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update zrotg

tags/v0.3.24
Martin Kroeker GitHub 2 years ago
parent
04cdf5efb4
commit
a2a184572c
No known key found for this signature in database GPG Key ID: 4AEE18F83AFDEB23
1 changed files with 143 additions and 128 deletions
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  1. +143
    -128
      interface/zrotg.c

+ 143
- 128
interface/zrotg.c View File

@@ -18,20 +18,26 @@ void CNAME(void *VDA, void *VDB, FLOAT *C, void *VS) {

#ifdef DOUBLE
long double safmin = DBL_MIN;
long double rtmin = sqrt(DBL_MIN/DBL_EPSILON);
#else
long double safmin = FLT_MIN;
long double rtmin = sqrt(FLT_MIN/FLT_EPSILON);
#endif

#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;
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;

long double ada = fabsl(da_r) + fabsl(da_i);
long double adb = sqrt(db_r * db_r + db_i * db_i);
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;

@@ -39,128 +45,137 @@ void CNAME(void *VDA, void *VDB, FLOAT *C, void *VS) {

FUNCTION_PROFILE_START();

if (ada == ZERO) {
*C = ZERO;
*(S + 0) = ONE;
if (db_r == ZERO && db_i == ZERO) {
*C = ONE;
*(S + 0) = ZERO;
*(S + 1) = ZERO;
*(DA + 0) = db_r;
*(DA + 1) = db_i;
} else {
long double alpha_r, alpha_i;
long double safmax = 1./safmin;
long double sigma;
long double maxab = MAX(ada,adb);
long double scale = MIN(MAX(safmin,maxab), safmax);


long double aa_r = da_r / scale;
long double aa_i = da_i / scale;
long double bb_r = db_r / scale;
long double bb_i = db_i / scale;

if (ada > adb)
sigma = copysign(1.,da_r);
else
sigma = copysign(1.,db_r);

r = sigma * 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;
return;
}
#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 = fabs(db_r) + fabs(db_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 safmax = 1./safmin;
FLOAT scale, sigma;
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);
}
FLOAT maxab = MAX(ada,adb);
scale = MIN(MAX(safmin,maxab), safmax);

aa_r = da_r / scale;
aa_i = da_i / scale;
bb_r = db_r / scale;
bb_i = db_i / scale;

if (ada > adb)
sigma = copysign(1.,da_r);
else
sigma = copysign(1.,db_r);

r = sigma * 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 safmax = 1./safmin;
#if defined DOUBLE
long double rtmax = safmax /DBL_EPSILON;
#else
long double rtmax = safmax /FLT_EPSILON;
#endif

FUNCTION_PROFILE_END(4, 4, 4);

IDEBUG_END;

return;
*(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;
}
}
}

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