Pi: Difference between revisions
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=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
<syntaxhighlight lang="basic">10 REM ADOPTED FROM COMMODORE BASIC
20 N = 100: REM N MAY BE INCREASED, BUT WILL SLOW EXECUTION
Line 700:
3.14159265358979323846264338327950288419716939937510582097494459230781...
</pre>
==={{header|Chipmunk Basic}}===
{{works with|Chipmunk Basic|3.6.4}}
{{works with|Applesoft BASIC}}
{{works with|MSX_BASIC}}
{{works with|QBasic}}
{{trans|Applesoft BASIC}}
<syntaxhighlight lang="qbasic">100 REM adopted from Applesoft BASIC
110 n = 100 : rem n may be increased, but will slow execution
120 ln = int(10*n/3)+16
130 nd = 1
140 dim a(ln)
150 n9 = 0
160 pd = 0 : rem First pre-digit is a 0
170 rem
180 for j = 1 to ln
190 a(j-1) = 2 : rem Start wirh 2S
200 next j
210 rem
220 for j = 1 to n
230 q = 0
240 for i = ln to 1 step -1 : rem Work backwards
250 x = 10*a(i-1)+q*i
260 a(i-1) = x-(2*i-1)*int(x/(2*i-1)) : rem X - Int ( X / Y) * Y
270 q = int(x/(2*i-1))
280 next i
290 a(0) = q-10*int(q/10)
300 q = int(q/10)
310 if q = 9 then n9 = n9+1 : goto 510
320 if q <> 10 then goto 440
330 rem Q == 10
340 d = pd+1 : gosub 560
350 if n9 <= 0 then goto 400
360 for k = 1 to n9
370 d = 0 : gosub 560
380 next k
390 rem End If
400 pd = 0
410 n9 = 0
420 goto 510
430 rem Q <> 10
440 d = pd : gosub 560
450 pd = q
460 if n9 = 0 then goto 510
470 for k = 1 to n9
480 d = 9 : gosub 560
490 next k
500 n9 = 0
510 next j
520 print str$(pd)
530 end
540 rem
550 rem Output digits
560 if nd = 0 then print str$(d); : return
570 if d = 0 then return
580 print str$(d);".";
590 nd = 0
600 return</syntaxhighlight>
==={{header|Commodore BASIC}}===
Line 746 ⟶ 804:
410 N9 = 0
450 NEXT J
460 PRINT RIGHT$(STR$(PD),1)
470 END
480 REM
490 REM OUTPUT DIGITS
500 IF ND=0 THEN PRINT RIGHT$(STR$(D),1);: RETURN
510 IF D=0 THEN RETURN
520 PRINT RIGHT$(STR$(D),1);".";
530 ND = 0
550 RETURN
</syntaxhighlight>
==={{header|
{{works with|PC-BASIC|any}}
The [[#Chipmunk_Basic|Chipmunk Basic]] solution works without any changes.
==={{header|Integer Basic}}===
Integer version was derived from the Pascal_spigot without any optimisation. It is more than 33% faster than the Applesoft version since it runs natively with integers.
Line 808 ⟶ 869:
</syntaxhighlight>
==={{header|
<syntaxhighlight lang="is-basic">100 PROGRAM "PI.bas"
110 LET N=100 ! Nuber of digits
120 LET LN=INT(10*N/3)+16
130 DIM A(LN)
140 LET PD,N9=0:LET ND=1
150 FOR J=1 TO LN
160 LET A(J-1)=2
170 NEXT
180 FOR J=1 TO N
190 LET Q=0
200 FOR I=LN TO 1 STEP-1
210 LET X=10*A(I-1)+Q*I
220 LET A(I-1)=X-(2*I-1)*INT(X/(2*I-1))
230 LET Q=INT(X/(2*I-1))
240 NEXT
250 LET A(0)=Q-10*INT(Q/10)
260 LET Q=INT(Q/10)
270 SELECT CASE Q
280 CASE 9
290 LET N9=N9+1
300 CASE 10
310 LET D=PD+1:CALL WRITE
320 IF N9>0 THEN
330 FOR K=1 TO N9
340 LET D=0:CALL WRITE
350 NEXT
360 END IF
370 LET PD,N9=0
380 CASE ELSE
390 LET D=PD:CALL WRITE
400 LET PD=Q
410 IF N9<>0 THEN
420 FOR K=1 TO N9
430 LET D=9:CALL WRITE
440 NEXT
450 LET N9=0
460 END IF
470 END SELECT
480 NEXT
490 PRINT STR$(PD)(1)
500 END
510 DEF WRITE
520 IF ND=0 THEN
530 PRINT STR$(D)(1);
540 ELSE IF D<>0 THEN
550 PRINT STR$(D)(1);".";
560 LET ND=0
570 END IF
580 END DEF</syntaxhighlight>
==={{header|MSX Basic}}===
The [[#Chipmunk_Basic|Chipmunk Basic]] solution works without any changes.
==={{header|Osborne 1 MBASIC}}===
Osborne 1 program is slightly different to allow it to keep the numbers all on the main screen rather than scrolling off to the right...
Line 3,818 ⟶ 3,932:
WriteString[$Output, RealDigits[Pi, 10, 1, i][[1, 1]]]; Pause[.05]];</syntaxhighlight>
=={{header|MATLAB
Requires the Variable Precision Integer (vpi) Toolbox
<syntaxhighlight lang="matlab"
function pi_str = piSpigot(N)
% Return N digits of pi using Gibbons's first spigot algorithm.
% If N is omitted, the digits are printed ad infinitum.
% Uses the expansion
% pi = sum_{i=0} (i!)^2 2^{i+1} /(2i+1)!
% = 2 + 1/3 * ( 2 + 2/5 * (2 + 3/7 * ( 2 + 4/9 * ( ..... )))))
% = (2 + 1/3 *)(2 + 2/5 *)(2 + 3/7 *)...
% where the terms in the last expression represent Linear Fractional
% Transforms (LFTs).
%
% Requires the Variable Precision Integer (vpi) Toolbox
%
% Reference:
% "Unbounded Spigot Algorithms for the Digits of Pi" by J. Gibbons, 2004
% American Mathematical Monthly, vol. 113.
if nargin < 1
N = Inf;
lineLength = 50;
else
pi_str = repmat(' ',1,N);
end
q = vpi(1);
r = vpi(0);
t = vpi(1);
k = 1; % If printing more than 3E15 digits, use k = vpi(1);
i = 1;
first_digit = true;
while i <= N
threeQplusR = 3*q + r;
n = double(threeQplusR / t);
if q+threeQplusR < (n+1)*t
d = num2str(n);
if isinf(N)
fprintf(1,'%s', d);
if first_digit
fprintf(1,'.');
first_digit = false;
i = i+1;
end
if i == lineLength
fprintf(1,'\n');
i = 0;
end
else
pi_str(i) = d;
end
q = 10*q;
r = 10*(r-n*t);
i = i + 1;
else
t = (2*k+1)*t;
r = (4*k+2)*q + (2*k+1)*r;
q = k*q;
k = k + 1;
end
end
end
</syntaxhighlight>
<pre>
>>
3.141592653589793238462643383279502884197169399375
10582097494459230781640628620899862803482534211706
79821480865132823066470938446095505822317253594081
28481117450284102701938521105559644622948954930381
96442881097566593344612847564823378678316527120190
91456485669234603486104543266482133936072602491412
</pre>
=={{header|MiniScript}}==
Calculate pi using the Rabinowitz-Wagon algorithm
<syntaxhighlight lang="miniscript">digits = input("Enter number of digits to calculate after decimal point: ").val
// I've seen variations of this "precision" calculation from
// 10 * digits
// to
// floor(10 * digits / 3) + 16
// A larger value provides a more precise calculation but also
// takes longer to run. Based on my testing, this calculation
// below for precision produces accurate output for inputs
// from 1 to 4000 - haven't tried larger than this.
precision = floor(10 * digits / 3) + 4
A = [2] * precision
nines = 0
predigit = 0
cnt = 0
while cnt <= digits
carry = 0
for i in range(precision - 1, 1, -1)
temp = 10 * A[i] + carry * i
A[i] = temp % (2 * i - 1)
carry = floor(temp/(2 * i - 1))
end for
A[1] = carry % 10
carry = floor(carry / 10)
current = carry
if current == 9 then
nines += 1
else if current == 10 then
print (predigit+1), ""
cnt += 1
if nines > 0 then
print "9" * nines, ""
cnt += nines
end if
predigit = 0
nines = 0
else
// the first digit produced is always a zero
// don't need to see that
if cnt != 0 then print predigit, ""
cnt += 1
predigit = current
if nines > 0 then
print "9" * nines, ""
cnt += nines
end if
nines = 0
end if
if cnt == 2 then print ".", ""
end while
print str(predigit) * (cnt < digits + 2)</syntaxhighlight>
{{out}}
<pre>
Enter number of digits to calculate after decimal point: 1000
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903690113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051329005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710199031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066139019278766111959092164201989
</pre>
=={{header|Nanoquery}}==
Line 5,851 ⟶ 6,081:
2000568127145263560827785771342757789609
...</pre>
=={{header|Standard ML}}==
{{works with|Poly/ML}}
{{works with|SML/NJ}}
{{works with|MLton}}
<syntaxhighlight lang="sml">(* https://www.cs.ox.ac.uk/people/jeremy.gibbons/publications/spigot.pdf *)
fun gibbons _ _ _ _ _ _ 0 = ()
| gibbons q r t k n l count =
let
val (q',r',t',k',n',l',count') =
if 4*q+r-t < n*t
then (10*q,10*(r-n*t),t,k,(10*(3*q+r)) div t-10*n,l,count-1) before print (IntInf.toString n)
else (q*k,(2*q+r)*l,t*l,k+1,(q*(7*k+2)+r*l) div (t*l),l+2,count)
in
gibbons q' r' t' k' n' l' count'
end
fun doGibbons n = gibbons 1 0 1 1 3 3 n
fun timeGibbons n =
let
val timer1 = Timer.startCPUTimer ()
val () = doGibbons n
val {usr=usr, sys=sys} = Timer.checkCPUTimer timer1
in
print "\n----------------------\n";
print ("usr: " ^ Time.toString usr ^ "\n");
print ("sys: " ^ Time.toString sys ^ "\n")
end
fun main () = timeGibbons 5000
</syntaxhighlight>
=={{header|Tailspin}}==
Line 6,159 ⟶ 6,424:
{{trans|Kotlin}}
{{libheader|Wren-big}}
<syntaxhighlight lang="
import "io" for Stdout
| |||