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2 . MPACK 0.6.7: Multiple precision version of BLAS and LAPACK MPACK (MBLAS and MLAPACK) BLAS/LAPACK (API) (2010/8/20); MLAPACK, MBLAS : Linux/Windows/MacOSX/FreeBSD : MPFR/MPC/GMP/DD/QD/double C++; 2- BSD ;

3 . Top500 Linpack 1... BLAS/LAPACK

4 . BLAS LAPACK? BLAS: -, -, - API : GotoBLAS, Intel MKL, ATLAS LAPACK: BLAS ( ) Netlib 8400 (2010/11/27) BLAS/LAPACK

5 . BLAS LAPACK? BLAS: -, -, - API : GotoBLAS, Intel MKL, ATLAS LAPACK: BLAS ( ) Netlib 8400 (2010/11/27) BLAS/LAPACK

6 . MPACK 0.6.7: Multiple precision version of BLAS and LAPACK MPACK (MBLAS and MLAPACK) BLAS/LAPACK (API) (2010/8/20); MLAPACK, MBLAS : Linux/Windows/MacOSX/FreeBSD : MPFR/MPC/GMP/DD/QD/double C++; 2- BSD ;

7 . MPACK 4,8 : : QD, DD : : GMP : ( ): MPFR/MPC : double

8 . ; ; Prefix float, double R eal, complex, double complex C omplex. daxpy, zaxpy Raxpy, Caxpy dgemm, zgemm Rgemm, Cgemm dsterf, dsyev Rsterf, Rsyev dzabs1, dzasum RCabs1, RCasum

9 . MBLAS LEVEL1 MBLAS Crotg Cscal Rrotg Rrot Rrotm CRrot Cswap Rswap CRscal Rscal Ccopy Rcopy Caxpy Raxpy Rdot Cdotc Cdotu RCnrm2 Rnrm2 Rasum icasum iramax RCabs1 Mlsame Mxerbla LEVEL2 MBLAS Cgemv Rgemv Cgbmv Rgbmv Chemv Chbmv Chpmv Rsymv Rsbmv Ctrmv Cgemv Rgemv Cgbmv Rgemv Chemv Chbmv Chpmv Rsymv Rsbmv Rspmv Ctrmv Rtrmv Ctbmv Ctpmv Rtpmv Ctrsv Rtrsv Ctbsv Rtbsv Ctpsv Rger Cgeru Cgerc Cher Chpr Cher2 Chpr2 Rsyr Rspr Rsyr2 Rspr2 LEVEL3 MBLAS Cgemm Rgemm Csymm Rsymm Chemm Csyrk Rsyrk Cherk Csyr2k Rsyr2k Cher2k Ctrmm Rtrmm Ctrsm Rtrsm

10 . MLAPACK Mutils Rlamch Rlae2 Rlaev2 Claev2 Rlassq Classq Rlanst Clanht Rlansy Clansy Clanhe Rlapy2 Rlarfg Rlapy3 Rladiv Cladiv Clarfg Rlartg Clartg Rlaset Claset Rlasr Clasr Rpotf2 Clacgv Cpotf2 Rlascl Clascl Rlasrt Rsytd2 Chetd2 Rsteqr Csteqr Rsterf Rlarf Clarf Rorg2l Cung2l Rorg2r Cung2r Rlarft Clarft Rlarfb Clarfb Rorgqr Cungqr Rorgql Cungql Rlatrd Clatrd Rsytrd Chetrd Rorgtr Cungtr Rsyev Cheev Rpotrf Cpotrf Clacrm Rtrti2 Ctrti2 Rtrtri Ctrtri Rgetf2 Cgetf2 Rlaswp Claswp Rgetrf Cgetrf Rgetri Cgetri Rgetrs Cgetrs Rgesv Cgesv Rtrtrs Ctrtrs Rlasyf Clasyf Clahef Clacrt Claesy Crot Cspmv Cspr Csymv Csyr icmax1 RCsum1 Rpotrs Rposv Rgeequ Rlatrs Rlange Rgecon Rlauu2 Rlauum Rpotri Rpocon

11 . ; ; call by value or call by reference MBLAS/MLAPACK: Rgemm("n", "n", n, n, n, alpha, A, n, B, n, beta, C, n); Rgetrf(n, n, A, n, ipiv, &info); Rgetri(n, A, n, ipiv, work, lwork, &info); Rsyev("V", "U", n, A, n, w, work, &lwork, &info); BLAS/LAPACK: dgemm_f77("n", "N", &n, &n, &n, &One, A, &n, A, &n, &Zero, C, & dgetri_f77(&n, A, &n, ipiv, work, &lwork, &info); (C++/C BLAS/LAPACK lapack.h, blas.h!)

12 . MBLAS : Caxpy; axpy void Caxpy(INTEGER n, COMPLEX ca, COMPLEX * cx, INTEGER incx, COMPLEX { REAL Zero = 0.0; if (n <= 0) return; if (RCabs1(ca) == Zero) return; INTEGER ix = 0; INTEGER iy = 0; if (incx < 0) ix = (-n + 1) * incx; if (incy < 0) iy = (-n + 1) * incy; for (INTEGER i = 0; i < n; i++) { cy[iy] = cy[iy] + ca * cx[ix]; ix = ix + incx;

13 . MLAPACK Rsyev; Rlascl(uplo, 0, 0, One, sigma, n, n, A, lda, info); } //Call DSYTRD to reduce symmetric matrix to tridiagonal form. inde = 1; indtau = inde + n; indwrk = indtau + n; llwork = *lwork - indwrk + 1; Rsytrd(uplo, n, &A[0], lda, &w[0], &work[inde - 1], &work[indtau - &work[indwrk - 1], llwork, &iinfo); //For eigenvalues only, call DSTERF. For eigenvectors, first call //DORGTR to generate the orthogonal matrix, then call DSTEQR. if (!wantz) { Rsterf(n, &w[0], &work[inde - 1], info); } else { Rorgtr(uplo, n, A, lda, &work[indtau - 1], &work[indwrk - 1], &iinfo); Rsteqr(jobz, n, w, &work[inde - 1], A, lda, &work[indtau - 1], } //If matrix was scaled, then rescale eigenvalues appropriately. if (iscale == 1) { if (*info == 0) {

14 . MPACK (MBLAS/MLAPACK) : :SDPA-GMP, -QD, -DD ( ; ) Google Multiple precision BLAS MPACK Project web hits , download (2010/11/24)

15 . MPACK (MBLAS/MLAPACK) Core i7 920/Ubuntu 10.04/9.04 amd64 DD(double-double) Raxpy 600MFlops (mpack 0.6.6; gotoblas 1.5GFlops) Rgemv 140MFlops (gotoblas 3.8GFlops) Rgemm 140MFlops (gotoblas 42.5GFlops; 2010: 30GFlops on RADEON HD GFlops) Rsyev 112s (1000 ; gotoblas 1.83s)

16 . : SDPA-GMP, SDPA-QD, SDPA-DD: Powered by MPACK

17 . MPACK 0.6.7: Multiple precision version of BLAS and LAPACK MPACK (MBLAS and MLAPACK) BLAS/LAPACK (API) (2010/8/20); MLAPACK, MBLAS : Linux/Windows/MacOSX/FreeBSD : MPFR/MPC/GMP/DD/QD/double C++; 2- BSD ;

MPACK 0.6.0: 多倍長精度版のBLAS/LAPACKの作成

MPACK 0.6.0: 多倍長精度版のBLAS/LAPACKの作成 MPACK 0.6.0: BLAS/LAPACK maho@riken.jp 2009/12/11 MPACK(MBLAS/MLAPACK) ( ) (2007-2010) ( ) http://accc.riken.jp/maho/ MPACK: BLAS/LAPACK http://mplapack.sourceforge.net/ MBLAS: BLAS(Basic Linear Algebra