Merge branch 'master' of github.com:Araq/Nimrod

This commit is contained in:
Araq 2013-07-20 20:18:21 +02:00
commit 84534ce4b8
30 changed files with 894 additions and 494 deletions

View file

@ -201,7 +201,10 @@ proc find*(s: string, pattern: TRegEx, start = 0): int =
return rawMatches[0]
iterator findAll*(s: string, pattern: TRegEx, start = 0): string =
## yields all matching *substrings* of `s` that match `pattern`.
## Yields all matching *substrings* of `s` that match `pattern`.
##
## Note that since this is an iterator you should not modify the string you
## are iterating over: bad things could happen.
var i = int32(start)
var rawMatches: array[0..maxSubpatterns * 3 - 1, cint]
while true:

View file

@ -460,7 +460,7 @@ proc untilElementEnd(x: var TXmlParser, result: PXmlNode,
if cmpIgnoreCase(x.elemName, result.tag) == 0:
next(x)
else:
echo "5; expected: ", result.htmltag, " ", x.elemName
#echo "5; expected: ", result.htmltag, " ", x.elemName
errors.add(expected(x, result))
# do not skip it here!
break

83
lib/pure/numeric.nim Normal file
View file

@ -0,0 +1,83 @@
#
#
# 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, tol:float,maxiter=1000):
tuple[rootx, rooty: float, success: 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 succes is set to false.
## Otherwise there exists at least one root and success is set to true.
## This root is searched for at most `maxiter` iterations.
## If `tol` tolerance is reached within `maxiter` iterations
## the root refinement stops and success=true.
# 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):
return (a,fa,false)
else:
return (b,fb,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
return (b,fb,true)

View file

@ -474,8 +474,17 @@ proc JoinPath*(head, tail: string): string {.
## .. code-block:: nimrod
## "usr/lib"
##
## If head is the empty string, tail is returned.
## If tail is the empty string, head is returned.
## If head is the empty string, tail is returned. If tail is the empty
## string, head is returned with a trailing path separator. If tail starts
## with a path separator it will be removed when concatenated to head. Other
## path separators not located on boundaries won't be modified. More
## examples on Unix:
##
## .. code-block:: nimrod
## assert JoinPath("usr", "") == "usr/"
## assert JoinPath("", "lib") == "lib"
## assert JoinPath("", "/lib") == "/lib"
## assert JoinPath("usr/", "/lib") == "usr/lib"
if len(head) == 0:
result = tail
elif head[len(head)-1] in {DirSep, AltSep}:
@ -491,15 +500,24 @@ proc JoinPath*(head, tail: string): string {.
proc JoinPath*(parts: varargs[string]): string {.noSideEffect,
rtl, extern: "nos$1OpenArray".} =
## The same as `JoinPath(head, tail)`, but works with any number
## of directory parts.
## The same as `JoinPath(head, tail)`, but works with any number of directory
## parts. You need to pass at least one element or the proc will assert in
## debug builds and crash on release builds.
result = parts[0]
for i in 1..high(parts):
result = JoinPath(result, parts[i])
proc `/` * (head, tail: string): string {.noSideEffect.} =
## The same as ``joinPath(head, tail)``
return joinPath(head, tail)
## The same as ``JoinPath(head, tail)``
##
## Here are some examples for Unix:
##
## .. code-block:: nimrod
## assert "usr" / "" == "usr/"
## assert "" / "lib" == "lib"
## assert "" / "/lib" == "/lib"
## assert "usr/" / "/lib" == "usr/lib"
return JoinPath(head, tail)
proc SplitPath*(path: string): tuple[head, tail: string] {.
noSideEffect, rtl, extern: "nos$1".} =
@ -814,8 +832,13 @@ proc sameFileContent*(path1, path2: string): bool {.rtl, extern: "nos$1",
proc copyFile*(source, dest: string) {.rtl, extern: "nos$1",
tags: [FReadIO, FWriteIO].} =
## Copies a file from `source` to `dest`. If this fails,
## `EOS` is raised.
## Copies a file from `source` to `dest`.
##
## If this fails, `EOS` is raised. On the Windows platform this proc will
## copy the source file's attributes into dest. On other platforms you need
## to use getFilePermissions and setFilePermissions to copy them by hand,
## otherwise `dest` will inherit the default permissions of a newly created
## file for the user.
when defined(Windows):
when useWinUnicode:
let s = newWideCString(source)
@ -1498,7 +1521,7 @@ proc getAppFilename*(): string {.rtl, extern: "nos$1", tags: [FReadIO].} =
if len(result) > 0 and result[0] != DirSep: # not an absolute path?
# iterate over any path in the $PATH environment variable
for p in split(string(getEnv("PATH")), {PathSep}):
var x = joinPath(p, result)
var x = JoinPath(p, result)
if ExistsFile(x): return x
proc getApplicationFilename*(): string {.rtl, extern: "nos$1", deprecated.} =

View file

@ -27,8 +27,24 @@ proc toLower(c: char): char {.inline.} =
proc parseHex*(s: string, number: var int, start = 0): int {.
rtl, extern: "npuParseHex", noSideEffect.} =
## parses a hexadecimal number and stores its value in ``number``. Returns
## the number of the parsed characters or 0 in case of an error.
## Parses a hexadecimal number and stores its value in ``number``.
##
## Returns the number of the parsed characters or 0 in case of an error. This
## proc is sensitive to the already existing value of ``number`` and will
## likely not do what you want unless you make sure ``number`` is zero. You
## can use this feature to *chain* calls, though the result int will quickly
## overflow. Example:
##
## .. code-block:: nimrod
## var value = 0
## discard parseHex("0x38", value)
## assert value == 56
## discard parseHex("0x34", value)
## assert value == 56 * 256 + 52
## value = -1
## discard parseHex("0x38", value)
## assert value == -200
##
var i = start
var foundDigit = false
if s[i] == '0' and (s[i+1] == 'x' or s[i+1] == 'X'): inc(i, 2)
@ -383,6 +399,14 @@ iterator interpolatedFragments*(s: string): tuple[kind: TInterpolatedKind,
when isMainModule:
for k, v in interpolatedFragments("$test{} $this is ${an{ example}} "):
echo "(", k, ", \"", v, "\")"
var value = 0
discard parseHex("0x38", value)
assert value == 56
discard parseHex("0x34", value)
assert value == 56 * 256 + 52
value = -1
discard parseHex("0x38", value)
assert value == -200
{.pop.}

367
lib/pure/poly.nim Normal file
View file

@ -0,0 +1,367 @@
#
#
# Nimrod's Runtime Library
# (c) Copyright 2013 Robert Persson
#
# See the file "copying.txt", included in this
# distribution, for details about the copyright.
#
import math
import strutils
import numeric
type
TPoly* = object
cofs:seq[float]
proc degree*(p:TPoly):int=
## Returns the degree of the polynomial,
## that is the number of coefficients-1
return p.cofs.len-1
proc eval*(p:TPoly,x:float):float=
## Evaluates a polynomial function value for `x`
## quickly using Horners method
var n=p.degree
result=p.cofs[n]
dec n
while n>=0:
result = result*x+p.cofs[n]
dec n
proc `[]` *(p:TPoly;idx:int):float=
## Gets a coefficient of the polynomial.
## p[2] will returns the quadric term, p[3] the cubic etc.
## Out of bounds index will return 0.0.
if idx<0 or idx>p.degree:
return 0.0
return p.cofs[idx]
proc `[]=` *(p:var TPoly;idx:int,v:float)=
## Sets an coefficient of the polynomial by index.
## p[2] set the quadric term, p[3] the cubic etc.
## If index is out of range for the coefficients,
## the polynomial grows to the smallest needed degree.
assert(idx>=0)
if idx>p.degree: #polynomial must grow
var oldlen=p.cofs.len
p.cofs.setLen(idx+1)
for q in oldlen.. <high(p.cofs):
p.cofs[q]=0.0 #new-grown coefficients set to zero
p.cofs[idx]=v
iterator items*(p:TPoly):float=
## Iterates through the corfficients of the polynomial.
var i=p.degree
while i>=0:
yield p[i]
dec i
proc clean*(p:var TPoly;zerotol=0.0)=
## Removes leading zero coefficients of the polynomial.
## An optional tolerance can be given for what's considered zero.
var n=p.degree
var relen=false
while n>0 and abs(p[n])<=zerotol: # >0 => keep at least one coefficient
dec n
relen=true
if relen: p.cofs.setLen(n+1)
proc `$` *(p:TPoly):string =
## Gets a somewhat reasonable string representation of the polynomial
## The format should be compatible with most online function plotters,
## for example directly in google search
result=""
var first=true #might skip + sign if first coefficient
for idx in countdown(p.degree,0):
let a=p[idx]
if a==0.0:
continue
if a>= 0.0 and not first:
result.add('+')
first=false
if a!=1.0 or idx==0:
result.add(formatFloat(a,ffDefault,0))
if idx>=2:
result.add("x^" & $idx)
elif idx==1:
result.add("x")
if result=="":
result="0"
proc derivative*(p:TPoly):TPoly=
## Returns a new polynomial, which is the derivative of `p`
newSeq[float](result.cofs,p.degree)
for idx in 0..high(result.cofs):
result.cofs[idx]=p.cofs[idx+1]*float(idx+1)
proc diff*(p:TPoly,x:float):float=
## Evaluates the differentiation of a polynomial with
## respect to `x` quickly using a modifed Horners method
var n=p.degree
result=p[n]*float(n)
dec n
while n>=1:
result = result*x+p[n]*float(n)
dec n
proc integral*(p:TPoly):TPoly=
## Returns a new polynomial which is the indefinite
## integral of `p`. The constant term is set to 0.0
newSeq(result.cofs,p.cofs.len+1)
result.cofs[0]=0.0 #constant arbitrary term, use 0.0
for i in 1..high(result.cofs):
result.cofs[i]=p.cofs[i-1]/float(i)
proc integrate*(p:TPoly;xmin,xmax:float):float=
## Computes the definite integral of `p` between `xmin` and `xmax`
## 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:
## intiPoly(1.0,-2.0,3.0)
if len(cofs)<=0:
result.cofs= @[0.0] #need at least one coefficient
else:
# reverse order of coefficients so indexing matches degree of
# coefficient...
result.cofs= @[]
for idx in countdown(cofs.len-1,0):
result.cofs.add(cofs[idx])
result.clean #remove leading zero terms
proc divMod*(p,d:TPoly;q,r:var TPoly)=
## Divides `p` with `d`, and stores the quotinent in `q` and
## the remainder in `d`
var
pdeg=p.degree
ddeg=d.degree
power=p.degree-d.degree
ratio:float
r.cofs = p.cofs #initial remainder=numerator
if power<0: #denominator is larger than numerator
q.cofs= @ [0.0] #quotinent is 0.0
return # keep remainder as numerator
q.cofs=newSeq[float](power+1)
for i in countdown(pdeg,ddeg):
ratio=r.cofs[i]/d.cofs[ddeg]
q.cofs[i-ddeg]=ratio
r.cofs[i]=0.0
for j in countup(0,<ddeg):
var idx=i-ddeg+j
r.cofs[idx] = r.cofs[idx] - d.cofs[j]*ratio
r.clean # drop zero coefficients in remainder
proc `+` *(p1:TPoly,p2:TPoly):TPoly=
## Adds two polynomials
var n=max(p1.cofs.len,p2.cofs.len)
newSeq(result.cofs,n)
for idx in countup(0,n-1):
result[idx]=p1[idx]+p2[idx]
result.clean # drop zero coefficients in remainder
proc `*` *(p1:TPoly,p2:TPoly):TPoly=
## Multiplies the polynomial `p1` with `p2`
var
d1=p1.degree
d2=p2.degree
n=d1+d2
idx:int
newSeq(result.cofs,n)
for i1 in countup(0,d1):
for i2 in countup(0,d2):
idx=i1+i2
result[idx]=result[idx]+p1[i1]*p2[i2]
result.clean
proc `*` *(p:TPoly,f:float):TPoly=
## Multiplies the polynomial `p` with a real number
newSeq(result.cofs,p.cofs.len)
for i in 0..high(p.cofs):
result[i]=p.cofs[i]*f
result.clean
proc `*` *(f:float,p:TPoly):TPoly=
## Multiplies a real number with a polynomial
return p*f
proc `-`*(p:TPoly):TPoly=
## Negates a polynomial
result=p
for i in countup(0,<result.cofs.len):
result.cofs[i]= -result.cofs[i]
proc `-` *(p1:TPoly,p2:TPoly):TPoly=
## Subtract `p1` with `p2`
var n=max(p1.cofs.len,p2.cofs.len)
newSeq(result.cofs,n)
for idx in countup(0,n-1):
result[idx]=p1[idx]-p2[idx]
result.clean # drop zero coefficients in remainder
proc `/`*(p:TPoly,f:float):TPoly=
## Divides polynomial `p` with a real number `f`
newSeq(result.cofs,p.cofs.len)
for i in 0..high(p.cofs):
result[i]=p.cofs[i]/f
result.clean
proc `/` *(p,q:TPoly):TPoly=
## Divides polynomial `p` with polynomial `q`
var dummy:TPoly
p.divMod(q,result,dummy)
proc `mod` *(p,q:TPoly):TPoly=
## Computes the polynomial modulo operation,
## that is the remainder of `p`/`q`
var dummy:TPoly
p.divMod(q,dummy,result)
proc normalize*(p:var TPoly)=
## Multiplies the polynomial inplace by a term so that
## the leading term is 1.0.
## This might lead to an unstable polynomial
## if the leading term is zero.
p=p/p[p.degree]
proc solveQuadric*(a,b,c:float;zerotol=0.0):seq[float]=
## Solves the quadric equation `ax^2+bx+c`, with a possible
## tolerance `zerotol` to find roots of curves just 'touching'
## the x axis. Returns sequence with 0,1 or 2 solutions.
var p,q,d:float
p=b/(2.0*a)
if p==inf or p==neginf: #linear equation..
var linrt= -c/b
if linrt==inf or linrt==neginf: #constant only
return @[]
return @[linrt]
q=c/a
d=p*p-q
if d<0.0:
#check for inside zerotol range for neg. roots
var err=a*p*p-b*p+c #evaluate error at parabola center axis
if(err<=zerotol): return @[-p]
return @[]
else:
var sr=sqrt(d)
result= @[-sr-p,sr-p]
proc getRangeForRoots(p:TPoly):tuple[xmin,xmax:float]=
## helper function for `roots` function
## quickly computes a range, guaranteed to contain
## all the real roots of the polynomial
# see http://www.mathsisfun.com/algebra/polynomials-bounds-zeros.html
var deg=p.degree
var d=p[deg]
var bound1,bound2:float
for i in countup(0,deg):
var c=abs(p.cofs[i]/d)
bound1=max(bound1,c+1.0)
bound2=bound2+c
bound2=max(1.0,bound2)
result.xmax=min(bound1,bound2)
result.xmin= -result.xmax
proc addRoot(p:TPoly,res:var seq[float],xp0,xp1,tol,zerotol,mergetol:float,maxiter:int)=
## helper function for `roots` function
## try to do a numeric search for a single root in range xp0-xp1,
## adding it to `res` (allocating `res` if nil)
var br=brent(xp0,xp1, proc(x:float):float=p.eval(x),tol)
if br.success:
if res.len==0 or br.rootx>=res[high(res)]+mergetol: #dont add equal roots.
res.add(br.rootx)
else:
#this might be a 'touching' case, check function value against
#zero tolerance
if abs(br.rooty)<=zerotol:
if res.len==0 or br.rootx>=res[high(res)]+mergetol: #dont add equal roots.
res.add(br.rootx)
proc roots*(p:TPoly,tol=1.0e-9,zerotol=1.0e-6,mergetol=1.0e-12,maxiter=1000):seq[float]=
## Computes the real roots of the polynomial `p`
## `tol` is the tolerance used to break searching for each root when reached.
## `zerotol` is the tolerance, which is 'close enough' to zero to be considered a root
## and is used to find roots for curves that only 'touch' the x-axis.
## `mergetol` is the tolerance, of which two x-values are considered beeing the same root.
## `maxiter` can be used to limit the number of iterations for each root.
## Returns a (possibly empty) sorted sequence with the solutions.
var deg=p.degree
if deg<=0: #constant only => no roots
return @[]
elif p.degree==1: #linear
var linrt= -p.cofs[0]/p.cofs[1]
if linrt==inf or linrt==neginf:
return @[] #constant only => no roots
return @[linrt]
elif p.degree==2:
return solveQuadric(p.cofs[2],p.cofs[1],p.cofs[0],zerotol)
else:
# degree >=3 , find min/max points of polynomial with recursive
# derivative and do a numerical search for root between each min/max
var range=p.getRangeForRoots()
var minmax=p.derivative.roots(tol,zerotol,mergetol)
result= @[]
if minmax!=nil: #ie. we have minimas/maximas in this function
for x in minmax.items:
addRoot(p,result,range.xmin,x,tol,zerotol,mergetol,maxiter)
range.xmin=x
addRoot(p,result,range.xmin,range.xmax,tol,zerotol,mergetol,maxiter)

View file

@ -440,16 +440,23 @@ proc repeatStr*(count: int, s: string): string {.noSideEffect,
result = newStringOfCap(count*s.len)
for i in 0..count-1: result.add(s)
proc align*(s: string, count: int): string {.
proc align*(s: string, count: int, padding = ' '): string {.
noSideEffect, rtl, extern: "nsuAlignString".} =
## Aligns a string `s` with spaces, so that is of length `count`. Spaces are
## added before `s` resulting in right alignment. If ``s.len >= count``, no
## spaces are added and `s` is returned unchanged. If you need to left align
## a string use the repeatChar proc.
## Aligns a string `s` with `padding`, so that is of length `count`.
## `padding` characters (by default spaces) are added before `s` resulting in
## right alignment. If ``s.len >= count``, no spaces are added and `s` is
## returned unchanged. If you need to left align a string use the
## ``repeatChar`` proc. Example:
##
## .. code-block:: nimrod
## assert align("abc", 4) == " abc"
## assert align("a", 0) == "a"
## assert align("1232", 6) == " 1232"
## assert align("1232", 6, '#') == "##1232"
if s.len < count:
result = newString(count)
var spaces = count - s.len
for i in 0..spaces-1: result[i] = ' '
for i in 0..spaces-1: result[i] = padding
for i in spaces..count-1: result[i] = s[i-spaces]
else:
result = s
@ -1211,6 +1218,7 @@ when isMainModule:
doAssert align("abc", 4) == " abc"
doAssert align("a", 0) == "a"
doAssert align("1232", 6) == " 1232"
doAssert align("1232", 6, '#') == "##1232"
echo wordWrap(""" this is a long text -- muchlongerthan10chars and here
it goes""", 10, false)
doAssert formatBiggestFloat(0.00000000001, ffDecimal, 11) == "0.00000000001"

View file

@ -2392,8 +2392,10 @@ proc `[]=`*[T](s: var seq[T], x: TSlice[int], b: openArray[T]) =
spliceImpl(s, a, L, b)
proc slurp*(filename: string): string {.magic: "Slurp".}
## This is an alias for ``staticRead``.
proc staticRead*(filename: string): string {.magic: "Slurp".}
## compile-time ``readFile`` proc for easy `resource`:idx: embedding:
## Compile-time ``readFile`` proc for easy `resource`:idx: embedding:
##
## .. code-block:: nimrod
## const myResource = staticRead"mydatafile.bin"
@ -2402,9 +2404,11 @@ proc staticRead*(filename: string): string {.magic: "Slurp".}
proc gorge*(command: string, input = ""): string {.
magic: "StaticExec".} = nil
## This is an alias for ``staticExec``.
proc staticExec*(command: string, input = ""): string {.
magic: "StaticExec".} = nil
## executes an external process at compile-time.
## Executes an external process at compile-time.
## if `input` is not an empty string, it will be passed as a standard input
## to the executed program.
##
@ -2412,7 +2416,9 @@ proc staticExec*(command: string, input = ""): string {.
## const buildInfo = "Revision " & staticExec("git rev-parse HEAD") &
## "\nCompiled on " & staticExec("uname -v")
##
## ``gorge`` is an alias for ``staticExec``.
## ``gorge`` is an alias for ``staticExec``. Note that you can use this proc
## inside a pragma like `passC <nimrodc.html#passc-pragma>`_ or `passL
## <nimrodc.html#passl-pragma>`_.
proc `+=`*[T: TOrdinal](x: var T, y: T) {.magic: "Inc", noSideEffect.}
## Increments an ordinal

View file

@ -51,7 +51,7 @@ when defined(unix) and not defined(useLibzipSrc):
when defined(macosx):
{.pragma: mydll, dynlib: "libzip2.dylib".}
else:
{.pragma: mydll, dynlib: "libzip2.so(|.2|.1|.0)".}
{.pragma: mydll, dynlib: "libzip(|2).so(|.2|.1|.0)".}
else:
when defined(unix):
{.passl: "-lz".}