#cmdline "-gen gcc -Wc -O3"
Function pie(n As Long) As String
Dim As String pi
#macro AddDigit(d)
pi+=Str(d)
#endmacro
Var _len = 20*n\4
Dim As long a(_len),j,i,k
Var nines = 0
Var Digit = 0
For j = 0 To _len-1:a(j) = 2:Next
For j = 1 To n
Var q = 0
For i = _len To 1 Step -1
Var x = 10*a(i-1) + q*i
Var m=(i Shl 1 - 1)
a(i-1) = x Mod m
q= x\m
Next i
a(0) = q Mod 10
q =q \ 10
If q = 9 Then
nines += 1
Else
If q = 10 Then
AddDigit((Digit+1))
If nines > 0 Then
For k = 1 To nines:AddDigit(0):Next
End If
Digit = 0
nines = 0
Else
AddDigit(Digit)
Digit = q
If nines <> 0 Then
For k = 1 To nines:AddDigit(9):Next
nines = 0
End If
End If
End If
Next j
Return "3."+Ltrim(pi,"03")
End Function
function getdecimals(s as string)as long
return len(mid(s,Instr(s,".")+1))
end function
var t=timer
Print pie(102)
print timer-t;" seconds"
'internet pi below
print "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679"
Sleep
dodicat
your function agrees with that of mine, when set to 100 digits of precision it prints
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214807461e+00000
relative error -3.788932442673339572 E-108
That's OK then, all digits are correct.
The problem with asm was expounded by deltarho recently with his random numbers.
I believe he now sticks to gcc optimizing standard basic code, which includes these builtin functions I suppose.
Anyway, thank you srvaldez.
dodicat
I was curious about the performance of your program vs mine, so I ran your program with Print pie(10002)
your time 4.68 seconds
mine was 4.53 seconds with -O2 but with -O3 the time was 2.73 seconds
however if I change the compile command in your program to #cmdline "-arch native -gen clang -Wc -O3" the time is 3.13 seconds
BigFloat-05 has some asm left in it so it won't compile with clang
Hi srvaldez, the algorithm I picked up years ago, It might have been in a pascal forum, I don't remember
I tried to speed it up and made a function out of it, so it is not original code from me, but it is a digit by digit pie.
I always thought it was a bit slow, but with #cmd optimisations it seems to have got a bit faster over the years.
I think that one uses a series type pi.
I have one also using Taylor series for atan.
Neither are digit by digit but an approximation converging within fb double.
#cmdline "-gen gcc -Wc -O3"
function pi as double
Dim As Double eps, Pii, x, y
x = 3
y = 1
Pii = x
eps = 1e-15
While (x > eps)
x = x * y / ((y + 1) * 4)
y += 2
Pii += x / y
Wend
return pii
end function
Function pie As Double
const y_=1.198422490593031e-005,f=262144
Dim As Double xx=y_*y_,term,p=y_,temp1=y_,temp2
Dim As long c=1,counter,sign
Do
c+=2
counter+=1
p*=xx
term=p/c
If (counter And 1) Then sign=-1 Else sign=1
temp2=temp1
temp1+=sign*term
Loop Until temp1=temp2
Return f*temp1
End Function
dim as double p
dim as double t
for k as long=1 to 10
dim as long limit=1000000
t=timer
for n as long=1 to limit
p= Pi
next
print p,timer-t," srvaldez"
t=timer
for n as long=1 to limit
p= Pie
next
print p,timer-t," dodicat"
print
next k
Sleep
