diff --git a/include/fast_float/dragonbox.h b/include/fast_float/dragonbox.h new file mode 100644 index 0000000..27e665b --- /dev/null +++ b/include/fast_float/dragonbox.h @@ -0,0 +1,208 @@ +#ifndef DRAGONBOX_H +#define DRAGONBOX_H + +#include + +/** + * Our objective is to integrate a fast binary to decimal converter which relies + * on our precomputed constants. + */ + +namespace fast_float { +// credit: https://github.com/jk-jeon/dragonbox +// credit: https://github.com/fmtlib/fmt/blob/012cc709d0abb0a963591413a746b988168e5e3a/include/fmt/format-inl.h +namespace dragonbox { + + + +// The main algorithm for shorter interval case +template +FMT_INLINE decimal_fp shorter_interval_case(int exponent) FMT_NOEXCEPT { + decimal_fp ret_value; + // Compute k and beta + const int minus_k = floor_log10_pow2_minus_log10_4_over_3(exponent); + const int beta_minus_1 = exponent + floor_log2_pow10(-minus_k); + + // Compute xi and zi + using cache_entry_type = typename cache_accessor::cache_entry_type; + const cache_entry_type cache = cache_accessor::get_cached_power(-minus_k); + + auto xi = cache_accessor::compute_left_endpoint_for_shorter_interval_case( + cache, beta_minus_1); + auto zi = cache_accessor::compute_right_endpoint_for_shorter_interval_case( + cache, beta_minus_1); + + // If the left endpoint is not an integer, increase it + if (!is_left_endpoint_integer_shorter_interval(exponent)) ++xi; + + // Try bigger divisor + ret_value.significand = zi / 10; + + // If succeed, remove trailing zeros if necessary and return + if (ret_value.significand * 10 >= xi) { + ret_value.exponent = minus_k + 1; + ret_value.exponent += remove_trailing_zeros(ret_value.significand); + return ret_value; + } + + // Otherwise, compute the round-up of y + ret_value.significand = + cache_accessor::compute_round_up_for_shorter_interval_case( + cache, beta_minus_1); + ret_value.exponent = minus_k; + + // When tie occurs, choose one of them according to the rule + if (exponent >= float_info::shorter_interval_tie_lower_threshold && + exponent <= float_info::shorter_interval_tie_upper_threshold) { + ret_value.significand = ret_value.significand % 2 == 0 + ? ret_value.significand + : ret_value.significand - 1; + } else if (ret_value.significand < xi) { + ++ret_value.significand; + } + return ret_value; +} + + + +/** + * This is the main function. + */ +template decimal_fp to_decimal(T x) noexcept { + // Step 1: integer promotion & Schubfach multiplier calculation. + + using carrier_uint = typename float_info::carrier_uint; + using cache_entry_type = typename cache_accessor::cache_entry_type; + auto br = bit_cast(x); + + // Extract significand bits and exponent bits. + const carrier_uint significand_mask = + (static_cast(1) << float_info::significand_bits) - 1; + carrier_uint significand = (br & significand_mask); + int exponent = static_cast((br & exponent_mask()) >> + float_info::significand_bits); + + if (exponent != 0) { // Check if normal. + exponent += float_info::exponent_bias - float_info::significand_bits; + + // Shorter interval case; proceed like Schubfach. + if (significand == 0) return shorter_interval_case(exponent); + + significand |= + (static_cast(1) << float_info::significand_bits); + } else { + // Subnormal case; the interval is always regular. + if (significand == 0) return {0, 0}; + exponent = float_info::min_exponent - float_info::significand_bits; + } + + const bool include_left_endpoint = (significand % 2 == 0); + const bool include_right_endpoint = include_left_endpoint; + + // Compute k and beta. + const int minus_k = floor_log10_pow2(exponent) - float_info::kappa; + const cache_entry_type cache = cache_accessor::get_cached_power(-minus_k); + const int beta_minus_1 = exponent + floor_log2_pow10(-minus_k); + + // Compute zi and deltai + // 10^kappa <= deltai < 10^(kappa + 1) + const uint32_t deltai = cache_accessor::compute_delta(cache, beta_minus_1); + const carrier_uint two_fc = significand << 1; + const carrier_uint two_fr = two_fc | 1; + const carrier_uint zi = + cache_accessor::compute_mul(two_fr << beta_minus_1, cache); + + // Step 2: Try larger divisor; remove trailing zeros if necessary + + // Using an upper bound on zi, we might be able to optimize the division + // better than the compiler; we are computing zi / big_divisor here + decimal_fp ret_value; + ret_value.significand = divide_by_10_to_kappa_plus_1(zi); + uint32_t r = static_cast(zi - float_info::big_divisor * + ret_value.significand); + + if (r > deltai) { + goto small_divisor_case_label; + } else if (r < deltai) { + // Exclude the right endpoint if necessary + if (r == 0 && !include_right_endpoint && + is_endpoint_integer(two_fr, exponent, minus_k)) { + --ret_value.significand; + r = float_info::big_divisor; + goto small_divisor_case_label; + } + } else { + // r == deltai; compare fractional parts + // Check conditions in the order different from the paper + // to take advantage of short-circuiting + const carrier_uint two_fl = two_fc - 1; + if ((!include_left_endpoint || + !is_endpoint_integer(two_fl, exponent, minus_k)) && + !cache_accessor::compute_mul_parity(two_fl, cache, beta_minus_1)) { + goto small_divisor_case_label; + } + } + ret_value.exponent = minus_k + float_info::kappa + 1; + + // We may need to remove trailing zeros + ret_value.exponent += remove_trailing_zeros(ret_value.significand); + return ret_value; + + // Step 3: Find the significand with the smaller divisor + +small_divisor_case_label: + ret_value.significand *= 10; + ret_value.exponent = minus_k + float_info::kappa; + + const uint32_t mask = (1u << float_info::kappa) - 1; + auto dist = r - (deltai / 2) + (float_info::small_divisor / 2); + + // Is dist divisible by 2^kappa? + if ((dist & mask) == 0) { + const bool approx_y_parity = + ((dist ^ (float_info::small_divisor / 2)) & 1) != 0; + dist >>= float_info::kappa; + + // Is dist divisible by 5^kappa? + if (check_divisibility_and_divide_by_pow5::kappa>(dist)) { + ret_value.significand += dist; + + // Check z^(f) >= epsilon^(f) + // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, + // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f) + // Since there are only 2 possibilities, we only need to care about the + // parity. Also, zi and r should have the same parity since the divisor + // is an even number + if (cache_accessor::compute_mul_parity(two_fc, cache, beta_minus_1) != + approx_y_parity) { + --ret_value.significand; + } else { + // If z^(f) >= epsilon^(f), we might have a tie + // when z^(f) == epsilon^(f), or equivalently, when y is an integer + if (is_center_integer(two_fc, exponent, minus_k)) { + ret_value.significand = ret_value.significand % 2 == 0 + ? ret_value.significand + : ret_value.significand - 1; + } + } + } + // Is dist not divisible by 5^kappa? + else { + ret_value.significand += dist; + } + } + // Is dist not divisible by 2^kappa? + else { + // Since we know dist is small, we might be able to optimize the division + // better than the compiler; we are computing dist / small_divisor here + ret_value.significand += + small_division_by_pow10::kappa>(dist); + } + return ret_value; +} + +} +} // fast_float + + +#endif