decmathlib-rs 0.4.0

Port of the Intel Decimal Floating-Point Math Library decimal128 type to Rust.
Documentation 
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

/* -------------------------------------------------------------------------------------------------- */
/* Port of the Intel Decimal Floating-Point Math Library decimal128 type to Rust.                     */
/* decmathlib-rs - Copyright (C) 2023-2024 Carlos Guzmán Álvarez                                      */
/* -------------------------------------------------------------------------------------------------- */
/* Licensed under the MIT license. See LICENSE file in the project root for full license information. */
/* -------------------------------------------------------------------------------------------------- */
/* Intel® Decimal Floating-Point Math Library - Copyright (c) 2018, Intel Corp.                       */
/* -------------------------------------------------------------------------------------------------- */

use crate::bid_b2d::{BID_B2D, BID_D2B};
use crate::bid_internal::{__add_128_64, __mul_128x128_high, __mul_64x128_full, __mul_64x64_to_128, __sub_128_128, BID_HIGH_128W, BID_LOW_128W, BID_UINT128, BID_UINT32, BID_UINT64};

/// Convert a 128-bit decimal floating-point value encoded in BID format
/// to the same value encoded in DPD
pub (crate) fn bid_to_dpd128(ba: &BID_UINT128) -> BID_UINT128 {
    let mut res: BID_UINT128 = Default::default();
    let mut sign: BID_UINT128 = Default::default();
    let comb: BID_UINT32;
    let exp: BID_UINT32;
    let mut trailing: BID_UINT128 = Default::default();
    let d0: BID_UINT128;
    let d1: BID_UINT128;
    let d2: BID_UINT128;
    let d3: BID_UINT128;
    let d4: BID_UINT128;
    let d5: BID_UINT128;
    let d6: BID_UINT128;
    let d7: BID_UINT128;
    let d8: BID_UINT128;
    let d9: BID_UINT128;
    let d10: BID_UINT128;
    let d11: BID_UINT128;
    let mut bcoeff: BID_UINT128 = Default::default();
    let mut dcoeff: BID_UINT128 = Default::default();
    let mut nanb: BID_UINT64 = 0;

    sign.w[1]     = ba.w[BID_HIGH_128W] & 0x8000000000000000u64;
    sign.w[0]     = 0;
    comb          = ((ba.w[BID_HIGH_128W] & 0x7fffc00000000000u64) >> 46) as BID_UINT32;
    trailing.w[1] = ba.w[BID_HIGH_128W] & 0x00003fffffffffffu64;
    trailing.w[0] = ba.w[BID_LOW_128W];
    // exp           = 0;

    if (comb & 0x1f000) == 0x1e000 {	// G0..G4 = 11110 -> Inf
        res.w[BID_HIGH_128W] = ba.w[BID_HIGH_128W] & 0xf800000000000000u64;
        res.w[BID_LOW_128W] = 0;
        return res;
        // Detect NaN, and canonicalize trailing
    } else if (comb & 0x1f000) == 0x1f000 {
        if (trailing.w[1]  > 0x0000314dc6448d93u64)        // significand is non-canonical
        || ((trailing.w[1] == 0x0000314dc6448d93u64)
         && (trailing.w[0] >= 0x38c15b0a00000000u64)) {    // significand is non-canonical
            trailing.w[1] = 0u64;
            trailing.w[0] = 0u64;
        }
        bcoeff.w[1] = trailing.w[1];
        bcoeff.w[0] = trailing.w[0];
        nanb = ba.w[BID_HIGH_128W] & 0xfe00000000000000u64;
        exp = 0;
    } else {	// Normal number
        if (comb & 0x18000) == 0x18000 {	// G0..G1 = 11 -> exp is G2..G11
            exp         = (comb >> 1) & 0x3fff;
            bcoeff.w[1] = (((8 + (comb & 1)) as u64) << 46u64) | trailing.w[1];
            bcoeff.w[0] = trailing.w[0];
        } else {
            exp         = (comb >> 3) & 0x3fff;
            bcoeff.w[1] = (((comb & 7) as u64) << 46u64) | trailing.w[1];
            bcoeff.w[0] = trailing.w[0];
        }
        // Zero the coefficient if non-canonical (>= 10^34)
        if bcoeff.w[1]  > 0x1ed09bead87c0u64
        || (bcoeff.w[1] == 0x1ed09bead87c0u64
         && bcoeff.w[0] >= 0x378D8E6400000000u64) {
            bcoeff.w[0] = 0;
            bcoeff.w[1] = 0;
        }
    }
    // Constant 2^128 / 1000 + 1
    {
        let mut t: BID_UINT128;
        let mut _t2: BID_UINT64;
        let mut d1000: BID_UINT128 = Default::default();
        let b11: BID_UINT128;
        let b10: BID_UINT128;
        let b9: BID_UINT128;
        let b8: BID_UINT128;
        let b7: BID_UINT128;
        let b6: BID_UINT128;
        let b5: BID_UINT128;
        let b4: BID_UINT128;
        let b3: BID_UINT128;
        let b2: BID_UINT128;
        let b1: BID_UINT128;

        d1000.w[1] = 0x4189374BC6A7EFu64;
        d1000.w[0] = 0x9DB22D0E56041894u64;

        b11 = __mul_128x128_high(&bcoeff, &d1000);
        b10 = __mul_128x128_high(&b11, &d1000);
        b9  = __mul_128x128_high(&b10, &d1000);
        b8  = __mul_128x128_high(&b9, &d1000);
        b7  = __mul_128x128_high(&b8, &d1000);
        b6  = __mul_128x128_high(&b7, &d1000);
        b5  = __mul_128x128_high(&b6, &d1000);
        b4  = __mul_128x128_high(&b5, &d1000);
        b3  = __mul_128x128_high(&b4, &d1000);
        b2  = __mul_128x128_high(&b3, &d1000);
        b1  = __mul_128x128_high(&b2, &d1000);

        (_t2, t) = __mul_64x128_full(1000u64, &b11);
        d11      = __sub_128_128(&bcoeff, &t);
        (_t2, t) = __mul_64x128_full(1000u64, &b10);
        d10      = __sub_128_128(&b11, &t);
        (_t2, t) = __mul_64x128_full(1000u64, &b9);
        d9       = __sub_128_128(&b10, &t);
        (_t2, t) = __mul_64x128_full(1000u64, &b8);
        d8       = __sub_128_128(&b9, &t);
        (_t2, t) = __mul_64x128_full(1000u64, &b7);
        d7       = __sub_128_128(&b8, &t);
        (_t2, t) = __mul_64x128_full(1000u64, &b6);
        d6       = __sub_128_128(&b7, &t);
        (_t2, t) = __mul_64x128_full(1000u64, &b5);
        d5       = __sub_128_128(&b6, &t);
        (_t2, t) = __mul_64x128_full(1000u64, &b4);
        d4       = __sub_128_128(&b5, &t);
        (_t2, t) = __mul_64x128_full(1000u64, &b3);
        d3       = __sub_128_128(&b4, &t);
        (_t2, t) = __mul_64x128_full(1000u64, &b2);
        d2       = __sub_128_128(&b3, &t);
        (_t2, t) = __mul_64x128_full(1000u64, &b1);
        d1       = __sub_128_128(&b2, &t);
        d0       = b1;
     }

    dcoeff.w[0] = BID_B2D[d11.w[0] as usize]
               | (BID_B2D[d10.w[0] as usize] << 10)
               | (BID_B2D[d9.w[0] as usize] << 20)
               | (BID_B2D[d8.w[0] as usize] << 30)
               | (BID_B2D[d7.w[0] as usize] << 40)
               | (BID_B2D[d6.w[0] as usize] << 50)
               | (BID_B2D[d5.w[0] as usize] << 60);
    dcoeff.w[1] = (BID_B2D[d5.w[0] as usize] >> 4)
                | (BID_B2D[d4.w[0] as usize] << 6)
                | (BID_B2D[d3.w[0] as usize] << 16)
                | (BID_B2D[d2.w[0] as usize] << 26)
                | (BID_B2D[d1.w[0] as usize] << 36);

    res.w[0] = dcoeff.w[0];
    if d0.w[0] >= 8 {
        res.w[1] = sign.w[1] | (((0x18000 | ((exp >> 12) << 13) | ((d0.w[0] & 1) << 12) as u32 | (exp & 0xfff)) as u64) << 46) | dcoeff.w[1];
    } else {
        res.w[1] = sign.w[1] | (((((exp >> 12) << 15) | (d0.w[0] << 12) as u32 | (exp & 0xfff)) as u64) << 46) | dcoeff.w[1];
    }

    res.w[1] |= nanb;

    #[cfg(target_endian = "big")]
    BID_SWAP128(&mut res);

    res
}

/// Convert a 128-bit decimal floating-point value encoded in DPD format
/// to the same value encoded in BID format
pub (crate) fn bid_dpd_to_bid128(da: &BID_UINT128) -> BID_UINT128 {
    let mut res: BID_UINT128 = Default::default();
    let mut sign: BID_UINT128 = Default::default();
    let mut exp: BID_UINT64;
    let comb: BID_UINT64;
    let mut trailing: BID_UINT128 = Default::default();
    let d0: BID_UINT64;
    let d1: BID_UINT64;
    let d2: BID_UINT64;
    let d3: BID_UINT64;
    let d4: BID_UINT64;
    let d5: BID_UINT64;
    let d6: BID_UINT64;
    let d7: BID_UINT64;
    let d8: BID_UINT64;
    let d9: BID_UINT64;
    let d10: BID_UINT64;
    let d11: BID_UINT64;
    let mut bcoeff: BID_UINT128;
    let tl: BID_UINT64;
    let th: BID_UINT64;
    let mut nanb: BID_UINT64 = 0;
    let da: BID_UINT128 = *da;

    sign.w[1]     = da.w[BID_HIGH_128W] & 0x8000000000000000u64;
    sign.w[0]     = 0;
    comb          = (da.w[BID_HIGH_128W] & 0x7fffc00000000000u64) >> 46;
    trailing.w[1] = da.w[BID_HIGH_128W] & 0x00003fffffffffffu64;
    trailing.w[0] = da.w[BID_LOW_128W];
    // exp           = 0;

    if (comb & 0x1f000) == 0x1e000 {	// G0..G4 = 11110 -> Inf
        res.w[BID_HIGH_128W] = da.w[BID_HIGH_128W] & 0xf800000000000000u64;
        res.w[BID_LOW_128W] = 0u64;
        return res;
    } else if (comb & 0x1f000) == 0x1f000 {	// G0..G4 = 11111 -> NaN
        nanb = da.w[BID_HIGH_128W] & 0xfe00000000000000u64;
        exp  = 0;
        d0   = 0;
    } else {	// Normal number
        if (comb & 0x18000) == 0x18000 {	// G0..G1 = 11 -> d0 = 8 + G4
            d0  = 8 + if (comb & 0x01000) == 0x01000 { 1 } else { 0 };
            exp = if (comb & 0x04000) == 0x04000 { 1 } else { 0 } * 0x2000
                + if (comb & 0x02000) == 0x02000 { 1 } else { 0 } * 0x1000;
            // exp leading bits are G2..G3
        } else {
            d0 = 4 * if (comb & 0x04000) == 0x04000 { 1 } else { 0 }
               + 2 * if (comb & 0x2000)  == 0x2000 { 1 } else { 0 }
               +     if (comb & 0x1000)  == 0x1000 { 1 } else { 0 };
            exp = if (comb & 0x10000) == 0x10000 { 1 } else { 0 } * 0x2000
                + if (comb & 0x08000) == 0x08000 { 1 } else { 0 } * 0x1000;
            // exp loading bits are G0..G1
        }
    }

    d11 = BID_D2B[((trailing.w[0]) & 0x3ff) as usize];
    d10 = BID_D2B[((trailing.w[0] >> 10) & 0x3ff) as usize];
    d9  = BID_D2B[((trailing.w[0] >> 20) & 0x3ff) as usize];
    d8  = BID_D2B[((trailing.w[0] >> 30) & 0x3ff) as usize];
    d7  = BID_D2B[((trailing.w[0] >> 40) & 0x3ff) as usize];
    d6  = BID_D2B[((trailing.w[0] >> 50) & 0x3ff) as usize];
    d5  = BID_D2B[((trailing.w[0] >> 60) | ((trailing.w[1] & 0x3f) << 4)) as usize];
    d4  = BID_D2B[((trailing.w[1] >> 6) & 0x3ff) as usize];
    d3  = BID_D2B[((trailing.w[1] >> 16) & 0x3ff) as usize];
    d2  = BID_D2B[((trailing.w[1] >> 26) & 0x3ff) as usize];
    d1  = BID_D2B[((trailing.w[1] >> 36) & 0x3ff) as usize];

    tl = d11 + (d10 * 1000u64)   + (d9 * 1000000u64) + (d8 * 1000000000u64)
       + (d7 * 1000000000000u64) + (d6 * 1000000000000000u64);
    th = d5  + (d4 * 1000u64)    + (d3 * 1000000u64) + (d2 * 1000000000u64)
       + (d1 * 1000000000000u64) + (d0 * 1000000000000000u64);

    bcoeff = __mul_64x64_to_128(th, 1000000000000000000u64);
    bcoeff = __add_128_64(&bcoeff, tl);

    if nanb == 0 {
        exp += comb & 0xfff;
    }

    res.w[0] = bcoeff.w[0];
    res.w[1] = (exp << 49) | sign.w[1] | bcoeff.w[1];

    res.w[1] |= nanb;

    #[cfg(target_endian = "big")]
    BID_SWAP128(&mut res);

    res
}