matmult_native.h File Reference

Contains macros and function definitions for common matrix multiplication. More...

Go to the source code of this file.

Macros
#define	MatMult(N, A, X, Y)
#define	MatMult2(N, A, X, Y)
#define	MatMult3(N, A, X, Y)
#define	MatMult4(N, A, X, Y)
#define	MatMult5(N, A, X, Y)
#define	MatVecMult(N, y, A, x)
#define	MatVecMult2(N, y, A, x)
#define	MatVecMult3(N, y, A, x)
#define	MatVecMult4(N, y, A, x)
#define	MatVecMult5(N, y, A, x)

Detailed Description

Contains macros and function definitions for common matrix multiplication.

Author

Debojyoti Ghosh

The macro names in this header file conflict with PETSc, so include it with care.

Definition in file matmult_native.h.

Macro Definition Documentation

MatMult

#define MatMult	(		N,
			A,
			X,
			Y
	)

Value:

{ \
    int i,j,k;  \
    for (i = 0; i < (N); i++) { \
      for (j = 0; j < (N); j++) { \
        A[i*(N)+j] = 0.0; \
        for (k = 0; k < (N); k++) A[i*(N)+j] += X[i*(N)+k]*Y[k*(N)+j]; \
      } \
    } \
  }

Matrix-Matrix multiplication: A = X Y, where A, X, Y are square matrices of size N, saved as 1D arrays in row-major format.

Definition at line 18 of file matmult_native.h.

MatMult2

#define MatMult2	(		N,
			A,
			X,
			Y
	)

Value:

{ \
    A[0] = X[0]*Y[0] + X[1]*Y[2]; \
    A[1] = X[0]*Y[1] + X[1]*Y[3]; \
    A[2] = X[2]*Y[0] + X[3]*Y[2]; \
    A[3] = X[2]*Y[1] + X[3]*Y[3]; \
  }

MatMult, loop unrolled for N = 2.

Definition at line 32 of file matmult_native.h.

MatMult3

#define MatMult3	(		N,
			A,
			X,
			Y
	)

Value:

{ \
    A[0] = X[0]*Y[0] + X[1]*Y[3] + X[2]*Y[6]; \
    A[1] = X[0]*Y[1] + X[1]*Y[4] + X[2]*Y[7]; \
    A[2] = X[0]*Y[2] + X[1]*Y[5] + X[2]*Y[8]; \
    A[3] = X[3]*Y[0] + X[4]*Y[3] + X[5]*Y[6]; \
    A[4] = X[3]*Y[1] + X[4]*Y[4] + X[5]*Y[7]; \
    A[5] = X[3]*Y[2] + X[4]*Y[5] + X[5]*Y[8]; \
    A[6] = X[6]*Y[0] + X[7]*Y[3] + X[8]*Y[6]; \
    A[7] = X[6]*Y[1] + X[7]*Y[4] + X[8]*Y[7]; \
    A[8] = X[6]*Y[2] + X[7]*Y[5] + X[8]*Y[8]; \
  }

MatMult, loop unrolled for N = 3.

Definition at line 43 of file matmult_native.h.

MatMult4

#define MatMult4	(		N,
			A,
			X,
			Y
	)

Value:

{ \
    A[0]  =  X[0]*Y[0]  +  X[1]*Y[4]  +  X[2]*Y[8]  +  X[3]*Y[12]; \
    A[1]  =  X[0]*Y[1]  +  X[1]*Y[5]  +  X[2]*Y[9]  +  X[3]*Y[13]; \
    A[2]  =  X[0]*Y[2]  +  X[1]*Y[6]  +  X[2]*Y[10] +  X[3]*Y[14]; \
    A[3]  =  X[0]*Y[3]  +  X[1]*Y[7]  +  X[2]*Y[11] +  X[3]*Y[15]; \
    A[4]  =  X[4]*Y[0]  +  X[5]*Y[4]  +  X[6]*Y[8]  +  X[7]*Y[12]; \
    A[5]  =  X[4]*Y[1]  +  X[5]*Y[5]  +  X[6]*Y[9]  +  X[7]*Y[13]; \
    A[6]  =  X[4]*Y[2]  +  X[5]*Y[6]  +  X[6]*Y[10] +  X[7]*Y[14]; \
    A[7]  =  X[4]*Y[3]  +  X[5]*Y[7]  +  X[6]*Y[11] +  X[7]*Y[15]; \
    A[8]  =  X[8]*Y[0]  +  X[9]*Y[4]  +  X[10]*Y[8]  + X[11]*Y[12];\
    A[9]  =  X[8]*Y[1]  +  X[9]*Y[5]  +  X[10]*Y[9]  + X[11]*Y[13];\
    A[10] =  X[8]*Y[2]  +  X[9]*Y[6]  +  X[10]*Y[10] + X[11]*Y[14];\
    A[11] =  X[8]*Y[3]  +  X[9]*Y[7]  +  X[10]*Y[11] + X[11]*Y[15];\
    A[12] =  X[12]*Y[0] +  X[13]*Y[4] +  X[14]*Y[8]  + X[15]*Y[12];\
    A[13] =  X[12]*Y[1] +  X[13]*Y[5] +  X[14]*Y[9]  + X[15]*Y[13];\
    A[14] =  X[12]*Y[2] +  X[13]*Y[6] +  X[14]*Y[10] + X[15]*Y[14];\
    A[15] =  X[12]*Y[3] +  X[13]*Y[7] +  X[14]*Y[11] + X[15]*Y[15];\
  }

MatMult, loop unrolled for N = 4.

Definition at line 59 of file matmult_native.h.

MatMult5

#define MatMult5	(		N,
			A,
			X,
			Y
	)

Value:

{ \
    A[0]  =  X[0]*Y[0]  +  X[1]*Y[5]  +  X[2]*Y[10]  +  X[3]*Y[15]  +  X[4]*Y[20]; \
    A[1]  =  X[0]*Y[1]  +  X[1]*Y[6]  +  X[2]*Y[11]  +  X[3]*Y[16]  +  X[4]*Y[21]; \
    A[2]  =  X[0]*Y[2]  +  X[1]*Y[7]  +  X[2]*Y[12]  +  X[3]*Y[17]  +  X[4]*Y[22]; \
    A[3]  =  X[0]*Y[3]  +  X[1]*Y[8]  +  X[2]*Y[13]  +  X[3]*Y[18]  +  X[4]*Y[23]; \
    A[4]  =  X[0]*Y[4]  +  X[1]*Y[9]  +  X[2]*Y[14]  +  X[3]*Y[19]  +  X[4]*Y[24]; \
    A[5]  =  X[5]*Y[0]  +  X[6]*Y[5]  +  X[7]*Y[10]  +  X[8]*Y[15]  +  X[9]*Y[20]; \
    A[6]  =  X[5]*Y[1]  +  X[6]*Y[6]  +  X[7]*Y[11]  +  X[8]*Y[16]  +  X[9]*Y[21]; \
    A[7]  =  X[5]*Y[2]  +  X[6]*Y[7]  +  X[7]*Y[12]  +  X[8]*Y[17]  +  X[9]*Y[22]; \
    A[8]  =  X[5]*Y[3]  +  X[6]*Y[8]  +  X[7]*Y[13]  +  X[8]*Y[18]  +  X[9]*Y[23]; \
    A[9]  =  X[5]*Y[4]  +  X[6]*Y[9]  +  X[7]*Y[14]  +  X[8]*Y[19]  +  X[9]*Y[24]; \
    A[10] =  X[10]*Y[0] +  X[11]*Y[5] +  X[12]*Y[10] +  X[13]*Y[15] +  X[14]*Y[20];\
    A[11] =  X[10]*Y[1] +  X[11]*Y[6] +  X[12]*Y[11] +  X[13]*Y[16] +  X[14]*Y[21];\
    A[12] =  X[10]*Y[2] +  X[11]*Y[7] +  X[12]*Y[12] +  X[13]*Y[17] +  X[14]*Y[22];\
    A[13] =  X[10]*Y[3] +  X[11]*Y[8] +  X[12]*Y[13] +  X[13]*Y[18] +  X[14]*Y[23];\
    A[14] =  X[10]*Y[4] +  X[11]*Y[9] +  X[12]*Y[14] +  X[13]*Y[19] +  X[14]*Y[24];\
    A[15] =  X[15]*Y[0] +  X[16]*Y[5] +  X[17]*Y[10] +  X[18]*Y[15] +  X[19]*Y[20];\
    A[16] =  X[15]*Y[1] +  X[16]*Y[6] +  X[17]*Y[11] +  X[18]*Y[16] +  X[19]*Y[21];\
    A[17] =  X[15]*Y[2] +  X[16]*Y[7] +  X[17]*Y[12] +  X[18]*Y[17] +  X[19]*Y[22];\
    A[18] =  X[15]*Y[3] +  X[16]*Y[8] +  X[17]*Y[13] +  X[18]*Y[18] +  X[19]*Y[23];\
    A[19] =  X[15]*Y[4] +  X[16]*Y[9] +  X[17]*Y[14] +  X[18]*Y[19] +  X[19]*Y[24];\
    A[20] =  X[20]*Y[0] +  X[21]*Y[5] +  X[22]*Y[10] +  X[23]*Y[15] +  X[24]*Y[20];\
    A[21] =  X[20]*Y[1] +  X[21]*Y[6] +  X[22]*Y[11] +  X[23]*Y[16] +  X[24]*Y[21];\
    A[22] =  X[20]*Y[2] +  X[21]*Y[7] +  X[22]*Y[12] +  X[23]*Y[17] +  X[24]*Y[22];\
    A[23] =  X[20]*Y[3] +  X[21]*Y[8] +  X[22]*Y[13] +  X[23]*Y[18] +  X[24]*Y[23];\
    A[24] =  X[20]*Y[4] +  X[21]*Y[9] +  X[22]*Y[14] +  X[23]*Y[19] +  X[24]*Y[24];\
  }

MatMult, loop unrolled for N = 5.

Definition at line 82 of file matmult_native.h.

MatVecMult

#define MatVecMult	(		N,
			y,
			A,
			x
	)

Value:

{ \
    int i,j; \
    for (i = 0; i < (N); i++) { \
      y[i] = 0; \
      for (j = 0; j < (N); j++) y[i] += A[i*(N)+j]*x[j]; \
    } \
  }

Matrix-Vector multiplication: y = A x, where x, y are vectors of size N, and A is a square matrix of size N saved as a 1D array in row-major format.

Definition at line 116 of file matmult_native.h.

MatVecMult2

#define MatVecMult2	(		N,
			y,
			A,
			x
	)

Value:

{ \
    y[0] = A[0]*x[0] + A[1]*x[1];\
    y[1] = A[2]*x[0] + A[3]*x[1];\
  }

MatVecMult, loop unrolled for N = 2.

Definition at line 128 of file matmult_native.h.

MatVecMult3

#define MatVecMult3	(		N,
			y,
			A,
			x
	)

Value:

{ \
    y[0] = A[0]*x[0] + A[1]*x[1] + A[2]*x[2];\
    y[1] = A[3]*x[0] + A[4]*x[1] + A[5]*x[2];\
    y[2] = A[6]*x[0] + A[7]*x[1] + A[8]*x[2];\
  }

MatVecMult, loop unrolled for N = 3.

Definition at line 137 of file matmult_native.h.

MatVecMult4

#define MatVecMult4	(		N,
			y,
			A,
			x
	)

Value:

{ \
    y[0] = A[0]*x[0]  +  A[1]*x[1]  +  A[2]*x[2]  +  A[3]*x[3]; \
    y[1] = A[4]*x[0]  +  A[5]*x[1]  +  A[6]*x[2]  +  A[7]*x[3]; \
    y[2] = A[8]*x[0]  +  A[9]*x[1]  +  A[10]*x[2] +  A[11]*x[3];\
    y[3] = A[12]*x[0] +  A[13]*x[1] +  A[14]*x[2] +  A[15]*x[3];\
  }

MatVecMult, loop unrolled for N = 4.

Definition at line 147 of file matmult_native.h.

MatVecMult5

#define MatVecMult5	(		N,
			y,
			A,
			x
	)

Value:

{ \
    y[0] = A[0]*x[0]  +  A[1]*x[1]  +  A[2]*x[2]  +  A[3]*x[3]  +  A[4]*x[4]; \
    y[1] = A[5]*x[0]  +  A[6]*x[1]  +  A[7]*x[2]  +  A[8]*x[3]  +  A[9]*x[4]; \
    y[2] = A[10]*x[0] + A[11]*x[1]  +  A[12]*x[2] +  A[13]*x[3] +  A[14]*x[4];\
    y[3] = A[15]*x[0] +  A[16]*x[1] +  A[17]*x[2] +  A[18]*x[3] +  A[19]*x[4];\
    y[4] = A[20]*x[0] +  A[21]*x[1] +  A[22]*x[2] +  A[23]*x[3] +  A[24]*x[4];\
  }

MatVecMult, loop unrolled for N = 5.

Definition at line 158 of file matmult_native.h.