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modified algorithm for better numerical stability

This commit is contained in:
wernsaar 2014-08-12 08:35:42 +02:00
parent 58b075daef
commit 07c66b1960
1 changed files with 27 additions and 87 deletions
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114
kernel/x86_64/zgemv_n.c
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@ -48,8 +48,7 @@ static void zgemv_kernel_16x4(BLASLONG n, FLOAT **ap, FLOAT *x, FLOAT *y)
for ( i=0; i< 2*n; i+=2 ) for ( i=0; i< 2*n; i+=2 )
{ {
#if !defined(CONJ) #if ( !defined(CONJ) && !defined(XCONJ) ) || ( defined(CONJ) && defined(XCONJ) )
#if !defined(XCONJ)
y[i] += a0[i]*x[0] - a0[i+1] * x[1]; y[i] += a0[i]*x[0] - a0[i+1] * x[1];
y[i+1] += a0[i]*x[1] + a0[i+1] * x[0]; y[i+1] += a0[i]*x[1] + a0[i+1] * x[0];
y[i] += a1[i]*x[2] - a1[i+1] * x[3]; y[i] += a1[i]*x[2] - a1[i+1] * x[3];
@ -67,29 +66,6 @@ static void zgemv_kernel_16x4(BLASLONG n, FLOAT **ap, FLOAT *x, FLOAT *y)
y[i+1] += a2[i]*x[5] - a2[i+1] * x[4]; y[i+1] += a2[i]*x[5] - a2[i+1] * x[4];
y[i] += a3[i]*x[6] + a3[i+1] * x[7]; y[i] += a3[i]*x[6] + a3[i+1] * x[7];
y[i+1] += a3[i]*x[7] - a3[i+1] * x[6]; y[i+1] += a3[i]*x[7] - a3[i+1] * x[6];
#endif
#else
#if !defined(XCONJ)
y[i] += a0[i]*x[0] + a0[i+1] * x[1];
y[i+1] -= a0[i]*x[1] - a0[i+1] * x[0];
y[i] += a1[i]*x[2] + a1[i+1] * x[3];
y[i+1] -= a1[i]*x[3] - a1[i+1] * x[2];
y[i] += a2[i]*x[4] + a2[i+1] * x[5];
y[i+1] -= a2[i]*x[5] - a2[i+1] * x[4];
y[i] += a3[i]*x[6] + a3[i+1] * x[7];
y[i+1] -= a3[i]*x[7] - a3[i+1] * x[6];
#else
y[i] += a0[i]*x[0] - a0[i+1] * x[1];
y[i+1] -= a0[i]*x[1] + a0[i+1] * x[0];
y[i] += a1[i]*x[2] - a1[i+1] * x[3];
y[i+1] -= a1[i]*x[3] + a1[i+1] * x[2];
y[i] += a2[i]*x[4] - a2[i+1] * x[5];
y[i+1] -= a2[i]*x[5] + a2[i+1] * x[4];
y[i] += a3[i]*x[6] - a3[i+1] * x[7];
y[i+1] -= a3[i]*x[7] + a3[i+1] * x[6];
#endif
#endif #endif
} }
} }
@ -104,23 +80,12 @@ static void zgemv_kernel_16x1(BLASLONG n, FLOAT *ap, FLOAT *x, FLOAT *y)
for ( i=0; i< 2*n; i+=2 ) for ( i=0; i< 2*n; i+=2 )
{ {
#if !defined(CONJ) #if ( !defined(CONJ) && !defined(XCONJ) ) || ( defined(CONJ) && defined(XCONJ) )
#if !defined(XCONJ)
y[i] += a0[i]*x[0] - a0[i+1] * x[1]; y[i] += a0[i]*x[0] - a0[i+1] * x[1];
y[i+1] += a0[i]*x[1] + a0[i+1] * x[0]; y[i+1] += a0[i]*x[1] + a0[i+1] * x[0];
#else #else
y[i] += a0[i]*x[0] + a0[i+1] * x[1]; y[i] += a0[i]*x[0] + a0[i+1] * x[1];
y[i+1] += a0[i]*x[1] - a0[i+1] * x[0]; y[i+1] += a0[i]*x[1] - a0[i+1] * x[0];
#endif
#else
#if !defined(XCONJ)
y[i] += a0[i]*x[0] + a0[i+1] * x[1];
y[i+1] -= a0[i]*x[1] - a0[i+1] * x[0];
#else
y[i] += a0[i]*x[0] - a0[i+1] * x[1];
y[i+1] -= a0[i]*x[1] + a0[i+1] * x[0];
#endif
#endif #endif
} }
@ -139,17 +104,24 @@ static void zero_y(BLASLONG n, FLOAT *dest)
static void add_y(BLASLONG n, FLOAT *src, FLOAT *dest, BLASLONG inc_dest) static void add_y(BLASLONG n, FLOAT *src, FLOAT *dest, BLASLONG inc_dest,FLOAT alpha_r, FLOAT alpha_i)
{ {
BLASLONG i; BLASLONG i;
FLOAT temp_r;
FLOAT temp_i;
for ( i=0; i<n; i++ ) for ( i=0; i<n; i++ )
{ {
*dest += *src; #if !defined(XCONJ)
#if ( !defined(CONJ) && !defined(XCONJ) ) || ( defined(CONJ) && defined(XCONJ) ) temp_r = alpha_r * src[0] - alpha_i * src[1];
*(dest+1) += *(src+1); temp_i = alpha_r * src[1] + alpha_i * src[0];
#else #else
*(dest+1) -= *(src+1); temp_r = alpha_r * src[0] + alpha_i * src[1];
temp_i = -alpha_r * src[1] + alpha_i * src[0];
#endif #endif
*dest += temp_r;
*(dest+1) += temp_i;
src+=2; src+=2;
dest += inc_dest; dest += inc_dest;
} }
@ -201,33 +173,18 @@ int CNAME(BLASLONG m, BLASLONG n, BLASLONG dummy1, FLOAT alpha_r,FLOAT alpha_i,
for( i = 0; i < n1 ; i++) for( i = 0; i < n1 ; i++)
{ {
#if !defined(XCONJ) xbuffer[0] = x_ptr[0];
xbuffer[0] = alpha_r * x_ptr[0] - alpha_i * x_ptr[1]; xbuffer[1] = x_ptr[1];
xbuffer[1] = alpha_r * x_ptr[1] + alpha_i * x_ptr[0];
x_ptr += inc_x; x_ptr += inc_x;
xbuffer[2] = alpha_r * x_ptr[0] - alpha_i * x_ptr[1]; xbuffer[2] = x_ptr[0];
xbuffer[3] = alpha_r * x_ptr[1] + alpha_i * x_ptr[0]; xbuffer[3] = x_ptr[1];
x_ptr += inc_x; x_ptr += inc_x;
xbuffer[4] = alpha_r * x_ptr[0] - alpha_i * x_ptr[1]; xbuffer[4] = x_ptr[0];
xbuffer[5] = alpha_r * x_ptr[1] + alpha_i * x_ptr[0]; xbuffer[5] = x_ptr[1];
x_ptr += inc_x; x_ptr += inc_x;
xbuffer[6] = alpha_r * x_ptr[0] - alpha_i * x_ptr[1]; xbuffer[6] = x_ptr[0];
xbuffer[7] = alpha_r * x_ptr[1] + alpha_i * x_ptr[0]; xbuffer[7] = x_ptr[1];
x_ptr += inc_x; x_ptr += inc_x;
#else
xbuffer[0] = alpha_r * x_ptr[0] + alpha_i * x_ptr[1];
xbuffer[1] = alpha_r * x_ptr[1] - alpha_i * x_ptr[0];
x_ptr += inc_x;
xbuffer[2] = alpha_r * x_ptr[0] + alpha_i * x_ptr[1];
xbuffer[3] = alpha_r * x_ptr[1] - alpha_i * x_ptr[0];
x_ptr += inc_x;
xbuffer[4] = alpha_r * x_ptr[0] + alpha_i * x_ptr[1];
xbuffer[5] = alpha_r * x_ptr[1] - alpha_i * x_ptr[0];
x_ptr += inc_x;
xbuffer[6] = alpha_r * x_ptr[0] + alpha_i * x_ptr[1];
xbuffer[7] = alpha_r * x_ptr[1] - alpha_i * x_ptr[0];
x_ptr += inc_x;
#endif
ap[0] = a_ptr; ap[0] = a_ptr;
ap[1] = a_ptr + lda; ap[1] = a_ptr + lda;
@ -239,24 +196,18 @@ int CNAME(BLASLONG m, BLASLONG n, BLASLONG dummy1, FLOAT alpha_r,FLOAT alpha_i,
for( i = 0; i < n2 ; i++) for( i = 0; i < n2 ; i++)
{ {
#if !defined(XCONJ) xbuffer[0] = x_ptr[0];
xbuffer[0] = alpha_r * x_ptr[0] - alpha_i * x_ptr[1]; xbuffer[1] = x_ptr[1];
xbuffer[1] = alpha_r * x_ptr[1] + alpha_i * x_ptr[0];
x_ptr += inc_x; x_ptr += inc_x;
#else
xbuffer[0] = alpha_r * x_ptr[0] + alpha_i * x_ptr[1];
xbuffer[1] = alpha_r * x_ptr[1] - alpha_i * x_ptr[0];
x_ptr += inc_x;
#endif
zgemv_kernel_16x1(NB,a_ptr,xbuffer,ybuffer); zgemv_kernel_16x1(NB,a_ptr,xbuffer,ybuffer);
a_ptr += 1 * lda; a_ptr += 1 * lda;
} }
add_y(NB,ybuffer,y_ptr,inc_y); add_y(NB,ybuffer,y_ptr,inc_y,alpha_r,alpha_i);
a += 2 * NB; a += 2 * NB;
y_ptr += NB * inc_y; y_ptr += NB * inc_y;
} }
j=0; j=0;
while ( j < (m % 16)) while ( j < (m % 16))
{ {
@ -266,24 +217,13 @@ int CNAME(BLASLONG m, BLASLONG n, BLASLONG dummy1, FLOAT alpha_r,FLOAT alpha_i,
FLOAT temp_i = 0.0; FLOAT temp_i = 0.0;
for( i = 0; i < n; i++ ) for( i = 0; i < n; i++ )
{ {
#if !defined(CONJ) #if ( !defined(CONJ) && !defined(XCONJ) ) || ( defined(CONJ) && defined(XCONJ) )
#if !defined(XCONJ)
temp_r += a_ptr[0] * x_ptr[0] - a_ptr[1] * x_ptr[1]; temp_r += a_ptr[0] * x_ptr[0] - a_ptr[1] * x_ptr[1];
temp_i += a_ptr[0] * x_ptr[1] + a_ptr[1] * x_ptr[0]; temp_i += a_ptr[0] * x_ptr[1] + a_ptr[1] * x_ptr[0];
#else #else
temp_r += a_ptr[0] * x_ptr[0] + a_ptr[1] * x_ptr[1]; temp_r += a_ptr[0] * x_ptr[0] + a_ptr[1] * x_ptr[1];
temp_i += a_ptr[0] * x_ptr[1] - a_ptr[1] * x_ptr[0]; temp_i += a_ptr[0] * x_ptr[1] - a_ptr[1] * x_ptr[0];
#endif #endif
#else
#if !defined(XCONJ)
temp_r += a_ptr[0] * x_ptr[0] + a_ptr[1] * x_ptr[1];
temp_i += a_ptr[0] * x_ptr[1] - a_ptr[1] * x_ptr[0];
#else
temp_r += a_ptr[0] * x_ptr[0] - a_ptr[1] * x_ptr[1];
temp_i += a_ptr[0] * x_ptr[1] + a_ptr[1] * x_ptr[0];
#endif
#endif
a_ptr += lda; a_ptr += lda;
x_ptr += inc_x; x_ptr += inc_x;