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.

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```