// Copyright 2018 - 2023 Ulf Adams // Copyright 2023 Matt Borland // Distributed under the Boost Software License, Version 1.0. // https://www.boost.org/LICENSE_1_0.txt #ifndef BOOST_DECIMAL_DETAIL_RYU_RYU_GENERIC_128_HPP #define BOOST_DECIMAL_DETAIL_RYU_RYU_GENERIC_128_HPP #include #include #include #include #include #ifndef BOOST_DECIMAL_BUILD_MODULE #include #include #endif #if !defined(BOOST_DECIMAL_DISABLE_IOSTREAM) #ifdef BOOST_DECIMAL_DEBUG_RYU # include #endif #endif namespace boost { namespace decimal { namespace detail { namespace ryu { BOOST_DECIMAL_INLINE_CONSTEXPR_VARIABLE int32_t fd128_exceptional_exponent = 0x7FFFFFFF; BOOST_DECIMAL_INLINE_CONSTEXPR_VARIABLE unsigned_128_type one = 1; #ifdef _MSC_VER # pragma warning(push) # pragma warning(disable : 4324) // Structure was padded due to alignment specifier #endif // Internal use only #ifdef __GNUC__ # pragma GCC diagnostic push # pragma GCC diagnostic ignored "-Wpadded" #endif struct floating_decimal_128 { unsigned_128_type mantissa; int32_t exponent; bool sign; }; #ifdef __GNUC__ # pragma GCC diagnostic pop #endif #ifdef _MSC_VER # pragma warning(pop) #endif #ifdef BOOST_DECIMAL_DEBUG_RYU static char* s(unsigned_128_type v) { int len = num_digits(v); char* b = (char*) malloc((len + 1) * sizeof(char)); for (int i = 0; i < len; i++) { const uint32_t c = (uint32_t) (v % 10); v /= 10; b[len - 1 - i] = (char) ('0' + c); } b[len] = 0; return b; } #endif inline constexpr auto generic_binary_to_decimal( const unsigned_128_type bits, const std::uint32_t mantissaBits, const std::uint32_t exponentBits, const bool explicitLeadingBit) noexcept -> struct floating_decimal_128 { #ifdef BOOST_DECIMAL_DEBUG_RYU printf("IN="); for (int32_t bit = 127; bit >= 0; --bit) { printf("%u", (uint32_t) ((bits >> bit) & 1)); } printf("\n"); #endif const std::uint32_t local_bias = (1u << (exponentBits - 1)) - 1; const bool ieeeSign = ((bits >> (mantissaBits + exponentBits)) & 1U) != 0U; const unsigned_128_type ieeeMantissa = bits & ((one << mantissaBits) - 1U); const auto ieeeExponent = static_cast((bits >> mantissaBits) & ((one << exponentBits) - 1u)); if (ieeeExponent == 0 && ieeeMantissa == 0U) { struct floating_decimal_128 fd {0, 0, ieeeSign}; return fd; } if (ieeeExponent == ((1u << exponentBits) - 1u)) { struct floating_decimal_128 fd {}; fd.mantissa = explicitLeadingBit ? ieeeMantissa & ((one << (mantissaBits - 1)) - 1U) : ieeeMantissa; fd.exponent = fd128_exceptional_exponent; fd.sign = ieeeSign; return fd; } std::int32_t e2 {}; unsigned_128_type m2 {}; // We subtract 2 in all cases so that the bounds computation has 2 additional bits. if (explicitLeadingBit) { // mantissaBits includes the explicit leading bit, so we need to correct for that here. if (BOOST_DECIMAL_UNLIKELY(ieeeExponent == 0)) { e2 = static_cast(1 - local_bias - mantissaBits + 1 - 2); // LCOV_EXCL_LINE } else { e2 = static_cast(ieeeExponent - local_bias - mantissaBits + 1 - 2); } m2 = ieeeMantissa; } else { if (BOOST_DECIMAL_UNLIKELY(ieeeExponent == 0)) { e2 = static_cast(1 - local_bias - mantissaBits - 2); // LCOV_EXCL_LINE m2 = ieeeMantissa; // LCOV_EXCL_LINE } else { e2 = static_cast(ieeeExponent - local_bias - mantissaBits - 2U); m2 = (one << mantissaBits) | ieeeMantissa; } } const bool even = (m2 & 1U) == 0U; const bool acceptBounds = even; #ifdef BOOST_DECIMAL_DEBUG_RYU printf("-> %s %s * 2^%d\n", ieeeSign ? "-" : "+", s(m2), e2 + 2); #endif // Step 2: Determine the interval of legal decimal representations. const unsigned_128_type mv = 4U * m2; // Implicit bool -> int conversion. True is 1, false is 0. const std::uint32_t mmShift = (ieeeMantissa != (explicitLeadingBit ? one << (mantissaBits - 1) : static_cast(0))) || (ieeeExponent == 0); // Step 3: Convert to a decimal power base using 128-bit arithmetic. unsigned_128_type vr {}; unsigned_128_type vp {}; unsigned_128_type vm {}; int32_t e10 {}; bool vmIsTrailingZeros = false; bool vrIsTrailingZeros = false; if (e2 >= 0) { // I tried special-casing q == 0, but there was no effect on performance. // This expression is slightly faster than max(0, log10Pow2(e2) - 1). const std::uint32_t q = log10Pow2(e2) - (e2 > 3); e10 = static_cast(q); const std::int32_t k = BOOST_DECIMAL_POW5_INV_BITCOUNT + static_cast(pow5bits(q)) - 1; const std::int32_t i = -e2 + static_cast(q) + k; std::uint64_t pow5[4] {}; generic_computeInvPow5(q, pow5); vr = mulShift(4U * m2, pow5, static_cast(i)); vp = mulShift(4U * m2 + 2U, pow5, static_cast(i)); vm = mulShift(4U * m2 - 1U - mmShift, pow5, static_cast(i)); #ifdef BOOST_DECIMAL_DEBUG_RYU printf("%s * 2^%d / 10^%d\n", s(mv), e2, q); printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm)); #endif // floor(log_5(2^128)) = 55, this is very conservative if (q <= 55) { // Only one of mp, mv, and mm can be a multiple of 5, if any. if (mv % 5U == 0U) { vrIsTrailingZeros = multipleOfPowerOf5(mv, q - 1); } else if (acceptBounds) { // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q // <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q // <=> true && pow5Factor(mm) >= q, since e2 >= q. vmIsTrailingZeros = multipleOfPowerOf5(mv - 1U - mmShift, q); } else { // Same as min(e2 + 1, pow5Factor(mp)) >= q. vp -= multipleOfPowerOf5(mv + 2U, q); } } } else { // This expression is slightly faster than max(0, log10Pow5(-e2) - 1). const uint32_t q = log10Pow5(-e2) - static_cast(-e2 > 1); e10 = static_cast(q) + e2; const int32_t i = -e2 - static_cast(q); const int32_t k = static_cast(pow5bits(static_cast(i))) - BOOST_DECIMAL_POW5_BITCOUNT; const int32_t j = static_cast(q) - k; uint64_t pow5[4U] {}; generic_computePow5(static_cast(i), pow5); vr = mulShift(4U * m2, pow5, static_cast(j)); vp = mulShift(4U * m2 + 2U, pow5, static_cast(j)); vm = mulShift(4U * m2 - 1U - mmShift, pow5, static_cast(j)); #ifdef BOOST_DECIMAL_DEBUG_RYU printf("%s * 5^%d / 10^%d\n", s(mv), -e2, q); printf("%d %d %d %d\n", q, i, k, j); printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm)); #endif if (q <= 1) { // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits. // mv = 4 m2, so it always has at least two trailing 0 bits. vrIsTrailingZeros = true; if (acceptBounds) { // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1. vmIsTrailingZeros = mmShift == 1; } else { // mp = mv + 2, so it always has at least one trailing 0 bit. --vp; } } else if (q < 127) { // We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q-1 // <=> ntz(mv) >= q-1 && pow5Factor(mv) - e2 >= q-1 // <=> ntz(mv) >= q-1 (e2 is negative and -e2 >= q) // <=> (mv & ((1 << (q-1)) - 1)) == 0 // We also need to make sure that the left shift does not overflow. vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1); #ifdef BOOST_DECIMAL_DEBUG_RYU printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif } } #ifdef BOOST_DECIMAL_DEBUG_RYU printf("e10=%d\n", e10); printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm)); printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false"); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif // Step 4: Find the shortest decimal representation in the interval of legal representations. uint32_t removed = 0; uint8_t lastRemovedDigit = 0; unsigned_128_type output {}; while (vp / UINT64_C(10) > vm / UINT64_C(10)) { vmIsTrailingZeros &= vm % 10U == 0U; vrIsTrailingZeros &= lastRemovedDigit == 0; lastRemovedDigit = static_cast(vr % 10U); vr /= 10U; vp /= 10U; vm /= 10U; ++removed; } #ifdef BOOST_DECIMAL_DEBUG_RYU printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm)); printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false"); #endif if (vmIsTrailingZeros) { while (vm % 10U == 0U) { vrIsTrailingZeros &= lastRemovedDigit == 0; lastRemovedDigit = static_cast(vr % 10U); vr /= 10U; vp /= 10U; vm /= 10U; ++removed; } } #ifdef BOOST_DECIMAL_DEBUG_RYU printf("%s %d\n", s(vr), lastRemovedDigit); printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false"); #endif if (vrIsTrailingZeros && (lastRemovedDigit == 5) && (vr % 2U == 0U)) { // Round even if the exact numbers is .....50..0. lastRemovedDigit = 4; } // We need to take vr+1 if vr is outside bounds, or we need to round up. output = vr + static_cast((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || (lastRemovedDigit >= 5)); const auto exp = e10 + static_cast(removed); #ifdef BOOST_DECIMAL_DEBUG_RYU printf("V+=%s\nV =%s\nV-=%s\n", s(vp), s(vr), s(vm)); printf("O=%s\n", s(output)); printf("EXP=%d\n", exp); #endif return {output, exp, ieeeSign}; } template BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(T val) noexcept -> floating_decimal_128; template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(float val) noexcept -> floating_decimal_128 { static_assert(sizeof(float) == sizeof(uint32_t), "Float is not 32 bits"); auto bits = bit_cast(val); return generic_binary_to_decimal(bits, 23, 8, false); } template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(double val) noexcept -> floating_decimal_128 { static_assert(sizeof(double) == sizeof(uint64_t), "Double is not 64 bits"); auto bits = bit_cast(val); return generic_binary_to_decimal(bits, 52, 11, false); } #if BOOST_DECIMAL_LDBL_BITS == 64 template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(long double val) noexcept -> floating_decimal_128 { static_assert(sizeof(long double) == sizeof(uint64_t), "Long double is not 64 bits"); auto bits = bit_cast(val); return generic_binary_to_decimal(bits, 52, 11, false); } #elif BOOST_DECIMAL_LDBL_BITS == 80 template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(long double val) noexcept -> floating_decimal_128 { auto bits = bit_cast(val); #ifdef BOOST_DECIMAL_DEBUG_RYU // For some odd reason, this ends up with noise in the top 48 bits. We can // clear out those bits with the following line; this is not required, the // conversion routine should ignore those bits, but the debug output can be // confusing if they aren't 0s. bits &= (one << 80) - 1; #endif return generic_binary_to_decimal(bits, 64, 15, true); } #elif BOOST_DECIMAL_LDBL_BITS == 128 template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(long double val) noexcept -> floating_decimal_128 { auto bits = bit_cast(val); return generic_binary_to_decimal(bits, 112, 15, false); } #elif BOOST_DECIMAL_LDBL_BITS == 0 template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(long double val) noexcept -> floating_decimal_128 { BOOST_DECIMAL_ASSERT_MSG(1==0, "Unsupported configuration"); auto bits = bit_cast(val); return generic_binary_to_decimal(bits, 112, 15, false); } #endif #if defined(BOOST_DECIMAL_HAS_FLOAT128) && !defined(BOOST_DECIMAL_LDBL_IS_FLOAT128) template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128<__float128>(__float128 val) noexcept -> floating_decimal_128 { auto bits = bit_cast(val); return generic_binary_to_decimal(bits, 112, 15, false); } #endif // Use float as an interchange format #ifdef BOOST_DECIMAL_HAS_FLOAT16 template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(std::float16_t val) noexcept -> floating_decimal_128 { auto f = static_cast(val); static_assert(sizeof(float) == sizeof(uint32_t), "Float is not 32 bits"); auto bits = bit_cast(f); return generic_binary_to_decimal(bits, 23, 8, false); } #endif // Use float as an interchange format #ifdef BOOST_DECIMAL_HAS_BRAINFLOAT16 template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(std::bfloat16_t val) noexcept -> floating_decimal_128 { float f = static_cast(val); static_assert(sizeof(float) == sizeof(uint32_t), "Float is not 32 bits"); auto bits = bit_cast(f); return generic_binary_to_decimal(bits, 23, 8, false); } #endif #ifdef BOOST_DECIMAL_HAS_FLOAT32 template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(std::float32_t f) noexcept -> floating_decimal_128 { static_assert(sizeof(std::float32_t) == sizeof(uint32_t), "Float is not 32 bits"); auto bits = bit_cast(f); return generic_binary_to_decimal(bits, 23, 8, false); } #endif #ifdef BOOST_DECIMAL_HAS_FLOAT64 template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(std::float64_t f) noexcept -> floating_decimal_128 { static_assert(sizeof(std::float64_t) == sizeof(uint64_t), "std::float64_t is not 64 bits"); auto bits = bit_cast(f); return generic_binary_to_decimal(bits, 52, 11, false); } #endif #ifdef BOOST_DECIMAL_HAS_STDFLOAT128 template <> BOOST_DECIMAL_CXX20_CONSTEXPR auto floating_point_to_fd128(std::float128_t d) noexcept -> floating_decimal_128 { auto bits = bit_cast(d); return generic_binary_to_decimal(bits, 112, 15, false); } #endif }}}} // Namespaces #endif //BOOST_DECIMAL_RYU_GENERIC_128_HPP