trueno 0.17.2

High-performance SIMD compute library with GPU support for matrix operations
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

//! SSE2 activation functions (exp, sigmoid, gelu, swish, tanh).

#[cfg(target_arch = "x86_64")]
use std::arch::x86_64::*;

/// SSE2 exp approximation helper (polynomial range reduction).
///
/// # Safety
///
/// Caller must ensure SSE2 is available on the current CPU.
#[inline]
#[target_feature(enable = "sse2")]
// SAFETY: caller verifies SSE2 support, input slices meet alignment/length requirements
pub(crate) unsafe fn exp_approx_sse2(x: __m128) -> __m128 {
    let ln2 = _mm_set1_ps(std::f32::consts::LN_2);
    let inv_ln2 = _mm_set1_ps(1.0 / std::f32::consts::LN_2);
    let one = _mm_set1_ps(1.0);
    let c2 = _mm_set1_ps(0.5);
    let c3 = _mm_set1_ps(0.166_666_67);
    let c4 = _mm_set1_ps(0.041_666_668);
    let c5 = _mm_set1_ps(0.008_333_334);
    let k = _mm_cvtps_epi32(_mm_mul_ps(x, inv_ln2));
    let kf = _mm_cvtepi32_ps(k);
    let r = _mm_sub_ps(x, _mm_mul_ps(kf, ln2));
    let mut poly = _mm_add_ps(one, _mm_mul_ps(r, c5));
    poly = _mm_add_ps(one, _mm_mul_ps(r, _mm_add_ps(c4, _mm_mul_ps(r, poly))));
    poly = _mm_add_ps(one, _mm_mul_ps(r, _mm_add_ps(c3, _mm_mul_ps(r, poly))));
    poly = _mm_add_ps(one, _mm_mul_ps(r, _mm_add_ps(c2, _mm_mul_ps(r, poly))));
    poly = _mm_add_ps(one, _mm_mul_ps(r, poly));
    let exp_k = _mm_castsi128_ps(_mm_slli_epi32(_mm_add_epi32(k, _mm_set1_epi32(127)), 23));
    _mm_mul_ps(poly, exp_k)
}

/// SSE2 exp (element-wise).
#[inline]
#[target_feature(enable = "sse2")]
// SAFETY: caller ensures preconditions are met for this unsafe function
pub(crate) unsafe fn exp(a: &[f32], result: &mut [f32]) {
    unsafe {
        // Polynomial approximation for exp - range reduction + polynomial
        let len = a.len();
        let mut i = 0;
        let ln2 = _mm_set1_ps(std::f32::consts::LN_2);
        let inv_ln2 = _mm_set1_ps(1.0 / std::f32::consts::LN_2);
        let c1 = _mm_set1_ps(1.0);
        let c2 = _mm_set1_ps(0.5);
        let c3 = _mm_set1_ps(0.166_666_67);
        let c4 = _mm_set1_ps(0.041_666_668);
        let c5 = _mm_set1_ps(0.008_333_334);
        while i + 4 <= len {
            let x = _mm_loadu_ps(a.as_ptr().add(i));
            let k = _mm_cvtps_epi32(_mm_mul_ps(x, inv_ln2));
            let kf = _mm_cvtepi32_ps(k);
            let r = _mm_sub_ps(x, _mm_mul_ps(kf, ln2));
            let mut poly = _mm_add_ps(c1, _mm_mul_ps(r, c5));
            poly = _mm_add_ps(c1, _mm_mul_ps(r, _mm_add_ps(c4, _mm_mul_ps(r, poly))));
            poly = _mm_add_ps(c1, _mm_mul_ps(r, _mm_add_ps(c3, _mm_mul_ps(r, poly))));
            poly = _mm_add_ps(c1, _mm_mul_ps(r, _mm_add_ps(c2, _mm_mul_ps(r, poly))));
            poly = _mm_add_ps(c1, _mm_mul_ps(r, poly));
            let exp_k = _mm_castsi128_ps(_mm_slli_epi32(_mm_add_epi32(k, _mm_set1_epi32(127)), 23));
            _mm_storeu_ps(result.as_mut_ptr().add(i), _mm_mul_ps(poly, exp_k));
            i += 4;
        }
        for j in i..len {
            result[j] = a[j].exp();
        }
    }
}

/// SSE2 sigmoid activation.
#[inline]
#[target_feature(enable = "sse2")]
// SAFETY: caller ensures preconditions are met for this unsafe function
pub(crate) unsafe fn sigmoid(a: &[f32], result: &mut [f32]) {
    unsafe {
        // sigmoid(x) = 1 / (1 + exp(-x))
        let len = a.len();
        let mut i = 0;
        let one = _mm_set1_ps(1.0);
        let neg_one = _mm_set1_ps(-1.0);
        let ln2 = _mm_set1_ps(std::f32::consts::LN_2);
        let inv_ln2 = _mm_set1_ps(1.0 / std::f32::consts::LN_2);
        let c2 = _mm_set1_ps(0.5);
        let c3 = _mm_set1_ps(0.166_666_67);
        let c4 = _mm_set1_ps(0.041_666_668);
        let c5 = _mm_set1_ps(0.008_333_334);
        while i + 4 <= len {
            let x = _mm_loadu_ps(a.as_ptr().add(i));
            let neg_x = _mm_mul_ps(x, neg_one);
            let k = _mm_cvtps_epi32(_mm_mul_ps(neg_x, inv_ln2));
            let kf = _mm_cvtepi32_ps(k);
            let r = _mm_sub_ps(neg_x, _mm_mul_ps(kf, ln2));
            let mut poly = _mm_add_ps(one, _mm_mul_ps(r, c5));
            poly = _mm_add_ps(one, _mm_mul_ps(r, _mm_add_ps(c4, _mm_mul_ps(r, poly))));
            poly = _mm_add_ps(one, _mm_mul_ps(r, _mm_add_ps(c3, _mm_mul_ps(r, poly))));
            poly = _mm_add_ps(one, _mm_mul_ps(r, _mm_add_ps(c2, _mm_mul_ps(r, poly))));
            poly = _mm_add_ps(one, _mm_mul_ps(r, poly));
            let exp_k = _mm_castsi128_ps(_mm_slli_epi32(_mm_add_epi32(k, _mm_set1_epi32(127)), 23));
            let exp_neg_x = _mm_mul_ps(poly, exp_k);
            _mm_storeu_ps(result.as_mut_ptr().add(i), _mm_div_ps(one, _mm_add_ps(one, exp_neg_x)));
            i += 4;
        }
        for j in i..len {
            result[j] = 1.0 / (1.0 + (-a[j]).exp());
        }
    }
}

/// SSE2 GELU activation.
#[inline]
#[target_feature(enable = "sse2")]
// SAFETY: caller ensures preconditions are met for this unsafe function
pub(crate) unsafe fn gelu(a: &[f32], result: &mut [f32]) {
    unsafe {
        // GELU(x) = 0.5 * x * (1 + tanh(sqrt(2/pi) * (x + 0.044715 * x^3)))
        let len = a.len();
        let mut i = 0;
        let half = _mm_set1_ps(0.5);
        let one = _mm_set1_ps(1.0);
        let sqrt_2_pi = _mm_set1_ps(0.797_884_56);
        let coeff = _mm_set1_ps(0.044_715);
        while i + 4 <= len {
            let x = _mm_loadu_ps(a.as_ptr().add(i));
            let x3 = _mm_mul_ps(_mm_mul_ps(x, x), x);
            let inner = _mm_mul_ps(sqrt_2_pi, _mm_add_ps(x, _mm_mul_ps(coeff, x3)));
            // tanh approximation: (e^2x - 1) / (e^2x + 1)
            let two_inner = _mm_add_ps(inner, inner);
            let exp_2x = exp_approx_sse2(two_inner);
            let tanh_val = _mm_div_ps(_mm_sub_ps(exp_2x, one), _mm_add_ps(exp_2x, one));
            _mm_storeu_ps(
                result.as_mut_ptr().add(i),
                _mm_mul_ps(half, _mm_mul_ps(x, _mm_add_ps(one, tanh_val))),
            );
            i += 4;
        }
        for j in i..len {
            let x = a[j];
            result[j] = 0.5
                * x
                * (1.0 + ((0.797_884_56 * (x + 0.044_715 * x * x * x)) as f64).tanh() as f32);
        }
    }
}

/// SSE2 swish activation.
#[inline]
#[target_feature(enable = "sse2")]
// SAFETY: caller ensures preconditions are met for this unsafe function
pub(crate) unsafe fn swish(a: &[f32], result: &mut [f32]) {
    unsafe {
        // swish(x) = x * sigmoid(x)
        let len = a.len();
        let mut i = 0;
        let one = _mm_set1_ps(1.0);
        let neg_one = _mm_set1_ps(-1.0);
        let ln2 = _mm_set1_ps(std::f32::consts::LN_2);
        let inv_ln2 = _mm_set1_ps(1.0 / std::f32::consts::LN_2);
        let c2 = _mm_set1_ps(0.5);
        let c3 = _mm_set1_ps(0.166_666_67);
        let c4 = _mm_set1_ps(0.041_666_668);
        let c5 = _mm_set1_ps(0.008_333_334);
        while i + 4 <= len {
            let x = _mm_loadu_ps(a.as_ptr().add(i));
            let neg_x = _mm_mul_ps(x, neg_one);
            let k = _mm_cvtps_epi32(_mm_mul_ps(neg_x, inv_ln2));
            let kf = _mm_cvtepi32_ps(k);
            let r = _mm_sub_ps(neg_x, _mm_mul_ps(kf, ln2));
            let mut poly = _mm_add_ps(one, _mm_mul_ps(r, c5));
            poly = _mm_add_ps(one, _mm_mul_ps(r, _mm_add_ps(c4, _mm_mul_ps(r, poly))));
            poly = _mm_add_ps(one, _mm_mul_ps(r, _mm_add_ps(c3, _mm_mul_ps(r, poly))));
            poly = _mm_add_ps(one, _mm_mul_ps(r, _mm_add_ps(c2, _mm_mul_ps(r, poly))));
            poly = _mm_add_ps(one, _mm_mul_ps(r, poly));
            let exp_k = _mm_castsi128_ps(_mm_slli_epi32(_mm_add_epi32(k, _mm_set1_epi32(127)), 23));
            let exp_neg_x = _mm_mul_ps(poly, exp_k);
            let sigmoid = _mm_div_ps(one, _mm_add_ps(one, exp_neg_x));
            _mm_storeu_ps(result.as_mut_ptr().add(i), _mm_mul_ps(x, sigmoid));
            i += 4;
        }
        for j in i..len {
            result[j] = a[j] / (1.0 + (-a[j]).exp());
        }
    }
}

/// SSE2 tanh activation.
#[inline]
#[target_feature(enable = "sse2")]
// SAFETY: caller ensures preconditions are met for this unsafe function
pub(crate) unsafe fn tanh(a: &[f32], result: &mut [f32]) {
    unsafe {
        // tanh(x) = (e^2x - 1) / (e^2x + 1)
        let len = a.len();
        let mut i = 0;
        let one = _mm_set1_ps(1.0);
        let two = _mm_set1_ps(2.0);
        while i + 4 <= len {
            let x = _mm_loadu_ps(a.as_ptr().add(i));
            let exp_2x = exp_approx_sse2(_mm_mul_ps(two, x));
            _mm_storeu_ps(
                result.as_mut_ptr().add(i),
                _mm_div_ps(_mm_sub_ps(exp_2x, one), _mm_add_ps(exp_2x, one)),
            );
            i += 4;
        }
        for j in i..len {
            let exp_2x = (2.0 * a[j]).exp();
            result[j] = (exp_2x - 1.0) / (exp_2x + 1.0);
        }
    }
}