pi is computed using the formula pi = 16*arctan(1/5) - 4*arctan(1/239) and
the arctangents are evaluated using the series

arctan(x) = x - x^3 + x^5 - x^7 ...
                ---   ---   ---
                 3     5     7

The arithmetic is done using 'digits' in base 2^39

      p1=100
      p10=1000			space for sum
      p11=200p10		space for term
      p12=200p11		space for x^(2n+1) referred to as proto-term

      70s200(60		adds (t=0) or subtracts (t=1) term p11 to/from sum p10
 ---> 79sp62(61		preserve digit count
 |    31s-2p11
 |    76t1		load + or - digit
 |    30s-2p11
 |    53p63   >--	ignore zero digit
 |    75sp61	|	go to next digit and exit at end
 |    60f0	|	exit setting s to position of last non-zero digit
 |              |
 | -> 62p80(64	|	mask off wrong bit
 | |  109s-2p10	|	store corrected digit, overflow not yet cleared
 | |  73s2	|	carry to next digit
 | |  31p81     |
 | |  76t1	|	load +1 or -1 to carry
 | |  30p81     | 
 | |  79s0(63 <--		store digit position in 0, set into s on exit
 | |  32s-2p10		add digit from sum
 | |  109s-2p10		store in sum, maybe wrong if overflow
 | -< 55p64		jump if overflow
 |    70s0(62		recover digit count after carrys
 --<  75sp61		go to next digit and exit at end
      60f0

      19f2(50		Divides pre-term (p12) by integer
      51r1		start at digit s since earlier ones zero
  --> 47sp12(52
  |   45f2
  |   48sp12		store result in pre-term p12
  |   76s198
  --< 74sp52
      60f0

      19f2(51		same as subroutine p50 except result in term p11
      51r1
      47sp12(53
      45f2
      48sp11
      76s198
      74sp53
      60f0

      102f0(3		start
      70s200
      9s-2p10		clear sum to zero
      75sr-1

      70t0		set t=0 for first series
----> 79tp99(98		preserve t
|
|     70s400
|     9s-2p11		clear pre-term and term to zero
|     75sr-1
|
|     4tp83
|     46f0		fetch multiplier 16 or 4
|     19p12		store in pre-term
|     4tp82
|     46f0		fetch denominator 5 or 239
|     19f4		save in 4
|     34f4		square it
|     48f6		save in 6
|
|     30f4		load denominator
|     70s0		s=0 to start division at most significant digit
|     58p50		divide
|     46f1
|     58p51		divide by 1 to move pre-term to term
|     58p60		add term to sum 
|
|     46f1
|     19f10		set count of terms in 10 to 1
|
|     70s0		start next division at most significan end
| --> 30f6(97		load 5^2 or 239^2
| |   58p50		divide pre-term by this
| |   46f2
| |   38f10		increment count of terms
| |   58p51		term = pre-term/count
| |
| |   3t0
| |   70t1		replace t by 1-t so next term subtracted
| |   58p60		add term to sum, s set to last non-zero digit
| |   73s4		adjust s for start of next division
| |
| |   76s180		continue until sufficient zero digits in term
| --< 50p97
|
|     70t0(99		restore t, destroyed by sign changes
|     72t1		set t=1 for second series
|     76t2		exit after two series
----< 50p98

      80s1p10(46		print rountine, get integer part
      110s951			look up tape code
      66s20
      107s30			print digit
      107f28			print .
      107f2			print cr
      107f8			print lf

      70t0			set count of groups of 10 decimal digits
----> 44f198p10(89		initial K to a 'digit' in base 2^39 =d
|     70s198			count of 'digits' in base 2^39
|     51r1			clear A
| --> 36*n1e10(88		10^10d in A
| |   44s-2p10			load next digit to K
| |   19s-2p10			store part of product, overwriting next digit
| |   48f2
| |   30f2
| |   32sp10			add other half of product
| |   109sp10			store ignoring overflow
| |   56r2			if overflow there is a carry
| |   51p87
| |   62p80			mask off wrong bit if overflow
| |   19sp10			store correct result
| |   51r1			clear A
| |   47p81			set L=1 if there was overflow
| ---<75sp88(87			count digits
|
|     6f39			move any carry from L to M
|     32p10			add on digit in base 10^10
|     59f21			print
|     76t198			test for 100 prints
----< 74tp89
      101f0			stop

r127r2047
127t2047(80			mask for removing overflow bit
0f0
0f1(81				1 as integer

0f5(82				denominators
0f239
0f16(83				multipliers
0f4

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