Modern Math Ulp

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Ulp

Returns the gap between a number and the next one its type can hold.

Syntax

Ulp( byval x as float64 ) as float64

Notes

• Unit in the Last Place: the spacing of the floating-point grid at this magnitude, which grows as the magnitude does.
• It is how an error bound is stated meaningfully -- "within 2 ulp" means something at 1e300 and at 1e-300, where "within 1e-15" does not.
• Overloaded on float64 and float32, and the answer differs between them because the grids differ.

Examples

#import "std/numeric"
using numeric

print Ulp( 1.0 ) > 0         '' -1 (true)

'' The grid gets coarser as the magnitude grows
print Ulp( 1e300 ) > Ulp( 1.0 )               '' -1 (true)

'' Adding less than half an ulp changes nothing
print ( 1.0 + Ulp( 1.0 ) / 4 ) = 1.0          '' -1 (true)

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Library: Math Library
Category: Math Library
Documented under: Members