Added poly and numeric modules

lib/pure/numeric.nim

@@ -0,0 +1,113 @@
+#
+#
+#            Nimrod's Runtime Library
+#        (c) Copyright 2013 Robert Persson
+#
+#    See the file "copying.txt", included in this
+#    distribution, for details about the copyright.
+#
+
+
+type TOneVarFunction* =proc (x:float):float
+
+proc brent*(xmin,xmax:float ,function:TOneVarFunction, rootx,rooty:var float,tol:float,maxiter=1000):bool=
+  ## Searches `function` for a root between `xmin` and `xmax` 
+  ## using brents method. If the function value at `xmin`and `xmax` has the
+  ## same sign, `rootx`/`rooty` is set too the extrema value closest to x-axis
+  ## and false is returned.
+  ## Otherwise there exists at least one root and true is always returned.
+  ## This root is searched for at most `maxiter` iterations.
+  ## If `tol` tolerance is reached within `maxiter` iterations 
+  ## the root refinement stops and true is returned.
+
+  # see http://en.wikipedia.org/wiki/Brent%27s_method
+  var 
+    a=xmin
+    b=xmax
+    c=a
+    d=1.0e308 
+    fa=function(a)
+    fb=function(b)
+    fc=fa
+    s=0.0
+    fs=0.0
+    mflag:bool
+    i=0
+    tmp2:float
+
+  if fa*fb>=0:
+    if abs(fa)<abs(fb):
+      rootx=a
+      rooty=fa
+      return false
+    else:
+      rootx=b
+      rooty=fb
+      return false
+  
+  if abs(fa)<abs(fb):
+    swap(fa,fb)
+    swap(a,b)
+  
+  while fb!=0.0 and abs(a-b)>tol:
+    if fa!=fc and fb!=fc: # inverse quadratic interpolation
+      s = a * fb * fc / (fa - fb) / (fa - fc) + b * fa * fc / (fb - fa) / (fb - fc) + c * fa * fb / (fc - fa) / (fc - fb)
+    else: #secant rule
+      s = b - fb * (b - a) / (fb - fa)
+    tmp2 = (3.0 * a + b) / 4.0
+    if (not(((s > tmp2) and (s < b)) or ((s < tmp2) and (s > b)))) or 
+      (mflag and (abs(s - b) >= (abs(b - c) / 2.0))) or 
+      (not mflag and (abs(s - b) >= (abs(c - d) / 2.0))):
+      s=(a+b)/2.0
+      mflag=true
+    else:
+      if ((mflag and (abs(b - c) < tol)) or (not mflag and (abs(c - d) < tol))):
+        s=(a+b)/2.0
+        mflag=true
+      else:
+        mflag=false
+    fs = function(s)
+    d = c
+    c = b
+    fc = fb
+    if fa * fs<0.0:
+      b=s
+      fb=fs
+    else:
+      a=s
+      fa=fs
+    if abs(fa)<abs(fb):
+      swap(a,b)
+      swap(fa,fb)
+    inc i
+    if i>maxiter:
+      break
+  
+  rootx=b
+  rooty=fb  
+  return true
+
+
+
+when isMainModule:
+  var rootx=0.0
+  var rooty=0.0
+  var err=0.0
+  
+  var cnt=0
+  proc myf(x:float):float=
+    inc cnt
+    echo ($cnt & " : " & $x)
+    return x*x-200
+
+  
+  var suc=brent(-10000.0,0.2,myf,rootx,rooty,1.0e-3)
+  
+  
+  echo suc
+  echo rootx
+  echo rooty
+  
+  
+  
+  discard(readline(stdin))