# SLEEF - DFT library reference

## Table of contents

- Introduction
- Compiling and installing the library
- Math library reference
- DFT library reference

- Tutorial
- Function reference

- Other tools included in the package
- Benchmark results
- Additional notes

## Tutorial

I now explain how to use this DFT library by referring to an example source code shown below. This source code is included in the distribution package under src/dft-tester directory.

    // gcc tutorial.c -lsleef -lsleefdft -lm
    #include <stdio.h>
    #include <stdlib.h>
    #include <stdint.h>
    #include <math.h>
    #include <complex.h>

    #include "sleef.h"
    #include "sleefdft.h"

    #define THRES 1e-4

    typedef double complex cmpl;

    cmpl omega(double n, double kn) {
      return cexp((-2 * M_PI * _Complex_I / n) * kn);
    }

    void forward(cmpl *ts, cmpl *fs, int len) {
      for(int k=0;k<len;k++) {
        fs[k] = 0;
        for(int n=0;n<len;n++) fs[k] += ts[n] * omega(len, n*k);
      }
    }

    int main(int argc, char **argv) {
      int n = 256;
      if (argc == 2) n = 1 << atoi(argv[1]);

      SleefDFT_setPlanFilePath("plan.txt", NULL, SLEEF_PLAN_AUTOMATIC);

      double *sx = (double *)Sleef_malloc(n*2 * sizeof(double));
      double *sy = (double *)Sleef_malloc(n*2 * sizeof(double));

      struct SleefDFT *p = SleefDFT_double_init1d(n, sx, sy, SLEEF_MODE_FORWARD);

      if (p == NULL) {
        printf("SleefDFT initialization failed\n");
        exit(-1);
      }

      cmpl *ts = (cmpl *)malloc(sizeof(cmpl)*n);
      cmpl *fs = (cmpl *)malloc(sizeof(cmpl)*n);

      for(int i=0;i<n;i++) {
        ts[i] =
          (2.0 * (rand() / (double)RAND_MAX) - 1) * 1.0 +
          (2.0 * (rand() / (double)RAND_MAX) - 1) * _Complex_I;

        sx[(i*2+0)] = creal(ts[i]);
        sx[(i*2+1)] = cimag(ts[i]);
      }

      forward(ts, fs, n);

      SleefDFT_double_execute(p, NULL, NULL);

      int success = 1;

      for(int i=0;i<n;i++) {
        if ((fabs(sy[(i*2+0)] - creal(fs[i])) > THRES) ||
            (fabs(sy[(i*2+1)] - cimag(fs[i])) > THRES)) {
          success = 0;
        }
      }

      printf("%s\n", success ? "OK" : "NG");

      free(fs); free(ts);
      Sleef_free(sy); Sleef_free(sx);

      SleefDFT_dispose(p);

      exit(success);
    }

Fig. 4.1: Test code for DFT subroutines

As shown in the first line, you can compile the source code with the following command, after you install the library.

    $ gcc tutorial.c -lsleef -lsleefdft -lm

This program takes one integer argument n. It executes forward complex transform with size 2n using a naive transform and the library. If the two results match, it prints OK.

For the first execution, this program takes a few seconds to finish. This is because the library measures computation speed with many different configurations to find the best execution plan. The best plan is saved to "plan.txt", as specified in line 28. Later executions will finish instantly as the library reads the plan from this file. Instead of specifying the file name in the program, the file can be specified by SLEEFDFTPLAN environment variable. Instead of constructing or loading a plan, the library can estimate a modestly good configuration, if SLEEF_MODE_ESTIMATE flag is specified at line 30.

This library executes transforms using the most suitable SIMD instructions available on the computer, in addition to multi-threading. In order to make the computation efficient, the library requires the input and output arrays to be aligned to some boundaries so that the data can be accessed with SIMD instructions. By using Sleef_malloc, as seen in line 37 and 38, this alignment is ensured. Memory allocated with Sleef_malloc has to be freed with Sleef_free, as seen in line 68. When a transform is executed, you need to pass the pointer returned by Sleef_malloc. You can allocate an aligned memory region yourself, and pass the pointer to the library.

The real and imaginary parts of the kth number are stored in (2k)-th and (2k+1)-th elements of the input and output array, respectively. At line 54, the transform is executed by the library. You can specify the same array as the input and output.

Under src/dft-tester directory, there are other examples showing how to execute transforms in a way that you get equivalent results to other libraries.

## Function reference

Sleef_malloc - allocate aligned memory

Synopsis

#include <stdlib.h>
#include <sleef.h>
void * Sleef_malloc(size_t z);
Link with -lsleef.

Description

Sleef_malloc allocates z bytes of aligned memory region, and return the pointer to that region. The returned pointer points an address that can be accessed by all SIMD load and store instructions available on that computer. Memory regions allocated by Sleef_malloc have to be freed with Sleef_free.

Sleef_free - free memory allocated by Sleef_malloc

Synopsis

#include <stdlib.h>
#include <sleef.h>
void Sleef_free(void *ptr);
Link with -lsleef.

Description

A memory region pointed by ptr that is allocated by Sleef_malloc can be freed with Sleef_free.

SleefDFT_setPlanFilePath - set the file path for storing execution plans

Synopsis

#include <stdint.h>
#include <sleefdft.h>
void SleefDFT_setPlanFilePath(const char *path, const char *arch, uint64_t mode);
Link with -lsleefdft -lsleef.

Description

File name for storing execution plan can be specified by this function. If NULL is specified as path, the file name is read from SLEEFDFTPLAN environment variable. A string for identifying system micro architecture can be also given. The library will automatically detect the marchitecture if NULL is given as arch. Management options for the plan file can be specified by the mode parameter, as shown below.

Table 4.2: Mode flags for SleefFT_setPlanFilePath
Flag | Meaning
SLEEF_PLAN_AUTOMATIC | Execution plans are automatically loaded and saved. Plans are generated if it does not exist.
SLEEF_PLAN_READONLY | Execution plans are automatically loaded, but not saved.
SLEEF_PLAN_RESET | Existing execution plans are reset and constructed from the beginning.

SleefDFT_double_init1d, SleefDFT_float_init1d - initialize the tables for 1D transform

Synopsis

#include <stdint.h>
#include <sleefdft.h>
struct SleefDFT * SleefDFT_double_init1d(uint32_t n, const double *in, double *out, uint64_t mode);
struct SleefDFT * SleefDFT_float_init1d(uint32_t n, const float *in, float *out, uint64_t mode);
Link with -lsleefdft -lsleef.

Description

These functions generates and initializes the tables that is used for 1D transform, and returns the pointer. Size of transform can be specified by n. Currently, power-of-two sizes can be only specified. The list of the flags that can be passed to mode is shown below.

Table 4.3: Mode flags for SleefDFT_double_init
Flag | Meaning
SLEEF_MODE_FORWARD | Tables are initialized for forward transforms.
SLEEF_MODE_BACKWARD | Tables are initialized for backward transforms.
SLEEF_MODE_COMPLEX | Tables are initialized for complex transforms.
SLEEF_MODE_REAL | Tables are initialized for real transforms.
SLEEF_MODE_ALT | Tables are initialized for alternative real transforms.
SLEEF_MODE_ESTIMATE | Execution plans are estimated.
SLEEF_MODE_MEASURE | Execution plans are measured when they are needed.
SLEEF_MODE_VERBOSE | Messages are displayed.
SLEEF_MODE_NO_MT | Multithreading will be disabled in the computation for transforms.

Return value

These functions return a pointer to the data that is used for 1D DFT computation, or NULL if an error occurred.

SleefDFT_double_init2d, SleefDFT_float_init2d - initialize the tables for 2D transform

Synopsis

#include <stdint.h>
#include <sleefdft.h>
struct SleefDFT * SleefDFT_double_init2d(uint32_t n, uint32_t m, const double *in, double *out, uint64_t mode);
struct SleefDFT * SleefDFT_float_init2d(uint32_t n, uint32_t m, const float *in, float *out, uint64_t mode);
Link with -lsleefdft -lsleef.

Description

These functions generates and initilizes the tables that is used for 2D transform, and returns the pointer. Size of transform can be specified by n. Currently, power-of-two sizes can be only specified. The list of the flags that can be passed to mode is shown below.

Return value

These functions return a pointer to the data that is used for 2D DFT computation, or NULL if an error occurred.

SleefDFT_double_execute, SleefDFT_float_execute - execute a transform

Synopsis

#include <stdint.h>
#include <sleefdft.h>
void SleefDFT_double_execute(struct SleefDFT *ptr, const double *in, double *out);
void SleefDFT_float_execute(struct SleefDFT *ptr, const float *in, float *out);
Link with -lsleefdft -lsleef.

Description

ptr is a pointer to the plan. in and out must be pointers returned from Sleef_malloc function. You can specify the same pointer to in and out.

SleefDFT_dispose - dispose the tables for transforms

Synopsis

#include <stdint.h>
#include <sleefdft.h>
void SleefDFT_dispose(struct SleefDFT *ptr);
Link with -lsleefdft -lsleef.

Description

This function frees a plan returned by SleefDFT_double_init1d, SleefDFT_float_init1d, SleefDFT_double_init2d, or SleefDFT_float_init2d functions.