1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
// 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<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,
    }
}