SAX
Revision as of 08:13, 13 November 2019 by Miraheze>Adám Brudzewsky
SAX (SHARP APL for UNIX) was a version of SHARP APL offered by Soliton Associates. Notable features of SAX include function rank, the Rank operator, and leading axis theory, as well as relative comparison tolerance and close composition operators including Under.
Primitive functions
Arithmetic
Scalar
All scalar functions have rank zero.
| Glyph | Monadic | Dyadic |
|---|---|---|
+ |
Conjugate/Identity | Addition |
- |
Negate | Subtraction |
× |
Signum | Multiplication |
÷ |
Reciprocal | Division |
* |
Exponential | Power |
⍟ |
Natural Logarithm | Base-⍺ Logarithm |
| |
Magnitude | Residue |
! |
Factorial | Out-Of/Combinations |
⌊ |
Floor | Minimum |
⌈ |
Ceiling | Maximum |
○ |
Pi Times | Circle functions |
∧ |
And/Least Common Multiple (LCM) | |
∨ |
Or/Greatest Common Divisor (GCD) | |
⍲ |
Nand | |
⍱ |
Nor | |
~ |
Not | See Miscellaneous |
? |
Roll | See Non-scalar |
Non-scalar
| Glyph | Rank | Monadic | Ranks | Dyadic |
|---|---|---|---|---|
⌹ |
2 | Matrix inverse | ∞ 2 | Matrix divide |
? |
See Scalar | * * | Deal | |
⊤ |
∞ ∞ | Encode | ||
⊥ |
∞ ∞ | Decode |
Relational
| Glyph | Rank | Monadic | Ranks | Dyadic |
|---|---|---|---|---|
= |
See Miscellaneous | 0 0 | Equals | |
≠ |
See Miscellaneous | 0 0 | Not Equals | |
< |
See Structural | 0 0 | Less Than | |
≤ |
0 0 | Less Than or Equal | ||
≥ |
0 0 | Greater Than or Equal | ||
> |
See Structural | 0 0 | Greater Than | |
≡ |
∞ ∞ | Match | ||
∊ |
0 ∞ | Membership | ||
⍷ |
∞ ∞ | Find |
Indexing
| Glyph | Rank | Monadic | Ranks | Dyadic |
|---|---|---|---|---|
@ |
See Miscellaneous | 0 ∞ | From | |
⍳ |
1 | Count | 1 0 | Index Of |
⍸ |
∞ ∞ | Index | ||
⍋ |
∞ | Numeric Grade up | ∞ ∞ | Character Grade up |
⍒ |
∞ | Numeric Grade down | ∞ ∞ | Character Grade down |
Structural
| Glyph | Rank | Monadic | Ranks | Dyadic |
|---|---|---|---|---|
⍴ |
∞ | Shape of | 1 ∞ | Reshape |
↑ |
See Miscellaneous | 1 ∞ | Take | |
↓ |
∞ | Raze | 1 ∞ | Drop |
< |
∞ | Enclose/Box | See Relational | |
⊃ |
∞ | Conditional Enclose | ∞ ∞ | Link |
> |
0 | Disclose/Open | See Relational | |
, |
∞ | Ravel | ∞ ∞ | Catenate |
⍪ |
∞ | Table | ∞ ∞ | Catenate-Down |
⌽ |
1 | Reverse | 0 1 | Rotate |
⊖ |
∞ | Reverse-Down | ∞ ∞ | Rotate-Down |
⍉ |
∞ | Monadic Transpose | 0 ∞ | Dyadic Transpose |
Miscellaneous
| Glyph | Rank | Monadic | Ranks | Dyadic |
|---|---|---|---|---|
⊣ |
∞ | Stop | ∞ ∞ | Left |
⊢ |
∞ | Pass | ∞ ∞ | Right |
≠ |
∞ | Nubsieve | See Relational | |
↑ |
∞ | Nub | See Structural | |
= |
∞ | Nubin | See Relational | |
~ |
See Scalar | ∞ ∞ | Less | |
@ |
1 | All | See Indexing | |
⍕ |
∞ | Monadic Format | * ∞ | Dyadic Format |
⍎ |
* | Execute |
Primitive Operators
| Glyph | Operands | Ranks | Monadic Call | Dyadic Call | ||
|---|---|---|---|---|---|---|
/ |
f |
∞ |
Reduce | |||
⌿ |
f |
∞ |
Reduce-down | |||
\ |
f |
∞ |
Scan | |||
⍀ |
f |
∞ |
Scan-down | |||
/ |
m |
∞ |
Copy/Compress | |||
⌿ |
m |
∞ |
Copy-down/Compress-down | |||
\ |
m |
∞ |
Expand | |||
⍀ |
m |
∞ |
Expand-down | |||
⊂ |
f |
∞ |
rf lf |
Swap | ||
& |
f |
∞ |
∞ ∞ |
Select | ||
⍤ |
f |
g |
mg |
mg mg |
On (close Over) | |
⍤ |
f |
n |
n |
n n |
Rank | |
⍤ |
m |
g |
mg |
mg mg |
Cut | |
⍥ |
f |
g |
mg |
mg mg |
Upon (close Atop) | |
¨ |
f |
g |
mg |
mg mg |
Under | |
¨ |
m |
g |
mg |
With (Bind) | ||
¨ |
f |
n |
mf |
|||
. |
f |
g |
2 |
∞ ∞ |
Alternant | Inner-product |
. |
m |
g |
∞ ∞ |
Tie, Outer-product | ||
. |
f |
m |
mf |
Ply | ||
Implementation
Numeric types
SHARP originally supported only real numbers using double (8-byte) precision. Numbers were stored in one of three types:
- Boolean, with one bit per value
- Integer, with four bytes per value
- Floating, with eight bytes per value
SATN-40 describes the addition of complex numbers to SHARP APL.