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// 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::*;
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,
}
}