diff options
Diffstat (limited to 'libc/src/__support/UInt.h')
| -rw-r--r-- | libc/src/__support/UInt.h | 1129 |
1 files changed, 568 insertions, 561 deletions
diff --git a/libc/src/__support/UInt.h b/libc/src/__support/UInt.h index 282efdba1c5f..c1e55ceef211 100644 --- a/libc/src/__support/UInt.h +++ b/libc/src/__support/UInt.h @@ -14,10 +14,11 @@ #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/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" // SumCarry, DiffBorrow +#include "src/__support/math_extras.h" // add_with_carry, sub_with_borrow #include "src/__support/number_pair.h" #include <stddef.h> // For size_t @@ -25,71 +26,324 @@ namespace LIBC_NAMESPACE { -namespace internal { -template <typename T> struct half_width; +namespace multiword { -template <> struct half_width<uint64_t> : cpp::type_identity<uint32_t> {}; -template <> struct half_width<uint32_t> : cpp::type_identity<uint16_t> {}; +// 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; -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; +// 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; +} - 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 +// 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)); +} - constexpr size_t HALF_BIT_WIDTH = sizeof(T) * CHAR_BIT / 2; +// 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(); } +}; - 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; +// 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(); +} - 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; +// 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(); +} - return prod; +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 <> -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; +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. +// TODO: Make the result UB when 'offset' is greater or equal to the number of +// bits in 'array'. This will allow for better code performance. +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; + constexpr size_t TOTAL_BITS = N * WORD_BITS; + if (LIBC_UNLIKELY(offset == 0)) + return array; + if (LIBC_UNLIKELY(offset >= TOTAL_BITS)) + return {}; #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; + 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 + 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; } -#endif // LIBC_TYPES_HAS_INT128 -} // namespace internal +#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 @@ -100,10 +354,7 @@ struct BigInt { 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{}; + cpp::array<WordType, WORD_COUNT> val{}; // zero initialized. LIBC_INLINE constexpr BigInt() = default; @@ -112,76 +363,67 @@ struct BigInt { template <size_t OtherBits, bool OtherSigned> LIBC_INLINE constexpr BigInt( const BigInt<OtherBits, OtherSigned, WordType> &other) { - if (OtherBits >= Bits) { + if (OtherBits >= Bits) { // truncate for (size_t i = 0; i < WORD_COUNT; ++i) val[i] = other[i]; - } else { + } else { // zero or sign extend 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; + extend(i, Signed && other.is_neg()); } } // 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) + 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]; + } - // If nums doesn't completely fill val, then fill the rest with zeroes. - for (; i < WORD_COUNT; ++i) - val[i] = 0; + 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) { - 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); + 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; } - return; - } - - size_t i = 1; - - if constexpr (WORD_SIZE < sizeof(T) * CHAR_BIT) - for (; i < sizeof(T) * CHAR_BIT / WORD_SIZE; ++i) { + val[i] = static_cast<WordType>(v); + if constexpr (T_SIZE > WORD_SIZE) 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; + else + v = 0; } } + LIBC_INLINE constexpr BigInt &operator=(const BigInt &other) = default; - 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]; + // 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 val.back() >> (WORD_SIZE - 1); - } + LIBC_INLINE constexpr bool is_neg() const { return SIGNED && get_msb(); } template <typename T> LIBC_INLINE constexpr explicit operator T() const { return to<T>(); @@ -191,200 +433,100 @@ struct BigInt { 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]); - - constexpr size_t T_BITS = sizeof(T) * CHAR_BIT; - - if constexpr (T_BITS <= WORD_SIZE) + if constexpr (T_SIZE <= WORD_SIZE) return lo; - constexpr size_t MAX_COUNT = - T_BITS > Bits ? WORD_COUNT : T_BITS / WORD_SIZE; + 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_BITS > Bits)) { + 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 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) + for (auto part : val) + if (part != 0) return false; - } return true; } - // Add x to this number and store the result in this number. + // 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(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 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; - 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; - } + 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 { - 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; + // 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(other); // Returned carry value is ignored. + add_overflow(other); // Returned carry value is ignored. return *this; } - // Subtract x to this number and store the result in this number. + // 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(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 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; - 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; - } + BigInt result = *this; + result.sub_overflow(other); // Returned carry value is ignored. 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; - } + 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(other); + sub_overflow(other); // Returned carry value is ignored. 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. + // Multiply this number with x and store the result in this number. 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 multiword::scalar_multiply_with_carry(val, x); } - // Return the full product, only unsigned for now. + // Return the full product. template <size_t OtherBits> - LIBC_INLINE constexpr BigInt<Bits + OtherBits, Signed, WordType> + LIBC_INLINE constexpr auto 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]; + 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 @@ -407,39 +549,17 @@ struct BigInt { // 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]; + BigInt result; + multiword::quick_mul_hi(result.val, val, other.val); return result; } - // pow takes a power and sets this to its starting value to that power. Zero - // to the zeroth power returns 1. + // BigInt(x).pow_n(n) computes x ^ n. + // Note 0 ^ 0 == 1. LIBC_INLINE constexpr void pow_n(uint64_t power) { - BigInt result = 1; + static_assert(!Signed); + BigInt result = one(); BigInt cur_power = *this; - while (power > 0) { if ((power % 2) > 0) result *= cur_power; @@ -449,38 +569,23 @@ struct BigInt { *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) { + // 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 ÷r) { + if (LIBC_UNLIKELY(divider.is_zero())) 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; + 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 @@ -496,19 +601,16 @@ struct BigInt { // 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) { + 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>(0); + *this = BigInt<Bits, false, WordType>(); return remainder; } - - BigInt quotient(0); + 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; @@ -633,189 +735,22 @@ struct BigInt { 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) { + val = multiword::shift<multiword::LEFT, SIGNED>(val, s); + return *this; } LIBC_INLINE constexpr BigInt operator<<(size_t s) const { - BigInt result(*this); - result.shift_left(s); - return result; + return BigInt(multiword::shift<multiword::LEFT, SIGNED>(val, s)); } - LIBC_INLINE constexpr BigInt &operator<<=(size_t s) { - shift_left(s); + LIBC_INLINE constexpr BigInt &operator>>=(size_t s) { + val = multiword::shift<multiword::RIGHT, SIGNED>(val, 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; + return BigInt(multiword::shift<multiword::RIGHT, SIGNED>(val, s)); } #define DEFINE_BINOP(OP) \ @@ -833,10 +768,9 @@ struct BigInt { return lhs; \ } - DEFINE_BINOP(&) - DEFINE_BINOP(|) - DEFINE_BINOP(^) - + DEFINE_BINOP(&) // & and &= + DEFINE_BINOP(|) // | and |= + DEFINE_BINOP(^) // ^ and ^= #undef DEFINE_BINOP LIBC_INLINE constexpr BigInt operator~() const { @@ -847,8 +781,8 @@ struct BigInt { } LIBC_INLINE constexpr BigInt operator-() const { - BigInt result = ~(*this); - result.add(BigInt(1)); + BigInt result(*this); + result.negate(); return result; } @@ -865,24 +799,6 @@ struct BigInt { 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; @@ -901,24 +817,24 @@ public: } LIBC_INLINE constexpr BigInt &operator++() { - add(BigInt(1)); + increment(); return *this; } LIBC_INLINE constexpr BigInt operator++(int) { BigInt oldval(*this); - add(BigInt(1)); + increment(); return oldval; } LIBC_INLINE constexpr BigInt &operator--() { - sub(BigInt(1)); + decrement(); return *this; } LIBC_INLINE constexpr BigInt operator--(int) { BigInt oldval(*this); - sub(BigInt(1)); + decrement(); return oldval; } @@ -930,9 +846,117 @@ public: // 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; } +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 const WordType *data() const { return val; } + 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 ÷nd, + const BigInt ÷r) { + 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 ÷nd, + const BigInt ÷r) { + // 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 { @@ -962,10 +986,8 @@ 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); } + 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; @@ -973,12 +995,8 @@ public: 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}); - } + 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; @@ -1112,30 +1130,28 @@ has_single_bit(T value) { 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(); + 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 value.clz(); + 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) { - // TODO : Implement a faster version not involving operator~. - return cpp::countl_zero<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) { - // TODO : Implement a faster version not involving operator~. - return cpp::countr_zero<T>(~value); + return multiword::countr_one(value.val); } // Specialization of cpp::bit_width ('bit.h') for BigInt. @@ -1182,65 +1198,59 @@ rotr(T value, int rotate) { 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; - } + 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); - 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; - } + 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> +[[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> +[[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; @@ -1248,16 +1258,14 @@ first_leading_zero(T value) { // 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> +[[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> +[[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; @@ -1265,8 +1273,7 @@ first_trailing_zero(T value) { // 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> +[[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; |