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APL Exercises 7
Indexing
⎕io←0 throughout.
7.0 Functions on Booleans
In mathematics,
a function is a set of ordered pairs.
(The ordered pairs are required to satisfy
that if (x,y0) and (x,y1)
are in the function, then y0=y1 .)
A small domain (the x’s) offers the possibility of
computing the function in a different way.
Use cmpx to compare the speed
of the following pairs of functions:
b←?1e5⍴2
cmpx '1+b' '1 2[b]'
cmpx '2×b' '0 2[b]'
cmpx '*b' '(*0 1)[b]'
7.1 Formatting Booleans
The APL primitive ⍕⍵ converts array ⍵
into a character representation.
When ⍵ is boolean (0-1 values), the number of possible
output for each element is rather limited.
This fact was exploited in Dyalog APL version 15.0 to get a
factor of 28 speed-up over version 14.1.
Write a function fmtbv ⍵ that models ⍕⍵ where ⍵
is a boolean vector.
b←?7⍴2
fmtbv b
0 1 0 1 1 0 1
⍕b
0 1 0 1 1 0 1
(⍕ ≡ fmtbv) b
1
⍴fmtbv b
13
⍴b
7
7.2 Functions on 1-Byte Integers
Dyalog APL has 1-byte integers as a datatype.
There are only 256 1-byte integers and some functions
are faster by indexing into a pre-computed table
than by computing from scratch. For example:
e←*¯128+⍳256 ⍝ pre-computed table
x←¯128+?1e5⍴256
⎕dr x ⍝ check that x are 1-byte integers
83
cmpx '*x' 'e[128+x]' ⍝ which is faster?
It is not recommended that you as an APL programmer actually
compute *x this way.
(Too cumbersome and prone to errors in management.)
The technique is however worthy of consideration
for the APL implementer.
7.3 Parentheses Nesting
Write a function plevel ⍵
which produces the parenthesis nesting level for each element of
string ⍵ . For example:
x←'⍵((∇S))⍵⌷⍨?≢⍵'
plevel x
0 1 2 2 2 2 1 1 1 1 1 2 2 2 2 1 0 0 0 0 0 0 0
x ,[¯0.5] plevel x
⍵ ( ( ∇ < S ) , = S , ( ∇ > S ) ) ⍵ ⌷ ⍨ ? ≢ ⍵
0 1 2 2 2 2 1 1 1 1 1 2 2 2 2 1 0 0 0 0 0 0 0
7.4 Bar Chart
Write a function bar ⍵ which produces
a barchart. ⍵ is a vector of non-negative integers.
bar 3 1 4 1 5 9
⎕⎕⎕......
⎕........
⎕⎕⎕⎕.....
⎕........
⎕⎕⎕⎕⎕....
⎕⎕⎕⎕⎕⎕⎕⎕⎕
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