# mul.rs.html -- source
Source to the Rust file `C:\Users\zcdziura\.cargo\registry\src\github.com-88ac128001ac3a9a\ramp-0.2.4\src\ll\mul.rs`.
Keywords: rust, rustlang, rust-lang

      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
    301
    302
    303
    304
    305
    306
    307
    308
    309
    310
    311
    312
    313
    314
    315
    316
    317
    318
    319
    320
    321
    322
    323
    324
    325
    326
    327
    328
    329
    330
    331
    332
    333
    334
    335
    336
    337
    338
    339
    340
    341
    342
    343
    344
    345
    346
    347
    348
    349
    350
    351
    352
    353
    354
    355
    356
    357
    358
    359
    360
    361
    362
    363
    364
    365
    366
    367
    368
    369
    370
    371
    372
    373
    374
    375
    376
    377
    378
    379
    380
    381
    382
    383
    384
    385
    386
    387
    388
    389
    390
    391
    392
    393
    394
    395
    396
    397
    398
    399
    400
    401
    402
    403
    404
    405
    406
    407
    408
    409
    410
    411
    412
    413
    414
    415
    416
    417
    418
    419
    420
    421
    422
    423
    424
    425
    426
    427
    428
    429
    430
    431
    432
    433
    434
    435
    436
    437
    438
    439
    440
    441
    442
    443
    444
    445
    446
    447
    448
    449
    450
    451
    452
    453
    454
    455
    456
    457
    458
    459
    460
    461
    462
    463
    464
    465
    466
    467
    468
    469
    470
    471
    472
    473
    474
    475
    476
    477
    478
    479
    480
    481
    482
    483
    484
    485
    486
    487
    488
    489
    490
    491
    492
    493
    494
    495
    496
    497
    498
    499
    500
    501
    502
    503
    504
    505
    506
    507
    508
    509
    510
    511
    512

    // Copyright 2015 The Ramp Developers
    //
    //    Licensed under the Apache License, Version 2.0 (the "License");
    //    you may not use this file except in compliance with the License.
    //    You may obtain a copy of the License at
    //
    //        http://www.apache.org/licenses/LICENSE-2.0
    //
    //    Unless required by applicable law or agreed to in writing, software
    //    distributed under the License is distributed on an "AS IS" BASIS,
    //    WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    //    See the License for the specific language governing permissions and
    //    limitations under the License.

    #![allow(improper_ctypes)]

    use std::cmp::Ordering;

    use ll;
    use ll::limb::Limb;
    use super::{overlap, same_or_separate, same_or_incr};
    use mem;

    use ll::limb_ptr::{Limbs, LimbsMut};

    const TOOM22_THRESHOLD : i32 = 20;

    #[allow(dead_code)]
    unsafe fn mul_1_generic(mut wp: LimbsMut, mut xp: Limbs, mut n: i32, vl: Limb) -> Limb {
        let mut cl = Limb(0);
        loop {
            let xl = *xp;
            let (hpl, lpl) = xl.mul_hilo(vl);
            let (lpl, carry) = lpl.add_overflow(cl);
            cl = hpl + carry;

            *wp = lpl;

            n -= 1;
            if n == 0 { break; }

            wp = wp.offset(1);
            xp = xp.offset(1);
        }

        return cl;
    }

    /**
     * Multiplies the `n` least-significant limbs of `xp` by `vl` storing the `n` least-significant
     * limbs of the product in `{wp, n}`.
     *
     * Returns the highest limb of the product
     */
    #[cfg(not(asm))]
    #[inline]
    pub unsafe fn mul_1(wp: LimbsMut, xp: Limbs, n: i32, vl: Limb) -> Limb {
        debug_assert!(n > 0);
        debug_assert!(same_or_incr(wp, n, xp, n));

        mul_1_generic(wp, xp, n, vl)
    }

    /**
     * Multiplies the `n` least-significant limbs of `xp` by `vl` storing the `n` least-significant
     * limbs of the product in `{wp, n}`.
     *
     * Returns the highest limb of the product
     */
    #[cfg(asm)]
    #[inline]
    pub unsafe fn mul_1(mut wp: LimbsMut, xp: Limbs, n: i32, vl: Limb) -> Limb {
        debug_assert!(n > 0);
        debug_assert!(same_or_incr(wp, n, xp, n));
        extern "C" {
            fn ramp_mul_1(wp: *mut Limb, xp: *const Limb, n: i32, vl: Limb) -> Limb;
        }

        ramp_mul_1(&mut *wp, &*xp, n, vl)
    }

    #[allow(dead_code)]
    unsafe fn addmul_1_generic(mut wp: LimbsMut, mut xp: Limbs, mut n: i32, vl: Limb) -> Limb {
        debug_assert!(n > 0);
        debug_assert!(same_or_separate(wp, n, xp, n));

        let mut cl = Limb(0);
        loop {
            let xl = *xp;
            let (hpl, lpl) = xl.mul_hilo(vl);
            let (lpl, carry) = lpl.add_overflow(cl);
            cl = hpl + carry;

            let (lpl, carry) = (*wp).add_overflow(lpl);
            cl = cl + carry;

            *wp = lpl;

            n -= 1;
            if n == 0 { break; }

            wp = wp.offset(1);
            xp = xp.offset(1);
        }

        return cl;
    }

    /**
     * Multiplies the `n` least-signficiant digits of `xp` by `vl` and adds them to the `n`
     * least-significant digits of `wp`. Returns the highest limb of the result.
     */
    #[cfg(not(asm))]
    #[inline]
    pub unsafe fn addmul_1(wp: LimbsMut, xp: Limbs, n: i32, vl: Limb) -> Limb {
        addmul_1_generic(wp, xp, n, vl)
    }

    /**
     * Multiplies the `n` least-signficiant digits of `xp` by `vl` and adds them to the `n`
     * least-significant digits of `wp`. Returns the highest limb of the result.
     */
    #[cfg(asm)]
    #[inline]
    pub unsafe fn addmul_1(mut wp: LimbsMut, xp:  Limbs, n: i32, vl: Limb) -> Limb {
        extern "C" {
            fn ramp_addmul_1(wp: *mut Limb, xp: *const Limb, n: i32, vl: Limb) -> Limb;
        }

        ramp_addmul_1(&mut *wp, &*xp, n, vl)
    }

    #[allow(dead_code)]
    unsafe fn submul_1_generic(mut wp: LimbsMut, mut xp: Limbs, mut n: i32, vl: Limb) -> Limb {
        debug_assert!(n > 0);
        debug_assert!(same_or_separate(wp, n, xp, n));

        let mut cl = Limb(0);
        loop {
            let xl = *xp;
            let (hpl, lpl) = xl.mul_hilo(vl);
            let (lpl, carry) = lpl.add_overflow(cl);
            cl = hpl + carry;

            let (lpl, carry) = (*wp).sub_overflow(lpl);
            cl = cl + carry;

            *wp = lpl;

            n -= 1;
            if n == 0 { break; }

            wp = wp.offset(1);
            xp = xp.offset(1);
        }

        return cl;
    }

    /**
     * Multiplies the `n` least-signficiant digits of `xp` by `vl` and subtracts them from the `n`
     * least-significant digits of `wp`. Returns the highest limb of the result, adjust for borrow.
     */
    #[cfg(not(asm))]
    #[inline]
    pub unsafe fn submul_1(wp: LimbsMut, xp: Limbs, n: i32, vl: Limb) -> Limb {
        submul_1_generic(wp, xp, n, vl)
    }

    /**
     * Multiplies the `n` least-signficiant digits of `xp` by `vl` and subtracts them from the `n`
     * least-significant digits of `wp`. Returns the highest limb of the result, adjust for borrow.
     */
    #[cfg(asm)]
    #[inline]
    pub unsafe fn submul_1(mut wp: LimbsMut, xp: Limbs, n: i32, vl: Limb) -> Limb {
        extern "C" {
            fn ramp_submul_1(wp: *mut Limb, xp: *const Limb, n: i32, vl: Limb) -> Limb;
        }

        ramp_submul_1(&mut *wp, &*xp, n, vl)
    }

    /**
     * Multiplies `{xp, xs}` by `{yp, ys}`, storing the result to `{wp, xs + ys}`.
     *
     * `{wp, xs + ys}` must be disjoint from both inputs.
     */
    pub unsafe fn mul(wp: LimbsMut, xp: Limbs, xs: i32, yp: Limbs, ys: i32) {
        debug_assert!(xs >= ys);
        debug_assert!(ys > 0);
        debug_assert!(!overlap(wp, xs + ys, xp, xs));
        debug_assert!(!overlap(wp, xs + ys, yp, ys));

        // TODO: Pick between algorithms based on input sizes
        if ys <= TOOM22_THRESHOLD {
            mul_basecase(wp, xp, xs, yp, ys);
        } else {
            let mut tmp = mem::TmpAllocator::new();
            let scratch = tmp.allocate((xs * 2) as usize);

            // Can't use xs >= (ys * 2) because if xs is odd, some other invariants
            // in toom22 don't hold
            if (xs * 2) >= (ys * 3) {
                mul_unbalanced(wp, xp, xs, yp, ys, scratch);
            } else {
                mul_toom22(wp, xp, xs, yp, ys, scratch);
            }
        }
    }

    unsafe fn mul_basecase(mut wp: LimbsMut, xp: Limbs, xs: i32, mut yp: Limbs, mut ys: i32) {

        *wp.offset(xs as isize) = ll::mul_1(wp, xp, xs, *yp);
        wp = wp.offset(1);
        yp = yp.offset(1);
        ys -= 1;

        while ys > 0 {
            *wp.offset(xs as isize) = ll::addmul_1(wp, xp, xs, *yp);

            wp = wp.offset(1);
            yp = yp.offset(1);
            ys -= 1;
        }
    }

    // Helper fn
    #[inline(always)]
    unsafe fn mul_rec(wp: LimbsMut,
               xp: Limbs, xs: i32,
               yp: Limbs, ys: i32,
               scratch: LimbsMut) {
        if ys < TOOM22_THRESHOLD {
            mul_basecase(wp, xp, xs, yp, ys);
        } else if (xs * 2) >= (ys*3) {
            mul_unbalanced(wp, xp, xs, yp, ys, scratch);
        } else {
            mul_toom22(wp, xp, xs, yp, ys, scratch);
        }
    }

    unsafe fn mul_toom22(wp: LimbsMut,
                         xp: Limbs, xs: i32,
                         yp: Limbs, ys: i32,
                         scratch: LimbsMut) {
        // Split x into x1, x0 where x = x1*(B^n) + x0
        // Split y into y1, y0 where y = y1*(B^n) + y0
        //
        // Which means the following holds:
        //
        //    x*y = (B^2n + B^n)*z2 - (B^n)*z1 + (B^n + 1)*z0
        //        = (B^2n)*z2 + (B^n)*(z2 + z0 - z1) + z0
        //
        // Where:
        //   z0 = x0*y0
        //   z1 = (x1-x0)*(y1-y0)
        //   z2 = x1*y1
        //
        // z1 is split further into:
        //
        //  zx1 = x1-x0
        //  zy1 = y1-y0
        //
        // So z1 = zx1*zy1

        debug_assert!(xs >= ys && xs < ys*2,
                      "assertion failed: `xs >= ys && xs < ys*2` xs: {}, ys: {}", xs, ys);

        let xh = xs >> 1; // Number of high limbs in x
        let nl = xs - xh; // Number of low limbs
        let yh = ys - nl; // Number of high limbs in y

        debug_assert!(0 < xh && xh <= nl);
        debug_assert!(0 < yh && yh <= xh,
                      "assertion failed: 0 < yh && yh <= xh, xs: {}, ys: {}, xh: {}, yh: {}",
                      xs, ys, xh, yh);

        let x0 = xp; // nl limbs
        let y0 = yp; // nl limbs

        let x1 = xp.offset(nl as isize); // xh limbs
        let y1 = yp.offset(nl as isize); // yh limbs

        let zx1 = wp; // nl limbs
        let zy1 = wp.offset(nl as isize); // nl limbs
        let mut z1_neg = false; // Keep track of whether the real z1 is negative

        // Calculate zx1
        if nl == xh {
            if ll::cmp(x0, x1, nl) == Ordering::Less {
                ll::sub_n(zx1, x1, x0, nl);
                z1_neg = true;
            } else {
                ll::sub_n(zx1, x0, x1, nl);
            }
        } else { // nl > xh
            if ll::is_zero(x0.offset(xh as isize), nl-xh) && ll::cmp(x0, x1, xh) == Ordering::Less {
                ll::sub_n(zx1, x1, x0, xh);
                ll::zero(zx1.offset(xh as isize), nl-xh); // Zero the extra limbs
                z1_neg = true;
            } else {
                ll::sub(zx1, x0, nl, x1, xh);
            }
        }

        // Calculate zy1
        if nl == yh {
            if ll::cmp(y0, y1, nl) == Ordering::Less {
                ll::sub_n(zy1, y1, y0, nl);
                z1_neg = !z1_neg;
            } else {
                ll::sub_n(zy1, y0, y1, nl);
            }
        } else { // nl > yh
            if ll::is_zero(y0.offset(yh as isize), nl-yh) && ll::cmp(y0, y1, yh) == Ordering::Less {
                ll::sub_n(zy1, y1, y0, yh);
                ll::zero(zy1.offset(yh as isize), nl-yh); // Zero the extra limbs
                z1_neg = !z1_neg;
            } else {
                ll::sub(zy1, y0, nl, y1, yh);
            }
        }

        let z0 = wp;
        let z1 = scratch;
        let z2 = wp.offset((nl * 2) as isize);
        let scratch_out = scratch.offset((nl * 2) as isize);

        // Calculate z1 - 2*nl limbs
        mul_rec(z1, zx1.as_const(), nl, zy1.as_const(), nl, scratch_out);

        // Calculate z0 - 2*nl limbs
        mul_rec(z0, x0, nl, y0, nl, scratch_out);

        // Calculate z2 - xh+yh limbs
        mul_rec(z2, x1, xh, y1, yh, scratch_out);

        // Now {wp, 2*nl} = z0 and {wp + 2*nl, xh+yh} = z2

        // {wp + nl, 2*nl} += z0 + z2 - z1
        //                 += {wp, 2*nl}
        //                  + {wp + 2*nl, xh+yh}
        //                  - z1
        //
        // So with {wp, xs+ys}:
        //
        // 0        nl      2*nl        xs+ys
        // +--------+--------+--------+---+
        // |       z0        |     z2     |
        // +--------+--------+--------+---+
        //   +      |        z0       |
        //          +--------+---+----+
        //   +      |       z2   |
        //          +------------+
        //
        // {wp + nl, nl} = HIGH(z0) + LOW(z0) + LOW(z2)
        // {wp + 2*nl, nl} = HIGH(z0) + HIGH(z2) + LOW(z2) + carry

        // LOW(z2) = HIGH(z0) + LOW(z2)
        let cy = ll::add_n(wp.offset((2*nl) as isize),
                           z2.as_const(), z0.offset(nl as isize).as_const(),
                           nl);

        // LOW(z0) + LOW(z2)
        let cy2 = cy + ll::add_n(wp.offset(nl as isize),
                                 z0.as_const(), z2.as_const(),
                                 nl);

        // LOW(z2) + HIGH(z2)
        let mut cy = cy + ll::add(wp.offset((2*nl) as isize),
                                  z2.as_const(), nl,
                                  z2.offset(nl as isize).as_const(), yh+xh-nl);

        // Add or subtract `z1` depending on the sign of the real result
        // (we calculate such that it's always positive, easier this way)
        if z1_neg {
            cy = cy + ll::add_n(wp.offset(nl as isize),
                                wp.offset(nl as isize).as_const(), z1.as_const(),
                                2*nl);
        } else {
            cy = cy - ll::sub_n(wp.offset(nl as isize),
                                wp.offset(nl as isize).as_const(), z1.as_const(),
                                2*nl);
        }

        // Apply the carries, has to be done last.
        ll::incr(wp.offset((nl * 2) as isize), cy2);
        ll::incr(wp.offset((nl * 3) as isize), cy);
    }

    /**
     * Handles multiplication when xs is much bigger than ys.
     *
     * Works basically the same way `mul_1` does, except with `ys` limbs
     * instead of a single limb.
     */
    unsafe fn mul_unbalanced(mut wp: LimbsMut,
                             mut xp: Limbs, mut xs: i32,
                             yp: Limbs, ys: i32,
                             scratch: LimbsMut) {
        debug_assert!(xs  > ys);

        mul_toom22(wp, xp, ys, yp, ys, scratch);

        xs -= ys;
        xp = xp.offset(ys as isize);
        wp = wp.offset(ys as isize);

        // Temporary storage for the output of the multiplication
        // in the loop, the loop only needs ys*2 limbs, but the last
        // multiplication needs slightly more than that, but no more
        // than ys*3
        let mut tmp = mem::TmpAllocator::new();
        let w_tmp = tmp.allocate((ys * 3) as usize);

        while xs >= (ys * 2) {
            mul_toom22(w_tmp, xp, ys, yp, ys, scratch);
            xs -= ys;
            xp = xp.offset(ys as isize);
            let cy = ll::add_n(wp, wp.as_const(), w_tmp.as_const(), ys);
            ll::copy_incr(w_tmp.offset(ys as isize).as_const(),
                          wp.offset(ys as isize),
                          ys);
            ll::incr(wp.offset(ys as isize), cy);

            wp = wp.offset(ys as isize);
        }

        if xs >= ys {
            mul_rec(w_tmp, xp, xs, yp, ys, scratch);
        } else {
            mul_rec(w_tmp, yp, ys, xp, xs, scratch);
        }

        let cy = ll::add_n(wp, wp.as_const(), w_tmp.as_const(), ys);
        ll::copy_incr(w_tmp.offset(ys as isize).as_const(),
                      wp.offset(ys as isize),
                      xs);
        ll::incr(wp.offset(ys as isize), cy);
    }

    /**
     * Squares the number in `{xp, xs}` storing the result in `{wp, xs*2}`.
     * This is slightly more efficient than regular multiplication with both
     * inputs the same.
     *
     * `{wp, xs*2}` must not overlap with `{xp, xs}`
     */
    pub unsafe fn sqr(wp: LimbsMut, xp: Limbs, xs: i32) {
        debug_assert!(xs > 0);
        debug_assert!(!overlap(wp, 2*xs, xp, xs));

        if xs <= TOOM22_THRESHOLD {
            mul_basecase(wp, xp, xs, xp, xs);
        } else {
            let mut tmp = mem::TmpAllocator::new();
            let scratch = tmp.allocate((xs * 2) as usize);

            sqr_toom2(wp, xp, xs, scratch);
        }
    }

    #[inline(always)]
    unsafe fn sqr_rec(wp: LimbsMut, xp: Limbs, xs: i32, scratch: LimbsMut) {
        if xs < TOOM22_THRESHOLD {
            mul_basecase(wp, xp, xs, xp, xs);
        } else {
            sqr_toom2(wp, xp, xs, scratch);
        }
    }

    unsafe fn sqr_toom2(wp: LimbsMut, xp: Limbs, xs: i32, scratch: LimbsMut) {
        // This is very similar to regular mul_toom22, however it is slightly more efficient
        // as it can take advantage of the coefficents being the same.
        //
        // Splitting x into x1, x0 to get x = x1*(B^n) + x0 means we get
        //
        //    x*x = (B^2n)*z2 + 2*(B^n)*z1 + z0
        //
        // Where:
        //   z0 = x0*x0
        //   z1 = x0*x1
        //   z2 = x1*x1

        let xh = xs >> 1;
        let xl = xs - xh;

        let x0 = xp;
        let x1 = xp.offset(xl as isize);

        let z0 = wp;
        let z1 = scratch;
        let z2 = wp.offset((xl * 2) as isize);
        let scratch_out = scratch.offset((xl * 2) as isize);

        // Calculate z1
        mul_rec(z1, x0, xl, x1, xh, scratch_out);
        // Calculate z0
        sqr_rec(z0, x0, xl, scratch_out);
        // Calculate z2
        sqr_rec(z2, x1, xh, scratch_out);

        // Calculate 2*z1
        let mut cy = ll::add_n(z1, z1.as_const(), z1.as_const(), xs);

        // wp now contains the result of (B^2n)*z2 + z0

        cy = cy + ll::add_n(wp.offset(xl as isize), wp.offset(xl as isize).as_const(), z1.as_const(), xs);

        ll::incr(wp.offset((xl + xs) as isize), cy);
    }

# Help

## Keyboard Shortcuts

?
  Show this help dialog
S
  Focus the search field
⇤
  Move up in search results
⇥
  Move down in search results
⏎
  Go to active search result

## Search Tricks

Prefix searches with a type followed by a colon (e.g. `fn:`) to restrict the search to a given type.

Accepted types are: `fn`, `mod`, `struct`, `enum`, `trait`, `type`, `macro`, and `const`.

Search functions by type signature (e.g. `vec -> usize` or `* -> vec`)