System Variable CT

⎕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

Keyboard

A+S

⍪

≡

≢

⍒

⍋

⌽

⍉

⊖

⍟

⍱

⍲

⍠

⌹

Alt

⋄

¨

¯

<

≤

∅

≥

>

≠

∨

∧

×

÷

Sh

~

!

@

#

$

%

^

&

*

(

)

_

+

Key

`

1

2

3

4

5

6

7

8

9

0

-

=

A+S

⍷

√

⍨

⍸

⍥

⍣

⍞

⍬

⊣

Alt

?

⍵

∊

⍴

§

↑

↓

⍳

○

π

←

→

⊢

Sh

Q

W

E

R

T

Y

U

I

O

P

{

}

|

Key

q

w

e

r

t

y

u

i

o

p

[

]

\

A+S

∫

∂

⌻

⍢

⍙

⍤

⍫

⌷

Alt

⍺

⌈

⌊

∞

∇

∆

∘

‼

⎕

⍎

⍕

Sh

A

S

D

F

G

H

J

K

L

:

"

Key

a

s

d

f

g

h

j

k

l

;

'

A+S

⊆

⊇

χ

⍡

⍭

⊙

Alt

⊂

⊃

∩

∪

⊥

⊤

⍦

⍝

⍀

⌿

Sh

Z

X

C

V

B

N

M

<

>

?

Key

z

x

c

v

b

n

m

,

.

/

{{#ifeq:{{{1}}}|4||title="match" style="border-width:thick; border-color:blue; background-color:yellow;"|≡ {{#ifeq:{{{1}}}|7||title="iota" style="border-width:thick; border-color:blue; background-color:yellow;" |⍳ {{#ifeq:{{{1}}}|9||title="slash" style="border-width:thick; border-color:blue; background-color:yellow;" |/ {{#ifeq:{{{1}}}|11||title="diamond" style="border-width:thick; border-color:blue; background-color:yellow;" |⋄ {{#switch: {{{1}}}

NARS 2000 Lang Tool Bar {{#ifeq:{{{1}}}|1||title="assign" style="border-width:thick; border-color:blue; background-color:yellow;" |←

→

bgcolor=cyan

title="assign" |←

→

}} {{#ifeq:{{{1}}}|2||title="plus" style="border-width:thick; border-color:blue; background-color:yellow;" |+

-

×

÷

*

⍟

⌹

○

!

?

√

bgcolor=cyan

title="plus" |+

-

×

÷

*

⍟

⌹

○

!

?

√

}} {{#ifeq:{{{1}}}|3||title="mod" style="border-width:thick; border-color:blue; background-color:yellow;" ||

⌈

⌊

⊥

⊤

⊣

⊢

⌈

⌊

⊥

⊤

⊣

⊢

≢

<

≤

=

≥

>

≠

bgcolor=cyan

title="match" |≡

≢

<

≤

=

≥

>

≠

}} {{#ifeq:{{{1}}}|5||title="down caret" style="border-width:thick; border-color:blue; background-color:yellow;" |∨

∧

⍱

⍲

bgcolor=cyan

title="down caret" |∨

∧

⍱

⍲

}} {{#ifeq:{{{1}}}|6||title="take" style="border-width:thick; border-color:blue; background-color:yellow;" |↑

↓

⊂

⊃

⌷

⍋

⍒

↓

⊂

⊃

⌷

⍋

⍒

∊

⍸

⍷

∪

∩

⊆

⊇

~

§

π

..

bgcolor=cyan

title="iota" |⍳

∊

⍸

⍷

∪

∩

⊆

⊇

~

§

π

..

}} {{#ifeq:{{{1}}}|8||title="comma" style="border-width:thick; border-color:blue; background-color:yellow;" |,

⍪

⍴

⌽

⊖

⍉

⍪

⍴

⌽

⊖

⍉

\

⌿

⍀

⊙

¨

⍨

⍤

⍡

⍥

⍦

.

∘

⍠

‼

⌻

∂

∫

bgcolor=cyan

title="slash" |/

\

⌿

⍀

⊙

¨

⍨

⍤

⍣

⍡

⍥

⍦

.

∘

⍠

‼

⌻

∂

∫

}} {{#ifeq:{{{1}}}|10||title="quotequad" style="border-width:thick; border-color:blue; background-color:yellow;" |⍞

⎕

⍎

⍕

⎕

⍎

⍕

⍝

∇

∆

⍙

_

⍺

⍵

bgcolor=cyan

title="diamond" |⋄

⍝

∇

∆

⍙

_

⍺

⍵

}} {{#ifeq:{{{1}}}|12||title="neg" style="border-width:thick; border-color:blue; background-color:yellow;" |¯

⍬

∞

title="neg" |¯

⍬

∞

∅

colspan=8 |Second Row

i j k

a

b

e

g

p

r

v

x

z

colspan=8 |Second Row

i j k

a

b

e

g

p

r

v

x

z

colspan=8 |Second Row

i j k

a

b

e

g

p

r

v

x

z

colspan=6 |Second Row

i j k

i j k l

g

p

r

v

x }}

{{#ifeq:{{{1}}}|0| |[[Category:Mouse Group {{{1}}}|{{{2}}}]]}}

---

This NARS2000 article is a stub and needs further work.