Modern Math Hypot

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Hypot

Returns the square root of xx + yy without overflowing for large values.

Syntax

Hypot( x, y )

Notes

• Delegates to libm's hypot, which is required not to overflow for a representable result.
• Sqr( x*x + y*y ) overflows at about 1.3e154 for a double, which is why the hand-rolled version is wrong at the extremes: Hypot( 1e200, 1e200 ) is finite where sqr( 1e200*1e200 + 1e200*1e200 ) is +inf.
• Overloaded on float64 and on float32, so a single-precision call does not silently widen and narrow.
• BOUNDED accuracy: correct to a stated ulp bound, with the platform libm as the dependency.

Examples

#import "std/numeric"
using numeric

print Hypot( 3.0, 4.0 )      '' 5

'' It does NOT overflow for a representable result: sqr( x*x + y*y )
'' overflows at about 1.3e154 for a double, which is why the
'' hand-rolled version is wrong at the extremes
print Hypot( 1e200, 1e200 )  '' 1.414213562373095e+200
print sqr( 1e200*1e200 + 1e200*1e200 )        '' 1.#INF

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Library: Math Library
Category: Math Library
Documented under: Nothing Becomes A Keyword