C:矢量化 For 循环

Question

我的代码的关键部分有以下两个循环。第一个是将复数 vector B(维度:N)乘以复数矩阵out1(维度:NxJ)并将结果存储在inc (尺寸:NxJ)。第二个循环将复数矩阵out2(维度:NxJ)转换为幅度和相位部分，并将其连续存储在t(维度为Nx2J)中。 inc、out1、out1 和 B 都是 fftw_complex 类型(2 double) 而 t 是一个 float 。

for (int i = 0; i < N * J; i++)
{
    k = i % N;
    inc[i][REAL] = out1[k][REAL] * B[i][REAL] - out1[k][IMAG] * B[i][IMAG];
    inc[i][IMAG] = out1[k][REAL] * B[i][IMAG] + out1[k][IMAG] * B[i][REAL];
}

for (int i = 0; i < N * J; i++)
{
    t[i]         = (float) sqrt(out2[i][REAL] * out2[i][REAL] 
                             +  out2[i][IMAG] * out2[i][IMAG]);
    t[N * J + i] = (float) atan2(out2[i][IMAG], out2[i][REAL]);
}

编译时使用:-Ofast -ftree-vectorize -fopt-info-vec-missed
-mavx2 -msse4，循环 1 的输出是:

note: not vectorized: not suitable for gather load _50 = *_49[0];
note: bad data references.
note: not vectorized: not enough data-refs in basic block.
note: not consecutive access _50 = *_49[0];
note: Build SLP failed: unrolling required in basic block SLP
note: not consecutive access _50 = *_49[0];
note: Build SLP failed: unvectorizable statement _50 = *_49[0];
note: Build SLP failed: different interleaving chains in one node _60 = *_49[0];

循环 2 的输出是:

note: versioning for alias required: can't determine dependence between *_70 and *_84
note: vector alignment may not be reachable
note: virtual phi. skip.
note: num. args = 4 (not unary/binary/ternary op).
note: not ssa-name.
note: use not simple.
note: no array mode for V4DF[2]
note: num. args = 4 (not unary/binary/ternary op).
note: not ssa-name.
note: use not simple.
note: no array mode for V4DF[2]
note: function is not vectorizable.
note: not vectorized: relevant stmt not supported: _85 = atan2 (_75, _73);
note: bad operation or unsupported loop bound.
note: versioning for alias required: can't determine dependence between *_70 and *_84
note: vector alignment may not be reachable
note: virtual phi. skip.
note: num. args = 4 (not unary/binary/ternary op).
note: not ssa-name.
note: use not simple.
note: no array mode for V2DF[2]
note: num. args = 4 (not unary/binary/ternary op).
note: not ssa-name.
note: use not simple.
note: no array mode for V2DF[2]
note: function is not vectorizable.
note: not vectorized: relevant stmt not supported: _85 = atan2 (_75, _73);
note: bad operation or unsupported loop bound.
note: not vectorized: no grouped stores in basic block.

我观察到这些循环是我代码中的瓶颈。我如何将它们向量化？

Answer 1

我的代码的可编译版本是

#include <math.h>

typedef double complex[2];
static const int REAL = 0;
static const int IMAG = 1;

void loop1(int N, int J, const complex B[], const complex out1[], complex inc[])
{
    const int NJ = N * J;
    for (int i = 0; i < NJ; ++i) {
        const int k = i % N;
        inc[i][IMAG] = out1[k][REAL] * B[i][IMAG] + out1[k][IMAG] * B[i][REAL];
        inc[i][REAL] = out1[k][REAL] * B[i][REAL] - out1[k][IMAG] * B[i][IMAG];
    }
}

void loop2(int N, int J, float t[], const complex out2[])
{
    const int NJ = N * J;
    float *const p = t + NJ;
    for (int i = 0; i < NJ; ++i) {
        /*t[i] = (float) hypot(out2[i][REAL], out2[i][IMAG]);*/
        t[i] = (float) sqrt(out2[i][REAL] * out2[i][REAL] + out2[i][IMAG] * out2[i][IMAG]);
        p[i] = (float) atan2(out2[i][IMAG], out2[i][REAL]);
    }
}

对于第一个循环，我得到:

42504487.c:10:5: note: not vectorized: not suitable for gather load _16 = *_15[0];
42504487.c:10:5: note: bad data references.
42504487.c:10:5: note: not vectorized: not enough data-refs in basic block.
42504487.c:15:1: note: not vectorized: not enough data-refs in basic block.
42504487.c:10:5: note: Two or more load stmts share the same dr.
42504487.c:10:5: note: Two or more load stmts share the same dr.
42504487.c:10:5: note: Build SLP failed: unrolling required in basic block SLP
42504487.c:10:5: note: Two or more load stmts share the same dr.
42504487.c:10:5: note: Two or more load stmts share the same dr.
42504487.c:10:5: note: can't determine dependence between *_11[1] and *_15[1]

对于第二个循环，我得到:

42504487.c:21:5: note: versioning for alias required: can't determine dependence between *_13 and *_25
42504487.c:21:5: note: vector alignment may not be reachable
42504487.c:21:5: note: virtual phi. skip.
42504487.c:21:5: note: num. args = 4 (not unary/binary/ternary op).
42504487.c:21:5: note: not ssa-name.
42504487.c:21:5: note: use not simple.
42504487.c:21:5: note: no array mode for V4DF[2]
42504487.c:21:5: note: num. args = 4 (not unary/binary/ternary op).
42504487.c:21:5: note: not ssa-name.
42504487.c:21:5: note: use not simple.
42504487.c:21:5: note: no array mode for V4DF[2]
42504487.c:21:5: note: function is not vectorizable.
42504487.c:21:5: note: not vectorized: relevant stmt not supported: _26 = atan2 (_19, _17);
42504487.c:21:5: note: bad operation or unsupported loop bound.
42504487.c:21:5: note: versioning for alias required: can't determine dependence between *_13 and *_25
42504487.c:21:5: note: vector alignment may not be reachable
42504487.c:21:5: note: virtual phi. skip.
42504487.c:21:5: note: num. args = 4 (not unary/binary/ternary op).
42504487.c:21:5: note: not ssa-name.
42504487.c:21:5: note: use not simple.
42504487.c:21:5: note: no array mode for V2DF[2]
42504487.c:21:5: note: num. args = 4 (not unary/binary/ternary op).
42504487.c:21:5: note: not ssa-name.
42504487.c:21:5: note: use not simple.
42504487.c:21:5: note: no array mode for V2DF[2]
42504487.c:21:5: note: function is not vectorizable.
42504487.c:21:5: note: not vectorized: relevant stmt not supported: _26 = atan2 (_19, _17);
42504487.c:21:5: note: bad operation or unsupported loop bound.
42504487.c:21:5: note: not vectorized: not enough data-refs in basic block.
42504487.c:26:1: note: not vectorized: not enough data-refs in basic block.
42504487.c:21:5: note: not vectorized: no grouped stores in basic block.

这里，我们有“no array mode for V4DF[2]”和“no array mode for V2DF[2]”，这表明我们没有适合矢量化的类型。

另外，“relevant stmt not supported: atan2”告诉我们没有atan2的 vector 实现。

此时，如果有足够的内核可用，我会改用 OpenMP，或许使用 -floop-parallelize-all。