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+// 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,
+ }
+}