diff options
Diffstat (limited to 'absl/strings/internal/str_format/float_conversion.cc')
| -rw-r--r-- | absl/strings/internal/str_format/float_conversion.cc | 497 |
1 files changed, 486 insertions, 11 deletions
diff --git a/absl/strings/internal/str_format/float_conversion.cc b/absl/strings/internal/str_format/float_conversion.cc index 6176db9cb5a2..20012b5876cc 100644 --- a/absl/strings/internal/str_format/float_conversion.cc +++ b/absl/strings/internal/str_format/float_conversion.cc @@ -2,15 +2,476 @@ #include <string.h> #include <algorithm> +#include <array> #include <cassert> #include <cmath> +#include <limits> #include <string> +#include "absl/base/attributes.h" +#include "absl/base/internal/bits.h" +#include "absl/base/optimization.h" +#include "absl/meta/type_traits.h" +#include "absl/numeric/int128.h" +#include "absl/types/span.h" + namespace absl { namespace str_format_internal { namespace { +// Calculates `10 * (*v) + carry` and stores the result in `*v` and returns +// the carry. +template <typename Int> +inline Int MultiplyBy10WithCarry(Int *v, Int carry) { + using NextInt = absl::conditional_t<sizeof(Int) == 4, uint64_t, uint128>; + static_assert(sizeof(void *) >= sizeof(Int), + "Don't want to use uint128 in 32-bit mode. It is too slow."); + NextInt tmp = 10 * static_cast<NextInt>(*v) + carry; + *v = static_cast<Int>(tmp); + return static_cast<Int>(tmp >> (sizeof(Int) * 8)); +} + +// Calculates `(2^64 * carry + *v) / 10`. +// Stores the quotient in `*v` and returns the remainder. +// Requires: `0 <= carry <= 9` +inline uint64_t DivideBy10WithCarry(uint64_t *v, uint64_t carry) { + constexpr uint64_t divisor = 10; + // 2^64 / divisor = word_quotient + word_remainder / divisor + constexpr uint64_t word_quotient = (uint64_t{1} << 63) / (divisor / 2); + constexpr uint64_t word_remainder = uint64_t{} - word_quotient * divisor; + + const uint64_t mod = *v % divisor; + const uint64_t next_carry = word_remainder * carry + mod; + *v = *v / divisor + carry * word_quotient + next_carry / divisor; + return next_carry % divisor; +} + +int LeadingZeros(uint64_t v) { return base_internal::CountLeadingZeros64(v); } +int LeadingZeros(uint128 v) { + auto high = static_cast<uint64_t>(v >> 64); + auto low = static_cast<uint64_t>(v); + return high != 0 ? base_internal::CountLeadingZeros64(high) + : 64 + base_internal::CountLeadingZeros64(low); +} + +int TrailingZeros(uint64_t v) { + return base_internal::CountTrailingZerosNonZero64(v); +} +int TrailingZeros(uint128 v) { + auto high = static_cast<uint64_t>(v >> 64); + auto low = static_cast<uint64_t>(v); + return low == 0 ? 64 + base_internal::CountTrailingZerosNonZero64(high) + : base_internal::CountTrailingZerosNonZero64(low); +} + +// The buffer must have an extra digit that is known to not need rounding. +// This is done below by having an extra '0' digit on the left. +void RoundUp(char *last_digit) { + char *p = last_digit; + while (*p == '9' || *p == '.') { + if (*p == '9') *p = '0'; + --p; + } + ++*p; +} + +void RoundToEven(char *last_digit) { + char *p = last_digit; + if (*p == '.') --p; + if (*p % 2 == 1) RoundUp(p); +} + +char *PrintIntegralDigitsFromRightDynamic(uint128 v, Span<uint32_t> array, + int exp, char *p) { + if (v == 0) { + *--p = '0'; + return p; + } + + int w = exp / 32; + const int offset = exp % 32; + // Left shift v by exp bits. + array[w] = static_cast<uint32_t>(v << offset); + for (v >>= (32 - offset); v; v >>= 32) array[++w] = static_cast<uint32_t>(v); + + // While we have more than one word available, go in chunks of 1e9. + // We are guaranteed to have at least those many digits. + // `w` holds the largest populated word, so keep it updated. + while (w > 0) { + uint32_t carry = 0; + for (int i = w; i >= 0; --i) { + uint64_t tmp = uint64_t{array[i]} + (uint64_t{carry} << 32); + array[i] = tmp / uint64_t{1000000000}; + carry = tmp % uint64_t{1000000000}; + } + // If the highest word is now empty, remove it from view. + if (array[w] == 0) --w; + + for (int i = 0; i < 9; ++i, carry /= 10) { + *--p = carry % 10 + '0'; + } + } + + // Print the leftover of the last word. + for (auto last = array[0]; last != 0; last /= 10) { + *--p = last % 10 + '0'; + } + + return p; +} + +struct FractionalResult { + const char *end; + int precision; +}; + +FractionalResult PrintFractionalDigitsDynamic(uint128 v, Span<uint32_t> array, + char *p, int exp, int precision) { + int w = exp / 32; + const int offset = exp % 32; + + // Right shift `v` by `exp` bits. + array[w] = static_cast<uint32_t>(v << (32 - offset)); + v >>= offset; + // Make sure we don't overflow the array. We already calculated that non-zero + // bits fit, so we might not have space for leading zero bits. + for (int pos = w; v; v >>= 32) array[--pos] = static_cast<uint32_t>(v); + + // Multiply the whole sequence by 10. + // On each iteration, the leftover carry word is the next digit. + // `w` holds the largest populated word, so keep it updated. + for (; w >= 0 && precision > 0; --precision) { + uint32_t carry = 0; + for (int i = w; i >= 0; --i) { + carry = MultiplyBy10WithCarry(&array[i], carry); + } + // If the lowest word is now empty, remove it from view. + if (array[w] == 0) --w; + *p++ = carry + '0'; + } + + constexpr uint32_t threshold = 0x80000000; + if (array[0] < threshold) { + // We round down, so nothing to do. + } else if (array[0] > threshold || + std::any_of(&array[1], &array[w + 1], + [](uint32_t word) { return word != 0; })) { + RoundUp(p - 1); + } else { + RoundToEven(p - 1); + } + return {p, precision}; +} + +// Generic digit printer. +// `bits` determines how many bits of termporary space it needs for the +// calcualtions. +template <int bits, typename = void> +class DigitPrinter { + static constexpr int kInts = (bits + 31) / 32; + + public: + // Quick upper bound for the number of decimal digits we need. + // This would be std::ceil(std::log10(std::pow(2, bits))), but that is not + // constexpr. + static constexpr int kDigits10 = 1 + (bits + 9) / 10 * 3 + bits / 900; + using InputType = uint128; + + static char *PrintIntegralDigitsFromRight(InputType v, int exp, char *end) { + std::array<uint32_t, kInts> array{}; + return PrintIntegralDigitsFromRightDynamic(v, absl::MakeSpan(array), exp, + end); + } + + static FractionalResult PrintFractionalDigits(InputType v, char *p, int exp, + int precision) { + std::array<uint32_t, kInts> array{}; + return PrintFractionalDigitsDynamic(v, absl::MakeSpan(array), p, exp, + precision); + } +}; + +// Specialiation for 64-bit working space. +// This is a performance optimization over the generic primary template. +// Only enabled in 64-bit platforms. The generic one is faster in 32-bit +// platforms. +template <int bits> +class DigitPrinter<bits, absl::enable_if_t<bits == 64 && (sizeof(void *) >= + sizeof(uint64_t))>> { + public: + static constexpr size_t kDigits10 = 20; + using InputType = uint64_t; + + static char *PrintIntegralDigitsFromRight(uint64_t v, int exp, char *p) { + v <<= exp; + do { + *--p = DivideBy10WithCarry(&v, 0) + '0'; + } while (v != 0); + return p; + } + + static FractionalResult PrintFractionalDigits(uint64_t v, char *p, int exp, + int precision) { + v <<= (64 - exp); + while (precision > 0) { + if (!v) return {p, precision}; + *p++ = MultiplyBy10WithCarry(&v, uint64_t{}) + '0'; + --precision; + } + + // We need to round. + if (v < 0x8000000000000000) { + // We round down, so nothing to do. + } else if (v > 0x8000000000000000) { + // We round up. + RoundUp(p - 1); + } else { + RoundToEven(p - 1); + } + + assert(precision == 0); + // Precision can only be zero here. Return a constant instead. + return {p, 0}; + } +}; + +// Specialiation for 128-bit working space. +// This is a performance optimization over the generic primary template. +template <int bits> +class DigitPrinter<bits, absl::enable_if_t<bits == 128 && (sizeof(void *) >= + sizeof(uint64_t))>> { + public: + static constexpr size_t kDigits10 = 40; + using InputType = uint128; + + static char *PrintIntegralDigitsFromRight(uint128 v, int exp, char *p) { + v <<= exp; + auto high = static_cast<uint64_t>(v >> 64); + auto low = static_cast<uint64_t>(v); + + do { + uint64_t carry = DivideBy10WithCarry(&high, 0); + carry = DivideBy10WithCarry(&low, carry); + *--p = carry + '0'; + } while (high != 0u); + + while (low != 0u) { + *--p = DivideBy10WithCarry(&low, 0) + '0'; + } + return p; + } + + static FractionalResult PrintFractionalDigits(uint128 v, char *p, int exp, + int precision) { + v <<= (128 - exp); + auto high = static_cast<uint64_t>(v >> 64); + auto low = static_cast<uint64_t>(v); + + // While we have digits to print and `low` is not empty, do the long + // multiplication. + while (precision > 0 && low != 0) { + uint64_t carry = MultiplyBy10WithCarry(&low, uint64_t{}); + carry = MultiplyBy10WithCarry(&high, carry); + + *p++ = carry + '0'; + --precision; + } + + // Now `low` is empty, so use a faster approach for the rest of the digits. + // This block is pretty much the same as the main loop for the 64-bit case + // above. + while (precision > 0) { + if (!high) return {p, precision}; + *p++ = MultiplyBy10WithCarry(&high, uint64_t{}) + '0'; + --precision; + } + + // We need to round. + if (high < 0x8000000000000000) { + // We round down, so nothing to do. + } else if (high > 0x8000000000000000 || low != 0) { + // We round up. + RoundUp(p - 1); + } else { + RoundToEven(p - 1); + } + + assert(precision == 0); + // Precision can only be zero here. Return a constant instead. + return {p, 0}; + } +}; + +struct FormatState { + char sign_char; + int precision; + const ConversionSpec &conv; + FormatSinkImpl *sink; +}; + +void FinalPrint(string_view data, int trailing_zeros, + const FormatState &state) { + if (state.conv.width() < 0) { + // No width specified. Fast-path. + if (state.sign_char != '\0') state.sink->Append(1, state.sign_char); + state.sink->Append(data); + state.sink->Append(trailing_zeros, '0'); + return; + } + + int left_spaces = 0, zeros = 0, right_spaces = 0; + int total_size = (state.sign_char != 0 ? 1 : 0) + + static_cast<int>(data.size()) + trailing_zeros; + int missing_chars = std::max(state.conv.width() - total_size, 0); + if (state.conv.flags().left) { + right_spaces = missing_chars; + } else if (state.conv.flags().zero) { + zeros = missing_chars; + } else { + left_spaces = missing_chars; + } + + state.sink->Append(left_spaces, ' '); + if (state.sign_char != '\0') state.sink->Append(1, state.sign_char); + state.sink->Append(zeros, '0'); + state.sink->Append(data); + state.sink->Append(trailing_zeros, '0'); + state.sink->Append(right_spaces, ' '); +} + +template <int num_bits, typename Int> +void FormatFPositiveExp(Int v, int exp, const FormatState &state) { + using IntegralPrinter = DigitPrinter<num_bits>; + char buffer[IntegralPrinter::kDigits10 + /* . */ 1]; + buffer[IntegralPrinter::kDigits10] = '.'; + + const char *digits = IntegralPrinter::PrintIntegralDigitsFromRight( + static_cast<typename IntegralPrinter::InputType>(v), exp, + buffer + sizeof(buffer) - 1); + size_t size = buffer + sizeof(buffer) - digits; + + // In `alt` mode (flag #) we keep the `.` even if there are no fractional + // digits. In non-alt mode, we strip it. + if (ABSL_PREDICT_FALSE(state.precision == 0 && !state.conv.flags().alt)) { + --size; + } + + FinalPrint(string_view(digits, size), state.precision, state); +} + +template <int num_bits, typename Int> +void FormatFNegativeExp(Int v, int exp, const FormatState &state) { + constexpr int input_bits = sizeof(Int) * 8; + + using IntegralPrinter = DigitPrinter<input_bits>; + using FractionalPrinter = DigitPrinter<num_bits>; + + static constexpr size_t integral_size = + 1 + /* in case we need to round up an extra digit */ + IntegralPrinter::kDigits10 + 1; + char buffer[integral_size + /* . */ 1 + num_bits]; + buffer[integral_size] = '.'; + char *const integral_digits_end = buffer + integral_size; + char *integral_digits_start; + char *const fractional_digits_start = buffer + integral_size + 1; + + if (exp < input_bits) { + integral_digits_start = IntegralPrinter::PrintIntegralDigitsFromRight( + v >> exp, 0, integral_digits_end); + } else { + integral_digits_start = integral_digits_end - 1; + *integral_digits_start = '0'; + } + + // PrintFractionalDigits may pull a carried 1 all the way up through the + // integral portion. + integral_digits_start[-1] = '0'; + auto fractional_result = FractionalPrinter::PrintFractionalDigits( + static_cast<typename FractionalPrinter::InputType>(v), + fractional_digits_start, exp, state.precision); + if (integral_digits_start[-1] != '0') --integral_digits_start; + + size_t size = fractional_result.end - integral_digits_start; + + // In `alt` mode (flag #) we keep the `.` even if there are no fractional + // digits. In non-alt mode, we strip it. + if (ABSL_PREDICT_FALSE(state.precision == 0 && !state.conv.flags().alt)) { + --size; + } + FinalPrint(string_view(integral_digits_start, size), + fractional_result.precision, state); +} + +template <typename Int> +void FormatF(Int mantissa, int exp, const FormatState &state) { + // Remove trailing zeros as they are not useful. + // This helps use faster implementations/less stack space in some cases. + if (mantissa != 0) { + int trailing = TrailingZeros(mantissa); + mantissa >>= trailing; + exp += trailing; + } + + // The table driven dispatch gives us two benefits: fast distpatch and + // prevent inlining. + // We must not inline any of the functions below (other than the ones for + // 64-bit) to avoid blowing up this stack frame. + + if (exp >= 0) { + // We will left shift the mantissa. Calculate how many bits we need. + // Special case 64-bit as we will use a uint64_t for it. Use a table for the + // rest and unconditionally use uint128. + const int total_bits = sizeof(Int) * 8 - LeadingZeros(mantissa) + exp; + + if (total_bits <= 64) { + return FormatFPositiveExp<64>(mantissa, exp, state); + } else { + using Formatter = void (*)(uint128, int, const FormatState &); + static constexpr Formatter kFormatters[] = { + FormatFPositiveExp<1 << 7>, FormatFPositiveExp<1 << 8>, + FormatFPositiveExp<1 << 9>, FormatFPositiveExp<1 << 10>, + FormatFPositiveExp<1 << 11>, FormatFPositiveExp<1 << 12>, + FormatFPositiveExp<1 << 13>, FormatFPositiveExp<1 << 14>, + FormatFPositiveExp<1 << 15>, + }; + static constexpr int max_total_bits = + sizeof(Int) * 8 + std::numeric_limits<long double>::max_exponent; + assert(total_bits <= max_total_bits); + static_assert(max_total_bits <= (1 << 15), ""); + const int log2 = + 64 - LeadingZeros((static_cast<uint64_t>(total_bits) - 1) / 128); + assert(log2 < std::end(kFormatters) - std::begin(kFormatters)); + kFormatters[log2](mantissa, exp, state); + } + } else { + exp = -exp; + + // We know we don't need more than Int itself for the integral part. + // We need `precision` fractional digits, but there are at most `exp` + // non-zero digits after the decimal point. The rest will be zeros. + // Special case 64-bit as we will use a uint64_t for it. Use a table for the + // rest and unconditionally use uint128. + + if (exp <= 64) { + return FormatFNegativeExp<64>(mantissa, exp, state); + } else { + using Formatter = void (*)(uint128, int, const FormatState &); + static constexpr Formatter kFormatters[] = { + FormatFNegativeExp<1 << 7>, FormatFNegativeExp<1 << 8>, + FormatFNegativeExp<1 << 9>, FormatFNegativeExp<1 << 10>, + FormatFNegativeExp<1 << 11>, FormatFNegativeExp<1 << 12>, + FormatFNegativeExp<1 << 13>, FormatFNegativeExp<1 << 14>}; + static_assert( + -std::numeric_limits<long double>::min_exponent <= (1 << 14), ""); + const int log2 = + 64 - LeadingZeros((static_cast<uint64_t>(exp) - 1) / 128); + assert(log2 < std::end(kFormatters) - std::begin(kFormatters)); + kFormatters[log2](mantissa, exp, state); + } + } +} + char *CopyStringTo(string_view v, char *out) { std::memcpy(out, v.data(), v.size()); return out + v.size(); @@ -95,7 +556,7 @@ template <typename Float> bool ConvertNonNumericFloats(char sign_char, Float v, const ConversionSpec &conv, FormatSinkImpl *sink) { char text[4], *ptr = text; - if (sign_char) *ptr++ = sign_char; + if (sign_char != '\0') *ptr++ = sign_char; if (std::isnan(v)) { ptr = std::copy_n(conv.conv().upper() ? "NAN" : "nan", 3, ptr); } else if (std::isinf(v)) { @@ -165,7 +626,12 @@ constexpr bool CanFitMantissa() { template <typename Float> struct Decomposed { - Float mantissa; + using MantissaType = + absl::conditional_t<std::is_same<long double, Float>::value, uint128, + uint64_t>; + static_assert(std::numeric_limits<Float>::digits <= sizeof(MantissaType) * 8, + ""); + MantissaType mantissa; int exponent; }; @@ -176,7 +642,8 @@ Decomposed<Float> Decompose(Float v) { Float m = std::frexp(v, &exp); m = std::ldexp(m, std::numeric_limits<Float>::digits); exp -= std::numeric_limits<Float>::digits; - return {m, exp}; + + return {static_cast<typename Decomposed<Float>::MantissaType>(m), exp}; } // Print 'digits' as decimal. @@ -334,7 +801,7 @@ bool FloatToBuffer(Decomposed<Float> decomposed, int precision, Buffer *out, static_cast<std::uint64_t>(decomposed.exponent), precision, out, exp)) return true; -#if defined(__SIZEOF_INT128__) +#if defined(ABSL_HAVE_INTRINSIC_INT128) // If that is not enough, try with __uint128_t. return CanFitMantissa<Float, __uint128_t>() && FloatToBufferImpl<__uint128_t, Float, mode>( @@ -362,7 +829,7 @@ void WriteBufferToSink(char sign_char, string_view str, } sink->Append(left_spaces, ' '); - if (sign_char) sink->Append(1, sign_char); + if (sign_char != '\0') sink->Append(1, sign_char); sink->Append(zeros, '0'); sink->Append(str); sink->Append(right_spaces, ' '); @@ -399,12 +866,9 @@ bool FloatToSink(const Float v, const ConversionSpec &conv, switch (conv.conv().id()) { case ConversionChar::f: case ConversionChar::F: - if (!FloatToBuffer<FormatStyle::Fixed>(decomposed, precision, &buffer, - nullptr)) { - return FallbackToSnprintf(v, conv, sink); - } - if (!conv.flags().alt && buffer.back() == '.') buffer.pop_back(); - break; + FormatF(decomposed.mantissa, decomposed.exponent, + {sign_char, precision, conv, sink}); + return true; case ConversionChar::e: case ConversionChar::E: @@ -466,11 +930,22 @@ bool FloatToSink(const Float v, const ConversionSpec &conv, bool ConvertFloatImpl(long double v, const ConversionSpec &conv, FormatSinkImpl *sink) { + if (std::numeric_limits<long double>::digits == + 2 * std::numeric_limits<double>::digits) { + // This is the `double-double` representation of `long double`. + // We do not handle it natively. Fallback to snprintf. + return FallbackToSnprintf(v, conv, sink); + } + return FloatToSink(v, conv, sink); } bool ConvertFloatImpl(float v, const ConversionSpec &conv, FormatSinkImpl *sink) { + // DivideBy10WithCarry is not actually used in some builds. This here silences + // the "unused" warning. We just need to put it in any function that is really + // used. + (void)&DivideBy10WithCarry; return FloatToSink(v, conv, sink); } |