Code: Select all
Debug "Long Intger Division"
k$="12345678987654321234567890987654321"
d=123456789
a$=""
i=1
t=Val (Mid(k$,i,1))
back:
While t<d
t=t*10+Val (Mid(k$,i+1,1))
i=i+1
Wend
i=i+1
While Len (k$)>i-1
a$=a$+Str(Int (t/d))
t=(t-d*Int (t/d))*10+Val (Mid(k$,i,1))
i=i+1
Wend
i=i+1
a$=a$+Str (Int (t/d))
Debug a$Code: Select all
Procedure.s MultiplyBigHelper(factor_1$, factor_2$) ;; Helle 2007!
Protected n.l,len_factor_1.l,len_factor_2.l
len_factor_1=Len(factor_1$)
len_factor_2=Len(factor_2$)
If len_factor_2>len_factor_1 ;make it so larger# is always factor_1
Swap factor_1$,factor_2$
Swap len_factor_1,len_factor_2
EndIf
n=len_factor_1
Protected n_2.l=n*2
Protected Dim factor_1.l(n)
Protected Dim factor_2.l(n)
Protected Dim prod.l(n_2)
Protected Prod$,I.l,J.l,s.l,temp.l
For I = 1 To n ;convert #'s
factor_1(I) = Val(Mid(factor_1$,I,1))
Next I
For I = n - len_factor_2 + 1 To n ;convert #'s
factor_2(I) = Val(Mid(factor_2$,I + len_factor_2 - n,1))
Next I
For I = n - len_factor_2 + 1 To n ;digit# for factor_1
For J = n To 1 Step -1 ;digit# for factor_2
prod(I + J) + factor_1(J) * factor_2(I)
Next J
Next I
For I = n_2 To 1 Step -1 ;digits# of product
temp=Int(prod(I) / 10) ;=carry
prod(I - 1) + temp ;add to next place value
prod(I) - 10 * temp ;subtract from previous place value
Next I
For I = 1 To n_2 ;digits# of product
If prod(I) >0 ;find first non-zero digit
Break
EndIf
Next I
If FindString(factor_1$,"-",1) ;get sign of factor_1
s=1
EndIf
If FindString(factor_2$,"-",1) ;combine with sign of factor_2
s ! 1
EndIf
If s=1 ;=sign will be negative
Prod$="-"
EndIf
For J = I To n_2 ;digits# of product
Prod$ + Str(prod(J))
Next J
ProcedureReturn Prod$
EndProcedure
Procedure.s MultiplyBig(f1$, f2$)
P$=MultiplyBigHelper(RemoveString(F1$, "."), RemoveString(F2$, "."))
If FindString(F1$, ".")
howmanydigitsafterpoint1 = Len(F1$) - FindString(F1$, ".")
Else
howmanydigitsafterpoint1 = 0
EndIf
If FindString(F2$, ".")
howmanydigitsafterpoint2 = Len(F2$) - FindString(F2$, ".")
Else
howmanydigitsafterpoint2 = 0
EndIf
leftpart$ = Left(p$, Len(p$) - (howmanydigitsafterpoint1+howmanydigitsafterpoint2))
rightpart$ = RTrim (Right(p$, (howmanydigitsafterpoint1+howmanydigitsafterpoint2)), "0")
If rightpart$ = "" : rightpart$ = "0" : EndIf
p$ = leftpart$ + "." + rightpart$
ProcedureReturn p$
EndProcedure
;; EXAMPLE
N1$= "42.0510000000000"
N2$= "3.00000040008287"
Debug MultiplyBig(N1$, N2$)
Thanks, it doesn't handle enough digits, they are not stored as strings, and the numbers overflow when too big.firace wrote: Sat Aug 10, 2024 2:10 pm Ah, this module seems to handle division too (didn't test):
https://www.purebasic.fr/english/viewtopic.php?t=61309
Code: Select all
' integer maths by TassyJim 07 Feb 2012
a$ = "13"
For i = 0 To 15 ' demo of the four operations
add( a$ , Str$( i ),res$ )
Print a$;" + ";i;" = ";res$
minus( a$ , Str$( i ),res$ )
Print a$;" - ";i;" = ";res$
multy( a$ , Str$( i ),res$ )
Print a$;" * ";i;" = ";res$
div( a$ , Str$( i ),res$ )
Print a$;" / ";i;" = ";res$
Print
Next i
a$="1"
For i = 1 To 55 ' printing up to factorial 55.
b$=Str$(i)
multy(a$, b$, res$)
Print b$;"! = ";res$;" (";len(res$);" )"
a$=res$
Next i
End
Sub div( a$ , b$, c$ ) ' given a$ and b$, returns a/b in c$
Local f, i, d, t, try$, nr$, a1$, b1$, a2$, z$
a1$=a$ : b1$=b$ : c$="" ' make copies of a$ and b$ to preserve originals
If Val( b$ ) = 0 Then ' divide by zero
c$ = "error"
Else
For i = Len( a1$ ) - Len( b1$ ) To 0 Step -1
f = 0
nr$ = "0"
z$=String$(i,"0")
For d = 0 To 9
md( b1$ + z$ , d, try$ )
'big( a1$ , try$, t )
If biggest( a1$ , try$ ) Then
f = d
nr$ = try$
EndIf
Next d
c$ = c$ + Str$( f )
If f > 0 Then
minus( a1$ , nr$, a2$ )
a1$ = a2$
EndIf
Next i
EndIf
c$=trim$(c$)
End Sub
Sub multy( a$ , b$, c$ ) ' given a$ and b$, returns the sum in c$
Local i, h$, a1$, b1$, t$, d$, z$
a1$=a$ : b1$=b$ : c$="" ' make copies of a$ and b$ to preserve originals
If Len( b1$ ) > Len( a1$ ) Then ' swap number for greater speed
h$ = a1$
a1$ = b1$
b1$ = h$
EndIf
For i = Len( a1$ ) To 1 Step -1
z$=String$(Len( a1$ )-i,"0")
md( b1$ , Val( Mid$( a1$ , i , 1 ) ) , t$)
add( c$ , t$+ z$ ,d$)
c$=d$
Next i
c$=trim$(d$)
End Sub
Sub md( a$ , nr, c$ ) ' multiply a$ by a single digit, result in c$
Local hold, carry, i
carry = 0 : c$=""
For i = Len( a$ ) To 1 Step -1
hold = Val( Mid$( a$ , i , 1 ) ) * nr + carry
carry = Int( hold / 10 )
c$ = Str$( hold Mod 10 ) + c$
Next i
If carry > 0 Then c$ = Str$( carry ) + c$
End Sub
Sub samelen (a$, b$) ' pads the shorter variable with leading zeros
dif=Abs(Len( a$ )-Len( b$ ))
z$=String$(dif,"0")
If Len( a$ ) < Len( b$ ) Then
a$ = z$+a$
Else
b$ = z$+b$
EndIf
End Sub
Sub add( a$ , b$, c$ ) ' given a$ and b$, returns the sum in c$
Local carry, hold, i,a1$, b1$
c$="" : a1$=a$ : b1$=b$
samelen a1$ , b1$
For i = Len( a1$ ) To 1 Step -1
hold = Val( Mid$( a1$ , i , 1 ) ) + Val( Mid$( b1$ , i , 1 ) ) + carry
carry = Int( hold / 10 )
x$=Str$( hold Mod 10 )
c$ = Right$( x$,1) + c$
Next i
If carry > 0 Then c$ = Str$( carry ) + c$
End Sub
Sub minus( a$ , b$, c$ ) ' given a$ and b$, returns the difference in c$
Local a1$, b1$, h$, i, hold, borrow
c$="" : s$="" :a1$=a$ : b1$=b$ ' initialise variables and preserve a$ and b$
samelen a1$ , b1$
If a1$<b1$ Then ' if result is going to be negative, swap a1 & b1
h$ = a1$
a1$ = b1$
b1$ = h$
s$="-"
EndIf
For i = Len( a1$ ) To 1 Step -1
hold = Val( Mid$( a1$ , i , 1 ) ) - Val( Mid$( b1$ , i , 1 ) ) + 10 - borrow
borrow = 1- Int( hold / 10 )
c$ = Str$( hold Mod 10 ) + c$
Next i
c$=trim$(c$)
c$ = s$+c$ ' add the sign
End Sub
function biggest( a$, b$) ' biggest = 1 if a$ >= b$
Local a1$, b1$ 'preserve a$ and b$
a1$ = a$ : b1$ = b$
biggest = 0
samelen (a1$ , b1$)
If a1$>=b1$ Then biggest = 1
End function
function trim$ (a$) ' given a$, leading zeros are stripped. a$ is altered.
Local s$, a1$
s$="" :a1$=a$
If Left$(a$,1)="-" Then ' if the number is negative, preserve the sign
s$="-"
a1$=Mid$(a1$,2)
EndIf
Do While Left$(a1$,1)="0" ' strip leading characters while they are "0"
a1$=Mid$(a1$,2)
Loop
If a1$="" Then a1$="0"
trim$=s$+a1$ ' replace the sign
End function
Code: Select all
; integer maths by TassyJim 07 Feb 2012
Procedure.s md( a$ , nr ) ; multiply a$ by a single digit, result in c$
Protected hold, carry, i
carry = 0 : c$=""
For i = Len( a$ ) To 1 Step -1
hold = Val( Mid( a$ , i , 1 ) ) * nr + carry
carry = Int( hold / 10 )
c$ = Str( Mod(hold,10) ) + c$
Next i
If carry > 0
c$ = Str( carry ) + c$
EndIf
ProcedureReturn c$
EndProcedure
Procedure.s trimit(a$) ; given a$, leading zeros are stripped. a$ is altered.
Protected s$, a1$
s$="" :a1$=a$
If Left(a$,1)="-" ; if the number is negative, preserve the sign
s$="-"
a1$=Mid(a1$,2)
EndIf
Repeat
If Left(a1$,1)="0" ; strip leading characters while they are "0"
a1$=Mid(a1$,2)
EndIf
Until Left(a1$,1)<>"0"
If a1$=""
a1$="0"
EndIf
t$=s$+a1$ ; replace the sign
ProcedureReturn t$
EndProcedure
Procedure.s samelen (a$, b$) ; pads the shorter variable with leading zeros
dif=Abs(Len( a$ )-Len( b$ ))
z$=Space(dif)
z$ = ReplaceString(z$," ","0")
If Len( a$ ) < Len( b$ )
c$ = z$+a$
Else
c$ = a$
EndIf
ProcedureReturn c$
EndProcedure
Procedure biggest( a$, b$) ; biggest = 1 if a$ >= b$
Protected a1$, b1$ ;preserve a$ and b$
a1$ = a$ : b1$ = b$
a1$ = samelen(a1$ , b1$)
b1$ = samelen(b1$ , a1$)
If a1$>=b1$
ProcedureReturn 1
Else
ProcedureReturn 0
EndIf
EndProcedure
Procedure.s add( a$ , b$ ) ; given a$ and b$, returns the sum in c$
Protected carry, hold, i,a1$, b1$
c$="" : a1$=a$ : b1$=b$
a1$ = samelen(a1$ , b1$)
b1$ = samelen(b1$ , a1$)
For i = Len( a1$ ) To 1 Step -1
hold = Val( Mid( a1$ , i , 1 ) ) + Val( Mid( b1$ , i , 1 ) ) + carry
carry = Int( hold / 10 )
x$=Str( Mod(hold,10 ))
c$ = Right( x$,1) + c$
Next i
If carry > 0
c$ = Str( carry ) + c$
EndIf
ProcedureReturn c$
EndProcedure
Procedure.s minus( a$ , b$ ) ; given a$ and b$, returns the difference in c$
Protected a1$, b1$, h$, i, hold, borrow, c$
c$="" : s$="" :a1$=a$ : b1$=b$ ; initialise variables and preserve a$ and b$
a1$ = samelen(a1$ , b1$)
b1$ = samelen(b1$ , a1$)
If a1$<b1$ ; if result is going to be negative, swap a1 & b1
h$ = a1$
a1$ = b1$
b1$ = h$
s$="-"
EndIf
For i = Len( a1$ ) To 1 Step -1
hold = Val( Mid( a1$ , i , 1 ) ) - Val( Mid( b1$ , i , 1 ) ) + 10 - borrow
borrow = 1- Int( hold / 10 )
c$ = Str( Mod(hold,10 )) + c$
Next i
c$=trimit(c$)
c$ = s$+c$ ; add the sign
ProcedureReturn c$
EndProcedure
Procedure.s div( a$ , b$ ) ; given a$ and b$, returns a/b in c$
Protected f, i, d, t, try$, nr$, a1$, b1$, a2$, z$, c$
a1$=a$ : b1$=b$ : c$="" ; make copies of a$ and b$ to preserve originals
If Val( b$ ) = 0 ; divide by zero
c$ = "error"
Else
For i = Len( a1$ ) - Len( b1$ ) To 0 Step -1
f = 0
nr$ = "0"
z$=Space(i)
z$ = ReplaceString(z$," ","0")
For d = 0 To 9
try$ = md( b1$ + z$ , d )
;big( a1$ , try$, t )
If biggest( a1$ , try$ )
f = d
nr$ = try$
EndIf
Next d
c$ = c$ + Str( f )
If f > 0
a2$ = minus( a1$ , nr$ )
a1$ = a2$
EndIf
Next i
EndIf
c$=trimit(c$)
ProcedureReturn c$
EndProcedure
Procedure.s multy( a$ , b$ ) ; given a$ and b$, returns the sum in c$
Protected i, h$, a1$, b1$, t$, d$, z$, c$
a1$=a$ : b1$=b$ : c$="" ; make copies of a$ and b$ to preserve originals
If Len( b1$ ) > Len( a1$ ) ; swap number for greater speed
h$ = a1$
a1$ = b1$
b1$ = h$
EndIf
For i = Len( a1$ ) To 1 Step -1
z$=Space(Len( a1$ )-i)
z$ = ReplaceString(z$," ","0")
t$ = md( b1$ , Val( Mid( a1$ , i , 1 ) ))
d$ = add( c$ , t$+ z$ )
c$=d$
Next i
c$=trimit(d$)
ProcedureReturn c$
EndProcedure
a$ = "13"
For i = 0 To 15 ; demo of the four operations
res$ = add( a$ , Str( i ) )
Debug a$+" + "+Str(i)+" = "+res$
res$ = minus( a$ , Str( i ) )
Debug a$+" - "+Str(i)+" = "+res$
res$ = multy( a$ , Str( i ) )
Debug a$+" * "+Str(i)+" = "+res$
res$ = div( a$ , Str( i ) )
Debug a$+" / "+Str(i)+" = "+res$
Next i
a$="1"
For i = 1 To 55 ; printing up to factorial 55.
b$=Str(i)
res$ = multy(a$, b$)
Debug b$+"! = "+res$+" ("+Str(Len(res$))+" )"
a$=res$
Next i
That's great Jim, thanks. If you add x zeroes at the end of a$ before division, then you get x digits after the decimal point in the division instead of only integer.TassyJim wrote: Sat Aug 10, 2024 10:38 pm Converted to PureBasic without any tidying up
Code: Select all
; integer maths by TassyJim 07 Feb 2012 Procedure.s md( a$ , nr ) ; multiply a$ by a single digit, result in c$ Protected hold, carry, i carry = 0 : c$="" For i = Len( a$ ) To 1 Step -1 hold = Val( Mid( a$ , i , 1 ) ) * nr + carry carry = Int( hold / 10 ) c$ = Str( Mod(hold,10) ) + c$ Next i If carry > 0 c$ = Str( carry ) + c$ EndIf ProcedureReturn c$ EndProcedure Procedure.s trimit(a$) ; given a$, leading zeros are stripped. a$ is altered. Protected s$, a1$ s$="" :a1$=a$ If Left(a$,1)="-" ; if the number is negative, preserve the sign s$="-" a1$=Mid(a1$,2) EndIf Repeat If Left(a1$,1)="0" ; strip leading characters while they are "0" a1$=Mid(a1$,2) EndIf Until Left(a1$,1)<>"0" If a1$="" a1$="0" EndIf t$=s$+a1$ ; replace the sign ProcedureReturn t$ EndProcedure Procedure.s samelen (a$, b$) ; pads the shorter variable with leading zeros dif=Abs(Len( a$ )-Len( b$ )) z$=Space(dif) z$ = ReplaceString(z$," ","0") If Len( a$ ) < Len( b$ ) c$ = z$+a$ Else c$ = a$ EndIf ProcedureReturn c$ EndProcedure Procedure biggest( a$, b$) ; biggest = 1 if a$ >= b$ Protected a1$, b1$ ;preserve a$ and b$ a1$ = a$ : b1$ = b$ a1$ = samelen(a1$ , b1$) b1$ = samelen(b1$ , a1$) If a1$>=b1$ ProcedureReturn 1 Else ProcedureReturn 0 EndIf EndProcedure Procedure.s add( a$ , b$ ) ; given a$ and b$, returns the sum in c$ Protected carry, hold, i,a1$, b1$ c$="" : a1$=a$ : b1$=b$ a1$ = samelen(a1$ , b1$) b1$ = samelen(b1$ , a1$) For i = Len( a1$ ) To 1 Step -1 hold = Val( Mid( a1$ , i , 1 ) ) + Val( Mid( b1$ , i , 1 ) ) + carry carry = Int( hold / 10 ) x$=Str( Mod(hold,10 )) c$ = Right( x$,1) + c$ Next i If carry > 0 c$ = Str( carry ) + c$ EndIf ProcedureReturn c$ EndProcedure Procedure.s minus( a$ , b$ ) ; given a$ and b$, returns the difference in c$ Protected a1$, b1$, h$, i, hold, borrow, c$ c$="" : s$="" :a1$=a$ : b1$=b$ ; initialise variables and preserve a$ and b$ a1$ = samelen(a1$ , b1$) b1$ = samelen(b1$ , a1$) If a1$<b1$ ; if result is going to be negative, swap a1 & b1 h$ = a1$ a1$ = b1$ b1$ = h$ s$="-" EndIf For i = Len( a1$ ) To 1 Step -1 hold = Val( Mid( a1$ , i , 1 ) ) - Val( Mid( b1$ , i , 1 ) ) + 10 - borrow borrow = 1- Int( hold / 10 ) c$ = Str( Mod(hold,10 )) + c$ Next i c$=trimit(c$) c$ = s$+c$ ; add the sign ProcedureReturn c$ EndProcedure Procedure.s div( a$ , b$ ) ; given a$ and b$, returns a/b in c$ Protected f, i, d, t, try$, nr$, a1$, b1$, a2$, z$, c$ a1$=a$ : b1$=b$ : c$="" ; make copies of a$ and b$ to preserve originals If Val( b$ ) = 0 ; divide by zero c$ = "error" Else For i = Len( a1$ ) - Len( b1$ ) To 0 Step -1 f = 0 nr$ = "0" z$=Space(i) z$ = ReplaceString(z$," ","0") For d = 0 To 9 try$ = md( b1$ + z$ , d ) ;big( a1$ , try$, t ) If biggest( a1$ , try$ ) f = d nr$ = try$ EndIf Next d c$ = c$ + Str( f ) If f > 0 a2$ = minus( a1$ , nr$ ) a1$ = a2$ EndIf Next i EndIf c$=trimit(c$) ProcedureReturn c$ EndProcedure Procedure.s multy( a$ , b$ ) ; given a$ and b$, returns the sum in c$ Protected i, h$, a1$, b1$, t$, d$, z$, c$ a1$=a$ : b1$=b$ : c$="" ; make copies of a$ and b$ to preserve originals If Len( b1$ ) > Len( a1$ ) ; swap number for greater speed h$ = a1$ a1$ = b1$ b1$ = h$ EndIf For i = Len( a1$ ) To 1 Step -1 z$=Space(Len( a1$ )-i) z$ = ReplaceString(z$," ","0") t$ = md( b1$ , Val( Mid( a1$ , i , 1 ) )) d$ = add( c$ , t$+ z$ ) c$=d$ Next i c$=trimit(d$) ProcedureReturn c$ EndProcedure a$ = "13" For i = 0 To 15 ; demo of the four operations res$ = add( a$ , Str( i ) ) Debug a$+" + "+Str(i)+" = "+res$ res$ = minus( a$ , Str( i ) ) Debug a$+" - "+Str(i)+" = "+res$ res$ = multy( a$ , Str( i ) ) Debug a$+" * "+Str(i)+" = "+res$ res$ = div( a$ , Str( i ) ) Debug a$+" / "+Str(i)+" = "+res$ Next i a$="1" For i = 1 To 55 ; printing up to factorial 55. b$=Str(i) res$ = multy(a$, b$) Debug b$+"! = "+res$+" ("+Str(Len(res$))+" )" a$=res$ Next i
Jim