Re: [fricas-devel] [PATCH] get inline optimization for some Integer functions
oldk1331 wrote:
>
> I said before that the following test takes too much time to run:
> testIntegrate("sqrt(tan(x)^2 + 2*tan(x) + 2)", "x", "alg")
>
> I did some profiling, and found that 40% time is spent in
> symmetricRemainder:
>
> Callers
> Total. Function
> Count % Count % Callees
>
> 3 0.0 |MODRING;reduce;RMod$;6| [76]
> 13 0.1 |INS-;symmetricRemainder;3S;27| [1]
>3431 39.3 |IDPO;map;M2$;6| [5]
>1104 12.7 3451 39.6 |INS-;symmetricRemainder;3S;27| [1]
> 13 0.1 |INS-;symmetricRemainder;3S;27| [1]
> 160 1.8 |INT;=;2$B;30| [4]
> 149 1.7 |ABELMON-;*;Pi2S;2| [14]
> 67 0.8 SB-VM::ALLOC-TRAMP [15]
> 228 2.6 |ORDSET-;>;2SB;4| [7]
> 173 2.0 |ORDSET-;<=;2SB;6| [20]
> 73 0.8 |INT;+;3$;34| [9]
> 160 1.8 |INT;*;3$;37| [6]
> 180 2.1 |ABELGRP-;*;Nni2S;3| [11]
> 366 4.2 |INT;rem;3$;44| [16]
> 369 4.2 IDENTITY [2]
> 407 4.7 |INT;<;2$B;31| [3]
>
>
> We can see that "=$INT, +$INT, *$INT, <$INT" are not inlined, and
> "*$ABELMON, *$ABELGRP, >, <=" are not defined in INT, thus impossible
> to get inlined.
>
> So I want to add inline optimization for these functions.
> (I also add inline support for "positive?, even?, ^")
>
> === test case
> )time on
> )lisp (require :sb-sprof)
>
> f := sqrt(tan(x)^2 + 2*tan(x) + 2)
> g := integrate(f, x)
>
> f2 := D(g, x)
>
> )lisp (sb-sprof:start-profiling)
> normalize(f-f2)
> )lisp (sb-sprof:stop-profiling)
>
> )lisp (sb-sprof:report)
> ===
>
> Benchmark result:
> D(g, x)normalize(f-f2)
> before patch40.3 s 87.4 s
> after patch 28.4 s 57.3 s
>
> So it's 30% faster, saves 40 seconds in testing.
OK, good. But I see some funny formatting below, which may be
due tabs. Please make sure there are no tabs when you commit.
>
> diff --git a/src/algebra/integer.spad b/src/algebra/integer.spad
> index 0e619c2f..35f673b2 100644
> --- a/src/algebra/integer.spad
> +++ b/src/algebra/integer.spad
> @@ -59,7 +59,6 @@
> ZP ==> SparseUnivariatePolynomial %
> ZZP ==> SparseUnivariatePolynomial Integer
> x, y : %
> - n : NonNegativeInteger
^^
Would be indentation error if real.
--
Waldek Hebisch
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Re: [fricas-devel] erf is left unevaluated in expression
On Wed, Nov 21, 2018 at 6:22 PM Slawomir Kolodynski wrote: > > lack of a basic form of referential transparency between variables and > literals. > Namely if you assign a literal to a variable and later in code use a variable, > the result may be different than if you had used the literal instead. For > example: This is not a problem about "referential transparency", this is about a old bug related with (numeric) evaluation of "erf", e.g. "eval(erf x, x, 1.0)" returns "erf(1.0)". https://groups.google.com/forum/#!msg/fricas-devel/Rz5_1iBadAY/B2g9GVibCwAJ > And another one using the variable which stores that literal > > C1(S:F,r:F,T:F,K:F,s:F):F == BS This usage is wrong, BS is already defined, with a type of Expression, so this line will never work. One way can work: First, use macro '==>' instead of assignment. Second, use "exp" instead of "%e", so that they are defined in DFLOAT: BS1 ==> ((S*erf(((2*log((S/K))+T*s^2+2*T*r)/(2*s*sqrt(2)*sqrt(T-K*exp((-T*r))*erf(((2*log((S/K))-T*s^2+2*T*r)/(2*s*sqrt(2)*sqrt(T-K*exp((-T*r))+S)/2) C1(S:F,r:F,T:F,K:F,s:F):F == BS1 C1(10.0,0.05,0.8,11.0,0.05) Compiling function C1 with type (DoubleFloat, DoubleFloat, DoubleFloat, DoubleFloat, DoubleFloat) -> DoubleFloat (18) 0.023903294619544546 I think after the bug I mentioned get fixed, using "numeric" will also work. -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
[fricas-devel] [PATCH] get inline optimization for some Integer functions
I said before that the following test takes too much time to run:
testIntegrate("sqrt(tan(x)^2 + 2*tan(x) + 2)", "x", "alg")
I did some profiling, and found that 40% time is spent in
symmetricRemainder:
Callers
Total. Function
Count % Count % Callees
3 0.0 |MODRING;reduce;RMod$;6| [76]
13 0.1 |INS-;symmetricRemainder;3S;27| [1]
3431 39.3 |IDPO;map;M2$;6| [5]
1104 12.7 3451 39.6 |INS-;symmetricRemainder;3S;27| [1]
13 0.1 |INS-;symmetricRemainder;3S;27| [1]
160 1.8 |INT;=;2$B;30| [4]
149 1.7 |ABELMON-;*;Pi2S;2| [14]
67 0.8 SB-VM::ALLOC-TRAMP [15]
228 2.6 |ORDSET-;>;2SB;4| [7]
173 2.0 |ORDSET-;<=;2SB;6| [20]
73 0.8 |INT;+;3$;34| [9]
160 1.8 |INT;*;3$;37| [6]
180 2.1 |ABELGRP-;*;Nni2S;3| [11]
366 4.2 |INT;rem;3$;44| [16]
369 4.2 IDENTITY [2]
407 4.7 |INT;<;2$B;31| [3]
We can see that "=$INT, +$INT, *$INT, <$INT" are not inlined, and
"*$ABELMON, *$ABELGRP, >, <=" are not defined in INT, thus impossible
to get inlined.
So I want to add inline optimization for these functions.
(I also add inline support for "positive?, even?, ^")
=== test case
)time on
)lisp (require :sb-sprof)
f := sqrt(tan(x)^2 + 2*tan(x) + 2)
g := integrate(f, x)
f2 := D(g, x)
)lisp (sb-sprof:start-profiling)
normalize(f-f2)
)lisp (sb-sprof:stop-profiling)
)lisp (sb-sprof:report)
===
Benchmark result:
D(g, x)normalize(f-f2)
before patch40.3 s 87.4 s
after patch 28.4 s 57.3 s
So it's 30% faster, saves 40 seconds in testing.
diff --git a/src/algebra/integer.spad b/src/algebra/integer.spad
index 0e619c2f..35f673b2 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
@@ -125,15 +125,21 @@
random(x) == RANDOM(x)$Lisp
x = y == EQL(x, y)$Lisp
x < y == (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)$Lisp
+ (m : PositiveInteger) * (y : %) == (m*y)$Lisp
+ (m : NonNegativeInteger) * (y : %) == (m*y)$Lisp
+ (x : %) ^ (n : NonNegativeInteger) == EXPT(x, n)$Lisp
+ (x : %) ^ (n : PositiveInteger) == EXPT(x, n)$Lisp
odd? x == ODDP(x)$Lisp
+ even? x == EVENP(x)$Lisp
max(x, y) == MAX(x, y)$Lisp
min(x, y) == MIN(x, y)$Lisp
divide(x, y) == DIVIDE2(x, y)$Lisp
@@ -196,6 +200,17 @@
zero?(n := shift(n, -1)) => return y
z := mulmod(z, z, p)
+ -- copied from IntegerNumberSystem to get inline optimization
+ 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:
++ Basic Operations:
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Re: [fricas-devel] erf is left unevaluated in expression
It sort of helps in the sense that the hint about specifying the types is useful. I could not apply the solution directly because it lead to another very surprising (to me) quirk of FriCAS: lack of a basic form of referential transparency between variables and literals. Namely if you assign a literal to a variable and later in code use a variable, the result may be different than if you had used the literal instead. For example: Let's assign an expression to a variable: BS := ((S*erf(((2*log((S/K))+T*s^2+2*T*r)/(2*s*sqrt(2)*sqrt(T-K*%e^((-T*r))*erf(((2*log((S/K))-T*s^2+2*T*r)/(2*s*sqrt(2)*sqrt(T-K*%e^((-T*r))+S)/2) define an abbreviation for DoubleFloat F:=DoubleFloat Now define a function using the literal C0(S:F,r:F,T:F,K:F,s:F):F == ((S*erf(((2*log((S/K))+T*s^2+2*T*r)/(2*s*sqrt(2)*sqrt(T-K*%e^((-T*r))*erf(((2*log((S/K))-T*s^2+2*T*r)/(2*s*sqrt(2)*sqrt(T-K*%e^((-T*r))+S)/2) And another one using the variable which stores that literal C1(S:F,r:F,T:F,K:F,s:F):F == BS Now the first function can be evaluated C0(10.0,0.05,0.8,11.0,0.05) 0.023903294619544546 But the second cannot C1(10.0,0.05,0.8,11.0,0.05) Cannot convert the value from type Expression(Integer) to DoubleFloat . It seems the only way to create a function when the expression is stored in a variable is to first declare the function C2:(F,F,F,F,F) -> F Then use the function operation to create the function from the expression function(BS,'C2,['S,'r,'T,'K,'s]) Then such function can be evaluated C2(10.0,0.05,0.8,11.0,0.05) 0.023903294619544546 On Saturday, November 10, 2018 at 12:07:44 PM UTC+1, Ralf Hemmecke wrote: > > Is there a way to force the evaluation of erf so that the function > > s+->C(11.0,s) can be plotted? > > Does the following help? > > The idea is that you specify the type so that the result is not > Expression(Float) (and must later be converted to (Double)Float, but > rather an element of DoubleFloat. > > Ralf > > F ==> DoubleFloat > > C0(S:F,r:F,T:F, > K:F,s:F):F==((S*erf(((2*log((S/K))+T*s^2+2*T*r)/(2*s*sqrt(2)*sqrt(T-K*%e^((-T*r))*erf(((2*log((S/K))-T*s^2+2*T*r)/(2*s*sqrt(2)*sqrt(T-K*%e^((-T*r))+S)/2) > > > > C(K:F, s:F):F==C0(10.0, 0.05, 0.8, K, s) > > CC(s:F):F==C(11.0, s) > > draw(CC, 2.0..3.0) > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To post to this group, send email to fricas-devel@googlegroups.com. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
