Calculate arctan x from series expansion

    arctan x = (x / (1 + x²)) * (1 + ((2/3)*(x²/(1+x²))) + ((2/3)*(4/5)*(x²/(1+x²))² + ...)

    V0      x (Input), arctan x (Output)
    V1      x²
    V2      prod
    V3      sum (initally 1.)
    V4      factor
    V5      term
    V6      num (initially 0)
    V7      f (intiially 1.)
    V8      0
    V9      scratch
    V10     1.
    V11     100000
    V12     50000
    V13     2.

A set decimal places to +5

N003 1.0
N006 0
N007 1.0
N008 0
N010 1.0
N011 100000
N012 50000
N013 2.0

    Scale input to add 5 decimal places for computation

×
L000
L011
S000

    x² = x × x

×
L000
L000
>
S001

    prod = x / (x² + 1)

+
L001
L010
S004

/
L000
<
L004
S002'

    factor = term = x² / (x² + 1)

/
L001
<
L004
S004'
S005'


(?

    num = num + 2

+
L006
L013
S006

    f = f * (num / (num + 1))

L006
L010
S009

/
L006
<
L009
S009'

*
L007
L009
>
S007

    sum = sum + (f * factor)

L007
L004
>
S009

+
L003
L009
S003

    factor = factor * term

*
L004
L005
>
S004

    Cycle if (f * factor) nonzero

-
L008
L009
)

    arctan = prod * sum

*
L002
L003
>
S000

    Add rounding constant

+
L000
L012
S000

    Scale to result, lopping off 5 guard digits

÷
L000
L011
S000'

A set decimal places to -5