System Variable IC

Indeterminate Control

Z←⎕IC returns the current value of the Indeterminate Control Vector.

Z is an integer vector whose elements each control a separate aspect of how indeterminates are handled by the system.

⎕IC←R sets all of the values of the Indeterminate Control Vector to R. ⎕IC←⍬ sets all of the values of the Indeterminate Control Vector to their system default state. ⎕IC[L]←R sets the value(s) of the Indeterminate Control Vector indexed by L to R.

This experimental feature attempts to collect together in one place control of various infinite and indeterminate calculations such as ÷0, 0÷0, and friends. The values of this multi-element vector each control a different calculation. In particular,

⎕IC Index (origin-0)	Indeterminate Calculation	Default Result
0	÷0	∞
1	⍟0	¯∞
2	!N for integer N<0	DOMAIN ERROR
3	0×∞ and ∞×0	DOMAIN ERROR
4	0ׯ∞ and ¯∞×0	DOMAIN ERROR
5	0÷0	1
6	∞÷∞ (same sign)	DOMAIN ERROR
7	∞÷∞ (different sign)	DOMAIN ERROR
8	∞-∞ (and related)	DOMAIN ERROR
9	L|∞ (either sign infinity)	DOMAIN ERROR
10	0*0	1
11	L*∞ for any L≤¯1	DOMAIN ERROR
12	0⍟0	DOMAIN ERROR
13	0⍟1	DOMAIN ERROR
14	1⍟0	DOMAIN ERROR
15	1⍟1	1

The values in each element of ⎕IC control the result of the calculation as follows:

⎕IC Value	Result
¯1	¯1
0	0
1	1
2	DOMAIN ERROR
3	∞
4	¯∞

For example,

      ⎕IO←0
      ⎕IC
3 4 2 2 2 1 2 2 2 2 1 2 2 2 2 1
      0÷0
1
      ⎕IC[5]←2
      0÷0
DOMAIN ERROR
      0÷0
       ∧
      ⎕IC←⍬
      ⎕IC
3 4 2 2 2 1 2 2 2 2 1 2 2 2 2 1

Incomplete List of Indeterminates

That there may be other indeterminates not covered by this feature. Please let us know if you think there are other cases that should be included.