1use core::arch::x86_64::*;
  2
  3// The following AVX2 implementation has been copied from plonky2:
  4// https://github.com/0xPolygonZero/plonky2/blob/main/plonky2/src/hash/arch/x86_64/poseidon_goldilocks_avx2_bmi2.rs
  5
  6// Preliminary notes:
  7// 1. AVX does not support addition with carry but 128-bit (2-word) addition can be easily emulated.
  8//    The method recognizes that for a + b overflowed iff (a + b) < a: i. res_lo = a_lo + b_lo ii.
  9//    carry_mask = res_lo < a_lo iii. res_hi = a_hi + b_hi - carry_mask Notice that carry_mask is
 10//    subtracted, not added. This is because AVX comparison instructions return -1 (all bits 1) for
 11//    true and 0 for false.
 12//
 13// 2. AVX does not have unsigned 64-bit comparisons. Those can be emulated with signed comparisons
 14//    by recognizing that a <u b iff a + (1 << 63) <s b + (1 << 63), where the addition wraps around
 15//    and the comparisons are unsigned and signed respectively. The shift function adds/subtracts 1
 16//    << 63 to enable this trick. Example: addition with carry. i. a_lo_s = shift(a_lo) ii. res_lo_s
 17//    = a_lo_s + b_lo iii. carry_mask = res_lo_s <s a_lo_s iv. res_lo = shift(res_lo_s) v. res_hi =
 18//    a_hi + b_hi - carry_mask The suffix _s denotes a value that has been shifted by 1 << 63. The
 19//    result of addition is shifted if exactly one of the operands is shifted, as is the case on
 20//    line ii. Line iii. performs a signed comparison res_lo_s <s a_lo_s on shifted values to
 21//    emulate unsigned comparison res_lo <u a_lo on unshifted values. Finally, line iv. reverses the
 22//    shift so the result can be returned. When performing a chain of calculations, we can often
 23//    save instructions by letting the shift propagate through and only undoing it when necessary.
 24//    For example, to compute the addition of three two-word (128-bit) numbers we can do: i. a_lo_s
 25//    = shift(a_lo) ii. tmp_lo_s = a_lo_s + b_lo iii. tmp_carry_mask = tmp_lo_s <s a_lo_s iv. tmp_hi
 26//    = a_hi + b_hi - tmp_carry_mask v. res_lo_s = tmp_lo_s + c_lo vi. res_carry_mask = res_lo_s <s
 27//    tmp_lo_s vii. res_lo = shift(res_lo_s) viii. res_hi = tmp_hi + c_hi - res_carry_mask Notice
 28//    that the above 3-value addition still only requires two calls to shift, just like our 2-value
 29//    addition.
 30
 31#[inline(always)]
 32pub fn branch_hint() {
 33    // NOTE: These are the currently supported assembly architectures. See the
 34    // [nightly reference](https://doc.rust-lang.org/nightly/reference/inline-assembly.html) for
 35    // the most up-to-date list.
 36    #[cfg(any(
 37        target_arch = "aarch64",
 38        target_arch = "arm",
 39        target_arch = "riscv32",
 40        target_arch = "riscv64",
 41        target_arch = "x86",
 42        target_arch = "x86_64",
 43    ))]
 44    unsafe {
 45        core::arch::asm!("", options(nomem, nostack, preserves_flags));
 46    }
 47}
 48
 49macro_rules! map3 {
 50    ($f:ident:: < $l:literal > , $v:ident) => {
 51        ($f::<$l>($v.0), $f::<$l>($v.1), $f::<$l>($v.2))
 52    };
 53    ($f:ident:: < $l:literal > , $v1:ident, $v2:ident) => {
 54        ($f::<$l>($v1.0, $v2.0), $f::<$l>($v1.1, $v2.1), $f::<$l>($v1.2, $v2.2))
 55    };
 56    ($f:ident, $v:ident) => {
 57        ($f($v.0), $f($v.1), $f($v.2))
 58    };
 59    ($f:ident, $v0:ident, $v1:ident) => {
 60        ($f($v0.0, $v1.0), $f($v0.1, $v1.1), $f($v0.2, $v1.2))
 61    };
 62    ($f:ident,rep $v0:ident, $v1:ident) => {
 63        ($f($v0, $v1.0), $f($v0, $v1.1), $f($v0, $v1.2))
 64    };
 65
 66    ($f:ident, $v0:ident,rep $v1:ident) => {
 67        ($f($v0.0, $v1), $f($v0.1, $v1), $f($v0.2, $v1))
 68    };
 69}
 70
 71#[inline(always)]
 72unsafe fn square3(
 73    x: (__m256i, __m256i, __m256i),
 74) -> ((__m256i, __m256i, __m256i), (__m256i, __m256i, __m256i)) {
 75    let x_hi = {
 76        // Move high bits to low position. The high bits of x_hi are ignored. Swizzle is faster than
 77        // bitshift. This instruction only has a floating-point flavor, so we cast to/from float.
 78        // This is safe and free.
 79        let x_ps = map3!(_mm256_castsi256_ps, x);
 80        let x_hi_ps = map3!(_mm256_movehdup_ps, x_ps);
 81        map3!(_mm256_castps_si256, x_hi_ps)
 82    };
 83
 84    // All pairwise multiplications.
 85    let mul_ll = map3!(_mm256_mul_epu32, x, x);
 86    let mul_lh = map3!(_mm256_mul_epu32, x, x_hi);
 87    let mul_hh = map3!(_mm256_mul_epu32, x_hi, x_hi);
 88
 89    // Bignum addition, but mul_lh is shifted by 33 bits (not 32).
 90    let mul_ll_hi = map3!(_mm256_srli_epi64::<33>, mul_ll);
 91    let t0 = map3!(_mm256_add_epi64, mul_lh, mul_ll_hi);
 92    let t0_hi = map3!(_mm256_srli_epi64::<31>, t0);
 93    let res_hi = map3!(_mm256_add_epi64, mul_hh, t0_hi);
 94
 95    // Form low result by adding the mul_ll and the low 31 bits of mul_lh (shifted to the high
 96    // position).
 97    let mul_lh_lo = map3!(_mm256_slli_epi64::<33>, mul_lh);
 98    let res_lo = map3!(_mm256_add_epi64, mul_ll, mul_lh_lo);
 99
100    (res_lo, res_hi)
101}
102
103#[inline(always)]
104unsafe fn mul3(
105    x: (__m256i, __m256i, __m256i),
106    y: (__m256i, __m256i, __m256i),
107) -> ((__m256i, __m256i, __m256i), (__m256i, __m256i, __m256i)) {
108    let epsilon = _mm256_set1_epi64x(0xffffffff);
109    let x_hi = {
110        // Move high bits to low position. The high bits of x_hi are ignored. Swizzle is faster than
111        // bitshift. This instruction only has a floating-point flavor, so we cast to/from float.
112        // This is safe and free.
113        let x_ps = map3!(_mm256_castsi256_ps, x);
114        let x_hi_ps = map3!(_mm256_movehdup_ps, x_ps);
115        map3!(_mm256_castps_si256, x_hi_ps)
116    };
117    let y_hi = {
118        let y_ps = map3!(_mm256_castsi256_ps, y);
119        let y_hi_ps = map3!(_mm256_movehdup_ps, y_ps);
120        map3!(_mm256_castps_si256, y_hi_ps)
121    };
122
123    // All four pairwise multiplications
124    let mul_ll = map3!(_mm256_mul_epu32, x, y);
125    let mul_lh = map3!(_mm256_mul_epu32, x, y_hi);
126    let mul_hl = map3!(_mm256_mul_epu32, x_hi, y);
127    let mul_hh = map3!(_mm256_mul_epu32, x_hi, y_hi);
128
129    // Bignum addition
130    // Extract high 32 bits of mul_ll and add to mul_hl. This cannot overflow.
131    let mul_ll_hi = map3!(_mm256_srli_epi64::<32>, mul_ll);
132    let t0 = map3!(_mm256_add_epi64, mul_hl, mul_ll_hi);
133    // Extract low 32 bits of t0 and add to mul_lh. Again, this cannot overflow.
134    // Also, extract high 32 bits of t0 and add to mul_hh.
135    let t0_lo = map3!(_mm256_and_si256, t0, rep epsilon);
136    let t0_hi = map3!(_mm256_srli_epi64::<32>, t0);
137    let t1 = map3!(_mm256_add_epi64, mul_lh, t0_lo);
138    let t2 = map3!(_mm256_add_epi64, mul_hh, t0_hi);
139    // Lastly, extract the high 32 bits of t1 and add to t2.
140    let t1_hi = map3!(_mm256_srli_epi64::<32>, t1);
141    let res_hi = map3!(_mm256_add_epi64, t2, t1_hi);
142
143    // Form res_lo by combining the low half of mul_ll with the low half of t1 (shifted into high
144    // position).
145    let t1_lo = {
146        let t1_ps = map3!(_mm256_castsi256_ps, t1);
147        let t1_lo_ps = map3!(_mm256_moveldup_ps, t1_ps);
148        map3!(_mm256_castps_si256, t1_lo_ps)
149    };
150    let res_lo = map3!(_mm256_blend_epi32::<0xaa>, mul_ll, t1_lo);
151
152    (res_lo, res_hi)
153}
154
155/// Addition, where the second operand is `0 <= y < 0xffffffff00000001`.
156#[inline(always)]
157unsafe fn add_small(
158    x_s: (__m256i, __m256i, __m256i),
159    y: (__m256i, __m256i, __m256i),
160) -> (__m256i, __m256i, __m256i) {
161    let res_wrapped_s = map3!(_mm256_add_epi64, x_s, y);
162    let mask = map3!(_mm256_cmpgt_epi32, x_s, res_wrapped_s);
163    let wrapback_amt = map3!(_mm256_srli_epi64::<32>, mask); // EPSILON if overflowed else 0.
164    let res_s = map3!(_mm256_add_epi64, res_wrapped_s, wrapback_amt);
165    res_s
166}
167
168#[inline(always)]
169unsafe fn maybe_adj_sub(res_wrapped_s: __m256i, mask: __m256i) -> __m256i {
170    // The subtraction is very unlikely to overflow so we're best off branching.
171    // The even u32s in `mask` are meaningless, so we want to ignore them. `_mm256_testz_pd`
172    // branches depending on the sign bit of double-precision (64-bit) floats. Bit cast `mask` to
173    // floating-point (this is free).
174    let mask_pd = _mm256_castsi256_pd(mask);
175    // `_mm256_testz_pd(mask_pd, mask_pd) == 1` iff all sign bits are 0, meaning that underflow
176    // did not occur for any of the vector elements.
177    if _mm256_testz_pd(mask_pd, mask_pd) == 1 {
178        res_wrapped_s
179    } else {
180        branch_hint();
181        // Highly unlikely: underflow did occur. Find adjustment per element and apply it.
182        let adj_amount = _mm256_srli_epi64::<32>(mask); // EPSILON if underflow.
183        _mm256_sub_epi64(res_wrapped_s, adj_amount)
184    }
185}
186
187/// Addition, where the second operand is much smaller than `0xffffffff00000001`.
188#[inline(always)]
189unsafe fn sub_tiny(
190    x_s: (__m256i, __m256i, __m256i),
191    y: (__m256i, __m256i, __m256i),
192) -> (__m256i, __m256i, __m256i) {
193    let res_wrapped_s = map3!(_mm256_sub_epi64, x_s, y);
194    let mask = map3!(_mm256_cmpgt_epi32, res_wrapped_s, x_s);
195    let res_s = map3!(maybe_adj_sub, res_wrapped_s, mask);
196    res_s
197}
198
199#[inline(always)]
200unsafe fn reduce3(
201    (lo0, hi0): ((__m256i, __m256i, __m256i), (__m256i, __m256i, __m256i)),
202) -> (__m256i, __m256i, __m256i) {
203    let sign_bit = _mm256_set1_epi64x(i64::MIN);
204    let epsilon = _mm256_set1_epi64x(0xffffffff);
205    let lo0_s = map3!(_mm256_xor_si256, lo0, rep sign_bit);
206    let hi_hi0 = map3!(_mm256_srli_epi64::<32>, hi0);
207    let lo1_s = sub_tiny(lo0_s, hi_hi0);
208    let t1 = map3!(_mm256_mul_epu32, hi0, rep epsilon);
209    let lo2_s = add_small(lo1_s, t1);
210    let lo2 = map3!(_mm256_xor_si256, lo2_s, rep sign_bit);
211    lo2
212}
213
214#[inline(always)]
215unsafe fn mul_reduce(
216    a: (__m256i, __m256i, __m256i),
217    b: (__m256i, __m256i, __m256i),
218) -> (__m256i, __m256i, __m256i) {
219    reduce3(mul3(a, b))
220}
221
222#[inline(always)]
223unsafe fn square_reduce(state: (__m256i, __m256i, __m256i)) -> (__m256i, __m256i, __m256i) {
224    reduce3(square3(state))
225}
226
227#[inline(always)]
228unsafe fn exp_acc(
229    high: (__m256i, __m256i, __m256i),
230    low: (__m256i, __m256i, __m256i),
231    exp: usize,
232) -> (__m256i, __m256i, __m256i) {
233    let mut result = high;
234    for _ in 0..exp {
235        result = square_reduce(result);
236    }
237    mul_reduce(result, low)
238}
239
240#[inline(always)]
241unsafe fn do_apply_sbox(state: (__m256i, __m256i, __m256i)) -> (__m256i, __m256i, __m256i) {
242    let state2 = square_reduce(state);
243    let state4_unreduced = square3(state2);
244    let state3_unreduced = mul3(state2, state);
245    let state4 = reduce3(state4_unreduced);
246    let state3 = reduce3(state3_unreduced);
247    let state7_unreduced = mul3(state3, state4);
248    let state7 = reduce3(state7_unreduced);
249    state7
250}
251
252#[inline(always)]
253unsafe fn do_apply_inv_sbox(state: (__m256i, __m256i, __m256i)) -> (__m256i, __m256i, __m256i) {
254    // compute base^10540996611094048183 using 72 multiplications per array element
255    // 10540996611094048183 = b1001001001001001001001001001000110110110110110110110110110110111
256
257    // compute base^10
258    let t1 = square_reduce(state);
259
260    // compute base^100
261    let t2 = square_reduce(t1);
262
263    // compute base^100100
264    let t3 = exp_acc(t2, t2, 3);
265
266    // compute base^100100100100
267    let t4 = exp_acc(t3, t3, 6);
268
269    // compute base^100100100100100100100100
270    let t5 = exp_acc(t4, t4, 12);
271
272    // compute base^100100100100100100100100100100
273    let t6 = exp_acc(t5, t3, 6);
274
275    // compute base^1001001001001001001001001001000100100100100100100100100100100
276    let t7 = exp_acc(t6, t6, 31);
277
278    // compute base^1001001001001001001001001001000110110110110110110110110110110111
279    let a = square_reduce(square_reduce(mul_reduce(square_reduce(t7), t6)));
280    let b = mul_reduce(t1, mul_reduce(t2, state));
281    mul_reduce(a, b)
282}
283
284#[inline(always)]
285unsafe fn avx2_load(state: &[u64; 12]) -> (__m256i, __m256i, __m256i) {
286    (
287        _mm256_loadu_si256((&state[0..4]).as_ptr().cast::<__m256i>()),
288        _mm256_loadu_si256((&state[4..8]).as_ptr().cast::<__m256i>()),
289        _mm256_loadu_si256((&state[8..12]).as_ptr().cast::<__m256i>()),
290    )
291}
292
293#[inline(always)]
294unsafe fn avx2_store(buf: &mut [u64; 12], state: (__m256i, __m256i, __m256i)) {
295    _mm256_storeu_si256((&mut buf[0..4]).as_mut_ptr().cast::<__m256i>(), state.0);
296    _mm256_storeu_si256((&mut buf[4..8]).as_mut_ptr().cast::<__m256i>(), state.1);
297    _mm256_storeu_si256((&mut buf[8..12]).as_mut_ptr().cast::<__m256i>(), state.2);
298}
299
300#[inline(always)]
301pub unsafe fn apply_sbox(buffer: &mut [u64; 12]) {
302    let mut state = avx2_load(&buffer);
303    state = do_apply_sbox(state);
304    avx2_store(buffer, state);
305}
306
307#[inline(always)]
308pub unsafe fn apply_inv_sbox(buffer: &mut [u64; 12]) {
309    let mut state = avx2_load(&buffer);
310    state = do_apply_inv_sbox(state);
311    avx2_store(buffer, state);
312}