運用 SIMD 來加速的演算法

目錄

SIMD 與 Rust

針對型別的支援 — feature(repr_simd)

加上 #[repr(simd)] 屬性的型別會被編譯成 SIMD vector, 此型別可以為泛型但必須是同種 primitive type 重複數次。 加上此屬性後該型別可能會根據不同平台而有不同的 alignment。

SIMD 操作 — feature(platform_intrinsics)

CPU 廠商通常會提供一個 C header 讓開發者使用 CPU 的 SIMD 功能, 例如 ARM 的 arm_neon.h 或是 x86 的 …mmintrin.h

這些功能都會以 compiler intrinsics 的形式來支援, 名稱也都會相似於 CPU 廠商所提供的 C header, 可以經由 extern block 選定適當的 ABI 來使用, 而不會放在 std 當中。

範例:

extern "platform-intrinsic" {
    fn x86_mm_abs_epi16(a: Simd8<i16>) -> Simd8<i16>;
    fn simd_add<T>(a: T, b: T) -> T;
    // ...
}

platform-intrinsic 中的函式會由 librustc_platform_intrinsics 來支援, 其中會用前綴來選擇對應平台的 SIMD 函式, 例如 x86_arm_aarch64 (可以由 rust/src/librustc_platform_intrinsics/lib.rs 而知), 在找到對應的平台後, 會再找到對應的 LLVM 定義(可以由 rust/src/librustc_platform_intrinsics/x86.rs 而知)。 這些 intrinsics 只在特定的 CPU 上可以使用, 如果 target CPU 不支援的話會產生編譯時期的錯誤。 ( librustc_platform_intrinsics 內針對各平台的程式是經由餵入不同的 JSON 設定檔給 rust/src/etc/platform-intrinsics/generator.py 所產生的)

除了上面提到的平台特定 SIMD 功能外, 有些功能是各個有支援 SIMD 的平台都能使用的, 這些功能會被包裝成更方便使用的形式, 例如 simd_addsimd_sub (可以在 rust/src/librustc_trans/intrinsic.rs 當中的 generic_simd_intrinsic 找到)。

更完整的通用列表:

extern "platform-intrinsic" {
    // Arithmetic
    fn simd_add<T>(x: T, y: T) -> T;
    fn simd_sub<T>(x: T, y: T) -> T;
    fn simd_mul<T>(x: T, y: T) -> T;
    fn simd_div<T>(x: T, y: T) -> T;
    fn simd_shl<T>(x: T, y: T) -> T;
    fn simd_shr<T>(x: T, y: T) -> T;
    fn simd_and<T>(x: T, y: T) -> T;
    fn simd_or<T>(x: T, y: T) -> T;
    fn simd_xor<T>(x: T, y: T) -> T;

    // Comparisons
    fn simd_eq<T, U>(v: T, w: T) -> U;
    fn simd_ne<T, U>(v: T, w: T) -> U;
    fn simd_lt<T, U>(v: T, w: T) -> U;
    fn simd_le<T, U>(v: T, w: T) -> U;
    fn simd_gt<T, U>(v: T, w: T) -> U;
    fn simd_ge<T, U>(v: T, w: T) -> U;

    // Shuffles (simd_shuffleN, N is usize)
    fn simd_shuffle2<T, U>(x: T, y: T, idx: [u32; 2]) -> U;
    fn simd_shuffle3<T, U>(x: T, y: T, idx: [u32; 3]) -> U;
    fn simd_shuffle4<T, U>(x: T, y: T, idx: [u32; 4]) -> U;
    fn simd_shuffle8<T, U>(x: T, y: T, idx: [u32; 8]) -> U;
    fn simd_shuffle16<T, U>(v: T, w: T, idx: [u32; 16]) -> U;

    // inserting/extracting elements
    fn simd_insert<T, E>(x: T, idx: u32, y: E) -> T;
    fn simd_extract<T, E>(x: T, idx: u32) -> E;

    // cast
    fn simd_cast<T, U>(x: T) -> U;
}

相關檔案:

平台偵測 — feature(cfg_target_feature)

要針對特定平台打開 SIMD 支援光是使用 cfg(target_arch = "...") 是不夠的, 因此需要 cfg(target_feature = "...") 的支援, 在 CPU 支援特定指令集時才開啟。 要特別指定開啟某個功能可以在編譯時加上參數, 例如 -C target-feature="+sse4.2" , 另外也可以藉由 -C target-cpu=native 來讓編譯器自動偵測現在的 CPU 來選擇要開啟的功能。

如果搭配第三方的 cfg-if 可能會讓程式長成這樣:

cfg_if_else! {
if #[cfg(target_feature = "avx")] {
    fn foo() { /* use AVX things */ }
} else if #[cfg(target_feature = "sse4.1")] {
    fn foo() { /* use SSE4.1 things */ }
} else if #[cfg(target_feature = "sse2")] {
    fn foo() { /* use SSE2 things */ }
} else if #[cfg(target_feature = "neon")] {
    fn foo() { /* use NEON things */ }
} else {
    fn foo() { /* universal fallback */ }
}

}

第三方套件 — simd

目前在 Rust 針對 SIMD 最常使用的套件是 simd

基本 SIMD 範例

加法 — simd_add

// Rust

#![feature(repr_simd)]
#![feature(platform_intrinsics)]

#[repr(simd)]
#[derive(Debug, Copy, Clone)]
pub struct f32x8(f32, f32, f32, f32,
                 f32, f32, f32, f32);

extern "platform-intrinsic" {
    fn simd_add<T>(a: T, b: T) -> T;
}

// 一般版本
fn inplace_add_array(lhs: &mut [f32; 8], rhs: &[f32; 8]) {
    for (i, j) in lhs.iter_mut().zip(rhs.iter()) {
        *i += *j;
    }
}

// SIMD 版本
fn inplace_add_array_simd(lhs: &mut f32x8, rhs: &f32x8) {
    unsafe {
        *lhs = simd_add(*lhs, *rhs);
    }
}

// 試用上面的函式
fn main() {
    use std::f32;

    // 沒有 overflow
    {
        let mut a = [0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5];
        let b = [70.5, 71.5, 72.5, 73.5, 74.5, 75.5, 76.5, 77.5];
        println!("{:?} +\n{:?} =", a, b);
        inplace_add_array(&mut a, &b);
        println!("{:?}", a);
    }
    {
        let mut a = f32x8(0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5);
        let b = f32x8(70.5, 71.5, 72.5, 73.5, 74.5, 75.5, 76.5, 77.5);
        println!("{:?} +\n{:?} =", a, b);
        inplace_add_array_simd(&mut a, &b);
        println!("{:?}", a);
    }

    // 有 overflow
    {
        let mut a = [0.5, f32::MAX, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5];
        let b = [70.5, f32::MAX/2.0, 72.5, 73.5, 74.5, 75.5, 76.5, 77.5];
        println!("{:?} +\n{:?} =", a, b);
        inplace_add_array(&mut a, &b);
        println!("{:?}", a);
    }
    {
        let mut a = f32x8(0.5, f32::MAX, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5);
        let b = f32x8(70.5, f32::MAX/2.0, 72.5, 73.5, 74.5, 75.5, 76.5, 77.5);
        println!("{:?} +\n{:?} =", a, b);
        inplace_add_array_simd(&mut a, &b);
        println!("{:?}", a);
    }
}

指令集說明

Byte Shuffle - pshufb (_mm_shuffle_epi8)

範例:

// C

#include <stdio.h>
#include <stdint.h>     // uint16_t
#include <tmmintrin.h>  // SSSE3

void print128_num(__m128i var) {
    uint16_t *val = (uint16_t*) &var;
    printf("Numerical: %i %i %i %i %i %i %i %i \n",
            val[0], val[1], val[2], val[3], val[4], val[5],
            val[6], val[7]);
}

int main() {
    // Set packed 16-bit integers
    // 128 bits, 8 short, per 16 bits
    __m128i v_in = _mm_setr_epi16(1, 2, 3, 4, 5, 6, 7, 8);
    // Set packed 8-bit integers
    // 128 bits, 16 chars, per 8 bits
    __m128i v_perm = _mm_setr_epi8(1, 0, 2, 3, 8, 9, 10, 11, 4, 5, 12, 13, 6, 7, 14, 15);
    // Shuffle packed 8-bit integers
    __m128i v_out = _mm_shuffle_epi8(v_in, v_perm); // pshufb
    print128_num(v_in);
    print128_num(v_out);
    return 0;
}

編譯並執行:

$ clang -mssse3 test.c
$ ./a.out
Numerical: 1 2 3 4 5 6 7 8
Numerical: 256 2 5 6 3 7 4 8

Byte Shuffle 操作:

Data (Number, Binary, Byte Index) :

    +---------------------+----------+----------+----------+----------+----------+----------+
    |          1          |          2          |          3          |          4          | Number
    +----------+----------+----------+----------+----------+----------+----------+----------+
    | 00000000 | 00000001 | 00000000 | 00000010 | 00000000 | 00000011 | 00000000 | 00000100 | Binary
    +----------+----------+----------+----------+----------+----------+----------+----------+
    |        0 |        1 |        2 |        3 |        4 |        5 |        6 |        7 | Index
    +----------+----------+----------+----------+----------+----------+----------+----------+

    +----------+----------+----------+----------+----------+----------+----------+----------+
    |          5          |          6          |          7          |          8          | Number
    +----------+----------+----------+----------+----------+----------+----------+----------+
    | 00000000 | 00000101 | 00000000 | 00000110 | 00000000 | 00000111 | 00000000 | 00001000 | Binary
    +----------+----------+----------+----------+----------+----------+----------+----------+
    |        8 |        9 |       10 |       11 |       12 |       13 |       14 |       15 | Index
    +----------+----------+----------+----------+----------+----------+----------+----------+

Index (Byte Index) :

    +------+------+------+------+------+------+------+------+
    |    1 |    0 |    2 |    3 |    8 |    9 |   10 |   11 |
    +------+------+------+------+------+------+------+------+

    +------+------+------+------+------+------+------+------+
    |    4 |    5 |   12 |   13 |    6 |    7 |   14 |   15 |
    +------+------+------+------+------+------+------+------+

Result :

    +----------+----------+----------+----------+----------+----------+----------+----------+
    |        1 |        0 |        2 |        3 |        8 |        9 |       10 |       11 | Index
    +----------+----------+----------+----------+----------+----------+----------+----------+
    | 00000001 | 00000000 | 00000000 | 00000010 | 00000000 | 00000101 | 00000000 | 00000110 | Binary
    +----------+----------+----------+----------+----------+----------+----------+----------+
    |         256         |          2          |          5          |          6          | Number
    +---------------------+----------+----------+----------+----------+----------+----------+

    +----------+----------+----------+----------+----------+----------+----------+----------+
    |        4 |        5 |       12 |       13 |        6 |        7 |       14 |       15 | Index
    +----------+----------+----------+----------+----------+----------+----------+----------+
    | 00000000 | 00000011 | 00000000 | 00000111 | 00000000 | 00000100 | 00000000 | 00001000 | Binary
    +----------+----------+----------+----------+----------+----------+----------+----------+
    |          3          |          7          |          4          |          8          | Number
    +---------------------+----------+----------+----------+----------+----------+----------+

編譯器 — Vectorization

介紹

這是讓編譯器自動將原本的程式轉換成使用 SIMD Instruction 的 Binary 的技術, 雖然目前已經有可以使用的技術, 但是還是有改進的空間, 程式設計師仍然能容易地利用 SIMD 自己寫出更好的程式。

Implicit:

Explicit:

相關參考:

Intel SPMD Program Compiler

ispc 是 Intel 開發的開放原始碼編譯器, 為的是有效地利用 CPU 上 SIMD 的支援來加速程式。 作法和 CUDA 還有 OpenCL 類似, 使用特別制定的 C-Like 語言來實做 ISPC Program (需要用 SIMD 來加速的 Function), 接著使用 ispc 來編譯, 剩餘程式則使用一般的 C 或 C++ 來撰寫即可, 最後搭配在一起達成加速的效果, 如此一來就不用自己去手寫利用 SSE 等指令的程式碼。

相關論文:

Mandelbrot 範例

取自 ispc/examples/mandelbrot/ , SIMD 版本:

mandelbrot_serial.cpp (一般版本):

static int mandel(float c_re, float c_im, int count) {
    float z_re = c_re, z_im = c_im;
    int i;
    for (i = 0; i < count; ++i) {
        if (z_re * z_re + z_im * z_im > 4.f)
            break;

        float new_re = z_re*z_re - z_im*z_im;
        float new_im = 2.f * z_re * z_im;
        z_re = c_re + new_re;
        z_im = c_im + new_im;
    }

    return i;
}

void mandelbrot_serial(float x0, float y0, float x1, float y1,
                       int width, int height, int maxIterations,
                       int output[])
{
    float dx = (x1 - x0) / width;
    float dy = (y1 - y0) / height;

    for (int j = 0; j < height; j++) {
        for (int i = 0; i < width; ++i) {
            float x = x0 + i * dx;
            float y = y0 + j * dy;

            int index = (j * width + i);
            output[index] = mandel(x, y, maxIterations);
        }
    }
}

mandelbrot.ispc (ispc 版本):

static inline int mandel(float c_re, float c_im, int count) {
    float z_re = c_re, z_im = c_im;
    int i;
    for (i = 0; i < count; ++i) {
        if (z_re * z_re + z_im * z_im > 4.)
            break;

        float new_re = z_re*z_re - z_im*z_im;
        float new_im = 2.f * z_re * z_im;
        unmasked {
            z_re = c_re + new_re;
            z_im = c_im + new_im;
        }
    }

    return i;
}

export void mandelbrot_ispc(uniform float x0, uniform float y0,
                            uniform float x1, uniform float y1,
                            uniform int width, uniform int height,
                            uniform int maxIterations,
                            uniform int output[])
{
    float dx = (x1 - x0) / width;
    float dy = (y1 - y0) / height;

    for (uniform int j = 0; j < height; j++) {
        // Note that we'll be doing programCount computations in parallel,
        // so increment i by that much.  This assumes that width evenly
        // divides programCount.
        foreach (i = 0 ... width) {
            // Figure out the position on the complex plane to compute the
            // number of iterations at.  Note that the x values are
            // different across different program instances, since its
            // initializer incorporates the value of the programIndex
            // variable.
            float x = x0 + i * dx;
            float y = y0 + j * dy;

            int index = j * width + i;
            output[index] = mandel(x, y, maxIterations);
        }
    }
}

mandelbrot.cpp :

#ifdef _MSC_VER
#define _CRT_SECURE_NO_WARNINGS
#define NOMINMAX
#pragma warning (disable: 4244)
#pragma warning (disable: 4305)
#endif

#include <stdio.h>
#include <algorithm>
#include "../timing.h"
#include "mandelbrot_ispc.h"
#include <string.h>
#include <cstdlib>
using namespace ispc;

extern void mandelbrot_serial(float x0, float y0, float x1, float y1,
                              int width, int height, int maxIterations,
                              int output[]);

/* Write a PPM image file with the image of the Mandelbrot set */
static void
writePPM(int *buf, int width, int height, const char *fn) {
    FILE *fp = fopen(fn, "wb");
    fprintf(fp, "P6\n");
    fprintf(fp, "%d %d\n", width, height);
    fprintf(fp, "255\n");
    for (int i = 0; i < width*height; ++i) {
        // Map the iteration count to colors by just alternating between
        // two greys.
        char c = (buf[i] & 0x1) ? 240 : 20;
        for (int j = 0; j < 3; ++j)
            fputc(c, fp);
    }
    fclose(fp);
    printf("Wrote image file %s\n", fn);
}


int main(int argc, char *argv[]) {
    static unsigned int test_iterations[] = {3, 3};
    unsigned int width = 768;
    unsigned int height = 512;
    float x0 = -2;
    float x1 = 1;
    float y0 = -1;
    float y1 = 1;

    if (argc > 1) {
        if (strncmp(argv[1], "--scale=", 8) == 0) {
            float scale = atof(argv[1] + 8);
            width *= scale;
            height *= scale;
        }
    }
    if ((argc == 3) || (argc == 4)) {
        for (int i = 0; i < 2; i++) {
            test_iterations[i] = atoi(argv[argc - 2 + i]);
        }
    }

    int maxIterations = 256;
    int *buf = new int[width*height];

    //
    // Compute the image using the ispc implementation; report the minimum
    // time of three runs.
    //
    double minISPC = 1e30;
    for (unsigned int i = 0; i < test_iterations[0]; ++i) {
        reset_and_start_timer();
        mandelbrot_ispc(x0, y0, x1, y1, width, height, maxIterations, buf);
        double dt = get_elapsed_mcycles();
        printf("@time of ISPC run:\t\t\t[%.3f] million cycles\n", dt);
        minISPC = std::min(minISPC, dt);
    }

    printf("[mandelbrot ispc]:\t\t[%.3f] million cycles\n", minISPC);
    writePPM(buf, width, height, "mandelbrot-ispc.ppm");

    // Clear out the buffer
    for (unsigned int i = 0; i < width * height; ++i)
        buf[i] = 0;

    //
    // And run the serial implementation 3 times, again reporting the
    // minimum time.
    //
    double minSerial = 1e30;
    for (unsigned int i = 0; i < test_iterations[1]; ++i) {
        reset_and_start_timer();
        mandelbrot_serial(x0, y0, x1, y1, width, height, maxIterations, buf);
        double dt = get_elapsed_mcycles();
        printf("@time of serial run:\t\t\t[%.3f] million cycles\n", dt);
        minSerial = std::min(minSerial, dt);
    }

    printf("[mandelbrot serial]:\t\t[%.3f] million cycles\n", minSerial);
    writePPM(buf, width, height, "mandelbrot-serial.ppm");

    printf("\t\t\t\t(%.2fx speedup from ISPC)\n", minSerial/minISPC);

    return 0;
}

timing.h :

#include <stdint.h>

#ifdef __arm__
#include <sys/time.h>
// There's no easy way to get a hardware clock counter on ARM, so instead
// we'll pretend it's a 1GHz processor and then compute pretend cycles
// based on elapsed time from gettimeofday().
__inline__ uint64_t rdtsc() {
  static bool first = true;
  static struct timeval tv_start;
  if (first) {
    gettimeofday(&tv_start, NULL);
    first = false;
    return 0;
  }

  struct timeval tv;
  gettimeofday(&tv, NULL);
  tv.tv_sec -= tv_start.tv_sec;
  tv.tv_usec -= tv_start.tv_usec;
  return (1000000ull * tv.tv_sec + tv.tv_usec) * 1000ull;
}

#include <sys/time.h>
static inline double rtc(void)
{
  struct timeval Tvalue;
  double etime;
  struct timezone dummy;

  gettimeofday(&Tvalue,&dummy);
  etime =  (double) Tvalue.tv_sec +
    1.e-6*((double) Tvalue.tv_usec);
  return etime;
}

#else // __arm__

#ifdef WIN32
#include <windows.h>
#define rdtsc __rdtsc
#else // WIN32
__inline__ uint64_t rdtsc() {
  uint32_t low, high;
#ifdef __x86_64
  __asm__ __volatile__ ("xorl %%eax,%%eax \n    cpuid"
                        ::: "%rax", "%rbx", "%rcx", "%rdx" );
#else
  __asm__ __volatile__ ("xorl %%eax,%%eax \n    cpuid"
                        ::: "%eax", "%ebx", "%ecx", "%edx" );
#endif
  __asm__ __volatile__ ("rdtsc" : "=a" (low), "=d" (high));
  return (uint64_t)high << 32 | low;
}

#include <sys/time.h>
static inline double rtc(void)
{
  struct timeval Tvalue;
  double etime;
  struct timezone dummy;

  gettimeofday(&Tvalue,&dummy);
  etime =  (double) Tvalue.tv_sec +
    1.e-6*((double) Tvalue.tv_usec);
  return etime;
}

#endif // !WIN32
#endif // !__arm__

static uint64_t start,  end;
static double  tstart, tend;

static inline void reset_and_start_timer()
{
    start = rdtsc();
#ifndef WIN32
    // Unused in Windows build, rtc() causing link errors
    tstart = rtc();
#endif
}

/* Returns the number of millions of elapsed processor cycles since the
   last reset_and_start_timer() call. */
static inline double get_elapsed_mcycles()
{
    end = rdtsc();
    return (end-start) / (1024. * 1024.);
}

#ifndef WIN32
// Unused in Windows build, rtc() causing link errors
static inline double get_elapsed_msec()
{
    tend = rtc();
    return (tend - tstart)*1e3;
}
#endif

編譯並執行:

$ mkdir objs
$ ispc -O3 --target=host mandelbrot.ispc -o objs/mandelbrot_ispc.o -h objs/mandelbrot_ispc.h
$ clang++ -O3 -I objs/ mandelbrot.cpp -c -o objs/mandelbrot.o
$ clang++ -O3 -I objs/ mandelbrot_serial.cpp -c -o objs/mandelbrot_serial.o
$ clang++ -O3 -I objs/ -o mandelbrot objs/mandelbrot.o objs/mandelbrot_ispc.o objs/mandelbrot_serial.o
$ ls -l mandelbrot
-rwxr-xr-x 1 user user 13424 Dec  3 13:06 mandelbrot
$ strip mandelbrot
$ ls -l mandelbrot
-rwxr-xr-x 1 user user 10432 Dec  3 13:06 mandelbrot
$ ldd mandelbrot
        linux-vdso.so.1 (0x00007ffc4b3fe000)
        libstdc++.so.6 => /usr/lib/libstdc++.so.6 (0x00007fc2108da000)
        libm.so.6 => /usr/lib/libm.so.6 (0x00007fc2105d6000)
        libgcc_s.so.1 => /usr/lib/libgcc_s.so.1 (0x00007fc2103bf000)
        libc.so.6 => /usr/lib/libc.so.6 (0x00007fc210021000)
        /lib64/ld-linux-x86-64.so.2 (0x00007fc210c62000)
$ ./mandelbrot  # Intel Xeon(R) CPU E5504 @ 2.00GHz
@time of ISPC run:                      [156.990] million cycles
@time of ISPC run:                      [154.923] million cycles
@time of ISPC run:                      [154.838] million cycles
[mandelbrot ispc]:              [154.838] million cycles
Wrote image file mandelbrot-ispc.ppm
@time of serial run:                    [319.032] million cycles
@time of serial run:                    [319.239] million cycles
@time of serial run:                    [318.566] million cycles
[mandelbrot serial]:            [318.566] million cycles
Wrote image file mandelbrot-serial.ppm
                                (2.06x speedup from ISPC)
$ ./mandelbrot  # Intel Core(TM) i5-6200U CPU @ 2.30GHz
@time of ISPC run:                      [64.837] million cycles
@time of ISPC run:                      [59.869] million cycles
@time of ISPC run:                      [61.037] million cycles
[mandelbrot ispc]:              [59.869] million cycles
Wrote image file mandelbrot-ispc.ppm
@time of serial run:                    [354.393] million cycles
@time of serial run:                    [353.565] million cycles
@time of serial run:                    [354.725] million cycles
[mandelbrot serial]:            [353.565] million cycles
Wrote image file mandelbrot-serial.ppm
                                (5.91x speedup from ISPC)

取自 ispc/examples/mandelbrot_tasks/ , SIMD + multithreading 版本:

$ ispc -O3 --target=host mandelbrot_tasks.ispc -o objs/mandelbrot_tasks_ispc.o -h objs/mandelbrot_tasks_ispc.h
$ clang++ -O3 -I objs/ mandelbrot_tasks.cpp -c -o objs/mandelbrot_tasks.o
$ clang++ -O3 -I objs/ mandelbrot_tasks_serial.cpp -c -o objs/mandelbrot_tasks_serial.o
$ clang++ -O3 tasksys.cpp -c -o objs/tasksys.o  # for ISPCAlloc, ISPCLaunch, ISPCSync
$ clang++ -O3 -I objs/ -o mandelbrot objs/mandelbrot_tasks.o objs/mandelbrot_tasks_ispc.o objs/mandelbrot_tasks_serial.o objs/tasksys.o -lpthread         # use pthread for multithreading
$ ls -l mandelbrot
-rwxr-xr-x 1 user user 28544 Dec  3 13:06 mandelbrot
$ strip mandelbrot
$ ls -l mandelbrot
-rwxr-xr-x 1 user user 23032 Dec  3 13:06 mandelbrot
$ ldd mandelbrot
        linux-vdso.so.1 (0x00007fffd6b38000)
        libpthread.so.0 => /usr/lib/libpthread.so.0 (0x00007f8396a40000)
        libstdc++.so.6 => /usr/lib/libstdc++.so.6 (0x00007f83966b8000)
        libm.so.6 => /usr/lib/libm.so.6 (0x00007f83963b4000)
        libgcc_s.so.1 => /usr/lib/libgcc_s.so.1 (0x00007f839619d000)
        libc.so.6 => /usr/lib/libc.so.6 (0x00007f8395dff000)
        /lib64/ld-linux-x86-64.so.2 (0x00007f8396c5d000)
$ ./mandelbrot  # Intel Xeon(R) CPU E5504 @ 2.00GHz
@time of ISPC + TASKS run:              [143.944] million cycles
@time of ISPC + TASKS run:              [114.246] million cycles
@time of ISPC + TASKS run:              [134.146] million cycles
@time of ISPC + TASKS run:              [131.987] million cycles
@time of ISPC + TASKS run:              [124.449] million cycles
@time of ISPC + TASKS run:              [118.815] million cycles
@time of ISPC + TASKS run:              [119.104] million cycles
[mandelbrot ispc+tasks]:        [114.246] million cycles
Wrote image file mandelbrot-ispc.ppm
@time of serial run:                    [2456.413] million cycles
[mandelbrot serial]:            [2456.413] million cycles
Wrote image file mandelbrot-serial.ppm
                                (21.50x speedup from ISPC + tasks)
$ ./mandelbrot  # Intel Core(TM) i5-6200U CPU @ 2.30GHz
@time of ISPC + TASKS run:              [100.304] million cycles
@time of ISPC + TASKS run:              [118.307] million cycles
@time of ISPC + TASKS run:              [99.052] million cycles
@time of ISPC + TASKS run:              [99.102] million cycles
@time of ISPC + TASKS run:              [98.825] million cycles
@time of ISPC + TASKS run:              [98.654] million cycles
@time of ISPC + TASKS run:              [108.323] million cycles
[mandelbrot ispc+tasks]:        [98.654] million cycles
Wrote image file mandelbrot-ispc.ppm
@time of serial run:                    [2760.993] million cycles
[mandelbrot serial]:            [2760.993] million cycles
Wrote image file mandelbrot-serial.ppm
                                (27.99x speedup from ISPC + tasks)

OpenMP SIMD

OpenMP 自 4.0 釋出後加入了 SIMD 的支援, 而各編譯器也漸漸有了支援:

使用方法如下:

#pragma omp simd
for (...) {
    ...
}

#pragma omp parallel for simd
for (...) {
    ...
}

相關參數可以參考 OpenMP 4.0 API C/C++ Syntax Quick Reference Card