ised(1)ised(1)NAMEised - generating integer and floating point sequences
SYNOPSISised [--m] [--p] [--n] [--f input_file] [--a load_file] [--l
apply_to_file] [--x modify_file] [--k awk_file] [--o output_file] [--t
code_line] [--d delimiter] [--D int_format] [--F float_format] code ...
DESCRIPTIONised processes arithmetic expressions involving arrays and returns out‐
put array of values. Options and code lines are processed in order of
appearance. If ised is called without arguments, it reads from standard
input. Press ^D (EOF) or enter a single q to exit when in interactive
mode.
When input consists only of arrays of length one (scalars), ised
behaves as an ordinary calculator.
Options can also be used from command line in interactive mode or in
files, invoked by --f.
OPTIONS--f input_file
Reads and processes input_file one line at a time, equivalent to
giving every line as separate command line argument.
ised--f - is not equivalent to running it without arguments, as
the latter also invokes interactive GNU readline prompt.
--a load_file
Loads load_file into memory. Every line has it's own memory
slot, starting at $1. At the end, line count is saved in memory
slot $0. All lines are evaluated before saving.
--l apply_to_file { code | --f file }
code or file is applied on every line of apply_to_file. Each
line is loaded into memory slot $1 while line number is in $0.
--x modify_file { code | --f file }
Similar to --l, but instead of direct evaluation of lines in
modify_file, it splits the line into numbers and strings. The
numbers are read and stored into $1, then the code or file is
applied. The output has the same form as the input, with the
numbers replaced with those returned by the code or file. The
$0 memory slot contains the current line number.
--k awk_file { code | --f file }
Similar to --x, but instead of smartly finding the numbers and
storing them all into the same array, it splits each input line
at delimiters and stores each column into a separate memory
slot, starting with $1. Non-numeric fields are preserved in the
output without warning. Changes to the memory slots by the user
are reflected in the output. The output is delimited by the
delimiter, provided by --d. If code is not terminated by a semi‐
colon, the return value of code or file is appended to the rest
of the output.
--o output_file
Sets the file where standard output is redirected to. Everything
after this call will be redirected to output_file, until the
next call to --o. Calling --o - reverts back to the standard
output.
--t code_line
code_line is evaluated as usual, but results of every semicolon-
terminated substatement are printed as columns. Essentially this
is a transposed version of --p option. If code_line contains
only one statement, the result is similar to setting delimiter
to newline (\n). If code_line is to be appled line-by-line to a
file, both --x and --k behave as --l.
--d delimiter
string delimiter is used to delimit values of output array.
Default is space.
--D int_format
format for printf function for integers. Default: %d.
--F float_format
format for printf function for floating point values. Default:
%g.
--m dump memory page.
--p,--n
--p forces ised to print results even when suppressed by semi‐
colon. Every semicolon-terminated substatement is output with
terminating newline, so this can be used to split lines when in
--l mode. This option persists until it is turned off with --n.
--v show program version and license disclaimer.
COMMANDSised operators all work on arrays of values. Even single values are
treated as arrays with length of one. Spacing between operators and
values is optional. Values can be either floating point or integers
and retain information about their type unless changed. Same operators
behave differently for each type.
In general, operators starting with colon (:) mean component-wise eval‐
uation.
Behaviour in case of illegal arithmetic output (such as division by
zero or root of negative values) is uncertain and may return either
nan, zero or some other non-standard result. This should not be relied
upon as it may change in future releases. The case of integer over‐
flows is to be avoided by user as the program does not issue a warning
and the output is wrong and unpredictable. The same holds for conver‐
sion of floats to integers. Since version 2.2.3, integer overflows are
handled by implicit conversion into floating point type if compiled for
x86-64 architecture, but caution is still advised, as the handling may
not catch all the problematic cases.
Comments
Lines are considered as comments if preceded by #!. If #! appears in
the middle of the line, everything behind it is commented out. Com‐
pletely blank lines are also ignored, but lines with whitespace charac‐
ters will be treated normally. This way user can seperate several
blocks of output by empty lines.
Scripts can be made executable and evaluated without invoking ised
explicitly. This is done by including declaration
#!/usr/local/bin/ised --f
in the first line of the script. This line is obviously treated as com‐
ment.
In apply-to-file mode, comments and blank lines are preserved in input,
but don't count as active lines and therefore don't increment line
counter. If a file contains mixed data, it can still be processed line-
by-line if non-numerical data is commented out.
Arrays and Separators
Values, separated by commas (,) of spaces ( ) are treated as components
of an array. Array separation has lowest precedence, so any operators
are evaluated before the array is collected. Nested arrays are flat‐
tened before further evaluation. Arrays are enclosed in braces {}, out‐
ermost braces are optional.
Output to terminal and history is suppressed by semicolon ; which can
occur any number of times in every line (putting it at the end suppre‐
ses all output, but still evaluates memory operations, if they're
present).
Examples:
{1 2 {3 4} 5,6} = {1 2 3 4 5 6}
{1 2+3 4 5*6+7} = {1 5 4 37}
1 5 1+1 = {1 5 2}
Array Constructors
[n] generates sequence 0..n-1
[n1 n2]
generates sequence n1..n2 with increment 1. If n2<n1, sequence
is descending.
[n1 m1..mi n2]
generates sequence between n1, n2, but with cycling increments,
given as m1..mi.
Example: [0 1 2 10]={0 1 3 4 6 7 9}
(x) repeats number x. This way parentheses can be used for evalua‐
tion precedence or for function arguments in scalar context.
(x n) generates array of n repetitions of number x.
(x m1..mi n)
generates sequence of length n, starting at x with cycling
increments m1..mi.
If n is negative, the increments are used |n| times, so for i
increments, the output sequence has |n|*i+1 elements.
Examples:
(0 1 2 10)={0 1 3 4 6 7 9 10 12 13}
(0 [1 5] -1)={0 1 3 6 10 15}
{x1..xi}
array grouping
Component-wise Operators
x:+y x:-y x:*y x:/y x:%y x:^y
result is an array, where each component is e.g. a sum (or other
binary operations above) of corresponding components of x and y.
In case of different lengths of arrays, smaller length is used.
Operations coresponding to above operators are: addition, sub‐
straction, multiplication, division, modulo, exponentiation.
Note that modulo works for both integer and non-integer values.
Modulo always satisfies this equation: i{x/dy}*y+x%y=x
Scalar-producing Operators
@+x returns sum of components of x.
@*x returns product of components of x.
x+*y returns a result of alternating addition and subtraction, in the
form ((x_0+y_0)*x_1+y_1)*x_2+y_2+...
If x is shorter than y, the elements of x are cyclically reused
from the beginning of the array. If y is shorter than x, it is
padded with zeroes. This way, a scalar x can be used to evaluate
a polynomial with unit leading coefficient.
gcd lcm
return greatest common divisor and least common multiple of the
numbers in the array, respectively. If the array includes non‐
integer numbers, a warning is issued and an empty array is
returned. The result of gcd is negative if an odd number of the
array are negative.
avg var
return linear average and variance (mean square dispersion).
avg{x} is shorter notation for @+x/d#x and doesn't require
inputting the array twice or storing it in memory.
Example: avg{0 1.5 3}={1.5}
nrm x y
returns generalized x-norm of vector y. If x is a vector, the
result contains all specified norms. x=2 corresponds to Pythago‐
ras' theorem, which is available also as operator @=.
Examples:
nrm2{1 1 1}={sqrt3}
nrm{1 3}{1 1}={2. cbrt2}
Function Maps
sin cos tan atn asn acs abs exp sqt cbt log
evaluates a function on every element of array, e.g. sin{1 2
3}={sin1 sin2 sin3}. Functions corresponding to above operators
are sine, cosine, tangent, arc tangent, arc sine, arc cosine,
magnitude, exponential, square root, cubic root, natural loga‐
rithm. Long operators atan asin acos sqrt cbrt are also valid.
Exponential function is also available as e^, but has a lower
precedence (the same as the operator ^). The unary / prefix is
also a function map: /x=1.0/x.
x! evaluates factorial on every element of array x. For floating
point values it evaluates gamma(x+1). For negative integers, it
returns 1.
r f i d
prefixes that modify values of array elements.
r rounds values to closest integer.
f returns fractional part of values. It is always in range
0..1 and represents distance to downwards rounded inte‐
ger, even for negative values.
i returns integer part of values. Expression fx+ix=x always
holds.
d converts values to floating point. For example, 1/2=0 but
1/d2=0.5.
ran randomizes elements of array. For integers, it returns random
integers strictly smaller than given value. For floating values
it returns real numbers.
phi calculates the Euler totient function for positive integers. The
nonpositive and noninteger values are skipped.
bj x y by x y
applies x-th Bessel function of first/second kind to array y. x
should be one or more integers. Floating point values are cast
to integers and a warning is issued.
Tensor Operators
x+y x-y x*y x/y x%y x^y
evaluate corresponding operations on every possible pair between
elements of x and y. Most useful when one of the arguments is a
scalar. Beware, the division operator / acts as an unary opera‐
tor (inversion) when it has no left operand, or has a space on
the left, but not on the right. For instance, /3 is equivalent
to 1.0/3.
Examples:
{1 2 3 4}*{1 -1}={1 -1 2 -2 3 -3 4 -4}
{2 3 -5}*2={4 6 -10}
xey operator for exponential notation. Useful mostly in scalar con‐
text, e.g. 1.3e-5, but can be used in general for evaluating
exponential notation for all combinations.
xcy evaluates binomial symbol (x over y). It supports floating point
values.
Example: 3c{0 1 2 3}={1 3 3 1}
Polynomial Operators
The following set of operators treat arrays as polynomial coefficients.
First element corresponds to zero-order term, and so on, e.g. {1 2 3}
<=> 3x^2 + 2x + 1.
x++y x--y
polynomial addition and substraction. This is similar to opera‐
tors :+ :-, but the length of output array is equal to length of
the larger array.
x**y computes product of two polynomials. It terms of arrays, this
evaluates to the convolution of x and y.
x//y x%%y
computes quotient and remainder in long polynomial division.
Returned arrays always contain floating point values, regardless
the input. Leading zeroes are trimmed from the output.
px x y evaluates polynomial x in points, given in array y.
pd x computes derivative of polynomial x. Equivalent to {x<<-1}:*[1
#x].
pz x returns all real roots of polynomial x. Resulting array is not
guaranteed to be sorted in any way.
This operator uses Sturm's sequence to isolate the roots, and
proceeds with Newton-Raphson iteration. It works quite well for
well-behaved polynomials. Accuracy is questionable if there are
roots with multiplicity 3 or higher.
The algorithms outputs warning messages if the accuracy is ques‐
tionable, or if the iteration fails to converge to a result.
zp x is the inverse of the pz operator. It takes the set of roots and
returns the minimal polynomial with given roots, with the lead‐
ing coefficient normalized to 1.
pzzp should return the same array as on the input, up to a
reordering of elements (excepting the numerical errors in root
finding, especially if there are multiple roots). Conversely,
zppz does not necessarily return the initial array, as it
ignores the normalization factor and irreducible factors that
don't have any real roots.
F x returns the prime factorization of x. If x has many components,
the factors are concatenated in a way that makes the product of
the output array equal to the product of the input array. That
makes the negative integer to produce an additional -1 factor,
while floating point input numbers stay intact.
Vector Operators
x@:y returns dot product of vectors x and y. In case of different
array lengths, overhead is discarded.
x@^y returns cross product of vectors x and y, if the vectors are
three-dimensional. In general case, it returns components
z_i=x_{i+1}*y_{i+2}-x_{i+2}*y_{i+1}.
This generalization is useful for polygon geometry. For polygon
with coordinates {x_i,y_i}, the area of the polygon is
0.5*@+{x@^y}. Similar formulas exist for polygon center and
other expressions.
@!x normalizes vector x.
@=x returns length of vector x. Shoter notation of general norm:
{@=x}={nrm2x}.
Set Operators
x&y returns elements that are in both x and y.
x|y concatenates arrays x and y. Produces the same result as {x y}.
[deprecated] This operator is an unnecessary waste of notation.
It should have had the interleaving effect, now represented by
Y.
x\y returns elements of x that are not present in y.
x|&y is the xor operation on arrays. Returns elements, present in
only one of the arrays.
xYy interleaves the arrays x and y.
~x reverses order of array x.
Sx sorts array in ascending order.
#x returns number of elements in array.
#_xy counts occurences of elements of x in y. This is selective vari‐
ant of # operator.
Example: #_{0 1 4}{1 2 3 4 4 1}={0 2 2}
#__xy distributes elements of y into a histogram where elements of x
divide the real numbers into bins. The size of the output is one
element more than the size of x. The first bin extends from neg‐
ative infinity to the first element of x and the last extends to
the positive infinity. x is expected to be in ascending order.
?x returns indices of nonzero elements of x. Only integer zero
counts as zero.
This operator is intended for use with index operator (_), to
select elements that satisfy some logical test. For example,
x_?{x<1000} returns only elements, smaller than 1000.
To skip an entire array if it doesn't satisfy a condition, use ?
operator in combination with +. For example, x+?{#x==3} prints x
only if its length equals 3. This functionality relies on the
fact that tensor summation with empty array returns empty array.
?_x y returns the indices of elements of x in the array y. If the ele‐
ment is found more than once, only the first index is returned.
If the element is not present in y, a value -1 is returned.
S_x returns the indices that would sort the array x. It's always
true that Sx=x_S_x.
x=y returns 1 if arrays are equal, 0 otherwise.
Element Selection Operators
x<<y for positive values of y, returns first y values of x (as unix
utility head). For negative values, it returns everything except
first y values. If y is an array, it concatenates all results.
y should be array of integers. Useful for array cycling: {1 2 3
4}<<{-2 2}={3 4 1 2}.
x>>y same as above, except it works from the back of the array.
x_y returns elements of x at indices y. It interpolates for noninte‐
ger indices and wraps around for indices out of range.
U P N O E I D X
conditional selectors. Return elements that satisfy a certain
condition.
U unique, deletes duplicate elements
P positive
N negative
O odd
E even
I integers
D floating point values
X prime numbers
min max
return the smallest and the largest component of the array
respectively.
Zx `zilch` returns an empty array. This operator is useful for sup‐
pressing output from functions with side-effects, such as the @
operator.
Constants
pi returns 3.14159265358979323846264
deg returns the value of angular degree in radians,
0.017453292519943295769
emc returns Euler-Mascheroni constant, 0.57721566490153286
pm mp plus/minus and minus/plus constants. They output arrays {1,-1}
and {-1,1} respectively. They can be used to compute results of
multivalued formulas simultaneously, for example quadratic equa‐
tion.
Memory Operators
Memory slots are enumerated by integers. For floating point values,
integer part is used. This may change in future versions.
Named variables can be used instead of integer enumeration with the use
of backticks.
@xy puts array y into memory slots, enumerated by elements of x. x
should be integers. Floating point numbers are cast to integers
and warning is issued.
$x concatenates arrays found at memory slots, enumerated by x. For
negative values, it returns array from history instead of mem‐
ory, $-1 being most recent entry. x should be integers.
@`<name>`y
puts array y into the memory slot, represented by the given
<name>.
$`<name>`
retrieves the variable, named by the given <name>.
ised manages memory as hashed map, so a memory position can be every
positive integer. Saving array to slot $100 doesn't allocate any more
memory than saving to slot $1. Results are added to history for input
lines from files (--f option) or interactive mode, unless the line ter‐
minates with a semicolon. Negative slots are reserved for internal use
by the named variable system and are not accessible by direct derefer‐
ence. Instead, history is accessed by the negative arguments of the $
operator.
Comparison and Equality operators
For logical evaluation, ised provides comparison operators. Result of
comparison is 1 for true and 0 for false. Equality and inequality oper‐
ators also check if types of both values are equal.
For boolean analysis of resulting arrays, use multiplication for and
operator and summation for or operator. Incorporating additional opera‐
tors for this functionality would be redundant, as the result is equiv‐
alent. But beware, multiplication and summation have higher precedence
than comparison operators, so use grouping operator {} to achieve
desirable effect.
x:<y x:>y x:<=y x:>=y x:==y x:<>y
Comparison and equality, evaluated component-wise. Result is an
array with size of the shorter of the input arrays.
x<y x>y x<=y x>=y x==y x<>y
Same as above, but evaluated on every possible pair of values.
Size of the output array is product of input sizes (see Tensor
operators for details and example).
Function definitions
ised implements a rudimentary mechanism for function definitions. It
enables storing an expression and evaluate it later upon command. The
functions are stored in a map structure and are accessed via integer
function ids. A function id is returned when the function is declared.
No particular order of the function ids should be assumed. The zero (0)
function id is reserved to for an identity function (no-op).
The functions may include memory manipulation, which makes them as ver‐
satile as functions in any programming language. They can be designed
as procedures ignoring input and output and operate on memory, plain-
old-functions that take an argument and return a result, or any combi‐
nation of both.
{:expression:}
Function declaration. The expression is parsed, stored into the
function memory and its unique id is returned. The id is guar‐
ranteed to be nonzero. The returned id may be stored in memory
and used later. Within the function, operator x is used to
refer to the function's argument. The function is not evaluated
at this point.
f::x Function evaluation. f is an array of function ids, which are
applied sequentially to the array x, left-to-right. It should be
understood as composition of function; the result from the pre‐
vious function is passed to the next as its argument.
f:::x Function iteration. Array of function ids f is evaluated repeat‐
edly on the argument x. The iteration stops when the argument no
longer changes or maximum number of iterations is reached. The
maximum number of iterations is 65536 by default, but can be
queried and changed using system call Q{105 ...} (see the sec‐
tion on system calls). This operator can be emulated by the
ordinary function evaluation and system call for setting the
instruction pointer, Q{103 ...}, but the implementation is quite
complex. As functional iteration until convergence is common in
math, this operator is a valuable shortcut.
f@::x Function map. Array of function ids f is evaluated on each ele‐
ment of the array x. This is meant to allow creation of user
functions that don't have to handle the array nature of the
argument themselves.
x This operator evaluates to the argument supplied to the func‐
tion. In case of nested functions, it refers to the innermost
function's argument. Outside a function, it has the value of the
current line (when used with --l or --x), or invalid otherwise.
The function evaluation operator (::) is enough to implement all basic
control structures. ised is therefore a Turing complete language.
function call:
{fun}::{arg}
conditional execution (if-statement):
{{false-fun true-fun}_{condition}}::{arg}
switch statement:
{{fun1 fun2 fun3 fun4 ...}_switch}::{arg}
static repetition (for-statement):
(fun n)::{arg}
recursion:
{@mem {:do-something-with $mem::x :}}::{arg} The implementation
of the function must be carefully devised, otherwise the execu‐
tion might get stuck in an infinite recursion.
general loop (while-statement):
{ body-fun jump-test }::{arg}
Such simple implementation has the loop contents in body-fun and
implements jump-fun such that its argument unchanged, but sets
the program counter to zero if a condition is met. The program
counter is set via system call operator Q{103 n} where n is sim‐
ply which function in left-hand side of the operator :: is eval‐
uated next. For example, { {:x+1:} {:x Q{103 -{x>10}}:}
}::{arg} increments the argument by one until it becomes greater
than 10. In that case, the system call sets the program counter
to -1, which is out of range and the evaluation stops.
More complex flow control is possible, as the operator Q{103 n}
can be used exactly like a goto statement. Q{102} can be used to
find the current program counter and calculate relative jumps.
System calls
The internal state of ised can be accessed and modified using the sys‐
tem call operator Qx. The argument x is an array, where the first com‐
ponent is system call id number and the rest are optional arguments to
the system call. The list of system calls will be expanded in future
versions of ised.
Example: use ised--l load_file '$1 Q{$1>3}' to output the specified
file, but terminate as soon as it encounters a number greater than 3.
The system call ids are available as named variables, specified between
the backticks as `<name>`. For instance, a call Q{`EXIT` 42} terminates
the program with a return value of 42.
The list of system call numbers and names:
0 [NOP]: no-op
1 [EXIT]: exit
Exits with return value 0 or the value specified as an optional
argument.
100 [BREAK]: break
Interrupts the loading of files by commands --f, --l, --a or --x
and aborts evaluation of the current line.
101 [CONT]: continue
Aborts evaluation of the current line and proceeds to the next
line in the file.
102 [PC]: get program counter
Returns the index of currently evaluated function in innermost
evaluation operator ::.
103 [PCSET]: set program counter
Sets the index of next evaluated function in innermost operator
::. If argument is out of bounds, it terminates the evaluation.
If without arguments, it does nothing.
104 [STACKDEPTH]: get stack depth
Return the number of nested functions around the call. If not in
a function, it returns 0.
105 [MAXITER]: get/set iteration limit
Without argument, the iteration limit for operator ::: is
returned. With argument, it is changed to the given (nonnega‐
tive) value.
1000 [HISTORY_COUNT]: get history count
Returns the number of history entries, or -1 if history is dis‐
abled.
1001 [HISTORY_ENABLE]: disable history
Disables remembering previous results or enables it, if called
with a nonzero argument.
1002 [HISTORY_CLEAR]: clear history
Clears the history.
2000 [MEM_INDEX]: get/set indexing memory slot
Without arguments, it sets the memory slot where current line
number is stored (default is 0). With argument, it sets it.
2001 [MEM_INPUT]: get/set input memory slot
Same as 2000, but for the memory slot where the current input
line is stored (default 1).
2002 [MEM_OFFSET]: get/set file loading offset
Same as 2000, but for the memory slot where --a continues load‐
ing lines to. At startup, this is 0 so the first memory slot
filled is $1 and is advanced with each loaded line.
2003 [MEM_CLEAR]: delete from memory
Clear entire contents of memory if called without arguments. The
optional argument is a list of memory slots to delete.
2004 [MEM_LIST]: get memory list
Lists the occupied memory slots.
2050 [FUN_CLEAR]: delete function
Clears all the functions if called without arguments. The
optional argument is a list of function ids to delete.
2051 [FUN_LIST]: get function list
Lists the occupied function ids.
3000 [VERSION]: ised version
Returns the array, containing the version number
{major,minor,revision}.
3001 [SIZEOF_INT]: int size
Returns the size of integer type in bytes.
3002 [SIZEOF_FLOAT]: float size
Returns the size of float type in bytes.
3003 [DEBUG]: debug level
Returns the debugging level, set at compile-time.
3004 [READLINE_STATUS]: readline status
Returns the array indicating if various libreadline functionali‐
ties are enabled (use --v for details).
3005 [OVERFLOW_STATUS]: overflow enabled
Returns 1 if overflow handling was enabled at compile-time and 0
otherwise.
5000 [TIME]: system time
Returns unix time in seconds if called without arguments. The
arguments can be list of values, which specify the time fields
to output:
0 [TIME.EPOCH] = epoch
1 [TIME.SEC] = sec
2 [TIME.MIN] = min
3 [TIME.HOUR] = hour
4 [TIME.MONTHDAY] = month-day
5 [TIME.MONTH] = month
6 [TIME.YEAR] = year
7 [TIME.WEEKDAY] = week-day
8 [TIME.YEARDAY] = year-day
For instance, a call Q{`TIME` `TIME.YEAR` `TIME.MONTH` `TIME.DAY`} may
return the array {2013 10 31}.
5001 [PROCESS_TIME]: process time
Returns array containing real time, user time and system time in
seconds.
5002 [SLEEP]: sleep
Sleep for the amount of seconds specified in the argument.
5050 [PID]: pid
Return the PID of this process.
EXAMPLESised '@0[2 100];$0\{$0*$0}'
returns all prime numbers up to 100. It utilises memory to pre‐
vent code repetition.
ised '(0 (1 2 10) 10)'
generates squares of numbers up to 10, by using nested construc‐
tors. Inner constructor generates increments for outer construc‐
tor.
ised--l file '$0 ~$1'
reverses lines of file and prepends line numbers.
ised '@0 {0.5*{1+sqt5}};r{{$0^[1 20]:-(-$0)^-[1 20]}/sqt5}'
generates Fibonacci sequence using direct exponential formula.
ised--d '\n' '[0 1/d5 10]'
generates evenly spaced values between 0 and 10, separated by a
newline. Same functionality as
seq 0 0.2 10
ised--d '\n' '[0 pi/100 pi]' | ised--F '%+12.6f' --l - 'd{$1 sin$1
cos$1 tan$1 exp$1 $1^2}'
generates nicely formatted table of several functions in range
between 0 and pi. Note the use of placeholder - for standard
input.
ised--o tmp_file --t '[0 pi/100 pi]' --o - --F '%+12.6f' --l tmp_file
'd{$1 sin$1 cos$1 tan$1 exp$1 $1^2}'
previous example, achieved in one pass using a temporary inter‐
mediate file. Note the use of placeholder - for standard output.
ised '{1.4^[11]}@:{1./[11]!} exp1.4'
calculation of exp(1.4) by summation of series, compared to
exact value.
ised '@1 60;@2 72;@3[1 $1];{$1%$3==0}:*{$2%$3==0}:*$3\0'
returns list of common divisors of 60 and 72. Numbers 60 and 72
are first stored in memory, together with list of possible divi‐
sors, for easier readability. Note the use of multiplication for
boolean and evaluation. The same can be achieved more elegantly
with operator ?:
ised '@1 60;@2 72;@3[1 $1];$3_?{{$1%$3==0}:*{$2%$3==0}}'
ised '@1 60;@2 72;{$1*[1 $2]&$2*[1 $1]}_0'
returns least common multiple of 60 and 72.
ised--d '+' '2^[10]' | ised
illustration how changing output format can produce useful input
for other programs, in this case, ised itself. This is useful
for easier input of operator repetition, for example the power
tower:
ised--d '^' '(1/sqt2 10)' | ised--l - '-$1' this outputs solu‐
tion of equation 2^x=x^2.
ised '@1{2}@2{3}@3{-5};{-$2+pm*sqt{$2^2-4*$1*$3}}/{2*$1}'
solves quadratic equation 2x^2+3x-5. Capability of handling
arrays is exploited to give both solutions at once. pm operator
is shorthand for array {1,-1}.
The same can be achieved with built-in polynomial solver:
ised '@1{2}@2{3}@3{-5};pz{$3 $2 $1}'
Note that the intermediate variables $1,$2,$3 were only used to
make the expression more readable.
yes 0 | ised '@2{145}' --l - '@2{{$2/2 3*$2+1}_{$2%2}} Q{100 $2==1}'
outputs the Hailstone sequence for the number 145. It uses GNU
core utility yes to produce an infinite loop and terminates
using a conditional system call 100 (break).
ised--D '%02d' --d ':' 'Q{5002 60-Q{5000 1}};Q{5000 3 2 1}'
Waits for the minute to change and then displays the current
time, so that the seconds will be zero. It uses the time-related
system call utilities 5000 (system time) and 5002 (sleep).
AUTHOR
Simon Copar
SEE ALSOseq(1)
May 1, 2014 ised(1)
