System Variable CT: Difference between revisions

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<h1>{quad}CT - DEFINITION NEEDED</h1>
<h1>{quad}CT - Comparison Tolerance</h1>
{{BoxStart|⎕CT
{{BoxStart|⎕CT
| DEFINITION NEEDED}}
| Value used by several primitive functions to determine whether two
{{BoxEnd|⎕CT←'<i>VALUE</i>'}}
numbers should be considered equal; default for a CLEAR NARS workspace is 3E¯15. }}
{{BoxEnd|⎕CT←<i>RealNumber</i>}}


Description here - to do
Due to computer storage formats, real numbers(e.g. 1E¯64) are normally expressed as n-bits of information<br>
and ''not necessarily an exact number''.  NARS allows ⎕CT to vary between no larger than 1E¯10 and no smaller than 0.<br>
The IEEE [minimum] standard for floating point real numbers is 64-bits(IEEE-754).


Examples:
<pre>
      ⎕CT        ⍝ View ⎕CT for a CLEAR NARS workspace.
3E¯15            ⍝ Default value.
      ⎕CT←45      ⍝ Attempt to change Comparison Tolerance to [+/-] 45 (an exaggerated engineering +/- tolerance.
      ⎕CT        ⍝ View ⎕CT after attempting to set its value at 45.
1E¯10            ⍝ This is the largest ⎕CT number NARS will allow = 1E¯10 (and NOT 45 as was attempted just above).
      4.0000000000005=4.0000000000008  ⍝ Comparison attempted.  Are these two different numbers equal? (No, but...).
1                ⍝ NARS/APL's Interpreter says YES(1), they ARE EQUAL - because the Comparison Tolerance is set high/large.
      ⎕CT←1E¯64  ⍝ Set NARS comparison tolerance to a much smaller number (for greater precision comparisons).
      ⎕CT        ⍝ View ⎕CT
1E¯64
      4.0000000000005=4.0000000000008  ⍝ Are these two different [but the same as above] numbers NOW equal? (No).
0            ⍝ NARS/APL's Interpreter says NO(0), they are NOT EQUAL - because the Comparison Tolerance is set below the threshold.
      ⎕CT←1E¯10000
      ⎕CT
0
      ⎕CT←3E¯15  ⍝ Reset ⎕CT to its default value.
      ⎕CT
3E¯15
</pre>
It is useful to think of ⎕CT as an engineering tolerance +/- for computer science engineers in comparing numbers in APL - sometimes comparing results from '''different computer programs''' or comparing results from '''different methodologies or a standard'''.  In Mechanical Engineering, tolerance is defined as the permissible deviation from a specified value of some dimension, often expressed as a percent, e.g. 0.01% and in Nanotechnology, for example, one nanometer is 1E-9 of a meter. <br><br>
'''See Also: [[System_Variable_FPC|⎕FPC - Floating Point Control]]'''<br><br>
{{System Variables}}
{{System Variables}}
{{Article footer}}
{{Article footer}}
{{stub}}
{{stub}}

Latest revision as of 00:06, 12 February 2015

⎕CT - Comparison Tolerance

⎕CT Value used by several primitive functions to determine whether two numbers should be considered equal; default for a CLEAR NARS workspace is 3E¯15.
⎕CT←RealNumber

Due to computer storage formats, real numbers(e.g. 1E¯64) are normally expressed as n-bits of information
and not necessarily an exact number. NARS allows ⎕CT to vary between no larger than 1E¯10 and no smaller than 0.
The IEEE [minimum] standard for floating point real numbers is 64-bits(IEEE-754).

Examples: 


      ⎕CT         ⍝ View ⎕CT for a CLEAR NARS workspace.
3E¯15             ⍝ Default value.
      ⎕CT←45      ⍝ Attempt to change Comparison Tolerance to [+/-] 45 (an exaggerated engineering +/- tolerance.
      ⎕CT         ⍝ View ⎕CT after attempting to set its value at 45.
1E¯10             ⍝ This is the largest ⎕CT number NARS will allow = 1E¯10 (and NOT 45 as was attempted just above).

      4.0000000000005=4.0000000000008   ⍝ Comparison attempted.  Are these two different numbers equal? (No, but...).
1                 ⍝ NARS/APL's Interpreter says YES(1), they ARE EQUAL - because the Comparison Tolerance is set high/large.
      ⎕CT←1E¯64   ⍝ Set NARS comparison tolerance to a much smaller number (for greater precision comparisons).
      ⎕CT         ⍝ View ⎕CT
1E¯64
      4.0000000000005=4.0000000000008   ⍝ Are these two different [but the same as above] numbers NOW equal? (No).
0            ⍝ NARS/APL's Interpreter says NO(0), they are NOT EQUAL - because the Comparison Tolerance is set below the threshold.

      ⎕CT←1E¯10000
      ⎕CT
0
      ⎕CT←3E¯15   ⍝ Reset ⎕CT to its default value.
      ⎕CT
3E¯15

It is useful to think of ⎕CT as an engineering tolerance +/- for computer science engineers in comparing numbers in APL - sometimes comparing results from different computer programs or comparing results from different methodologies or a standard. In Mechanical Engineering, tolerance is defined as the permissible deviation from a specified value of some dimension, often expressed as a percent, e.g. 0.01% and in Nanotechnology, for example, one nanometer is 1E-9 of a meter.

See Also: ⎕FPC - Floating Point Control

System Variables (A value may be assigned to these except for ⎕DM)
⎕ALX ⎕CT ⎕DM ⎕DT ⎕ELX ⎕FC ⎕FEATURE ⎕FPC ⎕IC ⎕IO
⎕LR ⎕LX ⎕PP ⎕PR ⎕PW ⎕RL ⎕SA ⎕WSID
Niladic System Functions (a value cannot be assigned to these)
⎕A ⎕AV ⎕EM ⎕ET ⎕LC ⎕NNAMES ⎕NNUMS ⎕SI ⎕SYSID ⎕SYSVER
⎕T ⎕TC ⎕TCBEL ⎕TCBS ⎕TCESC ⎕TCFF ⎕TCHT ⎕TCLF ⎕TCNL ⎕TCNUL
⎕TS ⎕WA
Monadic or dyadic system functions (a value cannot be assigned to these)
⎕AT ⎕CR ⎕DC ⎕DFT ⎕DL ⎕DR ⎕EA ⎕EC ⎕ERROR ⎕ES
⎕EX ⎕FMT ⎕FX ⎕MF ⎕NAPPEND ⎕NC ⎕NCREATE ⎕NERASE ⎕NINFO ⎕NL
⎕NLOCK ⎕NREAD ⎕NRENAME ⎕NREPLACE ⎕NRESIZE ⎕NSIZE ⎕NTIE ⎕NUNTIE ⎕STOP ⎕TF
⎕TRACE ⎕UCS ⎕VR
Note that quad functions and variables (except for the ⎕A family of functions) are case insensitive


See Also
System Commands System Variables and Functions Operators


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