// Translated from C to Rust. The original C code can be found at // https://github.com/ulfjack/ryu and carries the following license: // // Copyright 2018 Ulf Adams // // The contents of this file may be used under the terms of the Apache License, // Version 2.0. // // (See accompanying file LICENSE-Apache or copy at // http://www.apache.org/licenses/LICENSE-2.0) // // Alternatively, the contents of this file may be used under the terms of // the Boost Software License, Version 1.0. // (See accompanying file LICENSE-Boost or copy at // https://www.boost.org/LICENSE_1_0.txt) // // Unless required by applicable law or agreed to in writing, this software // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY // KIND, either express or implied. use crate::common::*; use crate::f2s_intrinsics::*; pub const FLOAT_MANTISSA_BITS: u32 = 23; pub const FLOAT_EXPONENT_BITS: u32 = 8; const FLOAT_BIAS: i32 = 127; pub use crate::f2s_intrinsics::{FLOAT_POW5_BITCOUNT, FLOAT_POW5_INV_BITCOUNT}; // A floating decimal representing m * 10^e. pub struct FloatingDecimal32 { pub mantissa: u32, // Decimal exponent's range is -45 to 38 // inclusive, and can fit in i16 if needed. pub exponent: i32, } #[cfg_attr(feature = "no-panic", inline)] pub fn f2d(ieee_mantissa: u32, ieee_exponent: u32) -> FloatingDecimal32 { let (e2, m2) = if ieee_exponent == 0 { ( // We subtract 2 so that the bounds computation has 2 additional bits. 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS as i32 - 2, ieee_mantissa, ) } else { ( ieee_exponent as i32 - FLOAT_BIAS - FLOAT_MANTISSA_BITS as i32 - 2, (1u32 << FLOAT_MANTISSA_BITS) | ieee_mantissa, ) }; let even = (m2 & 1) == 0; let accept_bounds = even; // Step 2: Determine the interval of valid decimal representations. let mv = 4 * m2; let mp = 4 * m2 + 2; // Implicit bool -> int conversion. True is 1, false is 0. let mm_shift = (ieee_mantissa != 0 || ieee_exponent <= 1) as u32; let mm = 4 * m2 - 1 - mm_shift; // Step 3: Convert to a decimal power base using 64-bit arithmetic. let mut vr: u32; let mut vp: u32; let mut vm: u32; let e10: i32; let mut vm_is_trailing_zeros = false; let mut vr_is_trailing_zeros = false; let mut last_removed_digit = 0u8; if e2 >= 0 { let q = log10_pow2(e2); e10 = q as i32; let k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q as i32) - 1; let i = -e2 + q as i32 + k; vr = mul_pow5_inv_div_pow2(mv, q, i); vp = mul_pow5_inv_div_pow2(mp, q, i); vm = mul_pow5_inv_div_pow2(mm, q, i); if q != 0 && (vp - 1) / 10 <= vm / 10 { // We need to know one removed digit even if we are not going to loop below. We could use // q = X - 1 above, except that would require 33 bits for the result, and we've found that // 32-bit arithmetic is faster even on 64-bit machines. let l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q as i32 - 1) - 1; last_removed_digit = (mul_pow5_inv_div_pow2(mv, q - 1, -e2 + q as i32 - 1 + l) % 10) as u8; } if q <= 9 { // The largest power of 5 that fits in 24 bits is 5^10, but q <= 9 seems to be safe as well. // Only one of mp, mv, and mm can be a multiple of 5, if any. if mv % 5 == 0 { vr_is_trailing_zeros = multiple_of_power_of_5_32(mv, q); } else if accept_bounds { vm_is_trailing_zeros = multiple_of_power_of_5_32(mm, q); } else { vp -= multiple_of_power_of_5_32(mp, q) as u32; } } } else { let q = log10_pow5(-e2); e10 = q as i32 + e2; let i = -e2 - q as i32; let k = pow5bits(i) - FLOAT_POW5_BITCOUNT; let mut j = q as i32 - k; vr = mul_pow5_div_pow2(mv, i as u32, j); vp = mul_pow5_div_pow2(mp, i as u32, j); vm = mul_pow5_div_pow2(mm, i as u32, j); if q != 0 && (vp - 1) / 10 <= vm / 10 { j = q as i32 - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT); last_removed_digit = (mul_pow5_div_pow2(mv, (i + 1) as u32, j) % 10) as u8; } 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. vr_is_trailing_zeros = true; if accept_bounds { // mm = mv - 1 - mm_shift, so it has 1 trailing 0 bit iff mm_shift == 1. vm_is_trailing_zeros = mm_shift == 1; } else { // mp = mv + 2, so it always has at least one trailing 0 bit. vp -= 1; } } else if q < 31 { // TODO(ulfjack): Use a tighter bound here. vr_is_trailing_zeros = multiple_of_power_of_2_32(mv, q - 1); } } // Step 4: Find the shortest decimal representation in the interval of valid representations. let mut removed = 0i32; let output = if vm_is_trailing_zeros || vr_is_trailing_zeros { // General case, which happens rarely (~4.0%). while vp / 10 > vm / 10 { vm_is_trailing_zeros &= vm - (vm / 10) * 10 == 0; vr_is_trailing_zeros &= last_removed_digit == 0; last_removed_digit = (vr % 10) as u8; vr /= 10; vp /= 10; vm /= 10; removed += 1; } if vm_is_trailing_zeros { while vm % 10 == 0 { vr_is_trailing_zeros &= last_removed_digit == 0; last_removed_digit = (vr % 10) as u8; vr /= 10; vp /= 10; vm /= 10; removed += 1; } } if vr_is_trailing_zeros && last_removed_digit == 5 && vr % 2 == 0 { // Round even if the exact number is .....50..0. last_removed_digit = 4; } // We need to take vr + 1 if vr is outside bounds or we need to round up. vr + ((vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5) as u32 } else { // Specialized for the common case (~96.0%). Percentages below are relative to this. // Loop iterations below (approximately): // 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01% while vp / 10 > vm / 10 { last_removed_digit = (vr % 10) as u8; vr /= 10; vp /= 10; vm /= 10; removed += 1; } // We need to take vr + 1 if vr is outside bounds or we need to round up. vr + (vr == vm || last_removed_digit >= 5) as u32 }; let exp = e10 + removed; FloatingDecimal32 { exponent: exp, mantissa: output, } }