Source code
Revision control
Copy as Markdown
Other Tools
// Translated from C to Rust. The original C code can be found at
//
// 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
//
// 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
//
// 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<u64> = MaybeUninit::uninit();
let mut vm_uninit: MaybeUninit<u64> = 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,
}
}