[libc-commits] [libc] [llvm] [libc] Add a Multiprecision type to math_extras (PR #86137)
Guillaume Chatelet via libc-commits
libc-commits at lists.llvm.org
Thu Mar 21 12:43:10 PDT 2024
https://github.com/gchatelet updated https://github.com/llvm/llvm-project/pull/86137
>From 71117a97dc25d5be305d9b3ff55aed3e591b625f Mon Sep 17 00:00:00 2001
From: Guillaume Chatelet <gchatelet at google.com>
Date: Fri, 8 Mar 2024 14:36:45 +0000
Subject: [PATCH] [libc] Add a Multiprecision type to math_extras
---
libc/src/__support/CPP/iterator.h | 2 +-
libc/src/__support/FPUtil/dyadic_float.h | 6 +-
libc/src/__support/UInt.h | 1077 ++++++++---------
libc/src/__support/float_to_string.h | 7 +-
libc/src/__support/integer_literals.h | 9 +
libc/src/__support/math_extras.h | 242 +---
libc/src/__support/number_pair.h | 11 -
libc/test/src/__support/math_extras_test.cpp | 57 +
libc/test/src/__support/uint_test.cpp | 232 +++-
.../libc/test/src/__support/BUILD.bazel | 1 +
10 files changed, 883 insertions(+), 761 deletions(-)
diff --git a/libc/src/__support/CPP/iterator.h b/libc/src/__support/CPP/iterator.h
index 4d06e181bcf064..b0fd5c9f22ae01 100644
--- a/libc/src/__support/CPP/iterator.h
+++ b/libc/src/__support/CPP/iterator.h
@@ -71,7 +71,7 @@ template <typename Iter> class reverse_iterator {
return lhs.base() <= rhs.base();
}
- LIBC_INLINE constexpr iterator_type base() const { current; }
+ LIBC_INLINE constexpr iterator_type base() const { return current; }
LIBC_INLINE constexpr reference operator*() const {
Iter tmp = current;
diff --git a/libc/src/__support/FPUtil/dyadic_float.h b/libc/src/__support/FPUtil/dyadic_float.h
index 73fd7381c3c838..e0c205f52383ba 100644
--- a/libc/src/__support/FPUtil/dyadic_float.h
+++ b/libc/src/__support/FPUtil/dyadic_float.h
@@ -58,9 +58,9 @@ template <size_t Bits> struct DyadicFloat {
// significant bit.
LIBC_INLINE constexpr DyadicFloat &normalize() {
if (!mantissa.is_zero()) {
- int shift_length = static_cast<int>(mantissa.clz());
+ int shift_length = cpp::countl_zero(mantissa);
exponent -= shift_length;
- mantissa.shift_left(static_cast<size_t>(shift_length));
+ mantissa <<= static_cast<size_t>(shift_length);
}
return *this;
}
@@ -233,7 +233,7 @@ LIBC_INLINE constexpr DyadicFloat<Bits> quick_add(DyadicFloat<Bits> a,
result.sign = a.sign;
result.exponent = a.exponent;
result.mantissa = a.mantissa;
- if (result.mantissa.add(b.mantissa)) {
+ if (result.mantissa.add_overflow(b.mantissa)) {
// Mantissa addition overflow.
result.shift_right(1);
result.mantissa.val[DyadicFloat<Bits>::MantissaType::WORD_COUNT - 1] |=
diff --git a/libc/src/__support/UInt.h b/libc/src/__support/UInt.h
index df01e081e3c19e..04710e697438a9 100644
--- a/libc/src/__support/UInt.h
+++ b/libc/src/__support/UInt.h
@@ -17,7 +17,7 @@
#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/math_extras.h" // add_with_carry, sub_with_borrow
#include "src/__support/number_pair.h"
#include <stddef.h> // For size_t
@@ -25,64 +25,296 @@
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 Double final : cpp::array<T, 2> {
+ using UP = cpp::array<T, 2>;
+ using UP::UP;
+ LIBC_INLINE constexpr Double(T lo, T hi) : UP({lo, hi}) {}
+};
- 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
+// Converts an unsigned value into a Double<half_width_t<T>>.
+template <typename T> LIBC_INLINE constexpr auto split(T value) {
+ static_assert(cpp::is_unsigned_v<T>);
+ return cpp::bit_cast<Double<half_width_t<T>>>(value);
+}
- constexpr size_t HALF_BIT_WIDTH = sizeof(T) * CHAR_BIT / 2;
+// The low part of a Double value.
+template <typename T> LIBC_INLINE constexpr T lo(const Double<T> &value) {
+ return value[0];
+}
+// The high part of a Double value.
+template <typename T> LIBC_INLINE constexpr T hi(const Double<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));
+}
- 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;
+// Returns 'a' times 'b' in a Double<word>. Cannot overflow by definition.
+template <typename word>
+LIBC_INLINE constexpr Double<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 zero_carry = 0;
+ word carry;
+ const auto add_with_carry = LIBC_NAMESPACE::add_with_carry<word>;
+ lo_digit = add_with_carry(lo_digit, shiftl(step2), zero_carry, &carry);
+ hi_digit = add_with_carry(hi_digit, shiftr(step2), carry, nullptr);
+ lo_digit = add_with_carry(lo_digit, shiftl(step3), zero_carry, &carry);
+ hi_digit = add_with_carry(hi_digit, shiftr(step3), carry, nullptr);
+ return Double<word>(lo_digit, hi_digit);
+ }
+}
- 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;
+// Inplace binary 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;
+}
- return prod;
+// Inplace 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);
}
-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;
+// Inplace 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);
}
-#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;
+// Inplace multiply-add. Returns carry.
+// i.e., 'dst += b x c'
+template <typename word, size_t N>
+LIBC_INLINE constexpr word mad_with_carry(cpp::array<word, N> &dst, word b,
+ word c) {
+ return add_with_carry(dst, mul2(b, c));
}
-#endif // LIBC_TYPES_HAS_INT128
-} // namespace internal
+// 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(); }
+};
+
+// Inplace 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 = mad_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 += mad_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 += mad_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 += mad_with_carry(acc, lhs[j], rhs[i - j]);
+ dst[i - N] = acc.sum();
+ }
+ dst.back() = acc.carry();
+}
+
+// An enum for the shift function below.
+enum Direction { LEFT, RIGHT };
+
+// A bitwise shift on an array of elements.
+template <Direction direction, typename word, size_t N>
+LIBC_INLINE constexpr void shift(cpp::array<word, N> &dst, size_t shift) {
+ constexpr size_t WORD_BITS = sizeof(word) * CHAR_BIT;
+ constexpr size_t TOTAL_BITS = N * WORD_BITS;
+ if (shift == 0)
+ return;
+ if (shift >= TOTAL_BITS) {
+ dst = {};
+ return;
+ }
+ const int index_offset = int(shift) / WORD_BITS;
+ const int bit_offset = int(shift) % WORD_BITS;
+ const auto val_at = [&](int index) -> word {
+ return index >= 0 && index < int(N) ? dst[index] : 0;
+ };
+ if constexpr (direction == RIGHT) {
+ for (int dst_index = 0; dst_index < int(N); ++dst_index) {
+ const int src_index = dst_index + index_offset;
+ word dst_val = val_at(src_index);
+ if (bit_offset) {
+ dst_val >>= bit_offset;
+ dst_val |= val_at(src_index + 1) << (WORD_BITS - bit_offset);
+ }
+ dst[dst_index] = dst_val;
+ }
+ } else if constexpr (direction == LEFT) {
+ for (int dst_index = N; dst_index > 0;) {
+ --dst_index;
+ const int src_index = dst_index - index_offset;
+ word dst_val = val_at(src_index);
+ if (bit_offset) {
+ dst_val <<= bit_offset;
+ dst_val |= val_at(src_index - 1) >> (WORD_BITS - bit_offset);
+ }
+ dst[dst_index] = dst_val;
+ }
+ } else {
+ static_assert(cpp::always_false<word>);
+ }
+}
+
+// A utility to reverse the for-loop iteration.
+// TODO: move to a utility header if needed
+template <typename T> struct Backward {
+ T *ptr;
+ LIBC_INLINE constexpr Backward(T &obj) : ptr(&obj) {}
+};
+template <typename T> LIBC_INLINE constexpr auto begin(Backward<T> f) {
+ return f.ptr->rbegin();
+}
+template <typename T> LIBC_INLINE constexpr auto end(Backward<T> f) {
+ return f.ptr->rend();
+}
+template <typename T> LIBC_INLINE constexpr auto backward(T &obj) {
+ return Backward<T>(obj);
+}
+
+#define DECLARE_COUNTBIT(NAME, ITERATE) \
+ template <typename word, size_t N> \
+ LIBC_INLINE constexpr int NAME(const cpp::array<word, N> &val) { \
+ int bit_count = 0; \
+ for (word part : ITERATE(val)) { \
+ const int word_count = cpp::NAME<word>(part); \
+ bit_count += word_count; \
+ if (word_count != cpp::numeric_limits<word>::digits) \
+ break; \
+ } \
+ return bit_count; \
+ }
+
+DECLARE_COUNTBIT(countr_zero, )
+DECLARE_COUNTBIT(countr_one, )
+DECLARE_COUNTBIT(countl_zero, backward)
+DECLARE_COUNTBIT(countl_one, backward)
+
+} // namespace multiword
template <size_t Bits, bool Signed, typename WordType = uint64_t>
struct BigInt {
@@ -90,6 +322,9 @@ struct BigInt {
"WordType must be unsigned integer.");
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 +335,7 @@ 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 +344,67 @@ 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 +414,100 @@ 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 +530,17 @@ 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 +550,63 @@ 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) {
- 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);
+ // 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) {
+ auto ÷nd = *this;
+ if constexpr (SIGNED) {
+ // Signed Multiword Division
+ // 1. Negate the dividend it it is negative, and similarly for the
+ // divisor.
+ // 2. Convert the divident and divisor to unsigned representation.
+ // 3. Use unsigned multiword division algorithm.
+ // 4. Convert the quotient and remainder to signed representation.
+ // 5. Negate the quotient if the dividend and divisor had opposite signs.
+ // 6. Negate the remainder if the dividend was negative.
+ const bool dividend_is_neg = dividend.is_neg();
+ const bool divider_is_neg = divider.is_neg();
+ unsigned_type udividend(dividend);
+ unsigned_type udivider(divider);
+ if (dividend_is_neg)
+ udividend.negate();
+ if (divider_is_neg)
+ udivider.negate();
+ auto maybe_remainder = udividend.div(udivider);
+ if (!maybe_remainder)
+ return cpp::nullopt;
+ unsigned_type remainder = *maybe_remainder;
+ if (dividend_is_neg != divider_is_neg)
+ udividend.negate(); // this is the quotient
+ dividend = signed_type(udividend);
+ if (dividend_is_neg)
+ remainder.negate();
+ return signed_type(remainder);
+ } else {
+ BigInt remainder;
+ if (divider.is_zero())
+ return cpp::nullopt;
+ if (divider == 1)
+ return remainder;
+ BigInt quotient;
+ if (dividend >= divider) {
+ BigInt subtractor = divider;
+ int cur_bit = multiword::countl_zero(subtractor.val) -
+ multiword::countl_zero(dividend.val);
+ subtractor <<= cur_bit;
+ for (; cur_bit >= 0 && dividend > 0; --cur_bit, subtractor >>= 1) {
+ if (dividend < subtractor)
+ continue;
+ dividend -= subtractor;
+ quotient.set_bit(cur_bit);
+ }
}
+ remainder = dividend;
+ dividend = quotient;
+ return remainder;
}
- remainder = *this;
- *this = quotient;
- return remainder;
}
// Efficiently perform BigInt / (x * 2^e), where x is a half-word-size
@@ -496,19 +622,16 @@ 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;
@@ -633,191 +756,28 @@ 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) {
+ multiword::shift<multiword::LEFT>(val, s);
+ return *this;
}
LIBC_INLINE constexpr BigInt operator<<(size_t s) const {
BigInt result(*this);
- result.shift_left(s);
+ result <<= s;
return result;
}
- LIBC_INLINE constexpr BigInt &operator<<=(size_t s) {
- shift_left(s);
+ LIBC_INLINE constexpr BigInt &operator>>=(size_t s) {
+ multiword::shift<multiword::RIGHT>(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);
+ result >>= 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) { \
@@ -833,10 +793,9 @@ 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 +806,8 @@ struct BigInt {
}
LIBC_INLINE constexpr BigInt operator-() const {
- BigInt result = ~(*this);
- result.add(BigInt(1));
+ BigInt result(*this);
+ result.negate();
return result;
}
@@ -865,24 +824,6 @@ 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 +842,24 @@ struct BigInt {
}
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 +871,67 @@ struct BigInt {
// 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) {
+ 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;
+ }
+
+ 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 const WordType *data() const { return val; }
+ 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);
+ }
+
+ friend signed_type;
+ friend unsigned_type;
};
namespace internal {
@@ -962,10 +961,8 @@ 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 +970,8 @@ template <> class cpp::numeric_limits<UInt<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});
- }
+ 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;
@@ -1101,30 +1094,28 @@ 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.
@@ -1171,53 +1162,49 @@ 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>();
+}
+
} // namespace LIBC_NAMESPACE
#endif // LLVM_LIBC_SRC___SUPPORT_UINT_H
diff --git a/libc/src/__support/float_to_string.h b/libc/src/__support/float_to_string.h
index 1287c3e9a84fac..4c59cfd99c2e6c 100644
--- a/libc/src/__support/float_to_string.h
+++ b/libc/src/__support/float_to_string.h
@@ -689,7 +689,7 @@ template <> class FloatToString<long double> {
wide_int float_as_int = mantissa;
- float_as_int.shift_left(exponent);
+ float_as_int <<= exponent;
int_block_index = 0;
while (float_as_int > 0) {
@@ -708,10 +708,11 @@ template <> class FloatToString<long double> {
const int SHIFT_AMOUNT = FLOAT_AS_INT_WIDTH + exponent;
static_assert(EXTRA_INT_WIDTH >= sizeof(long double) * 8);
- float_as_fixed.shift_left(SHIFT_AMOUNT);
+ float_as_fixed <<= SHIFT_AMOUNT;
// If there are still digits above the decimal point, handle those.
- if (float_as_fixed.clz() < static_cast<int>(EXTRA_INT_WIDTH)) {
+ if (cpp::countl_zero(float_as_fixed) <
+ static_cast<int>(EXTRA_INT_WIDTH)) {
UInt<EXTRA_INT_WIDTH> above_decimal_point =
float_as_fixed >> FLOAT_AS_INT_WIDTH;
diff --git a/libc/src/__support/integer_literals.h b/libc/src/__support/integer_literals.h
index de1f88fbd3f3f5..984826b4dd9b5b 100644
--- a/libc/src/__support/integer_literals.h
+++ b/libc/src/__support/integer_literals.h
@@ -169,6 +169,15 @@ LIBC_INLINE constexpr auto operator""_u256(const char *x) {
return internal::parse_with_prefix<UInt<256>>(x);
}
+template <typename T> LIBC_INLINE constexpr T parse_bigint(const char *x) {
+ if (x[0] == '-' || x[0] == '+') {
+ auto positive = internal::parse_with_prefix<T>(x + 1);
+ return x[0] == '-' ? -positive : positive;
+ } else {
+ return internal::parse_with_prefix<T>(x);
+ }
+}
+
} // namespace LIBC_NAMESPACE
#endif // LLVM_LIBC_SRC___SUPPORT_INTEGER_LITERALS_H
diff --git a/libc/src/__support/math_extras.h b/libc/src/__support/math_extras.h
index 28ee1be8b99997..248bd694d38fcb 100644
--- a/libc/src/__support/math_extras.h
+++ b/libc/src/__support/math_extras.h
@@ -11,8 +11,8 @@
#define LLVM_LIBC_SRC___SUPPORT_MATH_EXTRAS_H
#include "src/__support/CPP/bit.h" // countl_one, countr_zero
-#include "src/__support/CPP/limits.h" // CHAR_BIT, numeric_limits
-#include "src/__support/CPP/type_traits.h" // is_unsigned_v
+#include "src/__support/CPP/limits.h" // CHAR_BIT, numeric_limits
+#include "src/__support/CPP/type_traits.h" // is_unsigned_v, is_constant_evaluated
#include "src/__support/macros/attributes.h" // LIBC_INLINE
#include "src/__support/macros/config.h" // LIBC_HAS_BUILTIN
@@ -33,199 +33,91 @@ mask_trailing_ones() {
template <typename T, size_t count>
LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_unsigned_v<T>, T>
mask_leading_ones() {
- constexpr T MASK(mask_trailing_ones<T, CHAR_BIT * sizeof(T) - count>());
- return T(~MASK); // bitwise NOT performs integer promotion.
+ return T(~mask_trailing_ones<T, CHAR_BIT * sizeof(T) - count>());
}
-// Add with carry
-template <typename T> struct SumCarry {
- T sum;
- T carry;
-};
-
-// This version is always valid for constexpr.
-template <typename T>
-LIBC_INLINE constexpr cpp::enable_if_t<
- cpp::is_integral_v<T> && cpp::is_unsigned_v<T>, SumCarry<T>>
-add_with_carry_const(T a, T b, T carry_in) {
- T tmp = a + carry_in;
- T sum = b + tmp;
- T carry_out = (sum < b) + (tmp < a);
- return {sum, carry_out};
-}
-
-template <typename T>
-LIBC_INLINE constexpr cpp::enable_if_t<
- cpp::is_integral_v<T> && cpp::is_unsigned_v<T>, SumCarry<T>>
-add_with_carry(T a, T b, T carry_in) {
- return add_with_carry_const<T>(a, b, carry_in);
-}
-
-#if LIBC_HAS_BUILTIN(__builtin_addc)
-// https://clang.llvm.org/docs/LanguageExtensions.html#multiprecision-arithmetic-builtins
-
-template <>
-LIBC_INLINE constexpr SumCarry<unsigned char>
-add_with_carry<unsigned char>(unsigned char a, unsigned char b,
- unsigned char carry_in) {
- if (__builtin_is_constant_evaluated()) {
- return add_with_carry_const<unsigned char>(a, b, carry_in);
- } else {
- SumCarry<unsigned char> result{0, 0};
- result.sum = __builtin_addcb(a, b, carry_in, &result.carry);
- return result;
- }
-}
-
-template <>
-LIBC_INLINE constexpr SumCarry<unsigned short>
-add_with_carry<unsigned short>(unsigned short a, unsigned short b,
- unsigned short carry_in) {
- if (__builtin_is_constant_evaluated()) {
- return add_with_carry_const<unsigned short>(a, b, carry_in);
- } else {
- SumCarry<unsigned short> result{0, 0};
- result.sum = __builtin_addcs(a, b, carry_in, &result.carry);
- return result;
- }
-}
-
-template <>
-LIBC_INLINE constexpr SumCarry<unsigned int>
-add_with_carry<unsigned int>(unsigned int a, unsigned int b,
- unsigned int carry_in) {
- if (__builtin_is_constant_evaluated()) {
- return add_with_carry_const<unsigned int>(a, b, carry_in);
- } else {
- SumCarry<unsigned int> result{0, 0};
- result.sum = __builtin_addc(a, b, carry_in, &result.carry);
- return result;
- }
-}
-
-template <>
-LIBC_INLINE constexpr SumCarry<unsigned long>
-add_with_carry<unsigned long>(unsigned long a, unsigned long b,
- unsigned long carry_in) {
- if (__builtin_is_constant_evaluated()) {
- return add_with_carry_const<unsigned long>(a, b, carry_in);
- } else {
- SumCarry<unsigned long> result{0, 0};
- result.sum = __builtin_addcl(a, b, carry_in, &result.carry);
- return result;
- }
+// Create a bitmask with the count right-most bits set to 0, and all other bits
+// set to 1. Only unsigned types are allowed.
+template <typename T, size_t count>
+LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_unsigned_v<T>, T>
+mask_trailing_zeros() {
+ return mask_leading_ones<T, CHAR_BIT * sizeof(T) - count>();
}
-template <>
-LIBC_INLINE constexpr SumCarry<unsigned long long>
-add_with_carry<unsigned long long>(unsigned long long a, unsigned long long b,
- unsigned long long carry_in) {
- if (__builtin_is_constant_evaluated()) {
- return add_with_carry_const<unsigned long long>(a, b, carry_in);
- } else {
- SumCarry<unsigned long long> result{0, 0};
- result.sum = __builtin_addcll(a, b, carry_in, &result.carry);
- return result;
- }
+// Create a bitmask with the count left-most bits set to 0, and all other bits
+// set to 1. Only unsigned types are allowed.
+template <typename T, size_t count>
+LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_unsigned_v<T>, T>
+mask_leading_zeros() {
+ return mask_trailing_ones<T, CHAR_BIT * sizeof(T) - count>();
}
-#endif // LIBC_HAS_BUILTIN(__builtin_addc)
+#define RETURN_IF_BUILTIN(TYPE, BUILTIN) \
+ if constexpr (cpp::is_same_v<T, TYPE> && LIBC_HAS_BUILTIN(BUILTIN)) \
+ return BUILTIN(a, b, res);
-// Subtract with borrow
-template <typename T> struct DiffBorrow {
- T diff;
- T borrow;
-};
-
-// This version is always valid for constexpr.
template <typename T>
-LIBC_INLINE constexpr cpp::enable_if_t<
- cpp::is_integral_v<T> && cpp::is_unsigned_v<T>, DiffBorrow<T>>
-sub_with_borrow_const(T a, T b, T borrow_in) {
- T tmp = a - b;
- T diff = tmp - borrow_in;
- T borrow_out = (diff > tmp) + (tmp > a);
- return {diff, borrow_out};
+[[nodiscard]] LIBC_INLINE constexpr bool add_overflow(T a, T b, T *res) {
+ RETURN_IF_BUILTIN(T, __builtin_add_overflow)
+ if (res)
+ *res = a + b;
+ // https://stackoverflow.com/a/1514309
+ return (b > 0 && a > (cpp::numeric_limits<T>::max() - b)) ||
+ (b < 0 && a < (cpp::numeric_limits<T>::min() - b));
}
-// This version is not always valid for constepxr because it's overriden below
-// if builtins are available.
template <typename T>
-LIBC_INLINE constexpr cpp::enable_if_t<
- cpp::is_integral_v<T> && cpp::is_unsigned_v<T>, DiffBorrow<T>>
-sub_with_borrow(T a, T b, T borrow_in) {
- return sub_with_borrow_const<T>(a, b, borrow_in);
-}
-
-#if LIBC_HAS_BUILTIN(__builtin_subc)
-// https://clang.llvm.org/docs/LanguageExtensions.html#multiprecision-arithmetic-builtins
-
-template <>
-LIBC_INLINE constexpr DiffBorrow<unsigned char>
-sub_with_borrow<unsigned char>(unsigned char a, unsigned char b,
- unsigned char borrow_in) {
- if (__builtin_is_constant_evaluated()) {
- return sub_with_borrow_const<unsigned char>(a, b, borrow_in);
- } else {
- DiffBorrow<unsigned char> result{0, 0};
- result.diff = __builtin_subcb(a, b, borrow_in, &result.borrow);
- return result;
- }
+[[nodiscard]] LIBC_INLINE constexpr bool sub_overflow(T a, T b, T *res) {
+ RETURN_IF_BUILTIN(T, __builtin_sub_overflow)
+ if (res)
+ *res = a - b;
+ // https://stackoverflow.com/a/1514309
+ return (b < 0 && a > (cpp::numeric_limits<T>::max() + b)) ||
+ (b > 0 && a < (cpp::numeric_limits<T>::min() + b));
}
-template <>
-LIBC_INLINE constexpr DiffBorrow<unsigned short>
-sub_with_borrow<unsigned short>(unsigned short a, unsigned short b,
- unsigned short borrow_in) {
- if (__builtin_is_constant_evaluated()) {
- return sub_with_borrow_const<unsigned short>(a, b, borrow_in);
- } else {
- DiffBorrow<unsigned short> result{0, 0};
- result.diff = __builtin_subcs(a, b, borrow_in, &result.borrow);
- return result;
- }
-}
+#undef RETURN_IF_BUILTIN
+#define RETURN_IF_BUILTIN(TYPE, BUILTIN) \
+ if constexpr (cpp::is_same_v<T, TYPE> && LIBC_HAS_BUILTIN(BUILTIN)) \
+ return BUILTIN(a, b, carry_in, carry_out);
-template <>
-LIBC_INLINE constexpr DiffBorrow<unsigned int>
-sub_with_borrow<unsigned int>(unsigned int a, unsigned int b,
- unsigned int borrow_in) {
- if (__builtin_is_constant_evaluated()) {
- return sub_with_borrow_const<unsigned int>(a, b, borrow_in);
- } else {
- DiffBorrow<unsigned int> result{0, 0};
- result.diff = __builtin_subc(a, b, borrow_in, &result.borrow);
- return result;
- }
-}
-
-template <>
-LIBC_INLINE constexpr DiffBorrow<unsigned long>
-sub_with_borrow<unsigned long>(unsigned long a, unsigned long b,
- unsigned long borrow_in) {
- if (__builtin_is_constant_evaluated()) {
- return sub_with_borrow_const<unsigned long>(a, b, borrow_in);
- } else {
- DiffBorrow<unsigned long> result{0, 0};
- result.diff = __builtin_subcl(a, b, borrow_in, &result.borrow);
- return result;
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_unsigned_v<T>, T>
+add_with_carry(T a, T b, T carry_in, T *carry_out = nullptr) {
+ if constexpr (!cpp::is_constant_evaluated()) {
+ RETURN_IF_BUILTIN(unsigned char, __builtin_addcb)
+ RETURN_IF_BUILTIN(unsigned short, __builtin_addcs)
+ RETURN_IF_BUILTIN(unsigned int, __builtin_addc)
+ RETURN_IF_BUILTIN(unsigned long, __builtin_addcl)
+ RETURN_IF_BUILTIN(unsigned long long, __builtin_addcll)
}
+ T sum;
+ T carry1 = add_overflow(a, b, &sum);
+ T carry2 = add_overflow(sum, carry_in, &sum);
+ if (carry_out)
+ *carry_out = carry1 | carry2;
+ return sum;
}
-template <>
-LIBC_INLINE constexpr DiffBorrow<unsigned long long>
-sub_with_borrow<unsigned long long>(unsigned long long a, unsigned long long b,
- unsigned long long borrow_in) {
- if (__builtin_is_constant_evaluated()) {
- return sub_with_borrow_const<unsigned long long>(a, b, borrow_in);
- } else {
- DiffBorrow<unsigned long long> result{0, 0};
- result.diff = __builtin_subcll(a, b, borrow_in, &result.borrow);
- return result;
+template <typename T>
+[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_unsigned_v<T>, T>
+sub_with_borrow(T a, T b, T carry_in, T *carry_out = nullptr) {
+ if constexpr (!cpp::is_constant_evaluated()) {
+ RETURN_IF_BUILTIN(unsigned char, __builtin_subcb)
+ RETURN_IF_BUILTIN(unsigned short, __builtin_subcs)
+ RETURN_IF_BUILTIN(unsigned int, __builtin_subc)
+ RETURN_IF_BUILTIN(unsigned long, __builtin_subcl)
+ RETURN_IF_BUILTIN(unsigned long long, __builtin_subcll)
}
+ T sub;
+ T carry1 = sub_overflow(a, b, &sub);
+ T carry2 = sub_overflow(sub, carry_in, &sub);
+ if (carry_out)
+ *carry_out = carry1 | carry2;
+ return sub;
}
-#endif // LIBC_HAS_BUILTIN(__builtin_subc)
+#undef RETURN_IF
template <typename T>
[[nodiscard]] LIBC_INLINE constexpr cpp::enable_if_t<cpp::is_unsigned_v<T>, int>
diff --git a/libc/src/__support/number_pair.h b/libc/src/__support/number_pair.h
index ee6667b1299fe8..2f713fc03520f9 100644
--- a/libc/src/__support/number_pair.h
+++ b/libc/src/__support/number_pair.h
@@ -20,17 +20,6 @@ template <typename T> struct NumberPair {
T hi = T(0);
};
-template <typename T>
-cpp::enable_if_t<cpp::is_integral_v<T> && cpp::is_unsigned_v<T>,
- NumberPair<T>> constexpr split(T a) {
- constexpr size_t HALF_BIT_WIDTH = sizeof(T) * 4;
- constexpr T LOWER_HALF_MASK = (T(1) << HALF_BIT_WIDTH) - T(1);
- NumberPair<T> result;
- result.lo = a & LOWER_HALF_MASK;
- result.hi = a >> HALF_BIT_WIDTH;
- return result;
-}
-
} // namespace LIBC_NAMESPACE
#endif // LLVM_LIBC_SRC___SUPPORT_NUMBER_PAIR_H
diff --git a/libc/test/src/__support/math_extras_test.cpp b/libc/test/src/__support/math_extras_test.cpp
index e642248881a41c..8b7c9e61fb72b6 100644
--- a/libc/test/src/__support/math_extras_test.cpp
+++ b/libc/test/src/__support/math_extras_test.cpp
@@ -101,4 +101,61 @@ TYPED_TEST(LlvmLibcBitTest, CountZeros, UnsignedTypesNoBigInt) {
EXPECT_EQ(count_zeros<T>(cpp::numeric_limits<T>::max() >> i), i);
}
+using UnsignedTypes = testing::TypeList<
+#if defined(__SIZEOF_INT128__)
+ __uint128_t,
+#endif
+ unsigned char, unsigned short, unsigned int, unsigned long,
+ unsigned long long>;
+
+TYPED_TEST(LlvmLibcBlockMathExtrasTest, add_overflow, UnsignedTypes) {
+ constexpr T ZERO = cpp::numeric_limits<T>::min();
+ constexpr T ONE(1);
+ constexpr T MAX = cpp::numeric_limits<T>::max();
+ constexpr T BEFORE_MAX = MAX - 1;
+
+ const struct {
+ T lhs;
+ T rhs;
+ T sum;
+ bool carry;
+ } TESTS[] = {
+ {ZERO, ONE, ONE, false}, // 0x00 + 0x01 = 0x01
+ {BEFORE_MAX, ONE, MAX, false}, // 0xFE + 0x01 = 0xFF
+ {MAX, ONE, ZERO, true}, // 0xFF + 0x01 = 0x00 (carry)
+ {MAX, MAX, BEFORE_MAX, true}, // 0xFF + 0xFF = 0xFE (carry)
+ };
+ for (auto tc : TESTS) {
+ T sum;
+ bool carry = add_overflow<T>(tc.lhs, tc.rhs, &sum);
+ EXPECT_EQ(sum, tc.sum);
+ EXPECT_EQ(carry, tc.carry);
+ }
+}
+
+TYPED_TEST(LlvmLibcBlockMathExtrasTest, sub_overflow, UnsignedTypes) {
+ constexpr T ZERO = cpp::numeric_limits<T>::min();
+ constexpr T ONE(1);
+ constexpr T MAX = cpp::numeric_limits<T>::max();
+ constexpr T BEFORE_MAX = MAX - 1;
+
+ const struct {
+ T lhs;
+ T rhs;
+ T sub;
+ bool carry;
+ } TESTS[] = {
+ {ONE, ZERO, ONE, false}, // 0x01 - 0x00 = 0x01
+ {MAX, MAX, ZERO, false}, // 0xFF - 0xFF = 0x00
+ {ZERO, ONE, MAX, true}, // 0x00 - 0x01 = 0xFF (carry)
+ {BEFORE_MAX, MAX, MAX, true}, // 0xFE - 0xFF = 0xFF (carry)
+ };
+ for (auto tc : TESTS) {
+ T sub;
+ bool carry = sub_overflow<T>(tc.lhs, tc.rhs, &sub);
+ EXPECT_EQ(sub, tc.sub);
+ EXPECT_EQ(carry, tc.carry);
+ }
+}
+
} // namespace LIBC_NAMESPACE
diff --git a/libc/test/src/__support/uint_test.cpp b/libc/test/src/__support/uint_test.cpp
index 5764324ca28815..abd976acefdfa7 100644
--- a/libc/test/src/__support/uint_test.cpp
+++ b/libc/test/src/__support/uint_test.cpp
@@ -8,6 +8,7 @@
#include "src/__support/CPP/optional.h"
#include "src/__support/UInt.h"
+#include "src/__support/integer_literals.h" // parse_unsigned_bigint
#include "src/__support/macros/properties/types.h" // LIBC_TYPES_HAS_INT128
#include "include/llvm-libc-macros/math-macros.h" // HUGE_VALF, HUGE_VALF
@@ -15,6 +16,190 @@
namespace LIBC_NAMESPACE {
+enum Value { ZERO, ONE, TWO, MIN, MAX };
+
+template <typename T> auto create(Value value) {
+ switch (value) {
+ case ZERO:
+ return T(0);
+ case ONE:
+ return T(1);
+ case TWO:
+ return T(2);
+ case MIN:
+ return T::min();
+ case MAX:
+ return T::max();
+ }
+}
+
+using Types = testing::TypeList< //
+#ifdef LIBC_TYPES_HAS_INT64
+ BigInt<64, false, uint64_t>, // 64-bits unsigned (1 x uint64_t)
+ BigInt<64, true, uint64_t>, // 64-bits signed (1 x uint64_t)
+#endif
+#ifdef LIBC_TYPES_HAS_INT128
+ BigInt<128, false, __uint128_t>, // 128-bits unsigned (1 x __uint128_t)
+ BigInt<128, true, __uint128_t>, // 128-bits signed (1 x __uint128_t)
+#endif
+ BigInt<16, false, uint16_t>, // 16-bits unsigned (1 x uint16_t)
+ BigInt<16, true, uint16_t>, // 16-bits signed (1 x uint16_t)
+ BigInt<64, false, uint16_t>, // 64-bits unsigned (4 x uint16_t)
+ BigInt<64, true, uint16_t> // 64-bits signed (4 x uint16_t)
+ >;
+
+#define ASSERT_SAME(A, B) ASSERT_TRUE((A) == (B))
+
+TYPED_TEST(LlvmLibcUIntClassTest, Additions, Types) {
+ ASSERT_SAME(create<T>(ZERO) + create<T>(ZERO), create<T>(ZERO));
+ ASSERT_SAME(create<T>(ONE) + create<T>(ZERO), create<T>(ONE));
+ ASSERT_SAME(create<T>(ZERO) + create<T>(ONE), create<T>(ONE));
+ ASSERT_SAME(create<T>(ONE) + create<T>(ONE), create<T>(TWO));
+ // 2's complement addition works for signed and unsigned types.
+ // - unsigned : 0xff + 0x01 = 0x00 (255 + 1 = 0)
+ // - signed : 0xef + 0x01 = 0xf0 (127 + 1 = -128)
+ ASSERT_SAME(create<T>(MAX) + create<T>(ONE), create<T>(MIN));
+}
+
+TYPED_TEST(LlvmLibcUIntClassTest, Subtraction, Types) {
+ ASSERT_SAME(create<T>(ZERO) - create<T>(ZERO), create<T>(ZERO));
+ ASSERT_SAME(create<T>(ONE) - create<T>(ONE), create<T>(ZERO));
+ ASSERT_SAME(create<T>(ONE) - create<T>(ZERO), create<T>(ONE));
+ // 2's complement subtraction works for signed and unsigned types.
+ // - unsigned : 0x00 - 0x01 = 0xff ( 0 - 1 = 255)
+ // - signed : 0xf0 - 0x01 = 0xef (-128 - 1 = 127)
+ ASSERT_SAME(create<T>(MIN) - create<T>(ONE), create<T>(MAX));
+}
+
+TYPED_TEST(LlvmLibcUIntClassTest, Multiplication, Types) {
+ ASSERT_SAME(create<T>(ZERO) * create<T>(ZERO), create<T>(ZERO));
+ ASSERT_SAME(create<T>(ZERO) * create<T>(ONE), create<T>(ZERO));
+ ASSERT_SAME(create<T>(ONE) * create<T>(ZERO), create<T>(ZERO));
+ ASSERT_SAME(create<T>(ONE) * create<T>(ONE), create<T>(ONE));
+ ASSERT_SAME(create<T>(ONE) * create<T>(TWO), create<T>(TWO));
+ ASSERT_SAME(create<T>(TWO) * create<T>(ONE), create<T>(TWO));
+ // - unsigned : 0xff x 0xff = 0x01 (mod 0xff)
+ // - signed : 0xef x 0xef = 0x01 (mod 0xff)
+ ASSERT_SAME(create<T>(MAX) * create<T>(MAX), create<T>(ONE));
+}
+
+template <typename T> void print(const char *msg, T value) {
+ testing::tlog << msg;
+ IntegerToString<T, radix::Hex> buffer(value);
+ testing::tlog << buffer.view() << "\n";
+}
+
+TEST(LlvmLibcUIntClassTest, SignedAddSub) {
+ // Computations performed by https://www.wolframalpha.com/
+ using T = BigInt<128, true, uint32_t>;
+ const T a = parse_bigint<T>("1927508279017230597");
+ const T b = parse_bigint<T>("278789278723478925");
+ const T s = parse_bigint<T>("2206297557740709522");
+ // Addition
+ ASSERT_SAME(a + b, s);
+ ASSERT_SAME(b + a, s); // commutative
+ // Subtraction
+ ASSERT_SAME(a - s, -b);
+ ASSERT_SAME(s - a, b);
+}
+
+TEST(LlvmLibcUIntClassTest, SignedMulDiv) {
+ // Computations performed by https://www.wolframalpha.com/
+ using T = BigInt<128, true, uint16_t>;
+ struct {
+ const char *a;
+ const char *b;
+ const char *mul;
+ } const test_cases[] = {{"-4", "3", "-12"},
+ {"-3", "-3", "9"},
+ {"1927508279017230597", "278789278723478925",
+ "537368642840747885329125014794668225"}};
+ for (auto tc : test_cases) {
+ const T a = parse_bigint<T>(tc.a);
+ const T b = parse_bigint<T>(tc.b);
+ const T mul = parse_bigint<T>(tc.mul);
+ // Multiplication
+ ASSERT_SAME(a * b, mul);
+ ASSERT_SAME(b * a, mul); // commutative
+ ASSERT_SAME(a * -b, -mul); // sign
+ ASSERT_SAME(-a * b, -mul); // sign
+ ASSERT_SAME(-a * -b, mul); // sign
+ // Division
+ ASSERT_SAME(mul / a, b);
+ ASSERT_SAME(mul / b, a);
+ ASSERT_SAME(-mul / a, -b); // sign
+ ASSERT_SAME(mul / -a, -b); // sign
+ ASSERT_SAME(-mul / -a, b); // sign
+ }
+}
+
+TYPED_TEST(LlvmLibcUIntClassTest, Division, Types) {
+ ASSERT_SAME(create<T>(ZERO) / create<T>(ONE), create<T>(ZERO));
+ ASSERT_SAME(create<T>(MAX) / create<T>(ONE), create<T>(MAX));
+ ASSERT_SAME(create<T>(MAX) / create<T>(MAX), create<T>(ONE));
+ // - unsigned : 0xff / 0x02 = 0x7f
+ // - signed : 0xef / 0x02 = 0x77
+ ASSERT_SAME(create<T>(MAX) / create<T>(TWO), (create<T>(MAX) >> 1));
+
+ using word_type = typename T::word_type;
+ const T zero_one_repeated = T::all_ones() / T(0xff);
+ const word_type pattern = word_type(~0) / word_type(0xff);
+ for (const word_type part : zero_one_repeated.val) {
+ if constexpr (T::SIGNED == false) {
+ EXPECT_EQ(part, pattern);
+ }
+ }
+}
+
+TYPED_TEST(LlvmLibcUIntClassTest, is_neg, Types) {
+ EXPECT_FALSE(create<T>(ZERO).is_neg());
+ EXPECT_FALSE(create<T>(ONE).is_neg());
+ EXPECT_FALSE(create<T>(TWO).is_neg());
+ EXPECT_EQ(create<T>(MIN).is_neg(), T::SIGNED);
+ EXPECT_FALSE(create<T>(MAX).is_neg());
+}
+
+TYPED_TEST(LlvmLibcUIntClassTest, Masks, Types) {
+ if constexpr (!T::SIGNED) {
+ constexpr size_t BITS = T::BITS;
+ // mask_trailing_ones
+ ASSERT_SAME((mask_trailing_ones<T, 0>()), T::zero());
+ ASSERT_SAME((mask_trailing_ones<T, 1>()), T::one());
+ ASSERT_SAME((mask_trailing_ones<T, BITS - 1>()), T::all_ones() >> 1);
+ ASSERT_SAME((mask_trailing_ones<T, BITS>()), T::all_ones());
+ // mask_leading_ones
+ ASSERT_SAME((mask_leading_ones<T, 0>()), T::zero());
+ ASSERT_SAME((mask_leading_ones<T, 1>()), T::one() << (BITS - 1));
+ ASSERT_SAME((mask_leading_ones<T, BITS - 1>()), T::all_ones() - T::one());
+ ASSERT_SAME((mask_leading_ones<T, BITS>()), T::all_ones());
+ // mask_trailing_zeros
+ ASSERT_SAME((mask_trailing_zeros<T, 0>()), T::all_ones());
+ ASSERT_SAME((mask_trailing_zeros<T, 1>()), T::all_ones() - T::one());
+ ASSERT_SAME((mask_trailing_zeros<T, BITS - 1>()), T::one() << (BITS - 1));
+ ASSERT_SAME((mask_trailing_zeros<T, BITS>()), T::zero());
+ // mask_trailing_zeros
+ ASSERT_SAME((mask_leading_zeros<T, 0>()), T::all_ones());
+ ASSERT_SAME((mask_leading_zeros<T, 1>()), T::all_ones() >> 1);
+ ASSERT_SAME((mask_leading_zeros<T, BITS - 1>()), T::one());
+ ASSERT_SAME((mask_leading_zeros<T, BITS>()), T::zero());
+ }
+}
+
+TYPED_TEST(LlvmLibcUIntClassTest, CountBits, Types) {
+ if constexpr (!T::SIGNED) {
+ for (size_t i = 0; i <= T::BITS; ++i) {
+ const auto l_one = T::all_ones() << i; // 0b111...000
+ const auto r_one = T::all_ones() >> i; // 0b000...111
+ const int zeros = i;
+ const int ones = T::BITS - zeros;
+ ASSERT_EQ(cpp::countr_one(r_one), ones);
+ ASSERT_EQ(cpp::countl_one(l_one), ones);
+ ASSERT_EQ(cpp::countr_zero(l_one), zeros);
+ ASSERT_EQ(cpp::countl_zero(r_one), zeros);
+ }
+ }
+}
+
using LL_UInt64 = UInt<64>;
// We want to test UInt<128> explicitly. So, for
// convenience, we use a sugar which does not conflict with the UInt128 type
@@ -502,12 +687,13 @@ TEST(LlvmLibcUIntClassTest, UnaryPredecrement) {
}
TEST(LlvmLibcUIntClassTest, EqualsTests) {
- LL_UInt128 a1({0xffffffff00000000, 0xffff00000000ffff});
- LL_UInt128 a2({0xffffffff00000000, 0xffff00000000ffff});
- LL_UInt128 b({0xff00ff0000ff00ff, 0xf0f0f0f00f0f0f0f});
- LL_UInt128 a_reversed({0xffff00000000ffff, 0xffffffff00000000});
- LL_UInt128 a_upper(0xffff00000000ffff);
- LL_UInt128 a_lower(0xffffffff00000000);
+ auto a1 = parse_bigint<LL_UInt128>("0xffff00000000ffff'ffffffff00000000");
+ auto a2 = parse_bigint<LL_UInt128>("0xffff00000000ffff'ffffffff00000000");
+ auto b = parse_bigint<LL_UInt128>("0xf0f0f0f00f0f0f0f'ff00ff0000ff00ff");
+ auto a_reversed =
+ parse_bigint<LL_UInt128>("0xffffffff00000000'ffff00000000ffff");
+ auto a_upper = parse_bigint<LL_UInt128>("0xffff00000000ffff");
+ auto a_lower = parse_bigint<LL_UInt128>("0xffffffff00000000");
ASSERT_TRUE(a1 == a1);
ASSERT_TRUE(a1 == a2);
ASSERT_FALSE(a1 == b);
@@ -518,15 +704,15 @@ TEST(LlvmLibcUIntClassTest, EqualsTests) {
}
TEST(LlvmLibcUIntClassTest, ComparisonTests) {
- LL_UInt128 a({0xffffffff00000000, 0xffff00000000ffff});
- LL_UInt128 b({0xff00ff0000ff00ff, 0xf0f0f0f00f0f0f0f});
+ auto a = parse_bigint<LL_UInt128>("0xffff00000000ffff'ffffffff00000000");
+ auto b = parse_bigint<LL_UInt128>("0xf0f0f0f00f0f0f0f'ff00ff0000ff00ff");
EXPECT_GT(a, b);
EXPECT_GE(a, b);
EXPECT_LT(b, a);
EXPECT_LE(b, a);
- LL_UInt128 x(0xffffffff00000000);
- LL_UInt128 y(0x00000000ffffffff);
+ auto x = parse_bigint<LL_UInt128>("0xffffffff00000000");
+ auto y = parse_bigint<LL_UInt128>("0x00000000ffffffff");
EXPECT_GT(x, y);
EXPECT_GE(x, y);
EXPECT_LT(y, x);
@@ -537,20 +723,20 @@ TEST(LlvmLibcUIntClassTest, ComparisonTests) {
}
TEST(LlvmLibcUIntClassTest, FullMulTests) {
- LL_UInt128 a({0xffffffffffffffffULL, 0xffffffffffffffffULL});
- LL_UInt128 b({0xfedcba9876543210ULL, 0xfefdfcfbfaf9f8f7ULL});
- LL_UInt256 r({0x0123456789abcdf0ULL, 0x0102030405060708ULL,
- 0xfedcba987654320fULL, 0xfefdfcfbfaf9f8f7ULL});
- LL_UInt128 r_hi({0xfedcba987654320eULL, 0xfefdfcfbfaf9f8f7ULL});
+ auto a = parse_bigint<LL_UInt128>("0xffffffffffffffffffffffffffffffff");
+ auto b = parse_bigint<LL_UInt128>("0xfefdfcfbfaf9f8f7fedcba9876543210");
+ auto r1 = parse_bigint<LL_UInt128>("0xfefdfcfbfaf9f8f7fedcba987654320e");
+ auto r2 = parse_bigint<LL_UInt256>("0xfefdfcfbfaf9f8f7fedcba987654320f"
+ "01020304050607080123456789abcdf0");
- EXPECT_EQ(a.ful_mul(b), r);
- EXPECT_EQ(a.quick_mul_hi(b), r_hi);
+ EXPECT_EQ(a.quick_mul_hi(b), r1);
+ EXPECT_EQ(a.ful_mul(b), r2);
- LL_UInt192 c(
- {0x7766554433221101ULL, 0xffeeddccbbaa9988ULL, 0x1f2f3f4f5f6f7f8fULL});
- LL_UInt320 rr({0x8899aabbccddeeffULL, 0x0011223344556677ULL,
- 0x583715f4d3b29171ULL, 0xffeeddccbbaa9988ULL,
- 0x1f2f3f4f5f6f7f8fULL});
+ auto c = parse_bigint<LL_UInt192>(
+ "0x1f2f3f4f5f6f7f8fffeeddccbbaa99887766554433221101");
+ auto rr =
+ parse_bigint<LL_UInt320>("0x1f2f3f4f5f6f7f8fffeeddccbbaa9988583715f4d3b29"
+ "17100112233445566778899aabbccddeeff");
EXPECT_EQ(a.ful_mul(c), rr);
EXPECT_EQ(a.ful_mul(c), c.ful_mul(a));
@@ -561,7 +747,7 @@ TEST(LlvmLibcUIntClassTest, FullMulTests) {
LL_UInt##Bits a = ~LL_UInt##Bits(0); \
LL_UInt##Bits hi = a.quick_mul_hi(a); \
LL_UInt##Bits trunc = static_cast<LL_UInt##Bits>(a.ful_mul(a) >> Bits); \
- uint64_t overflow = trunc.sub(hi); \
+ uint64_t overflow = trunc.sub_overflow(hi); \
EXPECT_EQ(overflow, uint64_t(0)); \
EXPECT_LE(uint64_t(trunc), uint64_t(Error)); \
} while (0)
diff --git a/utils/bazel/llvm-project-overlay/libc/test/src/__support/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/test/src/__support/BUILD.bazel
index 4f976122967c4d..c0d402a89ea3ce 100644
--- a/utils/bazel/llvm-project-overlay/libc/test/src/__support/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/libc/test/src/__support/BUILD.bazel
@@ -87,6 +87,7 @@ libc_test(
srcs = ["uint_test.cpp"],
deps = [
"//libc:__support_cpp_optional",
+ "//libc:__support_integer_literals",
"//libc:__support_macros_properties_types",
"//libc:__support_uint",
"//libc:llvm_libc_macros_math_macros",
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