2016 Update
This commit is contained in:
Tina Müller
parent
948b86eafa
commit
dcf5d15da3
7965 changed files with 139854 additions and 31002 deletions
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@ -1,6 +1,14 @@
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Create a program to continually calculate and output the next digit of <math>\pi</math> (pi). The program should continue forever (until it is aborted by the user) calculating and outputting each digit in succession. The output should be a decimal sequence beginning 3.14159265 ...
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[[File:pi_symbol.jpg|500px||right]]
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Create a program to continually calculate and output the next decimal digit of <big><big><math>\pi</math></big></big> (pi).
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The program should continue forever (until it is aborted by the user) calculating and outputting each decimal digit in succession.
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The output should be a decimal sequence beginning 3.14159265 ...
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Note: this task is about calculating pi. For information on built-in pi constants see [[Real constants and functions]].
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Note: this task is about ''calculating'' pi. For information on built-in pi constants see [[Real constants and functions]].
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Related Task [[Arithmetic-geometric mean/Calculate Pi]]
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<br><br>
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104
Task/Pi/360-Assembly/pi.360
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104
Task/Pi/360-Assembly/pi.360
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@ -0,0 +1,104 @@
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* Spigot algorithm do the digits of PI 02/07/2016
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PISPIG CSECT
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USING PISPIG,R13 base register
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B 72(R15) skip savearea
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DC 17F'0' savearea
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STM R14,R12,12(R13) prolog
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ST R13,4(R15) "
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ST R15,8(R13) "
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LR R13,R15 "
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SR R0,R0 0
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ST R0,MORE more=0
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LA R6,1 i=1
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LOOPI1 C R6,=A(NBUF) do i=1 to hbound(buf)
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BH ELOOPI1 "
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SR R9,R9 karray=0
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L R7,=A(NVECT) j=hbound(vect)
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LR R1,R7 j
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SLA R1,2 .
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LA R10,VECT-4(R1) r10=@vect(j)
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LOOPJ EQU * do j=hbound(vect) to 1 by -1
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L R5,=F'100000' 100000
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M R4,0(R10) *vect(j)
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LR R2,R5 r2=100000*vect(j)
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LR R5,R9 karray
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MR R4,R7 karray*j
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AR R2,R5 r2+karray*j
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LR R11,R2 n=100000*vect(j)+karray*j
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LR R3,R7 j
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SLA R3,1 2*j
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BCTR R3,0 2*j-1)
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LR R4,R11 n
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SRDA R4,32 .
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DR R4,R3 n/(2*j-1)
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LR R9,R5 karray=n/(2*j-1)
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LR R5,R9 karray
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MR R4,R3 karray*(2*j-1)
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LR R1,R11 n
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SR R1,R5 n-karray*(2*j-1)
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ST R1,0(R10) vect(j)=n-karray*(2*j-1)
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SH R10,=H'4' r10=@vect(j)
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BCT R7,LOOPJ end do j
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LR R4,R9 karray
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SRDA R4,32 .
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D R4,=F'100000' karray/100000
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LR R11,R5 k=karray/100000
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L R2,MORE more
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AR R2,R11 +k
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LR R1,R6 i
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SLA R1,2 .
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ST R2,BUF-4(R1) buf(i)=more+k
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LR R5,R11 k
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M R4,=F'100000' *100000
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LR R1,R9 karray
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SR R1,R5 -k*100000
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ST R1,MORE more=karray-k*100000
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LA R6,1(R6) i=i+1
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B LOOPI1 end do i
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ELOOPI1 L R1,BUF buf(1)
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CVD R1,PACKED convert buf(1) to packed decimal
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OI PACKED+7,X'0F' prepare unpack
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UNPK PG(1),PACKED packed decimal to zoned printable
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MVI PG+1,C'.' output '.'
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XPRNT PG,80 print buffer
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MVC PG,=CL80' ' clear buffer
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LA R3,PG pgi=0
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LA R6,2 i=2
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LOOPI2 C R6,=A(NBUF) do i=2 to hbound(buf)
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BH ELOOPI2 "
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MVC 0(1,R3),=C' ' output ' '
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LA R3,1(R3) pgi=pgi+1
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LR R1,R6 i
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SLA R1,2 .
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L R2,BUF-4(R1) buf(i)
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CVD R2,PACKED convert v to packed decimal
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OI PACKED+7,X'0F' prepare unpack
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UNPK XDEC,PACKED packed decimal to zoned printable
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MVC 0(5,R3),XDEC+7 output buf(i) with 5 decimals
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LA R3,5(R3) pgi=pgi+5
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LR R4,R6 i
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BCTR R4,0 i-1
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SRDA R4,32 .
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D R4,=F'10' (i-1)/10
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LTR R4,R4 if (i-1)//10=0
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BNZ NOSKIP then
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XPRNT PG,80 print buffer
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LA R3,PG pgi=0
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MVC PG,=CL80' ' clear buffer
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NOSKIP LA R6,1(R6) i=i+1
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B LOOPI2 end do i
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ELOOPI2 L R13,4(0,R13) epilog
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LM R14,R12,12(R13) "
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XR R15,R15 "
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BR R14 exit
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LTORG
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MORE DS F more
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PACKED DS 0D,PL8 packed decimal
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PG DC CL80' ' buffer
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XDEC DS CL12 temp
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BUF DC (NBUF)F'0' buf(nbuf)
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VECT DC (NVECT)F'2' vect(nvect) init 2
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YREGS
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NBUF EQU 201 number of 5 decimals
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NVECT EQU 3350 nvect=ceil(nbuf*50/3)
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END PISPIG
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38
Task/Pi/Clojure/pi.clj
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38
Task/Pi/Clojure/pi.clj
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@ -0,0 +1,38 @@
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(ns pidigits
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(:gen-class))
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(def calc-pi
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; integer division rounding downwards to -infinity
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(let [div (fn [x y] (long (Math/floor (/ x y))))
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; Computations performed after yield clause in Python code
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update-after-yield (fn [[q r t k n l]]
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(let [nr (* 10 (- r (* n t)))
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nn (- (div (* 10 (+ (* 3 q) r)) t) (* 10 n))
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nq (* 10 q)]
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[nq nr t k nn l]))
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; Update of else clause in Python code: if (< (- (+ (* 4 q) r) t) (* n t))
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update-else (fn [[q r t k n l]]
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(let [nr (* (+ (* 2 q) r) l)
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nn (div (+ (* q 7 k) 2 (* r l)) (* t l))
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nq (* k q)
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nt (* l t)
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nl (+ 2 l)
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nk (+ 1 k)]
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[nq nr nt nk nn nl]))
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; Compute the lazy sequence of pi digits translating the Python code
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pi-from (fn pi-from [[q r t k n l]]
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(if (< (- (+ (* 4 q) r) t) (* n t))
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(lazy-seq (cons n (pi-from (update-after-yield [q r t k n l]))))
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(recur (update-else [q r t k n l]))))]
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; Use Clojure big numbers to perform the math (avoid integer overflow)
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(pi-from [1N 0N 1N 1N 3N 3N])))
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;; Indefinitely Output digits of pi, with 40 characters per line
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(doseq [[i q] (map-indexed vector calc-pi)]
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(when (= (mod i 40) 0)
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(println))
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(print q))
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15
Task/Pi/Fortran/pi-1.f
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15
Task/Pi/Fortran/pi-1.f
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@ -0,0 +1,15 @@
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Coded by Stanley Rabinowitz, 12 Vine Brook Road, Westford MA, 01886-4212.
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INTEGER VECT(3350),BUFFER(201)
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DATA VECT/3350*2/,MORE/0/
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DO 2 N = 1,201
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KARRAY = 0
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DO 3 L = 3350,1,-1
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NUM = 100000*VECT(L) + KARRAY*L
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KARRAY = NUM/(2*L - 1)
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3 VECT(L) = NUM - KARRAY*(2*L - 1)
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K = KARRAY/100000
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BUFFER(N) = MORE + K
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2 MORE = KARRAY - K*100000
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WRITE (*,100) BUFFER
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100 FORMAT (I2,"."/(1X,10I5.5))
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END
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48
Task/Pi/Fortran/pi-2.f
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48
Task/Pi/Fortran/pi-2.f
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!================================================
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program pi_spigot_unbounded
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!================================================
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do
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call print_next_pi_digit()
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end do
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contains
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!------------------------------------------------
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subroutine print_next_pi_digit()
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!------------------------------------------------
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use fmzm
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type (im) :: q, r, t, k, n, l, nr
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logical :: dot=.false., init=.false.
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save :: q, r, t, k, n, l
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if (.not.init) then
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q=to_im(1)
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r=to_im(0)
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t=to_im(1)
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k=to_im(1)
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n=to_im(3)
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l=to_im(3)
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init=.true.
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end if
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if (4*q+r-t < n*t) then
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write(6,fmt='(i1)',advance='no') to_int(n)
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if (.not.dot) then
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write(6,fmt='(a1)',advance='no') '.'
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dot=.true.
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end if
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flush(6)
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nr = 10 * ( r - n*t )
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n = 10 * ( (3*q + r) / t - n )
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q = 10 * q
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r = nr
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else
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nr = (2*q + r) * l
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n = ( (q * (7*k + 2) + r*l) / (t*l) )
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q = q * k
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t = t * l
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l = l + 2
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k = k + 1
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r = nr
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end if
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end subroutine
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end program
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14
Task/Pi/JavaScript/pi.js
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14
Task/Pi/JavaScript/pi.js
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var calcPi = function() {
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var n = 20000;
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var pi = 0;
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for (var i = 0; i < n; i++) {
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var temp = 4 / (i*2+1);
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if (i % 2 == 0) {
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pi += temp;
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}
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else {
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pi -= temp;
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}
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}
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return pi;
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}
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use bigint try=>"GMP"
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use bigint try=>"GMP";
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# Pi/4 = 4 arctan 1/5 - arctan 1/239
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# expanding it with Taylor series with what's probably the dumbest method
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/*REXX program spits out digits of π (pi) (one at a time) until Ctrl-Break.*/
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parse arg digs . /*obtain optional argument from the CL.*/
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if digs=='' | digs=="," then digs=1e6 /*Not specified? Then use one million.*/
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fn = 'PI_DIGITS.OUT' /*fileID used for output: the π digits.*/
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numeric digits digs /*with bigger digs, spitting is slower.*/
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call time 'Reset' /*reset the wall-clock (elapsed) timer.*/
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signal on halt /*───► HALT when Ctrl─Break is pressed.*/
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pi=0; s=16; r=4; v=5; vv=v*v; g=239; gg=g*g; spit=0; old=
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do n=1 by 2 /*calculate π with increasing accuracy */
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pi=pi + s/(n*v) - r/(n*g) /* ··· using John Machin's formula.*/
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if pi==old then leave /*have we exceeded the DIGITS accuracy?*/
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s=-s; r=-r; v=v*vv; g=g*gg /*compute some variables for shortcuts.*/
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do j=spit+1 to compare(pi,old) /*spit out some (new) digits of π (pi)*/
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parse var pi =(j) spit +1 /*equivalent to: spit=substr(pi,j,1) */
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call charout ,spit /*display one (new) decimal digit of π.*/
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call charout fn,spit /*··· and also write π digit to a file.*/
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end /*j*/ /* [↑] 0, 1, or 2 decimal dig are spit*/
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spit=j-1 /*adjust for DO loop index increment.*/
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old=pi /*use "OLD" value for the next COMPARE.*/
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end /*n*/
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say /*stick a fork in it, we're all done. */
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halt: say n%2+1 'iterations took' format(time("Elapsed"),,2) 'seconds.'
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/*REXX program spits out decimal digits of pi (one digit at a time) until Ctrl-Break.*/
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parse arg digs oFID . /*obtain optional argument from the CL.*/
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if digs=='' | digs=="," then digs=1e6 /*Not specified? Then use the default.*/
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if oFID=='' | oFID=="," then oFID='PI_SPIT.OUT' /* " " " " " " */
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numeric digits digs /*with bigger digs, spitting is slower.*/
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call time 'Reset' /*reset the wall─clock (elapsed) timer.*/
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signal on halt /*───► HALT when Ctrl─Break is pressed.*/
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pi=0; v=5; vv=v*v; g=239; gg=g*g; spit=0 /*assign some values to some variables.*/
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s=16 /*calculate π with increasing accuracy */
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r=4; do n=1 by 2 until old=pi; old=pi /*just calculate pi with odd integers*/
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pi=pi + s/(n*v) - r/(n*g) /* ··· using John Machin's formula.*/
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if pi==old then leave /*have we exceeded the DIGITS accuracy?*/
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s=-s; r=-r; v=v*vv; g=g*gg /*compute some variables for shortcuts.*/
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do j=spit+1 to compare(pi,old) /*spit out some (new) digits of π (pi)*/
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parse var pi =(j) spit +1 /*equivalent to: spit=substr(pi,j,1) */
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call charout ,spit /*display one (new) decimal digit of π.*/
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call charout oFID,spit /*··· and also write π digit to a file.*/
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end /*j*/ /* [↑] 0, 1, or 2 decimal dig are spit*/
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spit=j-1 /*adjust for DO loop index increment.*/
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end /*n*/
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say /*stick a fork in it, we're all done. */
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exit: say; say n%2+1 'iterations took' format(time("Elapsed"),,2) 'seconds.'; exit
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halt: say; say 'PI_SPIT halted via use of Ctrl-Break.'; signal exit /*show iterations.*/
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