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+, -, *, and / now handle inexact complex numbers.

This commit is contained in:
Abdulaziz Ghuloum 2008-05-25 10:37:41 -07:00
parent ab2e05e8b0
commit 467095677e
3 changed files with 170 additions and 24 deletions
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scheme/ikarus.boot.prebuilt
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scheme/ikarus.numerics.ss
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@ -478,6 +478,7 @@
(define (err who x) (define (err who x)
(die who (if (number? x) "invalid argument" "not a number") x)) (die who (if (number? x) "invalid argument" "not a number") x))
(define binary+ (define binary+
(lambda (x y) (lambda (x y)
(cond (cond
@ -497,6 +498,10 @@
($make-compnum ($make-compnum
(binary+ x ($compnum-real y)) (binary+ x ($compnum-real y))
($compnum-imag y))] ($compnum-imag y))]
[(cflonum? y)
($make-cflonum
(binary+ x ($cflonum-real y))
($cflonum-imag y))]
[else (err '+ y)])] [else (err '+ y)])]
[(bignum? x) [(bignum? x)
(cond (cond
@ -514,6 +519,10 @@
($make-compnum ($make-compnum
(binary+ x ($compnum-real y)) (binary+ x ($compnum-real y))
($compnum-imag y))] ($compnum-imag y))]
[(cflonum? y)
($make-cflonum
(binary+ x ($cflonum-real y))
($cflonum-imag y))]
[else (err '+ y)])] [else (err '+ y)])]
[(flonum? x) [(flonum? x)
(cond (cond
@ -525,6 +534,14 @@
($fl+ x y)] ($fl+ x y)]
[(ratnum? y) [(ratnum? y)
($fl+ x (ratnum->flonum y))] ($fl+ x (ratnum->flonum y))]
[(cflonum? y)
($make-cflonum
($fl+ x ($cflonum-real y))
($cflonum-imag y))]
[(compnum? y)
($make-cflonum
(binary+ x ($compnum-real y))
(inexact ($compnum-imag y)))]
[else (err '+ y)])] [else (err '+ y)])]
[(ratnum? x) [(ratnum? x)
(cond (cond
@ -543,6 +560,10 @@
($make-compnum ($make-compnum
(binary+ x ($compnum-real y)) (binary+ x ($compnum-real y))
($compnum-imag y))] ($compnum-imag y))]
[(cflonum? y)
($make-cflonum
(binary+ x ($cflonum-real y))
($cflonum-imag y))]
[else (err '+ y)])] [else (err '+ y)])]
[(compnum? x) [(compnum? x)
(cond (cond
@ -551,9 +572,36 @@
(binary+ ($compnum-real x) y) (binary+ ($compnum-real x) y)
($compnum-imag x))] ($compnum-imag x))]
[(compnum? y) [(compnum? y)
($make-compnum ($make-rectangular
(binary+ ($compnum-real x) ($compnum-real y)) (binary+ ($compnum-real x) ($compnum-real y))
(binary+ ($compnum-imag x) ($compnum-imag y)))] (binary+ ($compnum-imag x) ($compnum-imag y)))]
[(flonum? y)
($make-cflonum
(binary+ y ($compnum-real x))
(inexact ($compnum-imag x)))]
[(cflonum? y)
($make-rectangular
(binary+ ($compnum-real x) ($cflonum-real y))
(binary+ ($compnum-imag x) ($cflonum-imag y)))]
[else (err '+ y)])]
[(cflonum? x)
(cond
[(cflonum? y)
($make-rectangular
(binary+ ($cflonum-real x) ($cflonum-real y))
(binary+ ($cflonum-imag x) ($cflonum-imag y)))]
[(flonum? y)
($make-cflonum
($fl+ ($cflonum-real x) y)
($cflonum-imag x))]
[(or (fixnum? y) (bignum? y) (ratnum? y))
($make-compnum
(binary+ ($compnum-real x) y)
($compnum-imag x))]
[(compnum? y)
($make-rectangular
(binary+ ($cflonum-real x) ($compnum-real y))
(binary+ ($cflonum-imag x) ($compnum-imag y)))]
[else (err '+ y)])] [else (err '+ y)])]
[else (err '+ x)]))) [else (err '+ x)])))
@ -656,6 +704,10 @@
($make-compnum ($make-compnum
(binary- x ($compnum-real y)) (binary- x ($compnum-real y))
(binary- 0 ($compnum-imag y)))] (binary- 0 ($compnum-imag y)))]
[(cflonum? y)
($make-cflonum
(binary- x ($cflonum-real y))
($fl- 0.0 ($cflonum-imag y)))]
[else (err '- y)])] [else (err '- y)])]
[(bignum? x) [(bignum? x)
(cond (cond
@ -672,18 +724,30 @@
($make-compnum ($make-compnum
(binary- x ($compnum-real y)) (binary- x ($compnum-real y))
(binary- 0 ($compnum-imag y)))] (binary- 0 ($compnum-imag y)))]
[(cflonum? y)
($make-cflonum
(binary- x ($cflonum-real y))
($fl- 0.0 ($cflonum-imag y)))]
[else (err '- y)])] [else (err '- y)])]
[(flonum? x) [(flonum? x)
(cond (cond
[(flonum? y)
($fl- x y)]
[(cflonum? y)
($make-cflonum
($fl- x ($cflonum-real y))
($fl- 0.0 ($cflonum-imag y)))]
[(fixnum? y) [(fixnum? y)
($fl- x ($fixnum->flonum y))] ($fl- x ($fixnum->flonum y))]
[(bignum? y) [(bignum? y)
($fl- x (bignum->flonum y))] ($fl- x (bignum->flonum y))]
[(flonum? y) [(ratnum? y)
($fl- x y)]
[(ratnum? y)
(let ([n ($ratnum-n y)] [d ($ratnum-d y)]) (let ([n ($ratnum-n y)] [d ($ratnum-d y)])
(binary/ (binary- (binary* d x) n) d))] (binary/ (binary- (binary* d x) n) d))]
[(compnum? y)
($make-cflonum
(binary- x ($compnum-real y))
(binary- 0.0 ($compnum-imag y)))]
[else (err '- y)])] [else (err '- y)])]
[(ratnum? x) [(ratnum? x)
(let ([nx ($ratnum-n x)] [dx ($ratnum-d x)]) (let ([nx ($ratnum-n x)] [dx ($ratnum-d x)])
@ -698,6 +762,10 @@
($make-compnum ($make-compnum
(binary- x ($compnum-real y)) (binary- x ($compnum-real y))
(binary- 0 ($compnum-imag y)))] (binary- 0 ($compnum-imag y)))]
[(cflonum? y)
($make-cflonum
(binary- x ($cflonum-real y))
($fl- 0.0 ($cflonum-imag y)))]
[else (err '- y)]))] [else (err '- y)]))]
[(compnum? x) [(compnum? x)
(cond (cond
@ -709,8 +777,32 @@
($make-rectangular ($make-rectangular
(binary- ($compnum-real x) ($compnum-real y)) (binary- ($compnum-real x) ($compnum-real y))
(binary- ($compnum-imag x) ($compnum-imag y)))] (binary- ($compnum-imag x) ($compnum-imag y)))]
[(cflonum? y)
($make-rectangular
(binary- ($compnum-real x) ($cflonum-real y))
(binary- ($compnum-imag x) ($cflonum-imag y)))]
[else [else
(err '- y)])] (err '- y)])]
[(cflonum? x)
(cond
[(flonum? y)
($make-cflonum
($fl- ($cflonum-real x) y)
($cflonum-imag x))]
[(cflonum? y)
($make-rectangular
(binary- ($cflonum-real x) ($cflonum-real y))
(binary- ($cflonum-imag x) ($cflonum-imag y)))]
[(or (fixnum? y) (bignum? y) (ratnum? y))
($make-cflonum
(binary- ($cflonum-real x) y)
($cflonum-imag x))]
[(compnum? y)
($make-rectangular
(binary- ($cflonum-real x) ($compnum-real y))
(binary- ($cflonum-imag x) ($compnum-imag y)))]
[else
(err '- y)])]
[else (err '- x)]))) [else (err '- x)])))
(define binary* (define binary*
@ -730,6 +822,10 @@
($make-rectangular ($make-rectangular
(binary* x ($compnum-real y)) (binary* x ($compnum-real y))
(binary* x ($compnum-imag y)))] (binary* x ($compnum-imag y)))]
[(cflonum? y)
($make-rectangular
(binary* x ($cflonum-real y))
(binary* x ($cflonum-imag y)))]
[else (err '* y)])] [else (err '* y)])]
[(bignum? x) [(bignum? x)
(cond (cond
@ -745,17 +841,29 @@
($make-rectangular ($make-rectangular
(binary* x ($compnum-real y)) (binary* x ($compnum-real y))
(binary* x ($compnum-imag y)))] (binary* x ($compnum-imag y)))]
[(cflonum? y)
($make-rectangular
(binary* x ($cflonum-real y))
(binary* x ($cflonum-imag y)))]
[else (err '* y)])] [else (err '* y)])]
[(flonum? x) [(flonum? x)
(cond (cond
[(flonum? y)
($fl* x y)]
[(cflonum? y)
($make-rectangular
($fl* x ($cflonum-real y))
($fl* x ($cflonum-imag y)))]
[(fixnum? y) [(fixnum? y)
($fl* x ($fixnum->flonum y))] ($fl* x ($fixnum->flonum y))]
[(bignum? y) [(bignum? y)
($fl* x (bignum->flonum y))] ($fl* x (bignum->flonum y))]
[(flonum? y)
($fl* x y)]
[(ratnum? y) [(ratnum? y)
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))] (binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
[(compnum? y)
($make-rectangular
(binary* x ($compnum-real y))
(binary* x ($compnum-imag y)))]
[else (err '* y)])] [else (err '* y)])]
[(ratnum? x) [(ratnum? x)
(cond (cond
@ -766,9 +874,48 @@
($make-rectangular ($make-rectangular
(binary* x ($compnum-real y)) (binary* x ($compnum-real y))
(binary* x ($compnum-imag y)))] (binary* x ($compnum-imag y)))]
[(cflonum? y)
($make-rectangular
(binary* x ($cflonum-real y))
(binary* x ($cflonum-imag y)))]
[else (binary* y x)])] [else (binary* y x)])]
[(compnum? x) [(compnum? x)
(cond (cond
[(or (fixnum? y) (bignum? y) (ratnum? y) (flonum? y))
($make-rectangular
(binary* ($compnum-real x) y)
(binary* ($compnum-imag x) y))]
[(compnum? y)
(let ([r0 ($compnum-real x)]
[r1 ($compnum-real y)]
[i0 ($compnum-imag x)]
[i1 ($compnum-imag y)])
($make-rectangular
(- (* r0 r1) (* i0 i1))
(+ (* r0 i1) (* i0 r1))))]
[(cflonum? y)
(let ([r0 ($compnum-real x)]
[r1 ($cflonum-real y)]
[i0 ($compnum-imag x)]
[i1 ($cflonum-imag y)])
($make-rectangular
(- (* r0 r1) (* i0 i1))
(+ (* r0 i1) (* i0 r1))))]
[else (err '* y)])]
[(cflonum? x)
(cond
[(flonum? y)
($make-rectangular
($fl* ($cflonum-real x) y)
($fl* ($cflonum-imag x) y))]
[(cflonum? y)
(let ([r0 ($cflonum-real x)]
[r1 ($cflonum-real y)]
[i0 ($cflonum-imag x)]
[i1 ($cflonum-imag y)])
($make-rectangular
($fl- ($fl* r0 r1) ($fl* i0 i1))
($fl+ ($fl* r0 i1) ($fl* i0 r1))))]
[(or (fixnum? y) (bignum? y) (ratnum? y)) [(or (fixnum? y) (bignum? y) (ratnum? y))
($make-rectangular ($make-rectangular
(binary* ($compnum-real x) y) (binary* ($compnum-real x) y)
@ -783,7 +930,7 @@
(+ (* r0 i1) (* i0 r1))))] (+ (* r0 i1) (* i0 r1))))]
[else (err '* y)])] [else (err '* y)])]
[else (err '* x)]))) [else (err '* x)])))
(define + (define +
(case-lambda (case-lambda
[(x y) (binary+ x y)] [(x y) (binary+ x y)]
@ -970,28 +1117,26 @@
[else (f (lcm g (car ls)) (cdr ls))]))])) [else (f (lcm g (car ls)) (cdr ls))]))]))
(define binary/ (define binary/
(lambda (x y) (lambda (x y)
(define (x/compy x y) (define (x/compy x y)
(let ([yr ($compnum-real y)] (let ([yr (real-part y)]
[yi ($compnum-imag y)]) [yi (imag-part y)])
(let ([denom (+ (* yr yr) (* yi yi))]) (let ([denom (+ (* yr yr) (* yi yi))])
($make-rectangular ($make-rectangular
(binary/ (* x yr) denom) (binary/ (* x yr) denom)
(binary/ (* (- x) yi) denom))))) (binary/ (* (- x) yi) denom)))))
(define (compx/y x y) (define (compx/y x y)
(let ([xr ($compnum-real x)] (let ([xr (real-part x)]
[xi ($compnum-imag x)]) [xi (imag-part x)])
($make-rectangular ($make-rectangular
(binary/ xr y) (binary/ xr y)
(binary/ xi y)))) (binary/ xi y))))
(define (compx/compy x y) (define (compx/compy x y)
(let ([xr ($compnum-real x)] (let ([xr (real-part x)]
[xi ($compnum-imag x)] [xi (imag-part x)]
[yr ($compnum-real y)] [yr (real-part y)]
[yi ($compnum-imag y)]) [yi (imag-part y)])
(let ([denom (+ (* yr yr) (* yi yi))]) (let ([denom (+ (* yr yr) (* yi yi))])
($make-rectangular ($make-rectangular
(binary/ (+ (* xr yr) (* xi yi)) denom) (binary/ (+ (* xr yr) (* xi yi)) denom)
@ -1046,7 +1191,7 @@
(binary- 0 (quotient y g))))]))] (binary- 0 (quotient y g))))]))]
[(ratnum? y) [(ratnum? y)
(/ (* x ($ratnum-d y)) ($ratnum-n y))] (/ (* x ($ratnum-d y)) ($ratnum-n y))]
[(compnum? y) (x/compy x y)] [(or (compnum? y) (cflonum? y)) (x/compy x y)]
[else (err '/ y)])] [else (err '/ y)])]
[(bignum? x) [(bignum? x)
(cond (cond
@ -1095,7 +1240,7 @@
[(flonum? y) ($fl/ (bignum->flonum x) y)] [(flonum? y) ($fl/ (bignum->flonum x) y)]
[(ratnum? y) [(ratnum? y)
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))] (binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
[(compnum? y) (x/compy x y)] [(or (compnum? y) (cflonum? y)) (x/compy x y)]
[else (err '/ y)])] [else (err '/ y)])]
[(ratnum? x) [(ratnum? x)
(cond (cond
@ -1103,15 +1248,16 @@
(binary/ (binary/
(binary* ($ratnum-n x) ($ratnum-d y)) (binary* ($ratnum-n x) ($ratnum-d y))
(binary* ($ratnum-n y) ($ratnum-d x)))] (binary* ($ratnum-n y) ($ratnum-d x)))]
[(compnum? y) (x/compy x y)] [(or (compnum? y) (cflonum? y)) (x/compy x y)]
[else (binary/ 1 (binary/ y x))])] [else (binary/ 1 (binary/ y x))])]
[(compnum? x) [(or (compnum? x) (cflonum? x))
(cond (cond
[(compnum? y) (compx/compy x y)] [(or (compnum? y) (cflonum? y)) (compx/compy x y)]
[(or (fixnum? y) (bignum? y) (ratnum? y)) (compx/y x y)] [(or (fixnum? y) (bignum? y) (ratnum? y) (flonum? y)) (compx/y x y)]
[else (err '/ y)])] [else (err '/ y)])]
[else (err '/ x)]))) [else (err '/ x)])))
(define / (define /
(case-lambda (case-lambda
[(x y) (binary/ x y)] [(x y) (binary/ x y)]

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