Squares
Re: Squares
@dodicat
The new multiplier is slower than expected... it's a nogo
The new multiplier is slower than expected... it's a nogo
Re: Squares
If your multiplier gives the wrong answer then its a multip-liar
I'm working on as new different one
I'm working on as new different one
Re: Squares
Hello Guys!!
My newest multiplier... only does 7 digits so far. I'm working to make it work with long strings..
My newest multiplier... only does 7 digits so far. I'm working to make it work with long strings..
Code: Select all
screen 19
do
randomize
dim as string num1
for a as longint = 1 to 7 step 1
num1+=str(int(rnd*10))
next
if left(num1,1) = "0" then mid(num1,1,1)=str(int(rnd*9)+1)
'===============================================================================
dim as double n1 = 0
dim as double n2 = 0
dim as ulongint loops = 0
dim as ulongint ans( 1 )
dim as ulongint num( 1 )
num(1) = val(num1)
print num1
do
loops+=1
n1+=1e5
for a as longint = ubound( num ) to 1 step -1
ans(a)+=num(a)*1e5
next
loop until n1 > valulng(num1)-1e5 * 1.25
do
loops+=1
n1+=1e4
for a as longint = ubound( num ) to 1 step -1
ans(a)+=num(a)*1e4
next
loop until n1 > valulng(num1)-1e4 * 1.25
do
loops+=1
n1+=1e3
for a as longint = ubound( num ) to 1 step -1
ans(a)+=num(a)*1e3
next
loop until n1 > valulng(num1)-1e3*1.25
do
loops+=1
n1+=1e2
for a as longint = ubound( num ) to 1 step -1
ans(a)+=num(a)*1e2
next
loop until n1 > valulng(num1)-1e2*1.25
do
loops+=1
n1+=1e1
for a as longint = ubound( num ) to 1 step -1
ans(a)+=num(a)*1e1
next
loop until n1 > valulng(num1)-1e1*1.25
do
loops+=1
n1+=1
for a as longint = ubound( num ) to 1 step -1
ans(a)+=num(a)*1
next
loop until n1 = valulng(num1)
for a as longint = 1 to ubound(ans)
print ans(a) ; " " ;
n2+=ans(a)
n2*=10
next
n2\=10
'===============================================================================
print
locate ,1 : print "num1 = " ; num1
locate ,1 : print "n1 = " ; n1
locate ,1 : print "n1 * n1 = " ; valulng(num1)*valulng(num1)
locate ,1 : print "n2 =" ; n2
locate ,1 : print "loops = " ; loops
print
print "Press a key to continue.."
sleep
loop until inkey = chr(27)
'===============================================================================
sleep
end
Re: Squares
@Dodicat
My newest multiplier.... its 5 times slower than my multiplier_7 at 100x100 digits.
I've got to convert it to use pointers yet..
It currently steps by 1's , I've got to make it step by 7 digits..
My newest multiplier.... its 5 times slower than my multiplier_7 at 100x100 digits.
I've got to convert it to use pointers yet..
It currently steps by 1's , I've got to make it step by 7 digits..
Code: Select all
DECLARE FUNCTION multiplier_7(byref num1 as string, byref 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
screen 19
do
randomize
dim as string num1
for a as longint = 1 to 100 step 1
num1+=str(int(rnd*10))
next
if left(num1,1) = "0" then mid(num1,1,1)=str(int(rnd*9)+1)
dim as string num2
for a as longint = 1 to 100 step 1
num2+=str(int(rnd*10))
next
if left(num2,1) = "0" then mid(num2,1,1)=str(int(rnd*9)+1)
if num2 > num1 then swap num2 , num1
dim as double time1
dim as double time2
dim as double time3
dim as double time4
time1 = timer
'===============================================================================
dim as ulongint n1( 1 to len(num1) )
dim as ulongint n2( 1 to len(num2) )
dim as ulongint ans( 1 to len(num1) + len(num2) )
for a as longint = len(num1) to 1 step -1
n1(a) = val(mid(num1,a,1) )
next
for a as longint = len(num2) to 1 step -1
n2(a) = val(mid(num2,a,1) )
next
dim as ulongint place1 = len(num1)
dim as ulongint place_out = ubound(ans)
dim as ulongint start = len(num1) + len(num2)
dim as ulongint place = 0
for a as longint = place1 to 1 step -1
for b as longint = len(num2) - place to 1 step -1
ans(place_out)+= n1(a) * n2(b)
'print ans(place_out) ; " " ;
place_out-=1
next
place1-=1
start-=1
place_out = start
next
dim as ulongint val1 = 0
dim as ulongint carry = 0
dim as string my_answer
for a as longint = ubound(ans) to 1 step -1
val1 = (ans(a)) + carry
my_answer = str(val1 mod 10) + my_answer
carry = val1 \ 10
next
if carry > 0 then my_answer = str(carry) + my_answer
'===============================================================================
time2 = timer
time3 = timer
dim as string mul_answer = multiplier_7( num1,num2)
mul_answer = left(mul_answer,len(mul_answer)-1)
time4 = timer
dim as string difference = minus( mul_answer , my_answer )
print
locate ,1 : print "num1 = " ; num1
locate ,1 : print "num2 = " ; num2
locate ,1 : print "n1 * n1= " ; mul_answer
locate ,1 : print "answer = " ; my_answer
print
locate ,1 : print "difference = " ; difference
print
locate ,1 : print "new mul time = " ; time2-time1
locate ,1 : print "old mul time = " ; time4-time3
if difference <> "0" then sleep
if inkey = " " then sleep
if inkey = chr(27) then sleep : end
loop until inkey = chr(27)
'===============================================================================
sleep
end
'===============================================================================
'===============================================================================
'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
ADDQmod(z)=(z Mod 10+48)
ADDbool(z)=(-(10<=z))
Next z
Var _flag=0,n_=0
Dim As Ubyte addup=Any,addcarry=Any
#macro finish()
answer=Ltrim(answer,"0")
If _flag=1 Then Swap _num2,_num1
Return answer
#endmacro
If Len(_num2)>Len(_num1) Then
Swap _num2,_num1
_flag=1
End If
Var diff=Len(_num1)-Len(_num2)
Var answer="0"+_num1
addcarry=0
For n_=Len(_num1)-1 To diff Step -1
addup=_num2[n_-diff]+_num1[n_]-96
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
Next n_
If addcarry=0 Then
finish()
End If
If n_=-1 Then
answer[0]=addcarry+48
finish()
Endif
For n_=n_ To 0 Step -1
addup=_num1[n_]-48
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
If addcarry=0 Then Exit For
Next n_
answer[0]=addcarry+48
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
'===============================================================================
'===============================================================================
function multiplier_7(byref num1 as string, byref num2 as string) as string
dim as string number1,number2
dim as string answer,outtext
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
'convert answer back to ascii
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)
'trim leading zeros
outtext = trim(outtext,"0") 'if multiplying by 1, we have a zero in front.
outtext = outsign + outtext
return outtext
end function
'===============================================================================
'===============================================================================
Re: Squares
@Dodicat
Here it is stepping by 7's with pointers...100,000 x 100,000 digits.
It's a No Go, it's twice as slow as multiplier_7
Here it is stepping by 7's with pointers...100,000 x 100,000 digits.
It's a No Go, it's twice as slow as multiplier_7
Code: Select all
DECLARE FUNCTION multiplier_7(byref num1 as string, byref 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
screen 19
do
randomize
dim as string num1
for a as longint = 1 to 100000 step 1
num1+=str(int(rnd*10))
next
if left(num1,1) = "0" then mid(num1,1,1)=str(int(rnd*9)+1)
dim as string num2
for a as longint = 1 to 100000 step 1
num2+=str(int(rnd*10))
next
if left(num2,1) = "0" then mid(num2,1,1)=str(int(rnd*9)+1)
if num2 > num1 then swap num2 , num1
dim as double time1
dim as double time2
dim as double time3
dim as double time4
time1 = timer
'===============================================================================
dim as string str1
dim as ulongint dec1
do
str1 = str(len(num1)/7)
dec1=instr(1,str1,".")
if dec1 <> 0 then num1 = "0" + num1
loop until dec1=0
do
str1 = str(len(num2)/7)
dec1=instr(1,str1,".")
if dec1 <> 0 then num2 = "0" + num2
loop until dec1=0
dim as ulongint n1( 1 to len(num1) \ 7 )
dim as ulongint n2( 1 to len(num2) \ 7 )
dim as ulongint ele
ele = ubound(n1)
for a as longint = len(num1)-6 to 1 step -7
n1(ele) = val(mid(num1,a,7) )
ele-=1
next
ele = ubound(n2)
for a as longint = len(num2) -6 to 1 step -7
n2(ele) = val(mid(num2,a,7) )
ele-=1
next
dim as ulongint ans( 1 to ubound(n1) + ubound(n2) )
dim as ulongint place1 = ubound(n1)
dim as ulongint place_out = ubound(ans)
dim as ulongint start = ubound(ans)
dim as ulongint place = 0
for a as ulongint ptr = cptr( ulongint ptr , varptr(n1(ubound(n1))) ) to cptr(ulongint ptr , varptr((n1(1))) ) step -1
for b as ulongint ptr = cptr( ulongint ptr , varptr(n2(ubound(n2))) ) to cptr(ulongint ptr , varptr((n2(1))) ) step -1
ans(place_out)+= *a * *b
place_out-=1
next
place1-=1
start-=1
place_out = start
next
dim as ulongint val1 = 0
dim as ulongint carry = 0
dim as string my_answer
for a as longint = ubound(ans) to 1 step -1
val1 = (ans(a)) + carry
my_answer = right( "0000000" + str(val1 mod 1e7),7) + my_answer
carry = val1 \ 1e7
next
if carry > 0 then my_answer = str(carry) + my_answer
'===============================================================================
time2 = timer
time3 = timer
dim as string mul_answer = multiplier_7( num1,num2)
mul_answer = left(mul_answer,len(mul_answer)-1)
time4 = timer
dim as string difference = minus( mul_answer , my_answer )
print
locate ,1 : print "num1 = " ; num1
locate ,1 : print "num2 = " ; num2
locate ,1 : print "n1 * n1= " ; mul_answer
locate ,1 : print "answer = " ; my_answer
print
locate ,1 : print "difference = " ; difference
print
locate ,1 : print "new mul time = " ; time2-time1
locate ,1 : print "old mul time = " ; time4-time3
if difference <> "0" then sleep
if inkey = " " then sleep
if inkey = chr(27) then sleep : end
loop until inkey = chr(27)
'===============================================================================
sleep
end
'===============================================================================
'===============================================================================
'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
ADDQmod(z)=(z Mod 10+48)
ADDbool(z)=(-(10<=z))
Next z
Var _flag=0,n_=0
Dim As Ubyte addup=Any,addcarry=Any
#macro finish()
answer=Ltrim(answer,"0")
If _flag=1 Then Swap _num2,_num1
Return answer
#endmacro
If Len(_num2)>Len(_num1) Then
Swap _num2,_num1
_flag=1
End If
Var diff=Len(_num1)-Len(_num2)
Var answer="0"+_num1
addcarry=0
For n_=Len(_num1)-1 To diff Step -1
addup=_num2[n_-diff]+_num1[n_]-96
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
Next n_
If addcarry=0 Then
finish()
End If
If n_=-1 Then
answer[0]=addcarry+48
finish()
Endif
For n_=n_ To 0 Step -1
addup=_num1[n_]-48
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
If addcarry=0 Then Exit For
Next n_
answer[0]=addcarry+48
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
'===============================================================================
'===============================================================================
function multiplier_7(byref num1 as string, byref num2 as string) as string
dim as string number1,number2
dim as string answer,outtext
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
'convert answer back to ascii
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)
'trim leading zeros
outtext = trim(outtext,"0") 'if multiplying by 1, we have a zero in front.
outtext = outsign + outtext
return outtext
end function
'===============================================================================
'===============================================================================
Re: Squares
@Dodicat
I figured one thing out...
On a rectangle to figure the area, how ever you manipulate one side you have to do the opposite to the other side...
if you divide one side by 10 then you have to multiply the other side by 10..etc..
if you double one side , then you have to half the other side..
I figured one thing out...
On a rectangle to figure the area, how ever you manipulate one side you have to do the opposite to the other side...
if you divide one side by 10 then you have to multiply the other side by 10..etc..
if you double one side , then you have to half the other side..
Re: Squares
Well found !
So if the rectangle area a, is side length x, times side length y;
a = x * y
You found the area does not change if you use; a = (x*c) * (y/c)
Because; a = x*c * y/c
so; a = x * y * c/c
and; c/c must = 1;
But only so long as c <> 0.
So if the rectangle area a, is side length x, times side length y;
a = x * y
You found the area does not change if you use; a = (x*c) * (y/c)
Because; a = x*c * y/c
so; a = x * y * c/c
and; c/c must = 1;
But only so long as c <> 0.
Re: Squares
Thanks Albert.
About one second difference foe 100000 digits.
Regarding your rectangle, If a shape was drawn on the rectangle and the rectangle was re-shaped as you have described, keeping it's area the same, would the area of the shape remain the same?
Within the limits of integer pixels:
About one second difference foe 100000 digits.
Regarding your rectangle, If a shape was drawn on the rectangle and the rectangle was re-shaped as you have described, keeping it's area the same, would the area of the shape remain the same?
Within the limits of integer pixels:
Code: Select all
'resize an image
Function resize(im As Any Ptr,Wdth As Single,Hght As Single,dx As Long=0,dy As Long=0) As Any Ptr
#define putpixel(_x,_y,colour) *Cptr(Ulong Ptr,rowS+ (_y)*pitchS+ (_x) Shl 2) =(colour)
#define _getpixel(_x,_y) *Cptr(Ulong Ptr,row + (_y)*pitch + (_x) Shl 2)
#define map(a,b,x,c,d) ((d)-(c))*((x)-(a))\((b)-(a))+(c)
Static As Integer pitch,pitchs
Static As Any Ptr row,rowS
Static As Ulong Ptr pixel,pixels
Static As Integer ddx,ddy,resultx,resulty
Imageinfo im,ddx,ddy,,pitch,row
Dim As Any Ptr im2=Imagecreate(Wdth-dx,Hght-dy)
Imageinfo im2,,,,pitchS,rowS
For y As Long=0+dy To Hght-1 -dy
resulty=map(0,Hght,y,0,ddy)
For x As Long=0+dx To Wdth-1 -dx
resultx=map(0,Wdth,x,0,ddx)
putpixel(x,y,_getpixel(resultx,resulty))
Next x
Next y
Return im2
End Function
'count the pixels in the shape
Function getshapearea(i As Any Ptr) As Single
Dim As integer ctr,w,h
Imageinfo i,w,h
For x As Long=0 To w
For y As Long=0 To h
If Point(x,y,i)=Rgb(200,0,0) Then ctr+=1
Next
Next
Return ctr
End Function
'average of 10 shape areas
Function average(a() As String) As Double
Dim As Double av
For n As Long=Lbound(a) To Ubound(a)
av+=Val(a(n))
Next
Return av/Ubound(a)
End Function
'keep a record of 10 areas
Sub updatehistory(a() As String,nxt As String)
For n As Long=Lbound(a) To Ubound(a)-1
a(n)=a(n+1)
Next
a(Ubound(a))=nxt
End Sub
'screen display of history
Sub showhistory(a() As String,row As Long,col As Long)
Locate row,col
Print "Shape Area history"
For n As Long=Lbound(a) To Ubound(a)
Locate ,col
If Len(a(n)) Then Print a(n)
Next
Print
If a(Lbound(a))<>"" Then
Locate row+12,col
Print "History average"
Locate ,col
Print str(average(a()))
End If
End Sub
'draw a filled pentagon
Sub pentagon(cx As Long,cy As Long,size As Long,col As Ulong,im As Any Ptr)
Dim As Double pi=4*Atn(1),start=pi/10
Var count=0,rad=0.0,px=0.0,py=0.0
For z As Single=start To 2*pi+.01+start Step 2*pi/10
count=count+1
If count Mod 2=0 Then rad=size Else rad=.4*size
px=cx+rad*Cos(z)
py=cy+rad*Sin(z)
If count=1 Then Pset im,(px,py)Else Line im,-(px,py),col
Next z
Paint im,(cx,cy),col,col
End Sub
'================= =============
Dim As String history(1 To 10)
Screen 20,32
'first rectangle (a square)
Dim As double side1=400
Dim As double side2=400
Dim As Any Ptr i=Imagecreate(side1,side2,Rgb(0,100,255))
'draw a shape to i
pentagon(200,220,190,Rgb(200,0,0),i)
Put(30,40),i
Draw String(0,0),"Rect Area = " &(side1*side2)
Dim As Long area=getshapearea(i)
Draw String(0,20),"Shape Area = " &area
updatehistory(history(),Str(Area))
showhistory(history(),23,70)
print "press a key"
Sleep
Dim As double k
Do
Cls
Do
k=Rnd
Loop Until k>.5
'Albert's change
dim as double newside1=side1*k
dim as double newside2=side2/k
If Rnd>.5 Then Swap newside1,newside2
dim as any ptr i2=resize(i,newside1,newside2)
Put(20,40),i2
Draw String(0,0),"Rect Area = " &(newside1*newside2)
Area=getshapearea(i2)
Draw String(0,20),"Shape Area = " &area
updatehistory(history(),Str(Area))
showhistory(history(),23,70)
Sleep
imagedestroy i2
Loop Until Inkey=Chr(27)
imagedestroy i
Re: Squares
I'm working on manipulating the two sides x , y
adding doesn't work!!
If you add 1 to one side and subtract 1 from the other side , it doesn't work..
It should be the worlds fastest multiplier.. If i get it working , i'm gonna call it the Nobel Multiplier.
(!!~~OFF TOPIC~~!!)
I wrote a new song
chorus = "do you got a hole for me nuts" and "She ate me nuts fast"
( Genre = Pop )
( Title = Eight Minutes Fast )
( entry music )
do you got a whole four minutes?
she eight minutes fast
i got to check the time again
while we just have ourselves a blast
caught up in the ever after
i watch the minute hand go round
a twenty one a bunny run
dig a hole and hide from the sun
and another seven minutes
a twenty eight the bunny's ate
it's time to dig another hole
get headed for the pearly gate
( music )
do you got a whole four minutes?
she eight minutes fast
i got to check the time again
while we just have ourselves a blast
watching the hand of the second
as the minute is counting down
got a thirty and bo dirty
its like downtown and twice as round
and in another two minutes
a thirty two a purty jew
it's time for the marry-go-round
and the diamond shines pink and blue
( music )
do you got a whole four minutes?
she eight minutes fast
i got to check the time again
while we just have ourselves a blast
and the minute hand keeps ticking
goind around around and round
a thirty eight a purty ate
never mind if it ain't your fate
and in just another minute
a thirty nine a purty fine
and your feeling all so happy
the funny things we make with time
( music )
do you got a whole four minutes?
she eight minutes fast
i got to check the time again
while we just have ourselves a blast
( music )
do you got a whole four minutes?
she eight minutes fast
i got to check the time again
while we just have ourselves a blast
( exit music )
albert_redditt@yahoo.com
Albert Redditt
315 W. Carrillo St. #104
Santa Barbara, Ca. 93101 U.S.A.
adding doesn't work!!
If you add 1 to one side and subtract 1 from the other side , it doesn't work..
It should be the worlds fastest multiplier.. If i get it working , i'm gonna call it the Nobel Multiplier.
(!!~~OFF TOPIC~~!!)
I wrote a new song
chorus = "do you got a hole for me nuts" and "She ate me nuts fast"
( Genre = Pop )
( Title = Eight Minutes Fast )
( entry music )
do you got a whole four minutes?
she eight minutes fast
i got to check the time again
while we just have ourselves a blast
caught up in the ever after
i watch the minute hand go round
a twenty one a bunny run
dig a hole and hide from the sun
and another seven minutes
a twenty eight the bunny's ate
it's time to dig another hole
get headed for the pearly gate
( music )
do you got a whole four minutes?
she eight minutes fast
i got to check the time again
while we just have ourselves a blast
watching the hand of the second
as the minute is counting down
got a thirty and bo dirty
its like downtown and twice as round
and in another two minutes
a thirty two a purty jew
it's time for the marry-go-round
and the diamond shines pink and blue
( music )
do you got a whole four minutes?
she eight minutes fast
i got to check the time again
while we just have ourselves a blast
and the minute hand keeps ticking
goind around around and round
a thirty eight a purty ate
never mind if it ain't your fate
and in just another minute
a thirty nine a purty fine
and your feeling all so happy
the funny things we make with time
( music )
do you got a whole four minutes?
she eight minutes fast
i got to check the time again
while we just have ourselves a blast
( music )
do you got a whole four minutes?
she eight minutes fast
i got to check the time again
while we just have ourselves a blast
( exit music )
albert_redditt@yahoo.com
Albert Redditt
315 W. Carrillo St. #104
Santa Barbara, Ca. 93101 U.S.A.
Re: Squares
I got it working with added and subtracted values!!
what ever you add to one side , you have to subtract from the other side
Then you have to square the value added and subtracted , and add it to the n1*n2 :
answer = ( n1 * n2 ) + ( added * added )
Press space to stop scrolling
Press space to stop ten press esc to exit
what ever you add to one side , you have to subtract from the other side
Then you have to square the value added and subtracted , and add it to the n1*n2 :
answer = ( n1 * n2 ) + ( added * added )
Press space to stop scrolling
Press space to stop ten press esc to exit
Code: Select all
DECLARE FUNCTION multiplier_7(byref num1 as string, byref 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 half(fl As String) As String
declare function divide(as string,as string,as integer,as string ="s") as string
screen 19
do
randomize
dim as string num1
for a as longint = 1 to 2 step 1
num1+=str(int(rnd*10))
next
if left(num1,1) = "0" then mid(num1,1,1)=str(int(rnd*9)+1)
dim as double time1
dim as double time2
dim as double time3
dim as double time4
time1 = timer
'===============================================================================
dim as double n1 = val(num1)
dim as double n2 = val(num1)
dim as double add
do
if n1 mod 100 = 0 then exit do
n1+=1
n2-=1
add+=1
loop until n1 mod 100 = 0 or n2 <= 2
dim as longint answer = (n1*n2) + (add*add) 'add the squared multiplied added and subtracted value
print n1
print n2
print answer
dim as string my_answer = str(answer)
'===============================================================================
time2 = timer
time3 = timer
dim as string mul_answer = multiplier_7( num1,num1)
mul_answer = left(mul_answer,len(mul_answer)-1)
time4 = timer
dim as string difference = minus( mul_answer , my_answer )
print
locate ,1 : print "num1 = " ; num1
'locate ,1 : print "num2 = " ; num2
locate ,1 : print "n1 * n2 = " ; mul_answer
locate ,1 : print "answer = " ; my_answer
print
locate ,1 : print "difference = " ; difference
print
locate ,1 : print "new mul time = " ; time2-time1
locate ,1 : print "old mul time = " ; time4-time3
if difference <> "0" then sleep
if inkey = " " then sleep
if inkey = chr(27) then sleep : end
loop until inkey = chr(27)
'===============================================================================
sleep
end
'==================================================
'==================================================
Function divide(n1 As String,n2 As String,decimal_places As integer,dpflag As String="s") As String
Dim As String number=n1,divisor=n2
dpflag=lcase(dpflag)
'For MOD
dim as integer modstop
if dpflag="mod" then
if len(n1)<len(n2) then return n1
if len(n1)=len(n2) then
if n1<n2 then return n1
end if
modstop=len(n1)-len(n2)+1
end if
if dpflag<>"mod" then
If dpflag<>"s" Then dpflag="raw"
end if
Dim runcount As integer
'_______ LOOK UP TABLES ______________
Dim Qmod(0 To 19) As Ubyte
Dim bool(0 To 19) As Ubyte
For z As Integer=0 To 19
Qmod(z)=(z Mod 10+48)
bool(z)=(-(10>z))
Next z
Dim answer As String 'THE ANSWER STRING
'_______ SET THE DECIMAL WHERE IT SHOULD BE AT _______
Dim As String part1,part2
#macro set(decimal)
#macro insert(s,char,position)
If position > 0 And position <=Len(s) Then
part1=Mid$(s,1,position-1)
part2=Mid$(s,position)
s=part1+char+part2
End if
#endmacro
insert(answer,".",decpos)
answer=thepoint+zeros+answer
If dpflag="raw" Then
answer=Mid(answer,1,decimal_places)
End if
#endmacro
'______________________________________________
'__________ SPLIT A STRING ABOUT A CHARACTRR __________
Dim As String var1,var2
Dim pst As integer
#macro split(stri,char,var1,var2)
pst=Instr(stri,char)
var1="":var2=""
If pst<>0 Then
var1=Rtrim(Mid(stri,1,pst),".")
var2=Ltrim(Mid(stri,pst),".")
Else
var1=stri
End if
#endmacro
#macro Removepoint(s)
split(s,".",var1,var2)
#endmacro
'__________ GET THE SIGN AND CLEAR THE -ve __________________
Dim sign As String
If Left(number,1)="-" Xor Left (divisor,1)="-" Then sign="-"
If Left(number,1)="-" Then number=Ltrim(number,"-")
If Left (divisor,1)="-" Then divisor=Ltrim(divisor,"-")
'DETERMINE THE DECIMAL POSITION BEFORE THE DIVISION
Dim As integer lennint,lenddec,lend,lenn,difflen
split(number,".",var1,var2)
lennint=Len(var1)
split(divisor,".",var1,var2)
lenddec=Len(var2)
If Instr(number,".") Then
Removepoint(number)
number=var1+var2
End if
If Instr(divisor,".") Then
Removepoint(divisor)
divisor=var1+var2
End if
Dim As integer numzeros
numzeros=Len(number)
number=Ltrim(number,"0"):divisor=Ltrim (divisor,"0")
numzeros=numzeros-Len(number)
lend=Len(divisor):lenn=Len(number)
If lend>lenn Then difflen=lend-lenn
Dim decpos As integer=lenddec+lennint-lend+2-numzeros 'THE POSITION INDICATOR
Dim _sgn As Byte=-Sgn(decpos)
If _sgn=0 Then _sgn=1
Dim As String thepoint=String(_sgn,".") 'DECIMAL AT START (IF)
Dim As String zeros=String(-decpos+1,"0")'ZEROS AT START (IF) e.g. .0009
if dpflag<>"mod" then
If Len(zeros) =0 Then dpflag="s"
end if
Dim As integer runlength
If Len(zeros) Then
runlength=decimal_places
answer=String(Len(zeros)+runlength+10,"0")
If dpflag="raw" Then
runlength=1
answer=String(Len(zeros)+runlength+10,"0")
If decimal_places>Len(zeros) Then
runlength=runlength+(decimal_places-Len(zeros))
answer=String(Len(zeros)+runlength+10,"0")
End If
End If
Else
decimal_places=decimal_places+decpos
runlength=decimal_places
answer=String(Len(zeros)+runlength+10,"0")
End if
'___________DECIMAL POSITION DETERMINED _____________
'SET UP THE VARIABLES AND START UP CONDITIONS
number=number+String(difflen+decimal_places,"0")
Dim count As integer
Dim temp As String
Dim copytemp As String
Dim topstring As String
Dim copytopstring As String
Dim As integer lenf,lens
Dim As Ubyte takeaway,subtractcarry
Dim As integer n3,diff
If Ltrim(divisor,"0")="" Then Return "Error :division by zero"
lens=Len(divisor)
topstring=Left(number,lend)
copytopstring=topstring
Do
count=0
Do
count=count+1
copytemp=temp
Do
'___________________ QUICK SUBTRACTION loop _________________
lenf=Len(topstring)
If lens<lenf=0 Then 'not
If Lens>lenf Then
temp= "done"
Exit Do
End if
If divisor>topstring Then
temp= "done"
Exit Do
End if
End if
diff=lenf-lens
temp=topstring
subtractcarry=0
For n3=lenf-1 To diff Step -1
takeaway= topstring[n3]-divisor[n3-diff]+10-subtractcarry
temp[n3]=Qmod(takeaway)
subtractcarry=bool(takeaway)
Next n3
If subtractcarry=0 Then Exit Do
If n3=-1 Then Exit Do
For n3=n3 To 0 Step -1
takeaway= topstring[n3]-38-subtractcarry
temp[n3]=Qmod(takeaway)
subtractcarry=bool(takeaway)
if subtractcarry=0 then exit do
Next n3
Exit Do
Loop 'single run
temp=Ltrim(temp,"0")
If temp="" Then temp= "0"
topstring=temp
Loop Until temp="done"
' INDIVIDUAL CHARACTERS CARVED OFF ________________
runcount=runcount+1
If count=1 Then
topstring=copytopstring+Mid(number,lend+runcount,1)
Else
topstring=copytemp+Mid(number,lend+runcount,1)
End If
copytopstring=topstring
topstring=Ltrim(topstring,"0")
if dpflag="mod" then
if runcount=modstop then
if topstring="" then return "0"
return mid(topstring,1,len(topstring)-1)
end if
end if
answer[runcount-1]=count+47
If topstring="" And runcount>Len(n1)+1 Then
Exit Do
End if
Loop Until runcount=runlength+1
' END OF RUN TO REQUIRED DECIMAL PLACES
set(decimal) 'PUT IN THE DECIMAL POINT
'THERE IS ALWAYS A DECIMAL POINT SOMEWHERE IN THE ANSWER
'NOW GET RID OF IT IF IT IS REDUNDANT
answer=Rtrim(answer,"0")
answer=Rtrim(answer,".")
answer=Ltrim(answer,"0")
If answer="" Then Return "0"
Return sign+answer
End Function
'===============================================================================
'===============================================================================
Function half(fl As String) As String
Dim As Ubyte main,carry,temp
Dim As String sign , s
If Instr(fl,".")=0 Then s=fl+".0" Else s=fl+"0"
If Instr(s,"-") Then sign="-":s=Ltrim(s,"-")
Dim As String ans=s
For z As Integer=0 To Len(s)-1
If s[z]<>46 Then
temp=(s[z]-48+carry)
main=temp Shr 1
carry=(temp And 1) Shl 3 +(temp And 1) Shl 1
ans[z]=main+48
End If
Next z
If Instr(ans,".") Then ans=Rtrim(ans,"0")
ans=Rtrim(ans,".")
ans=Ltrim(ans,"0")
Return ans
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
ADDQmod(z)=(z Mod 10+48)
ADDbool(z)=(-(10<=z))
Next z
Var _flag=0,n_=0
Dim As Ubyte addup=Any,addcarry=Any
#macro finish()
answer=Ltrim(answer,"0")
If _flag=1 Then Swap _num2,_num1
Return answer
#endmacro
If Len(_num2)>Len(_num1) Then
Swap _num2,_num1
_flag=1
End If
Var diff=Len(_num1)-Len(_num2)
Var answer="0"+_num1
addcarry=0
For n_=Len(_num1)-1 To diff Step -1
addup=_num2[n_-diff]+_num1[n_]-96
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
Next n_
If addcarry=0 Then
finish()
End If
If n_=-1 Then
answer[0]=addcarry+48
finish()
Endif
For n_=n_ To 0 Step -1
addup=_num1[n_]-48
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
If addcarry=0 Then Exit For
Next n_
answer[0]=addcarry+48
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
'===============================================================================
'===============================================================================
function multiplier_7(byref num1 as string, byref num2 as string) as string
dim as string number1,number2
dim as string answer,outtext
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
'convert answer back to ascii
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)
'trim leading zeros
outtext = trim(outtext,"0") 'if multiplying by 1, we have a zero in front.
outtext = outsign + outtext
return outtext
end function
'===============================================================================
'===============================================================================
Re: Squares
That works for squares when n1 = n2, but what about when n1 <> n2 ?Albert wrote: I got it working with added and subtracted values!!
what ever you add to one side , you have to subtract from the other side
Then you have to square the value added and subtracted , and add it to the n1*n2 :
answer = ( n1 * n2 ) + ( added * added )
Should it then something more like; answer = ( n1 * n2 ) + ( added * ( added + n1 – n2 ) ) ?
Re: Squares
@Richard
It doesn't work, the added value you have to square is as big as the number.. so you might just as well multiply the two numbers.
It doesn't work, the added value you have to square is as big as the number.. so you might just as well multiply the two numbers.
Re: Squares
@Richard
I got it working with the two number being different...
dim as double n1 = val( "1" + string(len(num1),"0") )
dim as double n2 = val(num2) / (n1 / val(num1) )
dim as ulongint answer = ( n1 * n2 )
I got it working with the two number being different...
dim as double n1 = val( "1" + string(len(num1),"0") )
dim as double n2 = val(num2) / (n1 / val(num1) )
dim as ulongint answer = ( n1 * n2 )
Code: Select all
DECLARE FUNCTION multiplier_7(byref num1 as string, byref 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 half(fl As String) As String
declare function divide(as string,as string,as integer,as string ="s") as string
screen 19
do
randomize
dim as string num1
for a as longint = 1 to 2 step 1
num1+=str(int(rnd*10))
next
if left(num1,1) = "0" then mid(num1,1,1)=str(int(rnd*9)+1)
dim as string num2
for a as longint = 1 to 2 step 1
num2+=str(int(rnd*10))
next
if left(num2,1) = "0" then mid(num2,1,1)=str(int(rnd*9)+1)
if len(num2) > len(num1) then swap num1,num2
if len(num2) = len(num1) then if val(left(num2,1)) > val(left(num1,1)) then swap num1,num2
dim as double time1
dim as double time2
dim as double time3
dim as double time4
time1 = timer
'===============================================================================
dim as double n1 = val( "1" + string(len(num1),"0") )
dim as double n2 = val(num2) / (n1 / val(num1) )
dim as ulongint answer = ( n1 * n2 )
print n1
print n2
'print add
print answer
dim as string my_answer = str(answer)
'===============================================================================
time2 = timer
time3 = timer
dim as string mul_answer = multiplier_7( num1,num2)
mul_answer = left(mul_answer,len(mul_answer)-1)
time4 = timer
dim as string difference = minus( mul_answer , my_answer )
print
locate ,1 : print "num1 = " ; num1
locate ,1 : print "num2 = " ; num2
locate ,1 : print "n1 * n2 = " ; mul_answer
locate ,1 : print "answer = " ; my_answer
print
locate ,1 : print "difference = " ; difference
print
locate ,1 : print "new mul time = " ; time2-time1
locate ,1 : print "old mul time = " ; time4-time3
if difference <> "0" then sleep
if inkey = " " then sleep
if inkey = chr(27) then sleep : end
loop until inkey = chr(27)
'===============================================================================
sleep
end
'==================================================
'==================================================
Function divide(n1 As String,n2 As String,decimal_places As integer,dpflag As String="s") As String
Dim As String number=n1,divisor=n2
dpflag=lcase(dpflag)
'For MOD
dim as integer modstop
if dpflag="mod" then
if len(n1)<len(n2) then return n1
if len(n1)=len(n2) then
if n1<n2 then return n1
end if
modstop=len(n1)-len(n2)+1
end if
if dpflag<>"mod" then
If dpflag<>"s" Then dpflag="raw"
end if
Dim runcount As integer
'_______ LOOK UP TABLES ______________
Dim Qmod(0 To 19) As Ubyte
Dim bool(0 To 19) As Ubyte
For z As Integer=0 To 19
Qmod(z)=(z Mod 10+48)
bool(z)=(-(10>z))
Next z
Dim answer As String 'THE ANSWER STRING
'_______ SET THE DECIMAL WHERE IT SHOULD BE AT _______
Dim As String part1,part2
#macro set(decimal)
#macro insert(s,char,position)
If position > 0 And position <=Len(s) Then
part1=Mid$(s,1,position-1)
part2=Mid$(s,position)
s=part1+char+part2
End if
#endmacro
insert(answer,".",decpos)
answer=thepoint+zeros+answer
If dpflag="raw" Then
answer=Mid(answer,1,decimal_places)
End if
#endmacro
'______________________________________________
'__________ SPLIT A STRING ABOUT A CHARACTRR __________
Dim As String var1,var2
Dim pst As integer
#macro split(stri,char,var1,var2)
pst=Instr(stri,char)
var1="":var2=""
If pst<>0 Then
var1=Rtrim(Mid(stri,1,pst),".")
var2=Ltrim(Mid(stri,pst),".")
Else
var1=stri
End if
#endmacro
#macro Removepoint(s)
split(s,".",var1,var2)
#endmacro
'__________ GET THE SIGN AND CLEAR THE -ve __________________
Dim sign As String
If Left(number,1)="-" Xor Left (divisor,1)="-" Then sign="-"
If Left(number,1)="-" Then number=Ltrim(number,"-")
If Left (divisor,1)="-" Then divisor=Ltrim(divisor,"-")
'DETERMINE THE DECIMAL POSITION BEFORE THE DIVISION
Dim As integer lennint,lenddec,lend,lenn,difflen
split(number,".",var1,var2)
lennint=Len(var1)
split(divisor,".",var1,var2)
lenddec=Len(var2)
If Instr(number,".") Then
Removepoint(number)
number=var1+var2
End if
If Instr(divisor,".") Then
Removepoint(divisor)
divisor=var1+var2
End if
Dim As integer numzeros
numzeros=Len(number)
number=Ltrim(number,"0"):divisor=Ltrim (divisor,"0")
numzeros=numzeros-Len(number)
lend=Len(divisor):lenn=Len(number)
If lend>lenn Then difflen=lend-lenn
Dim decpos As integer=lenddec+lennint-lend+2-numzeros 'THE POSITION INDICATOR
Dim _sgn As Byte=-Sgn(decpos)
If _sgn=0 Then _sgn=1
Dim As String thepoint=String(_sgn,".") 'DECIMAL AT START (IF)
Dim As String zeros=String(-decpos+1,"0")'ZEROS AT START (IF) e.g. .0009
if dpflag<>"mod" then
If Len(zeros) =0 Then dpflag="s"
end if
Dim As integer runlength
If Len(zeros) Then
runlength=decimal_places
answer=String(Len(zeros)+runlength+10,"0")
If dpflag="raw" Then
runlength=1
answer=String(Len(zeros)+runlength+10,"0")
If decimal_places>Len(zeros) Then
runlength=runlength+(decimal_places-Len(zeros))
answer=String(Len(zeros)+runlength+10,"0")
End If
End If
Else
decimal_places=decimal_places+decpos
runlength=decimal_places
answer=String(Len(zeros)+runlength+10,"0")
End if
'___________DECIMAL POSITION DETERMINED _____________
'SET UP THE VARIABLES AND START UP CONDITIONS
number=number+String(difflen+decimal_places,"0")
Dim count As integer
Dim temp As String
Dim copytemp As String
Dim topstring As String
Dim copytopstring As String
Dim As integer lenf,lens
Dim As Ubyte takeaway,subtractcarry
Dim As integer n3,diff
If Ltrim(divisor,"0")="" Then Return "Error :division by zero"
lens=Len(divisor)
topstring=Left(number,lend)
copytopstring=topstring
Do
count=0
Do
count=count+1
copytemp=temp
Do
'___________________ QUICK SUBTRACTION loop _________________
lenf=Len(topstring)
If lens<lenf=0 Then 'not
If Lens>lenf Then
temp= "done"
Exit Do
End if
If divisor>topstring Then
temp= "done"
Exit Do
End if
End if
diff=lenf-lens
temp=topstring
subtractcarry=0
For n3=lenf-1 To diff Step -1
takeaway= topstring[n3]-divisor[n3-diff]+10-subtractcarry
temp[n3]=Qmod(takeaway)
subtractcarry=bool(takeaway)
Next n3
If subtractcarry=0 Then Exit Do
If n3=-1 Then Exit Do
For n3=n3 To 0 Step -1
takeaway= topstring[n3]-38-subtractcarry
temp[n3]=Qmod(takeaway)
subtractcarry=bool(takeaway)
if subtractcarry=0 then exit do
Next n3
Exit Do
Loop 'single run
temp=Ltrim(temp,"0")
If temp="" Then temp= "0"
topstring=temp
Loop Until temp="done"
' INDIVIDUAL CHARACTERS CARVED OFF ________________
runcount=runcount+1
If count=1 Then
topstring=copytopstring+Mid(number,lend+runcount,1)
Else
topstring=copytemp+Mid(number,lend+runcount,1)
End If
copytopstring=topstring
topstring=Ltrim(topstring,"0")
if dpflag="mod" then
if runcount=modstop then
if topstring="" then return "0"
return mid(topstring,1,len(topstring)-1)
end if
end if
answer[runcount-1]=count+47
If topstring="" And runcount>Len(n1)+1 Then
Exit Do
End if
Loop Until runcount=runlength+1
' END OF RUN TO REQUIRED DECIMAL PLACES
set(decimal) 'PUT IN THE DECIMAL POINT
'THERE IS ALWAYS A DECIMAL POINT SOMEWHERE IN THE ANSWER
'NOW GET RID OF IT IF IT IS REDUNDANT
answer=Rtrim(answer,"0")
answer=Rtrim(answer,".")
answer=Ltrim(answer,"0")
If answer="" Then Return "0"
Return sign+answer
End Function
'===============================================================================
'===============================================================================
Function half(fl As String) As String
Dim As Ubyte main,carry,temp
Dim As String sign , s
If Instr(fl,".")=0 Then s=fl+".0" Else s=fl+"0"
If Instr(s,"-") Then sign="-":s=Ltrim(s,"-")
Dim As String ans=s
For z As Integer=0 To Len(s)-1
If s[z]<>46 Then
temp=(s[z]-48+carry)
main=temp Shr 1
carry=(temp And 1) Shl 3 +(temp And 1) Shl 1
ans[z]=main+48
End If
Next z
If Instr(ans,".") Then ans=Rtrim(ans,"0")
ans=Rtrim(ans,".")
ans=Ltrim(ans,"0")
Return ans
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
ADDQmod(z)=(z Mod 10+48)
ADDbool(z)=(-(10<=z))
Next z
Var _flag=0,n_=0
Dim As Ubyte addup=Any,addcarry=Any
#macro finish()
answer=Ltrim(answer,"0")
If _flag=1 Then Swap _num2,_num1
Return answer
#endmacro
If Len(_num2)>Len(_num1) Then
Swap _num2,_num1
_flag=1
End If
Var diff=Len(_num1)-Len(_num2)
Var answer="0"+_num1
addcarry=0
For n_=Len(_num1)-1 To diff Step -1
addup=_num2[n_-diff]+_num1[n_]-96
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
Next n_
If addcarry=0 Then
finish()
End If
If n_=-1 Then
answer[0]=addcarry+48
finish()
Endif
For n_=n_ To 0 Step -1
addup=_num1[n_]-48
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
If addcarry=0 Then Exit For
Next n_
answer[0]=addcarry+48
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
'===============================================================================
'===============================================================================
function multiplier_7(byref num1 as string, byref num2 as string) as string
dim as string number1,number2
dim as string answer,outtext
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
'convert answer back to ascii
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)
'trim leading zeros
outtext = trim(outtext,"0") 'if multiplying by 1, we have a zero in front.
outtext = outsign + outtext
return outtext
end function
'===============================================================================
'===============================================================================
Re: Squares
Hi Guys!!
I got it working with strings and Dodicat's divider.
Here it is multiplying 100 x100 digits.. it's several hundred times slower..
I got it working with strings and Dodicat's divider.
Here it is multiplying 100 x100 digits.. it's several hundred times slower..
Code: Select all
DECLARE FUNCTION multiplier_7(byref num1 as string, byref 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 half(fl As String) As String
declare function divide(as string,as string,as integer,as string ="s") as string
screen 19
do
randomize
dim as string num1
for a as longint = 1 to 100 step 1
num1+=str(int(rnd*10))
next
if left(num1,1) = "0" then mid(num1,1,1)=str(int(rnd*9)+1)
dim as string num2
for a as longint = 1 to 100 step 1
num2+=str(int(rnd*10))
next
if left(num2,1) = "0" then mid(num2,1,1)=str(int(rnd*9)+1)
if len(num2) > len(num1) then swap num1,num2
if len(num2) = len(num1) then if val(left(num2,1)) > val(left(num1,1)) then swap num1,num2
dim as double time1
dim as double time2
dim as double time3
dim as double time4
time1 = timer
'===============================================================================
dim as string n1 = "1" + string(len(num1),"0")
'dim as double n2 = val(num2) / (n1 / val(num1) )
dim as string div = divide( n1 , num1 , len(num1) + len(num2) )
dim as string n2 = divide( num2 , div , len(num1) + len(num2) )
dim as string answer = n2 + mid( n1 , 2 )
dim as longint dec1 = instr( answer , "." )
answer = left( answer , dec1-1 ) + mid( answer , dec1+1 , len(n1)-1 )
print n1
print n2
print answer
dim as string my_answer = answer
'===============================================================================
time2 = timer
time3 = timer
dim as string mul_answer = multiplier_7( num1,num2)
mul_answer = left(mul_answer,len(mul_answer)-1)
time4 = timer
dim as string difference = minus( mul_answer , my_answer )
print
locate ,1 : print "num1 = " ; num1
locate ,1 : print "num2 = " ; num2
locate ,1 : print "n1 * n2 = " ; mul_answer
locate ,1 : print "answer = " ; my_answer
print
locate ,1 : print "difference = " ; difference
print
locate ,1 : print "new mul time = " ; time2-time1
locate ,1 : print "old mul time = " ; time4-time3
if difference <> "0" then sleep
if inkey = " " then sleep
if inkey = chr(27) then sleep : end
loop until inkey = chr(27)
'===============================================================================
sleep
end
'==================================================
'==================================================
Function divide(n1 As String,n2 As String,decimal_places As integer,dpflag As String="s") As String
Dim As String number=n1,divisor=n2
dpflag=lcase(dpflag)
'For MOD
dim as integer modstop
if dpflag="mod" then
if len(n1)<len(n2) then return n1
if len(n1)=len(n2) then
if n1<n2 then return n1
end if
modstop=len(n1)-len(n2)+1
end if
if dpflag<>"mod" then
If dpflag<>"s" Then dpflag="raw"
end if
Dim runcount As integer
'_______ LOOK UP TABLES ______________
Dim Qmod(0 To 19) As Ubyte
Dim bool(0 To 19) As Ubyte
For z As Integer=0 To 19
Qmod(z)=(z Mod 10+48)
bool(z)=(-(10>z))
Next z
Dim answer As String 'THE ANSWER STRING
'_______ SET THE DECIMAL WHERE IT SHOULD BE AT _______
Dim As String part1,part2
#macro set(decimal)
#macro insert(s,char,position)
If position > 0 And position <=Len(s) Then
part1=Mid$(s,1,position-1)
part2=Mid$(s,position)
s=part1+char+part2
End if
#endmacro
insert(answer,".",decpos)
answer=thepoint+zeros+answer
If dpflag="raw" Then
answer=Mid(answer,1,decimal_places)
End if
#endmacro
'______________________________________________
'__________ SPLIT A STRING ABOUT A CHARACTRR __________
Dim As String var1,var2
Dim pst As integer
#macro split(stri,char,var1,var2)
pst=Instr(stri,char)
var1="":var2=""
If pst<>0 Then
var1=Rtrim(Mid(stri,1,pst),".")
var2=Ltrim(Mid(stri,pst),".")
Else
var1=stri
End if
#endmacro
#macro Removepoint(s)
split(s,".",var1,var2)
#endmacro
'__________ GET THE SIGN AND CLEAR THE -ve __________________
Dim sign As String
If Left(number,1)="-" Xor Left (divisor,1)="-" Then sign="-"
If Left(number,1)="-" Then number=Ltrim(number,"-")
If Left (divisor,1)="-" Then divisor=Ltrim(divisor,"-")
'DETERMINE THE DECIMAL POSITION BEFORE THE DIVISION
Dim As integer lennint,lenddec,lend,lenn,difflen
split(number,".",var1,var2)
lennint=Len(var1)
split(divisor,".",var1,var2)
lenddec=Len(var2)
If Instr(number,".") Then
Removepoint(number)
number=var1+var2
End if
If Instr(divisor,".") Then
Removepoint(divisor)
divisor=var1+var2
End if
Dim As integer numzeros
numzeros=Len(number)
number=Ltrim(number,"0"):divisor=Ltrim (divisor,"0")
numzeros=numzeros-Len(number)
lend=Len(divisor):lenn=Len(number)
If lend>lenn Then difflen=lend-lenn
Dim decpos As integer=lenddec+lennint-lend+2-numzeros 'THE POSITION INDICATOR
Dim _sgn As Byte=-Sgn(decpos)
If _sgn=0 Then _sgn=1
Dim As String thepoint=String(_sgn,".") 'DECIMAL AT START (IF)
Dim As String zeros=String(-decpos+1,"0")'ZEROS AT START (IF) e.g. .0009
if dpflag<>"mod" then
If Len(zeros) =0 Then dpflag="s"
end if
Dim As integer runlength
If Len(zeros) Then
runlength=decimal_places
answer=String(Len(zeros)+runlength+10,"0")
If dpflag="raw" Then
runlength=1
answer=String(Len(zeros)+runlength+10,"0")
If decimal_places>Len(zeros) Then
runlength=runlength+(decimal_places-Len(zeros))
answer=String(Len(zeros)+runlength+10,"0")
End If
End If
Else
decimal_places=decimal_places+decpos
runlength=decimal_places
answer=String(Len(zeros)+runlength+10,"0")
End if
'___________DECIMAL POSITION DETERMINED _____________
'SET UP THE VARIABLES AND START UP CONDITIONS
number=number+String(difflen+decimal_places,"0")
Dim count As integer
Dim temp As String
Dim copytemp As String
Dim topstring As String
Dim copytopstring As String
Dim As integer lenf,lens
Dim As Ubyte takeaway,subtractcarry
Dim As integer n3,diff
If Ltrim(divisor,"0")="" Then Return "Error :division by zero"
lens=Len(divisor)
topstring=Left(number,lend)
copytopstring=topstring
Do
count=0
Do
count=count+1
copytemp=temp
Do
'___________________ QUICK SUBTRACTION loop _________________
lenf=Len(topstring)
If lens<lenf=0 Then 'not
If Lens>lenf Then
temp= "done"
Exit Do
End if
If divisor>topstring Then
temp= "done"
Exit Do
End if
End if
diff=lenf-lens
temp=topstring
subtractcarry=0
For n3=lenf-1 To diff Step -1
takeaway= topstring[n3]-divisor[n3-diff]+10-subtractcarry
temp[n3]=Qmod(takeaway)
subtractcarry=bool(takeaway)
Next n3
If subtractcarry=0 Then Exit Do
If n3=-1 Then Exit Do
For n3=n3 To 0 Step -1
takeaway= topstring[n3]-38-subtractcarry
temp[n3]=Qmod(takeaway)
subtractcarry=bool(takeaway)
if subtractcarry=0 then exit do
Next n3
Exit Do
Loop 'single run
temp=Ltrim(temp,"0")
If temp="" Then temp= "0"
topstring=temp
Loop Until temp="done"
' INDIVIDUAL CHARACTERS CARVED OFF ________________
runcount=runcount+1
If count=1 Then
topstring=copytopstring+Mid(number,lend+runcount,1)
Else
topstring=copytemp+Mid(number,lend+runcount,1)
End If
copytopstring=topstring
topstring=Ltrim(topstring,"0")
if dpflag="mod" then
if runcount=modstop then
if topstring="" then return "0"
return mid(topstring,1,len(topstring)-1)
end if
end if
answer[runcount-1]=count+47
If topstring="" And runcount>Len(n1)+1 Then
Exit Do
End if
Loop Until runcount=runlength+1
' END OF RUN TO REQUIRED DECIMAL PLACES
set(decimal) 'PUT IN THE DECIMAL POINT
'THERE IS ALWAYS A DECIMAL POINT SOMEWHERE IN THE ANSWER
'NOW GET RID OF IT IF IT IS REDUNDANT
answer=Rtrim(answer,"0")
answer=Rtrim(answer,".")
answer=Ltrim(answer,"0")
If answer="" Then Return "0"
Return sign+answer
End Function
'===============================================================================
'===============================================================================
Function half(fl As String) As String
Dim As Ubyte main,carry,temp
Dim As String sign , s
If Instr(fl,".")=0 Then s=fl+".0" Else s=fl+"0"
If Instr(s,"-") Then sign="-":s=Ltrim(s,"-")
Dim As String ans=s
For z As Integer=0 To Len(s)-1
If s[z]<>46 Then
temp=(s[z]-48+carry)
main=temp Shr 1
carry=(temp And 1) Shl 3 +(temp And 1) Shl 1
ans[z]=main+48
End If
Next z
If Instr(ans,".") Then ans=Rtrim(ans,"0")
ans=Rtrim(ans,".")
ans=Ltrim(ans,"0")
Return ans
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
ADDQmod(z)=(z Mod 10+48)
ADDbool(z)=(-(10<=z))
Next z
Var _flag=0,n_=0
Dim As Ubyte addup=Any,addcarry=Any
#macro finish()
answer=Ltrim(answer,"0")
If _flag=1 Then Swap _num2,_num1
Return answer
#endmacro
If Len(_num2)>Len(_num1) Then
Swap _num2,_num1
_flag=1
End If
Var diff=Len(_num1)-Len(_num2)
Var answer="0"+_num1
addcarry=0
For n_=Len(_num1)-1 To diff Step -1
addup=_num2[n_-diff]+_num1[n_]-96
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
Next n_
If addcarry=0 Then
finish()
End If
If n_=-1 Then
answer[0]=addcarry+48
finish()
Endif
For n_=n_ To 0 Step -1
addup=_num1[n_]-48
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
If addcarry=0 Then Exit For
Next n_
answer[0]=addcarry+48
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
'===============================================================================
'===============================================================================
function multiplier_7(byref num1 as string, byref num2 as string) as string
dim as string number1,number2
dim as string answer,outtext
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
'convert answer back to ascii
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)
'trim leading zeros
outtext = trim(outtext,"0") 'if multiplying by 1, we have a zero in front.
outtext = outsign + outtext
return outtext
end function
'===============================================================================
'===============================================================================
Last edited by albert on Jul 24, 2018 22:33, edited 1 time in total.
Re: Squares
I decided to work on a faster divider...
Heres my first attempt..
I got to make it to work with strings yet..
@Dodicat
Can you make your 1-9 divider in reverse , where you divide 1 to 9 by a value , instead of dividing a value by 1 to 9?
Heres my first attempt..
I got to make it to work with strings yet..
@Dodicat
Can you make your 1-9 divider in reverse , where you divide 1 to 9 by a value , instead of dividing a value by 1 to 9?
Code: Select all
DECLARE FUNCTION multiplier_7(byref num1 as string, byref 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 half(fl As String) As String
declare function divide(as string,as string,as integer,as string ="s") as string
screen 19
do
randomize
dim as string num1
for a as longint = 1 to 10 step 1
num1+=str(int(rnd*10))
next
if left(num1,1) = "0" then mid(num1,1,1)=str(int(rnd*9)+1)
dim as string num2
for a as longint = 1 to 10 step 1
num2+=str(int(rnd*10))
next
if left(num2,1) = "0" then mid(num2,1,1)=str(int(rnd*9)+1)
if len(num2) > len(num1) then swap num1,num2
if len(num2) = len(num1) then if val(left(num2,1)) > val(left(num1,1)) then swap num1,num2
dim as double time1
dim as double time2
dim as double time3
dim as double time4
time1 = timer
'===============================================================================
dim as double answer = 0
dim as string n1 = num1
dim as string n2 = num2
dim as ulongint value = 0
for a as longint = 1 to len(num1) step 1
value = val(mid(num1,a,1))
answer+= value / val(n2)
answer*=10
next
answer/=10
print n1
print n2
print answer
dim as string my_answer = left( str(answer) , len(num1)+len(num2)+1 )
if left( my_answer, 1) = "0" then my_answer = mid(my_answer,2)
'===============================================================================
time2 = timer
time3 = timer
dim as string div_answer = divide( num1,num2, len(num1)+len(num2)+1)
time4 = timer
dim as string difference = minus( div_answer , my_answer )
print
locate ,1 : print "num1 = " ; num1
locate ,1 : print "num2 = " ; num2
locate ,1 : print "n1 / n2 = " ; div_answer
locate ,1 : print "answer = " ; my_answer
print
locate ,1 : print "difference = " ; difference
print
locate ,1 : print "new mul time = " ; time2-time1
locate ,1 : print "old mul time = " ; time4-time3
if difference <> "0" then sleep
if inkey = " " then sleep
if inkey = chr(27) then sleep : end
loop until inkey = chr(27)
'===============================================================================
sleep
end
'==================================================
'==================================================
Function divide(n1 As String,n2 As String,decimal_places As integer,dpflag As String="s") As String
Dim As String number=n1,divisor=n2
dpflag=lcase(dpflag)
'For MOD
dim as integer modstop
if dpflag="mod" then
if len(n1)<len(n2) then return n1
if len(n1)=len(n2) then
if n1<n2 then return n1
end if
modstop=len(n1)-len(n2)+1
end if
if dpflag<>"mod" then
If dpflag<>"s" Then dpflag="raw"
end if
Dim runcount As integer
'_______ LOOK UP TABLES ______________
Dim Qmod(0 To 19) As Ubyte
Dim bool(0 To 19) As Ubyte
For z As Integer=0 To 19
Qmod(z)=(z Mod 10+48)
bool(z)=(-(10>z))
Next z
Dim answer As String 'THE ANSWER STRING
'_______ SET THE DECIMAL WHERE IT SHOULD BE AT _______
Dim As String part1,part2
#macro set(decimal)
#macro insert(s,char,position)
If position > 0 And position <=Len(s) Then
part1=Mid$(s,1,position-1)
part2=Mid$(s,position)
s=part1+char+part2
End if
#endmacro
insert(answer,".",decpos)
answer=thepoint+zeros+answer
If dpflag="raw" Then
answer=Mid(answer,1,decimal_places)
End if
#endmacro
'______________________________________________
'__________ SPLIT A STRING ABOUT A CHARACTRR __________
Dim As String var1,var2
Dim pst As integer
#macro split(stri,char,var1,var2)
pst=Instr(stri,char)
var1="":var2=""
If pst<>0 Then
var1=Rtrim(Mid(stri,1,pst),".")
var2=Ltrim(Mid(stri,pst),".")
Else
var1=stri
End if
#endmacro
#macro Removepoint(s)
split(s,".",var1,var2)
#endmacro
'__________ GET THE SIGN AND CLEAR THE -ve __________________
Dim sign As String
If Left(number,1)="-" Xor Left (divisor,1)="-" Then sign="-"
If Left(number,1)="-" Then number=Ltrim(number,"-")
If Left (divisor,1)="-" Then divisor=Ltrim(divisor,"-")
'DETERMINE THE DECIMAL POSITION BEFORE THE DIVISION
Dim As integer lennint,lenddec,lend,lenn,difflen
split(number,".",var1,var2)
lennint=Len(var1)
split(divisor,".",var1,var2)
lenddec=Len(var2)
If Instr(number,".") Then
Removepoint(number)
number=var1+var2
End if
If Instr(divisor,".") Then
Removepoint(divisor)
divisor=var1+var2
End if
Dim As integer numzeros
numzeros=Len(number)
number=Ltrim(number,"0"):divisor=Ltrim (divisor,"0")
numzeros=numzeros-Len(number)
lend=Len(divisor):lenn=Len(number)
If lend>lenn Then difflen=lend-lenn
Dim decpos As integer=lenddec+lennint-lend+2-numzeros 'THE POSITION INDICATOR
Dim _sgn As Byte=-Sgn(decpos)
If _sgn=0 Then _sgn=1
Dim As String thepoint=String(_sgn,".") 'DECIMAL AT START (IF)
Dim As String zeros=String(-decpos+1,"0")'ZEROS AT START (IF) e.g. .0009
if dpflag<>"mod" then
If Len(zeros) =0 Then dpflag="s"
end if
Dim As integer runlength
If Len(zeros) Then
runlength=decimal_places
answer=String(Len(zeros)+runlength+10,"0")
If dpflag="raw" Then
runlength=1
answer=String(Len(zeros)+runlength+10,"0")
If decimal_places>Len(zeros) Then
runlength=runlength+(decimal_places-Len(zeros))
answer=String(Len(zeros)+runlength+10,"0")
End If
End If
Else
decimal_places=decimal_places+decpos
runlength=decimal_places
answer=String(Len(zeros)+runlength+10,"0")
End if
'___________DECIMAL POSITION DETERMINED _____________
'SET UP THE VARIABLES AND START UP CONDITIONS
number=number+String(difflen+decimal_places,"0")
Dim count As integer
Dim temp As String
Dim copytemp As String
Dim topstring As String
Dim copytopstring As String
Dim As integer lenf,lens
Dim As Ubyte takeaway,subtractcarry
Dim As integer n3,diff
If Ltrim(divisor,"0")="" Then Return "Error :division by zero"
lens=Len(divisor)
topstring=Left(number,lend)
copytopstring=topstring
Do
count=0
Do
count=count+1
copytemp=temp
Do
'___________________ QUICK SUBTRACTION loop _________________
lenf=Len(topstring)
If lens<lenf=0 Then 'not
If Lens>lenf Then
temp= "done"
Exit Do
End if
If divisor>topstring Then
temp= "done"
Exit Do
End if
End if
diff=lenf-lens
temp=topstring
subtractcarry=0
For n3=lenf-1 To diff Step -1
takeaway= topstring[n3]-divisor[n3-diff]+10-subtractcarry
temp[n3]=Qmod(takeaway)
subtractcarry=bool(takeaway)
Next n3
If subtractcarry=0 Then Exit Do
If n3=-1 Then Exit Do
For n3=n3 To 0 Step -1
takeaway= topstring[n3]-38-subtractcarry
temp[n3]=Qmod(takeaway)
subtractcarry=bool(takeaway)
if subtractcarry=0 then exit do
Next n3
Exit Do
Loop 'single run
temp=Ltrim(temp,"0")
If temp="" Then temp= "0"
topstring=temp
Loop Until temp="done"
' INDIVIDUAL CHARACTERS CARVED OFF ________________
runcount=runcount+1
If count=1 Then
topstring=copytopstring+Mid(number,lend+runcount,1)
Else
topstring=copytemp+Mid(number,lend+runcount,1)
End If
copytopstring=topstring
topstring=Ltrim(topstring,"0")
if dpflag="mod" then
if runcount=modstop then
if topstring="" then return "0"
return mid(topstring,1,len(topstring)-1)
end if
end if
answer[runcount-1]=count+47
If topstring="" And runcount>Len(n1)+1 Then
Exit Do
End if
Loop Until runcount=runlength+1
' END OF RUN TO REQUIRED DECIMAL PLACES
set(decimal) 'PUT IN THE DECIMAL POINT
'THERE IS ALWAYS A DECIMAL POINT SOMEWHERE IN THE ANSWER
'NOW GET RID OF IT IF IT IS REDUNDANT
answer=Rtrim(answer,"0")
answer=Rtrim(answer,".")
answer=Ltrim(answer,"0")
If answer="" Then Return "0"
Return sign+answer
End Function
'===============================================================================
'===============================================================================
Function half(fl As String) As String
Dim As Ubyte main,carry,temp
Dim As String sign , s
If Instr(fl,".")=0 Then s=fl+".0" Else s=fl+"0"
If Instr(s,"-") Then sign="-":s=Ltrim(s,"-")
Dim As String ans=s
For z As Integer=0 To Len(s)-1
If s[z]<>46 Then
temp=(s[z]-48+carry)
main=temp Shr 1
carry=(temp And 1) Shl 3 +(temp And 1) Shl 1
ans[z]=main+48
End If
Next z
If Instr(ans,".") Then ans=Rtrim(ans,"0")
ans=Rtrim(ans,".")
ans=Ltrim(ans,"0")
Return ans
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
ADDQmod(z)=(z Mod 10+48)
ADDbool(z)=(-(10<=z))
Next z
Var _flag=0,n_=0
Dim As Ubyte addup=Any,addcarry=Any
#macro finish()
answer=Ltrim(answer,"0")
If _flag=1 Then Swap _num2,_num1
Return answer
#endmacro
If Len(_num2)>Len(_num1) Then
Swap _num2,_num1
_flag=1
End If
Var diff=Len(_num1)-Len(_num2)
Var answer="0"+_num1
addcarry=0
For n_=Len(_num1)-1 To diff Step -1
addup=_num2[n_-diff]+_num1[n_]-96
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
Next n_
If addcarry=0 Then
finish()
End If
If n_=-1 Then
answer[0]=addcarry+48
finish()
Endif
For n_=n_ To 0 Step -1
addup=_num1[n_]-48
answer[n_+1]=ADDQmod(addup+addcarry)
addcarry=ADDbool(addup+addcarry)
If addcarry=0 Then Exit For
Next n_
answer[0]=addcarry+48
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
'===============================================================================
'===============================================================================
function multiplier_7(byref num1 as string, byref num2 as string) as string
dim as string number1,number2
dim as string answer,outtext
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
'convert answer back to ascii
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)
'trim leading zeros
outtext = trim(outtext,"0") 'if multiplying by 1, we have a zero in front.
outtext = outsign + outtext
return outtext
end function
'===============================================================================
'===============================================================================