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Simplify and speed-up math.hypot() and math.dist() #102734

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Merged
rhettinger merged 6 commits into from
Mar 15, 2023
Merged

Simplify and speed-up math.hypot() and math.dist() #102734

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cd7cfc7
Move double and triple length helper functions to the top
rhettinger Mar 15, 2023
cd5fb29
Add more double length functions to support vector_norm
rhettinger Mar 15, 2023
8f3e73c
Use DoubleLength functions in hypot().
rhettinger Mar 15, 2023
58377df
Update comments
rhettinger Mar 15, 2023
47e878d
Remove unused code
rhettinger Mar 15, 2023
9a63c70
Merge branch 'main' into faster_hypot
rhettinger Mar 15, 2023
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Add more double length functions to support vector_norm
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@rhettinger
rhettinger committed Mar 15, 2023
commit cd5fb29fb43dfe4ad3c508aa98e16b768f03daa6
31 changes: 31 additions & 0 deletions Modules/mathmodule.c
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Original file line number Diff line number Diff line change
Expand Up @@ -104,6 +104,22 @@ Double and triple length extended precision algorithms from:

typedef struct{ double hi; double lo; } DoubleLength;

static DoubleLength
d_to_dl(double x)
{
return (DoubleLength) {x, 0.0};
}

static DoubleLength
dl_fast_sum(double a, double b)
{
/* Algorithm 1.1. Compensated summation of two floating point numbers. */
assert(fabs(a) >= fabs(b));
double x = a + b;
double y = (a - x) + b;
return (DoubleLength) {x, y};
}

static DoubleLength
dl_sum(double a, double b)
{
Expand Down Expand Up @@ -164,6 +180,21 @@ dl_mul(double x, double y)
return (DoubleLength) {z, zz};
}

static DoubleLength
dl_fma(double x, double y, DoubleLength total)
{
/* Algorithm 5.10 with SumKVert for K=2 */
DoubleLength pr = dl_mul(x, y);
DoubleLength sm = dl_sum(total.hi, pr.hi);
return DoubleLength {sm.hi, pr.lo + sm.lo + total.lo};
}

static double
dl_to_d(DoubleLength total):
{
return total.lo + total.hi;
}

#endif

typedef struct { double hi; double lo; double tiny; } TripleLength;
Expand Down