bola 0.1.1

A lightweight native rust linear algebra library.
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

#[cfg(feature = "profiling")]
use crate::profiling;

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

#[cfg(target_arch = "aarch64")]
use std::arch::aarch64::*;

/// Finds the index of the element with the largest absolute value in a vector.
///
/// # Arguments
/// * `n` - The number of elements in the vector `x`.
/// * `x` - A raw constant pointer to the first element of the vector.
///
/// # Returns
/// A `usize` representing the 0-based index of the first element with the
/// maximum absolute value. If `n` is 0, this function will return 0.
#[cfg(target_arch = "x86_64")]
#[inline]
#[allow(unsafe_op_in_unsafe_fn, clippy::missing_safety_doc)]
#[target_feature(enable = "avx2,fma")]
pub unsafe fn idamax(n: usize, x: *const f64) -> usize {
    #[cfg(feature = "profiling")]
    let _timer = profiling::ScopedTimer::new("IDAMAX");

    if n < 16 {
        let mut max_val = -1.0;
        let mut max_idx = 0;
        for i in 0..n {
            let val = (*x.add(i)).abs();
            if val > max_val {
                max_val = val;
                max_idx = i;
            }
        }
        return max_idx;
    }

    let abs_mask = _mm256_set1_pd(f64::from_bits(0x7FFFFFFFFFFFFFFF));

    let mut max_vals_vec0 = _mm256_setzero_pd();
    let mut max_idxs_vec0 = _mm256_setzero_pd();
    let mut max_vals_vec1 = _mm256_setzero_pd();
    let mut max_idxs_vec1 = _mm256_setzero_pd();
    let mut max_vals_vec2 = _mm256_setzero_pd();
    let mut max_idxs_vec2 = _mm256_setzero_pd();
    let mut max_vals_vec3 = _mm256_setzero_pd();
    let mut max_idxs_vec3 = _mm256_setzero_pd();

    let mut idxs0 = _mm256_set_pd(3.0, 2.0, 1.0, 0.0);
    let mut idxs1 = _mm256_set_pd(7.0, 6.0, 5.0, 4.0);
    let mut idxs2 = _mm256_set_pd(11.0, 10.0, 9.0, 8.0);
    let mut idxs3 = _mm256_set_pd(15.0, 14.0, 13.0, 12.0);
    let step_vec = _mm256_set1_pd(16.0);

    let n_chunks = n / 16;
    let mut x_ptr = x;
    for _ in 0..n_chunks {
        let vals0 = _mm256_loadu_pd(x_ptr);
        let abs_vals0 = _mm256_and_pd(vals0, abs_mask);
        let mask0 = _mm256_cmp_pd(abs_vals0, max_vals_vec0, _CMP_GT_OQ);
        max_vals_vec0 = _mm256_blendv_pd(max_vals_vec0, abs_vals0, mask0);
        max_idxs_vec0 = _mm256_blendv_pd(max_idxs_vec0, idxs0, mask0);

        let vals1 = _mm256_loadu_pd(x_ptr.add(4));
        let abs_vals1 = _mm256_and_pd(vals1, abs_mask);
        let mask1 = _mm256_cmp_pd(abs_vals1, max_vals_vec1, _CMP_GT_OQ);
        max_vals_vec1 = _mm256_blendv_pd(max_vals_vec1, abs_vals1, mask1);
        max_idxs_vec1 = _mm256_blendv_pd(max_idxs_vec1, idxs1, mask1);

        let vals2 = _mm256_loadu_pd(x_ptr.add(8));
        let abs_vals2 = _mm256_and_pd(vals2, abs_mask);
        let mask2 = _mm256_cmp_pd(abs_vals2, max_vals_vec2, _CMP_GT_OQ);
        max_vals_vec2 = _mm256_blendv_pd(max_vals_vec2, abs_vals2, mask2);
        max_idxs_vec2 = _mm256_blendv_pd(max_idxs_vec2, idxs2, mask2);

        let vals3 = _mm256_loadu_pd(x_ptr.add(12));
        let abs_vals3 = _mm256_and_pd(vals3, abs_mask);
        let mask3 = _mm256_cmp_pd(abs_vals3, max_vals_vec3, _CMP_GT_OQ);
        max_vals_vec3 = _mm256_blendv_pd(max_vals_vec3, abs_vals3, mask3);
        max_idxs_vec3 = _mm256_blendv_pd(max_idxs_vec3, idxs3, mask3);

        x_ptr = x_ptr.add(16);
        idxs0 = _mm256_add_pd(idxs0, step_vec);
        idxs1 = _mm256_add_pd(idxs1, step_vec);
        idxs2 = _mm256_add_pd(idxs2, step_vec);
        idxs3 = _mm256_add_pd(idxs3, step_vec);
    }

    let mask1 = _mm256_cmp_pd(max_vals_vec1, max_vals_vec0, _CMP_GT_OQ);
    max_vals_vec0 = _mm256_blendv_pd(max_vals_vec0, max_vals_vec1, mask1);
    max_idxs_vec0 = _mm256_blendv_pd(max_idxs_vec0, max_idxs_vec1, mask1);

    let mask2 = _mm256_cmp_pd(max_vals_vec2, max_vals_vec0, _CMP_GT_OQ);
    max_vals_vec0 = _mm256_blendv_pd(max_vals_vec0, max_vals_vec2, mask2);
    max_idxs_vec0 = _mm256_blendv_pd(max_idxs_vec0, max_idxs_vec2, mask2);

    let mask3 = _mm256_cmp_pd(max_vals_vec3, max_vals_vec0, _CMP_GT_OQ);
    max_vals_vec0 = _mm256_blendv_pd(max_vals_vec0, max_vals_vec3, mask3);
    max_idxs_vec0 = _mm256_blendv_pd(max_idxs_vec0, max_idxs_vec3, mask3);

    let mut max_vals_arr: [f64; 4] = [0.0; 4];
    let mut max_idxs_arr: [f64; 4] = [0.0; 4];
    _mm256_storeu_pd(max_vals_arr.as_mut_ptr(), max_vals_vec0);
    _mm256_storeu_pd(max_idxs_arr.as_mut_ptr(), max_idxs_vec0);

    let mut max_val = max_vals_arr[0];
    let mut max_idx = max_idxs_arr[0] as usize;

    if max_vals_arr[1] > max_val {
        max_val = max_vals_arr[1];
        max_idx = max_idxs_arr[1] as usize;
    }
    if max_vals_arr[2] > max_val {
        max_val = max_vals_arr[2];
        max_idx = max_idxs_arr[2] as usize;
    }
    if max_vals_arr[3] > max_val {
        max_val = max_vals_arr[3];
        max_idx = max_idxs_arr[3] as usize;
    }

    for i in (n_chunks * 16)..n {
        let val = (*x.add(i)).abs();
        if val > max_val {
            max_val = val;
            max_idx = i;
        }
    }

    max_idx
}

/// Finds the index of the element with the largest absolute value in a vector.
/// ... see above function
#[cfg(target_arch = "aarch64")]
#[inline]
#[allow(unsafe_op_in_unsafe_fn, clippy::missing_safety_doc)]
#[target_feature(enable = "neon")]
pub unsafe fn idamax(n: usize, x: *const f64) -> usize {
    #[cfg(feature = "profiling")]
    let _timer = profiling::ScopedTimer::new("IDAMAX");

    if n < 8 {
        let mut max_val = -1.0;
        let mut max_idx = 0;
        for i in 0..n {
            let val = (*x.add(i)).abs();
            if val > max_val {
                max_val = val;
                max_idx = i;
            }
        }
        return max_idx;
    }

    let mut max_vals_vec0 = vdupq_n_f64(0.0);
    let mut max_idxs_vec0 = vdupq_n_f64(0.0);
    let mut max_vals_vec1 = vdupq_n_f64(0.0);
    let mut max_idxs_vec1 = vdupq_n_f64(0.0);
    let mut max_vals_vec2 = vdupq_n_f64(0.0);
    let mut max_idxs_vec2 = vdupq_n_f64(0.0);
    let mut max_vals_vec3 = vdupq_n_f64(0.0);
    let mut max_idxs_vec3 = vdupq_n_f64(0.0);

    let mut idxs0 = vld1q_f64([0.0, 1.0].as_ptr());
    let mut idxs1 = vld1q_f64([2.0, 3.0].as_ptr());
    let mut idxs2 = vld1q_f64([4.0, 5.0].as_ptr());
    let mut idxs3 = vld1q_f64([6.0, 7.0].as_ptr());
    let step_vec = vdupq_n_f64(8.0);

    let n_chunks = n / 8;
    let mut x_ptr = x;
    for _ in 0..n_chunks {
        let vals0 = vld1q_f64(x_ptr);
        let abs_vals0 = vabsq_f64(vals0);
        let mask0 = vcgtq_f64(abs_vals0, max_vals_vec0);
        max_vals_vec0 = vbslq_f64(mask0, abs_vals0, max_vals_vec0);
        max_idxs_vec0 = vbslq_f64(mask0, idxs0, max_idxs_vec0);

        let vals1 = vld1q_f64(x_ptr.add(2));
        let abs_vals1 = vabsq_f64(vals1);
        let mask1 = vcgtq_f64(abs_vals1, max_vals_vec1);
        max_vals_vec1 = vbslq_f64(mask1, abs_vals1, max_vals_vec1);
        max_idxs_vec1 = vbslq_f64(mask1, idxs1, max_idxs_vec1);

        let vals2 = vld1q_f64(x_ptr.add(4));
        let abs_vals2 = vabsq_f64(vals2);
        let mask2 = vcgtq_f64(abs_vals2, max_vals_vec2);
        max_vals_vec2 = vbslq_f64(mask2, abs_vals2, max_vals_vec2);
        max_idxs_vec2 = vbslq_f64(mask2, idxs2, max_idxs_vec2);

        let vals3 = vld1q_f64(x_ptr.add(6));
        let abs_vals3 = vabsq_f64(vals3);
        let mask3 = vcgtq_f64(abs_vals3, max_vals_vec3);
        max_vals_vec3 = vbslq_f64(mask3, abs_vals3, max_vals_vec3);
        max_idxs_vec3 = vbslq_f64(mask3, idxs3, max_idxs_vec3);

        x_ptr = x_ptr.add(8);
        idxs0 = vaddq_f64(idxs0, step_vec);
        idxs1 = vaddq_f64(idxs1, step_vec);
        idxs2 = vaddq_f64(idxs2, step_vec);
        idxs3 = vaddq_f64(idxs3, step_vec);
    }

    let mask1 = vcgtq_f64(max_vals_vec1, max_vals_vec0);
    max_vals_vec0 = vbslq_f64(mask1, max_vals_vec1, max_vals_vec0);
    max_idxs_vec0 = vbslq_f64(mask1, max_idxs_vec1, max_idxs_vec0);

    let mask2 = vcgtq_f64(max_vals_vec2, max_vals_vec0);
    max_vals_vec0 = vbslq_f64(mask2, max_vals_vec2, max_vals_vec0);
    max_idxs_vec0 = vbslq_f64(mask2, max_idxs_vec2, max_idxs_vec0);

    let mask3 = vcgtq_f64(max_vals_vec3, max_vals_vec0);
    max_vals_vec0 = vbslq_f64(mask3, max_vals_vec3, max_vals_vec0);
    max_idxs_vec0 = vbslq_f64(mask3, max_idxs_vec3, max_idxs_vec0);

    let mut max_vals_arr: [f64; 2] = [0.0; 2];
    let mut max_idxs_arr: [f64; 2] = [0.0; 2];
    vst1q_f64(max_vals_arr.as_mut_ptr(), max_vals_vec0);
    vst1q_f64(max_idxs_arr.as_mut_ptr(), max_idxs_vec0);

    let mut max_val = max_vals_arr[0];
    let mut max_idx = max_idxs_arr[0] as usize;
    if max_vals_arr[1] > max_val {
        max_val = max_vals_arr[1];
        max_idx = max_idxs_arr[1] as usize;
    }

    for i in (n_chunks * 8)..n {
        let val = (*x.add(i)).abs();
        if val > max_val {
            max_val = val;
            max_idx = i;
        }
    }

    max_idx
}