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updated poly.nim

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This commit is contained in:
Araq
2014-08-28 08:50:01 +02:00
parent cca8887ba0
commit 649dfa09c4
2 changed files with 47 additions and 39 deletions
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62
lib/pure/poly.nim
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@@ -17,13 +17,13 @@ type
{.deprecated: [TPoly: Poly].} {.deprecated: [TPoly: Poly].}
proc degree*(p:TPoly):int= proc degree*(p:Poly):int=
## Returns the degree of the polynomial, ## Returns the degree of the polynomial,
## that is the number of coefficients-1 ## that is the number of coefficients-1
return p.cofs.len-1 return p.cofs.len-1
proc eval*(p:TPoly,x:float):float= proc eval*(p:Poly,x:float):float=
## Evaluates a polynomial function value for `x` ## Evaluates a polynomial function value for `x`
## quickly using Horners method ## quickly using Horners method
var n=p.degree var n=p.degree
@@ -33,7 +33,7 @@ proc eval*(p:TPoly,x:float):float=
result = result*x+p.cofs[n] result = result*x+p.cofs[n]
dec n dec n
proc `[]` *(p:TPoly;idx:int):float= proc `[]` *(p:Poly;idx:int):float=
## Gets a coefficient of the polynomial. ## Gets a coefficient of the polynomial.
## p[2] will returns the quadric term, p[3] the cubic etc. ## p[2] will returns the quadric term, p[3] the cubic etc.
## Out of bounds index will return 0.0. ## Out of bounds index will return 0.0.
@@ -41,7 +41,7 @@ proc `[]` *(p:TPoly;idx:int):float=
return 0.0 return 0.0
return p.cofs[idx] return p.cofs[idx]
proc `[]=` *(p:var TPoly;idx:int,v:float)= proc `[]=` *(p:var Poly;idx:int,v:float)=
## Sets an coefficient of the polynomial by index. ## Sets an coefficient of the polynomial by index.
## p[2] set the quadric term, p[3] the cubic etc. ## p[2] set the quadric term, p[3] the cubic etc.
## If index is out of range for the coefficients, ## If index is out of range for the coefficients,
@@ -57,14 +57,14 @@ proc `[]=` *(p:var TPoly;idx:int,v:float)=
p.cofs[idx]=v p.cofs[idx]=v
iterator items*(p:TPoly):float= iterator items*(p:Poly):float=
## Iterates through the corfficients of the polynomial. ## Iterates through the corfficients of the polynomial.
var i=p.degree var i=p.degree
while i>=0: while i>=0:
yield p[i] yield p[i]
dec i dec i
proc clean*(p:var TPoly;zerotol=0.0)= proc clean*(p:var Poly;zerotol=0.0)=
## Removes leading zero coefficients of the polynomial. ## Removes leading zero coefficients of the polynomial.
## An optional tolerance can be given for what's considered zero. ## An optional tolerance can be given for what's considered zero.
var n=p.degree var n=p.degree
@@ -77,7 +77,7 @@ proc clean*(p:var TPoly;zerotol=0.0)=
if relen: p.cofs.setLen(n+1) if relen: p.cofs.setLen(n+1)
proc `$` *(p:TPoly):string = proc `$` *(p:Poly):string =
## Gets a somewhat reasonable string representation of the polynomial ## Gets a somewhat reasonable string representation of the polynomial
## The format should be compatible with most online function plotters, ## The format should be compatible with most online function plotters,
## for example directly in google search ## for example directly in google search
@@ -105,13 +105,13 @@ proc `$` *(p:TPoly):string =
result="0" result="0"
proc derivative*(p: TPoly): TPoly= proc derivative*(p: Poly): Poly=
## Returns a new polynomial, which is the derivative of `p` ## Returns a new polynomial, which is the derivative of `p`
newSeq[float](result.cofs,p.degree) newSeq[float](result.cofs,p.degree)
for idx in 0..high(result.cofs): for idx in 0..high(result.cofs):
result.cofs[idx]=p.cofs[idx+1]*float(idx+1) result.cofs[idx]=p.cofs[idx+1]*float(idx+1)
proc diff*(p:TPoly,x:float):float= proc diff*(p:Poly,x:float):float=
## Evaluates the differentiation of a polynomial with ## Evaluates the differentiation of a polynomial with
## respect to `x` quickly using a modifed Horners method ## respect to `x` quickly using a modifed Horners method
var n=p.degree var n=p.degree
@@ -121,7 +121,7 @@ proc diff*(p:TPoly,x:float):float=
result = result*x+p[n]*float(n) result = result*x+p[n]*float(n)
dec n dec n
proc integral*(p:TPoly):TPoly= proc integral*(p:Poly):Poly=
## Returns a new polynomial which is the indefinite ## Returns a new polynomial which is the indefinite
## integral of `p`. The constant term is set to 0.0 ## integral of `p`. The constant term is set to 0.0
newSeq(result.cofs,p.cofs.len+1) newSeq(result.cofs,p.cofs.len+1)
@@ -130,7 +130,7 @@ proc integral*(p:TPoly):TPoly=
result.cofs[i]=p.cofs[i-1]/float(i) result.cofs[i]=p.cofs[i-1]/float(i)
proc integrate*(p:TPoly;xmin,xmax:float):float= proc integrate*(p:Poly;xmin,xmax:float):float=
## Computes the definite integral of `p` between `xmin` and `xmax` ## Computes the definite integral of `p` between `xmin` and `xmax`
## quickly using a modified version of Horners method ## quickly using a modified version of Horners method
var var
@@ -148,7 +148,7 @@ proc integrate*(p:TPoly;xmin,xmax:float):float=
result=s2*xmax-s1*xmin result=s2*xmax-s1*xmin
proc initPoly*(cofs:varargs[float]):TPoly= proc initPoly*(cofs:varargs[float]):Poly=
## Initializes a polynomial with given coefficients. ## Initializes a polynomial with given coefficients.
## The most significant coefficient is first, so to create x^2-2x+3: ## The most significant coefficient is first, so to create x^2-2x+3:
## intiPoly(1.0,-2.0,3.0) ## intiPoly(1.0,-2.0,3.0)
@@ -164,7 +164,7 @@ proc initPoly*(cofs:varargs[float]):TPoly=
result.clean #remove leading zero terms result.clean #remove leading zero terms
proc divMod*(p,d:TPoly;q,r:var TPoly)= proc divMod*(p,d:Poly;q,r:var Poly)=
## Divides `p` with `d`, and stores the quotinent in `q` and ## Divides `p` with `d`, and stores the quotinent in `q` and
## the remainder in `d` ## the remainder in `d`
var var
@@ -192,7 +192,7 @@ proc divMod*(p,d:TPoly;q,r:var TPoly)=
r.clean # drop zero coefficients in remainder r.clean # drop zero coefficients in remainder
proc `+` *(p1:TPoly,p2:TPoly):TPoly= proc `+` *(p1:Poly,p2:Poly):Poly=
## Adds two polynomials ## Adds two polynomials
var n=max(p1.cofs.len,p2.cofs.len) var n=max(p1.cofs.len,p2.cofs.len)
newSeq(result.cofs,n) newSeq(result.cofs,n)
@@ -202,7 +202,7 @@ proc `+` *(p1:TPoly,p2:TPoly):TPoly=
result.clean # drop zero coefficients in remainder result.clean # drop zero coefficients in remainder
proc `*` *(p1:TPoly,p2:TPoly):TPoly= proc `*` *(p1:Poly,p2:Poly):Poly=
## Multiplies the polynomial `p1` with `p2` ## Multiplies the polynomial `p1` with `p2`
var var
d1=p1.degree d1=p1.degree
@@ -219,24 +219,24 @@ proc `*` *(p1:TPoly,p2:TPoly):TPoly=
result.clean result.clean
proc `*` *(p:TPoly,f:float):TPoly= proc `*` *(p:Poly,f:float):Poly=
## Multiplies the polynomial `p` with a real number ## Multiplies the polynomial `p` with a real number
newSeq(result.cofs,p.cofs.len) newSeq(result.cofs,p.cofs.len)
for i in 0..high(p.cofs): for i in 0..high(p.cofs):
result[i]=p.cofs[i]*f result[i]=p.cofs[i]*f
result.clean result.clean
proc `*` *(f:float,p:TPoly):TPoly= proc `*` *(f:float,p:Poly):Poly=
## Multiplies a real number with a polynomial ## Multiplies a real number with a polynomial
return p*f return p*f
proc `-`*(p:TPoly):TPoly= proc `-`*(p:Poly):Poly=
## Negates a polynomial ## Negates a polynomial
result=p result=p
for i in countup(0,<result.cofs.len): for i in countup(0,<result.cofs.len):
result.cofs[i]= -result.cofs[i] result.cofs[i]= -result.cofs[i]
proc `-` *(p1:TPoly,p2:TPoly):TPoly= proc `-` *(p1:Poly,p2:Poly):Poly=
## Subtract `p1` with `p2` ## Subtract `p1` with `p2`
var n=max(p1.cofs.len,p2.cofs.len) var n=max(p1.cofs.len,p2.cofs.len)
newSeq(result.cofs,n) newSeq(result.cofs,n)
@@ -246,26 +246,26 @@ proc `-` *(p1:TPoly,p2:TPoly):TPoly=
result.clean # drop zero coefficients in remainder result.clean # drop zero coefficients in remainder
proc `/`*(p:TPoly,f:float):TPoly= proc `/`*(p:Poly,f:float):Poly=
## Divides polynomial `p` with a real number `f` ## Divides polynomial `p` with a real number `f`
newSeq(result.cofs,p.cofs.len) newSeq(result.cofs,p.cofs.len)
for i in 0..high(p.cofs): for i in 0..high(p.cofs):
result[i]=p.cofs[i]/f result[i]=p.cofs[i]/f
result.clean result.clean
proc `/` *(p,q:TPoly):TPoly= proc `/` *(p,q:Poly):Poly=
## Divides polynomial `p` with polynomial `q` ## Divides polynomial `p` with polynomial `q`
var dummy:TPoly var dummy:Poly
p.divMod(q,result,dummy) p.divMod(q,result,dummy)
proc `mod` *(p,q:TPoly):TPoly= proc `mod` *(p,q:Poly):Poly=
## Computes the polynomial modulo operation, ## Computes the polynomial modulo operation,
## that is the remainder of `p`/`q` ## that is the remainder of `p`/`q`
var dummy:TPoly var dummy:Poly
p.divMod(q,dummy,result) p.divMod(q,dummy,result)
proc normalize*(p:var TPoly)= proc normalize*(p:var Poly)=
## Multiplies the polynomial inplace by a term so that ## Multiplies the polynomial inplace by a term so that
## the leading term is 1.0. ## the leading term is 1.0.
## This might lead to an unstable polynomial ## This might lead to an unstable polynomial
@@ -282,9 +282,9 @@ proc solveQuadric*(a,b,c:float;zerotol=0.0):seq[float]=
p=b/(2.0*a) p=b/(2.0*a)
if p==inf or p==neginf: #linear equation.. if p==Inf or p==NegInf: #linear equation..
var linrt= -c/b var linrt= -c/b
if linrt==inf or linrt==neginf: #constant only if linrt==Inf or linrt==NegInf: #constant only
return @[] return @[]
return @[linrt] return @[linrt]
@@ -300,7 +300,7 @@ proc solveQuadric*(a,b,c:float;zerotol=0.0):seq[float]=
var sr=sqrt(d) var sr=sqrt(d)
result= @[-sr-p,sr-p] result= @[-sr-p,sr-p]
proc getRangeForRoots(p:TPoly):tuple[xmin,xmax:float]= proc getRangeForRoots(p:Poly):tuple[xmin,xmax:float]=
## helper function for `roots` function ## helper function for `roots` function
## quickly computes a range, guaranteed to contain ## quickly computes a range, guaranteed to contain
## all the real roots of the polynomial ## all the real roots of the polynomial
@@ -320,7 +320,7 @@ proc getRangeForRoots(p:TPoly):tuple[xmin,xmax:float]=
result.xmin= -result.xmax result.xmin= -result.xmax
proc addRoot(p:TPoly,res:var seq[float],xp0,xp1,tol,zerotol,mergetol:float,maxiter:int)= proc addRoot(p:Poly,res:var seq[float],xp0,xp1,tol,zerotol,mergetol:float,maxiter:int)=
## helper function for `roots` function ## helper function for `roots` function
## try to do a numeric search for a single root in range xp0-xp1, ## try to do a numeric search for a single root in range xp0-xp1,
## adding it to `res` (allocating `res` if nil) ## adding it to `res` (allocating `res` if nil)
@@ -336,7 +336,7 @@ proc addRoot(p:TPoly,res:var seq[float],xp0,xp1,tol,zerotol,mergetol:float,maxit
res.add(br.rootx) res.add(br.rootx)
proc roots*(p:TPoly,tol=1.0e-9,zerotol=1.0e-6,mergetol=1.0e-12,maxiter=1000):seq[float]= proc roots*(p:Poly,tol=1.0e-9,zerotol=1.0e-6,mergetol=1.0e-12,maxiter=1000):seq[float]=
## Computes the real roots of the polynomial `p` ## Computes the real roots of the polynomial `p`
## `tol` is the tolerance used to break searching for each root when reached. ## `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 ## `zerotol` is the tolerance, which is 'close enough' to zero to be considered a root
@@ -349,7 +349,7 @@ proc roots*(p:TPoly,tol=1.0e-9,zerotol=1.0e-6,mergetol=1.0e-12,maxiter=1000):seq
return @[] return @[]
elif p.degree==1: #linear elif p.degree==1: #linear
var linrt= -p.cofs[0]/p.cofs[1] var linrt= -p.cofs[0]/p.cofs[1]
if linrt==inf or linrt==neginf: if linrt==Inf or linrt==NegInf:
return @[] #constant only => no roots return @[] #constant only => no roots
return @[linrt] return @[linrt]
elif p.degree==2: elif p.degree==2:

24
lib/pure/terminal.nim
View File

@@ -31,7 +31,8 @@ when defined(windows):
proc getCursorPos(): tuple [x,y: int] = proc getCursorPos(): tuple [x,y: int] =
var c: TCONSOLESCREENBUFFERINFO var c: TCONSOLESCREENBUFFERINFO
if GetConsoleScreenBufferInfo(conHandle, addr(c)) == 0: raiseOSError(osLastError()) if GetConsoleScreenBufferInfo(conHandle, addr(c)) == 0:
raiseOSError(osLastError())
return (int(c.dwCursorPosition.x), int(c.dwCursorPosition.y)) return (int(c.dwCursorPosition.x), int(c.dwCursorPosition.y))
proc getAttributes(): int16 = proc getAttributes(): int16 =
@@ -61,10 +62,12 @@ proc setCursorXPos*(x: int) =
when defined(windows): when defined(windows):
var scrbuf: TCONSOLESCREENBUFFERINFO var scrbuf: TCONSOLESCREENBUFFERINFO
var hStdout = conHandle var hStdout = conHandle
if GetConsoleScreenBufferInfo(hStdout, addr(scrbuf)) == 0: raiseOSError(osLastError()) if GetConsoleScreenBufferInfo(hStdout, addr(scrbuf)) == 0:
raiseOSError(osLastError())
var origin = scrbuf.dwCursorPosition var origin = scrbuf.dwCursorPosition
origin.x = int16(x) origin.x = int16(x)
if SetConsoleCursorPosition(conHandle, origin) == 0: raiseOSError(osLastError()) if SetConsoleCursorPosition(conHandle, origin) == 0:
raiseOSError(osLastError())
else: else:
stdout.write("\e[" & $x & 'G') stdout.write("\e[" & $x & 'G')
@@ -75,10 +78,12 @@ when defined(windows):
when defined(windows): when defined(windows):
var scrbuf: TCONSOLESCREENBUFFERINFO var scrbuf: TCONSOLESCREENBUFFERINFO
var hStdout = conHandle var hStdout = conHandle
if GetConsoleScreenBufferInfo(hStdout, addr(scrbuf)) == 0: raiseOSError(osLastError()) if GetConsoleScreenBufferInfo(hStdout, addr(scrbuf)) == 0:
raiseOSError(osLastError())
var origin = scrbuf.dwCursorPosition var origin = scrbuf.dwCursorPosition
origin.y = int16(y) origin.y = int16(y)
if SetConsoleCursorPosition(conHandle, origin) == 0: raiseOSError(osLastError()) if SetConsoleCursorPosition(conHandle, origin) == 0:
raiseOSError(osLastError())
else: else:
discard discard
@@ -155,10 +160,12 @@ proc eraseLine* =
var scrbuf: TCONSOLESCREENBUFFERINFO var scrbuf: TCONSOLESCREENBUFFERINFO
var numwrote: DWORD var numwrote: DWORD
var hStdout = conHandle var hStdout = conHandle
if GetConsoleScreenBufferInfo(hStdout, addr(scrbuf)) == 0: raiseOSError(osLastError()) if GetConsoleScreenBufferInfo(hStdout, addr(scrbuf)) == 0:
raiseOSError(osLastError())
var origin = scrbuf.dwCursorPosition var origin = scrbuf.dwCursorPosition
origin.x = 0'i16 origin.x = 0'i16
if SetConsoleCursorPosition(conHandle, origin) == 0: raiseOSError(osLastError()) if SetConsoleCursorPosition(conHandle, origin) == 0:
raiseOSError(osLastError())
var ht = scrbuf.dwSize.Y - origin.Y var ht = scrbuf.dwSize.Y - origin.Y
var wt = scrbuf.dwSize.X - origin.X var wt = scrbuf.dwSize.X - origin.X
if FillConsoleOutputCharacter(hStdout,' ', ht*wt, if FillConsoleOutputCharacter(hStdout,' ', ht*wt,
@@ -178,7 +185,8 @@ proc eraseScreen* =
var numwrote: DWORD var numwrote: DWORD
var origin: TCOORD # is inititalized to 0, 0 var origin: TCOORD # is inititalized to 0, 0
var hStdout = conHandle var hStdout = conHandle
if GetConsoleScreenBufferInfo(hStdout, addr(scrbuf)) == 0: raiseOSError(osLastError()) if GetConsoleScreenBufferInfo(hStdout, addr(scrbuf)) == 0:
raiseOSError(osLastError())
if FillConsoleOutputCharacter(hStdout, ' ', scrbuf.dwSize.X*scrbuf.dwSize.Y, if FillConsoleOutputCharacter(hStdout, ' ', scrbuf.dwSize.X*scrbuf.dwSize.Y,
origin, addr(numwrote)) == 0: origin, addr(numwrote)) == 0:
raiseOSError(osLastError()) raiseOSError(osLastError())