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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/types.h" // LIBC_TYPES_HAS_INT128, LIBC_TYPES_HAS_INT64
#include "src/__support/math_extras.h" // SumCarry, DiffBorrow
#include "src/__support/number_pair.h"
#include <stddef.h> // For size_t
#include <stdint.h>
namespace LIBC_NAMESPACE {
namespace internal {
template <typename T> struct half_width;
template <> struct half_width<uint64_t> : cpp::type_identity<uint32_t> {};
template <> struct half_width<uint32_t> : cpp::type_identity<uint16_t> {};
template <> struct half_width<uint16_t> : cpp::type_identity<uint8_t> {};
#ifdef LIBC_TYPES_HAS_INT128
template <> struct half_width<__uint128_t> : cpp::type_identity<uint64_t> {};
#endif // LIBC_TYPES_HAS_INT128
template <typename T> using half_width_t = typename half_width<T>::type;
template <typename T> constexpr NumberPair<T> full_mul(T a, T b) {
NumberPair<T> pa = split(a);
NumberPair<T> pb = split(b);
NumberPair<T> prod;
prod.lo = pa.lo * pb.lo; // exact
prod.hi = pa.hi * pb.hi; // exact
NumberPair<T> lo_hi = split(pa.lo * pb.hi); // exact
NumberPair<T> hi_lo = split(pa.hi * pb.lo); // exact
constexpr size_t HALF_BIT_WIDTH = sizeof(T) * CHAR_BIT / 2;
auto r1 = add_with_carry(prod.lo, lo_hi.lo << HALF_BIT_WIDTH, T(0));
prod.lo = r1.sum;
prod.hi = add_with_carry(prod.hi, lo_hi.hi, r1.carry).sum;
auto r2 = add_with_carry(prod.lo, hi_lo.lo << HALF_BIT_WIDTH, T(0));
prod.lo = r2.sum;
prod.hi = add_with_carry(prod.hi, hi_lo.hi, r2.carry).sum;
return prod;
}
template <>
LIBC_INLINE constexpr NumberPair<uint32_t> full_mul<uint32_t>(uint32_t a,
uint32_t b) {
uint64_t prod = uint64_t(a) * uint64_t(b);
NumberPair<uint32_t> result;
result.lo = uint32_t(prod);
result.hi = uint32_t(prod >> 32);
return result;
}
#ifdef LIBC_TYPES_HAS_INT128
template <>
LIBC_INLINE constexpr NumberPair<uint64_t> full_mul<uint64_t>(uint64_t a,
uint64_t b) {
__uint128_t prod = __uint128_t(a) * __uint128_t(b);
NumberPair<uint64_t> result;
result.lo = uint64_t(prod);
result.hi = uint64_t(prod >> 64);
return result;
}
#endif // LIBC_TYPES_HAS_INT128
} // namespace internal
template <size_t Bits, bool Signed, typename WordType = uint64_t>
struct BigInt {
static_assert(cpp::is_integral_v<WordType> && cpp::is_unsigned_v<WordType>,
"WordType must be unsigned integer.");
using word_type = WordType;
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;
using unsigned_type = BigInt<BITS, false, word_type>;
using signed_type = BigInt<BITS, true, word_type>;
cpp::array<WordType, WORD_COUNT> val{};
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) {
for (size_t i = 0; i < WORD_COUNT; ++i)
val[i] = other[i];
} else {
size_t i = 0;
for (; i < OtherBits / WORD_SIZE; ++i)
val[i] = other[i];
WordType sign = 0;
if constexpr (Signed && OtherSigned) {
sign = static_cast<WordType>(
-static_cast<cpp::make_signed_t<WordType>>(other.is_neg()));
}
for (; i < WORD_COUNT; ++i)
val[i] = sign;
}
}
// Construct a BigInt from a C array.
template <size_t N, cpp::enable_if_t<N <= WORD_COUNT, int> = 0>
LIBC_INLINE constexpr BigInt(const WordType (&nums)[N]) {
size_t min_wordcount = N < WORD_COUNT ? N : WORD_COUNT;
size_t i = 0;
for (; i < min_wordcount; ++i)
val[i] = nums[i];
// If nums doesn't completely fill val, then fill the rest with zeroes.
for (; i < WORD_COUNT; ++i)
val[i] = 0;
}
// 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) {
val[0] = static_cast<WordType>(v);
if constexpr (WORD_COUNT == 1)
return;
if constexpr (Bits < sizeof(T) * CHAR_BIT) {
for (int i = 1; i < WORD_COUNT; ++i) {
v >>= WORD_SIZE;
val[i] = static_cast<WordType>(v);
}
return;
}
size_t i = 1;
if constexpr (WORD_SIZE < sizeof(T) * CHAR_BIT)
for (; i < sizeof(T) * CHAR_BIT / WORD_SIZE; ++i) {
v >>= WORD_SIZE;
val[i] = static_cast<WordType>(v);
}
WordType sign = (Signed && (v < 0)) ? ~WordType(0) : WordType(0);
for (; i < WORD_COUNT; ++i) {
val[i] = sign;
}
}
LIBC_INLINE constexpr explicit BigInt(
const cpp::array<WordType, WORD_COUNT> &words) {
for (size_t i = 0; i < WORD_COUNT; ++i)
val[i] = words[i];
}
// TODO: Reuse the Sign type.
LIBC_INLINE constexpr bool is_neg() const {
return val.back() >> (WORD_SIZE - 1);
}
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 {
T lo = static_cast<T>(val[0]);
constexpr size_t T_BITS = sizeof(T) * CHAR_BIT;
if constexpr (T_BITS <= WORD_SIZE)
return lo;
constexpr size_t MAX_COUNT =
T_BITS > Bits ? WORD_COUNT : T_BITS / WORD_SIZE;
for (size_t i = 1; i < MAX_COUNT; ++i)
lo += static_cast<T>(val[i]) << (WORD_SIZE * i);
if constexpr (Signed && (T_BITS > 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 BigInt &operator=(const BigInt &other) = default;
LIBC_INLINE constexpr bool is_zero() const {
for (size_t i = 0; i < WORD_COUNT; ++i) {
if (val[i] != 0)
return false;
}
return true;
}
// Add x to this number and store the result in this number.
// Returns the carry value produced by the addition operation.
LIBC_INLINE constexpr WordType add(const BigInt &x) {
SumCarry<WordType> s{0, 0};
for (size_t i = 0; i < WORD_COUNT; ++i) {
s = add_with_carry(val[i], x.val[i], s.carry);
val[i] = s.sum;
}
return s.carry;
}
LIBC_INLINE constexpr BigInt operator+(const BigInt &other) const {
BigInt result;
SumCarry<WordType> s{0, 0};
for (size_t i = 0; i < WORD_COUNT; ++i) {
s = add_with_carry(val[i], other.val[i], s.carry);
result.val[i] = s.sum;
}
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 {
BigInt result;
SumCarry<WordType> s{0, 0};
for (size_t i = 0; i < WORD_COUNT; ++i) {
s = add_with_carry(val[i], other.val[i], s.carry);
result.val[i] = s.sum;
}
return result;
}
LIBC_INLINE constexpr BigInt &operator+=(const BigInt &other) {
add(other); // Returned carry value is ignored.
return *this;
}
// Subtract x to this number and store the result in this number.
// Returns the carry value produced by the subtraction operation.
LIBC_INLINE constexpr WordType sub(const BigInt &x) {
DiffBorrow<WordType> d{0, 0};
for (size_t i = 0; i < WORD_COUNT; ++i) {
d = sub_with_borrow(val[i], x.val[i], d.borrow);
val[i] = d.diff;
}
return d.borrow;
}
LIBC_INLINE constexpr BigInt operator-(const BigInt &other) const {
BigInt result;
DiffBorrow<WordType> d{0, 0};
for (size_t i = 0; i < WORD_COUNT; ++i) {
d = sub_with_borrow(val[i], other.val[i], d.borrow);
result.val[i] = d.diff;
}
return result;
}
LIBC_INLINE constexpr BigInt operator-(BigInt &&other) const {
BigInt result;
DiffBorrow<WordType> d{0, 0};
for (size_t i = 0; i < WORD_COUNT; ++i) {
d = sub_with_borrow(val[i], other.val[i], d.borrow);
result.val[i] = d.diff;
}
return result;
}
LIBC_INLINE constexpr BigInt &operator-=(const BigInt &other) {
// TODO(lntue): Set overflow flag / errno when carry is true.
sub(other);
return *this;
}
// Multiply this number with x and store the result in this number. It is
// implemented using the long multiplication algorithm by splitting the
// 64-bit words of this number and |x| in to 32-bit halves but peforming
// the operations using 64-bit numbers. This ensures that we don't lose the
// carry bits.
// Returns the carry value produced by the multiplication operation.
LIBC_INLINE constexpr WordType mul(WordType x) {
BigInt<2 * WORD_SIZE, Signed, WordType> partial_sum(0);
for (size_t i = 0; i < WORD_COUNT; ++i) {
NumberPair<WordType> prod = internal::full_mul(val[i], x);
BigInt<2 * WORD_SIZE, Signed, WordType> tmp({prod.lo, prod.hi});
const WordType carry = partial_sum.add(tmp);
val[i] = partial_sum.val[0];
partial_sum.val[0] = partial_sum.val[1];
partial_sum.val[1] = carry;
}
return partial_sum.val[1];
}
LIBC_INLINE constexpr BigInt operator*(const BigInt &other) const {
if constexpr (Signed) {
BigInt<Bits, false, WordType> a(*this);
BigInt<Bits, false, WordType> b(other);
const bool a_neg = a.is_neg();
const bool b_neg = b.is_neg();
if (a_neg)
a = -a;
if (b_neg)
b = -b;
BigInt<Bits, false, WordType> prod = a * b;
if (a_neg != b_neg)
prod = -prod;
return static_cast<BigInt<Bits, true, WordType>>(prod);
} else {
if constexpr (WORD_COUNT == 1) {
return {val[0] * other.val[0]};
} else {
BigInt result(0);
BigInt<2 * WORD_SIZE, Signed, WordType> partial_sum(0);
WordType carry = 0;
for (size_t i = 0; i < WORD_COUNT; ++i) {
for (size_t j = 0; j <= i; j++) {
NumberPair<WordType> prod =
internal::full_mul(val[j], other.val[i - j]);
BigInt<2 * WORD_SIZE, Signed, WordType> tmp({prod.lo, prod.hi});
carry += partial_sum.add(tmp);
}
result.val[i] = partial_sum.val[0];
partial_sum.val[0] = partial_sum.val[1];
partial_sum.val[1] = carry;
carry = 0;
}
return result;
}
}
}
// Return the full product, only unsigned for now.
template <size_t OtherBits>
LIBC_INLINE constexpr BigInt<Bits + OtherBits, Signed, WordType>
ful_mul(const BigInt<OtherBits, Signed, WordType> &other) const {
BigInt<Bits + OtherBits, Signed, WordType> result(0);
BigInt<2 * WORD_SIZE, Signed, WordType> partial_sum(0);
WordType carry = 0;
constexpr size_t OTHER_WORDCOUNT =
BigInt<OtherBits, Signed, WordType>::WORD_COUNT;
for (size_t i = 0; i <= WORD_COUNT + OTHER_WORDCOUNT - 2; ++i) {
const size_t lower_idx =
i < OTHER_WORDCOUNT ? 0 : i - OTHER_WORDCOUNT + 1;
const size_t upper_idx = i < WORD_COUNT ? i : WORD_COUNT - 1;
for (size_t j = lower_idx; j <= upper_idx; ++j) {
NumberPair<WordType> prod =
internal::full_mul(val[j], other.val[i - j]);
BigInt<2 * WORD_SIZE, Signed, WordType> tmp({prod.lo, prod.hi});
carry += partial_sum.add(tmp);
}
result.val[i] = partial_sum.val[0];
partial_sum.val[0] = partial_sum.val[1];
partial_sum.val[1] = carry;
carry = 0;
}
result.val[WORD_COUNT + OTHER_WORDCOUNT - 1] = partial_sum.val[0];
return result;
}
// 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(0);
BigInt<2 * WORD_SIZE, Signed, WordType> partial_sum(0);
WordType carry = 0;
// First round of accumulation for those at WORD_COUNT - 1 in the full
// product.
for (size_t i = 0; i < WORD_COUNT; ++i) {
NumberPair<WordType> prod =
internal::full_mul(val[i], other.val[WORD_COUNT - 1 - i]);
BigInt<2 * WORD_SIZE, Signed, WordType> tmp({prod.lo, prod.hi});
carry += partial_sum.add(tmp);
}
for (size_t i = WORD_COUNT; i < 2 * WORD_COUNT - 1; ++i) {
partial_sum.val[0] = partial_sum.val[1];
partial_sum.val[1] = carry;
carry = 0;
for (size_t j = i - WORD_COUNT + 1; j < WORD_COUNT; ++j) {
NumberPair<WordType> prod =
internal::full_mul(val[j], other.val[i - j]);
BigInt<2 * WORD_SIZE, Signed, WordType> tmp({prod.lo, prod.hi});
carry += partial_sum.add(tmp);
}
result.val[i - WORD_COUNT] = partial_sum.val[0];
}
result.val[WORD_COUNT - 1] = partial_sum.val[1];
return result;
}
// pow takes a power and sets this to its starting value to that power. Zero
// to the zeroth power returns 1.
LIBC_INLINE constexpr void pow_n(uint64_t power) {
BigInt result = 1;
BigInt cur_power = *this;
while (power > 0) {
if ((power % 2) > 0)
result *= cur_power;
power >>= 1;
cur_power *= cur_power;
}
*this = result;
}
// TODO: Make division work correctly for signed integers.
// div takes another BigInt of the same size and divides this by it. The value
// of this will be set to the quotient, and the return value is the remainder.
LIBC_INLINE constexpr cpp::optional<BigInt> div(const BigInt &other) {
BigInt remainder(0);
if (*this < other) {
remainder = *this;
*this = BigInt(0);
return remainder;
}
if (other == 1) {
return remainder;
}
if (other == 0) {
return cpp::nullopt;
}
BigInt quotient(0);
BigInt subtractor = other;
int cur_bit = static_cast<int>(subtractor.clz() - this->clz());
subtractor.shift_left(cur_bit);
for (; cur_bit >= 0 && *this > 0; --cur_bit, subtractor.shift_right(1)) {
if (*this >= subtractor) {
this->sub(subtractor);
quotient = quotient | (BigInt(1) << cur_bit);
}
}
remainder = *this;
*this = quotient;
return 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(internal::half_width_t<WordType> x, size_t e) {
BigInt remainder(0);
if (x == 0) {
return cpp::nullopt;
}
if (e >= Bits) {
remainder = *this;
*this = BigInt<Bits, false, WordType>(0);
return remainder;
}
BigInt quotient(0);
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;
}
// TODO: remove and use cpp::countl_zero below.
[[nodiscard]] LIBC_INLINE constexpr int clz() const {
constexpr int word_digits = cpp::numeric_limits<word_type>::digits;
int leading_zeroes = 0;
for (auto i = val.size(); i > 0;) {
--i;
const int zeroes = cpp::countl_zero(val[i]);
leading_zeroes += zeroes;
if (zeroes != word_digits)
break;
}
return leading_zeroes;
}
// TODO: remove and use cpp::countr_zero below.
[[nodiscard]] LIBC_INLINE constexpr int ctz() const {
constexpr int word_digits = cpp::numeric_limits<word_type>::digits;
int trailing_zeroes = 0;
for (auto word : val) {
const int zeroes = cpp::countr_zero(word);
trailing_zeroes += zeroes;
if (zeroes != word_digits)
break;
}
return trailing_zeroes;
}
LIBC_INLINE constexpr void shift_left(size_t s) {
if constexpr (Bits == WORD_SIZE) {
// Use native types if possible.
if (s >= WORD_SIZE) {
val[0] = 0;
return;
}
val[0] <<= s;
return;
}
if constexpr ((Bits == 64) && (WORD_SIZE == 32)) {
// Use builtin 64 bits for 32-bit base type if available;
if (s >= 64) {
val[0] = 0;
val[1] = 0;
return;
}
uint64_t tmp = uint64__t(val[0]) + (uint64_t(val[1]) << 62);
tmp <<= s;
val[0] = uint32_t(tmp);
val[1] = uint32_t(tmp >> 32);
return;
}
#ifdef LIBC_TYPES_HAS_INT128
if constexpr ((Bits == 128) && (WORD_SIZE == 64)) {
// Use builtin 128 bits if available;
if (s >= 128) {
val[0] = 0;
val[1] = 0;
return;
}
__uint128_t tmp = __uint128_t(val[0]) + (__uint128_t(val[1]) << 64);
tmp <<= s;
val[0] = uint64_t(tmp);
val[1] = uint64_t(tmp >> 64);
return;
}
#endif // LIBC_TYPES_HAS_INT128
if (LIBC_UNLIKELY(s == 0))
return;
const size_t drop = s / WORD_SIZE; // Number of words to drop
const size_t shift = s % WORD_SIZE; // Bits to shift in the remaining words.
size_t i = WORD_COUNT;
if (drop < WORD_COUNT) {
i = WORD_COUNT - 1;
if (shift > 0) {
for (size_t j = WORD_COUNT - 1 - drop; j > 0; --i, --j) {
val[i] = (val[j] << shift) | (val[j - 1] >> (WORD_SIZE - shift));
}
val[i] = val[0] << shift;
} else {
for (size_t j = WORD_COUNT - 1 - drop; j > 0; --i, --j) {
val[i] = val[j];
}
val[i] = val[0];
}
}
for (size_t j = 0; j < i; ++j) {
val[j] = 0;
}
}
LIBC_INLINE constexpr BigInt operator<<(size_t s) const {
BigInt result(*this);
result.shift_left(s);
return result;
}
LIBC_INLINE constexpr BigInt &operator<<=(size_t s) {
shift_left(s);
return *this;
}
LIBC_INLINE constexpr void shift_right(size_t s) {
if constexpr ((Bits == 64) && (WORD_SIZE == 32)) {
// Use builtin 64 bits if available;
if (s >= 64) {
val[0] = 0;
val[1] = 0;
return;
}
uint64_t tmp = uint64_t(val[0]) + (uint64_t(val[1]) << 32);
if constexpr (Signed) {
tmp = static_cast<uint64_t>(static_cast<int64_t>(tmp) >> s);
} else {
tmp >>= s;
}
val[0] = uint32_t(tmp);
val[1] = uint32_t(tmp >> 32);
return;
}
#ifdef LIBC_TYPES_HAS_INT128
if constexpr ((Bits == 128) && (WORD_SIZE == 64)) {
// Use builtin 128 bits if available;
if (s >= 128) {
val[0] = 0;
val[1] = 0;
return;
}
__uint128_t tmp = __uint128_t(val[0]) + (__uint128_t(val[1]) << 64);
if constexpr (Signed) {
tmp = static_cast<__uint128_t>(static_cast<__int128_t>(tmp) >> s);
} else {
tmp >>= s;
}
val[0] = uint64_t(tmp);
val[1] = uint64_t(tmp >> 64);
return;
}
#endif // LIBC_TYPES_HAS_INT128
if (LIBC_UNLIKELY(s == 0))
return;
const size_t drop = s / WORD_SIZE; // Number of words to drop
const size_t shift = s % WORD_SIZE; // Bit shift in the remaining words.
size_t i = 0;
WordType sign = Signed ? is_neg() : 0;
if (drop < WORD_COUNT) {
if (shift > 0) {
for (size_t j = drop; j < WORD_COUNT - 1; ++i, ++j) {
val[i] = (val[j] >> shift) | (val[j + 1] << (WORD_SIZE - shift));
}
if constexpr (Signed) {
val[i] = static_cast<WordType>(
static_cast<cpp::make_signed_t<WordType>>(val[WORD_COUNT - 1]) >>
shift);
} else {
val[i] = val[WORD_COUNT - 1] >> shift;
}
++i;
} else {
for (size_t j = drop; j < WORD_COUNT; ++i, ++j) {
val[i] = val[j];
}
}
}
for (; i < WORD_COUNT; ++i) {
val[i] = sign;
}
}
LIBC_INLINE constexpr BigInt operator>>(size_t s) const {
BigInt result(*this);
result.shift_right(s);
return result;
}
LIBC_INLINE constexpr BigInt &operator>>=(size_t s) {
shift_right(s);
return *this;
}
#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(&)
DEFINE_BINOP(|)
DEFINE_BINOP(^)
#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.add(BigInt(1));
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);
}
private:
LIBC_INLINE friend constexpr int cmp(const BigInt &lhs, const BigInt &rhs) {
const 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;
}
public:
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++() {
add(BigInt(1));
return *this;
}
LIBC_INLINE constexpr BigInt operator++(int) {
BigInt oldval(*this);
add(BigInt(1));
return oldval;
}
LIBC_INLINE constexpr BigInt &operator--() {
sub(BigInt(1));
return *this;
}
LIBC_INLINE constexpr BigInt operator--(int) {
BigInt oldval(*this);
sub(BigInt(1));
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]; }
LIBC_INLINE WordType *data() { return val; }
LIBC_INLINE const WordType *data() const { return val; }
};
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>({0xffff'ffff'ffff'ffff, 0xffff'ffff'ffff'ffff});
}
LIBC_INLINE static constexpr UInt<128> min() { return UInt<128>(0); }
// 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>({0xffff'ffff'ffff'ffff, 0x7fff'ffff'ffff'ffff});
}
LIBC_INLINE static constexpr Int<128> min() {
return Int<128>({0, 0x8000'0000'0000'0000});
}
// 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 value.ctz();
}
// 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 value.clz();
}
// 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) {
// TODO : Implement a faster version not involving operator~.
return cpp::countl_zero<T>(~value);
}
// 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) {
// TODO : Implement a faster version not involving operator~.
return cpp::countr_zero<T>(~value);
}
// 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);
if (count == 0)
return T();
constexpr unsigned T_BITS = CHAR_BIT * sizeof(T);
static_assert(count <= T_BITS && "Invalid bit index");
using word_type = typename T::word_type;
T out;
constexpr int CHUNK_INDEX_CONTAINING_BIT =
static_cast<int>(count / T::WORD_SIZE);
int index = 0;
for (auto &word : out.val) {
if (index < CHUNK_INDEX_CONTAINING_BIT)
word = -1;
else if (index > CHUNK_INDEX_CONTAINING_BIT)
word = 0;
else
word = mask_trailing_ones<word_type, count % T::WORD_SIZE>();
++index;
}
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);
if (count == 0)
return T();
constexpr unsigned T_BITS = CHAR_BIT * sizeof(T);
static_assert(count <= T_BITS && "Invalid bit index");
using word_type = typename T::word_type;
T out;
constexpr int CHUNK_INDEX_CONTAINING_BIT =
static_cast<int>((T::BITS - count - 1ULL) / T::WORD_SIZE);
int index = 0;
for (auto &word : out.val) {
if (index < CHUNK_INDEX_CONTAINING_BIT)
word = 0;
else if (index > CHUNK_INDEX_CONTAINING_BIT)
word = -1;
else
word = mask_leading_ones<word_type, count % T::WORD_SIZE>();
++index;
}
return out;
}
// 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