We can speed up the function
/ : (INT, INT)->FRAC INT
by using Lisp intrinsic.
Note that in Lisp, when you create a fraction by
'(/ x y)', the gcd of x and y is not computed, aka
Lisp uses "lazy" representation.
Also note that you can't use '_/(a,b)$Lisp' in Spad
because in Spad '/' may indicate 'reduce'.
See the benchmark test I put in the end, this change
gives a 50% boost: 0.31s (div1) vs. 0.21s (div2).
I think that's because the new version has much
fewer function calls.
--- a/src/algebra/fraction.spad
+++ b/src/algebra/fraction.spad
@@ -367,10 +367,17 @@
x.den := xd :: S
d
- nn : S / dd : S ==
- zero? dd => error "division by zero"
- cancelGcd(z := [nn, dd])
- normalize z
+ if S is Integer then
+ opdiv ==> _/$Lisp
+ nn : S / dd : S ==
+ zero? dd => error "division by zero"
+ tmp : SExpression := opdiv(nn, dd)
+ [NUMERATOR(tmp)$Lisp pretend S, DENOMINATOR(tmp)$Lisp pretend S]
+ else
+ nn : S / dd : S ==
+ zero? dd => error "division by zero"
+ cancelGcd(z := [nn, dd])
+ normalize z
x + y ==
zero? y => x
============
Benchmark for this change:
)abbrev package TEST1 Test1
Test1() : Exports == Impl where
Exports == with
div1 : () -> Boolean
div2 : () -> Boolean
Impl == add
n ==> 10^6
opdiv ==> _/$Lisp
l1 : Vector Integer := vector [random x for x in 1..n]
l2 : Vector Integer := vector [1+random x for x in 1..n]
l3 : Vector Fraction Integer := new(n, 0)
l4 : Vector Fraction Integer := new(n, 0)
div1() ==
for i in 1..n repeat
l3.i := l1.i/l2.i
true
div2() ==
for i in 1..n repeat
tmp1 : SExpression := opdiv(l1.i,l2.i)
l4.i := CONS(NUMERATOR(tmp1)$Lisp,DENOMINATOR(tmp1)$Lisp)$Lisp
true
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