System Function DR
This function is available in both monadic and dyadic forms.
|R is an arbitrary array.|
|Z is a numeric scalar which represents the datatype of R.|
The datatypes are encoded with a unique index in the low-order two digits, and (where appropriate) the bits per element in the higher-order digits:
- 110: Boolean, one bit per element
- 1611: Character, 16 bits per element
- 6412: Integer, 64 bits per element
- 6413: Floating Point, 64 bits per element (double precision)
- 14: Rational, 16 bytes plus two 4- or 8-byte pointers plus size of limbs per element
- 15: Variable-precision Floating Point, 12 bytes plus one 4- or 8-byte pointer plus size of limbs per element
- 1216: 64-bit Integer Complex (two-dimensional) number
- 1316: 64-bit Floating Point Complex (two-dimensional) number
- 1416: Multiple-precision Integer/Rational Complex (two-dimensional) number
- 1516: Multiple-precision Floating Point Complex (two-dimensional) number
- 1217: 64-bit Integer Quaternion (four-dimensional) number
- 1317: 64-bit Floating Point Quaternion (four-dimensional) number
- 1417: Multiple-precision Integer/Rational Quaternion (four-dimensional) number
- 1517: Multiple-precision Floating Point Quaternion (four-dimensional) number
- 1218: 64-bit Integer Octonion (eight-dimensional) number
- 1318: 64-bit Floating Point Octonion (eight-dimensional) number
- 1418: Multiple-precision Integer/Rational Octonion (eight-dimensional) number
- 1518: Multiple-precision Floating Point Octonion (eight-dimensional) number
- 19: Arithmetic Progression Array, 64 bits each for the offset and multiplier
- 20: Heterogeneous, one 4- or 8-byte pointer per element
- 21: Nested, one 4- or 8-byte pointer per element
⎕DR 1 0 1 110 ⎕DR ⌈/⍬ 6413 ⎕DR 2 64⍴1 — Note this is really an APA, not Boolean 19 ⎕DR 2 64⍴1 1 — This one is Boolean because Reshape produces APAs for integer singleton right arguments only 110
|R is an arbitrary array.|
|L is an integer scalar or one-element vector datatype (see the table above), or a special value (see below).|
|Z is R where each of the values are converted to the datatype indicated by L.|
Returned value Z may alternatively be: numeric scalar, vector of numbers, or a character string - depending on what the value of left argument L is.
If the conversion is from a narrower datatype to a wider datatype, there must be exactly enough columns in the right argument to match a multiple of the size of the wider datatype. For example, when converting from character (16-bit) to integer (64-bit), the last column of the right argument must be a multiple of 4 (= 64/16); otherwise, a LENGTH ERROR is signalled.
In the following example, an 8-element character vector (=128 bits) is converted to two 64-bit integers (in both NARS2000 32- and 64-bit versions integers are stored in 64-bits):
6412 ⎕DR 'NARS2000' 23362775258562638 13511005043687474
If the conversion is from a wider datatype to a narrower datatype, the number of values in the result is a multiple of the ratio of the wider datatype to the narrower datatype. For example, when converting from integer (64-bit) to character (16-bit), the last column in the result is the product of last column of the right argument and 4 (= 64/16).
For example (inverse of the example just above),
⍴⎕←1611 ⎕DR 23362775258562638 13511005043687474 NARS2000 8
Keep in mind how Arithmetic Progression Arrays are created and represented; they can fool both the casual programmer as well as an experienced coder. For example, one might try the following to convert from Boolean to integer:
6412 ⎕DR 2 64⍴1 ⍝ Conversion of an APA to an integer 1 0 2 64
However, this doesn't produce the expected result because this particular right argument is an APA, and not a simple Boolean vector of 1s. That is, under certain circumstances, the reshape primitive creates an APA. In this case, the APA is an array with an offset of 1, a multiplier of 0 and a shape of 2 rows and 64 cols. The usefulness of APA's in reducing data storage and processing times outweighs their sometimes added code complexity or additional insight, which may be required.
On the other hand, this expression:
6412 ⎕DR 2 64⍴1 1 ⍝ Contrast this with the prior example - Boolean vector created here, NOT an APA ¯1 ¯1
produces the expected result because the right argument is not an integer-valued singleton (in fact, it is a two-element vector which is not eligible for conversion to an APA).
There are several special values you may use as a left argument to ⎕DR:
The value 0 displays the datatype of the right argument as a text string so you don't need to remember the datatype numbers.
⎕DR 0 110 0 ⎕DR 0 Boolean (110): 1 bit per element ⎕DR 23 6412 0 ⎕DR 23 24 Integer (6412): 64 bits per element ⎕DR 1.1 6413 0 ⎕DR 1.1 Floating Point (6413): 64 bits per element ⎕DR 'a' 1611 0 ⎕DR 'a' Character (1611): 16 bits per element ⎕DR ⍳12 19 0 ⎕DR ⍳12 Arithmetic Progression Array (19): 64 bit offset + 64 bit multiplier -- PV1 0 ⎕dr 1 2 3x Rational (14): arbitrary precision numerator and denominator 0 ⎕dr 1 2 3v VFP (15): variable precision mantissa, 32-bit exponent -- FPC128 0 ⎕DR 1v64 2v64 VFP (15): variable precision mantissa, 32-bit exponent -- FPC64 0 ⎕DR 1 2v64 VFP (15): variable precision mantissa, 32-bit exponent -- FPC-Mixed 0 ⎕DR ⍳¨⍳9 Nested Array (21): PTR bits per element 0 ⎕DR 'a' 1 Heterogeneous Array (20): PTR bits per element
Note that the storage format for integers (23 24 in the above examples) is 64-bits per element and APAs (⍳12) is 64-bits for both the offset and multiplier regardless of whether you are running the 32- or 64-bit version of NARS2000.
In the last two examples, the reference to PTR means that storage format consists of pointers and is either 32- or 64-bits per element in the 32- or 64-bit version of NARS2000, respectively.
Many times in programming - for debugging, data scrutiny or other purposes - it is very important to know exactly how the data is represented by the program. ⎕DR or Data Representation is a feature designed to allow close scrutiny of how data is stored in memory and operated on in NARS2000.
Some arrays have properties that may be displayed by this function:
PV0 This array is a Permutation Vector, origin-0 PV1 This array is a Permutation Vector, origin-1 All2s This array consists of all 2s FPCnnn This array is a VFP and all entries are represented in Precision nnn FPC-Mixed This array is a VFP whose entries are represented in two or more different precisions
The value 1 converts between hex-character and floating point computer formats. This argument makes it very useful to view representations of floating point numbers - in order to better understand numeric precisions, program storage formats, debug multi-precision floating-point math routines (by NARS developers) or examine perceived floating point issues. Because this function converts between floating point and character format, it is self-inverse.
⎕PP←99 1 ⎕DR 1.1 3FF199999999999A ⍴1 ⎕DR 1.1 16 1 ⎕DR 1 3FF0000000000000 1 ⎕DR ÷3 3FD5555555555555 1 ⎕DR '3fd',13⍴'5' 0.3333333333333333 1 ⎕DR ¯∞ ∞ FFF0000000000000 7FF0000000000000 1 ⎕DR '7fe',13⍴'f' ⍝ The largest positive number 1.7976931348623157E308 1 ⎕DR '001',13⍴'0' ⍝ The smallest positive number 2.2250738585072014E¯308 1 ⎕DR '801',13⍴'0' ⍝ The largest negative number ¯2.2250738585072014E¯308 1 ⎕DR 'ffe',13⍴'f' ⍝ The smallest negative number ¯1.7976931348623157E308
The value 2 converts between character and 64-bit integer. This argument makes it easy to see the representation of integers. Because this function converts between integer and character format, it is self-inverse.
2 ⎕DR ¯1 FFFFFFFFFFFFFFFF 2 ⎕DR 16⍴'f' ¯1 2 ⎕DR '7',15⍴'f' ⍝ The largest positive integer 9223372036854775807 2 ⎕DR '8',15⍴'0' ⍝ The smallest negative integer ¯9223372036854775808 2 ⎕DR 9223372036854775807 ¯9223372036854775808 7FFFFFFFFFFFFFFF 8000000000000000
The value 3 returns the precision of the right argument array as a simple scalar.
3 ⎕DR 0 1 1 3 ⎕DR ⍳3 64 3 ⎕DR ÷2 3 64 3 ⎕DR ÷2 3x ∞ 3 ⎕DR 2.3v ⍝ Returns the value of ⎕FPC when the constant was tokenized 128 3 ⎕DR 1v64 64 3 ⎕DR 'a' 0 3 ⎕DR 'a' 1 0 3 ⎕DR ⊂1 2 0
A Word of Caution
This system function allows you to create special numbers we don't support in that no other primitive generates these numbers and the behavior of all other primitives on these numbers is undefined. Examples of such special numbers include Quiet NaNs, Signaling NaNs, Negative Zero, and Denormals. If the system doesn't behave as you expect when using these special numbers, don't be surprised.
⎕CT←0 ⋄ ⎕PP←99 6413 ⎕DR ¯64↑1 ¯0 QNaN←6413 ⎕DR ¯64↑13⍴1 ⍝ The Real Indefinite (Quiet NaN) where NaN = Not a Number 1 ⎕DR QNaN FFF8000000000000 QNaN=QNaN 0 1 ⎕DR '000fffffffffffff' ⍝ The largest positive denormal 2.225073858507201E¯308 1 ⎕DR '0000000000000001' ⍝ The smallest positive denormal 5E¯324
There is incomplete support for negative zero (¯0) in NARS2000. It may be enabled by setting the second element of ⎕FEATURE to 1, i.e. ⎕FEATURE←1. If you dare to try this concept, please report any problems in the usual manner via the forum, but please understand this feature is not fully supported.
|System Variables (A value may be assigned to these except for ⎕DM)|
|Niladic System Functions (a value cannot be assigned to these)|
|Monadic or dyadic system functions (a value cannot be assigned to these)|
|Note that quad functions and variables (except for the ⎕A family of functions) are case insensitive|