System Function DR
|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 the bits per element in the remaining digits:
- 100: Boolean, one bit per element
- 1601: Character, 16 bits per element
- 6402: Integer, 64 bits per element
- 6403: Floating Point, 64 bits per element (double precision)
- 6404: Arithmetic Progression Array, 64 bits each for the offset and multiplier
- 3208: Heterogeneous, 32 bits per element (each is a pointer)
- 6408: Heterogeneous, 64 bits per element (each is a pointer)
- 3209: Nested, 32 bits per element (each is a pointer)
- 6409: Nested, 64 bits per element (each is a pointer)
- 3210: Rational, 16 bytes plus two 4-byte pointers plus size of limbs per element
- 6410: Rational, 16 bytes plus two 8-byte pointers plus size of limbs per element
⎕DR 1 0 1
⎕dr 2 64⍴1 — Note this is really an APA, not Boolean
⎕dr 2 64⍴1 1 — This one is Boolean because Reshape produces APAs for integer singleton right arguments only
|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.|
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.
6402 ⎕dr 'NARS2000' — Eight 16-bit characters (=128 bits) convert to two 64-bit integers
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).
⍴⎕←1601 ⎕dr 23362775258562638 13511005043687474
Keep in mind how Arithmetic Progression Arrays are created and represented as they can fool you. For example, you might try the following to convert from Boolean to integer:
6402 ⎕dr 2 64⍴1
1 0 2 64
However, this doesn't produce the expected result because this particular right argument is an APA, not a Boolean vector. 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 64.
On the other hand, this expression
6402 ⎕dr 2 64⍴1 1
produces the expected result because the right argument is now Boolean.
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.
0 ⎕dr 'a'
Character (1601): 16 bits per element
0 ⎕dr ⍳12
Arithmetic Progression Array (6404): 64 bit offset + 64 bit multiplier
The value 1 converts between character and floating point. This argument makes it easy to see the representation of floating point numbers in order to help understand precision and other floating point issues.
1 ⎕dr 1.1
1 ⎕dr '3fd',13⍴'5'
1 ⎕dr ¯∞ ∞
1 ⎕dr '7fe',13⍴'f' — The largest positive number
1 ⎕dr '001',13⍴'0' — The smallest positive number
1 ⎕dr '801',13⍴'0' — The largest negative number
1 ⎕dr 'ffe',13⍴'f' — The smallest negative number
The value 2 converts between character and 64-bit integer. This argument makes it easy to see the representation of integers.
2 ⎕dr ¯1
2 ⎕dr '7',15⍴'f' — The largest positive integer
2 ⎕dr '8',15⍴'0' — The smallest negative integer
2 ⎕dr 9223372036854775807 ¯9223372036854775808
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
6403 ⎕dr ¯64↑1
QNaN←6403 ⎕dr ¯64↑13⍴1 — A Quiet NaN (Not a Number)
1 ⎕dr QNaN
QNaN=1 2 3 ∞
1 1 1 1
1 ⎕dr '000fffffffffffff' — The largest positive denormal
1 ⎕dr '0000000000000001' — The smallest positive denormal