Generator/Exponential
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 description
- Create a function returning a generator 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 then show the next 10 values
Note that this task requires the use of generators in the calculation of the result.
See also
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<lang>529 576 625 676 784 841 900 961 1024 1089</lang>
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#
Note that types have been made static and variables made explicit as an aid to understanding.
Closure On Function Style <lang csharp>using System; using System.Collections.Generic; using System.Linq;
namespace RosettaGenerator {
class ClosureStyle
{
static void Main(string[] args)
{
Func<int> squaresGenerator = PowerGeneratorAsClosure(2);
Func<int> cubesGenerator = PowerGeneratorAsClosure(3);
Func<int> filter = FilterAsClosure(squaresGenerator, cubesGenerator);
foreach (int i in Enumerable.Range(0, 20))
filter();
foreach (int i in Enumerable.Range(21, 10))
Console.Write(filter() + " ");
Console.WriteLine();
}
public static Func<int> PowerGeneratorAsClosure(int exponent)
{
int x = 0;
return () => { return (int)Math.Pow(x++, exponent); };
}
public static Func<int> FilterAsClosure(Func<int> squaresGenerator, Func<int> cubesGenerator)
{
int squareValue;
int cubeValue = cubesGenerator();
return () =>
{
while (true)
{
squareValue = squaresGenerator();
while (squareValue > cubeValue)
cubeValue = cubesGenerator();
if (squareValue < cubeValue)
return squareValue;
}
};
}
}
}</lang> Coroutine As List Style <lang csharp>using System; using System.Collections.Generic; using System.Linq;
namespace RosettaGenerator {
class ListStyle
{
static void Main(string[] args)
{
IEnumerator<int> squaresGenerator = PowerGeneratorAsList(2);
IEnumerator<int> cubesGenerator = PowerGeneratorAsList(3);
IEnumerable<int> filter = FilterAsList(squaresGenerator, cubesGenerator);
foreach (int value in filter.Skip(20).Take(10))
Console.Write(value + " ");
Console.WriteLine();
}
public static IEnumerator<int> PowerGeneratorAsList(int exponent)
{
int x = 0;
while (true)
yield return (int)Math.Pow(x++, exponent);
}
public static IEnumerable<int> FilterAsList(IEnumerator<int> squaresGenerator, IEnumerator<int> cubesGenerator)
{
int squareValue;
int cubeValue = cubesGenerator.Current;
while (true)
{
squareValue = squaresGenerator.Current;
while (squareValue > cubeValue)
{
cubesGenerator.MoveNext();
cubeValue = cubesGenerator.Current;
}
if (squareValue < cubeValue)
yield return squareValue;
squaresGenerator.MoveNext();
}
}
}
}</lang>
Output (for either):
529 576 625 676 784 841 900 961 1024 1089
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
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 current, source, filter;
this(R1 r1, R2 r2) {
s1 = r1;
s2 = r2;
source = s1.front();
filter = s2.front();
_next();
}
const bool empty = false;
@property T front() { return current; }
void popFront() { _next(); }
private void _next() {
while (true) {
if (source > filter) {
s2.popFront();
filter = s2.front();
continue;
} else if (source < filter) {
current = source;
s1.popFront();
source = s1.front();
break;
}
s1.popFront();
source = s1.front();
}
}
}
auto filtered(R1, R2)(R1 r1, R2 r2) if (is(ElementType!R1 == ElementType!R2)) {
return Filtered!(R1, R2)(r1, r2);
}
struct Count(T) {
T n;
this(T n_) { this.n = n_; }
const bool empty = false;
@property T front() { return n; }
void popFront() { /* n++; */ n += 1; }
}
Count!T count(T)(T start) { return Count!T(start); } Count!T count(T)() { return Count!T(cast(T)0); }
void main() {
auto squares = count!BigInt().map!q{a ^^ 2}();
auto cubes = count!BigInt().map!q{a ^^ 3}();
auto f = filtered(squares, cubes);
popFrontN(f, 20); writeln(take(f, 10));
}</lang>
- Output:
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
Closures-Based Version
<lang d>import std.stdio;
auto powers(in double e) pure nothrow {
double i = 0.0; return () => i++ ^^ e;
}
auto filter(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 = filter(powers(2), powers(3));
foreach (i; 0 .. 20)
fgen();
foreach (i; 0 .. 10)
write(fgen(), " ");
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>
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
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>powers m = map (^ m) [0..]
filtered (x:xs) (y:ys) | x > y = filtered (x:xs) ys
| x < y = x : filtered xs (y:ys)
| otherwise = filtered xs (y:ys)
squares = powers 2 cubes = powers 3 f = filtered squares cubes
main :: IO () main = print $ take 10 $ drop 20 $ f</lang>
Sample 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 30 529 576 625 676 784 841 900 961 1024 1089</lang>
JavaScript
<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>
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>
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, $squares_without_cubes->() for (1..10); print "[", join(", ", @answer), "]\n";</lang>
Output:
[529, 57tt>next64()6, 625, 676, 784, 841, 900, 961, 1024, 1089]
Perl 6
As with Haskell, generators are disguised as lazy lists in Perl 6. <lang perl6>sub powers($m) { 0..* X** $m }
my @squares := powers(2); my @cubes := powers(3);
sub infix:<without> (@orig,@veto) {
gather for @veto -> $veto {
take @orig.shift while @orig[0] before $veto;
@orig.shift if @orig[0] eqv $veto;
}
}
say (@squares without @cubes)[20 ..^ 20+10].join(', ');</lang>
Output:
529, 576, 625, 676, 784, 841, 900, 961, 1024, 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
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>
Sample output
[529, 576, 625, 676, 784, 841, 900, 961, 1024, 1089]
REXX
Code was added to support listing of a specified number of values, the default is 0 (zero).
The generators lie dormant until a request is made (illustrated by the calling of "TELL" to display some values).
A lot of unnecessary iterator calls could be eliminated (and making the program a lot faster) if a check would be made to determine if a value has been emitted.
The REXX program can handle any numbers, not just positive integers; one only need to increase the size of the DIGITS if more digits are needed for extra-large numbers.
<lang rexx>/*REXX program to show how to use a generator (also known as iterators).*/
numeric digits 10000 /*just in case we need big 'uns. */
gen_.= /*have generators from scratch. */
/*how_many: show that many vals.*/
parse arg how_many; how_many=pick1(how_many 0)
do j=1 to how_many; call tell 'squares' ,gen_squares(j) ; end
do j=1 to how_many; call tell 'cubes' ,gen_cubes(j) ; end
do j=1 to how_many; call tell 'sq¬cubes',gen_sqNcubes(j) ; end
if how_many>0 then say 'dropping 1st ──► 20th values.'
do j=1 to 20; drop gen_.sqNcubes.j ; end
do j=20+1 for 10 ; call tell 'sq¬cubes',gen_sqNcubes(j) ; end
exit /*stick a fork in it, we're done.*/
/*─────────────────────────────────────generate powers iterator─────────*/ gen_powers: procedure expose gen_.; parse arg x,p; if x== then return if gen_.powers.x.p== then gen_.powers.x.p=x**p return gen_.powers.x.p
/*─────────────────────────────────────gen squares iterator─────────────*/ gen_squares: procedure expose gen_.; parse arg x; if x== then return if gen_.squares.x== then do
call gen_powers x,2
gen_.squares.x=gen_.powers.x.2
end
return gen_.squares.x
/*─────────────────────────────────────gen cubes iterator───────────────*/ gen_cubes: procedure expose gen_.; parse arg x; if x== then return if gen_.cubes.j== then do
call gen_powers x,3
gen_.cubes.x=gen_.powers.x.3
end
return gen_.cubes.x
/*─────────────────────────────────────gen squares not cubes iterator───*/ gen_sqNcubes: procedure expose gen_.; parse arg x; if x== then return s=1 if gen_.sqNcubes.x== then do j=1 to x
if gen_.sqNcubes\== then do
sq=sq+1
iterate
end
do s=s+1 /*slow way to weed out cubes*/
?=gen_squares(s)
do c=1 until gen_cubes(c)>?
if gen_cubes(c)==? then iterate s
end /*c*/
leave
end /*s*/
gen_.sqNcubes.x=?
gen_.sqNcubes.x=gen_.squares.s
end /*j*/
return gen_.sqNcubes.x
/*─────────────────────────────────────"1─liner" subroutines────────────*/ tell: if j==1 then say /*format args to be aligned up. */
say right(arg(1),20) right(j,5) right(arg(2),20); return
pick1: return word(arg(1) arg(2),1)</lang> output when using the default (no input)
sq¬cubes 21 529
sq¬cubes 22 576
sq¬cubes 23 625
sq¬cubes 24 676
sq¬cubes 25 784
sq¬cubes 26 841
sq¬cubes 27 900
sq¬cubes 28 961
sq¬cubes 29 1024
sq¬cubes 30 1089
output when using the following for input: 10
squares 1 1
squares 2 4
squares 3 9
squares 4 16
squares 5 25
squares 6 36
squares 7 49
squares 8 64
squares 9 81
squares 10 100
cubes 1 1
cubes 2 8
cubes 3 27
cubes 4 64
cubes 5 125
cubes 6 216
cubes 7 343
cubes 8 512
cubes 9 729
cubes 10 1000
sq¬cubes 1 4
sq¬cubes 2 9
sq¬cubes 3 16
sq¬cubes 4 25
sq¬cubes 5 36
sq¬cubes 6 49
sq¬cubes 7 81
sq¬cubes 8 100
sq¬cubes 9 121
sq¬cubes 10 144
dropping 1st ──► 20th values.
sq¬cubes 21 529
sq¬cubes 22 576
sq¬cubes 23 625
sq¬cubes 24 676
sq¬cubes 25 784
sq¬cubes 26 841
sq¬cubes 27 900
sq¬cubes 28 961
sq¬cubes 29 1024
sq¬cubes 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(:powers, m) unless block_given?
n = 0
loop { yield n ** m; n += 1 }
end
def squares_without_cubes
return enum_for(:squares_without_cubes) unless block_given?
cubes = powers(3) c = cubes.next powers(2) do |s| (c = cubes.next) until c >= s yield s unless c == s end
end
p squares_without_cubes.take(30).drop(20)</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(:powers, m) unless block_given?
n = 0
loop { yield n ** m; n += 1 }
end
def squares_without_cubes
return enum_for(:squares_without_cubes) unless block_given?
cubes = powers(3) c = cubes.next squares = powers(2) loop do s = squares.next (c = cubes.next) until c >= s yield s unless c == s end
end
answer = squares_without_cubes 20.times { answer.next } p (1..10).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.
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
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<lang>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