Some operations of Integer is not inlined, I'm
very suprised at that.
An example from integ.input:
)time on
f := sqrt(tan(x)^2 + 2*tan(x) + 2);
g := integrate(sqrt(tan(x)^2 + 2*tan(x) + 2),x);
h := D(g,x);
normalize(h-f)
Profile shows most time is spent at symmetricRemainder,
which is implemented in INS, not INT.
After this patch, the example is 30% faster.
diff --git a/src/algebra/integer.spad b/src/algebra/integer.spad
index 15aefa22..55d3da20 100644
--- a/src/algebra/integer.spad
+++ b/src/algebra/integer.spad
@@ -59,7 +59,6 @@
ZP ==> SparseUnivariatePolynomial %
ZZP ==> SparseUnivariatePolynomial Integer
x, y : %
- n : NonNegativeInteger
writeOMInt(dev : OpenMathDevice, x : %) : Void ==
if x < 0 then
@@ -87,6 +86,7 @@
dec x == x - 1
hashUpdate!(hs, s) == update!(hs, SXHASH(s)$Lisp)$HashState
negative? x == MINUSP(x)$Lisp
+ positive? x == PLUSP(x)$Lisp
coerce(x) : OutputForm == outputForm(x pretend Integer)
coerce(m : Integer) : % == m pretend %
convert(x : %) : Integer == x pretend Integer
@@ -125,14 +125,17 @@
random(x) == RANDOM(x)$Lisp
x = y == EQL(x, y)$Lisp
x < y == (x<y)$Lisp
+ x > y == (x>y)$Lisp
-- critical for coercions to NonNegativeInteger
x >= y == (x >= y)$Lisp
+ x <= y == (x <= y)$Lisp
- x == (-x)$Lisp
x + y == (x+y)$Lisp
x - y == (x-y)$Lisp
x * y == (x*y)$Lisp
(m : Integer) * (y : %) == (m*y)$Lisp -- for subsumption problem
- x ^ n == EXPT(x, n)$Lisp
+ (x : %) ^ (n : NonNegativeInteger) == EXPT(x, n)$Lisp
+ (x : %) ^ (n : PositiveInteger) == EXPT(x, n)$Lisp
odd? x == ODDP(x)$Lisp
max(x, y) == MAX(x, y)$Lisp
min(x, y) == MIN(x, y)$Lisp
@@ -184,6 +187,15 @@
-- TT := InnerModularGcd(%, ZP, 67108859 pretend %, myNextPrime)
-- gcdPolynomial(p, q) == modularGcd(p, q)$TT
+ symmetricRemainder(x, n) ==
+ r := x rem n
+ r = 0 => 0
+ if n < 0 then n := -n
+ r > 0 =>
+ 2::% * r > n => r - n
+ r
+ 2::% * r + n <= 0 => r + n
+ r
)abbrev domain NNI NonNegativeInteger
++ Author:
--
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