From 0d2f8d5079fc5f120ba376f57efe3981d83d3270 Mon Sep 17 00:00:00 2001 From: Robert Persson Date: Sun, 7 Jul 2013 01:26:00 +0200 Subject: Optimized integrate function in module poly Rewrote the integrate function since the old one was quite hacky. The new one is about 7 times faster in release and 3 times faster in debug --- lib/pure/poly.nim | 26 ++++++++++++++++---------- 1 file changed, 16 insertions(+), 10 deletions(-) (limited to 'lib') diff --git a/lib/pure/poly.nim b/lib/pure/poly.nim index d5f59cfa1..609e58bdc 100644 --- a/lib/pure/poly.nim +++ b/lib/pure/poly.nim @@ -11,9 +11,6 @@ import math import strutils import numeric - -import times #todo: remove - type TPoly* = object cofs:seq[float] @@ -141,11 +138,22 @@ proc integral*(p:TPoly):TPoly= proc integrate*(p:TPoly;xmin,xmax:float):float= ## Computes the definite integral of `p` between `xmin` and `xmax` - # TODO: this can be done faster using a modified horners method, - # see 'diff' function above. - var igr=p.integral - result=igr.eval(xmax)-igr.eval(xmin) + ## quickly using a modified version of Horners method + var + n=p.degree + s1=p[n]/float(n+1) + s2=s1 + fac:float + dec n + while n>=0: + fac=p[n]/float(n+1) + s1 = s1*xmin+fac + s2 = s2*xmax+fac + dec n + + result=s2*xmax-s1*xmin + proc initPoly*(cofs:varargs[float]):TPoly= ## Initializes a polynomial with given coefficients. ## The most significant coefficient is first, so to create x^2-2x+3: @@ -258,7 +266,7 @@ proc `/` *(p,q:TPoly):TPoly= proc `mod` *(p,q:TPoly):TPoly= ## Computes the polynomial modulo operation, - ## that is the remainder op `p`/`q` + ## that is the remainder of `p`/`q` var dummy:TPoly p.divMod(q,dummy,result) @@ -363,5 +371,3 @@ proc roots*(p:TPoly,tol=1.0e-9,zerotol=1.0e-6,mergetol=1.0e-12,maxiter=1000):seq addRoot(p,result,range.xmin,x,tol,zerotol,mergetol,maxiter) range.xmin=x addRoot(p,result,range.xmin,range.xmax,tol,zerotol,mergetol,maxiter) - - \ No newline at end of file -- cgit 1.4.1-2-gfad0 ue='grep'>log msg
path: root/compiler/seminst.nim
blob: a5149a842c57fd162f7eb977d7a138fe46746627 (plain) (blame) 
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