Skip to content

Simplify and improve accuracy for subnormals in hypot() #102785

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
merged 3 commits into from
Mar 17, 2023
Merged

Simplify and improve accuracy for subnormals in hypot() #102785

Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
48b37a1
Handle subnormals with a recursive call
rhettinger Mar 17, 2023
031b97a
Use lossless scaling
rhettinger Mar 17, 2023
cde1d6d
Invert the test so that the main code path has the least indentation
rhettinger Mar 17, 2023
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
63 changes: 28 additions & 35 deletions Modules/mathmodule.c
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -2498,7 +2498,7 @@ verified for 1 billion random inputs with n=5. [7]
static inline double
vector_norm(Py_ssize_t n, double *vec, double max, int found_nan)
{
double x, h, scale, oldcsum, csum = 1.0, frac1 = 0.0, frac2 = 0.0;
double x, h, scale, csum = 1.0, frac1 = 0.0, frac2 = 0.0;
DoubleLength pr, sm;
int max_e;
Py_ssize_t i;
Expand All @@ -2513,49 +2513,42 @@ vector_norm(Py_ssize_t n, double *vec, double max, int found_nan)
return max;
}
frexp(max, &max_e);
if (max_e >= -1023) {
scale = ldexp(1.0, -max_e);
assert(max * scale >= 0.5);
assert(max * scale < 1.0);
if (max_e < -1023) {
/* When max_e < -1023, ldexp(1.0, -max_e) would overflow.
So we first perform lossless scaling from subnormals back to normals,
then recurse back to vector_norm(), and then finally undo the scaling.
*/
for (i=0 ; i < n ; i++) {
x = vec[i];
assert(Py_IS_FINITE(x) && fabs(x) <= max);
vec[i] /= DBL_MIN;
}
return DBL_MIN * vector_norm(n, vec, max / DBL_MIN, found_nan);
}
scale = ldexp(1.0, -max_e);
assert(max * scale >= 0.5);
assert(max * scale < 1.0);
for (i=0 ; i < n ; i++) {
x = vec[i];
assert(Py_IS_FINITE(x) && fabs(x) <= max);

x *= scale;
assert(fabs(x) < 1.0);
x *= scale;
assert(fabs(x) < 1.0);

pr = dl_mul(x, x);
assert(pr.hi <= 1.0);
pr = dl_mul(x, x);
assert(pr.hi <= 1.0);

sm = dl_fast_sum(csum, pr.hi);
csum = sm.hi;
frac1 += pr.lo;
frac2 += sm.lo;
}
h = sqrt(csum - 1.0 + (frac1 + frac2));
pr = dl_mul(-h, h);
sm = dl_fast_sum(csum, pr.hi);
csum = sm.hi;
frac1 += pr.lo;
frac2 += sm.lo;
x = csum - 1.0 + (frac1 + frac2);
return (h + x / (2.0 * h)) / scale;
}
/* When max_e < -1023, ldexp(1.0, -max_e) overflows.
So instead of multiplying by a scale, we just divide by *max*.
*/
for (i=0 ; i < n ; i++) {
x = vec[i];
assert(Py_IS_FINITE(x) && fabs(x) <= max);
x /= max;
x = x*x;
assert(x <= 1.0);
assert(fabs(csum) >= fabs(x));
oldcsum = csum;
csum += x;
frac1 += (oldcsum - csum) + x;
}
return max * sqrt(csum - 1.0 + frac1);
h = sqrt(csum - 1.0 + (frac1 + frac2));
pr = dl_mul(-h, h);
sm = dl_fast_sum(csum, pr.hi);
csum = sm.hi;
frac1 += pr.lo;
frac2 += sm.lo;
x = csum - 1.0 + (frac1 + frac2);
return (h + x / (2.0 * h)) / scale;
}

#define NUM_STACK_ELEMS 16
Expand Down