Merge pull request #4143 from martin-frbg/issue4130

Update to use safe scaling algorithm from Reference-LAPACK PR 527
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Martin Kroeker 2023-09-01 14:20:25 +02:00 committed by GitHub
commit 33797c44fc
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2 changed files with 208 additions and 131 deletions

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@ -1,9 +1,11 @@
#include <math.h>
#include <float.h>
#include "common.h"
#ifdef FUNCTION_PROFILE
#include "functable.h"
#endif
#ifndef CBLAS
void NAME(FLOAT *DA, FLOAT *DB, FLOAT *C, FLOAT *S){
@ -14,17 +16,27 @@ void CNAME(FLOAT *DA, FLOAT *DB, FLOAT *C, FLOAT *S){
#endif
#ifdef DOUBLE
long double safmin = DBL_MIN;
#else
long double safmin = FLT_MIN;
#endif
#if defined(__i386__) || defined(__x86_64__) || defined(__ia64__) || defined(_M_X64) || defined(_M_IX86)
long double da = *DA;
long double db = *DB;
long double c;
long double s;
long double r, roe, z;
long double r, z;
long double sigma, dascal,dbscal;
long double ada = fabsl(da);
long double adb = fabsl(db);
long double scale = ada + adb;
long double maxab = MAX(ada,adb);
long double safmax;
long double scale;
#ifndef CBLAS
PRINT_DEBUG_NAME;
@ -32,17 +44,25 @@ void CNAME(FLOAT *DA, FLOAT *DB, FLOAT *C, FLOAT *S){
PRINT_DEBUG_CNAME;
#endif
roe = db;
if (ada > adb) roe = da;
if (scale == ZERO) {
if (adb == ZERO) {
*C = ONE;
*S = ZERO;
*DA = ZERO;
*DB = ZERO;
} else if (ada == ZERO) {
*C = ZERO;
*S = ONE;
*DA = *DB;
*DB = ONE;
} else {
r = sqrt(da * da + db * db);
if (roe < 0) r = -r;
safmax = 1./safmin;
scale = MIN(MAX(safmin,maxab), safmax);
if (ada > adb)
sigma = copysign(1.,da);
else
sigma = copysign(1.,db);
dascal = da / scale;
dbscal = db / scale;
r = sigma * (scale * sqrt(dascal * dascal + dbscal * dbscal));
c = da / r;
s = db / r;
z = ONE;
@ -65,11 +85,22 @@ void CNAME(FLOAT *DA, FLOAT *DB, FLOAT *C, FLOAT *S){
FLOAT db = *DB;
FLOAT c = *C;
FLOAT s = *S;
FLOAT r, roe, z;
FLOAT sigma;
FLOAT r, z;
FLOAT ada = fabs(da);
FLOAT adb = fabs(db);
FLOAT scale = ada + adb;
FLOAT maxab = MAX(ada,adb);
long double safmax ;
FLOAT scale ;
safmax = 1./safmin;
scale = MIN(MAX(safmin,maxab), safmax);
if (ada > adb)
sigma = copysign(1.,da);
else
sigma = copysign(1.,db);
#ifndef CBLAS
PRINT_DEBUG_NAME;
@ -77,20 +108,21 @@ void CNAME(FLOAT *DA, FLOAT *DB, FLOAT *C, FLOAT *S){
PRINT_DEBUG_CNAME;
#endif
roe = db;
if (ada > adb) roe = da;
if (scale == ZERO) {
if (adb == ZERO) {
*C = ONE;
*S = ZERO;
*DA = ZERO;
*DB = ZERO;
} else if (ada == ZERO) {
*C = ZERO;
*S = ONE;
*DA = *DB;
*DB = ONE;
} else {
FLOAT aa = da / scale;
FLOAT bb = db / scale;
r = scale * sqrt(aa * aa + bb * bb);
if (roe < 0) r = -r;
r = sigma * scale * sqrt(aa * aa + bb * bb);
c = da / r;
s = db / r;
z = ONE;

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@ -1,9 +1,11 @@
#include <math.h>
#include <float.h>
#include "common.h"
#ifdef FUNCTION_PROFILE
#include "functable.h"
#endif
#ifndef CBLAS
void NAME(FLOAT *DA, FLOAT *DB, FLOAT *C, FLOAT *S){
@ -14,123 +16,166 @@ void CNAME(void *VDA, void *VDB, FLOAT *C, void *VS) {
FLOAT *S = (FLOAT*) VS;
#endif /* CBLAS */
#if defined(__i386__) || defined(__x86_64__) || defined(__ia64__) || defined(_M_X64) || defined(_M_IX86)
long double da_r = *(DA + 0);
long double da_i = *(DA + 1);
long double db_r = *(DB + 0);
long double db_i = *(DB + 1);
long double r;
long double ada = fabsl(da_r) + fabsl(da_i);
PRINT_DEBUG_NAME;
IDEBUG_START;
FUNCTION_PROFILE_START();
if (ada == ZERO) {
*C = ZERO;
*(S + 0) = ONE;
*(S + 1) = ZERO;
*(DA + 0) = db_r;
*(DA + 1) = db_i;
} else {
long double alpha_r, alpha_i;
ada = sqrt(da_r * da_r + da_i * da_i);
r = sqrt(da_r * da_r + da_i * da_i + db_r * db_r + db_i * db_i);
alpha_r = da_r / ada;
alpha_i = da_i / ada;
*(C + 0) = ada / r;
*(S + 0) = (alpha_r * db_r + alpha_i *db_i) / r;
*(S + 1) = (alpha_i * db_r - alpha_r *db_i) / r;
*(DA + 0) = alpha_r * r;
*(DA + 1) = alpha_i * r;
}
#ifdef DOUBLE
long double safmin = DBL_MIN;
long double rtmin = sqrt(DBL_MIN/DBL_EPSILON);
#else
FLOAT da_r = *(DA + 0);
FLOAT da_i = *(DA + 1);
FLOAT db_r = *(DB + 0);
FLOAT db_i = *(DB + 1);
FLOAT r;
FLOAT ada = fabs(da_r) + fabs(da_i);
FLOAT adb;
PRINT_DEBUG_NAME;
IDEBUG_START;
FUNCTION_PROFILE_START();
if (ada == ZERO) {
*C = ZERO;
*(S + 0) = ONE;
*(S + 1) = ZERO;
*(DA + 0) = db_r;
*(DA + 1) = db_i;
} else {
FLOAT scale;
FLOAT aa_r, aa_i, bb_r, bb_i;
FLOAT alpha_r, alpha_i;
aa_r = fabs(da_r);
aa_i = fabs(da_i);
if (aa_i > aa_r) {
aa_r = fabs(da_i);
aa_i = fabs(da_r);
}
if (aa_r == ZERO) {
ada = 0.;
} else {
scale = (aa_i / aa_r);
ada = aa_r * sqrt(ONE + scale * scale);
}
bb_r = fabs(db_r);
bb_i = fabs(db_i);
if (bb_i > bb_r) {
bb_r = fabs(bb_i);
bb_i = fabs(bb_r);
}
if (bb_r == ZERO) {
adb = 0.;
} else {
scale = (bb_i / bb_r);
adb = bb_r * sqrt(ONE + scale * scale);
}
scale = ada + adb;
aa_r = da_r / scale;
aa_i = da_i / scale;
bb_r = db_r / scale;
bb_i = db_i / scale;
r = scale * sqrt(aa_r * aa_r + aa_i * aa_i + bb_r * bb_r + bb_i * bb_i);
alpha_r = da_r / ada;
alpha_i = da_i / ada;
*(C + 0) = ada / r;
*(S + 0) = (alpha_r * db_r + alpha_i *db_i) / r;
*(S + 1) = (alpha_i * db_r - alpha_r *db_i) / r;
*(DA + 0) = alpha_r * r;
*(DA + 1) = alpha_i * r;
}
long double safmin = FLT_MIN;
long double rtmin = sqrt(FLT_MIN/FLT_EPSILON);
#endif
FUNCTION_PROFILE_END(4, 4, 4);
IDEBUG_END;
FLOAT da_r = *(DA+0);
FLOAT da_i = *(DA+1);
FLOAT db_r = *(DB+0);
FLOAT db_i = *(DB+1);
//long double r;
FLOAT *r, *S1=(FLOAT *)malloc(2*sizeof(FLOAT));
FLOAT *R=(FLOAT *)malloc(2*sizeof(FLOAT));
long double d;
return;
FLOAT ada = da_r * da_r + da_i * da_i;
FLOAT adb = db_r * db_r + db_i * db_i;
FLOAT adart = sqrt( da_r * da_r + da_i * da_i);
FLOAT adbrt = sqrt( db_r * db_r + db_i * db_i);
PRINT_DEBUG_NAME;
IDEBUG_START;
FUNCTION_PROFILE_START();
if (db_r == ZERO && db_i == ZERO) {
*C = ONE;
*(S + 0) = ZERO;
*(S + 1) = ZERO;
return;
}
long double safmax = 1./safmin;
#if defined DOUBLE
long double rtmax = safmax /DBL_EPSILON;
#else
long double rtmax = safmax /FLT_EPSILON;
#endif
*(S1 + 0) = *(DB + 0);
*(S1 + 1) = *(DB + 1) *-1;
if (da_r == ZERO && da_i == ZERO) {
*C = ZERO;
if (db_r == ZERO) {
(*DA) = fabsl(db_i);
*S = *S1 /da_r;
*(S+1) = *(S1+1) /da_r;
return;
} else if ( db_i == ZERO) {
*DA = fabsl(db_r);
*S = *S1 /da_r;
*(S+1) = *(S1+1) /da_r;
return;
} else {
long double g1 = MAX( fabsl(db_r), fabsl(db_i));
rtmax =sqrt(safmax/2.);
if (g1 > rtmin && g1 < rtmax) { // unscaled
d = sqrt(adb);
*S = *S1 /d;
*(S+1) = *(S1+1) /d;
*DA = d ;
*(DA+1) = ZERO;
return;
} else { // scaled algorithm
long double u = MIN ( safmax, MAX ( safmin, g1));
FLOAT gs_r = db_r/u;
FLOAT gs_i = db_i/u;
d = sqrt ( gs_r*gs_r + gs_i*gs_i);
*S = gs_r / d;
*(S + 1) = (gs_i * -1) / d;
*DA = d * u;
*(DA+1) = ZERO;
return;
}
}
} else {
FLOAT f1 = MAX ( fabsl(da_r), fabsl(da_i));
FLOAT g1 = MAX ( fabsl(db_r), fabsl(db_i));
rtmax = sqrt(safmax / 4.);
if ( f1 > rtmin && f1 < rtmax && g1 > rtmin && g1 < rtmax) { //unscaled
long double h = ada + adb;
double adahsq = sqrt(ada * h);
if (ada >= h *safmin) {
*C = sqrt(ada/h);
*R = *DA / *C;
*(R+1) = *(DA+1) / *(C+1);
rtmax *= 2.;
if ( ada > rtmin && h < rtmax) { // no risk of intermediate overflow
*S = *S1 * (*DA / adahsq) - *(S1+1)* (*(DA+1)/adahsq);
*(S+1) = *S1 * (*(DA+1) / adahsq) + *(S1+1) * (*DA/adahsq);
} else {
*S = *S1 * (*R/h) - *(S1+1) * (*(R+1)/h);
*(S+1) = *S1 * (*(R+1)/h) + *(S1+1) * (*(R)/h);
}
} else {
*C = ada / adahsq;
if (*C >= safmin)
*R = *DA / *C;
else
*R = *DA * (h / adahsq);
*S = *S1 * ada / adahsq;
*(S+1) = *(S1+1) * ada / adahsq;
}
*DA=*R;
*(DA+1)=*(R+1);
return;
} else { // scaled
FLOAT fs_r, fs_i, gs_r, gs_i;
long double v,w,f2,g2,h;
long double u = MIN ( safmax, MAX ( safmin, MAX(f1,g1)));
gs_r = db_r/u;
gs_i = db_i/u;
g2 = sqrt ( gs_r*gs_r + gs_i*gs_i);
if (f1 /u < rtmin) {
v = MIN (safmax, MAX (safmin, f1));
w = v / u;
fs_r = *DA/ v;
fs_i = *(DA+1) / v;
f2 = sqrt ( fs_r*fs_r + fs_i*fs_i);
h = f2 * w * w + g2;
} else { // use same scaling for both
w = 1.;
fs_r = *DA/ u;
fs_i = *(DA+1) / u;
f2 = sqrt ( fs_r*fs_r + fs_i*fs_i);
h = f2 + g2;
}
if ( f2 >= h * safmin) {
*C = sqrt ( f2 / h );
*DA = fs_r / *C;
*(DA+1) = fs_i / *C;
rtmax *= 2;
if ( f2 > rtmin && h < rtmax) {
*S = gs_r * (fs_r /sqrt(f2*h)) - gs_i * (fs_i / sqrt(f2*h));
*(S+1) = gs_r * (fs_i /sqrt(f2*h)) + gs_i * -1. * (fs_r / sqrt(f2*h));
} else {
*S = gs_r * (*DA/h) - gs_i * (*(DA+1) / h);
*(S+1) = gs_r * (*(DA+1) /h) + gs_i * -1. * (*DA / h);
}
} else { // intermediates might overflow
d = sqrt ( f2 * h);
*C = f2 /d;
if (*C >= safmin) {
*DA = fs_r / *C;
*(DA+1) = fs_i / *C;
} else {
*DA = fs_r * (h / d);
*(DA+1) = fs_i / (h / d);
}
*S = gs_r * (fs_r /d) - gs_i * (fs_i / d);
*(S+1) = gs_r * (fs_i /d) + gs_i * -1. * (fs_r / d);
}
*C *= w;
*DA *= u;
*(DA+1) *= u;
return;
}
}
}