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Bigfloat support

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pavpanchekha committed Dec 12, 2013
1 parent 4564679 commit 0b3c6c237fca46d9e6a80591e2c1840be2bfeab5
Showing with 28 additions and 10 deletions.
  1. +28 −10 casio/main.rkt
@@ -4,16 +4,22 @@
(require racket/flonum)
(require racket/pretty)
(require data/order)
(require math/bigfloat)
; Programs are just lambda expressions
(define program-body caddr)
(define program-variables cadr)
; Functions used by our benchmarks
(define (cotan x)
(/ 1 (tan x)))
(define (square x)
(* x x))
; 256 is a big number.
(bf-precision 256)
;; We evaluate a program by comparing its results computed with single precision
;; to its results computed with extended precision.
@@ -28,14 +34,25 @@
(define (real-op->bigfloat-op op)
(hash-ref #hash([+ . bf+] [* . bf*] [- . bf-] [/ . bf/] [square . bfsqr]
[abs . bfabs] [sqrt . bfsqrt] [log . bflog] [exp . bfexp]
[expt . bfexpt] [sin . bfsin] [cos . bfcos] [tan . bftan]
[cotan . bfcot] [asin . bfasin] [acos . bfacos] [atan . bfatan]
[sinh . bfsinh] [cosh . bfcosh])
(define (->single-flonum x)
[(real? x) (real->single-flonum x)]
[(bigfloat? x) (real->single-flonum (bigfloat->flonum x))]))
(define (program-induct
#:toplevel [toplevel identity] #:constant [constant identity]
#:variable [variable identity] #:primitive [primitive identity])
#:variable [variable identity] #:primitive [primitive identity]
#:symbol [symbol-table identity])
(define (map-cdr f l)
(cons (car l) (map f (cdr l))))
(define (inductor prog)
[(real? prog) (constant prog)]
@@ -44,7 +61,7 @@
(let ([body* (inductor (program-body prog))])
(toplevel `(lambda ,(program-variables prog) ,body*)))]
[(list? prog)
(primitive (map-cdr inductor prog))]
(primitive (cons (symbol-table (car prog)) (map inductor (cdr prog))))]
(error "Invalid program expression" prog)]))
@@ -53,10 +70,10 @@
(define-namespace-anchor eval-prog-ns-anchor)
(define eval-prog-ns (namespace-anchor->namespace eval-prog-ns-anchor))
(define (eval-prog prog rule)
(let ([fn (eval (program-induct prog #:constant rule) eval-prog-ns)])
(define (eval-prog prog const-rule symbol-table)
(let ([fn (eval (program-induct prog #:constant const-rule #:symbol symbol-table) eval-prog-ns)])
(lambda (pts)
(real->single-flonum (real-part (apply fn (map rule pts)))))))
(->single-flonum (apply fn (map const-rule pts))))))
; We evaluate a program on random floating-point numbers.
@@ -87,14 +104,15 @@
(define (make-exacts prog pts)
"Given a list of arguments, produce a list of exact evaluations of a program at those arguments"
(map (eval-prog prog real->double-flonum) pts))
(map (eval-prog prog bf real-op->bigfloat-op) pts))
; (map (eval-prog prog real->single-flonum identity) pts))
(define (max-error prog pts-list exacts)
"Find the maximum error in a function's approximate evaluations at the given points
(compared to the given exact results), and the number of evaluations that yield
a special value."
(let ([errors
(let ([fn (eval-prog prog real->single-flonum)])
(let ([fn (eval-prog prog real->single-flonum identity)])
(for/list ([pts pts-list] [exact exacts])
(relative-error (fn pts) exact)))])
(let loop ([max-err 0] [specials 0] [errors errors])

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