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Added fast-flfsa/error and flfsa/error (fused square-and-add)

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Neil Toronto 2014-08-19 17:26:09 -04:00
parent 8cb4214586
commit 82dca13f97
1 changed files with 22 additions and 1 deletions
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23
pkgs/math-pkgs/math-lib/math/private/flonum/flonum-error.rkt
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@ -9,12 +9,14 @@
fast-flsqr/error
fast-fl//error
fast-flfma/error
fast-flfsa/error
fl+/error
fl-/error
fl*/error
flsqr/error
fl//error
flfma/error)
flfma/error
flfsa/error)
(module untyped-defs racket/base
(require (for-syntax racket/base)
@ -90,6 +92,14 @@
[(h3 h2) (fast-fl+/error h0 y2)])
(values h3 (fl+ h2 h1))))
;(: fast-flfsa/error (Flonum Flonum Flonum -> (Values Flonum Flonum)))
;; Returns a*a+b and its rounding error
(define-syntax-rule (fast-flfsa/error a-expr b-expr)
(let*-values ([(y2 y1) (fast-flsqr/error a-expr)]
[(h0 h1) (fast-fl+/error b-expr y1)]
[(h3 h2) (fast-fl+/error h0 y2)])
(values h3 (fl+ h2 h1))))
#;; If we had hardware fused multiply-add:
(define-syntax-rule (fast-fl*/error a-expr b-expr)
(let ([a a-expr] [b b-expr])
@ -196,6 +206,17 @@
(let-values ([(x2 x1) (fast-flfma/error (* a 1/n) (* b 1/n) (* c 1/n 1/n))])
(values (* n^2 x2) (* n^2 x1)))]))
(: flfsa/error (-> Flonum Flonum (Values Flonum Flonum)))
(define (flfsa/error a b)
(define-values (x2 x1) (fast-flfsa/error a b))
(cond [(flrational? (+ x2 x1)) (values x2 x1)]
[else
(define n (near-pow2 (flsqrt (abs a))))
(define 1/n (/ 1.0 n))
(define n^2 (* n n))
(let-values ([(x2 x1) (fast-flfsa/error (* a 1/n) (* b 1/n 1/n))])
(values (* n^2 x2) (* n^2 x1)))]))
) ; begin-encourage-inline
) ; module