numr 0.5.2

High-performance numerical computing with multi-backend GPU acceleration (CPU/CUDA/WebGPU)
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

//! Complex number unary operation kernels
//!
//! Provides element-wise unary operations for Complex64 and Complex128 types,
//! operating on interleaved (re, im) pairs.

use crate::ops::UnaryOp;

/// Complex64 unary operations operating on (re, im) pairs stored as f32
/// `len` is the number of complex elements; memory has `2*len` f32 values
#[inline]
pub(super) unsafe fn unary_op_complex64(op: UnaryOp, a: *const f32, out: *mut f32, len: usize) {
    let a_pairs = std::slice::from_raw_parts(a, len * 2);
    let out_pairs = std::slice::from_raw_parts_mut(out, len * 2);

    for i in 0..len {
        let re = a_pairs[2 * i] as f64;
        let im = a_pairs[2 * i + 1] as f64;
        let (ore, oim) = complex_unary_op(op, re, im);
        out_pairs[2 * i] = ore as f32;
        out_pairs[2 * i + 1] = oim as f32;
    }
}

/// Complex128 unary operations operating on (re, im) pairs stored as f64
#[inline]
pub(super) unsafe fn unary_op_complex128(op: UnaryOp, a: *const f64, out: *mut f64, len: usize) {
    let a_pairs = std::slice::from_raw_parts(a, len * 2);
    let out_pairs = std::slice::from_raw_parts_mut(out, len * 2);

    for i in 0..len {
        let re = a_pairs[2 * i];
        let im = a_pairs[2 * i + 1];
        let (ore, oim) = complex_unary_op(op, re, im);
        out_pairs[2 * i] = ore;
        out_pairs[2 * i + 1] = oim;
    }
}

/// Perform a unary operation on a complex number (re, im) → (re', im')
#[inline]
fn complex_unary_op(op: UnaryOp, re: f64, im: f64) -> (f64, f64) {
    match op {
        UnaryOp::Neg => (-re, -im),
        UnaryOp::Abs => {
            // |z| as a real complex number
            ((re * re + im * im).sqrt(), 0.0)
        }
        UnaryOp::Square => {
            // (a+bi)^2 = a^2-b^2 + 2abi
            (re * re - im * im, 2.0 * re * im)
        }
        UnaryOp::Recip => {
            // 1/(a+bi) = (a-bi)/(a^2+b^2)
            let denom = re * re + im * im;
            if denom == 0.0 {
                (f64::NAN, f64::NAN)
            } else {
                (re / denom, -im / denom)
            }
        }
        UnaryOp::Exp => {
            // e^(a+bi) = e^a * (cos(b) + i*sin(b))
            let ea = re.exp();
            (ea * im.cos(), ea * im.sin())
        }
        UnaryOp::Log => {
            // log(a+bi) = log|z| + i*arg(z)
            let abs = (re * re + im * im).sqrt();
            (abs.ln(), im.atan2(re))
        }
        UnaryOp::Sqrt => {
            // sqrt(a+bi) using polar form
            let abs = (re * re + im * im).sqrt();
            let r = ((abs + re) / 2.0).sqrt();
            let i_val = ((abs - re) / 2.0).sqrt();
            if im >= 0.0 { (r, i_val) } else { (r, -i_val) }
        }
        UnaryOp::Sign => {
            let abs = (re * re + im * im).sqrt();
            if abs == 0.0 {
                (0.0, 0.0)
            } else {
                (re / abs, im / abs)
            }
        }
        // For operations that don't have natural complex extensions,
        // apply to magnitude and return as real
        _ => {
            let mag = (re * re + im * im).sqrt();
            let result = match op {
                UnaryOp::Floor => mag.floor(),
                UnaryOp::Ceil => mag.ceil(),
                UnaryOp::Round => mag.round(),
                UnaryOp::Trunc => mag.trunc(),
                UnaryOp::Rsqrt => 1.0 / mag.sqrt(),
                UnaryOp::Cbrt => mag.cbrt(),
                UnaryOp::Sin => {
                    // sin(a+bi) = sin(a)cosh(b) + i*cos(a)sinh(b)
                    return (re.sin() * im.cosh(), re.cos() * im.sinh());
                }
                UnaryOp::Cos => {
                    // cos(a+bi) = cos(a)cosh(b) - i*sin(a)sinh(b)
                    return (re.cos() * im.cosh(), -re.sin() * im.sinh());
                }
                UnaryOp::Tan => {
                    // tan(z) = sin(z)/cos(z)
                    let (sr, si) = (re.sin() * im.cosh(), re.cos() * im.sinh());
                    let (cr, ci) = (re.cos() * im.cosh(), -re.sin() * im.sinh());
                    let denom = cr * cr + ci * ci;
                    if denom == 0.0 {
                        return (f64::NAN, f64::NAN);
                    }
                    return ((sr * cr + si * ci) / denom, (si * cr - sr * ci) / denom);
                }
                UnaryOp::Tanh => {
                    // tanh(z) = sinh(z)/cosh(z)
                    let (sr, si) = (re.sinh() * im.cos(), re.cosh() * im.sin());
                    let (cr, ci) = (re.cosh() * im.cos(), re.sinh() * im.sin());
                    let denom = cr * cr + ci * ci;
                    if denom == 0.0 {
                        return (f64::NAN, f64::NAN);
                    }
                    return ((sr * cr + si * ci) / denom, (si * cr - sr * ci) / denom);
                }
                UnaryOp::Sinh => {
                    return (re.sinh() * im.cos(), re.cosh() * im.sin());
                }
                UnaryOp::Cosh => {
                    return (re.cosh() * im.cos(), re.sinh() * im.sin());
                }
                UnaryOp::Exp2 => {
                    // 2^(a+bi) = 2^a * (cos(b*ln2) + i*sin(b*ln2))
                    let ln2 = std::f64::consts::LN_2;
                    let ea = (re * ln2).exp();
                    return (ea * (im * ln2).cos(), ea * (im * ln2).sin());
                }
                UnaryOp::Expm1 => {
                    // e^(a+bi) - 1
                    let ea = re.exp();
                    return (ea * im.cos() - 1.0, ea * im.sin());
                }
                UnaryOp::Log2 => {
                    // log2(z) = log(z) / ln(2)
                    let ln2 = std::f64::consts::LN_2;
                    let abs = (re * re + im * im).sqrt();
                    return (abs.ln() / ln2, im.atan2(re) / ln2);
                }
                UnaryOp::Log10 => {
                    // log10(z) = log(z) / ln(10)
                    let ln10 = std::f64::consts::LN_10;
                    let abs = (re * re + im * im).sqrt();
                    return (abs.ln() / ln10, im.atan2(re) / ln10);
                }
                UnaryOp::Log1p => {
                    // log(1 + z) = log((1+re) + im*i)
                    let new_re = 1.0 + re;
                    let abs = (new_re * new_re + im * im).sqrt();
                    return (abs.ln(), im.atan2(new_re));
                }
                UnaryOp::Asin => {
                    // asin(z) = -i * log(iz + sqrt(1 - z^2))
                    let (z2r, z2i) = (re * re - im * im, 2.0 * re * im);
                    let (sr, si) = (1.0 - z2r, -z2i);
                    let abs_s = (sr * sr + si * si).sqrt();
                    let (sqr, sqi) = (((abs_s + sr) / 2.0).sqrt(), ((abs_s - sr) / 2.0).sqrt());
                    let sqi = if si >= 0.0 { sqi } else { -sqi };
                    let (wr, wi) = (-im + sqr, re + sqi);
                    let abs_w = (wr * wr + wi * wi).sqrt();
                    return (wi.atan2(wr), -abs_w.ln());
                }
                UnaryOp::Acos => {
                    // acos(z) = pi/2 - asin(z)
                    let (z2r, z2i) = (re * re - im * im, 2.0 * re * im);
                    let (sr, si) = (1.0 - z2r, -z2i);
                    let abs_s = (sr * sr + si * si).sqrt();
                    let (sqr, sqi) = (((abs_s + sr) / 2.0).sqrt(), ((abs_s - sr) / 2.0).sqrt());
                    let sqi = if si >= 0.0 { sqi } else { -sqi };
                    let (wr, wi) = (-im + sqr, re + sqi);
                    let abs_w = (wr * wr + wi * wi).sqrt();
                    let asin_re = wi.atan2(wr);
                    let asin_im = -abs_w.ln();
                    return (std::f64::consts::FRAC_PI_2 - asin_re, -asin_im);
                }
                UnaryOp::Atan => {
                    // atan(z) = i/2 * log((1-iz)/(1+iz))
                    let (nr, ni) = (1.0 + im, -re);
                    let (dr, di) = (1.0 - im, re);
                    let dn = dr * dr + di * di;
                    if dn == 0.0 {
                        return (f64::NAN, f64::NAN);
                    }
                    let (qr, qi) = ((nr * dr + ni * di) / dn, (ni * dr - nr * di) / dn);
                    let abs_q = (qr * qr + qi * qi).sqrt();
                    return (-0.5 * qi.atan2(qr), 0.5 * abs_q.ln());
                }
                UnaryOp::Asinh => {
                    // asinh(z) = log(z + sqrt(z^2 + 1))
                    let (z2r, z2i) = (re * re - im * im + 1.0, 2.0 * re * im);
                    let abs_z2 = (z2r * z2r + z2i * z2i).sqrt();
                    let (sqr, sqi) = (((abs_z2 + z2r) / 2.0).sqrt(), ((abs_z2 - z2r) / 2.0).sqrt());
                    let sqi = if z2i >= 0.0 { sqi } else { -sqi };
                    let (wr, wi) = (re + sqr, im + sqi);
                    let abs_w = (wr * wr + wi * wi).sqrt();
                    return (abs_w.ln(), wi.atan2(wr));
                }
                UnaryOp::Acosh => {
                    // acosh(z) = log(z + sqrt(z^2 - 1))
                    let (z2r, z2i) = (re * re - im * im - 1.0, 2.0 * re * im);
                    let abs_z2 = (z2r * z2r + z2i * z2i).sqrt();
                    let (sqr, sqi) = (((abs_z2 + z2r) / 2.0).sqrt(), ((abs_z2 - z2r) / 2.0).sqrt());
                    let sqi = if z2i >= 0.0 { sqi } else { -sqi };
                    let (wr, wi) = (re + sqr, im + sqi);
                    let abs_w = (wr * wr + wi * wi).sqrt();
                    return (abs_w.ln(), wi.atan2(wr));
                }
                UnaryOp::Atanh => {
                    // atanh(z) = 1/2 * log((1+z)/(1-z))
                    let (nr, ni) = (1.0 + re, im);
                    let (dr, di) = (1.0 - re, -im);
                    let dn = dr * dr + di * di;
                    if dn == 0.0 {
                        return (f64::NAN, f64::NAN);
                    }
                    let (qr, qi) = ((nr * dr + ni * di) / dn, (ni * dr - nr * di) / dn);
                    let abs_q = (qr * qr + qi * qi).sqrt();
                    return (0.5 * abs_q.ln(), 0.5 * qi.atan2(qr));
                }
                // Rounding ops: no meaningful complex extension, return NaN
                _ => return (f64::NAN, f64::NAN),
            };
            (result, 0.0)
        }
    }
}