Comparison Tolerance ⎕CT

The value of ⎕CT determines the precision with which two numbers are judged to be equal.  Two numbers, X and Y, are judged to be equal if (|X-Y)≤⎕CT×(|X)⌈|Ywhere ≤ is applied without tolerance.

Thus ⎕CT is not used as an absolute value in comparisons, but rather specifies a relative value that is dependent on the magnitude of the number with the greater magnitude. It then follows that ⎕CT has no effect when either of the numbers is zero.

⎕CT may be assigned any value in the range from 0 to 2*¯32 (about 2.3E¯10). A value of 0 ensures exact comparison.  The value in a clear workspace is 1E¯14. ⎕CT has Namespace scope.

If ⎕FR is 1287, the system uses ⎕DCT. See Decimal Comparison Tolerance .

⎕CT and ⎕DCT are implicit arguments of the monadic primitive functions Ceiling (⌈), Floor (⌊) and Unique (∪), and of the dyadic functions Equal (=), Excluding (~), Find (⍷), Greater (>), Greater or Equal (≥), Greatest Common Divisor (∨), Index of (⍳), Intersection (∩), Less (<), Less or Equal (≤), Lowest Common Multiple (∧), Match (≡), Membership (∊), Not Match (≢), Not Equal (≠), Residue (|) and Union (∪), as well as ⎕FMT O-format.

Examples

      ⎕CT←1E¯10
      1.00000000001 1.0000001 = 1
1 0