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

This commit is contained in:
Abdulaziz Ghuloum 2008-05-18 21:41:53 -07:00
parent 82140f87ba
commit 4cb8165181
2 changed files with 133 additions and 48 deletions
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175
scheme/ikarus.numerics.ss
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@ -13,13 +13,6 @@
;;; You should have received a copy of the GNU General Public License
;;; along with this program. If not, see <http://www.gnu.org/licenses/>.
(library (ikarus flonums)
(export $flonum->exact $flonum->integer flonum-parts
inexact->exact exact $flonum-rational? $flonum-integer? $flzero?
@ -384,12 +377,7 @@
(foreign-call "ikrt_flfl_expt" x y ($make-flonum))]))
(die 'flexpt "not a flonum" y))
(die 'fllog "not a flonum" x)))
)
)
(library (ikarus generic-arithmetic)
@ -414,6 +402,7 @@
(ikarus system $flonums)
(ikarus system $ratnums)
(ikarus system $bignums)
(ikarus system $compnums)
(ikarus system $chars)
(ikarus system $strings)
(only (ikarus flonums) $flonum->exact $flzero? $flnegative?
@ -486,6 +475,8 @@
(pos n d)
(- (pos (- n) d)))))
(define (err who x)
(die who (if (number? x) "invalid argument" "not a number") x))
(define binary+
(lambda (x y)
@ -502,8 +493,11 @@
($make-ratnum
(+ (* x ($ratnum-d y)) ($ratnum-n y))
($ratnum-d y))]
[else
(die '+ "not a number" y)])]
[(compnum? y)
($make-compnum
(binary+ x ($compnum-real y))
($compnum-imag y))]
[else (err '+ y)])]
[(bignum? x)
(cond
[(fixnum? y)
@ -516,8 +510,11 @@
($make-ratnum
(+ (* x ($ratnum-d y)) ($ratnum-n y))
($ratnum-d y))]
[else
(die '+ "not a number" y)])]
[(compnum? y)
($make-compnum
(binary+ x ($compnum-real y))
($compnum-imag y))]
[else (err '+ y)])]
[(flonum? x)
(cond
[(fixnum? y)
@ -528,8 +525,7 @@
($fl+ x y)]
[(ratnum? y)
($fl+ x (ratnum->flonum y))]
[else
(die '+ "not a number" y)])]
[else (err '+ y)])]
[(ratnum? x)
(cond
[(or (fixnum? y) (bignum? y))
@ -543,9 +539,23 @@
[d0 ($ratnum-d x)] [d1 ($ratnum-d y)])
;;; FIXME: inefficient
(/ (+ (* n0 d1) (* n1 d0)) (* d0 d1)))]
[else
(die '+ "not a number" y)])]
[else (die '+ "not a number" x)])))
[(compnum? y)
($make-compnum
(binary+ x ($compnum-real y))
($compnum-imag y))]
[else (err '+ y)])]
[(compnum? x)
(cond
[(or (fixnum? y) (bignum? y) (ratnum? y))
($make-compnum
(binary+ ($compnum-real x) y)
($compnum-imag x))]
[(compnum? y)
($make-compnum
(binary+ ($compnum-real x) ($compnum-real y))
(binary+ ($compnum-imag x) ($compnum-imag y)))]
[else (err '+ y)])]
[else (err '+ x)])))
(define binary-bitwise-and
(lambda (x y)
@ -642,8 +652,11 @@
[(ratnum? y)
(let ([n ($ratnum-n y)] [d ($ratnum-d y)])
(binary/ (binary- (binary* d x) n) d))]
[else
(die '- "not a number" y)])]
[(compnum? y)
($make-compnum
(binary- x ($compnum-real y))
(binary- 0 ($compnum-imag y)))]
[else (err '- y)])]
[(bignum? x)
(cond
[(fixnum? y)
@ -655,8 +668,11 @@
[(ratnum? y)
(let ([n ($ratnum-n y)] [d ($ratnum-d y)])
(binary/ (binary- (binary* d x) n) d))]
[else
(die '- "not a number" y)])]
[(compnum? y)
($make-compnum
(binary- x ($compnum-real y))
(binary- 0 ($compnum-imag y)))]
[else (err '- y)])]
[(flonum? x)
(cond
[(fixnum? y)
@ -668,8 +684,7 @@
[(ratnum? y)
(let ([n ($ratnum-n y)] [d ($ratnum-d y)])
(binary/ (binary- (binary* d x) n) d))]
[else
(die '- "not a number" y)])]
[else (err '- y)])]
[(ratnum? x)
(let ([nx ($ratnum-n x)] [dx ($ratnum-d x)])
(cond
@ -679,9 +694,24 @@
(let ([ny ($ratnum-n y)] [dy ($ratnum-d y)])
(binary/ (binary- (binary* nx dy) (binary* ny dx))
(binary* dx dy)))]
[(compnum? y)
($make-compnum
(binary- x ($compnum-real y))
(binary- 0 ($compnum-imag y)))]
[else (err '- y)]))]
[(compnum? x)
(cond
[(or (fixnum? y) (bignum? y) (ratnum? y))
($make-compnum
(binary- ($compnum-real x) y)
($compnum-imag x))]
[(compnum? y)
($make-rectangular
(binary- ($compnum-real x) ($compnum-real y))
(binary- ($compnum-imag x) ($compnum-imag y)))]
[else
(die '- "not a number" y)]))]
[else (die '- "not a number" x)])))
(err '- y)])]
[else (err '- x)])))
(define binary*
(lambda (x y)
@ -696,8 +726,11 @@
($fl* ($fixnum->flonum x) y)]
[(ratnum? y)
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
[else
(die '* "not a number" y)])]
[(compnum? y)
($make-rectangular
(binary* x ($compnum-real y))
(binary* x ($compnum-imag y)))]
[else (err '* y)])]
[(bignum? x)
(cond
[(fixnum? y)
@ -708,8 +741,11 @@
($fl* (bignum->flonum x) y)]
[(ratnum? y)
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
[else
(die '* "not a number" y)])]
[(compnum? y)
($make-rectangular
(binary* x ($compnum-real y))
(binary* x ($compnum-imag y)))]
[else (err '* y)])]
[(flonum? x)
(cond
[(fixnum? y)
@ -720,14 +756,33 @@
($fl* x y)]
[(ratnum? y)
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
[else
(die '* "not a number" y)])]
[else (err '* y)])]
[(ratnum? x)
(if (ratnum? y)
(cond
[(ratnum? y)
(binary/ (binary* ($ratnum-n x) ($ratnum-n y))
(binary* ($ratnum-d x) ($ratnum-d y)))
(binary* y x))]
[else (die '* "not a number" x)])))
(binary* ($ratnum-d x) ($ratnum-d y)))]
[(compnum? y)
($make-rectangular
(binary* x ($compnum-real y))
(binary* x ($compnum-imag y)))]
[else (binary* y x)])]
[(compnum? x)
(cond
[(or (fixnum? y) (bignum? y) (ratnum? 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))))]
[else (err '* y)])]
[else (err '* x)])))
(define +
(case-lambda
@ -917,8 +972,30 @@
(define binary/ ;;; implements ratnums
(define binary/
(lambda (x y)
(define (x/compy x y)
(let ([yr ($compnum-real y)]
[yi ($compnum-imag y)])
(let ([denom (+ (* yr yr) (* yi yi))])
($make-rectangular
(binary/ (* x yr) denom)
(binary/ (* (- x) yi) denom)))))
(define (compx/y x y)
(let ([xr ($compnum-real x)]
[xi ($compnum-imag x)])
($make-rectangular
(binary/ xr y)
(binary/ xi y))))
(define (compx/compy x y)
(let ([xr ($compnum-real x)]
[xi ($compnum-imag x)]
[yr ($compnum-real y)]
[yi ($compnum-imag y)])
(let ([denom (+ (* yr yr) (* yi yi))])
($make-rectangular
(binary/ (+ (* xr yr) (* xi yi)) denom)
(binary/ (- (* xi yr) (* xr yi)) denom)))))
(cond
[(flonum? x)
(cond
@ -926,7 +1003,7 @@
[(fixnum? y) ($fl/ x ($fixnum->flonum y))]
[(bignum? y) ($fl/ x (bignum->flonum y))]
[(ratnum? y) ($fl/ x (ratnum->flonum y))]
[else (die '/ "not a number" y)])]
[else (err '/ y)])]
[(fixnum? x)
(cond
[(flonum? y) ($fl/ ($fixnum->flonum x) y)]
@ -969,7 +1046,8 @@
(binary- 0 (quotient y g))))]))]
[(ratnum? y)
(/ (* x ($ratnum-d y)) ($ratnum-n y))]
[else (die '/ "not a number" y)])]
[(compnum? y) (x/compy x y)]
[else (err '/ y)])]
[(bignum? x)
(cond
[(fixnum? y)
@ -1017,15 +1095,22 @@
[(flonum? y) ($fl/ (bignum->flonum x) y)]
[(ratnum? y)
(binary/ (binary* x ($ratnum-n y)) ($ratnum-d y))]
[else (die '/ "not a number" y)])]
[(compnum? y) (x/compy x y)]
[else (err '/ y)])]
[(ratnum? x)
(cond
[(ratnum? y)
(binary/
(binary* ($ratnum-n x) ($ratnum-d y))
(binary* ($ratnum-n y) ($ratnum-d x)))]
[(compnum? y) (x/compy x y)]
[else (binary/ 1 (binary/ y x))])]
[else (die '/ "not a number" x)])))
[(compnum? x)
(cond
[(compnum? y) (compx/compy x y)]
[(or (fixnum? y) (bignum? y) (ratnum? y)) (compx/y x y)]
[else (err '/ y)])]
[else (err '/ x)])))
(define /
(case-lambda

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