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bpo-41513: Improve hypot() accuracy with three separate accumulators #22032

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Sep 2, 2020
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bpo-41513: Improve hypot() accuracy with three separate accumulators #22032

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8 changes: 4 additions & 4 deletions Modules/mathmodule.c
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Original file line number Diff line number Diff line change
Expand Up @@ -2456,7 +2456,7 @@ Given that csum >= 1.0, we have:
Since lo**2 is less than 1/2 ulp(csum), we have csum+lo*lo == csum.

To minimize loss of information during the accumulation of fractional
values, the lo**2 term has a separate accumulator.
values, each term has a separate accumulator.

The square root differential correction is needed because a
correctly rounded square root of a correctly rounded sum of
Expand Down Expand Up @@ -2487,7 +2487,7 @@ static inline double
vector_norm(Py_ssize_t n, double *vec, double max, int found_nan)
{
const double T27 = 134217729.0; /* ldexp(1.0, 27)+1.0) */
double x, csum = 1.0, oldcsum, frac = 0.0, frac_lo = 0.0, scale;
double x, csum = 1.0, oldcsum, scale, frac=0.0, frac_mid=0.0, frac_lo=0.0;
double t, hi, lo, h;
int max_e;
Py_ssize_t i;
Expand Down Expand Up @@ -2529,12 +2529,12 @@ vector_norm(Py_ssize_t n, double *vec, double max, int found_nan)
assert(fabs(csum) >= fabs(x));
oldcsum = csum;
csum += x;
frac += (oldcsum - csum) + x;
frac_mid += (oldcsum - csum) + x;

assert(csum + lo * lo == csum);
frac_lo += lo * lo;
}
frac += frac_lo;
frac += frac_lo + frac_mid;
h = sqrt(csum - 1.0 + frac);

x = h;
Expand Down