Modern Math Fma

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Fma

Returns x * y + z with a single rounding at the end.

Syntax

Fma( byval x as float64, byval y as float64, byval z as float64 ) as float64

Notes

• The product is computed to full precision and only the final sum is rounded, so the intermediate rounding of a plain x * y + z is not there.
• That single rounding is what makes it the building block for exact dot products, polynomial evaluation and correctly-rounded division.
• Overloaded on float64 and float32; the single form does not widen.

Examples

#import "std/numeric"
using numeric

print Fma( 2.0, 3.0, 4.0 )   '' 10

'' One rounding, not two -- and the difference is the whole error term.
'' 0.1 * 10 is not exactly 1, but the product ROUNDS to 1, so the plain
'' expression subtracts it away to nothing.
print Fma( 0.1, 10.0, -1.0 ) '' 5.551115123125783e-017
print 0.1 * 10.0 - 1.0       '' 0 -- the error is gone

'' Recovering that term is what makes Fma the building block for exact
'' dot products and correctly-rounded division

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