Generator/Exponential: Difference between revisions
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===Functional=== |
===Functional=== |
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====ES6==== |
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Compositional derivation of custom generators: |
Compositional derivation of custom generators: |
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{{Works with|JavaScript|ES6}} |
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<lang javascript>(() => { |
<lang javascript>(() => { |
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'use strict'; |
'use strict'; |
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Revision as of 11:51, 1 April 2019
You are encouraged to solve this task according to the task description, using any language you may know.
A generator is an executable entity (like a function or procedure) that contains code that yields a sequence of values, one at a time, so that each time you call the generator, the next value in the sequence is provided.
Generators are often built on top of coroutines or objects so that the internal state of the object is handled “naturally”.
Generators are often used in situations where a sequence is potentially infinite, and where it is possible to construct the next value of the sequence with only minimal state.
- Task
- Create a function that returns a generation of the m'th powers of the positive integers starting from zero, in order, and without obvious or simple upper limit. (Any upper limit to the generator should not be stated in the source but should be down to factors such as the languages natural integer size limit or computational time/size).
- Use it to create a generator of:
- Squares.
- Cubes.
- Create a new generator that filters all cubes from the generator of squares.
- Drop the first 20 values from this last generator of filtered results, and then show the next 10 values.
Note that this task requires the use of generators in the calculation of the result.
- Also see
Ada
To modify the internal state, the function uses an access parameter. For a different approach, see the Random packages of the Ada compiler, which use the so-called "Rosen trick". With the next release of Ada 2012 functions are allowed to have in-out parameters, which would solve this problem, too. You could also use procedures instead of functions.
generator.ads: <lang Ada>package Generator is
type Generator is tagged private; procedure Reset (Gen : in out Generator); function Get_Next (Gen : access Generator) return Natural;
type Generator_Function is access function (X : Natural) return Natural;
procedure Set_Generator_Function (Gen : in out Generator;
Func : Generator_Function);
procedure Skip (Gen : access Generator'Class; Count : Positive := 1);
private
function Identity (X : Natural) return Natural;
type Generator is tagged record
Last_Source : Natural := 0;
Last_Value : Natural := 0;
Gen_Func : Generator_Function := Identity'Access;
end record;
end Generator;</lang>
generator-filtered.ads: <lang Ada>package Generator.Filtered is
type Filtered_Generator is new Generator with private; procedure Reset (Gen : in out Filtered_Generator); function Get_Next (Gen : access Filtered_Generator) return Natural;
procedure Set_Source (Gen : in out Filtered_Generator;
Source : access Generator);
procedure Set_Filter (Gen : in out Filtered_Generator;
Filter : access Generator);
private
type Filtered_Generator is new Generator with record
Last_Filter : Natural := 0;
Source, Filter : access Generator;
end record;
end Generator.Filtered;</lang>
generator.adb: <lang Ada>package body Generator is
-------------- -- Identity -- --------------
function Identity (X : Natural) return Natural is
begin
return X;
end Identity;
---------- -- Skip -- ----------
procedure Skip (Gen : access Generator'Class; Count : Positive := 1) is
Val : Natural;
pragma Unreferenced (Val);
begin
for I in 1 .. Count loop
Val := Gen.Get_Next;
end loop;
end Skip;
----------- -- Reset -- -----------
procedure Reset (Gen : in out Generator) is
begin
Gen.Last_Source := 0;
Gen.Last_Value := 0;
end Reset;
-------------- -- Get_Next -- --------------
function Get_Next (Gen : access Generator) return Natural is
begin
Gen.Last_Source := Gen.Last_Source + 1;
Gen.Last_Value := Gen.Gen_Func (Gen.Last_Source);
return Gen.Last_Value;
end Get_Next;
---------------------------- -- Set_Generator_Function -- ----------------------------
procedure Set_Generator_Function
(Gen : in out Generator;
Func : Generator_Function)
is
begin
if Func = null then
Gen.Gen_Func := Identity'Access;
else
Gen.Gen_Func := Func;
end if;
end Set_Generator_Function;
end Generator;</lang>
generator-filtered.adb: <lang Ada>package body Generator.Filtered is
----------- -- Reset -- -----------
procedure Reset (Gen : in out Filtered_Generator) is
begin
Reset (Generator (Gen));
Gen.Source.Reset;
Gen.Filter.Reset;
Gen.Last_Filter := 0;
end Reset;
-------------- -- Get_Next -- --------------
function Get_Next (Gen : access Filtered_Generator) return Natural is
Next_Source : Natural := Gen.Source.Get_Next;
Next_Filter : Natural := Gen.Last_Filter;
begin
loop
if Next_Source > Next_Filter then
Gen.Last_Filter := Gen.Filter.Get_Next;
Next_Filter := Gen.Last_Filter;
elsif Next_Source = Next_Filter then
Next_Source := Gen.Source.Get_Next;
else
return Next_Source;
end if;
end loop;
end Get_Next;
---------------- -- Set_Source -- ----------------
procedure Set_Source
(Gen : in out Filtered_Generator;
Source : access Generator)
is
begin
Gen.Source := Source;
end Set_Source;
---------------- -- Set_Filter -- ----------------
procedure Set_Filter
(Gen : in out Filtered_Generator;
Filter : access Generator)
is
begin
Gen.Filter := Filter;
end Set_Filter;
end Generator.Filtered;</lang>
example use: <lang Ada>with Ada.Text_IO; with Generator.Filtered;
procedure Generator_Test is
function Square (X : Natural) return Natural is
begin
return X * X;
end Square;
function Cube (X : Natural) return Natural is
begin
return X * X * X;
end Cube;
G1, G2 : aliased Generator.Generator; F : aliased Generator.Filtered.Filtered_Generator;
begin
G1.Set_Generator_Function (Func => Square'Unrestricted_Access); G2.Set_Generator_Function (Func => Cube'Unrestricted_Access);
F.Set_Source (G1'Unrestricted_Access); F.Set_Filter (G2'Unrestricted_Access);
F.Skip (20);
for I in 1 .. 10 loop
Ada.Text_IO.Put ("I:" & Integer'Image (I));
Ada.Text_IO.Put (", F:" & Integer'Image (F.Get_Next));
Ada.Text_IO.New_Line;
end loop;
end Generator_Test;</lang>
- Output:
I: 1, F: 529 I: 2, F: 576 I: 3, F: 625 I: 4, F: 676 I: 5, F: 784 I: 6, F: 841 I: 7, F: 900 I: 8, F: 961 I: 9, F: 1024 I: 10, F: 1089
ALGOL 68
File: Template.Generator.a68<lang algol68>MODE YIELDVALUE = PROC(VALUE)VOID; MODE GENVALUE = PROC(YIELDVALUE)VOID;
PROC gen filtered = (GENVALUE gen candidate, gen exclude, YIELDVALUE yield)VOID: (
VALUE candidate; SEMA have next exclude = LEVEL 0; VALUE exclude; SEMA get next exclude = LEVEL 0; BOOL initialise exclude := TRUE;
PAR ( # run each generator in a different thread #
- Thread 1 #
# FOR VALUE next exclude IN # gen exclude( # ) DO #
## (VALUE next exclude)VOID: (
DOWN get next exclude; exclude := next exclude;
IF candidate <= exclude THEN
UP have next exclude
ELSE
UP get next exclude
FI
# OD #)),
- Thread 2 #
# FOR VALUE next candidate IN # gen candidate( # ) DO #
## (VALUE next candidate)VOID: (
candidate := next candidate;
IF initialise exclude ORF candidate > exclude THEN
UP get next exclude;
DOWN have next exclude; # wait for result #
initialise exclude := FALSE
FI;
IF candidate < exclude THEN
yield(candidate)
FI
# OD #))
)
);
PROC gen slice = (GENVALUE t, VALUE start, stop, YIELDVALUE yield)VOID: (
INT index := 0;
# FOR VALUE i IN # t( # ) DO #
## (VALUE i)VOID: (
IF index >= stop THEN done
ELIF index >= start THEN yield(i) FI;
index +:= 1
# OD # ));
done: SKIP
);
PROC get list = (GENVALUE gen)[]VALUE: (
INT upb := 0;
INT ups := 2;
FLEX [ups]VALUE out;
# FOR VALUE i IN # gen( # ) DO #
## (VALUE i)VOID:(
upb +:= 1;
IF upb > ups THEN # dynamically grow the array 50% #
[ups +:= ups OVER 2]VALUE append; append[:upb-1] := out; out := append
FI;
out[upb] := i
# OD # ))
out[:upb]
);
PROC powers = (VALUE m, YIELDVALUE yield)VOID:
FOR n FROM 0 DO yield(n ** m) OD;</lang>File: test.Generator.a68<lang algol68>#!/usr/local/bin/a68g --script #
MODE VALUE = INT; PR READ "Template.Generator.a68" PR
GENVALUE squares = powers(2,), cubes = powers(3,); GENVALUE fil = gen filtered(squares, cubes,);
printf(($g(0)x$, get list(gen slice(fil, 20, 30, )) ))</lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
C
libco is a tiny library that adds cooperative multithreading, also known as coroutines, to the C language. Its co_switch(x) function pauses the current cothread and resumes the other cothread x.
This example provides next64() and yield64(), to generate 64-bit integers. next64() switches to a generator. Then the generator passes some 64-bit integer to yield64(), which switches to the first cothread, where next64() returns this 64-bit integer.
<lang c>#include <inttypes.h> /* int64_t, PRId64 */
- include <stdlib.h> /* exit() */
- include <stdio.h> /* printf() */
- include <libco.h> /* co_{active,create,delete,switch}() */
/* A generator that yields values of type int64_t. */ struct gen64 { cothread_t giver; /* this cothread calls yield64() */ cothread_t taker; /* this cothread calls next64() */ int64_t given; void (*free)(struct gen64 *); void *garbage; };
/* Yields a value. */ inline void yield64(struct gen64 *gen, int64_t value) { gen->given = value; co_switch(gen->taker); }
/* Returns the next value that the generator yields. */ inline int64_t next64(struct gen64 *gen) { gen->taker = co_active(); co_switch(gen->giver); return gen->given; }
static void gen64_free(struct gen64 *gen) { co_delete(gen->giver); }
struct gen64 *entry64;
/*
* Creates a cothread for the generator. The first call to next64(gen) * will enter the cothread; the entry function must copy the pointer * from the global variable struct gen64 *entry64. * * Use gen->free(gen) to free the cothread. */
inline void gen64_init(struct gen64 *gen, void (*entry)(void)) { if ((gen->giver = co_create(4096, entry)) == NULL) { /* Perhaps malloc() failed */ fputs("co_create: Cannot create cothread\n", stderr); exit(1); } gen->free = gen64_free; entry64 = gen; }
/*
* Generates the powers 0**m, 1**m, 2**m, .... */
void powers(struct gen64 *gen, int64_t m) { int64_t base, exponent, n, result;
for (n = 0;; n++) { /* * This computes result = base**exponent, where * exponent is a nonnegative integer. The result * is the product of repeated squares of base. */ base = n; exponent = m; for (result = 1; exponent != 0; exponent >>= 1) { if (exponent & 1) result *= base; base *= base; } yield64(gen, result); } /* NOTREACHED */ }
/* stuff for squares_without_cubes() */
- define ENTRY(name, code) static void name(void) { code; }
ENTRY(enter_squares, powers(entry64, 2)) ENTRY(enter_cubes, powers(entry64, 3))
struct swc { struct gen64 cubes; struct gen64 squares; void (*old_free)(struct gen64 *); };
static void swc_free(struct gen64 *gen) { struct swc *f = gen->garbage; f->cubes.free(&f->cubes); f->squares.free(&f->squares); f->old_free(gen); }
/*
* Generates the squares 0**2, 1**2, 2**2, ..., but removes the squares * that equal the cubes 0**3, 1**3, 2**3, .... */
void squares_without_cubes(struct gen64 *gen) { struct swc f; int64_t c, s;
gen64_init(&f.cubes, enter_cubes); c = next64(&f.cubes);
gen64_init(&f.squares, enter_squares); s = next64(&f.squares);
/* Allow other cothread to free this generator. */ f.old_free = gen->free; gen->garbage = &f; gen->free = swc_free;
for (;;) { while (c < s) c = next64(&f.cubes); if (c != s) yield64(gen, s); s = next64(&f.squares); } /* NOTREACHED */ }
ENTRY(enter_squares_without_cubes, squares_without_cubes(entry64))
/*
* Look at the sequence of numbers that are squares but not cubes. * Drop the first 20 numbers, then print the next 10 numbers. */
int main() { struct gen64 gen; int i;
gen64_init(&gen, enter_squares_without_cubes);
for (i = 0; i < 20; i++) next64(&gen); for (i = 0; i < 9; i++) printf("%" PRId64 ", ", next64(&gen)); printf("%" PRId64 "\n", next64(&gen));
gen.free(&gen); /* Free memory. */ return 0; }</lang>
One must download libco and give libco.c to the compiler.
$ libco=/home/kernigh/park/libco $ cc -I$libco -o main main.c $libco/libco.c $ ./main 529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089
Using struct to store state
<lang C>#include <stdio.h>
- include <stdlib.h>
- include <math.h>
typedef int (*seq_func)(void *);
- define SEQ_BASE seq_func f; int output
/* sort of polymorphing data structure */ typedef struct { SEQ_BASE; } gen_t;
int seq_next(void *state) { return ((gen_t*)state)->output = (*(seq_func*)state)(state); }
typedef struct { SEQ_BASE; int pos, n; } power_gen_t;
int power_next(void *s) { return (int)pow(++((power_gen_t*)s)->pos, ((power_gen_t*)s)->n); }
void *power_seq(int n) { power_gen_t *s = malloc(sizeof(power_gen_t)); s->output = -1; s->f = power_next; s->n = n; s->pos = -1; return s; }
typedef struct { SEQ_BASE; void *in, *without; } filter_gen_t;
int filter_next(void *s) { gen_t *in = ((filter_gen_t*)s)->in, *wo = ((filter_gen_t*)s)->without;
do{ seq_next(in); while (wo->output < in->output) seq_next(wo); } while(wo->output == in->output);
return in->output; }
void* filter_seq(gen_t *in, gen_t *without) { filter_gen_t *filt = malloc(sizeof(filter_gen_t)); filt->in = in; filt->without = without; filt->f = filter_next; filt->output = -1; return filt; }
int main() { int i; void *s = filter_seq(power_seq(2), power_seq(3));
for (i = 0; i < 20; i++) seq_next(s); for (i = 0; i < 10; i++) printf("%d\n", seq_next(s));
return 0; }</lang>
- Output:
529576 625 676 784 841 900 961 1024
1089
C++
A templated solution.
<lang cpp>#include <iostream> using namespace std;
template<class T> class Generator { public:
virtual T operator()() = 0;
};
// Does nothing unspecialized template<class T, T P> class PowersGenerator: Generator<T> {};
// Specialize with other types, or provide a generic version of pow template<int P> class PowersGenerator<int, P>: Generator<int> { public:
int i;
PowersGenerator() { i = 1; }
virtual int operator()()
{
int o = 1;
for(int j = 0; j < P; ++j) o *= i;
++i;
return o;
}
};
// Only works with non-decreasing generators template<class T, class G, class F> class Filter: Generator<T> { public:
G gen; F filter; T lastG, lastF;
Filter() { lastG = gen(); lastF = filter(); }
virtual T operator()()
{
while(lastG >= lastF)
{
if(lastG == lastF)
lastG = gen();
lastF = filter();
}
T out = lastG; lastG = gen(); return out; }
};
int main() {
Filter<int, PowersGenerator<int, 2>, PowersGenerator<int, 3>> gen;
for(int i = 0; i < 20; ++i) gen();
for(int i = 20; i < 30; ++i) cout << i << ": " << gen() << endl;
}</lang>
- Output:
20: 529 21: 576 22: 625 23: 676 24: 784 25: 841 26: 900 27: 961 28: 1024 29: 1089
C#
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
static class Program {
static void Main() {
Func<int, IEnumerable<int>> ms = m => Infinite().Select(i => (int)Math.Pow(i, m));
var squares = ms(2);
var cubes = ms(3);
var filtered = squares.Where(square => cubes.First(cube => cube >= square) != square);
var final = filtered.Skip(20).Take(10);
foreach (var i in final) Console.WriteLine(i);
}
static IEnumerable<int> Infinite() {
var i = 0;
while (true) yield return i++;
}
}</lang>
Clojure
In Clojure, the role that generator functions take in some other languages is generally filled by sequences. Most of the functions that produce sequences produce lazy sequences, many of the standard functions deal with sequences, and their use in Clojure is extremely idiomatic. Thus we can define squares and cubes as lazy sequences:
<lang clojure>(defn powers [m] (for [n (iterate inc 1)] (reduce * (repeat m n))))) (def squares (powers 2)) (take 5 squares) ; => (1 4 9 16 25)</lang>
The definition here of the squares-not-cubes lazy sequence uses the loop/recur construct, which isn't lazy. So we use lazy-seq explicity:
<lang clojure>(defn squares-not-cubes
([] (squares-not-cubes (powers 2) (powers 3)))
([squares cubes]
(loop [[p2first & p2rest :as p2s] squares, [p3first & p3rest :as p3s] cubes]
(cond
(= p2first p3first) (recur p2rest p3rest)
(> p2first p3first) (recur p2s p3rest)
:else (cons p2first (lazy-seq (squares-not-cubes p2rest p3s)))))))
(->> (squares-not-cubes) (drop 20) (take 10))
- => (529 576 625 676 784 841 900 961 1024 1089)</lang>
If we really need a generator function for some reason, any lazy sequence can be turned into a stateful function. (The inverse of seq->fn is the standard function repeatedly.)
<lang clojure>(defn seq->fn [sequence]
(let [state (atom (cons nil sequence))] (fn [] (first (swap! state rest)))
(def f (seq->fn (squares-not-cubes))) [(f) (f) (f)] ; => [4 9 16]</lang>
Common Lisp
<lang lisp>(defun take (seq &optional (n 1))
(values-list (loop repeat n collect (funcall seq))))
(defun power-seq (n)
(let ((x 0)) (lambda () (expt (incf x) n))))
(defun filter-seq (s1 s2) ;; remove s2 from s1
(let ((x1 (take s1)) (x2 (take s2)))
(lambda ()
(tagbody g
(if (= x1 x2) (progn (setf x1 (take s1) x2 (take s2)) (go g))) (if (> x1 x2) (progn (setf x2 (take s2)) (go g))))
(prog1 x1 (setf x1 (take s1))))))
(let ((2not3 (filter-seq (power-seq 2) (power-seq 3))))
(take 2not3 20) ;; drop 20 (princ (multiple-value-list (take 2not3 10))))</lang>
D
Efficient Standard Version
<lang d>void main() {
import std.stdio, std.bigint, std.range, std.algorithm;
auto squares = 0.sequence!"n".map!(i => i.BigInt ^^ 2); auto cubes = 0.sequence!"n".map!(i => i.BigInt ^^ 3);
squares.setDifference(cubes).drop(20).take(10).writeln;
}</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
Simple Ranges-Based Implementation
<lang d>void main() {
import std.stdio, std.bigint, std.range, std.algorithm;
auto squares = 0.sequence!"n".map!(i => i.BigInt ^^ 2); auto cubes = 0.sequence!"n".map!(i => i.BigInt ^^ 3);
squares .filter!(s => cubes.find!(c => c >= s).front != s) .drop(20) .take(10) .writeln;
}</lang> The output is the same.
More Efficient Ranges-Based Version
<lang d>import std.stdio, std.bigint, std.range, std.algorithm;
struct Filtered(R1, R2) if (is(ElementType!R1 == ElementType!R2)) {
R1 s1; R2 s2; alias ElementType!R1 T; T front, source, filter;
this(R1 r1, R2 r2) {
s1 = r1;
s2 = r2;
source = s1.front;
filter = s2.front;
popFront;
}
static immutable empty = false;
void popFront() {
while (true) {
if (source > filter) {
s2.popFront;
filter = s2.front;
continue;
} else if (source < filter) {
front = source;
s1.popFront;
source = s1.front;
break;
}
s1.popFront;
source = s1.front;
}
}
}
auto filtered(R1, R2)(R1 r1, R2 r2) // Helper function. if (isInputRange!R1 && isInputRange!R2 &&
is(ElementType!R1 == ElementType!R2)) {
return Filtered!(R1, R2)(r1, r2);
}
void main() {
auto squares = 0.sequence!"n".map!(i => i.BigInt ^^ 2); auto cubes = 0.sequence!"n".map!(i => i.BigInt ^^ 3); filtered(squares, cubes).drop(20).take(10).writeln;
}</lang> The output is the same.
Closures-Based Version
<lang d>import std.stdio;
auto powers(in double e) pure nothrow {
double i = 0; return () => i++ ^^ e;
}
auto filter2(D)(D af, D bf) {
double a = af(), b = bf();
return {
double r;
while (true) {
if (a < b) {
r = a;
a = af();
break;
}
if (b == a)
a = af();
b = bf();
}
return r;
};
}
void main() {
auto fgen = filter2(2.powers, 3.powers);
foreach (immutable i; 0 .. 20)
fgen();
foreach (immutable i; 0 .. 10)
write(fgen(), " ");
writeln;
}</lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
Generator Range Version
<lang d>import std.stdio, std.range, std.algorithm, std.concurrency, std.bigint;
auto powers(in uint m) pure nothrow @safe {
return 0.sequence!"n".map!(i => i.BigInt ^^ m);
}
auto filtered(R1, R2)(R1 r1, R2 r2) /*@safe*/ if (isForwardRange!R1 && isForwardRange!R2 &&
is(ElementType!R1 == ElementType!R2)) {
return new Generator!(ElementType!R1)({
auto v = r1.front; r1.popFront;
auto f = r2.front; r2.popFront;
while (true) {
if (v > f) {
f = r2.front; r2.popFront;
continue;
} else if (v < f)
yield(v);
v = r1.front; r1.popFront;
}
});
}
void main() {
auto squares = 2.powers, cubes = 3.powers; filtered(squares, cubes).drop(20).take(10).writeln;
}</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
E
E does not provide coroutines on the principle that interleaving of execution of code should be explicit to avoid unexpected interactions. However, this problem does not especially require them. Each generator here is simply a function that returns the next value in the sequence when called.
<lang e>def genPowers(exponent) {
var i := -1
return def powerGenerator() {
return (i += 1) ** exponent
}
}
def filtered(source, filter) {
var fval := filter()
return def filterGenerator() {
while (true) {
def sval := source()
while (sval > fval) {
fval := filter()
}
if (sval < fval) {
return sval
}
}
}
}
def drop(n, gen) {
for _ in 1..n { gen() }
}
def squares := genPowers(2)
def cubes := genPowers(3)
def squaresNotCubes := filtered(squares, cubes)
drop(20, squaresNotCubes)
for _ in 1..10 {
print(`${squaresNotCubes()} `)
} println()</lang>
EchoLisp
<lang scheme> (lib 'tasks) ;; for make-generator
- generator of generators
(define (gen-power power) (make-generator (lambda(n) (yield (expt n power)) (1+ n)) 1))
(define powers-2 (gen-power 2)) (define powers-3 (gen-power 3))
(take powers-3 10)
→ (1 8 27 64 125 216 343 512 729 1000)
- generators substraction
- input
- two generators ga, gb - Sequences must be increasing
- output
- new generator = ga sequence minus gb sequence
(define (gen-substract ga gb) (define (substract b (a)) (set! a (next ga)) (while (>= a b) ; avance b until > a (when (= a b) (set! a (next ga))) (set! b (next gb))) (yield a) b ) ;; b := next state (make-generator substract (next gb)))
- application
(define task (gen-substract (gen-power 2) (gen-power 3)))
(drop task 20) (take task 10)
→ (529 576 625 676 784 841 900 961 1024 1089)
- inspect
task → #generator:state: 1331 </lang>
Elixir
<lang elixir>defmodule Generator do
def filter( source_pid, remove_pid ) do
first_remove = next( remove_pid )
spawn( fn -> filter_loop(source_pid, remove_pid, first_remove) end )
end
def next( pid ) do
send(pid, {:next, self})
receive do
x -> x
end
end
def power( m ), do: spawn( fn -> power_loop(m, 0) end )
def task do
squares_pid = power( 2 )
cubes_pid = power( 3 )
filter_pid = filter( squares_pid, cubes_pid )
for _x <- 1..20, do: next(filter_pid)
for _x <- 1..10, do: next(filter_pid)
end
defp filter_loop( pid1, pid2, n2 ) do
receive do
{:next, pid} ->
{n, new_n2} = filter_loop_next( next(pid1), n2, pid1, pid2 )
send( pid, n )
filter_loop( pid1, pid2, new_n2 )
end
end
defp filter_loop_next( n1, n2, pid1, pid2 ) when n1 > n2, do:
filter_loop_next( n1, next(pid2), pid1, pid2 )
defp filter_loop_next( n, n, pid1, pid2 ), do:
filter_loop_next( next(pid1), next(pid2), pid1, pid2 )
defp filter_loop_next( n1, n2, _pid1, _pid2 ), do: {n1, n2}
defp power_loop( m, n ) do
receive do
{:next, pid} -> send( pid, round(:math.pow(n, m) ) )
end
power_loop( m, n + 1 )
end
end
IO.inspect Generator.task</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
Erlang
<lang Erlang> -module( generator ).
-export( [filter/2, next/1, power/1, task/0] ).
filter( Source_pid, Remove_pid ) -> First_remove = next( Remove_pid ),
erlang:spawn( fun() -> filter_loop(Source_pid, Remove_pid, First_remove) end ).
next( Pid ) ->
Pid ! {next, erlang:self()},
receive X -> X end.
power( M ) -> erlang:spawn( fun() -> power_loop(M, 0) end ).
task() ->
Squares_pid = power( 2 ), Cubes_pid = power( 3 ), Filter_pid = filter( Squares_pid, Cubes_pid ), [next(Filter_pid) || _X <- lists:seq(1, 20)], [next(Filter_pid) || _X <- lists:seq(1, 10)].
filter_loop( Pid1, Pid2, N2 ) ->
receive
{next, Pid} ->
{N, New_N2} = filter_loop_next( next(Pid1), N2, Pid1, Pid2 ),
Pid ! N
end,
filter_loop( Pid1, Pid2, New_N2 ).
filter_loop_next( N1, N2, Pid1, Pid2 ) when N1 > N2 -> filter_loop_next( N1, next(Pid2), Pid1, Pid2 ); filter_loop_next( N, N, Pid1, Pid2 ) -> filter_loop_next( next(Pid1), next(Pid2), Pid1, Pid2 ); filter_loop_next( N1, N2, _Pid1, _Pid2 ) -> {N1, N2}.
power_loop( M, N ) ->
receive {next, Pid} -> Pid ! erlang:round(math:pow(N, M) ) end,
power_loop( M, N + 1 ). </lang>
- Output:
31> generator:task(). [529,576,625,676,784,841,900,961,1024,1089]
F#
<lang fsharp>let m n = Seq.unfold(fun i -> Some(bigint.Pow(i, n), i + 1I)) 0I
let squares = m 2 let cubes = m 3
let (--) orig veto = Seq.where(fun n -> n <> (Seq.find(fun m -> m >= n) veto)) orig
let ``squares without cubes`` = squares -- cubes
Seq.take 10 (Seq.skip 20 (``squares without cubes``)) |> Seq.toList |> printfn "%A"</lang>
- Output:
[529; 576; 625; 676; 784; 841; 900; 961; 1024; 1089]
Factor
Using lazy lists for our generators: <lang factor>USING: fry kernel lists lists.lazy math math.functions prettyprint ; IN: rosetta-code.generator-exponential
- mth-powers-generator ( m -- lazy-list )
[ 0 lfrom ] dip [ ^ ] curry lmap-lazy ;
- lmember? ( elt list -- ? )
over '[ unswons dup _ >= ] [ drop ] until nip = ;
- 2-not-3-generator ( -- lazy-list )
2 mth-powers-generator [ 3 mth-powers-generator lmember? not ] <lazy-filter> ;
10 2-not-3-generator 20 [ unswons drop ] times ltake list>array .</lang>
- Output:
{ 529 576 625 676 784 841 900 961 1024 1089 }
Fantom
Using closures to implement generators.
<lang fantom> class Main {
// Create and return a function which generates mth powers when called
|->Int| make_generator (Int m)
{
current := 0
return |->Int|
{
current += 1
return (current-1).pow (m)
}
}
|->Int| squares_without_cubes ()
{
squares := make_generator (2)
cubes := make_generator (3)
c := cubes.call
return |->Int|
{
while (true)
{
s := squares.call
while (c < s) { c = cubes.call }
if (c != s) return s
}
return 0
}
}
Void main ()
{
swc := squares_without_cubes ()
20.times { swc.call } // drop 20 values
10.times // display the next 10
{
echo (swc.call)
}
}
} </lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
Forth
<lang Forth> \ genexp-rcode.fs Generator/Exponential for RosettaCode.org
\ Generator/filter implementation using return stack as continuations stack
- ENTER ( cont.addr -- ;borrowed from M.L.Gasanenko papers)
>R
- | ( f -- ;true->go ahead, false->return into generator )
IF EXIT THEN R> DROP
- GEN ( -- ;generate forever what is between 'GEN' and ';' )
BEGIN R@ ENTER AGAIN
- STOP ( f -- ;return to caller of word that contain 'GEN' )
IF R> DROP R> DROP R> DROP THEN
\ Problem at hand
- square ( n -- n^2 ) dup * ;
- cube ( n -- n^3 ) dup square * ;
\ Faster tests using info that tested numbers are monotonic growing
VARIABLE Sqroot \ last square root
VARIABLE Cbroot \ last cubic root
- square? ( u -- f ;test U for square number)
BEGIN
Sqroot @ square over <
WHILE
1 Sqroot +!
REPEAT
Sqroot @ square =
- cube? ( u -- f ;test U for cubic number)
BEGIN
Cbroot @ cube over <
WHILE
1 Cbroot +!
REPEAT
Cbroot @ cube =
VARIABLE Counter
- (go) ( u -- u' )
GEN 1+ Counter @ 30 >= STOP
dup square? | dup cube? 0= | Counter @ 20 >= 1 Counter +! | dup .
- noname 0 Counter ! 1 Sqroot ! 1 Cbroot ! 0 (go) drop ;
execute cr bye </lang>
- Output:
$ gforth -e "include genexp-rcode.fs" 529 576 625 676 784 841 900 961 1024 1089 $
FunL
(for the powers function)
(for the filter)
<lang funl>def powers( m ) = map( (^ m), 0.. )
def
filtered( s@sh:_, ch:ct ) | sh > ch = filtered( s, ct ) filtered( sh:st, c@ch:_ ) | sh < ch = sh # filtered( st, c ) filtered( _:st, c ) = filtered( st, c )
println( filtered(powers(2), powers(3)).drop(20).take(10) )</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
Go
Most direct and most efficient on a single core is implementing generators with closures. <lang go>package main
import (
"fmt" "math"
)
// note: exponent not limited to ints func newPowGen(e float64) func() float64 {
var i float64
return func() (r float64) {
r = math.Pow(i, e)
i++
return
}
}
// given two functions af, bf, both monotonically increasing, return a // new function that returns values of af not returned by bf. func newMonoIncA_NotMonoIncB_Gen(af, bf func() float64) func() float64 {
a, b := af(), bf()
return func() (r float64) {
for {
if a < b {
r = a
a = af()
break
}
if b == a {
a = af()
}
b = bf()
}
return
}
}
func main() {
fGen := newMonoIncA_NotMonoIncB_Gen(newPowGen(2), newPowGen(3))
for i := 0; i < 20; i++ {
fGen()
}
for i := 0; i < 10; i++ {
fmt.Print(fGen(), " ")
}
fmt.Println()
}</lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
Alternatively, generators can be implemented in Go with goroutines and channels. There are tradeoffs however, and often one technique is a significantly better choice.
Goroutines can run concurrently, but there is overhead associated with thread scheduling and channel communication. Flow control is also different. A generator implemented as a closure is a function with a single entry point fixed at the beginning. On repeated calls, execution always starts over at the beginning and ends when a value is returned. A generator implemented as a goroutine, on the other hand, "returns" a value by sending it on a channel, and then the goroutine continues execution from that point. This allows more flexibility in structuring code. <lang go>package main
import (
"fmt" "math"
)
func newPowGen(e float64) chan float64 {
ch := make(chan float64)
go func() {
for i := 0.; ; i++ {
ch <- math.Pow(i, e)
}
}()
return ch
}
// given two input channels, a and b, both known to return monotonically // increasing values, supply on channel c values of a not returned by b. func newMonoIncA_NotMonoIncB_Gen(a, b chan float64) chan float64 {
ch := make(chan float64)
go func() {
for va, vb := <-a, <-b; ; {
switch {
case va < vb:
ch <- va
fallthrough
case va == vb:
va = <-a
default:
vb = <-b
}
}
}()
return ch
}
func main() {
ch := newMonoIncA_NotMonoIncB_Gen(newPowGen(2), newPowGen(3))
for i := 0; i < 20; i++ {
<-ch
}
for i := 0; i < 10; i++ {
fmt.Print(<-ch, " ")
}
fmt.Println()
}</lang>
Haskell
Generators in most cases can be implemented using infinite lists in Haskell. Because Haskell is lazy, only as many elements as needed is computed from the infinite list: <lang haskell>import Data.List.Ordered
powers :: Int -> [Int] powers m = map (^ m) [0..]
squares :: [Int] squares = powers 2
cubes :: [Int] cubes = powers 3
foo :: [Int] foo = filter (not . has cubes) squares
main :: IO () main = print $ take 10 $ drop 20 foo</lang>
- Output:
[529,576,625,676,784,841,900,961,1024,1089]
Icon and Unicon
Generators are close to the heart and soul of Icon/Unicon. Co-expressions let us circumvent the normal backtracking mechanism and get results where we need them.
<lang Icon>procedure main()
write("Non-cube Squares (21st to 30th):") every (k := 0, s := noncubesquares()) do
if(k +:= 1) > 30 then break else write(20 < k," : ",s)
end
procedure mthpower(m) #: generate i^m for i = 0,1,... while (/i := 0) | (i +:= 1) do suspend i^m end
procedure noncubesquares() #: filter for squares that aren't cubes cu := create mthpower(3) # co-expressions so that we can sq := create mthpower(2) # ... get our results where we need
repeat {
if c === s then ( c := @cu , s := @sq )
else if s > c then c := @cu
else {
suspend s
s := @sq
}
}
end</lang>
Note: The task could be written without co-expressions but would be likely be ugly. If there is an elegant non-co-expression version please add it as an alternate example.
- Output:
Non-cube Squares (21st to 30th): 21 : 529 22 : 576 23 : 625 24 : 676 25 : 784 26 : 841 27 : 900 28 : 961 29 : 1024 30 : 1089
J
Generators are not very natural, in J, because they avoid the use of arrays and instead rely on sequential processing.
Here is a generator for mth powers of a number:
<lang j>coclass 'mthPower'
N=: 0 create=: 3 :0 M=: y ) next=: 3 :0 n=. N N=: N+1 n^M )</lang>
And, here are corresponding square and cube generators
<lang j>stateySquare=: 2 conew 'mthPower' stateyCube=: 3 conew 'mthPower'</lang>
Here is a generator for squares which are not cubes:
<lang j>coclass 'uncubicalSquares'
N=: 0 next=: 3 :0"0 while. (-: <.) 3 %: *: n=. N do. N=: N+1 end. N=: N+1 *: n )</lang>
And here is an example of its use:
<lang j> next__g i.10 [ next__g i.20 [ g=: conew 'uncubicalSquares' 529 576 625 676 784 841 900 961 1024 1089</lang>
That said, here is a more natural approach, for J.
<lang j>mthPower=: 1 :'^&m@i.' squares=: 2 mthPower cubes=: 3 mthPower uncubicalSquares=: squares -. cubes</lang>
The downside of this approach is that it is computing independent sequences. And for the "uncubicalSquares" verb, it is removing some elements from that sequence. So you must estimate how many values to generate. However, this can be made transparent to the user with a simplistic estimator:
<lang j>uncubicalSquares=: {. squares@<.@p.~&3 1.1 -. cubes</lang>
Example use:
<lang j>20 }. uncubicalSquares 30 NB. the 21st through 30th uncubical square 529 576 625 676 784 841 900 961 1024 1089</lang>
Java
<lang java>import java.util.function.LongSupplier; import static java.util.stream.LongStream.generate;
public class GeneratorExponential implements LongSupplier {
private LongSupplier source, filter; private long s, f;
public GeneratorExponential(LongSupplier source, LongSupplier filter) {
this.source = source;
this.filter = filter;
f = filter.getAsLong();
}
@Override
public long getAsLong() {
s = source.getAsLong();
while (s == f) {
s = source.getAsLong();
f = filter.getAsLong();
}
while (s > f) {
f = filter.getAsLong();
}
return s; }
public static void main(String[] args) {
generate(new GeneratorExponential(new SquaresGen(), new CubesGen()))
.skip(20).limit(10)
.forEach(n -> System.out.printf("%d ", n));
}
}
class SquaresGen implements LongSupplier {
private long n;
@Override
public long getAsLong() {
return n * n++;
}
}
class CubesGen implements LongSupplier {
private long n;
@Override
public long getAsLong() {
return n * n * n++;
}
}</lang>
529 576 625 676 784 841 900 961 1024 1089
JavaScript
Procedural
<lang JavaScript> function PowersGenerator(m) { var n=0; while(1) { yield Math.pow(n, m); n += 1; } }
function FilteredGenerator(g, f){ var value = g.next(); var filter = f.next();
while(1) { if( value < filter ) { yield value; value = g.next(); } else if ( value > filter ) { filter = f.next(); } else { value = g.next(); filter = f.next(); } } }
var squares = PowersGenerator(2); var cubes = PowersGenerator(3);
var filtered = FilteredGenerator(squares, cubes);
for( var x = 0; x < 20; x++ ) filtered.next() for( var x = 20; x < 30; x++ ) console.logfiltered.next());
</lang>
ES6
<lang JavaScript>function* nPowerGen(n) {
let e = 0;
while (1) { e++ && (yield Math.pow(e, n)); }
}
function* filterGen(gS, gC, skip=0) {
let s = 0; // The square value let c = 0; // The cube value let n = 0; // A skip counter
while(1) {
s = gS.next().value;
s > c && (c = gC.next().value);
s == c ?
c = gC.next().value :
n++ && n > skip && (yield s);
}
}
const filtered = filterGen(nPowerGen(2), nPowerGen(3), skip=20);</lang> <lang JavaScript>// Generate the first 10 values for (let n = 0; n < 10; n++) {
console.log(filtered.next().value)
}</lang>
529 576 625 676 784 841 900 961 1024 1089
Functional
ES6
Compositional derivation of custom generators: <lang javascript>(() => {
'use strict';
// main :: IO()
const main = () => {
// powers :: Gen [Int]
const powers = n =>
fmapGen(
x => Math.pow(x, n),
enumFrom(0)
);
// xs :: [Int]
const xs = take(10, drop(20,
differenceGen(
powers(2),
powers(3)
)
));
console.log(xs);
// -> [529,576,625,676,784,841,900,961,1024,1089]
};
// GENERIC FUNCTIONS ----------------------------------
// Just :: a -> Maybe a
const Just = x => ({
type: 'Maybe',
Nothing: false,
Just: x
});
// Nothing :: Maybe a
const Nothing = () => ({
type: 'Maybe',
Nothing: true,
});
// Tuple (,) :: a -> b -> (a, b)
const Tuple = (a, b) => ({
type: 'Tuple',
'0': a,
'1': b,
length: 2
});
// differenceGen :: Gen [a] -> Gen [a] -> Gen [a]
function* differenceGen(ga, gb) {
// All values of generator stream a except any
// already seen in generator stream b.
const
stream = zipGen(ga, gb),
sb = new Set([]);
while (true) {
const xy = take(1, stream);
if (0 < xy.length) {
const [x, y] = Array.from(xy[0]);
sb.add(y);
if (!sb.has(x)) yield x
}
}
};
// drop :: Int -> [a] -> [a]
// drop :: Int -> Generator [a] -> Generator [a]
// drop :: Int -> String -> String
const drop = (n, xs) =>
Infinity > length(xs) ? (
xs.slice(n)
) : (take(n, xs), xs);
// enumFrom :: Enum a => a -> [a]
function* enumFrom(x) {
let v = x;
while (true) {
yield v;
v = 1 + v;
}
}
// fmapGen <$> :: (a -> b) -> Gen [a] -> Gen [b]
function* fmapGen(f, gen) {
let v = take(1, gen);
while (0 < v.length) {
yield(f(v[0]))
v = take(1, gen)
}
}
// fst :: (a, b) -> a const fst = tpl => tpl[0];
// Returns Infinity over objects without finite length. // This enables zip and zipWith to choose the shorter // argument when one is non-finite, like cycle, repeat etc
// length :: [a] -> Int
const length = xs =>
(Array.isArray(xs) || 'string' === typeof xs) ? (
xs.length
) : Infinity;
// snd :: (a, b) -> b const snd = tpl => tpl[1];
// take :: Int -> [a] -> [a]
// take :: Int -> String -> String
const take = (n, xs) =>
'GeneratorFunction' !== xs.constructor.constructor.name ? (
xs.slice(0, n)
) : [].concat.apply([], Array.from({
length: n
}, () => {
const x = xs.next();
return x.done ? [] : [x.value];
}));
// uncons :: [a] -> Maybe (a, [a])
const uncons = xs => {
const lng = length(xs);
return (0 < lng) ? (
lng < Infinity ? (
Just(Tuple(xs[0], xs.slice(1))) // Finite list
) : (() => {
const nxt = take(1, xs);
return 0 < nxt.length ? (
Just(Tuple(nxt[0], xs))
) : Nothing();
})() // Lazy generator
) : Nothing();
};
// zipGen :: Gen [a] -> Gen [b] -> Gen [(a, b)]
const zipGen = (ga, gb) => {
function* go(ma, mb) {
let
a = ma,
b = mb;
while (!a.Nothing && !b.Nothing) {
let
ta = a.Just,
tb = b.Just
yield(Tuple(fst(ta), fst(tb)));
a = uncons(snd(ta));
b = uncons(snd(tb));
}
}
return go(uncons(ga), uncons(gb));
};
// MAIN --- return main();
})();</lang>
- Output:
[529,576,625,676,784,841,900,961,1024,1089]
jq
Part 1: i^m, 2^m and 3^m
jq is a purely functional language and so does not have generators with state. To generate a sequence of values one-by-one therefore requires a "next-value" function, the input of which must include relevant state information. For convenience, a counter is usually included. For generating i^m, therefore, we would have: <lang jq># Compute self^m where m is a non-negative integer: def pow(m): . as $in | reduce range(0;m) as $i (1; .*$in);
- state: [i, i^m]
def next_power(m): .[0] + 1 | [., pow(m) ];</lang> To make such generators easier to use, we shall define filters to skip and to emit a specified number of items: <lang jq># skip m states, and return the next state def skip(m; next):
if m <= 0 then . else next | skip(m-1; next) end;
- emit m states including the initial state
def emit(m; next):
if m <= 0 then empty else ., (next | emit(m-1; next)) end;</lang>
Examples: <lang jq># Generate the first 4 values in the sequence i^2: [0,0] | emit(4; next_power(2)) | .[1]
- Generate all the values in the sequence i^3 less than 100:
[0,0] | recurse(next_power(3) | if .[1] < 100 then . else empty end) | .[1]</lang> An aside on streams
Since the release of version jq 1.4, enhancements for processing streams of values have been added, notably "foreach" and "limit". If your version of jq has these enhancements, then it is often preferable to use them in conjunction with functions that emit streams of values rather than the "next-value" functions that are the focus of this page.
Part 2: selection from 2 ^ m <lang jq># Infrastructure: def last(f): reduce f as $i (null; $i);
- emit the last value that satisfies condition, or null
def while(condition; next):
def w: if condition then ., (next|w) else empty end; last(w);
- Powers of m1 that are not also powers of m2.
- filtered_next_power(m1;m2) produces [[i, i^m1], [j, j^m1]] where i^m1
- is not a power of m2 and j^m2 < i^m1
def filtered_next_power(m1; m2):
if . then . else [[0,0],[0,0]] end | (.[0] | next_power(m1)) as $next1 | (.[1] | while( .[1] <= $next1[1]; next_power(m2))) as $next2 | if $next1[1] == $next2[1] then [$next1, $next2] | filtered_next_power(m1;m2) else [$next1, $next2] end ;
- Emit ten powers of 2 that are NOT powers of 3,
- skipping the first 20 integers satisfying the condition, including 0.
filtered_next_power(2;3)
| skip(20; filtered_next_power(2;3)) | emit(10; filtered_next_power(2;3)) | .[0][1]</lang>
- Output:
<lang sh>$ jq -n -f generators.jq 529 576 625 676 784 841 900 961 1024 1089</lang>
Julia
The task can be achieved by using closures, iterators or tasks. Here is a solution using anonymous functions and closures.
<lang julia>drop(gen::Function, n::Integer) = (for _ in 1:n gen() end; gen) take(gen::Function, n::Integer) = collect(gen() for _ in 1:n)
function pgen(n::Number)
x = 0 return () -> (x += 1) ^ n
end
function genfilter(g1::Function, g2::Function)
local r1
local r2 = g2()
return () -> begin
r1 = g1()
while r2 < r1 r2 = g2() end
while r1 == r2 r1 = g1() end
return r1
end
end
@show take(drop(genfilter(pgen(2), pgen(3)), 20), 10)</lang>
- Output:
take(drop(genfilter(pgen(2), pgen(3)), 20), 10) = [529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
Kotlin
Coroutines were introduced in version 1.1 of Kotlin but, as yet, are an experimental feature: <lang scala>// version 1.1.0 // compiled with flag -Xcoroutines=enable to suppress 'experimental' warning
import kotlin.coroutines.experimental.buildSequence
fun generatePowers(m: Int) =
buildSequence {
var n = 0
val mm = m.toDouble()
while (true) yield(Math.pow((n++).toDouble(), mm).toLong())
}
fun generateNonCubicSquares(squares: Sequence<Long>, cubes: Sequence<Long>) =
buildSequence {
val iter2 = squares.iterator()
val iter3 = cubes.iterator()
var square = iter2.next()
var cube = iter3.next()
while (true) {
if (square > cube) {
cube = iter3.next()
continue
} else if (square < cube) {
yield(square)
}
square = iter2.next()
}
}
fun main(args: Array<String>) {
val squares = generatePowers(2)
val cubes = generatePowers(3)
val ncs = generateNonCubicSquares(squares, cubes)
print("Non-cubic squares (21st to 30th) : ")
ncs.drop(20).take(10).forEach { print("$it ") } // print 21st to 30th items
println()
}</lang>
- Output:
Non-cubic squares (21st to 30th) : 529 576 625 676 784 841 900 961 1024 1089
M2000 Interpreter
<lang M2000 Interpreter> Module Generator {
PowGen = Lambda (e)-> {
=lambda i=0, e -> {
i++
=i**e
}
}
Squares=lambda PowGen=PowGen(2) ->{
=PowGen()
}
Cubes=Lambda PowGen=PowGen(3) -> {
=PowGen()
}
Filter=Lambda z=Squares(), Squares, m, Cubes->{
while m<Z {m=cubes()}
if z=m then z=Squares()
=z
z=Squares()
}
For i=1 to 20 : dropit=Filter() :Next i
Document doc$="Non-cubic squares (21st to 30th)"
Print doc$
\\ a new line to doc$
doc$={
}
For i=1 to 10 {
f=Filter()
Print Format$("I: {0::-2}, F: {1}",i+20, f)
doc$=Format$("I: {0::-2}, F: {1}",i+20, f)+{
}
}
Clipboard doc$
} Generator </lang>
- Output:
Non-cubic squares (21st to 30th) I: 21, F: 529 I: 22, F: 576 I: 23, F: 625 I: 24, F: 676 I: 25, F: 784 I: 26, F: 841 I: 27, F: 900 I: 28, F: 961 I: 29, F: 1024 I: 30, F: 1089
Lingo
Lingo neither supports coroutines nor first-class functions, and also misses syntactic sugar for implementing real generators. But in the context of for or while loops, simple pseudo-generator objects that store states internally and manipulate data passed by reference can be used to implement generator-like behavior and solve the given task. <lang Lingo>squares = script("generator.power").new(2) cubes = script("generator.power").new(3) filter = script("generator.filter").new(squares, cubes) filter.skip(20) res = [] i = 0 repeat while filter.exec(res)
i = i + 1 if i>10 then exit repeat put res[1]
end repeat</lang>
- Output:
-- 529 -- 576 -- 625 -- 676 -- 784 -- 841 -- 900 -- 961 -- 1024 -- 1089
Parent script "generator.power"
<lang Lingo>property _exp property _index
-- @constructor on new (me, e)
me._exp = e me._index = 0 return me
end
on exec (me, input)
me._index = me._index+1 input[1] = integer(power(me._index, me._exp)) return TRUE
end
on skip (me, steps)
me._index = me._index + steps
end
on reset (me)
me._index = 0
end</lang>
Parent script "generator.filter"
<lang Lingo>property _genv property _genf
-- @constructor on new (me, genv, genf)
me._genv = genv me._genf = genf return me
end
on exec (me, input)
repeat while TRUE
me._genv.exec(input)
v = input[1]
ok = TRUE
me._genf.reset() -- reset filter generator
repeat while TRUE
me._genf.exec(input)
f = input[1]
if f>v then exit repeat
if f=v then
ok=FALSE
exit repeat
end if
end repeat
if ok then
input[1] = v
exit repeat
end if
end repeat
return TRUE
end
on skip (me, steps)
repeat with i = 1 to steps
me.exec([])
end repeat
end
on reset (me)
me._genv.reset() me._genf.reset()
end</lang>
Lua
Generators can be implemented both as closures and as coroutines. The following example demonstrates both.
<lang Lua> --could be done with a coroutine, but a simple closure works just as well. local function powgen(m)
local count = 0 return function() count = count + 1 return count^m end
end
local squares = powgen(2) local cubes = powgen(3)
local cowrap,coyield = coroutine.wrap, coroutine.yield
local function filter(f,g)
return cowrap(function()
local ff,gg = f(), g()
while true do
if ff == gg then
ff,gg = f(), g()
elseif ff < gg then
coyield(ff)
ff = f()
else
gg = g()
end
end
end)
end
filter = filter(squares,cubes)
for i = 1,30 do
local result = filter() if i > 20 then print(result) end
end </lang>
Nim
<lang nim>proc `^`*(base: int, exp: int): int =
var (base, exp) = (base, exp) result = 1
while exp != 0:
if (exp and 1) != 0:
result *= base
exp = exp shr 1
base *= base
proc next(s): int =
for n in s(): return n
proc powers(m): auto =
iterator it(): int{.closure.} =
for n in 0 .. <int.high:
yield n ^ m
return it
iterator filtered(s1, s2): int =
var v = next(s1)
var f = next(s2)
while true:
if v > f:
f = next(s2)
continue
elif v < f:
yield v
v = next(s1)
var
squares = powers(2) cubes = powers(3) i = 1
for x in filtered(squares, cubes):
if i > 20: echo x if i >= 30: break inc i</lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
PARI/GP
Define two generator functions genpow() and genpow2(). <lang parigp>g = List(1); \\ generator stack
genpow(p) = my(a=g[1]++);listput(g,[0,p]);()->g[a][1]++^g[a][2];
genpowf(p,f) = my(a=g[1]++);listput(g,[0,p]);(s=0)->my(q);while(ispower(p=g[a][1]++^g[a][2],f)||(s&&q++<=s),);p;</lang>
genpow(power) returns a function that returns a simple power generator.
genpowf(power,filter) returns a function thats returns a filtered power generator. This generator accepts an optional skip-parameter.
Create simple power generators:
gp > squares = genpow(2); gp > cubes = genpow(3); gp > cubes() 1 gp > cubes() 8 gp > squares() 1 gp > squares() 4 gp > cubes() 27 gp > squares() 9
Create filtered power generator, skip first 20 results and print next 10 values:
gp > powf2 = genpowf(2,3); gp > print(powf2(20)); for(i=1,9,print(powf2())) 529 576 625 676 784 841 900 961 1024 1089
Perl
These generators are anonymous subroutines, which are closures.
<lang perl># gen_pow($m) creates and returns an anonymous subroutine that will
- generate and return the powers 0**m, 1**m, 2**m, ...
sub gen_pow {
my $m = shift;
my $e = 0;
return sub { return $e++ ** $m; };
}
- gen_filter($g1, $g2) generates everything returned from $g1 that
- is not also returned from $g2. Both $g1 and $g2 must be references
- to subroutines that generate numbers in increasing order. gen_filter
- creates and returns an anonymous subroutine.
sub gen_filter {
my($g1, $g2) = @_;
my $v1;
my $v2 = $g2->();
return sub {
for (;;) {
$v1 = $g1->();
$v2 = $g2->() while $v1 > $v2;
return $v1 unless $v1 == $v2;
}
};
}
- Create generators.
my $squares = gen_pow(2); my $cubes = gen_pow(3); my $squares_without_cubes = gen_filter($squares, $cubes);
- Drop 20 values.
$squares_without_cubes->() for (1..20);
- Print 10 values.
my @answer; push @answer, $squares_without_cubes->() for (1..10); print "[", join(", ", @answer), "]\n";</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
Perl 6
As with Haskell, generators are disguised as lazy lists in Perl 6. <lang perl6>sub powers($m) { $m XR** 0..* }
my @squares = powers(2); my @cubes = powers(3);
sub infix:<with-out> (@orig,@veto) {
gather for @veto -> $veto {
take @orig.shift while @orig[0] before $veto;
@orig.shift if @orig[0] eqv $veto;
}
}
say (@squares with-out @cubes)[20 ..^ 20+10].join(', ');</lang>
- Output:
529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089
Phix
<lang Phix>-- -- demo\rosetta\Generator_Exponential.exw -- ====================================== -- bool terminate = false
atom res
procedure powers(integer p) integer i=0
while not terminate do
res = power(i,p)
task_suspend(task_self())
task_yield()
i += 1
end while
end procedure
constant squares = task_create(routine_id("powers"),{2}),
cubes = task_create(routine_id("powers"),{3})
atom square, cube task_schedule(cubes,1) task_yield() cube = res for i=1 to 30 do
while 1 do
task_schedule(squares,1)
task_yield()
square = res
while cube<square do
task_schedule(cubes,1)
task_yield()
cube = res
end while
if square!=cube then exit end if
end while
if i>20 then
?square
end if
end for terminate = 1</lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
PHP
<lang php><?php function powers($m) {
for ($n = 0; ; $n++) {
yield pow($n, $m);
}
}
function filtered($s1, $s2) {
while (true) {
list($v, $f) = [$s1->current(), $s2->current()];
if ($v > $f) {
$s2->next();
continue;
} else if ($v < $f) {
yield $v;
}
$s1->next();
}
}
list($squares, $cubes) = [powers(2), powers(3)]; $f = filtered($squares, $cubes); foreach (range(0, 19) as $i) {
$f->next();
} foreach (range(20, 29) as $i) {
echo $i, "\t", $f->current(), "\n"; $f->next();
} ?></lang>
- Output:
20 529 21 576 22 625 23 676 24 784 25 841 26 900 27 961 28 1024 29 1089
PicoLisp
Coroutines are available only in the 64-bit version. <lang PicoLisp>(de powers (M)
(co (intern (pack 'powers M))
(for (I 0 (inc 'I))
(yield (** I M)) ) ) )
(de filtered (N M)
(co 'filtered
(let (V (powers N) F (powers M))
(loop
(if (> V F)
(setq F (powers M))
(and (> F V) (yield V))
(setq V (powers N)) ) ) ) ) )
(do 20 (filtered 2 3)) (do 10 (println (filtered 2 3)))</lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
PL/I
<lang PL/I> Generate: procedure options (main); /* 27 October 2013 */
declare j fixed binary;
declare r fixed binary;
/* Ignore the first 20 values */
do j = 1 to 20;
/* put edit (filter() ) (f(6)); */
r = filter ();
end;
put skip;
do j = 1 to 10;
put edit (filter() ) (f(6));
end;
/* filters out cubes from the result of the square generator. */ filter: procedure returns (fixed binary);
declare n fixed binary static initial (-0); declare (i, j, m) fixed binary;
do while ('1'b);
m = squares();
r = 0;
do j = 1 to m;
if m = cubes() then go to ignore;
end;
return (m);
ignore:
end;
end filter;
squares: procedure returns (fixed binary);
declare i fixed binary static initial (-0);
i = i + 1;
return (i**2);
end squares;
cubes: procedure returns (fixed binary);
r = r + 1;
return (r**3);
end cubes;
end Generate; </lang>
20 dropped values:
4 9 16 25 36 49 81 100 121 144 169 196 225
256 289 324 361 400 441 484
Next 10 values:
529 576 625 676 784 841 900 961 1024 1089
Python
In Python, any function that contains a yield statement becomes a generator. The standard libraries itertools module provides the following functions used in the solution: count, that will count up from zero; and islice, which will take a slice from an iterator/generator.
(in versions prior to 2.6, replace next(something) with something.next())
<lang python>from itertools import islice, count
def powers(m):
for n in count():
yield n ** m
def filtered(s1, s2):
v, f = next(s1), next(s2)
while True:
if v > f:
f = next(s2)
continue
elif v < f:
yield v
v = next(s1)
squares, cubes = powers(2), powers(3) f = filtered(squares, cubes) print(list(islice(f, 20, 30)))</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
Or, deriving custom generators compositionally:
<lang python>Exponentials as generators
from itertools import count, islice
- powers :: Gen [Int]
def powers(n):
A non-finite succession of integers,
starting at zero,
raised to the nth power.
def f(x):
return pow(x, n)
return map(f, count(0))
- main :: IO ()
def main():
Taking the difference between two derived generators.
print(
take(10)(
drop(20)(
differenceGen(powers(2))(
powers(3)
)
)
)
)
- GENERIC -------------------------------------------------
- differenceGen :: Gen [a] -> Gen [a] -> Gen [a]
def differenceGen(ga):
All values of ga except any
already seen in gb.
def go(a, b):
stream = zip(a, b)
bs = set([])
while True:
xy = next(stream, None)
if None is not xy:
x, y = xy
bs.add(y)
if x not in bs:
yield x
else:
return
return lambda gb: go(ga, gb)
- drop :: Int -> [a] -> [a]
- drop :: Int -> String -> String
def drop(n):
The sublist of xs beginning at
(zero-based) index n.
def go(xs):
if isinstance(xs, list):
return xs[n:]
else:
take(n)(xs)
return xs
return lambda xs: go(xs)
- take :: Int -> [a] -> [a]
- take :: Int -> String -> String
def take(n):
The prefix of xs of length n,
or xs itself if n > length xs.
return lambda xs: (
xs[0:n]
if isinstance(xs, list)
else list(islice(xs, n))
)
- MAIN ---
if __name__ == '__main__':
main()</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
R
<lang rsplus>powers = function(m)
{n = -1
function()
{n <<- n + 1
n^m}}
noncubic.squares = local(
{squares = powers(2)
cubes = powers(3)
cube = cubes()
function()
{square = squares()
while (1)
{if (square > cube)
{cube <<- cubes()
next}
else if (square < cube)
{return(square)}
else
{square = squares()}}}})
for (i in 1:20)
noncubic.squares()
for (i in 1:10)
message(noncubic.squares())</lang>
Racket
<lang racket>
- lang racket
(require racket/generator)
- this is a function that returns a powers generator, not a generator
(define (powers m)
(generator () (for ([n (in-naturals)]) (yield (expt n m)))))
(define squares (powers 2)) (define cubes (powers 3))
- same here
(define (filtered g1 g2)
(generator ()
(let loop ([n1 (g1)] [n2 (g2)])
(cond [(< n1 n2) (yield n1) (loop (g1) n2)]
[(> n1 n2) (loop n1 (g2))]
[else (loop (g1) (g2))]))))
(for/list ([x (in-producer (filtered squares cubes) (lambda (_) #f))]
[i 30] #:when (>= i 20)) x)
</lang>
- Output:
'(529 576 625 676 784 841 900 961 1024 1089)
REXX
The generators (below, the Gxxxxx functions) lie dormant until a request is made for a specific generator index.
<lang rexx>/*REXX program demonstrates how to use a generator (also known as an iterator). */
parse arg N .; if N== | N=="," then N=20 /*N not specified? Then use default.*/
@.= /* [↓] calculate squares,cubes,pureSq.*/
do i=1 for N; call Gsquare i
call Gcube i
call GpureSquare i /*these are cube─free square numbers.*/
end /*i*/
do k=1 for N; @.pureSquare.k=; end /*k*/ /*this is used to drop 1st N values.*/
w=length(N+10); ps= 'pure square' /*the width of the numbers; a literal.*/
do m=N+1 for 10; say ps right(m, w)":" right(GpureSquare(m), 3*w)
end /*m*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ Gpower: procedure expose @.; parse arg x,p; q=@.pow.x.p
if q\== then return q; _=x**p; @.pow.x.p=_
return _
/*──────────────────────────────────────────────────────────────────────────────────────*/ Gsquare: procedure expose @.; parse arg x; q=@.square.x
if q== then @.square.x=Gpower(x, 2)
return @.square.x
/*──────────────────────────────────────────────────────────────────────────────────────*/ Gcube: procedure expose @.; parse arg x; q=@.cube.x
if q== then @.cube.x=Gpower(x, 3) _=@.cube.x; @.3pow._=1
return @.cube.x
/*──────────────────────────────────────────────────────────────────────────────────────*/ GpureSquare: procedure expose @.; parse arg x; q=@.pureSquare.x
if q\== then return q
#=0
do j=1 until #==x; ?=Gpower(j, 2) /*search for pure square. */
if @.3pow.?==1 then iterate /*is it a power of three? */
#=#+1; @.pureSquare.#=? /*assign next pureSquare. */
end /*j*/
return @.pureSquare.x</lang>
output when using the default value:
pure square 21: 529 pure square 22: 576 pure square 23: 625 pure square 24: 676 pure square 25: 784 pure square 26: 841 pure square 27: 900 pure square 28: 961 pure square 29: 1024 pure square 30: 1089
Ruby
This first solution cheats and uses only one generator! It has three iterators powers(2), powers(3) and squares_without_cubes, but the only generator runs powers(3).
An iterator is a Ruby method that takes a block parameter, and loops the block for each element. So powers(2) { |i| puts "Got #{i}" } would loop forever and print Got 0, Got 1, Got 4, Got 9 and so on. Starting with Ruby 1.8.7, one can use Object#enum_for to convert an iterator method to an Enumerator object. The Enumerator#next method is a generator that runs the iterator method on a separate coroutine. Here cubes.next generates the next cube number.
<lang ruby># This solution cheats and uses only one generator!
def powers(m)
return enum_for(__method__, m) unless block_given?
0.step{|n| yield n**m}
end
def squares_without_cubes
return enum_for(__method__) unless block_given? cubes = powers(3) c = cubes.next powers(2) do |s| c = cubes.next while c < s yield s unless c == s end
end
p squares_without_cubes.take(30).drop(20)
- p squares_without_cubes.lazy.drop(20).first(10) # Ruby 2.0+</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
Here is the correct solution, which obeys the requirement of three generators.
<lang ruby># This solution uses three generators.
def powers(m)
return enum_for(__method__, m) unless block_given?
0.step{|n| yield n**m}
end
def squares_without_cubes
return enum_for(__method__) unless block_given? cubes = powers(3) #no block, so this is the first generator c = cubes.next squares = powers(2) # second generator loop do s = squares.next c = cubes.next while c < s yield s unless c == s end
end
answer = squares_without_cubes # third generator 20.times { answer.next } p 10.times.map { answer.next }</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
If we change both programs to drop the first 1_000_020 values (output: [1000242014641, 1000244014884, 1000246015129, 1000248015376, 1000250015625, 1000252015876, 1000254016129, 1000256016384, 1000258016641, 1000260016900]), then the one-generator solution runs much faster than the three-generator solution on a machine with MRI 1.9.2.
The other way. Powers method is the same as the above.
<lang ruby>def filtered(s1, s2)
return enum_for(__method__, s1, s2) unless block_given? v, f = s1.next, s2.next loop do v > f and f = s2.next and next v < f and yield v v = s1.next end
end
squares, cubes = powers(2), powers(3) f = filtered(squares, cubes) p f.take(30).last(10)
- p f.lazy.drop(20).first(10) # Ruby 2.0+</lang>
Output is the same as the above.
Scala
<lang scala>object Generators {
def main(args: Array[String]): Unit = {
def squares(n:Int=0):Stream[Int]=(n*n) #:: squares(n+1)
def cubes(n:Int=0):Stream[Int]=(n*n*n) #:: cubes(n+1)
def filtered(s:Stream[Int], c:Stream[Int]):Stream[Int]={
if(s.head>c.head) filtered(s, c.tail)
else if(s.head<c.head) Stream.cons(s.head, filtered(s.tail, c))
else filtered(s.tail, c)
}
filtered(squares(), cubes()) drop 20 take 10 print }
}</lang> Here is an alternative filter implementation using pattern matching. <lang scala>def filtered2(s:Stream[Int], c:Stream[Int]):Stream[Int]=(s, c) match {
case (sh#::_, ch#::ct) if (sh>ch) => filtered2(s, ct) case (sh#::st, ch#::_) if (sh<ch) => sh #:: filtered2(st, c) case (_#::st, _) => filtered2(st, c)
}</lang>
- Output:
529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089, empty
Rust
<lang Rust>use std::cmp::Ordering; use std::iter::Peekable;
fn powers(m: u32) -> impl Iterator<Item = u64> {
(0u64..).map(move |x| x.pow(m))
}
fn noncubic_squares() -> impl Iterator<Item = u64> {
NoncubicSquares {
squares: powers(2).peekable(),
cubes: powers(3).peekable(),
}
}
struct NoncubicSquares<T: Iterator<Item = u64>, U: Iterator<Item = u64>> {
squares: Peekable<T>, cubes: Peekable,
}
impl<T: Iterator<Item = u64>, U: Iterator<Item = u64>> Iterator for NoncubicSquares<T, U> {
type Item = u64;
fn next(&mut self) -> Option<u64> {
loop {
match self.squares.peek()?.cmp(self.cubes.peek()?) {
Ordering::Equal => self.squares.next(),
Ordering::Greater => self.cubes.next(),
Ordering::Less => return self.squares.next(),
};
}
}
}
fn main() {
noncubic_squares()
.skip(20)
.take(10)
.for_each(|x| print!("{} ", x));
println!();
}</lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
Scheme
<lang lisp>(define (power-seq n)
(let ((i 0))
(lambda ()
(set! i (+ 1 i))
(expt i n))))
(define (filter-seq m n)
(let* ((s1 (power-seq m)) (s2 (power-seq n))
(a 0) (b 0))
(lambda ()
(set! a (s1))
(let loop ()
(if (>= a b) (begin (cond ((> a b) (set! b (s2))) ((= a b) (set! a (s1)))) (loop))))
a)))
(let loop ((seq (filter-seq 2 3)) (i 0))
(if (< i 30)
(begin
(if (> i 20)
(begin (display (seq)) (newline)) (seq))
(loop seq (+ 1 i)))))</lang>
- Output:
576 625 676 784 841 900 961 1024 1089
Sidef
<lang ruby>func gen_pow(m) {
var e = 0;
func { e++ ** m };
}
func gen_filter(g1, g2) {
var v2 = g2.run;
func {
loop {
var v1 = g1.run;
while (v1 > v2) { v2 = g2.run };
v1 == v2 || return v1;
}
}
}
- Create generators.
var squares = gen_pow(2); var cubes = gen_pow(3); var squares_without_cubes = gen_filter(squares, cubes);
- Drop 20 values.
20.times { squares_without_cubes() };
- Print 10 values.
var answer = []; 10.times { answer.append(squares_without_cubes()) }; say answer;</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
Swift
<lang swift>func powGen(m: Int) -> GeneratorOf<Int> {
let power = Double(m)
var cur: Double = 0
return GeneratorOf { Int(pow(cur++, power)) }
}
var squares = powGen(2) var cubes = powGen(3)
var nCube = cubes.next()
var filteredSqs = GeneratorOf<Int> {
for var nSq = squares.next() ;; nCube = cubes.next() {
if nCube > nSq {
return nSq
} else if nCube == nSq {
nSq = squares.next()
}
}
}
extension GeneratorOf {
func drop(n: Int) -> GeneratorOf<T> {
var g = self
for _ in 0..<n {g.next()}
return GeneratorOf{g.next()}
}
func take(n: Int) -> GeneratorOf<T> {
var (i, g) = (0, self)
return GeneratorOf{++i > n ? nil : g.next()}
}
}
for num in filteredSqs.drop(20).take(10) {
print(num)
}
//529 //576 //625 //676 //784 //841 //900 //961 //1024 //1089</lang>
SuperCollider
<lang SuperCollider> f = { |m| {:x, x<-(0..) } ** m }; g = f.(2); g.nextN(10); // answers [ 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 ] </lang>
patterns are stream generators:
<lang SuperCollider>( f = Pseries(0, 1) g = f ** 2; g.asStream.nextN(10); // answers [ 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 ] ) </lang>
supercollider has no "without" stream function, this builds one:
<lang SuperCollider>( var filter = { |a, b, func| // both streams are assumed to be ordered Prout { var astr, bstr; var aval, bval; astr = a.asStream; bstr = b.asStream; bval = bstr.next; while { aval = astr.next; aval.notNil } { while { bval.notNil and: { bval < aval } } { bval = bstr.next; }; if(func.value(aval, bval)) { aval.yield }; } } }; var without = filter.(_, _, { |a, b| a != b }); // partially apply function
f = Pseries(0, 1);
g = without.(f ** 2, f ** 3); h = g.drop(20); h.asStream.nextN(10); )
answers: [ 529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089 ] </lang>
Tcl
Tcl implements generators in terms of coroutines.
If these generators were terminating, they would finish by doing return -code break so as to terminate the calling loop context that is doing the extraction of the values from the generator.
<lang tcl>package require Tcl 8.6
proc powers m {
yield
for {set n 0} true {incr n} {
yield [expr {$n ** $m}]
}
} coroutine squares powers 2 coroutine cubes powers 3 coroutine filtered apply {{s1 s2} {
yield
set f [$s2]
set v [$s1]
while true {
if {$v > $f} { set f [$s2] continue } elseif {$v < $f} { yield $v } set v [$s1]
}
}} squares cubes
- Drop 20
for {set i 0} {$i<20} {incr i} {filtered}
- Take/print 10
for {} {$i<30} {incr i} {
puts [filtered]
}</lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
VBA
<lang vb>Public lastsquare As Long Public nextsquare As Long Public lastcube As Long Public midcube As Long Public nextcube As Long Private Sub init()
lastsquare = 1 nextsquare = -1 lastcube = -1 midcube = 0 nextcube = 1
End Sub
Private Function squares() As Long
lastsquare = lastsquare + nextsquare nextsquare = nextsquare + 2 squares = lastsquare
End Function
Private Function cubes() As Long
lastcube = lastcube + nextcube nextcube = nextcube + midcube midcube = midcube + 6 cubes = lastcube
End Function
Public Sub main()
init
cube = cubes
For i = 1 To 30
Do While True
square = squares
Do While cube < square
cube = cubes
Loop
If square <> cube Then
Exit Do
End If
Loop
If i > 20 Then
Debug.Print square;
End If
Next i
End Sub</lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
XPL0
<lang XPL0>code ChOut=8, IntOut=11;
func Gen(M); \Generate Mth powers of positive integers int M; int N, R, I; [N:= [0, 0, 0, 0]; \provides own/static variables R:= 1; for I:= 1 to M do R:= R*N(M); N(M):= N(M)+1; return R; ];
func Filter; \Generate squares of positive integers that aren't cubes int S, C; [C:= [0]; \static variable = smallest cube > current square repeat S:= Gen(2);
while S > C(0) do C(0):= Gen(3);
until S # C(0); return S; ];
int I; [for I:= 1 to 20 do Filter; \drop first 20 values
for I:= 1 to 10 do [IntOut(0, Filter); ChOut(0, ^ )]; \show next 10 values
]</lang>
- Output:
529 576 625 676 784 841 900 961 1024 1089
zkl
Generators are implemented with fibers (aka VMs) and return [lazy] iterators. <lang zkl>fcn powers(m){ n:=0.0; while(1){vm.yield(n.pow(m).toInt()); n+=1} } var squared=Utils.Generator(powers,2), cubed=Utils.Generator(powers,3);
fcn filtered(sg,cg){s:=sg.next(); c:=cg.next();
while(1){
if(s>c){c=cg.next(); continue;}
else if(s<c) vm.yield(s);
s=sg.next()
}
} var f=Utils.Generator(filtered,squared,cubed); f.drop(20); f.walk(10).println();</lang>
- Output:
L(529,576,625,676,784,841,900,961,1024,1089)
For this task, generators are overkill and overweight, and lazy infinite squences can be used. There is no real change to the algorithms (since generators are lazy sequences), it just has been rewritten in a more functional style.
<lang zkl>fcn powers(m){[0.0..].tweak(fcn(n,m){a:=n; do(m-1){a*=n} a}.fp1(m))} var squared=powers(2), cubed=powers(3);
fcn filtered(sg,cg){s:=sg.peek(); c:=cg.peek();
if(s==c){ cg.next(); sg.next(); return(self.fcn(sg,cg)) }
if(s>c) { cg.next(); return(self.fcn(sg,cg)); }
sg.next(); return(s);
} var f=[0..].tweak(filtered.fp(squared,cubed)) f.drop(20).walk(10).println();</lang>
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