void Mjoin(PATL,gpmm)
(const enum PACK_UPLO UA, const enum PACK_TRANS TA,
const enum PACK_UPLO UB, const enum PACK_TRANS TB, const enum PACK_UPLO UC,
const int M, const int N, const int K, const SCALAR alpha,
const TYPE *A, const int IA, const int JA, const int lda,
const TYPE *B, const int IB, const int JB, const int ldb,
const SCALAR beta, TYPE *C, const int IC, const int JC, const int ldc)
{
int j;
#ifdef CacheEdge
static const int CE_K = ((ATL_DivBySize(CacheEdge)-(NBNB SHIFT)) /
(NB*(NB+NB)))*NB;
#else
#define CE_K K
#endif
if (!M || !N) return;
if (!K || SCALAR_IS_ZERO(alpha))
{
for (j=0; j != N; j++)
Mjoin(PATL,scal)(M, beta, C+MindexP(UC,IC,JC+j,ldc), 1);
return;
}
/*
* Packed gpmm not yet implemented for complex,
* so die if not really a dense gemm
*/
#ifdef TCPLX
ATL_assert (UA == PackGen && UB == PackGen && UC == PackGen);
Mjoin(PATL,gemm)(TA, TB, M, N, K, alpha, A, lda, B, ldb, beta, C, ldc);
#else
Mjoin(PATL,prankK)(UA, TA, UB, TB, M, N, K, CE_K, alpha,
A+MindexP(UA,IA,JA,lda), Mpld(UA,JA,lda), B+MindexP(UB,IB,JB,ldb),
Mpld(UB,JB,ldb), beta, UC, C+MindexP(UC,IB,JB,ldc), Mpld(UC,JC,ldc));
#endif
}
void Mjoin(PATL,sprk)
(const enum PACK_UPLO UA, const enum PACK_TRANS TA,
const enum ATLAS_UPLO UC, const int CP,
const int N, const int K, const SCALAR alpha,
const TYPE *A, const int IA, const int JA, const int lda,
const SCALAR beta, TYPE *C, const int IC, const int JC, const int ldc)
{
const enum PACK_UPLO UC2 = ((CP) ? UC : PackGen);
int j;
#ifdef CacheEdge
static const int CE_K = ((ATL_DivBySize(CacheEdge SHIFT)-(NBNB SHIFT)) /
(NB*(NB+NB)))*NB;
#else
#define CE_K K
#endif
if ((!N) || ((SCALAR_IS_ZERO(alpha) || (!K)) && (SCALAR_IS_ONE(beta))))
return;
if (!K || SCALAR_IS_ZERO(alpha))
{
if (UC == CblasLower)
{
for (j=0; j != N; j++)
Mjoin(PATL,scal)(N-j, beta, C+MindexP(UC2,IC+j,JC+j,ldc), 1);
}
else /* UC == CblasUpper */
{
for (j=0; j != N; j++)
Mjoin(PATL,scal)(j+1, beta, C+MindexP(UC2,IC,JC+j,ldc), 1);
}
return;
}
Mjoin(PATL,sprk_rK)(UA, TA, UC, CP, N, K, CE_K, alpha, A, lda, beta, C, ldc);
}
static double RunTiming
(enum CBLAS_ORDER Order, enum TEST_UPLO Uplo, int N, int lda,
int CacheSize, int nreps)
{
TYPE *A, *a;
const int incA = N*lda;
int i, k;
double t0, t1=0.0;
if (nreps < 1) nreps = 1;
i = ATL_DivBySize(2*CacheSize) ATL_PTCACHEMUL;
k = i = (i + N*N-1) / (N*N);
if (nreps > i) k = i = nreps;
a = A = malloc(i * ATL_MulBySize(incA));
if (A)
{
if (Uplo == TestGE)
for (i=0; i < k; i++) Mjoin(PATL,gegen)(N, N, A+i*incA, lda, N+lda);
else for (i=0; i < k; i++) hegen(Order, Uplo, N, A+i*incA, lda);
t0 = time00();
for (i=nreps; i; i--, a += incA) test_inv(Order, Uplo, N, a, lda);
t1 = time00() - t0;
free(A);
}
else fprintf(stderr, " WARNING: not enough mem to run timings!\n");
return(t1/nreps);
}
int RunCase(int CacheSize, TYPE thresh, int MFLOP, enum ATLAS_ORDER Order,
enum ATLAS_UPLO Uplo, int N, int lda)
{
char *Ups, *Ord;
TYPE resid = 0.0;
double mflop, mflops, t0, tim=0.0;
int nreps=1, passed, i, imem;
const int incA = lda*N;
TYPE *a, *A;
mflops = N;
mflops = (mflops*mflops*mflops) / 4.0;
#ifdef TCPLX
mflops *= 4.0;
#endif
mflops /= 1000000.0;
if (thresh > ATL_rzero) resid =
uumtest(Order, Uplo, CacheSize, N, lda, &tim);
else resid = -1.0;
if (MFLOP > mflops || thresh <= ATL_rzero) /* need to time repetitively */
{
nreps = (mflops * 1000000);
nreps = (MFLOP*1000000 + nreps-1) / nreps;
if (nreps < 1) nreps = 1;
imem = ATL_DivBySize(CacheSize) ATL_PTCACHEMUL;
imem = (imem + 2*N*N-1) / (N*N);
if (imem < nreps) imem = nreps;
a = A = malloc(imem * ATL_MulBySize(incA));
if (A != NULL)
{
for (i=0; i < imem; i++) lltgen(Uplo, N, A+i*incA, lda, N*1029+lda);
t0 = time00();
for (i=nreps; i; i--, a += incA)
test_lauum(Order, Uplo, N, a, lda);
tim = time00() - t0;
tim /= nreps;
free(A);
}
else fprintf(stderr, " WARNING: not enough mem to run timings!\n");
}
if (tim > 0.0) mflop = mflops / tim;
else mflop = 0.0;
if (Uplo == AtlasUpper) Ups = "Upper";
else Ups = "Lower";
if (Order == CblasColMajor) Ord = "Col";
else Ord = "Row";
fprintf(stdout, "%5d %3s %5s %6d %6d %12.5f %12.3f %12e\n",
nreps, Ord, Ups, N, lda, tim, mflop, resid);
if (resid > thresh || resid != resid) passed = 0;
else if (resid < 0.0) passed = -1;
else passed = 1;
return(passed);
}
void Mjoin(Mjoin(PATL,t),MY_GER)
(ATL_CINT M, ATL_CINT N, const SCALAR alpha, const TYPE *X,
ATL_CINT incX, const TYPE *Y, ATL_CINT incY, TYPE *A, ATL_CINT lda)
{
ATL_INT mb, nb, mu, nu, nblks, nrblks, ncblks, ldaP;
ATL_TGER_t pd;
int P;
static TYPE *A0=NULL, *A0e=NULL;
if (M < 1 || N < 1 || SCALAR_IS_ZERO(alpha)) /* quick return if no-op */
return;
pd.M = M;
pd.N = N;
pd.incX = incX;
pd.incY = incY;
pd.lda = lda;
pd.alpha = alpha;
pd.X = X;
pd.Y = Y;
pd.A = A;
pd.flg = (A0 == A || A0e == A+(M SHIFT)) ? 1 : 2;
A0 = A;
A0e = A+(M SHIFT);
P = ATL_DivBySize(CacheEdge);
P = ((size_t)M*N+P-1) / P; /* add more procs only when cache is full */
P = (P&1 && P > 1)?P+1 : P; /* don't use odd P, since it hurts alignment */
// printf("TGER, P=%d\n", P);
P = Mmin(ATL_NTHREADS, P);
/*
* Make sure we don't overflow 32-bit integer lda
*/
ldaP = P * lda;
while ((size_t)ldaP != ((size_t)lda)*P)
{
P--;
ldaP = P * lda;
}
if (P > 1)
ATL_goparallel(P, MY_DOWORK_cols, &pd, NULL);
else
MY_GER1(M, N, alpha, X, incX, Y, incY, A, lda);
}
void Mjoin(PATL,tgemv)
(const enum ATLAS_TRANS TA, ATL_CINT M, ATL_CINT N, const SCALAR alpha,
const TYPE *A, ATL_CINT lda, const TYPE *X, ATL_CINT incX,
const SCALAR beta, TYPE *Y, ATL_CINT incY)
{
static size_t ALb=0, ALe=0;
size_t at = (size_t) A;
ATL_INT n, P, ldaP;
ATL_TGEMV_t pd;
/*
* quick return if possible.
*/
if (M < 1 || N < 1)
return;
if (SCALAR_IS_ZERO(alpha)) /* No contrib from alpha*A*x */
{
ATL_CINT NY = (TA == AtlasTrans || TA == AtlasConjTrans) ? N : M;
if (!SCALAR_IS_ONE(beta))
{
if (SCALAR_IS_ZERO(beta))
Mjoin(PATL,zero)(NY, Y, incY);
else
Mjoin(PATL,scal)(NY, beta, Y, incY);
}
return;
}
pd.flg = (at >= ALb && at <= ALe) ? 1 : 0;
ALb = (size_t)A;
ALe = (size_t)(A+(M SHIFT));
#ifdef TREAL
pd.flg |= (TA == AtlasTrans || TA == AtlasConjTrans) ? 2 : 0;
#else
if (TA != AtlasNoTrans)
{
if (TA == AtlasConj)
pd.flg |= 4;
else if (TA == AtlasTrans)
pd.flg |= 2;
else /* if (TA == AtlasConjTrans) */
pd.flg |= (2|4);
}
#endif
P = ATL_DivBySize(CacheEdge);
P = ((size_t)M*N+P-1) / P; /* add more procs only when cache is full */
P = (P&1 && P > 1)?P+1 : P; /* don't use odd P; it hurts alignment */
P = Mmin(ATL_NTHREADS, P);
if (TA == AtlasNoTrans || TA == AtlasConj)
P=1;
//fprintf(stderr, "P=%d, TA=%d, M=%d, N=%d\n", P, (TA==AtlasTrans), M, N);
/*
* Make sure we don't overflow 32-bit integer lda
*/
ldaP = P * lda;
while ((size_t)ldaP != ((size_t)lda)*P)
{
P--;
ldaP = P * lda;
}
if (P > 1)
{
pd.M = M; pd.N = N; pd.incX = incX; pd.incY = incY; pd.lda = lda;
pd.alpha = alpha; pd.beta = beta;
pd.X = X; pd.Y = Y; pd.A = A;
pd.P = P;
n = N / P;
pd.n = n;
pd.nr = N - n*P;
if (pd.flg & 2) /* Transpose case */
{
ATL_goparallel(P, Mjoin(PATL,DOMVTWORK_cols), &pd, NULL);
return;
}
/*
* For gemvN, everyone needs a private M-length y. Don't do this unless
* we are sure the combine cost is likely dominated by the parallelism
*/
else if (n > Mmax(P,8))
{
int vrank;
const TYPE *a;
TYPE *y, *y0;
#ifdef TCPLX
TYPE one[2] = {ATL_rone, ATL_rzero};
TYPE zero[2] = {ATL_rzero, ATL_rzero};
#endif
y0 = y = malloc(P*(ATL_Cachelen+ATL_MulBySize(M)));
ATL_assert(y);
pd.Y = y;
pd.incY = 1;
#ifdef TREAL
pd.alpha = ATL_rone;
pd.beta = ATL_rzero;
#else
pd.alpha = one;
pd.beta = zero;
#endif
ATL_goparallel(P, Mjoin(PATL,DOMVNWORK_cols), &pd,
Mjoin(PATL,CombineMVN));
/*
* goparallel reduces all node's Ys to node 0's. Extract his from the
* work array, and combine it with input array, applying both alpha
* and beta in the process
*/
vrank = (!pd.nr || (pd.flg & 1)) ? 0 : pd.nr-1;
a = A + (lda SHIFT)*vrank;
y = ATL_Align2Ptr(y, a);
Mjoin(PATL,axpby)(M, alpha, y, 1, beta, Y, incY);
free(y0);
return;
}
}
/*
* If we haven't parallelized this thing, just do it serial
*/
Mjoin(PATL,gemv)(TA, M, N, alpha, A, lda, X, incX, beta, Y, incY);
}
int RunCase(int CacheSize, TYPE thresh, int MFLOP, enum ATLAS_ORDER Order,
int M, int N, int lda)
{
char *cord = (Order == AtlasColMajor ? "Col" : "Row");
const double maxMN = Mmax(M,N), minMN = Mmin(M,N);
unsigned long nreps=0;
int npiv=(-1), *ipiv;
const int incA = (Order == AtlasColMajor ? N*lda : M*lda);
double mflops, mflop, resid, tim=(-1.0), t0;
TYPE *A, *a;
int i;
#ifdef TREAL
mflops = maxMN * minMN * minMN - ((minMN*minMN*minMN) / 3.0) -
(minMN*minMN) / 2.0;
#else
mflops = (maxMN * minMN * minMN - ((minMN*minMN*minMN) / 3.0) +
(maxMN*minMN) / 2.0)*4.0 - 3.0 * minMN*minMN;
#endif
mflops /= 1000000.0;
if (thresh > ATL_rzero)
{
if (Order == AtlasColMajor)
resid = lutestC(CacheSize, M, N, lda, &npiv, &tim);
else resid = lutestR(CacheSize, M, N, lda, &npiv, &tim);
}
else resid = -1.0;
if (MFLOP > mflops || thresh <= ATL_rzero) /* need to time repetitively */
{
nreps = (mflops*1000000);
nreps = (MFLOP*1000000 + nreps-1) / nreps;
if (nreps < 1) nreps = 1;
i = ATL_DivBySize(2*CacheSize) ATL_PTCACHEMUL;
i = (i + M*N) / (M*N);
if (i < nreps) i = nreps; /* don't reuse mem or no pivoting */
a = A = malloc(i * ATL_MulBySize(incA));
if (A != NULL)
{
ipiv = malloc(Mmin(M,N)*sizeof(int)); /* what the hell - reuse ipiv */
if (ipiv)
{
Mjoin(PATL,gegen)(i*incA, 1, A, i*incA, incA+M+3012);
t0 = time00();
for (i=nreps; i; i--, a += incA)
test_getrf(Order, M, N, a, lda, ipiv);
tim = time00() - t0;
tim /= nreps;
if (npiv == 0) npiv = findnpvt(Mmin(M,N), ipiv);
free(ipiv);
}
else fprintf(stderr, " WARNING: not enough mem to run timings!\n");
free(A);
}
else fprintf(stderr, " WARNING: not enough mem to run timings!\n");
}
if (tim > 0.0) mflop = mflops / tim;
else mflop = 0.0;
fprintf(stdout, "%5d %3s %6d %6d %6d %6d %9.3f %9.3f %9.3e\n",
nreps, cord, M, N, lda, npiv, tim, mflop, resid);
return(resid <= thresh);
}
double gemvcase(const int MFLOP, const enum ATLAS_TRANS TA, const int l2size,
const int M, const int N, const SCALAR alpha, const int lda,
const SCALAR beta)
{
unsigned long reps;
int i, lx, ly, la;
#ifdef TREAL
const double flops = 2.0 * M * N;
#else
const double flops = 8.0 * M * N;
#endif
double ttest, mftest, t0;
const int aincY=1, aincX=1, incY=1, incX=1;
const int inca = (TA == AtlasNoTrans) ? lda * (N SHIFT) : lda * (M SHIFT);
const int incx = N*incX SHIFT, incy = M*incY SHIFT;
TYPE *a, *A, *stA, *A0, *x, *X, *X0, *stX, *y, *Y, *Y0, *stY;
#ifdef TREAL
const TYPE nbeta = -beta;
TYPE bet = beta;
#else
const TYPE *bet = beta;
TYPE nbeta[2];
nbeta[0] = -beta[0]; nbeta[1] = -beta[1];
#endif
i = (ATL_DivBySize(l2size)+N-1)/N;
if (i < 1) i = 1;
lx = i * N * aincX;
X0 = X = x = malloc(ATL_MulBySize(lx));
if (x == NULL) return(-1);
i = (ATL_DivBySize(l2size)+M-1)/M;
if (i < 1) i = 1;
ly = i * M * aincY;
Y0 = Y = y = malloc(ATL_MulBySize(ly));
if (y == NULL)
{
free(x);
return(-1);
}
i = (ATL_DivBySize(l2size)+M*N)/(M*N);
la = i * inca;
A0 = A = a = malloc(ATL_MulBySize(la));
if (a == NULL)
{
free(x);
free(y);
return(-1);
}
if (incX < 1)
{
stX = x;
x = X = x + (lx SHIFT);
}
else stX = x + (lx SHIFT);
if (incY < 1)
{
stY = y;
y = Y = y + (ly SHIFT);
}
else stY = y + (ly SHIFT);
stA = a + (la SHIFT);
reps = (MFLOP * 1000000.0) / flops;
if (reps < 1) reps = 1;
Mjoin(PATL,gegen)(ly, 1, Y0, ly, M*incY);
Mjoin(PATL,gegen)(lx, 1, X0, lx, N*incY+127*50+77);
Mjoin(PATL,gegen)(la, 1, A0, la, N*M+513*7+90);
t0 = time00();
for (i=reps; i; i--)
{
#ifdef SYMM_
Mjoin(PATL,symv)(AtlasLower, N, alpha, a, lda, x, incX, beta, y, incY);
#else
Mjoin(PATL,gemv)(TA, M, N, alpha, a, lda, x, incX, beta, y, incY);
#endif
x += incx;
y += incy;
a += inca;
if (x == stX) x = X;
if (y == stY)
{
y = Y;
if (bet == beta) bet = nbeta;
else bet = beta;
}
if (a == stA) a = A;
}
ttest = time00() - t0;
if (ttest > 0.0) mftest = (reps * flops) / (1000000.0 * ttest);
else mftest = 0.0;
free(A0);
free(X0);
free(Y0);
return(mftest);
}
/*
* This routine handles the case where N <= maxNB && K <= maxKB, so B is
* only one block. It is particularly important for the panel factorizations
* of both LU and QR.
*/
int Mjoin(PATL,tammm_tNK)
(
enum ATLAS_TRANS TA,
enum ATLAS_TRANS TB,
ATL_CINT M,
ATL_CINT N,
ATL_CINT K,
const SCALAR alpha,
const TYPE *A,
ATL_CINT lda,
const TYPE *B,
ATL_CINT ldb,
const SCALAR beta,
TYPE *C,
ATL_CINT ldc
)
{
ATL_SZT nmblks;
amminfo_t mminfo;
unsigned int i, mb, nb, kb, mu, nu, ku, P, mr;
ATL_tamm_tNK_t pd; /* problem definition structure */
void *vp;
/*
* Special case for tiny N&K, and large M
*/
if (N >= ATL_AMM_MAXNB || K >= ATL_AMM_MAXKB || M < ATL_AMM_MAXMB ||
M < Mmin(8,ATL_NTHREADS)*ATL_AMM_MAXMB)
return(1);
Mjoin(PATL,GetRankKInfo)(&mminfo, TA, TB, M, N, K, alpha, beta);
pd.a2blk = mminfo.a2blk;
pd.b2blk = mminfo.b2blk;
pd.blk2c = mminfo.Cblk2cm;
pd.amm_b0 = mminfo.amm_b0;
pd.TA = (TA == AtlasTrans);
pd.TB = (TB == AtlasTrans);
pd.N = N;
pd.K = K;
pd.A = A;
pd.B = B;
pd.C = C;
pd.lda = lda;
pd.ldb = ldb;
pd.ldc = ldc;
pd.alpha = α
pd.beta = β
mu = mminfo.mu;
nu = mminfo.nu;
ku = mminfo.ku;
pd.mb = mb = mminfo.mb;
pd.nmu = mb / mu;
pd.nnu = (N+nu-1)/nu;
nb = pd.nnu * nu;
kb = mminfo.kb;
nmblks = M / mb;
mr = M - nmblks*mb;
if (!mr)
{
pd.mbL = mr = mb;
pd.nmuL = pd.nmu;
}
else
{
nmblks++;
pd.nmuL = (mr+mu-1)/mu;
pd.mbL = pd.nmuL * mu;
}
pd.mr = mr;
pd.nmblks = nmblks;
pd.KB0 = K;
#if ATL_MAXKMAJ_RKK > 1
if (ATL_AMMFLG_KMAJOR(mminfo.flag))
pd.KB0 = ((K+ku-1)/ku)*ku;
#endif
/*
* Maximum scale is limited by NTHREADS or max number of M-blocks
*/
P = (ATL_NTHREADS <= nmblks) ? ATL_NTHREADS : nmblks;
/*
* We have a common B wrk of size KB0*nb, then
* for each node, we need workspace: sz(A,C) = mb*K, K*nb, mb*N, laid out
* in memory as A,C, then we add safety margin mu*nu*ku so advance loads don't
* seg fault, and we add space for aligning the ptrs
*/
pd.bsz = pd.KB0*nb;
pd.wsz = mb*(pd.nnu*nu + pd.bsz) + 2*ATL_DivBySize(ATL_Cachelen);
vp = malloc(ATL_MulBySize(pd.wsz*P + pd.bsz+mu*nu*ku) + ATL_Cachelen);
if (!vp)
return(2);
pd.w = ATL_AlignPtr(vp);
pd.MbCtr = ATL_SetGlobalAtomicCount(ATL_EstNctr(nmblks, P), nmblks, 0);
pd.BassgCtr = ATL_SetAtomicCount(1);
pd.BdoneCtr = ATL_SetAtomicCount(1);
#ifdef DEBUG1
{
ATL_LAUNCHSTRUCT_t ls;
ATL_thread_t ts;
ts.rank = 0;
ts.P = 1;
ls.opstruct = &pd;
Mjoin(PATL,DoWork_tamm_tNK)(&ls, &ts);
}
#else
ATL_goparallel(P, Mjoin(PATL,DoWork_tamm_tNK), &pd, NULL);
#endif
ATL_FreeAtomicCount(pd.BdoneCtr);
ATL_FreeAtomicCount(pd.BassgCtr);
ATL_FreeGlobalAtomicCount(pd.MbCtr);
free(vp);
return(0);
}
static void ATL_symvL
(
ATL_symvK_t symvK,
const int NB,
ATL_CINT N,
const TYPE *A,
ATL_CINT lda,
const TYPE *x,
TYPE *y,
const TYPE *xt,
TYPE *yt
)
{
const TYPE one[2] = {ATL_rone, ATL_rzero};
ATL_INT Mmb2;
ATL_INT Mmb, mr, MB, j;
const size_t incA = (NB SHIFT)*lda;
const size_t opsize = ((size_t)(N+8)*(N+4))*(sizeof(TYPE)>>1)SHIFT;
void (*gemvT)(ATL_CINT, ATL_CINT, const SCALAR, const TYPE*, ATL_CINT,
const TYPE*, ATL_CINT, const SCALAR, TYPE*, ATL_CINT);
void (*gemvN)(ATL_CINT, ATL_CINT, const SCALAR, const TYPE*, ATL_CINT,
const TYPE*, ATL_CINT, const SCALAR, TYPE*, ATL_CINT);
if (opsize > MY_CE)
{
gemvT = Mjoin(PATL,gemvT);
gemvN = Mjoin(PATL,gemvN_L2);
}
else if (opsize <= ATL_MulBySize(ATL_L1elts))
{
gemvT = Mjoin(PATL,gemvT_L1);
gemvN = Mjoin(PATL,gemvN_L1);
}
else
{
gemvT = Mjoin(PATL,gemvT_L2);
gemvN = Mjoin(PATL,gemvN_L2);
}
/*
* Choose MB such that A is retained in L2 cache for second GEMV call
* If partial block is tiny, absorbe it into last block since cache is not
* precise anyway.
*/
MB = ATL_DivBySize(MY_CE) / NB;
MB = (MB > N || MB < 240) ? N : MB;
Mmb2 = Mmb+Mmb;
for (j=0; j < N; j += NB, A += incA)
{
const register size_t j2 = j+j;
register int i, nb=N-j;
nb = (nb >= NB) ? NB : nb;
symvK(AtlasLower, nb, one, A+j2, lda, x+j2, 1, one, y+j2, 1);
for (i=j+nb; i < N; i += MB)
{
const register size_t i2 = i+i;
register int mb = N-i;
mb = (mb >= MB) ? MB : mb;
gemvT(mb, nb, one, A+i2, lda, xt+i2, 1, one, yt+j2, 1);
gemvN(mb, nb, one, A+i2, lda, x+j2, 1, one, y+i2, 1);
}
}
}