tract-linalg 0.23.5

Tiny, no-nonsense, self contained, TensorFlow and ONNX inference
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
254
255
256
257
258
259
260
261
262
263
264

// Fused SiLU kernel
//
// Exact formula computed per element (z = clamp(x, -18.6, 18.6), w = z²):
//   SiLU(x) = f * max(0.5 + z * P(w) / Q(w), 0)
// where P is the degree-6 Horner polynomial over coeffs COEFFS[2..=8], Q the
// degree-3 Horner polynomial over coeffs COEFFS[9..=12], and f = max(x, -18.6)
// the factor the sigmoid multiplies.
//
// Reuses the polynomial coefficients used in the numerical approximation of the Sigmoid kernel
// defined in arm64simd_sigmoid_f32_4n.S.j2.
//
// The sigmoid factor f is clamped below at -18.6 but left unclamped above: the upper clamp is
// only needed to keep the sigmoid polynomial in range (z), whereas SiLU(x) ~ x as x -> +inf, so
// the factor must stay unbounded above. The lower clamp keeps the kernel total: without it, the
// negative tail would return x * sigmoid(-18.6), whose magnitude grows toward -inf instead of
// decaying to 0. With it, x < -18.6 saturates at the constant -18.6 * sigmoid(-18.6) ~= -1.55e-7,
// which the true SiLU approaches from below as x -> -inf, so the error is bounded and tiny.
//
// The sigmoid factor is floored at 0 before it multiplies f: `0.5 + z * P(w) / Q(w)` cancels
// down to ~1e-8 on the negative tail, below the rounding error of the division, and a sigmoid
// that came out negative there would flip the sign of the whole result. It needs no matching
// ceiling — the sigmoid kernel clamps at 1 to keep its own range, but here an overshoot of one
// ulp only scales f by 1 + 2^-23, and SiLU has no upper bound to violate.

ew_impl_wrap!(
    f32,
    arm64simd_silu_f32_4n_fused,
    4,
    4,
    (),
    #[inline(never)]
    fn run(buf: &mut [f32], _: ()) {
        static COEFFS: [f32; 16] = [
            -18.6,
            18.6,
            -4.433153405e-18,
            1.169974371e-14,
            -1.875289645e-11,
            4.257889523e-8,
            0.00004811817576,
            0.008163842030,
            0.2499999971,
            3.922935744e-6,
            0.001524872358,
            0.1159886749,
            1.0,
            0.5,
            0.0,
            0.0,
        ];

        assert!(buf.len() % 4 == 0);
        if buf.is_empty() {
            return;
        }

        unsafe {
            let len = buf.len();
            let ptr = buf.as_mut_ptr();
            let coef_ptr = COEFFS.as_ptr();

            std::arch::asm!("
                ld1 {{ v0.4s, v1.4s, v2.4s, v3.4s }}, [{coef}]
                dup v5.4s, v0.s[0]             // v5 <- low, broadcasted
                dup v6.4s, v0.s[1]             // v6 <- high, broadcasted
                dup v7.4s, v3.s[1]             // v7 <- 0.5, broadcasted
                movi v4.4s, #0                 // v4 <- 0, the sigmoid floor

                cmp {len}, #16
                blt 9f

                1:
                    ld1 {{ v8.4s, v9.4s, v10.4s, v11.4s }}, [{ptr}]

                    fmax v8.4s, v8.4s, v5.4s
                    fmax v9.4s, v9.4s, v5.4s
                    fmax v10.4s, v10.4s, v5.4s
                    fmax v11.4s, v11.4s, v5.4s     // v8 <- max(x, -18.6): SiLU factor

                    fmin v16.4s, v8.4s, v6.4s
                    fmin v17.4s, v9.4s, v6.4s
                    fmin v18.4s, v10.4s, v6.4s
                    fmin v19.4s, v11.4s, v6.4s     // v16 <- z (clamped for sigmoid)

                    fmul v20.4s, v16.4s, v16.4s
                    fmul v21.4s, v17.4s, v17.4s
                    fmul v22.4s, v18.4s, v18.4s
                    fmul v23.4s, v19.4s, v19.4s    // v20 <- x2

                    dup v24.4s, v0.s[3]
                    fmla v24.4s, v20.4s, v0.s[2]
                    dup v25.4s, v0.s[3]
                    fmla v25.4s, v21.4s, v0.s[2]
                    dup v26.4s, v0.s[3]
                    fmla v26.4s, v22.4s, v0.s[2]
                    dup v27.4s, v0.s[3]
                    fmla v27.4s, v23.4s, v0.s[2]

                    dup v28.4s, v1.s[0]
                    fmla v28.4s, v20.4s, v24.4s
                    dup v29.4s, v1.s[0]
                    fmla v29.4s, v21.4s, v25.4s
                    dup v30.4s, v1.s[0]
                    fmla v30.4s, v22.4s, v26.4s
                    dup v31.4s, v1.s[0]
                    fmla v31.4s, v23.4s, v27.4s

                    dup v24.4s, v1.s[1]
                    fmla v24.4s, v20.4s, v28.4s
                    dup v25.4s, v1.s[1]
                    fmla v25.4s, v21.4s, v29.4s
                    dup v26.4s, v1.s[1]
                    fmla v26.4s, v22.4s, v30.4s
                    dup v27.4s, v1.s[1]
                    fmla v27.4s, v23.4s, v31.4s

                    dup v28.4s, v1.s[2]
                    fmla v28.4s, v20.4s, v24.4s
                    dup v29.4s, v1.s[2]
                    fmla v29.4s, v21.4s, v25.4s
                    dup v30.4s, v1.s[2]
                    fmla v30.4s, v22.4s, v26.4s
                    dup v31.4s, v1.s[2]
                    fmla v31.4s, v23.4s, v27.4s

                    dup v24.4s, v1.s[3]
                    fmla v24.4s, v20.4s, v28.4s
                    dup v25.4s, v1.s[3]
                    fmla v25.4s, v21.4s, v29.4s
                    dup v26.4s, v1.s[3]
                    fmla v26.4s, v22.4s, v30.4s
                    dup v27.4s, v1.s[3]
                    fmla v27.4s, v23.4s, v31.4s

                    dup v28.4s, v2.s[0]
                    fmla v28.4s, v20.4s, v24.4s
                    dup v29.4s, v2.s[0]
                    fmla v29.4s, v21.4s, v25.4s
                    dup v30.4s, v2.s[0]
                    fmla v30.4s, v22.4s, v26.4s
                    dup v31.4s, v2.s[0]
                    fmla v31.4s, v23.4s, v27.4s

                    fmul v16.4s, v16.4s, v28.4s
                    fmul v17.4s, v17.4s, v29.4s
                    fmul v18.4s, v18.4s, v30.4s
                    fmul v19.4s, v19.4s, v31.4s    // v16 <- numerator

                    dup v24.4s, v2.s[2]
                    fmla v24.4s, v20.4s, v2.s[1]
                    dup v25.4s, v2.s[2]
                    fmla v25.4s, v21.4s, v2.s[1]
                    dup v26.4s, v2.s[2]
                    fmla v26.4s, v22.4s, v2.s[1]
                    dup v27.4s, v2.s[2]
                    fmla v27.4s, v23.4s, v2.s[1]

                    dup v28.4s, v2.s[3]
                    fmla v28.4s, v20.4s, v24.4s
                    dup v29.4s, v2.s[3]
                    fmla v29.4s, v21.4s, v25.4s
                    dup v30.4s, v2.s[3]
                    fmla v30.4s, v22.4s, v26.4s
                    dup v31.4s, v2.s[3]
                    fmla v31.4s, v23.4s, v27.4s

                    dup v24.4s, v3.s[0]
                    fmla v24.4s, v20.4s, v28.4s
                    dup v25.4s, v3.s[0]
                    fmla v25.4s, v21.4s, v29.4s
                    dup v26.4s, v3.s[0]
                    fmla v26.4s, v22.4s, v30.4s
                    dup v27.4s, v3.s[0]
                    fmla v27.4s, v23.4s, v31.4s    // v24 <- denum

                    fdiv v16.4s, v16.4s, v24.4s
                    fdiv v17.4s, v17.4s, v25.4s
                    fdiv v18.4s, v18.4s, v26.4s
                    fdiv v19.4s, v19.4s, v27.4s

                    fadd v16.4s, v16.4s, v7.4s
                    fadd v17.4s, v17.4s, v7.4s
                    fadd v18.4s, v18.4s, v7.4s
                    fadd v19.4s, v19.4s, v7.4s     // v16 <- sigmoid

                    fmax v16.4s, v16.4s, v4.4s
                    fmax v17.4s, v17.4s, v4.4s
                    fmax v18.4s, v18.4s, v4.4s
                    fmax v19.4s, v19.4s, v4.4s     // v16 <- sigmoid, floored at 0

                    fmul v16.4s, v16.4s, v8.4s
                    fmul v17.4s, v17.4s, v9.4s
                    fmul v18.4s, v18.4s, v10.4s
                    fmul v19.4s, v19.4s, v11.4s    // v16 <- SiLU (sigmoid * clamped-below x)

                    st1 {{ v16.4s, v17.4s, v18.4s, v19.4s }}, [{ptr}], #64
                    sub {len}, {len}, #16
                    cmp {len}, #16
                    bge 1b

                9:
                cbz {len}, 3f

                2:
                    ld1 {{ v8.4s }}, [{ptr}]

                    fmax v8.4s, v8.4s, v5.4s       // v8 <- max(x, -18.6): SiLU factor
                    fmin v16.4s, v8.4s, v6.4s      // v16 <- z (clamped for sigmoid)
                    fmul v20.4s, v16.4s, v16.4s    // v20 <- x2

                    dup v24.4s, v0.s[3]
                    fmla v24.4s, v20.4s, v0.s[2]
                    dup v28.4s, v1.s[0]
                    fmla v28.4s, v20.4s, v24.4s
                    dup v24.4s, v1.s[1]
                    fmla v24.4s, v20.4s, v28.4s
                    dup v28.4s, v1.s[2]
                    fmla v28.4s, v20.4s, v24.4s
                    dup v24.4s, v1.s[3]
                    fmla v24.4s, v20.4s, v28.4s
                    dup v28.4s, v2.s[0]
                    fmla v28.4s, v20.4s, v24.4s
                    fmul v16.4s, v16.4s, v28.4s    // v16 <- numerator

                    dup v24.4s, v2.s[2]
                    fmla v24.4s, v20.4s, v2.s[1]
                    dup v28.4s, v2.s[3]
                    fmla v28.4s, v20.4s, v24.4s
                    dup v24.4s, v3.s[0]
                    fmla v24.4s, v20.4s, v28.4s    // v24 <- denum

                    fdiv v16.4s, v16.4s, v24.4s
                    fadd v16.4s, v16.4s, v7.4s
                    fmax v16.4s, v16.4s, v4.4s     // v16 <- sigmoid, floored at 0

                    fmul v16.4s, v16.4s, v8.4s     // v16 <- SiLU (sigmoid * clamped-below x)

                    st1 {{ v16.4s }}, [{ptr}], #16
                    subs {len}, {len}, 4
                    bne 2b

                3:
            ",
            coef = in(reg) coef_ptr,
            ptr = inout(reg) ptr => _,
            len = inout(reg) len => _,
            out("v0") _, out("v1") _, out("v2") _, out("v3") _,
            out("v4") _, out("v5") _, out("v6") _, out("v7") _,
            out("v8") _, out("v9") _, out("v10") _, out("v11") _,
            out("v16") _, out("v17") _, out("v18") _, out("v19") _,
            out("v20") _, out("v21") _, out("v22") _, out("v23") _,
            out("v24") _, out("v25") _, out("v26") _, out("v27") _,
            out("v28") _, out("v29") _, out("v30") _, out("v31") _,
            options(nostack),
            );
        }
    }
);

#[cfg(test)]
pub mod test_arm64simd_silu_f32_4n_fused {
    use super::*;
    silu_frame_tests!(true, f32, arm64simd_silu_f32_4n_fused);
}