word value) -> word {
+ return value << cpp::numeric_limits<half_word>::digits;
+ };
+ const auto shiftr = [](word value) -> word {
+ return value >> cpp::numeric_limits<half_word>::digits;
+ };
+ // Here we do a one digit multiplication where 'a' and 'b' are of type
+ // word. We split 'a' and 'b' into half words and perform the classic long
+ // multiplication with 'a' and 'b' being two-digit numbers.
+
+ // a a_hi a_lo
+ // x b => x b_hi b_lo
+ // ---- -----------
+ // c result
+ // We convert 'lo' and 'hi' from 'half_word' to 'word' so multiplication
+ // doesn't overflow.
+ const word a_lo = lo(a);
+ const word b_lo = lo(b);
+ const word a_hi = hi(a);
+ const word b_hi = hi(b);
+ const word step1 = b_lo * a_lo; // no overflow;
+ const word step2 = b_lo * a_hi; // no overflow;
+ const word step3 = b_hi * a_lo; // no overflow;
+ const word step4 = b_hi * a_hi; // no overflow;
+ word lo_digit = step1;
+ word hi_digit = step4;
+ const word no_carry = 0;
+ word carry;
+ word _; // unused carry variable.
+ lo_digit = add_with_carry<word>(lo_digit, shiftl(step2), no_carry, carry);
+ hi_digit = add_with_carry<word>(hi_digit, shiftr(step2), carry, _);
+ lo_digit = add_with_carry<word>(lo_digit, shiftl(step3), no_carry, carry);
+ hi_digit = add_with_carry<word>(hi_digit, shiftr(step3), carry, _);
+ return DoubleWide<word>(lo_digit, hi_digit);
+ }
+}
+
+// In-place 'dst op= rhs' with operation with carry propagation. Returns carry.
+template <typename Function, typename word, size_t N, size_t M>
+LIBC_INLINE constexpr word inplace_binop(Function op_with_carry,
+ cpp::array<word, N> &dst,
+ const cpp::array<word, M> &rhs) {
+ static_assert(N >= M);
+ word carry_out = 0;
+ for (size_t i = 0; i < N; ++i) {
+ const bool has_rhs_value = i < M;
+ const word rhs_value = has_rhs_value ? rhs[i] : 0;
+ const word carry_in = carry_out;
+ dst[i] = op_with_carry(dst[i], rhs_value, carry_in, carry_out);
+ // stop early when rhs is over and no carry is to be propagated.
+ if (!has_rhs_value && carry_out == 0)
+ break;
+ }
+ return carry_out;
+}
+
+// In-place addition. Returns carry.
+template <typename word, size_t N, size_t M>
+LIBC_INLINE constexpr word add_with_carry(cpp::array<word, N> &dst,
+ const cpp::array<word, M> &rhs) {
+ return inplace_binop(LIBC_NAMESPACE::add_with_carry<word>, dst, rhs);
+}
+
+// In-place subtraction. Returns borrow.
+template <typename word, size_t N, size_t M>
+LIBC_INLINE constexpr word sub_with_borrow(cpp::array<word, N> &dst,
+ const cpp::array<word, M> &rhs) {
+ return inplace_binop(LIBC_NAMESPACE::sub_with_borrow<word>, dst, rhs);
+}
+
+// In-place multiply-add. Returns carry.
+// i.e., 'dst += b * c'
+template <typename word, size_t N>
+LIBC_INLINE constexpr word mul_add_with_carry(cpp::array<word, N> &dst, word b,
+ word c) {
+ return add_with_carry(dst, mul2(b, c));
+}
+
+// An array of two elements serving as an accumulator during multiword
+// computations.
+template <typename T> struct Accumulator final : cpp::array<T, 2> {
+ using UP = cpp::array<T, 2>;
+ LIBC_INLINE constexpr Accumulator() : UP({0, 0}) {}
+ LIBC_INLINE constexpr T advance(T carry_in) {
+ auto result = UP::front();
+ UP::front() = UP::back();
+ UP::back() = carry_in;
+ return result;
+ }
+ LIBC_INLINE constexpr T sum() const { return UP::front(); }
+ LIBC_INLINE constexpr T carry() const { return UP::back(); }
+};
+
+// In-place multiplication by a single word. Returns carry.
+template <typename word, size_t N>
+LIBC_INLINE constexpr word scalar_multiply_with_carry(cpp::array<word, N> &dst,
+ word x) {
+ Accumulator<word> acc;
+ for (auto &val : dst) {
+ const word carry = mul_add_with_carry(acc, val, x);
+ val = acc.advance(carry);
+ }
+ return acc.carry();
+}
+
+// Multiplication of 'lhs' by 'rhs' into 'dst'. Returns carry.
+// This function is safe to use for signed numbers.
+// https://stackoverflow.com/a/20793834
+// https://pages.cs.wisc.edu/%7Emarkhill/cs354/Fall2008/beyond354/int.mult.html
+template <typename word, size_t O, size_t M, size_t N>
+LIBC_INLINE constexpr word multiply_with_carry(cpp::array<word, O> &dst,
+ const cpp::array<word, M> &lhs,
+ const cpp::array<word, N> &rhs) {
+ static_assert(O >= M + N);
+ Accumulator<word> acc;
+ for (size_t i = 0; i < O; ++i) {
+ const size_t lower_idx = i < N ? 0 : i - N + 1;
+ const size_t upper_idx = i < M ? i : M - 1;
+ word carry = 0;
+ for (size_t j = lower_idx; j <= upper_idx; ++j)
+ carry += mul_add_with_carry(acc, lhs[j], rhs[i - j]);
+ dst[i] = acc.advance(carry);
+ }
+ return acc.carry();
+}
+
+template <typename word, size_t N>
+LIBC_INLINE constexpr void quick_mul_hi(cpp::array<word, N> &dst,
+ const cpp::array<word, N> &lhs,
+ const cpp::array<word, N> &rhs) {
+ Accumulator<word> acc;
+ word carry = 0;
+ // First round of accumulation for those at N - 1 in the full product.
+ for (size_t i = 0; i < N; ++i)
+ carry += mul_add_with_carry(acc, lhs[i], rhs[N - 1 - i]);
+ for (size_t i = N; i < 2 * N - 1; ++i) {
+ acc.advance(carry);
+ carry = 0;
+ for (size_t j = i - N + 1; j < N; ++j)
+ carry += mul_add_with_carry(acc, lhs[j], rhs[i - j]);
+ dst[i - N] = acc.sum();
+ }
+ dst.back() = acc.carry();
+}
+
+template <typename word, size_t N>
+LIBC_INLINE constexpr bool is_negative(cpp::array<word, N> &array) {
+ using signed_word = cpp::make_signed_t<word>;
+ return cpp::bit_cast<signed_word>(array.back()) < 0;
+}
+
+// An enum for the shift function below.
+enum Direction { LEFT, RIGHT };
+
+// A bitwise shift on an array of elements.
+// 'offset' must be less than TOTAL_BITS (i.e., sizeof(word) * CHAR_BIT * N)
+// otherwise the behavior is undefined.
+template <Direction direction, bool is_signed, typename word, size_t N>
+LIBC_INLINE constexpr cpp::array<word, N> shift(cpp::array<word, N> array,
+ size_t offset) {
+ static_assert(direction == LEFT || direction == RIGHT);
+ constexpr size_t WORD_BITS = cpp::numeric_limits<word>::digits;
+#ifdef LIBC_TYPES_HAS_INT128
+ constexpr size_t TOTAL_BITS = N * WORD_BITS;
+ if constexpr (TOTAL_BITS == 128) {
+ using type = cpp::conditional_t<is_signed, __int128_t, __uint128_t>;
+ auto tmp = cpp::bit_cast<type>(array);
+ if constexpr (direction == LEFT)
+ tmp <<= offset;
+ else
+ tmp >>= offset;
+ return cpp::bit_cast<cpp::array<word, N>>(tmp);
+ }
+#endif
+ if (LIBC_UNLIKELY(offset == 0))
+ return array;
+ const bool is_neg = is_signed && is_negative(array);
+ constexpr auto at = [](size_t index) -> int {
+ // reverse iteration when direction == LEFT.
+ if constexpr (direction == LEFT)
+ return int(N) - int(index) - 1;
+ return int(index);
+ };
+ const auto safe_get_at = [&](size_t index) -> word {
+ // return appropriate value when accessing out of bound elements.
+ const int i = at(index);
+ if (i < 0)
+ return 0;
+ if (i >= int(N))
+ return is_neg ? -1 : 0;
+ return array[i];
+ };
+ const size_t index_offset = offset / WORD_BITS;
+ const size_t bit_offset = offset % WORD_BITS;
+#ifdef LIBC_COMPILER_IS_CLANG
+ __builtin_assume(index_offset < N);
+#endif
+ cpp::array<word, N> out = {};
+ for (size_t index = 0; index < N; ++index) {
+ const word part1 = safe_get_at(index + index_offset);
+ const word part2 = safe_get_at(index + index_offset + 1);
+ word &dst = out[at(index)];
+ if (bit_offset == 0)
+ dst = part1; // no crosstalk between parts.
+ else if constexpr (direction == LEFT)
+ dst = (part1 << bit_offset) | (part2 >> (WORD_BITS - bit_offset));
+ else
+ dst = (part1 >> bit_offset) | (part2 << (WORD_BITS - bit_offset));
+ }
+ return out;
+}
+
+#define DECLARE_COUNTBIT(NAME, INDEX_EXPR) \
+ template <typename word, size_t N> \
+ LIBC_INLINE constexpr int NAME(const cpp::array<word, N> &val) { \
+ int bit_count = 0; \
+ for (size_t i = 0; i < N; ++i) { \
+ const int word_count = cpp::NAME<word>(val[INDEX_EXPR]); \
+ bit_count += word_count; \
+ if (word_count != cpp::numeric_limits<word>::digits) \
+ break; \
+ } \
+ return bit_count; \
+ }
+
+DECLARE_COUNTBIT(countr_zero, i) // iterating forward
+DECLARE_COUNTBIT(countr_one, i) // iterating forward
+DECLARE_COUNTBIT(countl_zero, N - i - 1) // iterating backward
+DECLARE_COUNTBIT(countl_one, N - i - 1) // iterating backward
+
+} // namespace multiword
+
+template <size_t Bits, bool Signed, typename WordType = uint64_t>
+struct BigInt {
+private:
+ static_assert(cpp::is_integral_v<WordType> && cpp::is_unsigned_v<WordType>,
+ "WordType must be unsigned integer.");
+
+ struct Division {
+ BigInt quotient;
+ BigInt remainder;
+ };
+
+public:
+ using word_type = WordType;
+ using unsigned_type = BigInt<Bits, false, word_type>;
+ using signed_type = BigInt<Bits, true, word_type>;
+
+ LIBC_INLINE_VAR static constexpr bool SIGNED = Signed;
+ LIBC_INLINE_VAR static constexpr size_t BITS = Bits;
+ LIBC_INLINE_VAR
+ static constexpr size_t WORD_SIZE = sizeof(WordType) * CHAR_BIT;
+
+ static_assert(Bits > 0 && Bits % WORD_SIZE == 0,
+ "Number of bits in BigInt should be a multiple of WORD_SIZE.");
+
+ LIBC_INLINE_VAR static constexpr size_t WORD_COUNT = Bits / WORD_SIZE;
+
+ cpp::array<WordType, WORD_COUNT> val{}; // zero initialized.
+
+ LIBC_INLINE constexpr BigInt() = default;
+
+ LIBC_INLINE constexpr BigInt(const BigInt &other) = default;
+
+ template <size_t OtherBits, bool OtherSigned>
+ LIBC_INLINE constexpr BigInt(
+ const BigInt<OtherBits, OtherSigned, WordType> &other) {
+ if (OtherBits >= Bits) { // truncate
+ for (size_t i = 0; i < WORD_COUNT; ++i)
+ val[i] = other[i];
+ } else { // zero or sign extend
+ size_t i = 0;
+ for (; i < OtherBits / WORD_SIZE; ++i)
+ val[i] = other[i];
+ extend(i, Signed && other.is_neg());
+ }
+ }
+
+ // Construct a BigInt from a C array.
+ template <size_t N> LIBC_INLINE constexpr BigInt(const WordType (&nums)[N]) {
+ static_assert(N == WORD_COUNT);
+ for (size_t i = 0; i < WORD_COUNT; ++i)
+ val[i] = nums[i];
+ }
+
+ LIBC_INLINE constexpr explicit BigInt(
+ const cpp::array<WordType, WORD_COUNT> &words) {
+ val = words;
+ }
+
+ // Initialize the first word to |v| and the rest to 0.
+ template <typename T, typename = cpp::enable_if_t<cpp::is_integral_v<T>>>
+ LIBC_INLINE constexpr BigInt(T v) {
+ constexpr size_t T_SIZE = sizeof(T) * CHAR_BIT;
+ const bool is_neg = Signed && (v < 0);
+ for (size_t i = 0; i < WORD_COUNT; ++i) {
+ if (v == 0) {
+ extend(i, is_neg);
+ return;
+ }
+ val[i] = static_cast<WordType>(v);
+ if constexpr (T_SIZE > WORD_SIZE)
+ v >>= WORD_SIZE;
+ else
+ v = 0;
+ }
+ }
+ LIBC_INLINE constexpr BigInt &operator=(const BigInt &other) = default;
+
+ // constants
+ LIBC_INLINE static constexpr BigInt zero() { return BigInt(); }
+ LIBC_INLINE static constexpr BigInt one() { return BigInt(1); }
+ LIBC_INLINE static constexpr BigInt all_ones() { return ~zero(); }
+ LIBC_INLINE static constexpr BigInt min() {
+ BigInt out;
+ if constexpr (SIGNED)
+ out.set_msb();
+ return out;
+ }
+ LIBC_INLINE static constexpr BigInt max() {
+ BigInt out = all_ones();
+ if constexpr (SIGNED)
+ out.clear_msb();
+ return out;
+ }
+
+ // TODO: Reuse the Sign type.
+ LIBC_INLINE constexpr bool is_neg() const { return SIGNED && get_msb(); }
+
+ template <typename T> LIBC_INLINE constexpr explicit operator T() const {
+ return to<T>();
+ }
+
+ template <typename T>
+ LIBC_INLINE constexpr cpp::enable_if_t<
+ cpp::is_integral_v<T> && !cpp::is_same_v<T, bool>, T>
+ to() const {
+ constexpr size_t T_SIZE = sizeof(T) * CHAR_BIT;
+ T lo = static_cast<T>(val[0]);
+ if constexpr (T_SIZE <= WORD_SIZE)
+ return lo;
+ constexpr size_t MAX_COUNT =
+ T_SIZE > Bits ? WORD_COUNT : T_SIZE / WORD_SIZE;
+ for (size_t i = 1; i < MAX_COUNT; ++i)
+ lo += static_cast<T>(val[i]) << (WORD_SIZE * i);
+ if constexpr (Signed && (T_SIZE > Bits)) {
+ // Extend sign for negative numbers.
+ constexpr T MASK = (~T(0) << Bits);
+ if (is_neg())
+ lo |= MASK;
+ }
+ return lo;
+ }
+
+ LIBC_INLINE constexpr explicit operator bool() const { return !is_zero(); }
+
+ LIBC_INLINE constexpr bool is_zero() const {
+ for (auto part : val)
+ if (part != 0)
+ return false;
+ return true;
+ }
+
+ // Add 'rhs' to this number and store the result in this number.
+ // Returns the carry value produced by the addition operation.
+ LIBC_INLINE constexpr WordType add_overflow(const BigInt &rhs) {
+ return multiword::add_with_carry(val, rhs.val);
+ }
+
+ LIBC_INLINE constexpr BigInt operator+(const BigInt &other) const {
+ BigInt result = *this;
+ result.add_overflow(other);
+ return result;
+ }
+
+ // This will only apply when initializing a variable from constant values, so
+ // it will always use the constexpr version of add_with_carry.
+ LIBC_INLINE constexpr BigInt operator+(BigInt &&other) const {
+ // We use addition commutativity to reuse 'other' and prevent allocation.
+ other.add_overflow(*this); // Returned carry value is ignored.
+ return other;
+ }
+
+ LIBC_INLINE constexpr BigInt &operator+=(const BigInt &other) {
+ add_overflow(other); // Returned carry value is ignored.
+ return *this;
+ }
+
+ // Subtract 'rhs' to this number and store the result in this number.
+ // Returns the carry value produced by the subtraction operation.
+ LIBC_INLINE constexpr WordType sub_overflow(const BigInt &rhs) {
+ return multiword::sub_with_borrow(val, rhs.val);
+ }
+
+ LIBC_INLINE constexpr BigInt operator-(const BigInt &other) const {
+ BigInt result = *this;
+ result.sub_overflow(other); // Returned carry value is ignored.
+ return result;
+ }
+
+ LIBC_INLINE constexpr BigInt operator-(BigInt &&other) const {
+ BigInt result = *this;
+ result.sub_overflow(other); // Returned carry value is ignored.
+ return result;
+ }
+
+ LIBC_INLINE constexpr BigInt &operator-=(const BigInt &other) {
+ // TODO(lntue): Set overflow flag / errno when carry is true.
+ sub_overflow(other); // Returned carry value is ignored.
+ return *this;
+ }
+
+ // Multiply this number with x and store the result in this number.
+ LIBC_INLINE constexpr WordType mul(WordType x) {
+ return multiword::scalar_multiply_with_carry(val, x);
+ }
+
+ // Return the full product.
+ template <size_t OtherBits>
+ LIBC_INLINE constexpr auto
+ ful_mul(const BigInt<OtherBits, Signed, WordType> &other) const {
+ BigInt<Bits + OtherBits, Signed, WordType> result;
+ multiword::multiply_with_carry(result.val, val, other.val);
+ return result;
+ }
+
+ LIBC_INLINE constexpr BigInt operator*(const BigInt &other) const {
+ // Perform full mul and truncate.
+ return BigInt(ful_mul(other));
+ }
+
+ // Fast hi part of the full product. The normal product `operator*` returns
+ // `Bits` least significant bits of the full product, while this function will
+ // approximate `Bits` most significant bits of the full product with errors
+ // bounded by:
+ // 0 <= (a.full_mul(b) >> Bits) - a.quick_mul_hi(b)) <= WORD_COUNT - 1.
+ //
+ // An example usage of this is to quickly (but less accurately) compute the
+ // product of (normalized) mantissas of floating point numbers:
+ // (mant_1, mant_2) -> quick_mul_hi -> normalize leading bit
+ // is much more efficient than:
+ // (mant_1, mant_2) -> ful_mul -> normalize leading bit
+ // -> convert back to same Bits width by shifting/rounding,
+ // especially for higher precisions.
+ //
+ // Performance summary:
+ // Number of 64-bit x 64-bit -> 128-bit multiplications performed.
+ // Bits WORD_COUNT ful_mul quick_mul_hi Error bound
+ // 128 2 4 3 1
+ // 196 3 9 6 2
+ // 256 4 16 10 3
+ // 512 8 64 36 7
+ LIBC_INLINE constexpr BigInt quick_mul_hi(const BigInt &other) const {
+ BigInt result;
+ multiword::quick_mul_hi(result.val, val, other.val);
+ return result;
+ }
+
+ // BigInt(x).pow_n(n) computes x ^ n.
+ // Note 0 ^ 0 == 1.
+ LIBC_INLINE constexpr void pow_n(uint64_t power) {
+ static_assert(!Signed);
+ BigInt result = one();
+ BigInt cur_power = *this;
+ while (power > 0) {
+ if ((power % 2) > 0)
+ result *= cur_power;
+ power >>= 1;
+ cur_power *= cur_power;
+ }
+ *this = result;
+ }
+
+ // Performs inplace signed / unsigned division. Returns remainder if not
+ // dividing by zero.
+ // For signed numbers it behaves like C++ signed integer division.
+ // That is by truncating the fractionnal part
+ // https://stackoverflow.com/a/3602857
+ LIBC_INLINE constexpr cpp::optional<BigInt> div(const BigInt &divider) {
+ if (LIBC_UNLIKELY(divider.is_zero()))
+ return cpp::nullopt;
+ if (LIBC_UNLIKELY(divider == BigInt::one()))
+ return BigInt::zero();
+ Division result;
+ if constexpr (SIGNED)
+ result = divide_signed(*this, divider);
+ else
+ result = divide_unsigned(*this, divider);
+ *this = result.quotient;
+ return result.remainder;
+ }
+
+ // Efficiently perform BigInt / (x * 2^e), where x is a half-word-size
+ // unsigned integer, and return the remainder. The main idea is as follow:
+ // Let q = y / (x * 2^e) be the quotient, and
+ // r = y % (x * 2^e) be the remainder.
+ // First, notice that:
+ // r % (2^e) = y % (2^e),
+ // so we just need to focus on all the bits of y that is >= 2^e.
+ // To speed up the shift-and-add steps, we only use x as the divisor, and
+ // performing 32-bit shiftings instead of bit-by-bit shiftings.
+ // Since the remainder of each division step < x < 2^(WORD_SIZE / 2), the
+ // computation of each step is now properly contained within WordType.
+ // And finally we perform some extra alignment steps for the remaining bits.
+ LIBC_INLINE constexpr cpp::optional<BigInt>
+ div_uint_half_times_pow_2(multiword::half_width_t<WordType> x, size_t e) {
+ BigInt remainder;
+ if (x == 0)
+ return cpp::nullopt;
+ if (e >= Bits) {
+ remainder = *this;
+ *this = BigInt<Bits, false, WordType>();
+ return remainder;
+ }
+ BigInt quotient;
+ WordType x_word = static_cast<WordType>(x);
+ constexpr size_t LOG2_WORD_SIZE = cpp::bit_width(WORD_SIZE) - 1;
+ constexpr size_t HALF_WORD_SIZE = WORD_SIZE >> 1;
+ constexpr WordType HALF_MASK = ((WordType(1) << HALF_WORD_SIZE) - 1);
+ // lower = smallest multiple of WORD_SIZE that is >= e.
+ size_t lower = ((e >> LOG2_WORD_SIZE) + ((e & (WORD_SIZE - 1)) != 0))
+ << LOG2_WORD_SIZE;
+ // lower_pos is the index of the closest WORD_SIZE-bit chunk >= 2^e.
+ size_t lower_pos = lower / WORD_SIZE;
+ // Keep track of current remainder mod x * 2^(32*i)
+ WordType rem = 0;
+ // pos is the index of the current 64-bit chunk that we are processing.
+ size_t pos = WORD_COUNT;
+
+ // TODO: look into if constexpr(Bits > 256) skip leading zeroes.
+
+ for (size_t q_pos = WORD_COUNT - lower_pos; q_pos > 0; --q_pos) {
+ // q_pos is 1 + the index of the current WORD_SIZE-bit chunk of the
+ // quotient being processed. Performing the division / modulus with
+ // divisor:
+ // x * 2^(WORD_SIZE*q_pos - WORD_SIZE/2),
+ // i.e. using the upper (WORD_SIZE/2)-bit of the current WORD_SIZE-bit
+ // chunk.
+ rem <<= HALF_WORD_SIZE;
+ rem += val[--pos] >> HALF_WORD_SIZE;
+ WordType q_tmp = rem / x_word;
+ rem %= x_word;
+
+ // Performing the division / modulus with divisor:
+ // x * 2^(WORD_SIZE*(q_pos - 1)),
+ // i.e. using the lower (WORD_SIZE/2)-bit of the current WORD_SIZE-bit
+ // chunk.
+ rem <<= HALF_WORD_SIZE;
+ rem += val[pos] & HALF_MASK;
+ quotient.val[q_pos - 1] = (q_tmp << HALF_WORD_SIZE) + rem / x_word;
+ rem %= x_word;
+ }
+
+ // So far, what we have is:
+ // quotient = y / (x * 2^lower), and
+ // rem = (y % (x * 2^lower)) / 2^lower.
+ // If (lower > e), we will need to perform an extra adjustment of the
+ // quotient and remainder, namely:
+ // y / (x * 2^e) = [ y / (x * 2^lower) ] * 2^(lower - e) +
+ // + (rem * 2^(lower - e)) / x
+ // (y % (x * 2^e)) / 2^e = (rem * 2^(lower - e)) % x
+ size_t last_shift = lower - e;
+
+ if (last_shift > 0) {
+ // quotient * 2^(lower - e)
+ quotient <<= last_shift;
+ WordType q_tmp = 0;
+ WordType d = val[--pos];
+ if (last_shift >= HALF_WORD_SIZE) {
+ // The shifting (rem * 2^(lower - e)) might overflow WordTyoe, so we
+ // perform a HALF_WORD_SIZE-bit shift first.
+ rem <<= HALF_WORD_SIZE;
+ rem += d >> HALF_WORD_SIZE;
+ d &= HALF_MASK;
+ q_tmp = rem / x_word;
+ rem %= x_word;
+ last_shift -= HALF_WORD_SIZE;
+ } else {
+ // Only use the upper HALF_WORD_SIZE-bit of the current WORD_SIZE-bit
+ // chunk.
+ d >>= HALF_WORD_SIZE;
+ }
+
+ if (last_shift > 0) {
+ rem <<= HALF_WORD_SIZE;
+ rem += d;
+ q_tmp <<= last_shift;
+ x_word <<= HALF_WORD_SIZE - last_shift;
+ q_tmp += rem / x_word;
+ rem %= x_word;
+ }
+
+ quotient.val[0] += q_tmp;
+
+ if (lower - e <= HALF_WORD_SIZE) {
+ // The remainder rem * 2^(lower - e) might overflow to the higher
+ // WORD_SIZE-bit chunk.
+ if (pos < WORD_COUNT - 1) {
+ remainder[pos + 1] = rem >> HALF_WORD_SIZE;
+ }
+ remainder[pos] = (rem << HALF_WORD_SIZE) + (val[pos] & HALF_MASK);
+ } else {
+ remainder[pos] = rem;
+ }
+
+ } else {
+ remainder[pos] = rem;
+ }
+
+ // Set the remaining lower bits of the remainder.
+ for (; pos > 0; --pos) {
+ remainder[pos - 1] = val[pos - 1];
+ }
+
+ *this = quotient;
+ return remainder;
+ }
+
+ LIBC_INLINE constexpr BigInt operator/(const BigInt &other) const {
+ BigInt result(*this);
+ result.div(other);
+ return result;
+ }
+
+ LIBC_INLINE constexpr BigInt &operator/=(const BigInt &other) {
+ div(other);
+ return *this;
+ }
+
+ LIBC_INLINE constexpr BigInt operator%(const BigInt &other) const {
+ BigInt result(*this);
+ return *result.div(other);
+ }
+
+ LIBC_INLINE constexpr BigInt &operator*=(const BigInt &other) {
+ *this = *this * other;
+ return *this;
+ }
+
+ LIBC_INLINE constexpr BigInt &operator<<=(size_t s) {
+ val = multiword::shift<multiword::LEFT, SIGNED>(val, s);
+ return *this;
+ }
+
+ LIBC_INLINE constexpr BigInt operator<<(size_t s) const {
+ return BigInt(multiword::shift<multiword::LEFT, SIGNED>(val, s));
+ }
+
+ LIBC_INLINE constexpr BigInt &operator>>=(size_t s) {
+ val = multiword::shift<multiword::RIGHT, SIGNED>(val, s);
+ return *this;
+ }
+
+ LIBC_INLINE constexpr BigInt operator>>(size_t s) const {
+ return BigInt(multiword::shift<multiword::RIGHT, SIGNED>(val, s));
+ }
+
+#define DEFINE_BINOP(OP) \
+ LIBC_INLINE friend constexpr BigInt operator OP(const BigInt &lhs, \
+ const BigInt &rhs) { \
+ BigInt result; \
+ for (size_t i = 0; i < WORD_COUNT; ++i) \
+ result[i] = lhs[i] OP rhs[i]; \
+ return result; \
+ } \
+ LIBC_INLINE friend constexpr BigInt operator OP##=(BigInt &lhs, \
+ const BigInt &rhs) { \
+ for (size_t i = 0; i < WORD_COUNT; ++i) \
+ lhs[i] OP## = rhs[i]; \
+ return lhs; \
+ }
+
+ DEFINE_BINOP(&) // & and &=
+ DEFINE_BINOP(|) // | and |=
+ DEFINE_BINOP(^) // ^ and ^=
+#undef DEFINE_BINOP
+
+ LIBC_INLINE constexpr BigInt operator~() const {
+ BigInt result;
+ for (size_t i = 0; i < WORD_COUNT; ++i)
+ result[i] = ~val[i];
+ return result;
+ }
+
+ LIBC_INLINE constexpr BigInt operator-() const {
+ BigInt result(*this);
+ result.negate();
+ return result;
+ }
+
+ LIBC_INLINE friend constexpr bool operator==(const BigInt &lhs,
+ const BigInt &rhs) {
+ for (size_t i = 0; i < WORD_COUNT; ++i)
+ if (lhs.val[i] != rhs.val[i])
+ return false;
+ return true;
+ }
+
+ LIBC_INLINE friend constexpr bool operator!=(const BigInt &lhs,
+ const BigInt &rhs) {
+ return !(lhs == rhs);
+ }
+
+ LIBC_INLINE friend constexpr bool operator>(const BigInt &lhs,
+ const BigInt &rhs) {
+ return cmp(lhs, rhs) > 0;
+ }
+ LIBC_INLINE friend constexpr bool operator>=(const BigInt &lhs,
+ const BigInt &rhs) {
+ return cmp(lhs, rhs) >= 0;
+ }
+ LIBC_INLINE friend constexpr bool operator<(const BigInt &lhs,
+ const BigInt &rhs) {
+ return cmp(lhs, rhs) < 0;
+ }
+ LIBC_INLINE friend constexpr bool operator<=(const BigInt &lhs,
+ const BigInt &rhs) {
+ return cmp(lhs, rhs) <= 0;
+ }
+
+ LIBC_INLINE constexpr BigInt &operator++() {
+ increment();
+ return *this;
+ }
+
+ LIBC_INLINE constexpr BigInt operator++(int) {
+ BigInt oldval(*this);
+ increment();
+ return oldval;
+ }
+
+ LIBC_INLINE constexpr BigInt &operator--() {
+ decrement();
+ return *this;
+ }
+
+ LIBC_INLINE constexpr BigInt operator--(int) {
+ BigInt oldval(*this);
+ decrement();
+ return oldval;
+ }
+
+ // Return the i-th word of the number.
+ LIBC_INLINE constexpr const WordType &operator[](size_t i) const {
+ return val[i];
+ }
+
+ // Return the i-th word of the number.
+ LIBC_INLINE constexpr WordType &operator[](size_t i) { return val[i]; }
+
+private:
+ LIBC_INLINE friend constexpr int cmp(const BigInt &lhs, const BigInt &rhs) {
+ constexpr auto compare = [](WordType a, WordType b) {
+ return a == b ? 0 : a > b ? 1 : -1;
+ };
+ if constexpr (Signed) {
+ const bool lhs_is_neg = lhs.is_neg();
+ const bool rhs_is_neg = rhs.is_neg();
+ if (lhs_is_neg != rhs_is_neg)
+ return rhs_is_neg ? 1 : -1;
+ }
+ for (size_t i = WORD_COUNT; i-- > 0;)
+ if (auto cmp = compare(lhs[i], rhs[i]); cmp != 0)
+ return cmp;
+ return 0;
+ }
+
+ LIBC_INLINE constexpr void bitwise_not() {
+ for (auto &part : val)
+ part = ~part;
+ }
+
+ LIBC_INLINE constexpr void negate() {
+ bitwise_not();
+ increment();
+ }
+
+ LIBC_INLINE constexpr void increment() {
+ multiword::add_with_carry(val, cpp::array<WordType, 1>{1});
+ }
+
+ LIBC_INLINE constexpr void decrement() {
+ multiword::add_with_carry(val, cpp::array<WordType, 1>{1});
+ }
+
+ LIBC_INLINE constexpr void extend(size_t index, bool is_neg) {
+ const WordType value = is_neg ? cpp::numeric_limits<WordType>::max()
+ : cpp::numeric_limits<WordType>::min();
+ for (size_t i = index; i < WORD_COUNT; ++i)
+ val[i] = value;
+ }
+
+ LIBC_INLINE constexpr bool get_msb() const {
+ return val.back() >> (WORD_SIZE - 1);
+ }
+
+ LIBC_INLINE constexpr void set_msb() {
+ val.back() |= mask_leading_ones<WordType, 1>();
+ }
+
+ LIBC_INLINE constexpr void clear_msb() {
+ val.back() &= mask_trailing_ones<WordType, WORD_SIZE - 1>();
+ }
+
+ LIBC_INLINE constexpr void set_bit(size_t i) {
+ const size_t word_index = i / WORD_SIZE;
+ val[word_index] |= WordType(1) << (i % WORD_SIZE);
+ }
+
+ LIBC_INLINE constexpr static Division divide_unsigned(const BigInt &dividend,
+ const BigInt &divider) {
+ BigInt remainder = dividend;
+ BigInt quotient;
+ if (remainder >= divider) {
+ BigInt subtractor = divider;
+ int cur_bit = multiword::countl_zero(subtractor.val) -
+ multiword::countl_zero(remainder.val);
+ subtractor <<= cur_bit;
+ for (; cur_bit >= 0 && remainder > 0; --cur_bit, subtractor >>= 1) {
+ if (remainder < subtractor)
+ continue;
+ remainder -= subtractor;
+ quotient.set_bit(cur_bit);
+ }
+ }
+ return Division{quotient, remainder};
+ }
+
+ LIBC_INLINE constexpr static Division divide_signed(const BigInt &dividend,
+ const BigInt &divider) {
+ // Special case because it is not possible to negate the min value of a
+ // signed integer.
+ if (dividend == min() && divider == min())
+ return Division{one(), zero()};
+ // 1. Convert the dividend and divisor to unsigned representation.
+ unsigned_type udividend(dividend);
+ unsigned_type udivider(divider);
+ // 2. Negate the dividend if it's negative, and similarly for the divisor.
+ const bool dividend_is_neg = dividend.is_neg();
+ const bool divider_is_neg = divider.is_neg();
+ if (dividend_is_neg)
+ udividend.negate();
+ if (divider_is_neg)
+ udivider.negate();
+ // 3. Use unsigned multiword division algorithm.
+ const auto unsigned_result = divide_unsigned(udividend, udivider);
+ // 4. Convert the quotient and remainder to signed representation.
+ Division result;
+ result.quotient = signed_type(unsigned_result.quotient);
+ result.remainder = signed_type(unsigned_result.remainder);
+ // 5. Negate the quotient if the dividend and divisor had opposite signs.
+ if (dividend_is_neg != divider_is_neg)
+ result.quotient.negate();
+ // 6. Negate the remainder if the dividend was negative.
+ if (dividend_is_neg)
+ result.remainder.negate();
+ return result;
+ }
+
+ friend signed_type;
+ friend unsigned_type;
+};
+
+namespace internal {
+// We default BigInt's WordType to 'uint64_t' or 'uint32_t' depending on type
+// availability.
+template <size_t Bits>
+struct WordTypeSelector : cpp::type_identity<
+#ifdef LIBC_TYPES_HAS_INT64
+ uint64_t
+#else
+ uint32_t
+#endif // LIBC_TYPES_HAS_INT64
+ > {
+};
+// Except if we request 32 bits explicitly.
+template <> struct WordTypeSelector<32> : cpp::type_identity<uint32_t> {};
+template <size_t Bits>
+using WordTypeSelectorT = typename WordTypeSelector<Bits>::type;
+} // namespace internal
+
+template <size_t Bits>
+using UInt = BigInt<Bits, false, internal::WordTypeSelectorT<Bits>>;
+
+template <size_t Bits>
+using Int = BigInt<Bits, true, internal::WordTypeSelectorT<Bits>>;
+
+// Provides limits of U/Int<128>.
+template <> class cpp::numeric_limits<UInt<128>> {
+public:
+ LIBC_INLINE static constexpr UInt<128> max() { return UInt<128>::max(); }
+ LIBC_INLINE static constexpr UInt<128> min() { return UInt<128>::min(); }
+ // Meant to match std::numeric_limits interface.
+ // NOLINTNEXTLINE(readability-identifier-naming)
+ LIBC_INLINE_VAR static constexpr int digits = 128;
+};
+
+template <> class cpp::numeric_limits<Int<128>> {
+public:
+ LIBC_INLINE static constexpr Int<128> max() { return Int<128>::max(); }
+ LIBC_INLINE static constexpr Int<128> min() { return Int<128>::min(); }
+ // Meant to match std::numeric_limits interface.
+ // NOLINTNEXTLINE(readability-identifier-naming)
+ LIBC_INLINE_VAR static constexpr int digits = 128;
+};
+
+// type traits to determine whether a T is a BigInt.
+template <typename T> struct is_big_int : cpp::false_type {};
+
+template <size_t Bits, bool Signed, typename T>
+struct is_big_int<BigInt<Bits, Signed, T>> : cpp::true_type {};
+
+template <class T>
+LIBC_INLINE_VAR constexpr bool is_big_int_v = is_big_int<T>::value;
+
+// extensions of type traits to include BigInt
+
+// is_integral_or_big_int
+template <typename T>
+struct is_integral_or_big_int
+ : cpp::bool_constant<(cpp::is_integral_v<T> || is_big_int_v<T>)> {};
+
+template <typename T>
+LIBC_INLINE_VAR constexpr bool is_integral_or_big_int_v =
+ is_integral_or_big_int<T>::value;
+
+// make_big_int_unsigned
+template <typename T> struct make_big_int_unsigned;
+
+template <size_t Bits, bool Signed, typename T>
+struct make_big_int_unsigned<BigInt<Bits, Signed, T>>
+ : cpp::type_identity<BigInt<Bits, false, T>> {};
+
+template <typename T>
+using make_big_int_unsigned_t = typename make_big_int_unsigned<T>::type;
+
+// make_big_int_signed
+template <typename T> struct make_big_int_signed;
+
+template <size_t Bits, bool Signed, typename T>
+struct make_big_int_signed<BigInt<Bits, Signed, T>>
+ : cpp::type_identity<BigInt<Bits, true, T>> {};
+
+template <typename T>
+using make_big_int_signed_t = typename make_big_int_signed<T>::type;
+
+// make_integral_or_big_int_unsigned
+template <typename T, class = void> struct make_integral_or_big_int_unsigned;
+
+template <typename T>
+struct make_integral_or_big_int_unsigned<
+ T, cpp::enable_if_t<cpp::is_integral_v<T>>> : cpp::make_unsigned<T> {};
+
+template <typename T>
+struct make_integral_or_big_int_unsigned<T, cpp::enable_if_t<is_big_int_v<T>>>
+ : make_big_int_unsigned<T> {};
+
+template <typename T>
+using make_integral_or_big_int_unsigned_t =
+ typename make_integral_or_big_int_unsigned<T>::type;
+
+// make_integral_or_big_int_signed
+template <typename T, class = void> struct make_integral_or_big_int_signed;
+
+template <typename T>
+struct make_integral_or_big_int_signed<T,
+ cpp::enable_if_t<cpp::is_integral_v<T>>>
+ : cpp::make_signed<T> {};
+
+template <typename T>
+struct make_integral_or_big_int_signed<T, cpp::enable_if_t<is_big_int_v<T>>>
+ : make_big_int_signed<T> {};
+
+template <typename T>
+using make_integral_or_big_int_signed_t =
+ typename make_integral_or_big_int_signed<T>::type;
+
+namespace cpp {
+
+// Specialization of cpp::bit_cast ('bit.h') from T to BigInt.
+template <typename To, typename From>
+LIBC_INLINE constexpr cpp::enable_if_t<
+ (sizeof(To) == sizeof(From)) && cpp::is_trivially_copyable<To>::value &&
+ cpp::is_trivially_copyable<From>::value && is_big_int<To>::value,
+ To>
+bit_cast(const From &from) {
+ To out;
+ using Storage = decltype(out.val);
+ out.val = cpp::bit_cast<Storage>(from);
+ return out;
+}
+
+// Specialization of cpp::bit_cast ('bit.h') from BigInt to T.
+template <typename To, size_t Bits>
+LIBC_INLINE constexpr cpp::enable_if_t<
+ sizeof(To) == sizeof(UInt<Bits>) &&
+ cpp::is_trivially_constructible<To>::value &&
+ cpp::is_trivially_copyable<To>::value &&
+ cpp::is_trivially_copyable<UInt<Bits>>::value,
+ To>
+bit_cast(const UInt<Bits> &from) {
+ return cpp::bit_cast<To>(from.val);
+}
+
+// Specialization of cpp::popcount ('bit.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+popcount(T value) {
+ int bits = 0;
+ for (auto word : value.val)
+ if (word)
+ bits += popcount(word);
+ return bits;
+}
+
+// Specialization of cpp::has_single_bit ('bit.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, bool>
+has_single_bit(T value) {
+ int bits = 0;
+ for (auto word : value.val) {
+ if (word == 0)
+ continue;
+ bits += popcount(word);
+ if (bits > 1)
+ return false;
+ }
+ return bits == 1;
+}
+
+// Specialization of cpp::countr_zero ('bit.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+countr_zero(const T &value) {
+ return multiword::countr_zero(value.val);
+}
+
+// Specialization of cpp::countl_zero ('bit.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+countl_zero(const T &value) {
+ return multiword::countl_zero(value.val);
+}
+
+// Specialization of cpp::countl_one ('bit.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+countl_one(T value) {
+ return multiword::countl_one(value.val);
+}
+
+// Specialization of cpp::countr_one ('bit.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+countr_one(T value) {
+ return multiword::countr_one(value.val);
+}
+
+// Specialization of cpp::bit_width ('bit.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+bit_width(T value) {
+ return cpp::numeric_limits<T>::digits - cpp::countl_zero(value);
+}
+
+// Forward-declare rotr so that rotl can use it.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
+rotr(T value, int rotate);
+
+// Specialization of cpp::rotl ('bit.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
+rotl(T value, int rotate) {
+ constexpr unsigned N = cpp::numeric_limits<T>::digits;
+ rotate = rotate % N;
+ if (!rotate)
+ return value;
+ if (rotate < 0)
+ return cpp::rotr<T>(value, -rotate);
+ return (value << rotate) | (value >> (N - rotate));
+}
+
+// Specialization of cpp::rotr ('bit.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
+rotr(T value, int rotate) {
+ constexpr unsigned N = cpp::numeric_limits<T>::digits;
+ rotate = rotate % N;
+ if (!rotate)
+ return value;
+ if (rotate < 0)
+ return cpp::rotl<T>(value, -rotate);
+ return (value >> rotate) | (value << (N - rotate));
+}
+
+} // namespace cpp
+
+// Specialization of mask_trailing_ones ('math_extras.h') for BigInt.
+template <typename T, size_t count>
+LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
+mask_trailing_ones() {
+ static_assert(!T::SIGNED && count <= T::BITS);
+ if (count == T::BITS)
+ return T::all_ones();
+ constexpr size_t QUOTIENT = count / T::WORD_SIZE;
+ constexpr size_t REMAINDER = count % T::WORD_SIZE;
+ T out; // zero initialized
+ for (size_t i = 0; i <= QUOTIENT; ++i)
+ out[i] = i < QUOTIENT
+ ? -1
+ : mask_trailing_ones<typename T::word_type, REMAINDER>();
+ return out;
+}
+
+// Specialization of mask_leading_ones ('math_extras.h') for BigInt.
+template <typename T, size_t count>
+LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T> mask_leading_ones() {
+ static_assert(!T::SIGNED && count <= T::BITS);
+ if (count == T::BITS)
+ return T::all_ones();
+ constexpr size_t QUOTIENT = (T::BITS - count - 1U) / T::WORD_SIZE;
+ constexpr size_t REMAINDER = count % T::WORD_SIZE;
+ T out; // zero initialized
+ for (size_t i = QUOTIENT; i < T::WORD_COUNT; ++i)
+ out[i] = i > QUOTIENT
+ ? -1
+ : mask_leading_ones<typename T::word_type, REMAINDER>();
+ return out;
+}
+
+// Specialization of mask_trailing_zeros ('math_extras.h') for BigInt.
+template <typename T, size_t count>
+LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
+mask_trailing_zeros() {
+ return mask_leading_ones<T, T::BITS - count>();
+}
+
+// Specialization of mask_leading_zeros ('math_extras.h') for BigInt.
+template <typename T, size_t count>
+LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, T>
+mask_leading_zeros() {
+ return mask_trailing_ones<T, T::BITS - count>();
+}
+
+// Specialization of count_zeros ('math_extras.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+count_zeros(T value) {
+ return cpp::popcount(~value);
+}
+
+// Specialization of first_leading_zero ('math_extras.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+first_leading_zero(T value) {
+ return value == cpp::numeric_limits<T>::max() ? 0
+ : cpp::countl_one(value) + 1;
+}
+
+// Specialization of first_leading_one ('math_extras.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+first_leading_one(T value) {
+ return first_leading_zero(~value);
+}
+
+// Specialization of first_trailing_zero ('math_extras.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+first_trailing_zero(T value) {
+ return value == cpp::numeric_limits<T>::max() ? 0
+ : cpp::countr_zero(~value) + 1;
+}
+
+// Specialization of first_trailing_one ('math_extras.h') for BigInt.
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<is_big_int_v<T>, int>
+first_trailing_one(T value) {
+ return value == cpp::numeric_limits<T>::max() ? 0
+ : cpp::countr_zero(value) + 1;
+}
+
+} // namespace LIBC_NAMESPACE
+
+#endif // LLVM_LIBC_SRC___SUPPORT_UINT_H
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