// 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::*; #[cfg(not(feature = "small"))] pub use crate::d2s_full_table::*; use crate::d2s_intrinsics::*; #[cfg(feature = "small")] pub use crate::d2s_small_table::*; use core::mem::MaybeUninit; pub const DOUBLE_MANTISSA_BITS: u32 = 52; pub const DOUBLE_EXPONENT_BITS: u32 = 11; pub const DOUBLE_BIAS: i32 = 1023; pub const DOUBLE_POW5_INV_BITCOUNT: i32 = 125; pub const DOUBLE_POW5_BITCOUNT: i32 = 125; #[cfg_attr(feature = "no-panic", inline)] pub fn decimal_length17(v: u64) -> u32 { // This is slightly faster than a loop. // The average output length is 16.38 digits, so we check high-to-low. // Function precondition: v is not an 18, 19, or 20-digit number. // (17 digits are sufficient for round-tripping.) debug_assert!(v < 100000000000000000); if v >= 10000000000000000 { 17 } else if v >= 1000000000000000 { 16 } else if v >= 100000000000000 { 15 } else if v >= 10000000000000 { 14 } else if v >= 1000000000000 { 13 } else if v >= 100000000000 { 12 } else if v >= 10000000000 { 11 } else if v >= 1000000000 { 10 } else if v >= 100000000 { 9 } else if v >= 10000000 { 8 } else if v >= 1000000 { 7 } else if v >= 100000 { 6 } else if v >= 10000 { 5 } else if v >= 1000 { 4 } else if v >= 100 { 3 } else if v >= 10 { 2 } else { 1 } } // A floating decimal representing m * 10^e. pub struct FloatingDecimal64 { pub mantissa: u64, // Decimal exponent's range is -324 to 308 // inclusive, and can fit in i16 if needed. pub exponent: i32, } #[cfg_attr(feature = "no-panic", inline)] pub fn d2d(ieee_mantissa: u64, ieee_exponent: u32) -> FloatingDecimal64 { let (e2, m2) = if ieee_exponent == 0 { ( // We subtract 2 so that the bounds computation has 2 additional bits. 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS as i32 - 2, ieee_mantissa, ) } else { ( ieee_exponent as i32 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS as i32 - 2, (1u64 << DOUBLE_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; // Implicit bool -> int conversion. True is 1, false is 0. let mm_shift = (ieee_mantissa != 0 || ieee_exponent <= 1) as u32; // We would compute mp and mm like this: // uint64_t mp = 4 * m2 + 2; // uint64_t mm = mv - 1 - mm_shift; // Step 3: Convert to a decimal power base using 128-bit arithmetic. let mut vr: u64; let mut vp: u64; let mut vm: u64; let mut vp_uninit: MaybeUninit = MaybeUninit::uninit(); let mut vm_uninit: MaybeUninit = MaybeUninit::uninit(); let e10: i32; let mut vm_is_trailing_zeros = false; let mut vr_is_trailing_zeros = 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, log10_pow2(e2) - 1). let q = log10_pow2(e2) - (e2 > 3) as u32; e10 = q as i32; let k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q as i32) - 1; let i = -e2 + q as i32 + k; vr = unsafe { mul_shift_all_64( m2, #[cfg(feature = "small")] &compute_inv_pow5(q), #[cfg(not(feature = "small"))] { debug_assert!(q < DOUBLE_POW5_INV_SPLIT.len() as u32); DOUBLE_POW5_INV_SPLIT.get_unchecked(q as usize) }, i as u32, vp_uninit.as_mut_ptr(), vm_uninit.as_mut_ptr(), mm_shift, ) }; vp = unsafe { vp_uninit.assume_init() }; vm = unsafe { vm_uninit.assume_init() }; if q <= 21 { // This should use q <= 22, but I think 21 is also safe. Smaller values // may still be safe, but it's more difficult to reason about them. // Only one of mp, mv, and mm can be a multiple of 5, if any. let mv_mod5 = (mv as u32).wrapping_sub(5u32.wrapping_mul(div5(mv) as u32)); if mv_mod5 == 0 { vr_is_trailing_zeros = multiple_of_power_of_5(mv, q); } else if accept_bounds { // Same as min(e2 + (~mm & 1), pow5_factor(mm)) >= q // <=> e2 + (~mm & 1) >= q && pow5_factor(mm) >= q // <=> true && pow5_factor(mm) >= q, since e2 >= q. vm_is_trailing_zeros = multiple_of_power_of_5(mv - 1 - mm_shift as u64, q); } else { // Same as min(e2 + 1, pow5_factor(mp)) >= q. vp -= multiple_of_power_of_5(mv + 2, q) as u64; } } } else { // This expression is slightly faster than max(0, log10_pow5(-e2) - 1). let q = log10_pow5(-e2) - (-e2 > 1) as u32; e10 = q as i32 + e2; let i = -e2 - q as i32; let k = pow5bits(i) - DOUBLE_POW5_BITCOUNT; let j = q as i32 - k; vr = unsafe { mul_shift_all_64( m2, #[cfg(feature = "small")] &compute_pow5(i as u32), #[cfg(not(feature = "small"))] { debug_assert!(i < DOUBLE_POW5_SPLIT.len() as i32); DOUBLE_POW5_SPLIT.get_unchecked(i as usize) }, j as u32, vp_uninit.as_mut_ptr(), vm_uninit.as_mut_ptr(), mm_shift, ) }; vp = unsafe { vp_uninit.assume_init() }; vm = unsafe { vm_uninit.assume_init() }; 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 < 63 { // TODO(ulfjack): Use a tighter bound here. // We want to know if the full product has at least q trailing zeros. // We need to compute min(p2(mv), p5(mv) - e2) >= q // <=> p2(mv) >= q && p5(mv) - e2 >= q // <=> p2(mv) >= q (because -e2 >= q) vr_is_trailing_zeros = multiple_of_power_of_2(mv, q); } } // Step 4: Find the shortest decimal representation in the interval of valid representations. let mut removed = 0i32; let mut last_removed_digit = 0u8; // On average, we remove ~2 digits. let output = if vm_is_trailing_zeros || vr_is_trailing_zeros { // General case, which happens rarely (~0.7%). loop { let vp_div10 = div10(vp); let vm_div10 = div10(vm); if vp_div10 <= vm_div10 { break; } let vm_mod10 = (vm as u32).wrapping_sub(10u32.wrapping_mul(vm_div10 as u32)); let vr_div10 = div10(vr); let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32)); vm_is_trailing_zeros &= vm_mod10 == 0; vr_is_trailing_zeros &= last_removed_digit == 0; last_removed_digit = vr_mod10 as u8; vr = vr_div10; vp = vp_div10; vm = vm_div10; removed += 1; } if vm_is_trailing_zeros { loop { let vm_div10 = div10(vm); let vm_mod10 = (vm as u32).wrapping_sub(10u32.wrapping_mul(vm_div10 as u32)); if vm_mod10 != 0 { break; } let vp_div10 = div10(vp); let vr_div10 = div10(vr); let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32)); vr_is_trailing_zeros &= last_removed_digit == 0; last_removed_digit = vr_mod10 as u8; vr = vr_div10; vp = vp_div10; vm = vm_div10; 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 u64 } else { // Specialized for the common case (~99.3%). Percentages below are relative to this. let mut round_up = false; let vp_div100 = div100(vp); let vm_div100 = div100(vm); // Optimization: remove two digits at a time (~86.2%). if vp_div100 > vm_div100 { let vr_div100 = div100(vr); let vr_mod100 = (vr as u32).wrapping_sub(100u32.wrapping_mul(vr_div100 as u32)); round_up = vr_mod100 >= 50; vr = vr_div100; vp = vp_div100; vm = vm_div100; removed += 2; } // Loop iterations below (approximately), without optimization above: // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02% // Loop iterations below (approximately), with optimization above: // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02% loop { let vp_div10 = div10(vp); let vm_div10 = div10(vm); if vp_div10 <= vm_div10 { break; } let vr_div10 = div10(vr); let vr_mod10 = (vr as u32).wrapping_sub(10u32.wrapping_mul(vr_div10 as u32)); round_up = vr_mod10 >= 5; vr = vr_div10; vp = vp_div10; vm = vm_div10; removed += 1; } // We need to take vr + 1 if vr is outside bounds or we need to round up. vr + (vr == vm || round_up) as u64 }; let exp = e10 + removed; FloatingDecimal64 { exponent: exp, mantissa: output, } }