reproBLAS.h defines reproducible BLAS Methods. More...

#include <complex.h>

Functions
double	reproBLAS_rdsum (const int fold, const int N, const double *X, const int incX)
	Compute the reproducible sum of double precision vector X. More...

double	reproBLAS_rdasum (const int fold, const int N, const double *X, const int incX)
	Compute the reproducible absolute sum of double precision vector X. More...

double	reproBLAS_rdnrm2 (const int fold, const int N, const double *X, const int incX)
	Compute the reproducible Euclidian norm of double precision vector X. More...

double	reproBLAS_rddot (const int fold, const int N, const double X, const int incX, const double Y, const int incY)
	Compute the reproducible dot product of double precision vectors X and Y. More...

float	reproBLAS_rsdot (const int fold, const int N, const float X, const int incX, const float Y, const int incY)
	Compute the reproducible dot product of single precision vectors X and Y. More...

float	reproBLAS_rsasum (const int fold, const int N, const float *X, const int incX)
	Compute the reproducible absolute sum of single precision vector X. More...

float	reproBLAS_rssum (const int fold, const int N, const float *X, const int incX)
	Compute the reproducible sum of single precision vector X. More...

float	reproBLAS_rsnrm2 (const int fold, const int N, const float *X, const int incX)
	Compute the reproducible Euclidian norm of single precision vector X. More...

void	reproBLAS_rzsum_sub (const int fold, const int N, const void X, int incX, void sum)
	Compute the reproducible sum of complex double precision vector X. More...

double	reproBLAS_rdzasum (const int fold, const int N, const void *X, const int incX)
	Compute the reproducible absolute sum of complex double precision vector X. More...

double	reproBLAS_rdznrm2 (const int fold, const int N, const void *X, int incX)
	Compute the reproducible Euclidian norm of complex double precision vector X. More...

void	reproBLAS_rzdotc_sub (const int fold, const int N, const void X, const int incX, const void Y, const int incY, void *dotc)
	Compute the reproducible conjugated dot product of complex double precision vectors X and Y. More...

void	reproBLAS_rzdotu_sub (const int fold, const int N, const void X, const int incX, const void Y, const int incY, void *dotu)
	Compute the reproducible unconjugated dot product of complex double precision vectors X and Y. More...

void	reproBLAS_rcsum_sub (const int fold, const int N, const void X, const int incX, void sum)
	Compute the reproducible sum of complex single precision vector X. More...

float	reproBLAS_rscasum (const int fold, const int N, const void *X, const int incX)
	Compute the reproducible absolute sum of complex single precision vector X. More...

float	reproBLAS_rscnrm2 (const int fold, const int N, const void *X, const int incX)
	Compute the reproducible Euclidian norm of complex single precision vector X. More...

void	reproBLAS_rcdotc_sub (const int fold, const int N, const void X, const int incX, const void Y, const int incY, void *dotc)
	Compute the reproducible conjugated dot product of complex single precision vectors X and Y. More...

void	reproBLAS_rcdotu_sub (const int fold, const int N, const void X, const int incX, const void Y, const int incY, void *dotu)
	Compute the reproducible unconjugated dot product of complex single precision vectors X and Y. More...

void	reproBLAS_rdgemv (const int fold, const char Order, const char TransA, const int M, const int N, const double alpha, const double A, const int lda, const double X, const int incX, const double beta, double *Y, const int incY)
	Add to double precision vector Y the reproducible matrix-vector product of double precision matrix A and double precision vector X. More...

void	reproBLAS_rdgemm (const int fold, const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const double alpha, const double A, const int lda, const double B, const int ldb, const double beta, double *C, const int ldc)
	Add to double precision matrix C the reproducible matrix-matrix product of double precision matrices A and B. More...

void	reproBLAS_rsgemv (const int fold, const char Order, const char TransA, const int M, const int N, const float alpha, const float A, const int lda, const float X, const int incX, const float beta, float *Y, const int incY)
	Add to single precision vector Y the reproducible matrix-vector product of single precision matrix A and single precision vector X. More...

void	reproBLAS_rsgemm (const int fold, const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const float alpha, const float A, const int lda, const float B, const int ldb, const float beta, float *C, const int ldc)
	Add to single precision matrix C the reproducible matrix-matrix product of single precision matrices A and B. More...

void	reproBLAS_rzgemv (const int fold, const char Order, const char TransA, const int M, const int N, const void alpha, const void A, const int lda, const void X, const int incX, const void beta, void *Y, const int incY)
	Add to complex double precision vector Y the reproducible matrix-vector product of complex double precision matrix A and complex double precision vector X. More...

void	reproBLAS_rzgemm (const int fold, const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const void alpha, const void A, const int lda, const void B, const int ldb, const void beta, void *C, const int ldc)
	Add to complex double precision matrix C the reproducible matrix-matrix product of complex double precision matrices A and B. More...

void	reproBLAS_rcgemv (const int fold, const char Order, const char TransA, const int M, const int N, const void alpha, const void A, const int lda, const void X, const int incX, const void beta, void *Y, const int incY)
	Add to complex single precision vector Y the reproducible matrix-vector product of complex single precision matrix A and complex single precision vector X. More...

void	reproBLAS_rcgemm (const int fold, const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const void alpha, const void A, const int lda, const void B, const int ldb, const void beta, void *C, const int ldc)
	Add to complex single precision matrix C the reproducible matrix-matrix product of complex single precision matrices A and B. More...

double	reproBLAS_dsum (const int N, const double *X, const int incX)
	Compute the reproducible sum of double precision vector X. More...

double	reproBLAS_dasum (const int N, const double *X, const int incX)
	Compute the reproducible absolute sum of double precision vector X. More...

double	reproBLAS_dnrm2 (const int N, const double *X, const int incX)
	Compute the reproducible Euclidian norm of double precision vector X. More...

double	reproBLAS_ddot (const int N, const double X, const int incX, const double Y, const int incY)
	Compute the reproducible dot product of double precision vectors X and Y. More...

float	reproBLAS_sdot (const int N, const float X, const int incX, const float Y, const int incY)
	Compute the reproducible dot product of single precision vectors X and Y. More...

float	reproBLAS_sasum (const int N, const float *X, const int incX)
	Compute the reproducible absolute sum of single precision vector X. More...

float	reproBLAS_ssum (const int N, const float *X, const int incX)
	Compute the reproducible sum of single precision vector X. More...

float	reproBLAS_snrm2 (const int N, const float *X, const int incX)
	Compute the reproducible Euclidian norm of single precision vector X. More...

void	reproBLAS_zsum_sub (const int N, const void X, int incX, void sum)
	Compute the reproducible sum of complex double precision vector X. More...

double	reproBLAS_dzasum (const int N, const void *X, const int incX)
	Compute the reproducible absolute sum of complex double precision vector X. More...

double	reproBLAS_dznrm2 (const int N, const void *X, int incX)
	Compute the reproducible Euclidian norm of complex double precision vector X. More...

void	reproBLAS_zdotc_sub (const int N, const void X, const int incX, const void Y, const int incY, void *dotc)
	Compute the reproducible conjugated dot product of complex double precision vectors X and Y. More...

void	reproBLAS_zdotu_sub (const int N, const void X, const int incX, const void Y, const int incY, void *dotu)
	Compute the reproducible unconjugated dot product of complex double precision vectors X and Y. More...

void	reproBLAS_csum_sub (const int N, const void X, const int incX, void sum)
	Compute the reproducible sum of complex single precision vector X. More...

float	reproBLAS_scasum (const int N, const void *X, const int incX)
	Compute the reproducible absolute sum of complex single precision vector X. More...

float	reproBLAS_scnrm2 (const int N, const void *X, const int incX)
	Compute the reproducible Euclidian norm of complex single precision vector X. More...

void	reproBLAS_cdotc_sub (const int N, const void X, const int incX, const void Y, const int incY, void *dotc)
	Compute the reproducible conjugated dot product of complex single precision vectors X and Y. More...

void	reproBLAS_cdotu_sub (const int N, const void X, const int incX, const void Y, const int incY, void *dotu)
	Compute the reproducible unconjugated dot product of complex single precision vectors X and Y. More...

void	reproBLAS_dgemv (const char Order, const char TransA, const int M, const int N, const double alpha, const double A, const int lda, const double X, const int incX, const double beta, double *Y, const int incY)
	Add to double precision vector Y the reproducible matrix-vector product of double precision matrix A and double precision vector X. More...

void	reproBLAS_dgemm (const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const double alpha, const double A, const int lda, const double B, const int ldb, const double beta, double *C, const int ldc)
	Add to double precision matrix C the reproducible matrix-matrix product of double precision matrices A and B. More...

void	reproBLAS_sgemv (const char Order, const char TransA, const int M, const int N, const float alpha, const float A, const int lda, const float X, const int incX, const float beta, float *Y, const int incY)
	Add to single precision vector Y the reproducible matrix-vector product of single precision matrix A and single precision vector X. More...

void	reproBLAS_sgemm (const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const float alpha, const float A, const int lda, const float B, const int ldb, const float beta, float *C, const int ldc)
	Add to single precision matrix C the reproducible matrix-matrix product of single precision matrices A and B. More...

void	reproBLAS_zgemv (const char Order, const char TransA, const int M, const int N, const void alpha, const void A, const int lda, const void X, const int incX, const void beta, void *Y, const int incY)
	Add to complex double precision vector Y the reproducible matrix-vector product of complex double precision matrix A and complex double precision vector X. More...

void	reproBLAS_zgemm (const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const void alpha, const void A, const int lda, const void B, const int ldb, const void beta, void *C, const int ldc)
	Add to complex double precision matrix C the reproducible matrix-matrix product of complex double precision matrices A and B. More...

void	reproBLAS_cgemv (const char Order, const char TransA, const int M, const int N, const void alpha, const void A, const int lda, const void X, const int incX, const void beta, void *Y, const int incY)
	Add to complex single precision vector Y the reproducible matrix-vector product of complex single precision matrix A and complex single precision vector X. More...

void	reproBLAS_cgemm (const char Order, const char TransA, const char TransB, const int M, const int N, const int K, const void alpha, const void A, const int lda, const void B, const int ldb, const void beta, void *C, const int ldc)
	Add to complex single precision matrix C the reproducible matrix-matrix product of complex single precision matrices A and B. More...

Detailed Description

reproBLAS.h defines reproducible BLAS Methods.

This header is modeled after cblas.h, and as such functions are prefixed with character sets describing the data types they operate upon. For example, the function dfoo would perform the function foo on double possibly returning a double.

If two character sets are prefixed, the first set of characters describes the output and the second the input type. For example, the function dzbar would perform the function bar on double complex and return a double.

Such character sets are listed as follows:

d - double (double)
z - complex double (*void)
s - float (float)
c - complex float (*void)

Throughout the library, complex types are specified via *void pointers. These routines will sometimes be suffixed by sub, to represent that a function has been made into a subroutine. This allows programmers to use whatever complex types they are already using, as long as the memory pointed to is of the form of two adjacent floating point types, the first and second representing real and imaginary components of the complex number.

The goal of using binned types is to obtain either more accurate or reproducible summation of floating point numbers. In reproducible summation, floating point numbers are split into several slices along predefined boundaries in the exponent range. The space between two boundaries is called a bin. Binned types are composed of several accumulators, each accumulating the slices in a particular bin. The accumulators correspond to the largest consecutive nonzero bins seen so far.

The parameter fold describes how many accumulators are used in the binned types supplied to a subroutine (an binned type with k accumulators is k-fold). The default value for this parameter can be set in config.h. If you are unsure of what value to use for fold, we recommend 3. Note that the fold of binned types must be the same for all binned types that interact with each other. Operations on more than one binned type assume all binned types being operated upon have the same fold. Note that the fold of an binned type may not be changed once the type has been allocated. A common use case would be to set the value of fold as a global macro in your code and supply it to all binned functions that you use.

In reproBLAS, two copies of the BLAS are provided. The functions that share the same name as their BLAS counterparts perform reproducible versions of their corresponding operations using the default fold value specified in config.h. The functions that are prefixed by the character 'r' allow the user to specify their own fold for the underlying binned types.

Function Documentation

void reproBLAS_cdotc_sub	(	const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		void *	dotc
	)

Compute the reproducible conjugated dot product of complex single precision vectors X and Y.

Return the sum of the pairwise products of X and conjugated Y.

The reproducible dot product is computed with binned types of default fold using binnedBLAS_cbcdotc()

Parameters

N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	complex single precision vector
incY	Y vector stride (use every incY'th element)
dotc	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_cdotu_sub	(	const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		void *	dotu
	)

Compute the reproducible unconjugated dot product of complex single precision vectors X and Y.

Return the sum of the pairwise products of X and Y.

The reproducible dot product is computed with binned types of default fold using binnedBLAS_cbcdotu()

Parameters

N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	complex single precision vector
incY	Y vector stride (use every incY'th element)
dotu	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_cgemm	(	const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	B,
		const int	ldb,
		const void *	beta,
		void *	C,
		const int	ldc
	)

Add to complex single precision matrix C the reproducible matrix-matrix product of complex single precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + beta*C,

where op(X) is one of

op(X) = X or op(X) = X**T or op(X) = X**H,

alpha and beta are scalars, A and B and C are matrices with op(A) an M by K matrix, op(B) a K by N matrix, and C is an M by N matrix.

The matrix-matrix product is computed using binned types of default fold with binnedBLAS_cbcgemm()

Parameters

Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	complex single precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	complex single precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
beta	scalar beta
C	complex single precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_cgemv	(	const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	X,
		const int	incX,
		const void *	beta,
		void *	Y,
		const int	incY
	)

Add to complex single precision vector Y the reproducible matrix-vector product of complex single precision matrix A and complex single precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + beta*y or y := alpha*A**T*x + beta*y or y := alpha*A**H*x + beta*y,

where alpha and beta are scalars, x and y are vectors, and A is an M by N matrix.

The matrix-vector product is computed using binned types of default fold with binnedBLAS_cbcgemv()

Parameters

Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	complex single precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	complex single precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
beta	scalar beta
Y	complex single precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_csum_sub	(	const int	N,
		const void *	X,
		const int	incX,
		void *	sum
	)

Compute the reproducible sum of complex single precision vector X.

Return the sum of X.

The reproducible sum is computed with binned types of default fold using binnedBLAS_cbcsum()

Parameters

N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
sum	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

double reproBLAS_dasum	(	const int	N,
		const double *	X,
		const int	incX
	)

Compute the reproducible absolute sum of double precision vector X.

Return the sum of absolute values of elements in X.

The reproducible absolute sum is computed with binned types of default fold using binnedBLAS_dbdasum()

Parameters

N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)

Returns: absolute sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

double reproBLAS_ddot	(	const int	N,
		const double *	X,
		const int	incX,
		const double *	Y,
		const int	incY
	)

Compute the reproducible dot product of double precision vectors X and Y.

Return the sum of the pairwise products of X and Y.

The reproducible dot product is computed with binned types of default fold using binnedBLAS_dbddot()

Parameters

N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
Y	double precision vector
incY	Y vector stride (use every incY'th element)

Returns: the dot product of X and Y

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_dgemm	(	const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const double	alpha,
		const double *	A,
		const int	lda,
		const double *	B,
		const int	ldb,
		const double	beta,
		double *	C,
		const int	ldc
	)

Add to double precision matrix C the reproducible matrix-matrix product of double precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + beta*C,

where op(X) is one of

op(X) = X or op(X) = X**T,

alpha and beta are scalars, A and B and C are matrices with op(A) an M by K matrix, op(B) a K by N matrix, and C is an M by N matrix.

The matrix-matrix product is computed using binned types of default fold with binnedBLAS_dbdgemm()

Parameters

Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	double precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	double precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
beta	scalar beta
C	double precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_dgemv	(	const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const double	alpha,
		const double *	A,
		const int	lda,
		const double *	X,
		const int	incX,
		const double	beta,
		double *	Y,
		const int	incY
	)

Add to double precision vector Y the reproducible matrix-vector product of double precision matrix A and double precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + beta*y or y := alpha*A**T*x + beta*y,

where alpha and beta are scalars, x and y are vectors, and A is an M by N matrix.

The matrix-vector product is computed using binned types of default fold with binnedBLAS_dbdgemv()

Parameters

Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	double precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	double precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
beta	scalar beta
Y	double precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

double reproBLAS_dnrm2	(	const int	N,
		const double *	X,
		const int	incX
	)

Compute the reproducible Euclidian norm of double precision vector X.

Return the square root of the sum of the squared elements of X.

The reproducible Euclidian norm is computed with scaled binned types of default fold using binnedBLAS_dbdssq()

Parameters

N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)

Returns: Euclidian norm of X

Author: Peter Ahrens

Date: 15 Jan 2016

double reproBLAS_dsum	(	const int	N,
		const double *	X,
		const int	incX
	)

Compute the reproducible sum of double precision vector X.

Return the sum of X.

The reproducible sum is computed with binned types of default fold using binnedBLAS_dbdsum()

Parameters

N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)

Returns: sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

double reproBLAS_dzasum	(	const int	N,
		const void *	X,
		const int	incX
	)

Compute the reproducible absolute sum of complex double precision vector X.

Return the sum of magnitudes of elements of X.

The reproducible absolute sum is computed with binned types of default fold using binnedBLAS_dbzasum()

Parameters

N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)

Returns: absolute sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

double reproBLAS_dznrm2	(	const int	N,
		const void *	X,
		const int	incX
	)

Compute the reproducible Euclidian norm of complex double precision vector X.

Return the square root of the sum of the squared elements of X.

The reproducible Euclidian norm is computed with scaled binned types of default fold using binnedBLAS_dbzssq()

Parameters

N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)

Returns: Euclidian norm of X

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_rcdotc_sub	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		void *	dotc
	)

Compute the reproducible conjugated dot product of complex single precision vectors X and Y.

Return the sum of the pairwise products of X and conjugated Y.

The reproducible dot product is computed with binned types using binnedBLAS_cbcdotc()

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	complex single precision vector
incY	Y vector stride (use every incY'th element)
dotc	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_rcdotu_sub	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		void *	dotu
	)

Compute the reproducible unconjugated dot product of complex single precision vectors X and Y.

Return the sum of the pairwise products of X and Y.

The reproducible dot product is computed with binned types using binnedBLAS_cbcdotu()

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)
Y	complex single precision vector
incY	Y vector stride (use every incY'th element)
dotu	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_rcgemm	(	const int	fold,
		const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	B,
		const int	ldb,
		const void *	beta,
		void *	C,
		const int	ldc
	)

Add to complex single precision matrix C the reproducible matrix-matrix product of complex single precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + beta*C,

where op(X) is one of

op(X) = X or op(X) = X**T or op(X) = X**H,

alpha and beta are scalars, A and B and C are matrices with op(A) an M by K matrix, op(B) a K by N matrix, and C is an M by N matrix.

The matrix-matrix product is computed using binned types with binnedBLAS_cbcgemm()

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	complex single precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	complex single precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
beta	scalar beta
C	complex single precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_rcgemv	(	const int	fold,
		const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	X,
		const int	incX,
		const void *	beta,
		void *	Y,
		const int	incY
	)

Add to complex single precision vector Y the reproducible matrix-vector product of complex single precision matrix A and complex single precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + beta*y or y := alpha*A**T*x + beta*y or y := alpha*A**H*x + beta*y,

where alpha and beta are scalars, x and y are vectors, and A is an M by N matrix.

The matrix-vector product is computed using binned types with binnedBLAS_cbcgemv()

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	complex single precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	complex single precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
beta	scalar beta
Y	complex single precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_rcsum_sub	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		void *	sum
	)

Compute the reproducible sum of complex single precision vector X.

Return the sum of X.

The reproducible sum is computed with binned types using binnedBLAS_cbcsum()

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
sum	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

double reproBLAS_rdasum	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX
	)

Compute the reproducible absolute sum of double precision vector X.

Return the sum of absolute values of elements in X.

The reproducible absolute sum is computed with binned types using binnedBLAS_dbdasum()

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)

Returns: absolute sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

double reproBLAS_rddot	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX,
		const double *	Y,
		const int	incY
	)

Compute the reproducible dot product of double precision vectors X and Y.

Return the sum of the pairwise products of X and Y.

The reproducible dot product is computed with binned types using binnedBLAS_dbddot()

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)
Y	double precision vector
incY	Y vector stride (use every incY'th element)

Returns: the dot product of X and Y

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_rdgemm	(	const int	fold,
		const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const double	alpha,
		const double *	A,
		const int	lda,
		const double *	B,
		const int	ldb,
		const double	beta,
		double *	C,
		const int	ldc
	)

Add to double precision matrix C the reproducible matrix-matrix product of double precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + beta*C,

where op(X) is one of

op(X) = X or op(X) = X**T,

alpha and beta are scalars, A and B and C are matrices with op(A) an M by K matrix, op(B) a K by N matrix, and C is an M by N matrix.

The matrix-matrix product is computed using binned types with binnedBLAS_dbdgemm()

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	double precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	double precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
beta	scalar beta
C	double precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_rdgemv	(	const int	fold,
		const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const double	alpha,
		const double *	A,
		const int	lda,
		const double *	X,
		const int	incX,
		const double	beta,
		double *	Y,
		const int	incY
	)

Add to double precision vector Y the reproducible matrix-vector product of double precision matrix A and double precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + beta*y or y := alpha*A**T*x + beta*y,

where alpha and beta are scalars, x and y are vectors, and A is an M by N matrix.

The matrix-vector product is computed using binned types with binnedBLAS_dbdgemv()

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	double precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	double precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
beta	scalar beta
Y	double precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

double reproBLAS_rdnrm2	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX
	)

Compute the reproducible Euclidian norm of double precision vector X.

Return the square root of the sum of the squared elements of X.

The reproducible Euclidian norm is computed with scaled binned types using binnedBLAS_dbdssq()

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)

Returns: Euclidian norm of X

Author: Peter Ahrens

Date: 15 Jan 2016

double reproBLAS_rdsum	(	const int	fold,
		const int	N,
		const double *	X,
		const int	incX
	)

Compute the reproducible sum of double precision vector X.

Return the sum of X.

The reproducible sum is computed with binned types using binnedBLAS_dbdsum()

Parameters

fold	the fold of the binned types
N	vector length
X	double precision vector
incX	X vector stride (use every incX'th element)

Returns: sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

double reproBLAS_rdzasum	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX
	)

Compute the reproducible absolute sum of complex double precision vector X.

Return the sum of magnitudes of elements of X.

The reproducible absolute sum is computed with binned types using binnedBLAS_dbzasum()

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)

Returns: absolute sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

double reproBLAS_rdznrm2	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX
	)

Compute the reproducible Euclidian norm of complex double precision vector X.

Return the square root of the sum of the squared elements of X.

The reproducible Euclidian norm is computed with scaled binned types using binnedBLAS_dbzssq()

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)

Returns: Euclidian norm of X

Author: Peter Ahrens

Date: 15 Jan 2016

float reproBLAS_rsasum	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX
	)

Compute the reproducible absolute sum of single precision vector X.

Return the sum of absolute values of elements in X.

The reproducible absolute sum is computed with binned types using binnedBLAS_sbsasum()

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)

Returns: absolute sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

float reproBLAS_rscasum	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX
	)

Compute the reproducible absolute sum of complex single precision vector X.

Return the sum of magnitudes of elements of X.

The reproducible absolute sum is computed with binned types using binnedBLAS_sbcasum()

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)

Returns: absolute sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

float reproBLAS_rscnrm2	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX
	)

Compute the reproducible Euclidian norm of complex single precision vector X.

Return the square root of the sum of the squared elements of X.

The reproducible Euclidian norm is computed with scaled binned types using binnedBLAS_sbcssq()

Parameters

fold	the fold of the binned types
N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)

Returns: Euclidian norm of X

Author: Peter Ahrens

Date: 15 Jan 2016

float reproBLAS_rsdot	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX,
		const float *	Y,
		const int	incY
	)

Compute the reproducible dot product of single precision vectors X and Y.

Return the sum of the pairwise products of X and Y.

The reproducible dot product is computed with binned types using binnedBLAS_sbsdot()

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
Y	single precision vector
incY	Y vector stride (use every incY'th element)

Returns: the dot product of X and Y

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_rsgemm	(	const int	fold,
		const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const float	alpha,
		const float *	A,
		const int	lda,
		const float *	B,
		const int	ldb,
		const float	beta,
		float *	C,
		const int	ldc
	)

Add to single precision matrix C the reproducible matrix-matrix product of single precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + beta*C,

where op(X) is one of

op(X) = X or op(X) = X**T,

alpha and beta are scalars, A and B and C are matrices with op(A) an M by K matrix, op(B) a K by N matrix, and C is an M by N matrix.

The matrix-matrix product is computed using binned types with binnedBLAS_sbsgemm()

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	single precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	single precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
beta	scalar beta
C	single precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_rsgemv	(	const int	fold,
		const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const float	alpha,
		const float *	A,
		const int	lda,
		const float *	X,
		const int	incX,
		const float	beta,
		float *	Y,
		const int	incY
	)

Add to single precision vector Y the reproducible matrix-vector product of single precision matrix A and single precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + beta*y or y := alpha*A**T*x + beta*y,

where alpha and beta are scalars, x and y are vectors, and A is an M by N matrix.

The matrix-vector product is computed using binned types with binnedBLAS_sbsgemv()

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	single precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	single precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
beta	scalar beta
Y	single precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

float reproBLAS_rsnrm2	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX
	)

Compute the reproducible Euclidian norm of single precision vector X.

Return the square root of the sum of the squared elements of X.

The reproducible Euclidian norm is computed with scaled binned types using binnedBLAS_sbsssq()

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)

Returns: Euclidian norm of X

Author: Peter Ahrens

Date: 15 Jan 2016

float reproBLAS_rssum	(	const int	fold,
		const int	N,
		const float *	X,
		const int	incX
	)

Compute the reproducible sum of single precision vector X.

Return the sum of X.

The reproducible sum is computed with binned types using binnedBLAS_sbssum()

Parameters

fold	the fold of the binned types
N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)

Returns: sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_rzdotc_sub	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		void *	dotc
	)

Compute the reproducible conjugated dot product of complex double precision vectors X and Y.

Return the sum of the pairwise products of X and conjugated Y.

The reproducible dot product is computed with binned types using binnedBLAS_zbzdotc()

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	complex double precision vector
incY	Y vector stride (use every incY'th element)
dotc	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_rzdotu_sub	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		void *	dotu
	)

Compute the reproducible unconjugated dot product of complex double precision vectors X and Y.

Return the sum of the pairwise products of X and Y.

The reproducible dot product is computed with binned types using binnedBLAS_zbzdotu()

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	complex double precision vector
incY	Y vector stride (use every incY'th element)
dotu	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_rzgemm	(	const int	fold,
		const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	B,
		const int	ldb,
		const void *	beta,
		void *	C,
		const int	ldc
	)

Add to complex double precision matrix C the reproducible matrix-matrix product of complex double precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + beta*C,

where op(X) is one of

op(X) = X or op(X) = X**T or op(X) = X**H,

alpha and beta are scalars, A and B and C are matrices with op(A) an M by K matrix, op(B) a K by N matrix, and C is an M by N matrix.

The matrix-matrix product is computed using binned types with binnedBLAS_zbzgemm()

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	complex double precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	complex double precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
beta	scalar beta
C	complex double precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_rzgemv	(	const int	fold,
		const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	X,
		const int	incX,
		const void *	beta,
		void *	Y,
		const int	incY
	)

Add to complex double precision vector Y the reproducible matrix-vector product of complex double precision matrix A and complex double precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + beta*y or y := alpha*A**T*x + beta*y or y := alpha*A**H*x + beta*y,

where alpha and beta are scalars, x and y are vectors, and A is an M by N matrix.

The matrix-vector product is computed using binned types with binnedBLAS_zbzgemv()

Parameters

fold	the fold of the binned types
Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	complex double precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	complex double precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
beta	scalar beta
Y	complex double precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_rzsum_sub	(	const int	fold,
		const int	N,
		const void *	X,
		const int	incX,
		void *	sum
	)

Compute the reproducible sum of complex double precision vector X.

Return the sum of X.

The reproducible sum is computed with binned types using binnedBLAS_zbzsum()

Parameters

fold	the fold of the binned types
N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
sum	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

float reproBLAS_sasum	(	const int	N,
		const float *	X,
		const int	incX
	)

Compute the reproducible absolute sum of single precision vector X.

Return the sum of absolute values of elements in X.

The reproducible absolute sum is computed with binned types of default fold using binnedBLAS_sbsasum()

Parameters

N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)

Returns: absolute sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

float reproBLAS_scasum	(	const int	N,
		const void *	X,
		const int	incX
	)

Compute the reproducible absolute sum of complex single precision vector X.

Return the sum of magnitudes of elements of X.

The reproducible absolute sum is computed with binned types of default fold using binnedBLAS_sbcasum()

Parameters

N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)

Returns: absolute sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

float reproBLAS_scnrm2	(	const int	N,
		const void *	X,
		const int	incX
	)

Compute the reproducible Euclidian norm of complex single precision vector X.

Return the square root of the sum of the squared elements of X.

The reproducible Euclidian norm is computed with scaled binned types of default fold using binnedBLAS_sbcssq()

Parameters

N	vector length
X	complex single precision vector
incX	X vector stride (use every incX'th element)

Returns: Euclidian norm of X

Author: Peter Ahrens

Date: 15 Jan 2016

float reproBLAS_sdot	(	const int	N,
		const float *	X,
		const int	incX,
		const float *	Y,
		const int	incY
	)

Compute the reproducible dot product of single precision vectors X and Y.

Return the sum of the pairwise products of X and Y.

The reproducible dot product is computed with binned types of default fold using binnedBLAS_sbsdot()

Parameters

N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)
Y	single precision vector
incY	Y vector stride (use every incY'th element)

Returns: the dot product of X and Y

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_sgemm	(	const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const float	alpha,
		const float *	A,
		const int	lda,
		const float *	B,
		const int	ldb,
		const float	beta,
		float *	C,
		const int	ldc
	)

Add to single precision matrix C the reproducible matrix-matrix product of single precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + beta*C,

where op(X) is one of

op(X) = X or op(X) = X**T,

alpha and beta are scalars, A and B and C are matrices with op(A) an M by K matrix, op(B) a K by N matrix, and C is an M by N matrix.

The matrix-matrix product is computed using binned types of default fold with binnedBLAS_sbsgemm()

Parameters

Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	single precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	single precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
beta	scalar beta
C	single precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_sgemv	(	const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const float	alpha,
		const float *	A,
		const int	lda,
		const float *	X,
		const int	incX,
		const float	beta,
		float *	Y,
		const int	incY
	)

Add to single precision vector Y the reproducible matrix-vector product of single precision matrix A and single precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + beta*y or y := alpha*A**T*x + beta*y,

where alpha and beta are scalars, x and y are vectors, and A is an M by N matrix.

The matrix-vector product is computed using binned types of default fold with binnedBLAS_sbsgemv()

Parameters

Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' or 'c' or 'C' to transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	single precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	single precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
beta	scalar beta
Y	single precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

float reproBLAS_snrm2	(	const int	N,
		const float *	X,
		const int	incX
	)

Compute the reproducible Euclidian norm of single precision vector X.

Return the square root of the sum of the squared elements of X.

The reproducible Euclidian norm is computed with scaled binned types of default fold using binnedBLAS_sbsssq()

Parameters

N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)

Returns: Euclidian norm of X

Author: Peter Ahrens

Date: 15 Jan 2016

float reproBLAS_ssum	(	const int	N,
		const float *	X,
		const int	incX
	)

Compute the reproducible sum of single precision vector X.

Return the sum of X.

The reproducible sum is computed with binned types of default fold using binnedBLAS_sbssum()

Parameters

N	vector length
X	single precision vector
incX	X vector stride (use every incX'th element)

Returns: sum of X

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_zdotc_sub	(	const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		void *	dotc
	)

Compute the reproducible conjugated dot product of complex double precision vectors X and Y.

Return the sum of the pairwise products of X and conjugated Y.

The reproducible dot product is computed with binned types of default fold using binnedBLAS_zbzdotc()

Parameters

N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	complex double precision vector
incY	Y vector stride (use every incY'th element)
dotc	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_zdotu_sub	(	const int	N,
		const void *	X,
		const int	incX,
		const void *	Y,
		const int	incY,
		void *	dotu
	)

Compute the reproducible unconjugated dot product of complex double precision vectors X and Y.

Return the sum of the pairwise products of X and Y.

The reproducible dot product is computed with binned types of default fold using binnedBLAS_zbzdotu()

Parameters

N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
Y	complex double precision vector
incY	Y vector stride (use every incY'th element)
dotu	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

void reproBLAS_zgemm	(	const char	Order,
		const char	TransA,
		const char	TransB,
		const int	M,
		const int	N,
		const int	K,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	B,
		const int	ldb,
		const void *	beta,
		void *	C,
		const int	ldc
	)

Add to complex double precision matrix C the reproducible matrix-matrix product of complex double precision matrices A and B.

Performs one of the matrix-matrix operations

C := alpha*op(A)*op(B) + beta*C,

where op(X) is one of

op(X) = X or op(X) = X**T or op(X) = X**H,

alpha and beta are scalars, A and B and C are matrices with op(A) an M by K matrix, op(B) a K by N matrix, and C is an M by N matrix.

The matrix-matrix product is computed using binned types of default fold with binnedBLAS_zbzgemm()

Parameters

Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
TransB	a character specifying whether or not to transpose B before taking the matrix-matrix product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix op(A) and of the matrix C.
N	number of columns of matrix op(B) and of the matrix C.
K	number of columns of matrix op(A) and columns of the matrix op(B).
alpha	scalar alpha
A	complex double precision matrix of dimension (ma, lda) in row-major or (lda, na) in column-major. (ma, na) is (M, K) if A is not transposed and (K, M) otherwise.
lda	the first dimension of A as declared in the calling program. lda must be at least na in row major or ma in column major.
B	complex double precision matrix of dimension (mb, ldb) in row-major or (ldb, nb) in column-major. (mb, nb) is (K, N) if B is not transposed and (N, K) otherwise.
ldb	the first dimension of B as declared in the calling program. ldb must be at least nb in row major or mb in column major.
beta	scalar beta
C	complex double precision matrix of dimension (M, ldc) in row-major or (ldc, N) in column-major.
ldc	the first dimension of C as declared in the calling program. ldc must be at least N in row major or M in column major.

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_zgemv	(	const char	Order,
		const char	TransA,
		const int	M,
		const int	N,
		const void *	alpha,
		const void *	A,
		const int	lda,
		const void *	X,
		const int	incX,
		const void *	beta,
		void *	Y,
		const int	incY
	)

Add to complex double precision vector Y the reproducible matrix-vector product of complex double precision matrix A and complex double precision vector X.

Performs one of the matrix-vector operations

y := alpha*A*x + beta*y or y := alpha*A**T*x + beta*y or y := alpha*A**H*x + beta*y,

where alpha and beta are scalars, x and y are vectors, and A is an M by N matrix.

The matrix-vector product is computed using binned types of default fold with binnedBLAS_zbzgemv()

Parameters

Order	a character specifying the matrix ordering ('r' or 'R' for row-major, 'c' or 'C' for column major)
TransA	a character specifying whether or not to transpose A before taking the matrix-vector product ('n' or 'N' not to transpose, 't' or 'T' to transpose, 'c' or 'C' to conjugate transpose)
M	number of rows of matrix A
N	number of columns of matrix A
alpha	scalar alpha
A	complex double precision matrix of dimension (M, lda) in row-major or (lda, N) in column-major
lda	the first dimension of A as declared in the calling program
X	complex double precision vector of at least size N if not transposed or size M otherwise
incX	X vector stride (use every incX'th element)
beta	scalar beta
Y	complex double precision vector Y of at least size M if not transposed or size N otherwise
incY	Y vector stride (use every incY'th element)

Author: Peter Ahrens

Date: 18 Jan 2016

void reproBLAS_zsum_sub	(	const int	N,
		const void *	X,
		const int	incX,
		void *	sum
	)

Compute the reproducible sum of complex double precision vector X.

Return the sum of X.

The reproducible sum is computed with binned types of default fold using binnedBLAS_zbzsum()

Parameters

N	vector length
X	complex double precision vector
incX	X vector stride (use every incX'th element)
sum	scalar return

Author: Peter Ahrens

Date: 15 Jan 2016

Functions

Detailed Description

Function Documentation