## Squares

General FreeBASIC programming questions.
Richard
Posts: 2953
Joined: Jan 15, 2007 20:44
Location: Australia

### Re: Squares

@Albert.
My code showed you how to propagate carry, or to repair simple examples of delayed carry. Your code must avoid delaying carry for so long that local carry overflows within your register.
dodicat
Posts: 5913
Joined: Jan 10, 2006 20:30
Location: Scotland

### Re: Squares

Albert.
I have tested Richard's conversions with a binary multiply (bit by bit) here.
They look to be spot on.

Code: Select all

'=======================================================================
' Convert base two ASCII binary string to base ten ASCII decimal string (RICHARD)
'=======================================================================
Function base_2_to_10( Byref b As String ) As String    ' b may be lengthened
' lengthen input string by up to 28 zero bits to make 29 bit blocks
Dim As Integer n = Len( b ) Mod 29
If n Then b = String( 29 - n, "0" ) + b
n = Len( b ) \ 29  ' number of input blocks
Dim As Ulong acc( 0 To n )  ' accumulator array
' convert blocks of 9 digits to binary in 32 bit Ulong
Dim As Ulongint product, carry  ' 64 bit Unsigned Integer
Dim As Integer i, j, k = 1      ' loop counters
For j = 1 To Len( b ) Step 29   ' the blocks to convert
carry = Valulng( "&b" + Mid( b, j, 29 ) ) ' value of 29 bit block
For i = 0 To k  ' Multiply Accumulate,   2^29 = 536870912
product = ( Culngint( acc( i ) ) * 536870912ull ) + carry
acc( i ) = product Mod 1000000000ull    ' sum is low part
carry = product \ 1000000000ull     ' carry is the high part
Next i
If carry Then   ' extend accumulator by one element when needed
k += 1
acc( k ) = carry
End If
Next j  ' accumulator now contains result blocks of base 1 billion
' unpack and return acc as decimal ASCII string
Dim As String txt
For i = n To 0 Step -1
txt += Right( "000000000" + Str( acc( i ) ), 9 )
Next i
Return Ltrim( txt, "0" )
End Function

'=======================================================================
' Convert base ten ASCII decimal string to base two ASCII binary string(RICHARD)
'=======================================================================
Function base_10_to_2( Byref d As String ) As String  ' d may be lengthened
' lengthen input string by up to 8 digits to make 9 digit blocks
Dim As Integer n = Len( d ) Mod 9
If n Then d = String( 9 - n, "0" ) + d
n = Len( d ) \ 9  ' number of input blocks
Dim As Ulong acc( 0 To n )  ' the accumulator array
' convert blocks of 9 digits to binary in 32 bit Ulong
Dim As Ulongint product, carry  ' 64 bit Unsigned Integer
Dim As Integer i, j, k = 1      ' loop counters
For j = 1 To Len( d ) Step 9     ' the blocks to convert
carry = Valulng( Mid( d, j, 9 ) ) ' get value of 9 digit block
For i = 0 To k  ' Multiply Accumulate
product = ( Culngint( acc( i ) ) * 1000000000ull ) + carry
acc( i ) = product And &hFFFFFFFFull ' sum is low order 32 bits
carry = product Shr 32 ' carry is the high order 32 bits
Next i
If carry Then   ' extend accumulator by one element when needed
k += 1
acc( k ) = carry
End If
Next j  ' accumulator now contains result in packed binary
' unpack and return it as binary ASCII string
Dim As String txt
For i = n To 0 Step -1
txt += Bin( acc( i ), 32 )
Next i
Return Ltrim( txt, "0" )
End Function

'multiply via change to bimary
Function Qmult(Byval a As String,Byval b As String) As String
a= base_10_to_2(a) 'convert to binary
b= base_10_to_2(b)
For n As Long=0 To Len(a)-1 'make bits 0 and 1 as ubyte
a[n]-=48
Next
For n As Long=0 To Len(b)-1
b[n]-=48
Next
Var flag=0,la = Len(a),lb = Len(b)
If Len(b)>Len(a) Then Swap a,b:Swap la,lb
Dim As Ubyte n,carry
Var c =String(la+lb,0)
For i As Integer =la-1 To 0 Step -1
carry=0
For j As Integer =lb-1 To 0 Step -1
n=(a[i] And b[j])+(c[i+j+1]) + carry
carry =n Shr 1:c[i+j+1]=n And 1
Next j
c[i]=carry
Next i
For n As Long=0 To Len(c)-1 'convert ubyte bits to string 1 and 0
c[n]+=48
Next
c= base_2_to_10(c) 'convert back th base 10
Return Ltrim(c,"0")
End Function

Dim Shared As Ubyte _Mod(0 To 99),_Div(0 To 99)
For z As Integer=0 To 99:_Mod(z)=(z Mod 10+48):_Div(z)=z\10:Next
' normal decimal string multiply
Function Qmult2( a As String,b As String) As String
Var flag=0,la = Len(a),lb = Len(b)
If Len(b)>Len(a) Then flag=1:Swap a,b:Swap la,lb
Dim As Ubyte n,carry,ai
Var c =String(la+lb,"0")
For i As Integer =la-1 To 0 Step -1
carry=0:ai=a[i]-48
For j As Integer =lb-1 To 0 Step -1
Var n = ai * (b[j]-48) + (c[i+j+1]-48) + carry
carry =_Div(n):c[i+j+1]=_Mod(n)
Next j
c[i]+=carry
Next i
If flag Then Swap a,b
Return Ltrim(c,"0")
End Function

#define range(f,l) Int(Rnd*((l+1)-(f))+(f))

#macro create(g)
g[0]=range(49,57)
For n As Long=1 To Len(g)-1
g[n]=range(48,57)
Next
#endmacro

Dim As String n1=String(1000,0)
Dim As String n2=String(1000,0)
Do
create(n1)
create(n2)

Dim As String tobin=qmult(n1,n2)
Dim As String todec=qmult2(n1,n2)
Print tobin
Print
Print todec

Print Iif(todec=tobin,"OK","ERROR")
Sleep
Loop Until Inkey=Chr(27)

albert
Posts: 4952
Joined: Sep 28, 2006 2:41
Location: California, USA

### Re: Squares

@Dodicat

Richards base conversions tamper with the passed vars..and alter them..So you can't use them later on..
They put some zeros in front of them..

So i put some code into them to set the var for the function..

dim as string ?? = passed var_string..
then function works with ?? string..( passed string)
albert
Posts: 4952
Joined: Sep 28, 2006 2:41
Location: California, USA

### Re: Squares

"!!~~OFF TOPIC~~!!"

Deleted at request of imortis

imortis you can contact me at

albert_redditt@yahoo.com
Last edited by albert on Jan 19, 2019 19:00, edited 1 time in total.
dodicat
Posts: 5913
Joined: Jan 10, 2006 20:30
Location: Scotland

### Re: Squares

Thanks Albert.
Sadly it will probably all happen again so some other culture in some other place.
Here is an update of my perpetual machine.
Red - north pole, green - south pole, white stuff - magnetic insulator.
It is boring to watch because perpetual motion will probably be boring when it is invented (in squares hopefully).

Code: Select all

dim shared as long cx,cy
cx=400
cy=300
#define map(a,b,x,c,d) ((d)-(c))*((x)-(a))/((b)-(a))+(c)
Type Point
As single x,y  'need floats for smoothness when moving or rotating points
Declare sub rotate(As Point,As Single,As Single)' As Point
End Type

sub point.rotate(pivot As Point,a As Single,d As Single)' As Point
dim as point t=type(d*(Cos(a*.0174533)*(x-pivot.x)-Sin(a*.0174533)*(y-pivot.y)) +pivot.x,_
d*(Sin(a*.0174533)*(x-pivot.x)+Cos(a*.0174533)*(y-pivot.y)) +pivot.y)
this=t
End sub

Type Rectangle
As Ushort wide
As Ushort high
As Single aspect
As Byte   pflag 'fill or not
As Ulong  clr   'colour
im as any ptr=0
Declare  Constructor(As Point=type(0,0),As Ushort=0,As Ushort=0,As Single =0,As Ulong=0,As Byte=0,as any ptr=0)
As Point v(1 To 4) 'extra points for vertices/centroid
As Point centroid
Declare Sub Draw()
End Type

Constructor rectangle(c As Point,w As Ushort,h As Ushort,a As Single,col As Ulong,pf As Byte,i as any ptr)
v(1)=type(c.x-w/2,c.y-h/2)
v(2)=type(c.x-w/2,c.y+h/2)
v(3)=type(c.x+w/2,c.y+h/2)
v(4)=type(c.x+w/2,c.y-h/2)
For n As Long=1 To 4
v(n).rotate(c,a,1)
Next
pflag=pf
clr=col
aspect=a
wide=w
high=h
centroid=c
im=i
End Constructor

Sub fill(a() As Point,c As Ulong,min As Long,max As Long,im as any ptr=0)
#define dist(x1,y1,x2,y2) sqr( (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2))
'translation of a c snippet
static As Long i,j,k,dy,dx, x,y,temp
Static As Long NewX (1 To Ubound(a))
Static As Single Grad(1 To Ubound(a))
For i=1 To Ubound(a) - 1
dy=a(i+1).y-a(i).y
dx=a(i+1).x-a(i).x
If ((dy <> 0) And (dx <> 0)) Then
End If
Next i
For y=min To max
k = 1
For i=1 To Ubound(a) - 1
If( ((a(i).y<=y) Andalso (a(i+1).y>y)) Or ((a(i).y>y) _
Andalso (a(i+1).y<=y))) Then
k +=1
End If
Next i
For j = 1 To k-2
For i = 1 To k-2
If NewX(i) > NewX(i+1) Then
temp = NewX(i)
NewX(i) = NewX(i+1)
NewX(i+1) = temp
End If
Next i
Next j

For i = 1 To k - 2 Step 2
Line im,(NewX(i),y)-(NewX(i+1)+1,y),c
Next i
Next y
End Sub

Sub rectangle.draw()
Static As Single miny=1e6,maxy=-1e6
Static As Point V1(1 To  Ubound(v)+1)
For n as long =1 To Ubound(v)
If pflag=0 Then If n<Ubound(v) Then  Line(v(n).x,v(n).y)-(v(n+1).x,v(n+1).y),clr
If miny>v(n).y Then miny=v(n).y
If maxy<v(n).y Then maxy=v(n).y
V1(n)=v(n)
Next
If pflag=0 Then Line -(v(1).x,v(1).y),clr
v1(Ubound(v1))=v(Lbound(v))
If pflag Then fill(v1(),clr,miny,maxy,im)
End Sub

Function Regulate(Byval MyFps As long,Byref fps As long) As Integer
Static As Double timervalue,lastsleeptime,t3,frames
Var t=Timer
frames+=1
If (t-t3)>=1 Then t3=t:fps=frames:frames=0
Var sleeptime=lastsleeptime+((1/myfps)-T+timervalue)*1000
If sleeptime<1 Then sleeptime=1
lastsleeptime=sleeptime
timervalue=T
Return sleeptime
End Function

function DrawBox(x as long,y as long,w as long,h as long, _
angle as single,length as long,col as ulong,f as byte=1,i as any ptr=0) as point
dim as rectangle r
dim as single c=-angle
angle=angle*.0174532925199433  '=4*atn(1)/180
var x2=x+length*cos(angle),y2=y-length*sin(angle)
r=rectangle(type<point>(x2,y2),w,h,c,col,f,i)
r.draw
return type(x2,y2)
end function

screen 19,32
dim as any ptr i=imagecreate(800,600,0)
for n as long=0 to 360 step 15
DrawBox(400,300,50,21,n+.5,100+100+5,rgb(200,200,200),1,i)
DrawBox(400,300,50,20,n,150+108,rgb(200,0,0),1,i)
DrawBox(400,300,50,20,n,100+108,rgb(0,200,0),1,i)
next
dim as single a
dim as long fps
do
a+=.2
if a>360 then a=0
screenlock
cls
put(0,0),i,pset
draw string(10,10),"Fps  " & fps
for n as long=0 to 360 step 20
DrawBox(400,300,50,21,a+n-.5,152,rgb(200,200,200),1)
DrawBox(400,300,50,20,a+n,150,rgb(200,0,0))
DrawBox(400,300,50,20,a+n,100,rgb(0,200,0))
next
screenunlock
sleep regulate(160,fps),1
loop until len(inkey)
sleep
albert
Posts: 4952
Joined: Sep 28, 2006 2:41
Location: California, USA

### Re: Squares

@Dodicat

How about a ring magnet , where you have herring bone north and south strips around the ring.
Then you have a floating magnet attached to the shaft that travels around the circle??

The floating magnet would be both attracted and repelled around the circle...
albert
Posts: 4952
Joined: Sep 28, 2006 2:41
Location: California, USA

### Mul Bin

@Dodicat

I did a bin multiplier....

Code: Select all

screen 19

do

dim as string binari = bin( int( rnd*256 ) )

dim as longint mul = int(rnd*100) + 1

dim as string added = string( len(binari) ,  "0" )
dim as longint carry = 0
dim as longint val1
for a as longint = len(binari)-1 to 0 step -1
val1 = ( ( binari[ a ] - 48 ) * mul ) + carry
carry = val1 \ 2
next

print
print binari  , val("&B" + binari)
print
print bin(val("&B" + binari) * mul) , val("&B" + binari) * mul

sleep

loop until inkey = chr(27)

sleep
end

Now to incorporate it into my multiplier...
albert
Posts: 4952
Joined: Sep 28, 2006 2:41
Location: California, USA

### Re: Squares

@Dodicat
@Richard

I don't know what Hitler did with the infants and toddlers under the reading age??
But they rounded up whole households and charged them with espionage , if they possessed any of the books..
Some 7,000,000 Jews were executed from 1939 to 1948..
At 4 people per household , that's a little more than 1,500,000 households in Germany , Austria , Poland , that were rounded up..

Here's the bin mul with strings...It only works for up to 64 bits..Now , to make it step by more than 1 digit , at a time..

Code: Select all

screen 19

do

dim as string num1 = bin( int( rnd * 2^24 ) + 1 )
dim as string num2 = bin( int( rnd * 2^24 ) + 1 )

dim as ulongint added( 0 to len(num1)+len(num2))
dim as longint val1
dim as longint val2
dim as longint place_a = ubound(added)+1
dim as longint place_b = place_a
for a as longint = len(num1)-1 to 0 step -1
val1 = ( num1[ a ] - 48 )
place_a-= 1
place_b = place_a
for b as longint = len(num2)-1 to 0 step -1
val2 = (num2[ b ] - 48 ) * val1
place_b-=1
next
next
dim as longint carry = 0
carry = val1 \ 2
next

print
print "========================================================================="
print num1  , val("&B" + num1) ; " x " ; val("&B" + num2)
print
print bin(val("&B" + num1) * val("&B" + num2) ) , val("&B" + num1) * val("&B"+num2)
print "========================================================================="

sleep

loop until inkey = chr(27)

sleep
end

dodicat
Posts: 5913
Joined: Jan 10, 2006 20:30
Location: Scotland

### Re: Squares

val2 mod 2 is equal to val2 and 1 which is faster.
albert
Posts: 4952
Joined: Sep 28, 2006 2:41
Location: California, USA

### Re: Squares

@Dodicat

Thanks for the idea.. val AND 1 worked..

Any idea on how to make it step by more than 1 digit ??

=============================================================================
@Dodicat

I wrote a sea faring song... It's a Classical Ballad..

Code: Select all

( Genre = Classic Ballad )

( Title = Sail The Mighty Ocean )

sail the mighty ocean
sail the mighty sea
sail the mighty ocean
my true love , for to see

she lives across the waters
she lives across the sea
she lives across the waters
my true love , waits for me

all aboard the vessle
all aboard the "Lee"
all aboard the vessle

sail the mighty ocean
sail the mighty sea
sail the mighty ocean
my true love , for to see

a hail to the captain
a hail to the "Lee"
a hail to the captian

embark upon a voyage
embark upon the sea
embark upon a voyage
my true love waits for me

sail the mighty ocean
sail the mighty sea
sail the mighty ocean
my true love , for to see

several weeks on the ocean
several weeks on the sea
several weeks on the ocean
my true love for to see

she lives across the waters
she lives across the sea
she lives across the waters
my true love , waits for me

sail the mighty ocean
sail the mighty sea
sail the mighty ocean
my true love , for to see

batten down the hatches
batten down the "Lee"
batten down the hatches
theres a strom upon the sea

not long i will see her
not long i'll be there
not long i will see her
and smell her precious hair

sail the mighty ocean
sail the mighty sea
sail the mighty ocean
my true love , for to see

sail the mighty ocean
sail the mighty sea
sail the mighty ocean
my true love , for to see

albert_redditt@yahoo.com

Albert Redditt
315 W. Carrillo St. #104
Santa Barbara, Ca. 93101 U.S.A.

I edited it to make some minor changes..
Last edited by albert on Jan 15, 2019 17:50, edited 1 time in total.
albert
Posts: 4952
Joined: Sep 28, 2006 2:41
Location: California, USA

### Re: Squares

@Dodicat

I got it stepping by 24 bits...see mul_var()

I'd like to make the bits var , to self adjust to the highest val possible for the length of the strings.
It takes 4,500 seconds to run for 1,000,000 length. So i have to speed it up...

Code: Select all

Declare Function mul_var( n1 as string , n2 as string ) as string

Declare Function multiplier_7( num1 as string, num2 as string) as string

Declare Function base_2_to_10( Byref num As String ) As String    ' b may be lengthened
Declare Function base_10_to_2( Byref num As String ) As String  ' d may be lengthened

Declare Function minus(NUM1 As String,NUM2 As String) As String
Declare Function       plus( NUMber1 As String  ,  NUMber2 As String ) As String

screen 19

dim as double time1 , time2 , time3 , time4

do

'=======================================================
'begin create binary numbers
'=======================================================
dim as longint size = 100
dim as string num1 = ""
do
num1=""
for x as longint = 1 to size
num1+= str( int( rnd*2 ) )
next
num1 = ltrim(num1,"0")
loop until num1 > "0"

dim as string num2 = ""
do
num2 = ""
for x as longint = 1 to size
num2+= str( int( rnd*2 ) )
next
num2 = ltrim(num2,"0")
loop until num2 > "0"

if len(num2) > len(num1) then swap num1 , num2
if num2 > num1 then swap num1 , num2
'=======================================================
'end create binary numbers
'=======================================================
time1=timer
dim as string mul1 = base_2_to_10( num1 )
dim as string mul2 = base_2_to_10( num2 )
dim as string mul_bin = multiplier_7( mul1 , mul2 )
mul_bin = left( mul_bin , len( mul_bin ) - 1 )
mul_bin = base_10_to_2(mul_bin)
time2 = timer

time3 = timer
dim as string answer = mul_var( num1 , num2 )
time4 = timer

dim as string diff = minus( mul_bin , answer )

print
print "========================================================================="
print base_2_to_10( num1 )
print base_2_to_10( num2 )
print
print mul_bin
print
print "diff = " ; diff
print "Time multiplier_7 = " ; time2-time1
print "Time mul loop     = "  ; time4-time3
print "========================================================================="

if diff <> "0" then print "ERROR" : sleep

sleep

loop until inkey = chr(27)

sleep
end
'=======================================================================
'=======================================================================
' subs and functions below here
'=======================================================================
'=======================================================================
'=======================================================================
Function mul_var( n1 as string , n2 as string ) as string
dim as string num1 = n1
dim as string num2 = n2
'=======================================================
'make equal lenths
'=======================================================
dim as ubyte bits = 24 ' set val for mul loop stepping.. I want to make the bits variable..to ( auto_adust ) to the largest val possible...
if len(num1) > len(num2) then num2 = string( len(num1) - len(num2) , "0" ) + num2
if len(num2) > len(num1) then num1 = string( len(num2) - len(num1) , "0" ) + num1
if len(num1) mod bits > 0 then num1 = string( ( bits - len(num1) mod bits ) , "0") + num1
if len(num2) mod bits > 0 then num2 = string( ( bits - len(num2) mod bits ) , "0") + num2
'=======================================================
'end make equal lenths
'=======================================================

'=======================================================
'begin mul loop
'=======================================================
dim as ulongint added( 0 to len(num1)+len(num2))
dim as longint val1
dim as longint val2
dim as longint place_a = ubound(added)+bits
dim as longint place_b = place_a
dim as longint carry
for a as longint = len(num1)-(bits-1) to 1 step -bits
val1 = val("&B"+mid( num1 , a , bits ))
place_a-= bits
place_b = place_a
if val1 > 0 then
for b as longint = len(num2)-(bits-1) to 1 step -bits
val2 = val("&B"+mid( num2 , b , bits )) * val1
place_b-=bits
next
end if
next
carry = 0
'print added(a) ; " " ;
carry = val1 \ 2
next
'=======================================================
'end mul loop
'=======================================================
end function
'===============================================================================
'===============================================================================
'Dodicats plus & Minus functions
'===============================================================================
'===============================================================================
Function plus(_num1 As String,_num2 As String) As String
Dim  ADDQmod(0 To 19) As Ubyte
Dim  ADDbool(0 To 19) As Ubyte
For z As Integer=0 To 19
Next z
Var _flag=0,n_=0
#macro finish()
If _flag=1 Then Swap _num2,_num1
#endmacro
If Len(_num2)>Len(_num1) Then
Swap _num2,_num1
_flag=1
End If
Var diff=Len(_num1)-Len(_num2)
For n_=Len(_num1)-1 To diff Step -1
Next n_
finish()
End If
If n_=-1 Then
finish()
Endif
For n_=n_ To 0 Step -1
Next n_
finish()
End Function
'===============================================================================
'===============================================================================
Function minus(NUM1 As String,NUM2 As String) As String
'Dim As String copyfirstnum=mul_num_1,copysecondnum=mul_num_2
Dim As Byte swapflag
Dim As Long lenf,lens
Dim sign As String * 1
'Dim As String part1,part2
Dim bigger As Byte
'set up tables
Dim As Ubyte Qmod(0 To 19)
Dim bool(0 To 19) As Ubyte

For z As Integer=0 To 19
Qmod(z)=cubyte(z Mod 10+48)
bool(z)=cubyte(-(10>z))
Next z
lenf=Len(NUM1)
lens=Len(NUM2)
#macro compare(numbers)
If Lens>lenf Then bigger= -1:Goto fin
If Lens<lenf Then bigger =0:Goto fin
If NUM2>NUM1 Then
bigger=-1
Else
bigger= 0
End If
fin:
#endmacro

compare(numbers)
If bigger Then
sign="-"
Swap NUM2,NUM1
Swap lens,lenf
swapflag=1
Endif
'lenf=Len(NUM1)
'lens=Len(NUM2)
Dim diff As Long=lenf-lens-Sgn(lenf-lens)
Dim As String one,two,three
three=NUM1
two=String(lenf-lens,"0")+NUM2
one=NUM1
Dim As Long n2
Dim As Ubyte takeaway,subtractcarry
Dim As Ubyte ten=10
'Dim z As Long
subtractcarry=0
Do
For n2=lenf-1 To diff Step -1
takeaway= one[n2]-two[n2]+ten-subtractcarry
three[n2]=Qmod(takeaway)
subtractcarry=bool(takeaway)
Next n2
If subtractcarry=0 Then Exit Do
If n2=-1 Then Exit Do
For n2=n2 To 0 Step -1
takeaway= one[n2]-two[n2]+ten-subtractcarry
three[n2]=Qmod(takeaway)
subtractcarry=bool(takeaway)
Next n2
Exit Do
Loop

three=Ltrim(three,"0")
If three="" Then Return "0"
If swapflag=1 Then Swap NUM1,NUM2

Return sign+three

End Function
'=======================================================================
'=======================================================================
'Richards base converters
'=======================================================================
'=======================================================================
'=======================================================================
' Convert base two ASCII binary string to base ten ASCII decimal string
'=======================================================================
Function base_2_to_10( Byref num As String ) As String    ' b may be lengthened
dim as string b = num
' lengthen input string by up to 28 zero bits to make 29 bit blocks
Dim As Integer n = Len( b ) Mod 29
If n Then b = String( 29 - n, "0" ) + b
n = Len( b ) \ 29  ' number of input blocks
Dim As Ulong acc( 0 To n )  ' accumulator array
' convert blocks of 9 digits to binary in 32 bit Ulong
Dim As Ulongint product, carry  ' 64 bit Unsigned Integer
Dim As Integer i, j, k = 1      ' loop counters
For j = 1 To Len( b ) Step 29   ' the blocks to convert
carry = Valulng( "&b" + Mid( b, j, 29 ) ) ' value of 29 bit block
For i = 0 To k  ' Multiply Accumulate,   2^29 = 536870912
product = ( Culngint( acc( i ) ) * 536870912ull ) + carry
acc( i ) = product Mod 1000000000ull    ' sum is low part
carry = product \ 1000000000ull     ' carry is the high part
Next i
If carry Then   ' extend accumulator by one element when needed
k += 1
acc( k ) = carry
End If
Next j  ' accumulator now contains result blocks of base 1 billion
' unpack and return acc as decimal ASCII string
Dim As String txt
For i = n To 0 Step -1
txt += Right( "000000000" + Str( acc( i ) ), 9 )
Next i
Return Ltrim( txt, "0" )
End Function

'=======================================================================
' Convert base ten ASCII decimal string to base two ASCII binary string
'=======================================================================
Function base_10_to_2( Byref num As String ) As String  ' d may be lengthened
dim as string d = num
'================================================
'================================================
dim as string number = d
dim as string str1
dim as longint dec1
do
str1 = str( len(number) / 9 )
dec1 = instr(1,str1,".")
if dec1 <> 0 then number = "0" + number
loop until dec1 = 0
'convert the numeric strings to use pointers
'convert number1
dim as string n1 = string(len(number)*8,chr(0))
dim as ulongint ptr ulp1
ulp1 = cptr(ulongint ptr,strptr(n1))
dim as longint val1
dim as longint len_1 = 0
dim as uinteger a
for a = 0 to len(number)-1 step 9
val1  = (number[a+0]-48)*100000000ull
val1+= (number[a+1]-48)*10000000ull
val1+= (number[a+2]-48)*1000000ull
val1+= (number[a+3]-48)*100000ull
val1+= (number[a+4]-48)*10000ull
val1+= (number[a+5]-48)*1000ull
val1+= (number[a+6]-48)*100ull
val1+= (number[a+7]-48)*10ull
val1+= (number[a+8]-48)*1
*ulp1 = val1
ulp1+=1
len_1+=8
next
number = left(n1,len_1)
n1=""
'================================================
'================================================
Dim As ulongint acc( 0 To len(number) \ 8 )  ' the accumulator array
Dim As Ulongint product, carry  ' 64 bit Unsigned Integer
Dim As Integer k = 1      ' loop counters
dim as ulongint ptr ulp2
ulp1 = cptr(ulongint ptr,strptr(number))
For j as longint = 1 To Len(number)  Step 8     ' the blocks to convert
'carry = Valulng( Mid( d, j, 9 ) ) ' get value of 9 digit block
carry = *ulp1
ulp1+=1
ulp2 = cptr( ulongint ptr , varptr( acc(0) ) )
For i as longint = 0 To k ' Multiply Accumulate
product = culngint( *ulp2  * 1000000000ull ) + carry
*ulp2 = product and 4294967295 ' sum is low order 32 bits
carry = product shr 32 ' carry is the high order 32 bits
ulp2+=1
Next i
If carry Then   ' extend accumulator by one element when needed
k+=1
*ulp2 = carry
End If
Next j  ' accumulator now contains result in packed binary
' unpack and return it as binary ASCII string
Dim As String txt
For i as longint = k to lbound(acc) Step -1
txt+= Bin( acc(i) ,32 )
Next i
Return ltrim( txt , "0")
End Function
'===============================================================================
'===============================================================================
function multiplier_7(byref num1 as string, byref num2 as string) as string

dim as string number1,number2

dim as string int1,frac1,int2,frac2
dim as ulongint dec,dec1,len1,len2
dim as string str1
dim as string sign1,sign2,outsign

number1 = num1
number2 = num2

sign1 = left(number1,1)
if sign1 = "+" or sign1 = "-" then number1 = mid(number1,2) else sign1 = ""

sign2 = left(number2,1)
if sign2 = "+" or sign2 = "-" then number2 = mid(number2,2) else sign2 = ""

if (sign1 = sign2) then outsign = ""
if (sign1 <> sign2) then outsign = "-"

dec = instr(1,number1,".")
if dec > 0 then
int1 = left(number1,dec-1)
frac1 = mid(number1,dec+1)
else
int1 = number1
frac1 = ""
end if

dec = instr(1,number2,".")
if dec > 0 then
int2 = left(number2,dec-1)
frac2 = mid(number2,dec+1)
else
int2 = number2
frac2 = ""
end if

dec = len(frac1)+len(frac2)
number1 = int1+frac1
number2 = int2+frac2

'swap numbers so that bigger number is number1 and smaller is number2
if len(number2) > len(number1) then swap number1,number2
if len(number1) = len(number2) then
if val(left(number2,1)) > val(left(number1,1)) then swap number1,number2
end if

'make numbers equal multiple of 7 bytes
do
str1 = str(len(number1)/7)
dec1 = instr(1,str1,".")
if dec1 <> 0 then number1 = "0" + number1
loop until dec1 = 0
do
str1 = str(len(number2)/7)
dec1 = instr(1,str1,".")
if dec1 <> 0 then number2 = "0" + number2
loop until dec1 = 0

'convert the numeric strings to use pointers
'convert number1
dim as string n1 = string(len(number1)*8,chr(0))
dim as ulongint ptr ulp1
ulp1 = cptr(ulongint ptr,strptr(n1))
dim as longint val1
dim as longint len_1 = 0
dim as uinteger a
for a = 0 to len(number1)-1 step 7
val1 = (number1[a+0]-48)*1000000ull
val1+= (number1[a+1]-48)*100000ull
val1+= (number1[a+2]-48)*10000ull
val1+= (number1[a+3]-48)*1000ull
val1+= (number1[a+4]-48)*100ull
val1+= (number1[a+5]-48)*10ull
val1+= (number1[a+6]-48)*1ull
*ulp1 = val1
ulp1+=1
len_1+=8
next
number1 = left(n1,len_1)
n1=""

'convert the numeric strings to use pointers
'convert number2
dim as string n2 = string(len(number2)*8,chr(0))
dim as ulongint ptr ulp2
ulp2 = cptr(ulongint ptr,strptr(n2))
dim as longint val2
dim as longint len_2 = 0
for a = 0 to len(number2)-1 step 7
val2 = (number2[a+0]-48)*1000000ull
val2+= (number2[a+1]-48)*100000ull
val2+= (number2[a+2]-48)*10000ull
val2+= (number2[a+3]-48)*1000ull
val2+= (number2[a+4]-48)*100ull
val2+= (number2[a+5]-48)*10ull
val2+= (number2[a+6]-48)*1ull
*ulp2 = val2
ulp2+=1
len_2+=8
next
number2 = left(n2,len_2)
n2=""

'create accumulator
answer = string( len(number1) + len(number2) + 8 , chr(0) )
'dimension vars for the mul
dim as longint ptr start1,stop1,start2,stop2 'use longint because the pointers go negative
dim as longint ptr chk_1 , chk_2
dim as longint ptr inc1,inc2
dim as longint ptr outplace
dim as ulongint carry
dim as ulongint total
dim as ulongint blocknumber1 = len(number1)/8
dim as ulongint blocknumber2 = len(number2)/8
dim as ulongint outblocks = len(answer)/8

'set initial accumulator place
outplace = cptr(longint ptr , strptr(answer)) + (outblocks - 1)
'set initial pointers into number1
start1 = cptr(longint ptr , strptr(number1))+(blocknumber1-1)
stop1 =  cptr(longint ptr , strptr(number1))+(blocknumber1-1)
'set initial pointers into number2
start2 = cptr(longint ptr , strptr(number2))+(blocknumber2-1)
stop2 =  cptr(longint ptr , strptr(number2))+(blocknumber2-1)
'set comparison to beg of numbers
chk_1 = cptr( longint ptr , strptr(number1))
chk_2 = cptr( longint ptr , strptr(number2))

'zero the carry
carry = 0

'begin looping thru strings multiplying
do
'set total to zero
total = 0
'we are going to be incrementing thru number2 while decrementing thru number1
'working in opposite directions from start1 to stop1 and start2 to stop2
'inc1 works from right to left in the top number1 string
'inc2 works from start2 to stop 2, in the bottom number2 string, decrementing each loop.
inc1 = start1
inc2 = start2
do
total += *inc1 * *inc2
inc1-= 1
inc2+= 1
loop until inc2 = stop2+1

total = total + carry
carry = total \ 1e7
*outplace = total mod 1e7
'*outplace = imod(total , 1e7)

outplace -= 1

'each loop we need to decrement stop1
'if stop1 goes negative we reset it to zero and decrement stop2
stop1 -= 1
if stop1 < chk_1 then
stop1 += 1
stop2 -=1
if stop2 < chk_2 then stop2+= 1
end if
'each loop we decrement start2 to the left
start2 -= 1
'if start2 goes negative we reset it to zero and decrement start1
'start1 is the rightmost digit of number1 we need to multiply
if start2 < chk_2 then
start2 += 1
start1 -= 1
if start1 < chk_1 then start1+=1
end if

loop until outplace = cptr(ulongint ptr,strptr(answer))+1

'put in the carry at the end
if carry > 0  then *outplace = carry else *outplace = 0

for a as ulongint = 1 to outblocks-1 step 1
val1 = *outplace
outplace +=1
outtext = outtext + right("0000000" + str(val1),7)
next

'put in the decimal point
outtext = left(outtext,len(outtext)-dec) + "." +  mid(outtext,(len(outtext)-dec)+1)
outtext = trim(outtext,"0") 'if multiplying by 1, we have a zero in front.
outtext = outsign + outtext

return outtext

end function

Imortis
Moderator
Posts: 1628
Joined: Jun 02, 2005 15:10
Location: USA
Contact:

### Re: Squares

albert wrote:"!!~~OFF TOPIC~~!!"
...

@albert,
I tried to find a way to reach out to you privately regarding this post, but you don't have a publicly accessible contact. I would have preferred to contact you privately, but I don't have the same access to user info that full Admins have so was unable.

You understand that the above linked post has no purpose here (as you marked it off-topic), and I also think you can understand how it is in-appropriate for this forum. I would like to request that you edit the post to remove the content. If you do not, I can and will do it for you, but would prefer not to.

I would like to request that you keep this kind of post off of the forum. I understand that we are pretty easy going when it comes to off-topic stuff, but this is not the first time in this thread that you have gone off-topic in this particular direction.

I don't want to discourage you from posting here or anywhere else on the forum, but please keep in mind that the purpose of this forum is to discuss the freeBASIC programming language.
albert
Posts: 4952
Joined: Sep 28, 2006 2:41
Location: California, USA

### Re: Squares

@Dodicat
@Richard

I tried and tried but i can't get the following code to step by more than 26 bits..
See mul_26_bit() at bottom of code..

Any ideas????

Code: Select all

Declare Function mul_1_bit( num1 as string , num2 as string ) as string
Declare Function mul_26_bit(byref num1 as string, byref num2 as string) as string

Declare Function multiplier_7( num1 as string, num2 as string) as string

Declare Function base_2_to_10( Byref num As String ) As String    ' b may be lengthened
Declare Function base_10_to_2( Byref num As String ) As String  ' d may be lengthened

Declare Function minus(NUM1 As String,NUM2 As String) As String
Declare Function       plus( NUMber1 As String  ,  NUMber2 As String ) As String

screen 19

dim as double time1 , time2 , time3 , time4

do

dim as longint size = 26

dim as string n1 = ""
for x as longint = 1 to size
n1+= str( int( rnd*2 ) )
next
if left( n1 ,1)  = "0" then mid( n1 , 1 , 1 ) = "1"

dim as string n2 = ""
for x as longint = 1 to size
n2+= str( int( rnd*2 ) )
next
if left( n2 ,1)  = "0" then mid( n2 , 1 , 1 ) = "1"

if len( n2 ) > len( n1 ) then swap n1 , n2

time1=timer
dim as string mul1 = base_2_to_10( n1 )
dim as string mul2 = base_2_to_10( n2 )
dim as string mul_7 = multiplier_7( mul1 , mul2 )
mul_7 = left( mul_7 , len( mul_7 ) - 1 )
mul_7 = base_10_to_2(mul_7)
mul_7 = ltrim( mul_7 , "0")
time2 = timer

time3=timer
dim as string mul_albert = mul_26_bit( n1 , n2 )
time4=timer

dim as string diff = minus( mul_7 , mul_albert)

print
print  "n1  = "  ; n1
print  "n2  = "  ; n2
print  "multiplier_7 = " ; mul_7
print  "mul_1_bit    = " ; mul_albert
print
print  "diff  = " ; diff
print
print "time mul    = " ; time2-time1
print "time albert = "; time4-time3

if diff <> "0" then print "ERROR" : sleep

if inkey = " " then sleep
if inkey = chr(27) then end

loop

END

'==================================================
'==================================================
'begin functions
'==================================================
'==================================================
'===============================================================================
'===============================================================================
'Dodicats plus & Minus functions
'===============================================================================
'===============================================================================
Function plus(_num1 As String,_num2 As String) As String
Dim  ADDQmod(0 To 19) As Ubyte
Dim  ADDbool(0 To 19) As Ubyte
For z As Integer=0 To 19
Next z
Var _flag=0,n_=0
#macro finish()
If _flag=1 Then Swap _num2,_num1
#endmacro
If Len(_num2)>Len(_num1) Then
Swap _num2,_num1
_flag=1
End If
Var diff=Len(_num1)-Len(_num2)
For n_=Len(_num1)-1 To diff Step -1
Next n_
finish()
End If
If n_=-1 Then
finish()
Endif
For n_=n_ To 0 Step -1
Next n_
finish()
End Function
'===============================================================================
'===============================================================================
Function minus(NUM1 As String,NUM2 As String) As String
'Dim As String copyfirstnum=mul_num_1,copysecondnum=mul_num_2
Dim As Byte swapflag
Dim As Long lenf,lens
Dim sign As String * 1
'Dim As String part1,part2
Dim bigger As Byte
'set up tables
Dim As Ubyte Qmod(0 To 19)
Dim bool(0 To 19) As Ubyte

For z As Integer=0 To 19
Qmod(z)=cubyte(z Mod 10+48)
bool(z)=cubyte(-(10>z))
Next z
lenf=Len(NUM1)
lens=Len(NUM2)
#macro compare(numbers)
If Lens>lenf Then bigger= -1:Goto fin
If Lens<lenf Then bigger =0:Goto fin
If NUM2>NUM1 Then
bigger=-1
Else
bigger= 0
End If
fin:
#endmacro

compare(numbers)
If bigger Then
sign="-"
Swap NUM2,NUM1
Swap lens,lenf
swapflag=1
Endif
'lenf=Len(NUM1)
'lens=Len(NUM2)
Dim diff As Long=lenf-lens-Sgn(lenf-lens)
Dim As String one,two,three
three=NUM1
two=String(lenf-lens,"0")+NUM2
one=NUM1
Dim As Long n2
Dim As Ubyte takeaway,subtractcarry
Dim As Ubyte ten=10
'Dim z As Long
subtractcarry=0
Do
For n2=lenf-1 To diff Step -1
takeaway= one[n2]-two[n2]+ten-subtractcarry
three[n2]=Qmod(takeaway)
subtractcarry=bool(takeaway)
Next n2
If subtractcarry=0 Then Exit Do
If n2=-1 Then Exit Do
For n2=n2 To 0 Step -1
takeaway= one[n2]-two[n2]+ten-subtractcarry
three[n2]=Qmod(takeaway)
subtractcarry=bool(takeaway)
Next n2
Exit Do
Loop

three=Ltrim(three,"0")
If three="" Then Return "0"
If swapflag=1 Then Swap NUM1,NUM2

Return sign+three

End Function
'=======================================================================
' Convert base two ASCII binary string to base ten ASCII decimal string
'=======================================================================
Function base_2_to_10( Byref num As String ) As String    ' b may be lengthened
dim as string b = num
' lengthen input string by up to 28 zero bits to make 29 bit blocks
Dim As Integer n = Len( b ) Mod 29
If n Then b = String( 29 - n, "0" ) + b
n = Len( b ) \ 29  ' number of input blocks
Dim As Ulong acc( 0 To n )  ' accumulator array
' convert blocks of 9 digits to binary in 32 bit Ulong
Dim As Ulongint product, carry  ' 64 bit Unsigned Integer
Dim As Integer i, j, k = 1      ' loop counters
For j = 1 To Len( b ) Step 29   ' the blocks to convert
carry = Valulng( "&b" + Mid( b, j, 29 ) ) ' value of 29 bit block
For i = 0 To k  ' Multiply Accumulate,   2^29 = 536870912
product = ( Culngint( acc( i ) ) * 536870912ull ) + carry
acc( i ) = product Mod 1000000000ull    ' sum is low part
carry = product \ 1000000000ull     ' carry is the high part
Next i
If carry Then   ' extend accumulator by one element when needed
k += 1
acc( k ) = carry
End If
Next j  ' accumulator now contains result blocks of base 1 billion
' unpack and return acc as decimal ASCII string
Dim As String txt
For i = n To 0 Step -1
txt += Right( "000000000" + Str( acc( i ) ), 9 )
Next i
Return Ltrim( txt, "0" )
End Function

'=======================================================================
' Convert base ten ASCII decimal string to base two ASCII binary string
'=======================================================================
Function base_10_to_2( Byref num As String ) As String  ' d may be lengthened
dim as string d = num
'================================================
'================================================
dim as string number = d
dim as string str1
dim as longint dec1
do
str1 = str( len(number) / 9 )
dec1 = instr(1,str1,".")
if dec1 <> 0 then number = "0" + number
loop until dec1 = 0
'convert the numeric strings to use pointers
'convert number1
dim as string n1 = string(len(number)*8,chr(0))
dim as ulongint ptr ulp1
ulp1 = cptr(ulongint ptr,strptr(n1))
dim as longint val1
dim as longint len_1 = 0
dim as uinteger a
for a = 0 to len(number)-1 step 9
val1  = (number[a+0]-48)*100000000ull
val1+= (number[a+1]-48)*10000000ull
val1+= (number[a+2]-48)*1000000ull
val1+= (number[a+3]-48)*100000ull
val1+= (number[a+4]-48)*10000ull
val1+= (number[a+5]-48)*1000ull
val1+= (number[a+6]-48)*100ull
val1+= (number[a+7]-48)*10ull
val1+= (number[a+8]-48)*1
*ulp1 = val1
ulp1+=1
len_1+=8
next
number = left(n1,len_1)
n1=""
'================================================
'================================================
Dim As ulongint acc( 0 To len(number) \ 8 )  ' the accumulator array
Dim As Ulongint product, carry  ' 64 bit Unsigned Integer
Dim As Integer k = 1      ' loop counters
dim as ulongint ptr ulp2
ulp1 = cptr(ulongint ptr,strptr(number))
For j as longint = 1 To Len(number)  Step 8     ' the blocks to convert
'carry = Valulng( Mid( d, j, 9 ) ) ' get value of 9 digit block
carry = *ulp1
ulp1+=1
ulp2 = cptr( ulongint ptr , varptr( acc(0) ) )
For i as longint = 0 To k ' Multiply Accumulate
product = culngint( *ulp2  * 1000000000ull ) + carry
*ulp2 = product and 4294967295 ' sum is low order 32 bits
carry = product shr 32 ' carry is the high order 32 bits
ulp2+=1
Next i
If carry Then   ' extend accumulator by one element when needed
k+=1
*ulp2 = carry
End If
Next j  ' accumulator now contains result in packed binary
' unpack and return it as binary ASCII string
Dim As String txt
For i as longint = k to lbound(acc) Step -1
txt+= Bin( acc(i) ,32 )
Next i
Return ltrim( txt , "0")
End Function
'===============================================================================
'===============================================================================
function multiplier_7(byref num1 as string, byref num2 as string) as string

dim as string number1,number2

dim as string int1,frac1,int2,frac2
dim as ulongint dec,dec1,len1,len2
dim as string str1
dim as string sign1,sign2,outsign

number1 = num1
number2 = num2

sign1 = left(number1,1)
if sign1 = "+" or sign1 = "-" then number1 = mid(number1,2) else sign1 = ""

sign2 = left(number2,1)
if sign2 = "+" or sign2 = "-" then number2 = mid(number2,2) else sign2 = ""

if (sign1 = sign2) then outsign = ""
if (sign1 <> sign2) then outsign = "-"

dec = instr(1,number1,".")
if dec > 0 then
int1 = left(number1,dec-1)
frac1 = mid(number1,dec+1)
else
int1 = number1
frac1 = ""
end if

dec = instr(1,number2,".")
if dec > 0 then
int2 = left(number2,dec-1)
frac2 = mid(number2,dec+1)
else
int2 = number2
frac2 = ""
end if

dec = len(frac1)+len(frac2)
number1 = int1+frac1
number2 = int2+frac2

'swap numbers so that bigger number is number1 and smaller is number2
if len(number2) > len(number1) then swap number1,number2
if len(number1) = len(number2) then
if val(left(number2,1)) > val(left(number1,1)) then swap number1,number2
end if

'make numbers equal multiple of 7 bytes
do
str1 = str(len(number1)/7)
dec1 = instr(1,str1,".")
if dec1 <> 0 then number1 = "0" + number1
loop until dec1 = 0
do
str1 = str(len(number2)/7)
dec1 = instr(1,str1,".")
if dec1 <> 0 then number2 = "0" + number2
loop until dec1 = 0

'convert the numeric strings to use pointers
'convert number1
dim as string n1 = string(len(number1)*8,chr(0))
dim as ulongint ptr ulp1
ulp1 = cptr(ulongint ptr,strptr(n1))
dim as longint val1
dim as longint len_1 = 0
dim as uinteger a
for a = 0 to len(number1)-1 step 7
val1 = (number1[a+0]-48)*1000000ull
val1+= (number1[a+1]-48)*100000ull
val1+= (number1[a+2]-48)*10000ull
val1+= (number1[a+3]-48)*1000ull
val1+= (number1[a+4]-48)*100ull
val1+= (number1[a+5]-48)*10ull
val1+= (number1[a+6]-48)*1ull
*ulp1 = val1
ulp1+=1
len_1+=8
next
number1 = left(n1,len_1)
n1=""

'convert the numeric strings to use pointers
'convert number2
dim as string n2 = string(len(number2)*8,chr(0))
dim as ulongint ptr ulp2
ulp2 = cptr(ulongint ptr,strptr(n2))
dim as longint val2
dim as longint len_2 = 0
for a = 0 to len(number2)-1 step 7
val2 = (number2[a+0]-48)*1000000ull
val2+= (number2[a+1]-48)*100000ull
val2+= (number2[a+2]-48)*10000ull
val2+= (number2[a+3]-48)*1000ull
val2+= (number2[a+4]-48)*100ull
val2+= (number2[a+5]-48)*10ull
val2+= (number2[a+6]-48)*1ull
*ulp2 = val2
ulp2+=1
len_2+=8
next
number2 = left(n2,len_2)
n2=""

'create accumulator
answer = string( len(number1) + len(number2) + 8 , chr(0) )
'dimension vars for the mul
dim as longint ptr start1,stop1,start2,stop2 'use longint because the pointers go negative
dim as longint ptr chk_1 , chk_2
dim as longint ptr inc1,inc2
dim as longint ptr outplace
dim as ulongint carry
dim as ulongint total
dim as ulongint blocknumber1 = len(number1)/8
dim as ulongint blocknumber2 = len(number2)/8
dim as ulongint outblocks = len(answer)/8

'set initial accumulator place
outplace = cptr(longint ptr , strptr(answer)) + (outblocks - 1)
'set initial pointers into number1
start1 = cptr(longint ptr , strptr(number1))+(blocknumber1-1)
stop1 =  cptr(longint ptr , strptr(number1))+(blocknumber1-1)
'set initial pointers into number2
start2 = cptr(longint ptr , strptr(number2))+(blocknumber2-1)
stop2 =  cptr(longint ptr , strptr(number2))+(blocknumber2-1)
'set comparison to beg of numbers
chk_1 = cptr( longint ptr , strptr(number1))
chk_2 = cptr( longint ptr , strptr(number2))

'zero the carry
carry = 0

'begin looping thru strings multiplying
do
'set total to zero
total = 0
'we are going to be incrementing thru number2 while decrementing thru number1
'working in opposite directions from start1 to stop1 and start2 to stop2
'inc1 works from right to left in the top number1 string
'inc2 works from start2 to stop 2, in the bottom number2 string, decrementing each loop.
inc1 = start1
inc2 = start2
do
total += *inc1 * *inc2
inc1-= 1
inc2+= 1
loop until inc2 = stop2+1

total = total + carry
carry = total \ 1e7
*outplace = total mod 1e7
'*outplace = imod(total , 1e7)

outplace -= 1

'each loop we need to decrement stop1
'if stop1 goes negative we reset it to zero and decrement stop2
stop1 -= 1
if stop1 < chk_1 then
stop1 += 1
stop2 -=1
if stop2 < chk_2 then stop2+= 1
end if
'each loop we decrement start2 to the left
start2 -= 1
'if start2 goes negative we reset it to zero and decrement start1
'start1 is the rightmost digit of number1 we need to multiply
if start2 < chk_2 then
start2 += 1
start1 -= 1
if start1 < chk_1 then start1+=1
end if

loop until outplace = cptr(ulongint ptr,strptr(answer))+1

'put in the carry at the end
if carry > 0  then *outplace = carry else *outplace = 0

for a as ulongint = 1 to outblocks-1 step 1
val1 = *outplace
outplace +=1
outtext = outtext + right("0000000" + str(val1),7)
next

'put in the decimal point
outtext = left(outtext,len(outtext)-dec) + "." +  mid(outtext,(len(outtext)-dec)+1)
outtext = trim(outtext,"0") 'if multiplying by 1, we have a zero in front.
outtext = outsign + outtext

return outtext

end function
'=======================================================================
'=======================================================================
function mul_1_bit( num1 as string , num2 as string ) as string

dim as string number1 = num1
dim as string number2 = num2

dim as longint size = 1

if len(number1) > len(number2) then number2 = string( len(number1) - len(number2) , "0" ) + number2
if len(number2) > len(number1) then number1 = string( len(number2) - len(number1) , "0" ) + number1
if len(number1) mod size > 0 then number1 = string( ( size - len(number1) mod size ) , "0") + number1
if len(number2) mod size > 0 then number2 = string( ( size - len(number2) mod size ) , "0") + number2

dim as ulongint added( 0 to len(number1)+len(number2) )
dim as longint place_a = ubound(added)

dim as longint start1 = (len(number1)-size)+1
dim as longint stop1 = (len(number1)-size)+1
dim as longint start2 = (len(number2)-size)+1
dim as longint stop2 = (len(number2)-size)+1

dim as longint inc1 , inc2

dim as ulongint total
dim as ulongint carry = 0
dim as longint place = len(number1) + len(number2)
do
total = 0
inc1 = start1
inc2 = start2
do
total+= valulng( mid(number1,inc1,size) )  * valulng( mid(number2,inc2,size) )
inc2 += size
inc1 -= size
loop until inc1 < size

stop1 -= size
if stop1 <= 0 then
stop1+= 1
stop2-= size
if stop2 <= 0 then stop2 += 1
end if
start2 -= size
if start2 <= 0 then
start2 += 1
start1 -= size
if start1 <= 0 then start1 +=1
end if

total+=carry
carry = total \ 2

place_a-=1
place-=size

loop until place < size+1

dim as ulongint val1
next
end function
'===============================================================================
'===============================================================================
'===============================================================================
'===============================================================================
function mul_26_bit(byref num1 as string, byref num2 as string) as string

dim as string number1,number2

number1 = num1
number2 = num2

dim as longint size = 26

if len(number1) mod size > 0 then number1 = string( ( size - len(number1) mod size ) , "0") + number1
if len(number2) mod size > 0 then number2 = string( ( size - len(number2) mod size ) , "0") + number2

'convert the numeric strings to use pointers
'convert number1
dim as string n1 = string(len(number1)*8,chr(0))
dim as ulongint ptr ulp1
ulp1 = cptr(ulongint ptr,strptr(n1))
dim as longint val1
dim as longint len_1 = 0
for a as longint = 1 to len(number1) step size
val1 = valulng("&B" + mid( number1 , a , size ) )
*ulp1 = val1
ulp1+=1
len_1+=8
next
number1 = left(n1,len_1)
n1=""

'convert the numeric strings to use pointers
'convert number2
dim as string n2 = string(len(number2)*8,chr(0))
dim as ulongint ptr ulp2
ulp2 = cptr(ulongint ptr,strptr(n2))
dim as longint val2
dim as longint len_2 = 0
for a as longint = 1 to len(number2) step size
val2 = valulng("&B" + mid( number2 , a , size) )
*ulp2 = val2
ulp2+=1
len_2+=8
next
number2 = left(n2,len_2)
n2=""

'create accumulator
dim as string answer = string( len(number1) + len(number2) , chr(0) )
dim as ulongint outblocks = ( len(answer) \ 8 )
dim as ulongint ptr outplace = cptr(ulongint ptr , strptr(answer)) + (outblocks - 1 )
dim as ulongint stops = ( (len(number1)\8) + (len(number2)\8) )
dim as ulongint value = 0
dim as longint hold = -1
dim as longint locat = 0
dim as longint vals = 0
dim as ulongint high1 = ( len(number1)  \ 8 ) - 1
dim as ulongint high2 = ( len(number2)  \ 8 ) - 1
dim as longint ptr num1_ptr = cptr( ulongint ptr , strptr(number1) ) + high1
dim as longint ptr num2_ptr = cptr( ulongint ptr , strptr(number2) ) + high2
do
hold+=1
vals = hold
locat = 0
if vals > high2 then vals = high2 : locat = (hold - high2)
num1_ptr = cptr( ulongint ptr , strptr(number1) ) + high1 - locat
num2_ptr = cptr( ulongint ptr , strptr(number2) ) + high2 - vals
do
value+= *( num1_ptr ) * *( num2_ptr )
num1_ptr-=1
num2_ptr+=1
if num1_ptr = cptr( ulongint ptr , strptr(number1) ) - 1 then goto done
if num2_ptr > cptr( ulongint ptr , strptr(number2) ) + high2  then goto done
loop
Done:
*outplace = value mod 1e8
outplace-= 1
value = value \ 1e8
loop until hold = stops-2

*outplace = value mod 1e8

dim as string outtext=""
outplace = cptr( ulongint ptr , strptr(answer) )
for a as ulongint = 1 to outblocks step 1
value = *outplace
outplace+=1
outtext+= right("00000000" + str(value),8)
next

outtext = ltrim(outtext,"0")

return bin( valulng( outtext ) )

end function

albert
Posts: 4952
Joined: Sep 28, 2006 2:41
Location: California, USA

### Re: Squares

@Richard

How do you tell if a "size" is too big for a number of digits. overflows a ulongint

I want to make my multiplier , step-size , variable..

Smaller numbers of digits , you can step by bigger sizes.
Larger numbers of digits , you need to step by smaller sizes..

What's the formula to set the size , for different lengths of numbers??
albert
Posts: 4952
Joined: Sep 28, 2006 2:41
Location: California, USA

### Re: Squares

I did a ( shift & add ) mul loop...

I need to speed it up... How would you do a binary adder that steps by 16 or 18 bits??

Code: Select all

Declare Function multiplier_7( num1 as string, num2 as string) as string

Declare Function minus(NUM1 As String,NUM2 As String) As String
Declare Function       plus( NUMber1 As String  ,  NUMber2 As String ) As String

Declare Function base_2_to_10( Byref num As String ) As String    ' b may be lengthened
Declare Function base_10_to_2( Byref num As String ) As String  ' d may be lengthened

Declare Function bin_add( num1 as string , num2 as string ) as string

screen 19

dim as ulongint loops = 0
dim as ulongint correct = 0

dim as double time1 , time2 , time3 , time4

do

loops+=1

dim as longint size = 45

dim as string n1 = ""
for x as longint = 1 to size
n1+= str( int( rnd*2 ) )
next
if left( n1 ,1)  = "0" then mid( n1 , 1 , 1 ) = "1"

dim as string n2 = ""
for x as longint = 1 to size
n2+= str( int( rnd*2 ) )
next
if left( n2 ,1)  = "0" then mid( n2 , 1 , 1 ) = "1"

if len( n2 ) > len( n1 ) then swap n1 , n2

time1=timer
dim as string mul1 = base_2_to_10( n1 )
dim as string mul2 = base_2_to_10( n2 )
dim as string multiplier = multiplier_7( mul1 , mul2 )
multiplier = left( multiplier , len( multiplier) - 1 )
multiplier = base_10_to_2(multiplier)
time2 = timer

'begin ( shift & add ) mul loop
time3 = timer
dim as string result = string( len(n1) + len(n2) ,"0" )
dim as ubyte val1
dim as string shft = ""
for a as longint = len(n2) to 1 step -1
val1 = n2[ a - 1 ]
if val1 = 49 then
shft =  n1 + string( len(n2) - a , "0" )
result = bin_add( result , shft )
end if
next
result = ltrim( result , "0" )
time4 = timer
'end ( shift & add ) mul loop

dim as string diff = minus( multiplier , result )
if diff = "0" then correct+=1

print
print "n1 = " ; n1
print "n2 = " ; n2
print
print "ans = " ; multiplier
print "me  = " ;  result
print
print "diff = " ; diff
print
print "time multiplier_7 = " ; time2 - time1
print "time bin loop     = "; time4 - time3

if diff <> "0" then print "ERROR" : sleep

if inkey = " " then sleep

loop until inkey = chr(27)

sleep
end
'===============================================================================
'===============================================================================
'functions below here
'===============================================================================
'===============================================================================
Function bin_add( num1 as string , num2 as string ) as string

dim as string n2      = num2
dim as string result = num1

dim as ubyte ptr n_2 = cptr( ubyte ptr , strptr( n2 ) + len( n2 ) - 1 )
dim as ubyte ptr res  = cptr( ubyte ptr , strptr( result ) + len(result) - 1 )

dim as ubyte val1
for a as longint = 1 to len(n2)
*res+= (*n_2 - 48)
val1 = *res
if val1 = 50 then *res = 48 : *(res-1) += 1
if val1 = 51 then *res = 49 : *(res-1) += 1
res-= 1
n_2-= 1
next

return result

end function
'===============================================================================
'===============================================================================

'===============================================================================
'===============================================================================
'Dodicats plus & Minus functions
'===============================================================================
'===============================================================================
Function plus(_num1 As String,_num2 As String) As String
Dim  ADDQmod(0 To 19) As Ubyte
Dim  ADDbool(0 To 19) As Ubyte
For z As Integer=0 To 19
Next z
Var _flag=0,n_=0
#macro finish()
If _flag=1 Then Swap _num2,_num1
#endmacro
If Len(_num2)>Len(_num1) Then
Swap _num2,_num1
_flag=1
End If
Var diff=Len(_num1)-Len(_num2)
For n_=Len(_num1)-1 To diff Step -1
Next n_
finish()
End If
If n_=-1 Then
finish()
Endif
For n_=n_ To 0 Step -1
Next n_
finish()
End Function
'===============================================================================
'===============================================================================
Function minus(NUM1 As String,NUM2 As String) As String
'Dim As String copyfirstnum=mul_num_1,copysecondnum=mul_num_2
Dim As Byte swapflag
Dim As Long lenf,lens
Dim sign As String * 1
'Dim As String part1,part2
Dim bigger As Byte
'set up tables
Dim As Ubyte Qmod(0 To 19)
Dim bool(0 To 19) As Ubyte

For z As Integer=0 To 19
Qmod(z)=cubyte(z Mod 10+48)
bool(z)=cubyte(-(10>z))
Next z
lenf=Len(NUM1)
lens=Len(NUM2)
#macro compare(numbers)
If Lens>lenf Then bigger= -1:Goto fin
If Lens<lenf Then bigger =0:Goto fin
If NUM2>NUM1 Then
bigger=-1
Else
bigger= 0
End If
fin:
#endmacro

compare(numbers)
If bigger Then
sign="-"
Swap NUM2,NUM1
Swap lens,lenf
swapflag=1
Endif
'lenf=Len(NUM1)
'lens=Len(NUM2)
Dim diff As Long=lenf-lens-Sgn(lenf-lens)
Dim As String one,two,three
three=NUM1
two=String(lenf-lens,"0")+NUM2
one=NUM1
Dim As Long n2
Dim As Ubyte takeaway,subtractcarry
Dim As Ubyte ten=10
'Dim z As Long
subtractcarry=0
Do
For n2=lenf-1 To diff Step -1
takeaway= one[n2]-two[n2]+ten-subtractcarry
three[n2]=Qmod(takeaway)
subtractcarry=bool(takeaway)
Next n2
If subtractcarry=0 Then Exit Do
If n2=-1 Then Exit Do
For n2=n2 To 0 Step -1
takeaway= one[n2]-two[n2]+ten-subtractcarry
three[n2]=Qmod(takeaway)
subtractcarry=bool(takeaway)
Next n2
Exit Do
Loop

three=Ltrim(three,"0")
If three="" Then Return "0"
If swapflag=1 Then Swap NUM1,NUM2

Return sign+three

End Function
'=======================================================================
' Convert base two ASCII binary string to base ten ASCII decimal string
'=======================================================================
Function base_2_to_10( Byref num As String ) As String    ' b may be lengthened
dim as string b = num
' lengthen input string by up to 28 zero bits to make 29 bit blocks
Dim As Integer n = Len( b ) Mod 29
If n Then b = String( 29 - n, "0" ) + b
n = Len( b ) \ 29  ' number of input blocks
Dim As Ulong acc( 0 To n )  ' accumulator array
' convert blocks of 9 digits to binary in 32 bit Ulong
Dim As Ulongint product, carry  ' 64 bit Unsigned Integer
Dim As Integer i, j, k = 1      ' loop counters
For j = 1 To Len( b ) Step 29   ' the blocks to convert
carry = Valulng( "&b" + Mid( b, j, 29 ) ) ' value of 29 bit block
For i = 0 To k  ' Multiply Accumulate,   2^29 = 536870912
product = ( Culngint( acc( i ) ) * 536870912ull ) + carry
acc( i ) = product Mod 1000000000ull    ' sum is low part
carry = product \ 1000000000ull     ' carry is the high part
Next i
If carry Then   ' extend accumulator by one element when needed
k += 1
acc( k ) = carry
End If
Next j  ' accumulator now contains result blocks of base 1 billion
' unpack and return acc as decimal ASCII string
Dim As String txt
For i = n To 0 Step -1
txt += Right( "000000000" + Str( acc( i ) ), 9 )
Next i
Return Ltrim( txt, "0" )
End Function
'=======================================================================
' Convert base ten ASCII decimal string to base two ASCII binary string
'=======================================================================
Function base_10_to_2( Byref num As String ) As String  ' d may be lengthened
dim as string d = num
'================================================
'================================================
dim as string number = d
dim as string str1
dim as longint dec1
do
str1 = str( len(number) / 9 )
dec1 = instr(1,str1,".")
if dec1 <> 0 then number = "0" + number
loop until dec1 = 0
'convert the numeric strings to use pointers
'convert number1
dim as string n1 = string(len(number)*8,chr(0))
dim as ulongint ptr ulp1
ulp1 = cptr(ulongint ptr,strptr(n1))
dim as longint val1
dim as longint len_1 = 0
dim as uinteger a
for a = 0 to len(number)-1 step 9
val1  = (number[a+0]-48)*100000000ull
val1+= (number[a+1]-48)*10000000ull
val1+= (number[a+2]-48)*1000000ull
val1+= (number[a+3]-48)*100000ull
val1+= (number[a+4]-48)*10000ull
val1+= (number[a+5]-48)*1000ull
val1+= (number[a+6]-48)*100ull
val1+= (number[a+7]-48)*10ull
val1+= (number[a+8]-48)*1
*ulp1 = val1
ulp1+=1
len_1+=8
next
number = left(n1,len_1)
n1=""
'================================================
'================================================
Dim As ulongint acc( 0 To len(number) \ 8 )  ' the accumulator array
Dim As Ulongint product, carry  ' 64 bit Unsigned Integer
Dim As Integer k = 1      ' loop counters
dim as ulongint ptr ulp2
ulp1 = cptr(ulongint ptr,strptr(number))
For j as longint = 1 To Len(number)  Step 8     ' the blocks to convert
'carry = Valulng( Mid( d, j, 9 ) ) ' get value of 9 digit block
carry = *ulp1
ulp1+=1
ulp2 = cptr( ulongint ptr , varptr( acc(0) ) )
For i as longint = 0 To k ' Multiply Accumulate
product = culngint( *ulp2  * 1000000000ull ) + carry
*ulp2 = product and 4294967295 ' sum is low order 32 bits
carry = product shr 32 ' carry is the high order 32 bits
ulp2+=1
Next i
If carry Then   ' extend accumulator by one element when needed
k+=1
*ulp2 = carry
End If
Next j  ' accumulator now contains result in packed binary
' unpack and return it as binary ASCII string
Dim As String txt
For i as longint = k to lbound(acc) Step -1
txt+= Bin( acc(i) ,32 )
Next i
Return ltrim( txt , "0")
End Function
'===============================================================================
'===============================================================================
function multiplier_7(byref num1 as string, byref num2 as string) as string

dim as string number1,number2

dim as string int1,frac1,int2,frac2
dim as ulongint dec,dec1,len1,len2
dim as string str1
dim as string sign1,sign2,outsign

number1 = num1
number2 = num2

sign1 = left(number1,1)
if sign1 = "+" or sign1 = "-" then number1 = mid(number1,2) else sign1 = ""

sign2 = left(number2,1)
if sign2 = "+" or sign2 = "-" then number2 = mid(number2,2) else sign2 = ""

if (sign1 = sign2) then outsign = ""
if (sign1 <> sign2) then outsign = "-"

dec = instr(1,number1,".")
if dec > 0 then
int1 = left(number1,dec-1)
frac1 = mid(number1,dec+1)
else
int1 = number1
frac1 = ""
end if

dec = instr(1,number2,".")
if dec > 0 then
int2 = left(number2,dec-1)
frac2 = mid(number2,dec+1)
else
int2 = number2
frac2 = ""
end if

dec = len(frac1)+len(frac2)
number1 = int1+frac1
number2 = int2+frac2

'swap numbers so that bigger number is number1 and smaller is number2
if len(number2) > len(number1) then swap number1,number2
if len(number1) = len(number2) then
if val(left(number2,1)) > val(left(number1,1)) then swap number1,number2
end if

'make numbers equal multiple of 7 bytes
do
str1 = str(len(number1)/7)
dec1 = instr(1,str1,".")
if dec1 <> 0 then number1 = "0" + number1
loop until dec1 = 0
do
str1 = str(len(number2)/7)
dec1 = instr(1,str1,".")
if dec1 <> 0 then number2 = "0" + number2
loop until dec1 = 0

'convert the numeric strings to use pointers
'convert number1
dim as string n1 = string(len(number1)*8,chr(0))
dim as ulongint ptr ulp1
ulp1 = cptr(ulongint ptr,strptr(n1))
dim as longint val1
dim as longint len_1 = 0
dim as uinteger a
for a = 0 to len(number1)-1 step 7
val1 = (number1[a+0]-48)*1000000ull
val1+= (number1[a+1]-48)*100000ull
val1+= (number1[a+2]-48)*10000ull
val1+= (number1[a+3]-48)*1000ull
val1+= (number1[a+4]-48)*100ull
val1+= (number1[a+5]-48)*10ull
val1+= (number1[a+6]-48)*1ull
*ulp1 = val1
ulp1+=1
len_1+=8
next
number1 = left(n1,len_1)
n1=""

'convert the numeric strings to use pointers
'convert number2
dim as string n2 = string(len(number2)*8,chr(0))
dim as ulongint ptr ulp2
ulp2 = cptr(ulongint ptr,strptr(n2))
dim as longint val2
dim as longint len_2 = 0
for a = 0 to len(number2)-1 step 7
val2 = (number2[a+0]-48)*1000000ull
val2+= (number2[a+1]-48)*100000ull
val2+= (number2[a+2]-48)*10000ull
val2+= (number2[a+3]-48)*1000ull
val2+= (number2[a+4]-48)*100ull
val2+= (number2[a+5]-48)*10ull
val2+= (number2[a+6]-48)*1ull
*ulp2 = val2
ulp2+=1
len_2+=8
next
number2 = left(n2,len_2)
n2=""

'create accumulator
answer = string( len(number1) + len(number2) + 8 , chr(0) )
'dimension vars for the mul
dim as longint ptr start1,stop1,start2,stop2 'use longint because the pointers go negative
dim as longint ptr chk_1 , chk_2
dim as longint ptr inc1,inc2
dim as longint ptr outplace
dim as ulongint carry
dim as ulongint total
dim as ulongint blocknumber1 = len(number1)/8
dim as ulongint blocknumber2 = len(number2)/8
dim as ulongint outblocks = len(answer)/8

'set initial accumulator place
outplace = cptr(longint ptr , strptr(answer)) + (outblocks - 1)
'set initial pointers into number1
start1 = cptr(longint ptr , strptr(number1))+(blocknumber1-1)
stop1 =  cptr(longint ptr , strptr(number1))+(blocknumber1-1)
'set initial pointers into number2
start2 = cptr(longint ptr , strptr(number2))+(blocknumber2-1)
stop2 =  cptr(longint ptr , strptr(number2))+(blocknumber2-1)
'set comparison to beg of numbers
chk_1 = cptr( longint ptr , strptr(number1))
chk_2 = cptr( longint ptr , strptr(number2))

'zero the carry
carry = 0

'begin looping thru strings multiplying
do
'set total to zero
total = 0
'we are going to be incrementing thru number2 while decrementing thru number1
'working in opposite directions from start1 to stop1 and start2 to stop2
'inc1 works from right to left in the top number1 string
'inc2 works from start2 to stop 2, in the bottom number2 string, decrementing each loop.
inc1 = start1
inc2 = start2
do
total += *inc1 * *inc2
inc1-= 1
inc2+= 1
loop until inc2 = stop2+1

total = total + carry
carry = total \ 1e7
*outplace = total mod 1e7
'*outplace = imod(total , 1e7)

outplace -= 1

'each loop we need to decrement stop1
'if stop1 goes negative we reset it to zero and decrement stop2
stop1 -= 1
if stop1 < chk_1 then
stop1 += 1
stop2 -=1
if stop2 < chk_2 then stop2+= 1
end if
'each loop we decrement start2 to the left
start2 -= 1
'if start2 goes negative we reset it to zero and decrement start1
'start1 is the rightmost digit of number1 we need to multiply
if start2 < chk_2 then
start2 += 1
start1 -= 1
if start1 < chk_1 then start1+=1
end if

loop until outplace = cptr(ulongint ptr,strptr(answer))+1

'put in the carry at the end
if carry > 0  then *outplace = carry else *outplace = 0

for a as ulongint = 1 to outblocks-1 step 1
val1 = *outplace
outplace +=1
outtext = outtext + right("0000000" + str(val1),7)
next

'put in the decimal point
outtext = left(outtext,len(outtext)-dec) + "." +  mid(outtext,(len(outtext)-dec)+1)