I am trying to use Lapack for a 128 bit precision calculation of a matrix singular value decomposition (SVD) and I found out that there is some black compiler magic to accomplish this. The Intel Fortran compiler (ifort) supports the option -r16
which instructs the compiler to take all variables declared as DOUBLE PRECISION
to be 128 bit reals. So I compiled Lapack and BLAS using:
ifort -O3 -r16 -c isamax.f -o isamax.o
ifort -O3 -r16 -c sasum.f -o sasum.o
...
To incorporate this in my program (which is C++) I can use the Intel C++ compiler (icc) with the option -Qoption,cpp,--extended_float_type
which creates a data type _Quad
that is a 128 bit floating point variable. My SVD example looks like this:
#include "stdio.h"
#include "iostream"
#include "vector"
using namespace std;
typedef _Quad scalar;
//FORTRAN BINDING
extern "C" void dgesvd_(char *JOBU, char *JOBVT, int *M, int *N,
scalar *A, int *LDA,
scalar *S,
scalar *U, int *LDU,
scalar *VT, int *LDVT,
scalar *WORK, int *LWORK, int *INFO);
int main() {
cout << "Size of scalar: " << sizeof(scalar) << endl;
int N=2;
vector< scalar > A(N*N);
vector< scalar > S(N);
vector< scalar > U(N*N);
vector< scalar > VT(N*N);
// dummy input matrix
A[0] = 1.q;
A[1] = 2.q;
A[2] = 2.q;
A[3] = 3.q;
cout << "Input matrix: " << endl;
for(int i = 0; i < N; i++) {
for(int j = 0;j < N; j++)
cout << double(A[i*N+j]) << "\t";
cout << endl;
}
cout << endl;
char JOBU='A';
char JOBVT='A';
int LWORK=-1;
scalar test;
int INFO;
// allocate memory
dgesvd_(&JOBU, &JOBVT, &N, &N,
&A[0], &N,
&S[0],
&U[0], &N,
&VT[0], &N,
&test, &LWORK, &INFO);
LWORK=test;
int size=int(test);
cout<<"Needed workspace size: "<<int(test)<<endl<<endl;
vector< scalar > WORK(size);
// run...
dgesvd_(&JOBU, &JOBVT, &N, &N,
&A[0], &N,
&S[0],
&U[0], &N,
&VT[0], &N,
&WORK[0], &LWORK, &INFO);
// output as doubles
cout << "Singular values: " << endl;
for(int i = 0;i < N; i++)
cout << double(S[i]) << endl;
cout << endl;
cout << "U: " << endl;
for(int i = 0;i < N; i++) {
for(int j = 0;j < N; j++)
cout << double(U[N*i+j]) << "\t";
cout << endl;
}
cout << "VT: " << endl;
for(int i = 0;i < N; i++) {
for(int j = 0;j < N; j++)
cout << double(VT[N*i+j]) << "\t";
cout << endl;
}
return 0;
}
compiled with
icc test.cpp -g -Qoption,cpp,--extended_float_type -lifcore ../lapack-3.4.0/liblapack.a ../BLAS/blas_LINUX.a
Everything works fine this far. But the output is:
Size of scalar: 16 Input matrix: 1 2 2 3 Needed workspace size: 134 Singular values: inf inf U: -0.525731 -0.850651 -0.850651 0.525731 VT: -0.525731 0.850651 -0.850651 -0.525731
I checked that U and VT are correct, but the singular values are obviously not. Has anyone got an idea why this happens or how one could circumvent it?
Thanks for your help.
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