Enhance FFT Radix2 & vectorisation part #262
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lamphamsy
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src/simd_fnt.h
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| const unsigned vec_size = countof<T>(); | ||
| const T max = 1 << (element_size * 8 - 1); | ||
| const T max = 1U << (sizeof(T) * 8 - 1); |
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minor: could use CHAR_BIT instead of 8 (to be 100% portable, even so 8 is probably enough for the platform we target).
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1. Butterfly CT
1.1. single-layer butterfly
For each pair `(P, Q) = (buf[i], buf[i + m]` for `step = 2 * m`
```
coef r1 = W[start * n / (2 * m)]
P = P + r1 * Q
Q = P - r1 * Q
```
1.2. 2-layer butterfly
For each quadruple `(P, Q, R, S) = (buf[i], buf[i + m], buf[i + 2 * m],
buf[i + 3 * m])`
First layer: butterfly on `(P, Q)` and` (R, S)` for `step = 2 * m`
```
coef r1 = W[start * n / (2 * m)]
P = P + r1 * Q
Q = P - r1 * Q
R = R + r1 * S
S = R - r1 * S
```
Second layer: butterfly on `(P, R)` and `(Q, S)` for `step = 4 * m`
```
coef r2 = W[start * n / (4 * m)]
coef r3 = W[(start + m) * n / (4 * m)]
P = P + r2 * R
R = P - r2 * R
Q = Q + r3 * S
S = Q - r3 * S
```
2. Butterfly GS
2.1. single-layer butterfly
For each pair `(P, Q) = (buf[i], buf[i + m]` for `step = 2 * m`
```
coef r = inv_W[start * n / (2 * m)]
P = P + Q
Q = r * (P - Q)
```
The SIMD parts will be re-implemented in next commits
1. Essential operations - simd_128.h contains essential wrappers of SIMD operations on SSE - simd_256.h contains essential wrappers of SIMD operations on AVX 2. Basic operations - simd_basic.h contain basic operations used in following cases, and also operations for RingModN 3. Vectorized operations - simd_fnt.h contains vectorized operations dedicated for FNT - simd_nf4.h contains vectorized operations dedicated for nf4
It implements basic operations that will be used everywhere. It includes also operations for RingModN
- Indices for SIMD parts are computed once in FFT function - Define butterfly_ct_two_layers_step_slow for non-vectorized functions
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slaperche-scality
approved these changes
Dec 20, 2018
|
@slaperche-scality thanks a lot! |
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The branch is the target of the two PRs:
Part1: Part1: Radix-2 FFT enhancement by working on two layers per iteration #253
Part2: Part2: Vectorize operations for Radix-2 FFT & re-work vectorization part #254
The PR is active when the PRs are merged.