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http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #C | C |
#include<graphics.h>
#include<stdio.h>
#include<math.h>
#define pi M_PI
int main(){
double a,b,cycles,incr,i;
int steps,x=500,y=500;
printf("Enter the parameters a and b : ");
scanf("%lf%lf",&a,&b);
printf("Enter cycles : ");
scanf("%lf",&cycles);
printf("Enter divisional steps : ");
scanf("%d",&steps);
incr = 1.0/steps;
initwindow(1000,1000,"Archimedean Spiral");
for(i=0;i<=cycles*pi;i+=incr){
putpixel(x + (a + b*i)*cos(i),x + (a + b*i)*sin(i),15);
}
getch();
closegraph();
}
|
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #Aikido | Aikido |
var doors = new int [100]
foreach pass 100 {
for (var door = pass ; door < 100 ; door += pass+1) {
doors[door] = !doors[door]
}
}
var d = 1
foreach door doors {
println ("door " + d++ + " is " + (door ? "open" : "closed"))
}
|
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #BQN | BQN | # Stranding:
arr ← 1‿2‿'a'‿+‿5
# General List Syntax:
arr1 ← ⟨1,2,'a',+,5⟩
•Show arr ≡ arr1 # both arrays are the same.
•Show arr
•Show arr1
# Taking nth element(⊑):
•Show 3⊑arr
# Modifying the array(↩):
arr ↩ "hello"⌾(4⊸⊑) arr |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Forth | Forth | S" fsl-util.fs" REQUIRED
S" complex.fs" REQUIRED
zvariable x
zvariable y
1e 1e x z!
pi 1.2e y z!
x z@ y z@ z+ z.
x z@ y z@ z* z.
1e 0e zconstant 1+0i
1+0i x z@ z/ z.
x z@ znegate z. |
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #Go | Go | package main
import (
"fmt"
"math"
"math/big"
)
func main() {
var recip big.Rat
max := int64(1 << 19)
for candidate := int64(2); candidate < max; candidate++ {
sum := big.NewRat(1, candidate)
max2 := int64(math.Sqrt(float64(candidate)))
for factor := int64(2); factor <= max2; factor++ {
if candidate%factor == 0 {
sum.Add(sum, recip.SetFrac64(1, factor))
if f2 := candidate / factor; f2 != factor {
sum.Add(sum, recip.SetFrac64(1, f2))
}
}
}
if sum.Denom().Int64() == 1 {
perfectstring := ""
if sum.Num().Int64() == 1 {
perfectstring = "perfect!"
}
fmt.Printf("Sum of recipr. factors of %d = %d exactly %s\n",
candidate, sum.Num().Int64(), perfectstring)
}
}
} |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #jq | jq | def naive_agm(a; g; tolerance):
def abs: if . < 0 then -. else . end;
def _agm:
# state [an,gn]
if ((.[0] - .[1])|abs) > tolerance
then [add/2, ((.[0] * .[1])|sqrt)] | _agm
else .
end;
[a, g] | _agm | .[0] ; |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #Julia | Julia | function agm(x, y, e::Real = 5)
(x ≤ 0 || y ≤ 0 || e ≤ 0) && throw(DomainError("x, y must be strictly positive"))
g, a = minmax(x, y)
while e * eps(x) < a - g
a, g = (a + g) / 2, sqrt(a * g)
end
a
end
x, y = 1.0, 1 / √2
println("# Using literal-precision float numbers:")
@show agm(x, y)
println("# Using half-precision float numbers:")
x, y = Float32(x), Float32(y)
@show agm(x, y)
println("# Using ", precision(BigFloat), "-bit float numbers:")
x, y = big(1.0), 1 / √big(2.0)
@show agm(x, y) |
http://rosettacode.org/wiki/Arithmetic/Integer | Arithmetic/Integer |
Basic Data Operation
This is a basic data operation. It represents a fundamental action on a basic data type.
You may see other such operations in the Basic Data Operations category, or:
Integer Operations
Arithmetic |
Comparison
Boolean Operations
Bitwise |
Logical
String Operations
Concatenation |
Interpolation |
Comparison |
Matching
Memory Operations
Pointers & references |
Addresses
Task
Get two integers from the user, and then (for those two integers), display their:
sum
difference
product
integer quotient
remainder
exponentiation (if the operator exists)
Don't include error handling.
For quotient, indicate how it rounds (e.g. towards zero, towards negative infinity, etc.).
For remainder, indicate whether its sign matches the sign of the first operand or of the second operand, if they are different.
| #ZX_Spectrum_Basic | ZX Spectrum Basic | 5 LET a=5: LET b=3
10 PRINT a;" + ";b;" = ";a+b
20 PRINT a;" - ";b;" = ";a-b
30 PRINT a;" * ";b;" = ";a*b
40 PRINT a;" / ";b;" = ";INT (a/b)
50 PRINT a;" mod ";b;" = ";a-INT (a/b)*b
60 PRINT a;" to the power of ";b;" = ";a^b
|
http://rosettacode.org/wiki/Arithmetic_evaluation | Arithmetic evaluation | Create a program which parses and evaluates arithmetic expressions.
Requirements
An abstract-syntax tree (AST) for the expression must be created from parsing the input.
The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.)
The expression will be a string or list of symbols like "(1+3)*7".
The four symbols + - * / must be supported as binary operators with conventional precedence rules.
Precedence-control parentheses must also be supported.
Note
For those who don't remember, mathematical precedence is as follows:
Parentheses
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
C.f
24 game Player.
Parsing/RPN calculator algorithm.
Parsing/RPN to infix conversion.
| #Elena | Elena | import system'routines;
import extensions;
import extensions'text;
class Token
{
object theValue;
rprop int Level;
constructor new(int level)
{
theValue := new StringWriter();
Level := level + 9;
}
append(ch)
{
theValue.write(ch)
}
Number = theValue.toReal();
}
class Node
{
prop object Left;
prop object Right;
rprop int Level;
constructor new(int level)
{
Level := level
}
}
class SummaryNode : Node
{
constructor new(int level)
<= new(level + 1);
Number = Left.Number + Right.Number;
}
class DifferenceNode : Node
{
constructor new(int level)
<= new(level + 1);
Number = Left.Number - Right.Number;
}
class ProductNode : Node
{
constructor new(int level)
<= new(level + 2);
Number = Left.Number * Right.Number;
}
class FractionNode : Node
{
constructor new(int level)
<= new(level + 2);
Number = Left.Number / Right.Number;
}
class Expression
{
rprop int Level;
prop object Top;
constructor new(int level)
{
Level := level
}
Right
{
get() = Top;
set(object node)
{
Top := node
}
}
get Number() => Top;
}
singleton operatorState
{
eval(ch)
{
ch =>
$40 { // (
^ __target.newBracket().gotoStarting()
}
: {
^ __target.newToken().append(ch).gotoToken()
}
}
}
singleton tokenState
{
eval(ch)
{
ch =>
$41 { // )
^ __target.closeBracket().gotoToken()
}
$42 { // *
^ __target.newProduct().gotoOperator()
}
$43 { // +
^ __target.newSummary().gotoOperator()
}
$45 { // -
^ __target.newDifference().gotoOperator()
}
$47 { // /
^ __target.newFraction().gotoOperator()
}
: {
^ __target.append:ch
}
}
}
singleton startState
{
eval(ch)
{
ch =>
$40 { // (
^ __target.newBracket().gotoStarting()
}
$45 { // -
^ __target.newToken().append("0").newDifference().gotoOperator()
}
: {
^ __target.newToken().append:ch.gotoToken()
}
}
}
class Scope
{
object theState;
int theLevel;
object theParser;
object theToken;
object theExpression;
constructor new(parser)
{
theState := startState;
theLevel := 0;
theExpression := Expression.new(0);
theParser := parser
}
newToken()
{
theToken := theParser.appendToken(theExpression, theLevel)
}
newSummary()
{
theToken := nil;
theParser.appendSummary(theExpression, theLevel)
}
newDifference()
{
theToken := nil;
theParser.appendDifference(theExpression, theLevel)
}
newProduct()
{
theToken := nil;
theParser.appendProduct(theExpression, theLevel)
}
newFraction()
{
theToken := nil;
theParser.appendFraction(theExpression, theLevel)
}
newBracket()
{
theToken := nil;
theLevel := theLevel + 10;
theParser.appendSubexpression(theExpression, theLevel)
}
closeBracket()
{
if (theLevel < 10)
{ InvalidArgumentException.new:"Invalid expression".raise() };
theLevel := theLevel - 10
}
append(ch)
{
if(ch >= $48 && ch < $58)
{
theToken.append:ch
}
else
{
InvalidArgumentException.new:"Invalid expression".raise()
}
}
append(string s)
{
s.forEach:(ch){ self.append:ch }
}
gotoStarting()
{
theState := startState
}
gotoToken()
{
theState := tokenState
}
gotoOperator()
{
theState := operatorState
}
get Number() => theExpression;
dispatch() => theState;
}
class Parser
{
appendToken(object expression, int level)
{
var token := Token.new(level);
expression.Top := self.append(expression.Top, token);
^ token
}
appendSummary(object expression, int level)
{
expression.Top := self.append(expression.Top, SummaryNode.new(level))
}
appendDifference(object expression, int level)
{
expression.Top := self.append(expression.Top, DifferenceNode.new(level))
}
appendProduct(object expression, int level)
{
expression.Top := self.append(expression.Top, ProductNode.new(level))
}
appendFraction(object expression, int level)
{
expression.Top := self.append(expression.Top, FractionNode.new(level))
}
appendSubexpression(object expression, int level)
{
expression.Top := self.append(expression.Top, Expression.new(level))
}
append(lastNode, newNode)
{
if(nil == lastNode)
{ ^ newNode };
if (newNode.Level <= lastNode.Level)
{ newNode.Left := lastNode; ^ newNode };
var parent := lastNode;
var current := lastNode.Right;
while (nil != current && newNode.Level > current.Level)
{ parent := current; current := current.Right };
if (nil == current)
{
parent.Right := newNode
}
else
{
newNode.Left := current; parent.Right := newNode
};
^ lastNode
}
run(text)
{
var scope := Scope.new(self);
text.forEach:(ch){ scope.eval:ch };
^ scope.Number
}
}
public program()
{
var text := new StringWriter();
var parser := new Parser();
while (console.readLine().saveTo(text).Length > 0)
{
try
{
console.printLine("=",parser.run:text)
}
catch(Exception e)
{
console.writeLine:"Invalid Expression"
};
text.clear()
}
} |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #C.23 | C# | using System;
using System.Linq;
using System.Drawing;
using System.Diagnostics;
using System.Drawing.Drawing2D;
class Program
{
const int width = 380;
const int height = 380;
static PointF archimedeanPoint(int degrees)
{
const double a = 1;
const double b = 9;
double t = degrees * Math.PI / 180;
double r = a + b * t;
return new PointF { X = (float)(width / 2 + r * Math.Cos(t)), Y = (float)(height / 2 + r * Math.Sin(t)) };
}
static void Main(string[] args)
{
var bm = new Bitmap(width, height);
var g = Graphics.FromImage(bm);
g.SmoothingMode = SmoothingMode.AntiAlias;
g.FillRectangle(new SolidBrush(Color.White), new Rectangle { X = 0, Y = 0, Width = width, Height = height });
var pen = new Pen(Color.OrangeRed, 1.5f);
var spiral = Enumerable.Range(0, 360 * 3).AsParallel().AsOrdered().Select(archimedeanPoint);
var p0 = new PointF(width / 2, height / 2);
foreach (var p1 in spiral)
{
g.DrawLine(pen, p0, p1);
p0 = p1;
}
g.Save(); // is this really necessary ?
bm.Save("archimedes-csharp.png");
Process.Start("archimedes-csharp.png"); // Launches default photo viewing app
}
}
|
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #ALGOL_60 | ALGOL 60 |
begin
comment - 100 doors problem in ALGOL-60;
boolean array doors[1:100];
integer i, j;
boolean open, closed;
open := true;
closed := not true;
outstring(1,"100 Doors Problem\n");
comment - all doors are initially closed;
for i := 1 step 1 until 100 do
doors[i] := closed;
comment
cycle through at increasing intervals
and flip each door encountered;
for i := 1 step 1 until 100 do
for j := i step i until 100 do
doors[j] := not doors[j];
comment - show which doors are open;
outstring(1,"The open doors are:");
for i := 1 step 1 until 100 do
if doors[i] then
outinteger(1,i);
end
|
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #Bracmat | Bracmat | ( tbl$(mytable,100)
& 5:?(30$mytable)
& 9:?(31$mytable)
& out$(!(30$mytable))
& out$(!(-169$mytable)) { -169 mod 100 == 31 }
& out$!mytable { still index 31 }
& tbl$(mytable,0)
& (!mytable & out$"mytable still exists"
| out$"mytable is gone"
)
); |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Fortran | Fortran | program cdemo
complex :: a = (5,3), b = (0.5, 6.0) ! complex initializer
complex :: absum, abprod, aneg, ainv
absum = a + b
abprod = a * b
aneg = -a
ainv = 1.0 / a
end program cdemo |
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #Groovy | Groovy | class Rational extends Number implements Comparable {
final BigInteger num, denom
static final Rational ONE = new Rational(1)
static final Rational ZERO = new Rational(0)
Rational(BigDecimal decimal) {
this(
decimal.scale() < 0 ? decimal.unscaledValue() * 10 ** -decimal.scale() : decimal.unscaledValue(),
decimal.scale() < 0 ? 1 : 10 ** decimal.scale()
)
}
Rational(BigInteger n, BigInteger d = 1) {
if (!d || n == null) { n/d }
(num, denom) = reduce(n, d)
}
private List reduce(BigInteger n, BigInteger d) {
BigInteger sign = ((n < 0) ^ (d < 0)) ? -1 : 1
(n, d) = [n.abs(), d.abs()]
BigInteger commonFactor = gcd(n, d)
[n.intdiv(commonFactor) * sign, d.intdiv(commonFactor)]
}
Rational toLeastTerms() { reduce(num, denom) as Rational }
private BigInteger gcd(BigInteger n, BigInteger m) {
n == 0 ? m : { while(m%n != 0) { (n, m) = [m%n, n] }; n }()
}
Rational plus(Rational r) { [num*r.denom + r.num*denom, denom*r.denom] }
Rational plus(BigInteger n) { [num + n*denom, denom] }
Rational plus(Number n) { this + ([n] as Rational) }
Rational next() { [num + denom, denom] }
Rational minus(Rational r) { [num*r.denom - r.num*denom, denom*r.denom] }
Rational minus(BigInteger n) { [num - n*denom, denom] }
Rational minus(Number n) { this - ([n] as Rational) }
Rational previous() { [num - denom, denom] }
Rational multiply(Rational r) { [num*r.num, denom*r.denom] }
Rational multiply(BigInteger n) { [num*n, denom] }
Rational multiply(Number n) { this * ([n] as Rational) }
Rational div(Rational r) { new Rational(num*r.denom, denom*r.num) }
Rational div(BigInteger n) { new Rational(num, denom*n) }
Rational div(Number n) { this / ([n] as Rational) }
BigInteger intdiv(BigInteger n) { num.intdiv(denom*n) }
Rational negative() { [-num, denom] }
Rational abs() { [num.abs(), denom] }
Rational reciprocal() { new Rational(denom, num) }
Rational power(BigInteger n) {
def (nu, de) = (n < 0 ? [denom, num] : [num, denom])*.power(n.abs())
new Rational (nu, de)
}
boolean asBoolean() { num != 0 }
BigDecimal toBigDecimal() { (num as BigDecimal)/(denom as BigDecimal) }
BigInteger toBigInteger() { num.intdiv(denom) }
Double toDouble() { toBigDecimal().toDouble() }
double doubleValue() { toDouble() as double }
Float toFloat() { toBigDecimal().toFloat() }
float floatValue() { toFloat() as float }
Integer toInteger() { toBigInteger().toInteger() }
int intValue() { toInteger() as int }
Long toLong() { toBigInteger().toLong() }
long longValue() { toLong() as long }
Object asType(Class type) {
switch (type) {
case this.class: return this
case [Boolean, Boolean.TYPE]: return asBoolean()
case BigDecimal: return toBigDecimal()
case BigInteger: return toBigInteger()
case [Double, Double.TYPE]: return toDouble()
case [Float, Float.TYPE]: return toFloat()
case [Integer, Integer.TYPE]: return toInteger()
case [Long, Long.TYPE]: return toLong()
case String: return toString()
default: throw new ClassCastException("Cannot convert from type Rational to type " + type)
}
}
boolean equals(o) { compareTo(o) == 0 }
int compareTo(o) {
o instanceof Rational
? compareTo(o as Rational)
: o instanceof Number
? compareTo(o as Number)
: (Double.NaN as int)
}
int compareTo(Rational r) { num*r.denom <=> denom*r.num }
int compareTo(Number n) { num <=> denom*(n as BigInteger) }
int hashCode() { [num, denom].hashCode() }
String toString() {
"${num}//${denom}"
}
} |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #Klingphix | Klingphix | include ..\Utilitys.tlhy
:agm [ over over + 2 / rot rot * sqrt ] [ over over tostr swap tostr # ] while drop ;
1 1 2 sqrt / agm
pstack
" " input |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #Kotlin | Kotlin | // version 1.0.5-2
fun agm(a: Double, g: Double): Double {
var aa = a // mutable 'a'
var gg = g // mutable 'g'
var ta: Double // temporary variable to hold next iteration of 'aa'
val epsilon = 1.0e-16 // tolerance for checking if limit has been reached
while (true) {
ta = (aa + gg) / 2.0
if (Math.abs(aa - ta) <= epsilon) return ta
gg = Math.sqrt(aa * gg)
aa = ta
}
}
fun main(args: Array<String>) {
println(agm(1.0, 1.0 / Math.sqrt(2.0)))
} |
http://rosettacode.org/wiki/Arithmetic_evaluation | Arithmetic evaluation | Create a program which parses and evaluates arithmetic expressions.
Requirements
An abstract-syntax tree (AST) for the expression must be created from parsing the input.
The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.)
The expression will be a string or list of symbols like "(1+3)*7".
The four symbols + - * / must be supported as binary operators with conventional precedence rules.
Precedence-control parentheses must also be supported.
Note
For those who don't remember, mathematical precedence is as follows:
Parentheses
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
C.f
24 game Player.
Parsing/RPN calculator algorithm.
Parsing/RPN to infix conversion.
| #Emacs_Lisp | Emacs Lisp | #!/usr/bin/env emacs --script
;; -*- mode: emacs-lisp; lexical-binding: t -*-
;;> ./arithmetic-evaluation '(1 + 2) * 3'
(defun advance ()
(let ((rtn (buffer-substring-no-properties (point) (match-end 0))))
(goto-char (match-end 0))
rtn))
(defvar current-symbol nil)
(defun next-symbol ()
(when (looking-at "[ \t\n]+")
(goto-char (match-end 0)))
(cond
((eobp)
(setq current-symbol 'eof))
((looking-at "[0-9]+")
(setq current-symbol (string-to-number (advance))))
((looking-at "[-+*/()]")
(setq current-symbol (advance)))
((looking-at ".")
(error "Unknown character '%s'" (advance)))))
(defun accept (sym)
(when (equal sym current-symbol)
(next-symbol)
t))
(defun expect (sym)
(unless (accept sym)
(error "Expected symbol %s, but found %s" sym current-symbol))
t)
(defun p-expression ()
" expression = term { ('+' | '-') term } . "
(let ((rtn (p-term)))
(while (or (equal current-symbol "+") (equal current-symbol "-"))
(let ((op current-symbol)
(left rtn))
(next-symbol)
(setq rtn (list op left (p-term)))))
rtn))
(defun p-term ()
" term = factor { ('*' | '/') factor } . "
(let ((rtn (p-factor)))
(while (or (equal current-symbol "*") (equal current-symbol "/"))
(let ((op current-symbol)
(left rtn))
(next-symbol)
(setq rtn (list op left (p-factor)))))
rtn))
(defun p-factor ()
" factor = constant | variable | '(' expression ')' . "
(let (rtn)
(cond
((numberp current-symbol)
(setq rtn current-symbol)
(next-symbol))
((accept "(")
(setq rtn (p-expression))
(expect ")"))
(t (error "Syntax error")))
rtn))
(defun ast-build (expression)
(let (rtn)
(with-temp-buffer
(insert expression)
(goto-char (point-min))
(next-symbol)
(setq rtn (p-expression))
(expect 'eof))
rtn))
(defun ast-eval (v)
(pcase v
((pred numberp) v)
(`("+" ,a ,b) (+ (ast-eval a) (ast-eval b)))
(`("-" ,a ,b) (- (ast-eval a) (ast-eval b)))
(`("*" ,a ,b) (* (ast-eval a) (ast-eval b)))
(`("/" ,a ,b) (/ (ast-eval a) (float (ast-eval b))))
(_ (error "Unknown value %s" v))))
(dolist (arg command-line-args-left)
(let ((ast (ast-build arg)))
(princ (format " ast = %s\n" ast))
(princ (format " value = %s\n" (ast-eval ast)))
(terpri)))
(setq command-line-args-left nil)
|
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #C.2B.2B | C++ |
#include <windows.h>
#include <string>
#include <iostream>
const int BMP_SIZE = 600;
class myBitmap {
public:
myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {}
~myBitmap() {
DeleteObject( pen ); DeleteObject( brush );
DeleteDC( hdc ); DeleteObject( bmp );
}
bool create( int w, int h ) {
BITMAPINFO bi;
ZeroMemory( &bi, sizeof( bi ) );
bi.bmiHeader.biSize = sizeof( bi.bmiHeader );
bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
bi.bmiHeader.biCompression = BI_RGB;
bi.bmiHeader.biPlanes = 1;
bi.bmiHeader.biWidth = w;
bi.bmiHeader.biHeight = -h;
HDC dc = GetDC( GetConsoleWindow() );
bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );
if( !bmp ) return false;
hdc = CreateCompatibleDC( dc );
SelectObject( hdc, bmp );
ReleaseDC( GetConsoleWindow(), dc );
width = w; height = h;
return true;
}
void clear( BYTE clr = 0 ) {
memset( pBits, clr, width * height * sizeof( DWORD ) );
}
void setBrushColor( DWORD bClr ) {
if( brush ) DeleteObject( brush );
brush = CreateSolidBrush( bClr );
SelectObject( hdc, brush );
}
void setPenColor( DWORD c ) {
clr = c; createPen();
}
void setPenWidth( int w ) {
wid = w; createPen();
}
void saveBitmap( std::string path ) {
BITMAPFILEHEADER fileheader;
BITMAPINFO infoheader;
BITMAP bitmap;
DWORD wb;
GetObject( bmp, sizeof( bitmap ), &bitmap );
DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];
ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) );
ZeroMemory( &infoheader, sizeof( BITMAPINFO ) );
ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );
infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;
infoheader.bmiHeader.biCompression = BI_RGB;
infoheader.bmiHeader.biPlanes = 1;
infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader );
infoheader.bmiHeader.biHeight = bitmap.bmHeight;
infoheader.bmiHeader.biWidth = bitmap.bmWidth;
infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );
fileheader.bfType = 0x4D42;
fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER );
fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;
GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );
HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS,
FILE_ATTRIBUTE_NORMAL, NULL );
WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL );
WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL );
WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL );
CloseHandle( file );
delete [] dwpBits;
}
HDC getDC() const { return hdc; }
int getWidth() const { return width; }
int getHeight() const { return height; }
private:
void createPen() {
if( pen ) DeleteObject( pen );
pen = CreatePen( PS_SOLID, wid, clr );
SelectObject( hdc, pen );
}
HBITMAP bmp; HDC hdc;
HPEN pen; HBRUSH brush;
void *pBits; int width, height, wid;
DWORD clr;
};
class spiral {
public:
spiral() {
bmp.create( BMP_SIZE, BMP_SIZE );
}
void draw( int c, int s ) {
double a = .2, b = .3, r, x, y;
int w = BMP_SIZE >> 1;
HDC dc = bmp.getDC();
for( double d = 0; d < c * 6.28318530718; d += .002 ) {
r = a + b * d; x = r * cos( d ); y = r * sin( d );
SetPixel( dc, ( int )( s * x + w ), ( int )( s * y + w ), 255 );
}
// saves the bitmap
bmp.saveBitmap( "./spiral.bmp" );
}
private:
myBitmap bmp;
};
int main(int argc, char* argv[]) {
spiral s; s.draw( 16, 8 ); return 0;
}
|
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #ALGOL_68 | ALGOL 68 | # declare some constants #
INT limit = 100;
PROC doors = VOID:
(
MODE DOORSTATE = BOOL;
BOOL closed = FALSE;
BOOL open = NOT closed;
MODE DOORLIST = [limit]DOORSTATE;
DOORLIST the doors;
FOR i FROM LWB the doors TO UPB the doors DO the doors[i]:=closed OD;
FOR i FROM LWB the doors TO UPB the doors DO
FOR j FROM LWB the doors TO UPB the doors DO
IF j MOD i = 0 THEN
the doors[j] := NOT the doors[j]
FI
OD
OD;
FOR i FROM LWB the doors TO UPB the doors DO
printf(($g" is "gl$,i,(the doors[i]|"opened"|"closed")))
OD
);
doors; |
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #Brainf.2A.2A.2A | Brainf*** |
===========[
ARRAY DATA STRUCTURE
AUTHOR: Keith Stellyes
WRITTEN: June 2016
This is a zero-based indexing array data structure, it assumes the following
precondition:
>INDEX<|NULL|VALUE|NULL|VALUE|NULL|VALUE|NULL
(Where >< mark pointer position, and | separates addresses)
It relies heavily on [>] and [<] both of which are idioms for
finding the next left/right null
HOW INDEXING WORKS:
It runs a loop _index_ number of times, setting that many nulls
to a positive, so it can be skipped by the mentioned idioms.
Basically, it places that many "milestones".
EXAMPLE:
If we seek index 2, and our array is {1 , 2 , 3 , 4 , 5}
FINDING INDEX 2:
(loop to find next null, set to positive, as a milestone
decrement index)
index
2 |0|1|0|2|0|3|0|4|0|5|0
1 |0|1|1|2|0|3|0|4|0|5|0
0 |0|1|1|2|1|3|0|4|0|5|0
===========]
=======UNIT TEST=======
SET ARRAY {48 49 50}
>>++++++++++++++++++++++++++++++++++++++++++++++++>>
+++++++++++++++++++++++++++++++++++++++++++++++++>>
++++++++++++++++++++++++++++++++++++++++++++++++++
<<<<<<++ Move back to index and set it to 2
=======================
===RETRIEVE ELEMENT AT INDEX===
=ACCESS INDEX=
[>>[>]+[<]<-] loop that sets a null to a positive for each iteration
First it moves the pointer from index to first value
Then it uses a simple loop that finds the next null
it sets the null to a positive (1 in this case)
Then it uses that same loop reversed to find the first
null which will always be one right of our index
so we decrement our index
Finally we decrement pointer from the null byte to our
index and decrement it
>> Move pointer to the first value otherwise we can't loop
[>]< This will find the next right null which will always be right
of the desired value; then go one left
. Output the value (In the unit test this print "2"
[<[-]<] Reset array
===ASSIGN VALUE AT INDEX===
STILL NEED TO ADJUST UNIT TESTS
NEWVALUE|>INDEX<|NULL|VALUE etc
[>>[>]+[<]<-] Like above logic except it empties the value and doesn't reset
>>[>]<[-]
[<]< Move pointer to desired value note that where the index was stored
is null because of the above loop
[->>[>]+[<]<] If NEWVALUE is GREATER than 0 then decrement it & then find the
newly emptied cell and increment it
[>>[>]<+[<]<<-] Move pointer to first value find right null move pointer left
then increment where we want our NEWVALUE to be stored then
return back by finding leftmost null then decrementing pointer
twice then decrement our NEWVALUE cell
|
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #FreeBASIC | FreeBASIC | ' FB 1.05.0 Win64
Type Complex
As Double real, imag
Declare Constructor(real As Double, imag As Double)
Declare Function invert() As Complex
Declare Function conjugate() As Complex
Declare Operator cast() As String
End Type
Constructor Complex(real As Double, imag As Double)
This.real = real
This.imag = imag
End Constructor
Function Complex.invert() As Complex
Dim denom As Double = real * real + imag * imag
Return Complex(real / denom, -imag / denom)
End Function
Function Complex.conjugate() As Complex
Return Complex(real, -imag)
End Function
Operator Complex.Cast() As String
If imag >= 0 Then
Return Str(real) + "+" + Str(imag) + "j"
End If
Return Str(real) + Str(imag) + "j"
End Operator
Operator - (c As Complex) As Complex
Return Complex(-c.real, -c.imag)
End Operator
Operator + (c1 As Complex, c2 As Complex) As Complex
Return Complex(c1.real + c2.real, c1.imag + c2.imag)
End Operator
Operator - (c1 As Complex, c2 As Complex) As Complex
Return c1 + (-c2)
End Operator
Operator * (c1 As Complex, c2 As Complex) As Complex
Return Complex(c1.real * c2.real - c1.imag * c2.imag, c1.real * c2.imag + c2.real * c1.imag)
End Operator
Operator / (c1 As Complex, c2 As Complex) As Complex
Return c1 * c2.invert
End Operator
Var x = Complex(1, 3)
Var y = Complex(5, 2)
Print "x = "; x
Print "y = "; y
Print "x + y = "; x + y
Print "x - y = "; x - y
Print "x * y = "; x * y
Print "x / y = "; x / y
Print "-x = "; -x
Print "1 / x = "; x.invert
Print "x* = "; x.conjugate
Print
Print "Press any key to quit"
Sleep |
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #Haskell | Haskell | import Data.Ratio ((%))
-- Prints the first N perfect numbers.
main = do
let n = 4
mapM_ print $
take
n
[ candidate
| candidate <- [2 .. 2 ^ 19]
, getSum candidate == 1 ]
where
getSum candidate =
1 % candidate +
sum
[ 1 % factor + 1 % (candidate `div` factor)
| factor <- [2 .. floor (sqrt (fromIntegral candidate))]
, candidate `mod` factor == 0 ]
|
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #LFE | LFE |
(defun agm (a g)
(agm a g 1.0e-15))
(defun agm (a g tol)
(if (=< (- a g) tol)
a
(agm (next-a a g)
(next-g a g)
tol)))
(defun next-a (a g)
(/ (+ a g) 2))
(defun next-g (a g)
(math:sqrt (* a g)))
|
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #Liberty_BASIC | Liberty BASIC |
print agm(1, 1/sqr(2))
print using("#.#################",agm(1, 1/sqr(2)))
function agm(a,g)
do
absdiff = abs(a-g)
an=(a+g)/2
gn=sqr(a*g)
a=an
g=gn
loop while abs(an-gn)< absdiff
agm = a
end function
|
http://rosettacode.org/wiki/Arithmetic_evaluation | Arithmetic evaluation | Create a program which parses and evaluates arithmetic expressions.
Requirements
An abstract-syntax tree (AST) for the expression must be created from parsing the input.
The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.)
The expression will be a string or list of symbols like "(1+3)*7".
The four symbols + - * / must be supported as binary operators with conventional precedence rules.
Precedence-control parentheses must also be supported.
Note
For those who don't remember, mathematical precedence is as follows:
Parentheses
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
C.f
24 game Player.
Parsing/RPN calculator algorithm.
Parsing/RPN to infix conversion.
| #ERRE | ERRE |
PROGRAM EVAL
!
! arithmetic expression evaluator
!
!$KEY
LABEL 98,100,110
DIM STACK$[50]
PROCEDURE DISEGNA_STACK
!$RCODE="LOCATE 3,1"
!$RCODE="COLOR 0,7"
PRINT(TAB(35);"S T A C K";TAB(79);)
!$RCODE="COLOR 7,0"
FOR TT=1 TO 38 DO
IF TT>=20 THEN
!$RCODE="LOCATE 3+TT-19,40"
ELSE
!$RCODE="LOCATE 3+TT,1"
END IF
IF TT=NS THEN PRINT(">";) ELSE PRINT(" ";) END IF
PRINT(RIGHT$(STR$(TT),2);"³ ";STACK$[TT];" ")
END FOR
REPEAT
GET(Z$)
UNTIL LEN(Z$)<>0
END PROCEDURE
PROCEDURE COMPATTA_STACK
IF NS>1 THEN
R=1
WHILE R<NS DO
IF INSTR(OP_LIST$,STACK$[R])=0 AND INSTR(OP_LIST$,STACK$[R+1])=0 THEN
FOR R1=R TO NS-1 DO
STACK$[R1]=STACK$[R1+1]
END FOR
NS=NS-1
END IF
R=R+1
END WHILE
END IF
DISEGNA_STACK
END PROCEDURE
PROCEDURE CALC_ARITM
L=NS1
WHILE L<=NS2 DO
IF STACK$[L]="^" THEN
IF L>=NS2 THEN GOTO 100 END IF
N1#=VAL(STACK$[L-1]) N2#=VAL(STACK$[L+1]) NOP=NOP-1
IF STACK$[L]="^" THEN
RI#=N1#^N2#
END IF
STACK$[L-1]=STR$(RI#)
N=L
WHILE N<=NS2-2 DO
STACK$[N]=STACK$[N+2]
N=N+1
END WHILE
NS2=NS2-2
L=NS1-1
END IF
L=L+1
END WHILE
L=NS1
WHILE L<=NS2 DO
IF STACK$[L]="*" OR STACK$[L]="/" THEN
IF L>=NS2 THEN GOTO 100 END IF
N1#=VAL(STACK$[L-1]) N2#=VAL(STACK$[L+1]) NOP=NOP-1
IF STACK$[L]="*" THEN RI#=N1#*N2# ELSE RI#=N1#/N2# END IF
STACK$[L-1]=STR$(RI#)
N=L
WHILE N<=NS2-2 DO
STACK$[N]=STACK$[N+2]
N=N+1
END WHILE
NS2=NS2-2
L=NS1-1
END IF
L=L+1
END WHILE
L=NS1
WHILE L<=NS2 DO
IF STACK$[L]="+" OR STACK$[L]="-" THEN
EXIT IF L>=NS2
N1#=VAL(STACK$[L-1]) N2#=VAL(STACK$[L+1]) NOP=NOP-1
IF STACK$[L]="+" THEN RI#=N1#+N2# ELSE RI#=N1#-N2# END IF
STACK$[L-1]=STR$(RI#)
N=L
WHILE N<=NS2-2 DO
STACK$[N]=STACK$[N+2]
N=N+1
END WHILE
NS2=NS2-2
L=NS1-1
END IF
L=L+1
END WHILE
100:
IF NOP<2 THEN ! operator priority
DB#=VAL(STACK$[NS1])
ELSE
IF NOP<3 THEN
DB#=VAL(STACK$[NS1+2])
ELSE
DB#=VAL(STACK$[NS1+4])
END IF
END IF
END PROCEDURE
PROCEDURE SVOLGI_PAR
NPA=NPA-1
FOR J=NS TO 1 STEP -1 DO
EXIT IF STACK$[J]="("
END FOR
IF J=0 THEN
NS1=1 NS2=NS CALC_ARITM
NERR=7
ELSE
FOR R=J TO NS-1 DO
STACK$[R]=STACK$[R+1]
END FOR
NS1=J NS2=NS-1 CALC_ARITM
IF NS1=2 THEN NS1=1 STACK$[1]=STACK$[2] END IF
NS=NS1
COMPATTA_STACK
END IF
END PROCEDURE
BEGIN
OP_LIST$="+-*/^("
NOP=0 NPA=0 NS=1 K$=""
STACK$[1]="@" ! init stack
PRINT(CHR$(12);)
INPUT(LINE,EXPRESSION$)
FOR W=1 TO LEN(EXPRESSION$) DO
LOOP
CODE=ASC(MID$(EXPRESSION$,W,1))
IF (CODE>=48 AND CODE<=57) OR CODE=46 THEN
K$=K$+CHR$(CODE)
W=W+1 IF W>LEN(EXPRESSION$) THEN GOTO 98 END IF
ELSE
EXIT IF K$=""
IF NS>1 OR (NS=1 AND STACK$[1]<>"@") THEN NS=NS+1 END IF
IF FLAG=0 THEN STACK$[NS]=K$ ELSE STACK$[NS]=STR$(VAL(K$)*FLAG) END IF
K$="" FLAG=0
EXIT
END IF
END LOOP
IF CODE=43 THEN K$="+" END IF
IF CODE=45 THEN K$="-" END IF
IF CODE=42 THEN K$="*" END IF
IF CODE=47 THEN K$="/" END IF
IF CODE=94 THEN K$="^" END IF
CASE CODE OF
43,45,42,47,94->
IF MID$(EXPRESSION$,W+1,1)="-" THEN FLAG=-1 W=W+1 END IF
IF INSTR(OP_LIST$,STACK$[NS])<>0 THEN
NERR=5
ELSE
NS=NS+1 STACK$[NS]=K$ NOP=NOP+1
IF NOP>=2 THEN
FOR J=NS TO 1 STEP -1 DO
IF STACK$[J]<>"(" THEN
CONTINUE FOR
END IF
IF J<NS-2 THEN
EXIT
ELSE
GOTO 110
END IF
END FOR
NS1=J+1 NS2=NS CALC_ARITM
NS=NS2 STACK$[NS]=K$
REGISTRO_X#=VAL(STACK$[NS-1])
END IF
END IF
110:
END ->
40->
IF NS>1 OR (NS=1 AND STACK$[1]<>"@") THEN NS=NS+1 END IF
STACK$[NS]="(" NPA=NPA+1
IF MID$(EXPRESSION$,W+1,1)="-" THEN FLAG=-1 W=W+1 END IF
END ->
41->
SVOLGI_PAR
IF NERR=7 THEN
NERR=0 NOP=0 NPA=0 NS=1
ELSE
IF NERR=0 OR NERR=1 THEN
DB#=VAL(STACK$[NS])
REGISTRO_X#=DB#
ELSE
NOP=0 NPA=0 NS=1
END IF
END IF
END ->
OTHERWISE
NERR=8
END CASE
K$=""
DISEGNA_STACK
END FOR
98:
IF K$<>"" THEN
IF NS>1 OR (NS=1 AND STACK$[1]<>"@") THEN NS=NS+1 END IF
IF FLAG=0 THEN STACK$[NS]=K$ ELSE STACK$[NS]=STR$(VAL(K$)*FLAG) END IF
END IF
DISEGNA_STACK
IF INSTR(OP_LIST$,STACK$[NS])<>0 THEN
NERR=6
ELSE
WHILE NPA<>0 DO
SVOLGI_PAR
END WHILE
IF NERR<>7 THEN NS1=1 NS2=NS CALC_ARITM END IF
END IF
NS=1 NOP=0 NPA=0
!$RCODE="LOCATE 23,1"
IF NERR>0 THEN PRINT("Internal Error #";NERR) ELSE PRINT("Value is ";DB#) END IF
END PROGRAM
|
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Clojure | Clojure |
(use '(incanter core stats charts io))
(defn Arquimidean-function
[a b theta]
(+ a (* theta b)))
(defn transform-pl-xy [r theta]
(let [x (* r (sin theta))
y (* r (cos theta))]
[x y]))
(defn arq-spiral [t] (transform-pl-xy (Arquimidean-function 0 7 t) t))
(view (parametric-plot arq-spiral 0 (* 10 Math/PI)))
|
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Common_Lisp | Common Lisp | (defun draw-coords-as-text (coords size fill-char)
(let* ((min-x (apply #'min (mapcar #'car coords)))
(min-y (apply #'min (mapcar #'cdr coords)))
(max-x (apply #'max (mapcar #'car coords)))
(max-y (apply #'max (mapcar #'cdr coords)))
(real-size (max (+ (abs min-x) (abs max-x)) ; bounding square
(+ (abs min-y) (abs max-y))))
(scale-factor (* (1- size) (/ 1 real-size)))
(center-x (* scale-factor -1 min-x))
(center-y (* scale-factor -1 min-y))
(intermediate-result (make-array (list size size)
:element-type 'char
:initial-element #\space)))
(dolist (c coords)
(let ((final-x (floor (+ center-x (* scale-factor (car c)))))
(final-y (floor (+ center-y (* scale-factor (cdr c))))))
(setf (aref intermediate-result final-x final-y)
fill-char)))
; print results to output
(loop for i below (array-total-size intermediate-result) do
(when (zerop (mod i size))
(terpri))
(princ (row-major-aref intermediate-result i)))))
(defun spiral (a b step-resolution step-count)
"Returns a list of coordinates for r=a+b*theta stepping theta by step-resolution"
(loop for theta
from 0 upto (* step-count step-resolution)
by step-resolution
for r = (+ a (* b theta))
for x = (* r (cos theta))
for y = (* r (sin theta))
collect (cons x y)))
(draw-coords-as-text (spiral 10 10 0.01 1500) 30 #\*)
; Output:
;
; *
; ****** *
; **** *** **
; *** ** *
; ** ** *
; ** ** *
; * ** **
; ** * *
; ** ****** * *
; * ** ** ** *
; * ** * * *
; * ** * * **
; * * * * *
; * * * ** * *
; * * *** ** *
; * ** * *
; * * ** *
; * ** ** **
; ** ** ** *
; * ** ** **
; ** ******** *
; * **
; ** **
; ** **
; ** ***
; ** **
; **** ***
; *******
;
|
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #ALGOL_W | ALGOL W | begin
% find the first few squares via the unoptimised door flipping method %
integer doorMax;
doorMax := 100;
begin
% need to start a new block so the array can have variable bounds %
% array of doors - door( i ) is true if open, false if closed %
logical array door( 1 :: doorMax );
% set all doors to closed %
for i := 1 until doorMax do door( i ) := false;
% repeatedly flip the doors %
for i := 1 until doorMax
do begin
for j := i step i until doorMax
do begin
door( j ) := not door( j )
end
end;
% display the results %
i_w := 1; % set integer field width %
s_w := 1; % and separator width %
for i := 1 until doorMax do if door( i ) then writeon( i )
end
end. |
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #C | C | int myArray2[10] = { 1, 2, 0 }; /* the rest of elements get the value 0 */
float myFloats[] ={1.2, 2.5, 3.333, 4.92, 11.2, 22.0 }; /* automatically sizes */ |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Free_Pascal | Free Pascal | Program ComplexDemo;
uses
ucomplex;
var
a, b, absum, abprod, aneg, ainv, acong: complex;
function complex(const re, im: real): ucomplex.complex; overload;
begin
complex.re := re;
complex.im := im;
end;
begin
a := complex(5, 3);
b := complex(0.5, 6.0);
absum := a + b;
writeln ('(5 + i3) + (0.5 + i6.0): ', absum.re:3:1, ' + i', absum.im:3:1);
abprod := a * b;
writeln ('(5 + i3) * (0.5 + i6.0): ', abprod.re:5:1, ' + i', abprod.im:4:1);
aneg := -a;
writeln ('-(5 + i3): ', aneg.re:3:1, ' + i', aneg.im:3:1);
ainv := 1.0 / a;
writeln ('1/(5 + i3): ', ainv.re:3:1, ' + i', ainv.im:3:1);
acong := cong(a);
writeln ('conj(5 + i3): ', acong.re:3:1, ' + i', acong.im:3:1);
end.
|
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #Icon_and_Unicon | Icon and Unicon | procedure main()
limit := 2^19
write("Perfect numbers up to ",limit," (using rational arithmetic):")
every write(is_perfect(c := 2 to limit))
write("End of perfect numbers")
# verify the rest of the implementation
zero := makerat(0) # from integer
half := makerat(0.5) # from real
qtr := makerat("1/4") # from strings ...
one := makerat("1")
mone := makerat("-1")
verifyrat("eqrat",zero,zero)
verifyrat("ltrat",zero,half)
verifyrat("ltrat",half,zero)
verifyrat("gtrat",zero,half)
verifyrat("gtrat",half,zero)
verifyrat("nerat",zero,half)
verifyrat("nerat",zero,zero)
verifyrat("absrat",mone,)
end
procedure is_perfect(c) #: test for perfect numbers using rational arithmetic
rsum := rational(1, c, 1)
every f := 2 to sqrt(c) do
if 0 = c % f then
rsum := addrat(rsum,addrat(rational(1,f,1),rational(1,integer(c/f),1)))
if rsum.numer = rsum.denom = 1 then
return c
end |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #LiveCode | LiveCode | function agm aa,g
put abs(aa-g) into absdiff
put (aa+g)/2 into aan
put sqrt(aa*g) into gn
repeat while abs(aan - gn) < absdiff
put abs(aa-g) into absdiff
put (aa+g)/2 into aan
put sqrt(aa*g) into gn
put aan into aa
put gn into g
end repeat
return aa
end agm |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #LLVM | LLVM | ; This is not strictly LLVM, as it uses the C library function "printf".
; LLVM does not provide a way to print values, so the alternative would be
; to just load the string into memory, and that would be boring.
; Additional comments have been inserted, as well as changes made from the output produced by clang such as putting more meaningful labels for the jumps
$"ASSERTION" = comdat any
$"OUTPUT" = comdat any
@"ASSERTION" = linkonce_odr unnamed_addr constant [48 x i8] c"arithmetic-geometric mean undefined when x*y<0\0A\00", comdat, align 1
@"OUTPUT" = linkonce_odr unnamed_addr constant [42 x i8] c"The arithmetic-geometric mean is %0.19lf\0A\00", comdat, align 1
;--- The declarations for the external C functions
declare i32 @printf(i8*, ...)
declare void @exit(i32) #1
declare double @sqrt(double) #1
declare double @llvm.fabs.f64(double) #2
;----------------------------------------------------------------
;-- arithmetic geometric mean
define double @agm(double, double) #0 {
%3 = alloca double, align 8 ; allocate local g
%4 = alloca double, align 8 ; allocate local a
%5 = alloca double, align 8 ; allocate iota
%6 = alloca double, align 8 ; allocate a1
%7 = alloca double, align 8 ; allocate g1
store double %1, double* %3, align 8 ; store param g in local g
store double %0, double* %4, align 8 ; store param a in local a
store double 1.000000e-15, double* %5, align 8 ; store 1.0e-15 in iota (1.0e-16 was causing the program to hang)
%8 = load double, double* %4, align 8 ; load a
%9 = load double, double* %3, align 8 ; load g
%10 = fmul double %8, %9 ; a * g
%11 = fcmp olt double %10, 0.000000e+00 ; a * g < 0.0
br i1 %11, label %enforce, label %loop
enforce:
%12 = call i32 (i8*, ...) @printf(i8* getelementptr inbounds ([48 x i8], [48 x i8]* @"ASSERTION", i32 0, i32 0))
call void @exit(i32 1) #6
unreachable
loop:
%13 = load double, double* %4, align 8 ; load a
%14 = load double, double* %3, align 8 ; load g
%15 = fsub double %13, %14 ; a - g
%16 = call double @llvm.fabs.f64(double %15) ; fabs(a - g)
%17 = load double, double* %5, align 8 ; load iota
%18 = fcmp ogt double %16, %17 ; fabs(a - g) > iota
br i1 %18, label %loop_body, label %eom
loop_body:
%19 = load double, double* %4, align 8 ; load a
%20 = load double, double* %3, align 8 ; load g
%21 = fadd double %19, %20 ; a + g
%22 = fdiv double %21, 2.000000e+00 ; (a + g) / 2.0
store double %22, double* %6, align 8 ; store %22 in a1
%23 = load double, double* %4, align 8 ; load a
%24 = load double, double* %3, align 8 ; load g
%25 = fmul double %23, %24 ; a * g
%26 = call double @sqrt(double %25) #4 ; sqrt(a * g)
store double %26, double* %7, align 8 ; store %26 in g1
%27 = load double, double* %6, align 8 ; load a1
store double %27, double* %4, align 8 ; store a1 in a
%28 = load double, double* %7, align 8 ; load g1
store double %28, double* %3, align 8 ; store g1 in g
br label %loop
eom:
%29 = load double, double* %4, align 8 ; load a
ret double %29 ; return a
}
;----------------------------------------------------------------
;-- main
define i32 @main() #0 {
%1 = alloca double, align 8 ; allocate x
%2 = alloca double, align 8 ; allocate y
store double 1.000000e+00, double* %1, align 8 ; store 1.0 in x
%3 = call double @sqrt(double 2.000000e+00) #4 ; calculate the square root of two
%4 = fdiv double 1.000000e+00, %3 ; divide 1.0 by %3
store double %4, double* %2, align 8 ; store %4 in y
%5 = load double, double* %2, align 8 ; reload y
%6 = load double, double* %1, align 8 ; reload x
%7 = call double @agm(double %6, double %5) ; agm(x, y)
%8 = call i32 (i8*, ...) @printf(i8* getelementptr inbounds ([42 x i8], [42 x i8]* @"OUTPUT", i32 0, i32 0), double %7)
ret i32 0 ; finished
}
attributes #0 = { noinline nounwind optnone uwtable "correctly-rounded-divide-sqrt-fp-math"="false" "disable-tail-calls"="false" "less-precise-fpmad"="false" "no-frame-pointer-elim"="false" "no-infs-fp-math"="false" "no-jump-tables"="false" "no-nans-fp-math"="false" "no-signed-zeros-fp-math"="false" "no-trapping-math"="false" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+fxsr,+mmx,+sse,+sse2,+x87" "unsafe-fp-math"="false" "use-soft-float"="false" }
attributes #1 = { noreturn "correctly-rounded-divide-sqrt-fp-math"="false" "disable-tail-calls"="false" "less-precise-fpmad"="false" "no-frame-pointer-elim"="false" "no-infs-fp-math"="false" "no-nans-fp-math"="false" "no-signed-zeros-fp-math"="false" "no-trapping-math"="false" "stack-protector-buffer-size"="8" "target-cpu"="x86-64" "target-features"="+fxsr,+mmx,+sse,+sse2,+x87" "unsafe-fp-math"="false" "use-soft-float"="false" }
attributes #2 = { nounwind readnone speculatable }
attributes #4 = { nounwind }
attributes #6 = { noreturn } |
http://rosettacode.org/wiki/Arithmetic_evaluation | Arithmetic evaluation | Create a program which parses and evaluates arithmetic expressions.
Requirements
An abstract-syntax tree (AST) for the expression must be created from parsing the input.
The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.)
The expression will be a string or list of symbols like "(1+3)*7".
The four symbols + - * / must be supported as binary operators with conventional precedence rules.
Precedence-control parentheses must also be supported.
Note
For those who don't remember, mathematical precedence is as follows:
Parentheses
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
C.f
24 game Player.
Parsing/RPN calculator algorithm.
Parsing/RPN to infix conversion.
| #F.23 | F# | module AbstractSyntaxTree
type Expression =
| Int of int
| Plus of Expression * Expression
| Minus of Expression * Expression
| Times of Expression * Expression
| Divide of Expression * Expression |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #FOCAL | FOCAL | 1.1 S A=1.5
1.2 S B=2
1.3 S N=250
1.4 F T=1,N; D 2
1.5 X FSKP(2*N)
1.6 Q
2.1 S R=A+B*T; D 3
2.2 X FPT(2*T,X1+512,Y1+390)
2.3 S R=A+B*(T+1); D 4
2.4 X FVEC(2*T+1,X2-X1,Y2-Y1)
3.1 S X1=R*FSIN(.2*T)
3.2 S Y1=R*FCOS(.2*T)
4.1 S X2=R*FSIN(.2*(T+1))
4.2 S Y2=R*FCOS(.2*(T+1)) |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Frege | Frege | module Archimedean where
import Java.IO
import Prelude.Math
data BufferedImage = native java.awt.image.BufferedImage where
pure native type_3byte_bgr "java.awt.image.BufferedImage.TYPE_3BYTE_BGR" :: Int
native new :: Int -> Int -> Int -> STMutable s BufferedImage
native createGraphics :: Mutable s BufferedImage -> STMutable s Graphics2D
data Color = pure native java.awt.Color where
pure native orange "java.awt.Color.orange" :: Color
pure native white "java.awt.Color.white" :: Color
pure native new :: Int -> Color
data BasicStroke = pure native java.awt.BasicStroke where
pure native new :: Float -> BasicStroke
data RenderingHints = native java.awt.RenderingHints where
pure native key_antialiasing "java.awt.RenderingHints.KEY_ANTIALIASING" :: RenderingHints_Key
pure native value_antialias_on "java.awt.RenderingHints.VALUE_ANTIALIAS_ON" :: Object
data RenderingHints_Key = pure native java.awt.RenderingHints.Key
data Graphics2D = native java.awt.Graphics2D where
native drawLine :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
native drawOval :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
native fillRect :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
native setColor :: Mutable s Graphics2D -> Color -> ST s ()
native setRenderingHint :: Mutable s Graphics2D -> RenderingHints_Key -> Object -> ST s ()
native setStroke :: Mutable s Graphics2D -> BasicStroke -> ST s ()
data ImageIO = mutable native javax.imageio.ImageIO where
native write "javax.imageio.ImageIO.write" :: MutableIO BufferedImage -> String -> MutableIO File -> IO Bool throws IOException
width = 640
center = width `div` 2
roundi = fromIntegral . round
drawGrid :: Mutable s Graphics2D -> ST s ()
drawGrid g = do
g.setColor $ Color.new 0xEEEEEE
g.setStroke $ BasicStroke.new 2
let angle = toRadians 45
margin = 10
numRings = 8
spacing = (width - 2 * margin) `div` (numRings * 2)
forM_ [0 .. numRings-1] $ \i -> do
let pos = margin + i * spacing
size = width - (2 * margin + i * 2 * spacing)
ia = fromIntegral i * angle
multiplier = fromIntegral $ (width - 2 * margin) `div` 2
x2 = center + (roundi (cos ia * multiplier))
y2 = center - (roundi (sin ia * multiplier))
g.drawOval pos pos size size
g.drawLine center center x2 y2
drawSpiral :: Mutable s Graphics2D -> ST s ()
drawSpiral g = do
g.setStroke $ BasicStroke.new 2
g.setColor $ Color.orange
let degrees = toRadians 0.1
end = 360 * 2 * 10 * degrees
a = 0
b = 20
c = 1
drSp theta = do
let r = a + b * theta ** (1 / c)
x = r * cos theta
y = r * sin theta
theta' = theta + degrees
plot g (center + roundi x) (center - roundi y)
when (theta' < end) (drSp (theta' + degrees))
drSp 0
plot :: Mutable s Graphics2D -> Int -> Int -> ST s ()
plot g x y = g.drawOval x y 1 1
main = do
buffy <- BufferedImage.new width width BufferedImage.type_3byte_bgr
g <- buffy.createGraphics
g.setRenderingHint RenderingHints.key_antialiasing RenderingHints.value_antialias_on
g.setColor Color.white
g.fillRect 0 0 width width
drawGrid g
drawSpiral g
f <- File.new "SpiralFrege.png"
void $ ImageIO.write buffy "png" f |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Go | Go | package main
import (
"image"
"image/color"
"image/draw"
"image/png"
"log"
"math"
"os"
)
func main() {
const (
width, height = 600, 600
centre = width / 2.0
degreesIncr = 0.1 * math.Pi / 180
turns = 2
stop = 360 * turns * 10 * degreesIncr
fileName = "spiral.png"
)
img := image.NewNRGBA(image.Rect(0, 0, width, height)) // create new image
bg := image.NewUniform(color.RGBA{255, 255, 255, 255}) // prepare white for background
draw.Draw(img, img.Bounds(), bg, image.ZP, draw.Src) // fill the background
fgCol := color.RGBA{255, 0, 0, 255} // red plot
a := 1.0
b := 20.0
for theta := 0.0; theta < stop; theta += degreesIncr {
r := a + b*theta
x := r * math.Cos(theta)
y := r * math.Sin(theta)
img.Set(int(centre+x), int(centre-y), fgCol)
}
imgFile, err := os.Create(fileName)
if err != nil {
log.Fatal(err)
}
defer imgFile.Close()
if err := png.Encode(imgFile, img); err != nil {
imgFile.Close()
log.Fatal(err)
}
} |
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #ALGOL-M | ALGOL-M |
BEGIN
INTEGER ARRAY DOORS[1:100];
INTEGER I, J, OPEN, CLOSED;
OPEN := 1;
CLOSED := 0;
% ALL DOORS ARE INITIALLY CLOSED %
FOR I := 1 STEP 1 UNTIL 100 DO
BEGIN
DOORS[I] := CLOSED;
END;
% PASS THROUGH AT INCREASING INTERVALS AND FLIP %
FOR I := 1 STEP 1 UNTIL 100 DO
BEGIN
FOR J := I STEP I UNTIL 100 DO
BEGIN
DOORS[J] := 1 - DOORS[J];
END;
END;
% SHOW RESULTS %
WRITE("THE OPEN DOORS ARE:");
WRITE("");
FOR I := 1 STEP 1 UNTIL 100 DO
BEGIN
IF DOORS[I] = OPEN THEN
WRITEON(I);
END;
END |
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #C.23 | C# | int[] numbers = new int[10]; |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Frink | Frink |
add[x,y] := x + y
multiply[x,y] := x * y
negate[x] := -x
invert[x] := 1/x // Could also use inv[x] or recip[x]
conjugate[x] := Re[x] - Im[x] i
a = 3 + 2.5i
b = 7.3 - 10i
println["$a + $b = " + add[a,b]]
println["$a * $b = " + multiply[a,b]]
println["-$a = " + negate[a]]
println["1/$a = " + invert[a]]
println["conjugate[$a] = " + conjugate[a]]
|
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #J | J | (x: 3) % (x: -4)
_3r4
3 %&x: -4
_3r4 |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #Logo | Logo | to about :a :b
output and [:a - :b < 1e-15] [:a - :b > -1e-15]
end
to agm :arith :geom
if about :arith :geom [output :arith]
output agm (:arith + :geom)/2 sqrt (:arith * :geom)
end
show agm 1 1/sqrt 2
|
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #Lua | Lua | function agm(a, b, tolerance)
if not tolerance or tolerance < 1e-15 then
tolerance = 1e-15
end
repeat
a, b = (a + b) / 2, math.sqrt(a * b)
until math.abs(a-b) < tolerance
return a
end
print(string.format("%.15f", agm(1, 1 / math.sqrt(2)))) |
http://rosettacode.org/wiki/Arithmetic_evaluation | Arithmetic evaluation | Create a program which parses and evaluates arithmetic expressions.
Requirements
An abstract-syntax tree (AST) for the expression must be created from parsing the input.
The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.)
The expression will be a string or list of symbols like "(1+3)*7".
The four symbols + - * / must be supported as binary operators with conventional precedence rules.
Precedence-control parentheses must also be supported.
Note
For those who don't remember, mathematical precedence is as follows:
Parentheses
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
C.f
24 game Player.
Parsing/RPN calculator algorithm.
Parsing/RPN to infix conversion.
| #Factor | Factor | USING: accessors kernel locals math math.parser peg.ebnf ;
IN: rosetta.arith
TUPLE: operator left right ;
TUPLE: add < operator ; C: <add> add
TUPLE: sub < operator ; C: <sub> sub
TUPLE: mul < operator ; C: <mul> mul
TUPLE: div < operator ; C: <div> div
EBNF: expr-ast
spaces = [\n\t ]*
digit = [0-9]
number = (digit)+ => [[ string>number ]]
value = spaces number:n => [[ n ]]
| spaces "(" exp:e spaces ")" => [[ e ]]
fac = fac:a spaces "*" value:b => [[ a b <mul> ]]
| fac:a spaces "/" value:b => [[ a b <div> ]]
| value
exp = exp:a spaces "+" fac:b => [[ a b <add> ]]
| exp:a spaces "-" fac:b => [[ a b <sub> ]]
| fac
main = exp:e spaces !(.) => [[ e ]]
;EBNF
GENERIC: eval-ast ( ast -- result )
M: number eval-ast ;
: recursive-eval ( ast -- left-result right-result )
[ left>> eval-ast ] [ right>> eval-ast ] bi ;
M: add eval-ast recursive-eval + ;
M: sub eval-ast recursive-eval - ;
M: mul eval-ast recursive-eval * ;
M: div eval-ast recursive-eval / ;
: evaluate ( string -- result )
expr-ast eval-ast ; |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Haskell | Haskell | #!/usr/bin/env stack
-- stack --resolver lts-7.0 --install-ghc runghc --package Rasterific --package JuicyPixels
import Codec.Picture( PixelRGBA8( .. ), writePng )
import Graphics.Rasterific
import Graphics.Rasterific.Texture
import Graphics.Rasterific.Transformations
archimedeanPoint a b t = V2 x y
where r = a + b * t
x = r * cos t
y = r * sin t
main :: IO ()
main = do
let white = PixelRGBA8 255 255 255 255
drawColor = PixelRGBA8 0xFF 0x53 0x73 255
size = 800
points = map (archimedeanPoint 0 10) [0, 0.01 .. 60]
hSize = fromIntegral size / 2
img = renderDrawing size size white $
withTransformation (translate $ V2 hSize hSize) $
withTexture (uniformTexture drawColor) $
stroke 4 JoinRound (CapRound, CapRound) $
polyline points
writePng "SpiralHaskell.png" img |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #J | J | require'plot'
'aspect 1' plot (*^)j.0.01*i.1400 |
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #AmigaE | AmigaE | PROC main()
DEF t[100]: ARRAY,
pass, door
FOR door := 0 TO 99 DO t[door] := FALSE
FOR pass := 0 TO 99
door := pass
WHILE door <= 99
t[door] := Not(t[door])
door := door + pass + 1
ENDWHILE
ENDFOR
FOR door := 0 TO 99 DO WriteF('\d is \s\n', door+1,
IF t[door] THEN 'open' ELSE 'closed')
ENDPROC |
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #C.2B.2B | C++ | #include <array>
#include <vector>
// These headers are only needed for the demonstration
#include <algorithm>
#include <iostream>
#include <iterator>
#include <string>
// This is a template function that works for any array-like object
template <typename Array>
void demonstrate(Array& array)
{
// Array element access
array[2] = "Three"; // Fast, but unsafe - if the index is out of bounds you
// get undefined behaviour
array.at(1) = "Two"; // *Slightly* less fast, but safe - if the index is out
// of bounds, an exception is thrown
// Arrays can be used with standard algorithms
std::reverse(begin(array), end(array));
std::for_each(begin(array), end(array),
[](typename Array::value_type const& element) // in C++14, you can just use auto
{
std::cout << element << ' ';
});
std::cout << '\n';
}
int main()
{
// Compile-time sized fixed-size array
auto fixed_size_array = std::array<std::string, 3>{ "One", "Four", "Eight" };
// If you do not supply enough elements, the remainder are default-initialized
// Dynamic array
auto dynamic_array = std::vector<std::string>{ "One", "Four" };
dynamic_array.push_back("Eight"); // Dynamically grows to accept new element
// All types of arrays can be used more or less interchangeably
demonstrate(fixed_size_array);
demonstrate(dynamic_array);
} |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Futhark | Futhark |
type complex = (f64,f64)
fun complexAdd((a,b): complex) ((c,d): complex): complex =
(a + c,
b + d)
fun complexMult((a,b): complex) ((c,d): complex): complex =
(a*c - b * d,
a*d + b * c)
fun complexInv((r,i): complex): complex =
let denom = r*r + i * i
in (r / denom,
-i / denom)
fun complexNeg((r,i): complex): complex =
(-r, -i)
fun complexConj((r,i): complex): complex =
(r, -i)
fun main (o: int) (a: complex) (b: complex): complex =
if o == 0 then complexAdd a b
else if o == 1 then complexMult a b
else if o == 2 then complexInv a
else if o == 3 then complexNeg a
else complexConj a
|
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #GAP | GAP | # GAP knows gaussian integers, gaussian rationals (i.e. Q[i]), and cyclotomic fields. Here are some examples.
# E(n) is an nth primitive root of 1
i := Sqrt(-1);
# E(4)
(3 + 2*i)*(5 - 7*i);
# 29-11*E(4)
1/i;
# -E(4)
Sqrt(-3);
# E(3)-E(3)^2
i in GaussianIntegers;
# true
i/2 in GaussianIntegers;
# false
i/2 in GaussianRationals;
# true
Sqrt(-3) in Cyclotomics;
# true |
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #Java | Java | public class BigRationalFindPerfectNumbers {
public static void main(String[] args) {
int MAX_NUM = 1 << 19;
System.out.println("Searching for perfect numbers in the range [1, " + (MAX_NUM - 1) + "]");
BigRational TWO = BigRational.valueOf(2);
for (int i = 1; i < MAX_NUM; i++) {
BigRational reciprocalSum = BigRational.ONE;
if (i > 1)
reciprocalSum = reciprocalSum.add(BigRational.valueOf(i).reciprocal());
int maxDivisor = (int) Math.sqrt(i);
if (maxDivisor >= i)
maxDivisor--;
for (int divisor = 2; divisor <= maxDivisor; divisor++) {
if (i % divisor == 0) {
reciprocalSum = reciprocalSum.add(BigRational.valueOf(divisor).reciprocal());
int dividend = i / divisor;
if (divisor != dividend)
reciprocalSum = reciprocalSum.add(BigRational.valueOf(dividend).reciprocal());
}
}
if (reciprocalSum.equals(TWO))
System.out.println(String.valueOf(i) + " is a perfect number");
}
}
} |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #M2000_Interpreter | M2000 Interpreter |
Module Checkit {
Function Agm {
\\ new stack constructed at calling the Agm() with two values
Repeat {
Read a0, b0
Push Sqrt(a0*b0), (a0+b0)/2
' last pushed first read
} Until Stackitem(1)==Stackitem(2)
=Stackitem(1)
\\ stack deconstructed at exit of function
}
Print Agm(1,1/Sqrt(2))
}
Checkit
|
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #Maple | Maple |
> evalf( GaussAGM( 1, 1 / sqrt( 2 ) ) ); # default precision is 10 digits
0.8472130847
> evalf[100]( GaussAGM( 1, 1 / sqrt( 2 ) ) ); # to 100 digits
0.847213084793979086606499123482191636481445910326942185060579372659\
7340048341347597232002939946112300
|
http://rosettacode.org/wiki/Arithmetic_evaluation | Arithmetic evaluation | Create a program which parses and evaluates arithmetic expressions.
Requirements
An abstract-syntax tree (AST) for the expression must be created from parsing the input.
The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.)
The expression will be a string or list of symbols like "(1+3)*7".
The four symbols + - * / must be supported as binary operators with conventional precedence rules.
Precedence-control parentheses must also be supported.
Note
For those who don't remember, mathematical precedence is as follows:
Parentheses
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
C.f
24 game Player.
Parsing/RPN calculator algorithm.
Parsing/RPN to infix conversion.
| #FreeBASIC | FreeBASIC |
'Arithmetic evaluation
'
'Create a program which parses and evaluates arithmetic expressions.
'
'Requirements
'
' * An abstract-syntax tree (AST) for the expression must be created from parsing the
' input.
' * The AST must be used in evaluation, also, so the input may not be directly evaluated
' (e.g. by calling eval or a similar language feature.)
' * The expression will be a string or list of symbols like "(1+3)*7".
' * The four symbols + - * / must be supported as binary operators with conventional
' precedence rules.
' * Precedence-control parentheses must also be supported.
'
'Standard mathematical precedence should be followed:
'
' Parentheses
' Multiplication/Division (left to right)
' Addition/Subtraction (left to right)
'
' test cases:
' 2*-3--4+-0.25 : returns -2.25
' 1 + 2 * (3 + (4 * 5 + 6 * 7 * 8) - 9) / 10 : returns 71
enum
false = 0
true = -1
end enum
enum Symbol
unknown_sym
minus_sym
plus_sym
lparen_sym
rparen_sym
number_sym
mul_sym
div_sym
unary_minus_sym
unary_plus_sym
done_sym
eof_sym
end enum
type Tree
as Tree ptr leftp, rightp
op as Symbol
value as double
end type
dim shared sym as Symbol
dim shared tokenval as double
dim shared usr_input as string
declare function expr(byval p as integer) as Tree ptr
function isdigit(byval ch as string) as long
return ch <> "" and Asc(ch) >= Asc("0") and Asc(ch) <= Asc("9")
end function
sub error_msg(byval msg as string)
print msg
system
end sub
' tokenize the input string
sub getsym()
do
if usr_input = "" then
line input usr_input
usr_input += chr(10)
endif
dim as string ch = mid(usr_input, 1, 1) ' get the next char
usr_input = mid(usr_input, 2) ' remove it from input
sym = unknown_sym
select case ch
case " ": continue do
case chr(10), "": sym = done_sym: return
case "+": sym = plus_sym: return
case "-": sym = minus_sym: return
case "*": sym = mul_sym: return
case "/": sym = div_sym: return
case "(": sym = lparen_sym: return
case ")": sym = rparen_sym: return
case else
if isdigit(ch) then
dim s as string = ""
dim dot as integer = 0
do
s += ch
if ch = "." then dot += 1
ch = mid(usr_input, 1, 1) ' get the next char
usr_input = mid(usr_input, 2) ' remove it from input
loop while isdigit(ch) orelse ch = "."
if ch = "." or dot > 1 then error_msg("bogus number")
usr_input = ch + usr_input ' prepend the char to input
tokenval = val(s)
sym = number_sym
end if
return
end select
loop
end sub
function make_node(byval op as Symbol, byval leftp as Tree ptr, byval rightp as Tree ptr) as Tree ptr
dim t as Tree ptr
t = callocate(len(Tree))
t->op = op
t->leftp = leftp
t->rightp = rightp
return t
end function
function is_binary(byval op as Symbol) as integer
select case op
case mul_sym, div_sym, plus_sym, minus_sym: return true
case else: return false
end select
end function
function prec(byval op as Symbol) as integer
select case op
case unary_minus_sym, unary_plus_sym: return 100
case mul_sym, div_sym: return 90
case plus_sym, minus_sym: return 80
case else: return 0
end select
end function
function primary as Tree ptr
dim t as Tree ptr = 0
select case sym
case minus_sym, plus_sym
dim op as Symbol = sym
getsym()
t = expr(prec(unary_minus_sym))
if op = minus_sym then return make_node(unary_minus_sym, t, 0)
if op = plus_sym then return make_node(unary_plus_sym, t, 0)
case lparen_sym
getsym()
t = expr(0)
if sym <> rparen_sym then error_msg("expecting rparen")
getsym()
return t
case number_sym
t = make_node(sym, 0, 0)
t->value = tokenval
getsym()
return t
case else: error_msg("expecting a primary")
end select
end function
function expr(byval p as integer) as Tree ptr
dim t as Tree ptr = primary()
while is_binary(sym) andalso prec(sym) >= p
dim t1 as Tree ptr
dim op as Symbol = sym
getsym()
t1 = expr(prec(op) + 1)
t = make_node(op, t, t1)
wend
return t
end function
function eval(byval t as Tree ptr) as double
if t <> 0 then
select case t->op
case minus_sym: return eval(t->leftp) - eval(t->rightp)
case plus_sym: return eval(t->leftp) + eval(t->rightp)
case mul_sym: return eval(t->leftp) * eval(t->rightp)
case div_sym: return eval(t->leftp) / eval(t->rightp)
case unary_minus_sym: return -eval(t->leftp)
case unary_plus_sym: return eval(t->leftp)
case number_sym: return t->value
case else: error_msg("unexpected tree node")
end select
end if
return 0
end function
do
getsym()
if sym = eof_sym then exit do
if sym = done_sym then continue do
dim t as Tree ptr = expr(0)
print"> "; eval(t)
if sym = eof_sym then exit do
if sym <> done_sym then error_msg("unexpected input")
loop
|
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Java | Java | import java.awt.*;
import static java.lang.Math.*;
import javax.swing.*;
public class ArchimedeanSpiral extends JPanel {
public ArchimedeanSpiral() {
setPreferredSize(new Dimension(640, 640));
setBackground(Color.white);
}
void drawGrid(Graphics2D g) {
g.setColor(new Color(0xEEEEEE));
g.setStroke(new BasicStroke(2));
double angle = toRadians(45);
int w = getWidth();
int center = w / 2;
int margin = 10;
int numRings = 8;
int spacing = (w - 2 * margin) / (numRings * 2);
for (int i = 0; i < numRings; i++) {
int pos = margin + i * spacing;
int size = w - (2 * margin + i * 2 * spacing);
g.drawOval(pos, pos, size, size);
double ia = i * angle;
int x2 = center + (int) (cos(ia) * (w - 2 * margin) / 2);
int y2 = center - (int) (sin(ia) * (w - 2 * margin) / 2);
g.drawLine(center, center, x2, y2);
}
}
void drawSpiral(Graphics2D g) {
g.setStroke(new BasicStroke(2));
g.setColor(Color.orange);
double degrees = toRadians(0.1);
double center = getWidth() / 2;
double end = 360 * 2 * 10 * degrees;
double a = 0;
double b = 20;
double c = 1;
for (double theta = 0; theta < end; theta += degrees) {
double r = a + b * pow(theta, 1 / c);
double x = r * cos(theta);
double y = r * sin(theta);
plot(g, (int) (center + x), (int) (center - y));
}
}
void plot(Graphics2D g, int x, int y) {
g.drawOval(x, y, 1, 1);
}
@Override
public void paintComponent(Graphics gg) {
super.paintComponent(gg);
Graphics2D g = (Graphics2D) gg;
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
drawGrid(g);
drawSpiral(g);
}
public static void main(String[] args) {
SwingUtilities.invokeLater(() -> {
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
f.setTitle("Archimedean Spiral");
f.setResizable(false);
f.add(new ArchimedeanSpiral(), BorderLayout.CENTER);
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
});
}
} |
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #APL | APL | doors←{100⍴((⍵-1)⍴0),1}
≠⌿⊃doors¨ ⍳100 |
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #Ceylon | Ceylon | import ceylon.collection {
ArrayList
}
shared void run() {
// you can get an array from the Array.ofSize named constructor
value array = Array.ofSize(10, "hello");
value a = array[3];
print(a);
array[4] = "goodbye";
print(array);
// for a dynamic list import ceylon.collection in your module.ceylon file
value list = ArrayList<String>();
list.push("hello");
list.push("hello again");
print(list);
} |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Go | Go | package main
import (
"fmt"
"math/cmplx"
)
func main() {
a := 1 + 1i
b := 3.14159 + 1.25i
fmt.Println("a: ", a)
fmt.Println("b: ", b)
fmt.Println("a + b: ", a+b)
fmt.Println("a * b: ", a*b)
fmt.Println("-a: ", -a)
fmt.Println("1 / a: ", 1/a)
fmt.Println("a̅: ", cmplx.Conj(a))
} |
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #JavaScript | JavaScript | // the constructor
function Rational(numerator, denominator) {
if (denominator === undefined)
denominator = 1;
else if (denominator == 0)
throw "divide by zero";
this.numer = numerator;
if (this.numer == 0)
this.denom = 1;
else
this.denom = denominator;
this.normalize();
}
// getter methods
Rational.prototype.numerator = function() {return this.numer};
Rational.prototype.denominator = function() {return this.denom};
// clone a rational
Rational.prototype.dup = function() {
return new Rational(this.numerator(), this.denominator());
};
// conversion methods
Rational.prototype.toString = function() {
if (this.denominator() == 1) {
return this.numerator().toString();
} else {
// implicit conversion of numbers to strings
return this.numerator() + '/' + this.denominator()
}
};
Rational.prototype.toFloat = function() {return eval(this.toString())}
Rational.prototype.toInt = function() {return Math.floor(this.toFloat())};
// reduce
Rational.prototype.normalize = function() {
// greatest common divisor
var a=Math.abs(this.numerator()), b=Math.abs(this.denominator())
while (b != 0) {
var tmp = a;
a = b;
b = tmp % b;
}
// a is the gcd
this.numer /= a;
this.denom /= a;
if (this.denom < 0) {
this.numer *= -1;
this.denom *= -1;
}
return this;
}
// absolute value
// returns a new rational
Rational.prototype.abs = function() {
return new Rational(Math.abs(this.numerator()), this.denominator());
};
// inverse
// returns a new rational
Rational.prototype.inv = function() {
return new Rational(this.denominator(), this.numerator());
};
//
// arithmetic methods
// variadic, modifies receiver
Rational.prototype.add = function() {
for (var i = 0; i < arguments.length; i++) {
this.numer = this.numer * arguments[i].denominator() + this.denom * arguments[i].numerator();
this.denom = this.denom * arguments[i].denominator();
}
return this.normalize();
};
// variadic, modifies receiver
Rational.prototype.subtract = function() {
for (var i = 0; i < arguments.length; i++) {
this.numer = this.numer * arguments[i].denominator() - this.denom * arguments[i].numerator();
this.denom = this.denom * arguments[i].denominator();
}
return this.normalize();
};
// unary "-" operator
// returns a new rational
Rational.prototype.neg = function() {
return (new Rational(0)).subtract(this);
};
// variadic, modifies receiver
Rational.prototype.multiply = function() {
for (var i = 0; i < arguments.length; i++) {
this.numer *= arguments[i].numerator();
this.denom *= arguments[i].denominator();
}
return this.normalize();
};
// modifies receiver
Rational.prototype.divide = function(rat) {
return this.multiply(rat.inv());
}
// increment
// modifies receiver
Rational.prototype.inc = function() {
this.numer += this.denominator();
return this.normalize();
}
// decrement
// modifies receiver
Rational.prototype.dec = function() {
this.numer -= this.denominator();
return this.normalize();
}
//
// comparison methods
Rational.prototype.isZero = function() {
return (this.numerator() == 0);
}
Rational.prototype.isPositive = function() {
return (this.numerator() > 0);
}
Rational.prototype.isNegative = function() {
return (this.numerator() < 0);
}
Rational.prototype.eq = function(rat) {
return this.dup().subtract(rat).isZero();
}
Rational.prototype.ne = function(rat) {
return !(this.eq(rat));
}
Rational.prototype.lt = function(rat) {
return this.dup().subtract(rat).isNegative();
}
Rational.prototype.gt = function(rat) {
return this.dup().subtract(rat).isPositive();
}
Rational.prototype.le = function(rat) {
return !(this.gt(rat));
}
Rational.prototype.ge = function(rat) {
return !(this.lt(rat));
} |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #Mathematica.2FWolfram_Language | Mathematica/Wolfram Language | PrecisionDigits = 85;
AGMean[a_, b_] := FixedPoint[{ Tr@#/2, Sqrt[Times@@#] }&, N[{a,b}, PrecisionDigits]]〚1〛 |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #MATLAB_.2F_Octave | MATLAB / Octave | function [a,g]=agm(a,g)
%%arithmetic_geometric_mean(a,g)
while (1)
a0=a;
a=(a0+g)/2;
g=sqrt(a0*g);
if (abs(a0-a) < a*eps) break; end;
end;
end |
http://rosettacode.org/wiki/Arithmetic_evaluation | Arithmetic evaluation | Create a program which parses and evaluates arithmetic expressions.
Requirements
An abstract-syntax tree (AST) for the expression must be created from parsing the input.
The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.)
The expression will be a string or list of symbols like "(1+3)*7".
The four symbols + - * / must be supported as binary operators with conventional precedence rules.
Precedence-control parentheses must also be supported.
Note
For those who don't remember, mathematical precedence is as follows:
Parentheses
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
C.f
24 game Player.
Parsing/RPN calculator algorithm.
Parsing/RPN to infix conversion.
| #Go | Go | enum Op {
ADD('+', 2),
SUBTRACT('-', 2),
MULTIPLY('*', 1),
DIVIDE('/', 1);
static {
ADD.operation = { a, b -> a + b }
SUBTRACT.operation = { a, b -> a - b }
MULTIPLY.operation = { a, b -> a * b }
DIVIDE.operation = { a, b -> a / b }
}
final String symbol
final int precedence
Closure operation
private Op(String symbol, int precedence) {
this.symbol = symbol
this.precedence = precedence
}
String toString() { symbol }
static Op fromSymbol(String symbol) {
Op.values().find { it.symbol == symbol }
}
}
interface Expression {
Number evaluate();
}
class Constant implements Expression {
Number value
Constant (Number value) { this.value = value }
Constant (String str) {
try { this.value = str as BigInteger }
catch (e) { this.value = str as BigDecimal }
}
Number evaluate() { value }
String toString() { "${value}" }
}
class Term implements Expression {
Op op
Expression left, right
Number evaluate() { op.operation(left.evaluate(), right.evaluate()) }
String toString() { "(${op} ${left} ${right})" }
}
void fail(String msg, Closure cond = {true}) {
if (cond()) throw new IllegalArgumentException("Cannot parse expression: ${msg}")
}
Expression parse(String expr) {
def tokens = tokenize(expr)
def elements = groupByParens(tokens, 0)
parse(elements)
}
List tokenize(String expr) {
def tokens = []
def constStr = ""
def captureConstant = { i ->
if (constStr) {
try { tokens << new Constant(constStr) }
catch (NumberFormatException e) { fail "Invalid constant '${constStr}' near position ${i}" }
constStr = ''
}
}
for(def i = 0; i<expr.size(); i++) {
def c = expr[i]
def constSign = c in ['+','-'] && constStr.empty && (tokens.empty || tokens[-1] != ')')
def isConstChar = { it in ['.'] + ('0'..'9') || constSign }
if (c in ([')'] + Op.values()*.symbol) && !constSign) { captureConstant(i) }
switch (c) {
case ~/\s/: break
case isConstChar: constStr += c; break
case Op.values()*.symbol: tokens << Op.fromSymbol(c); break
case ['(',')']: tokens << c; break
default: fail "Invalid character '${c}' at position ${i+1}"
}
}
captureConstant(expr.size())
tokens
}
List groupByParens(List tokens, int depth) {
def deepness = depth
def tokenGroups = []
for (def i = 0; i < tokens.size(); i++) {
def token = tokens[i]
switch (token) {
case '(':
fail("'(' too close to end of expression") { i+2 > tokens.size() }
def subGroup = groupByParens(tokens[i+1..-1], depth+1)
tokenGroups << subGroup[0..-2]
i += subGroup[-1] + 1
break
case ')':
fail("Unbalanced parens, found extra ')'") { deepness == 0 }
tokenGroups << i
return tokenGroups
default:
tokenGroups << token
}
}
fail("Unbalanced parens, unclosed groupings at end of expression") { deepness != 0 }
def n = tokenGroups.size()
fail("The operand/operator sequence is wrong") { n%2 == 0 }
(0..<n).each {
def i = it
fail("The operand/operator sequence is wrong") { (i%2 == 0) == (tokenGroups[i] instanceof Op) }
}
tokenGroups
}
Expression parse(List elements) {
while (elements.size() > 1) {
def n = elements.size()
fail ("The operand/operator sequence is wrong") { n%2 == 0 }
def groupLoc = (0..<n).find { i -> elements[i] instanceof List }
if (groupLoc != null) {
elements[groupLoc] = parse(elements[groupLoc])
continue
}
def opLoc = (0..<n).find { i -> elements[i] instanceof Op && elements[i].precedence == 1 } \
?: (0..<n).find { i -> elements[i] instanceof Op && elements[i].precedence == 2 }
if (opLoc != null) {
fail ("Operator out of sequence") { opLoc%2 == 0 }
def term = new Term(left:elements[opLoc-1], op:elements[opLoc], right:elements[opLoc+1])
elements[(opLoc-1)..(opLoc+1)] = [term]
continue
}
}
return elements[0] instanceof List ? parse(elements[0]) : elements[0]
} |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #JavaScript | JavaScript |
<!-- ArchiSpiral.html -->
<html>
<head><title>Archimedean spiral</title></head>
<body onload="pAS(35,'navy');">
<h3>Archimedean spiral</h3> <p id=bo></p>
<canvas id="canvId" width="640" height="640" style="border: 2px outset;"></canvas>
<script>
// Plotting Archimedean_spiral aev 3/17/17
// lps - number of loops, clr - color.
function pAS(lps,clr) {
var a=.0,ai=.1,r=.0,ri=.1,as=lps*2*Math.PI,n=as/ai;
var cvs=document.getElementById("canvId");
var ctx=cvs.getContext("2d");
ctx.fillStyle="white"; ctx.fillRect(0,0,cvs.width,cvs.height);
var x=y=0, s=cvs.width/2;
ctx.beginPath();
for (var i=1; i<n; i++) {
x=r*Math.cos(a), y=r*Math.sin(a);
ctx.lineTo(x+s,y+s);
r+=ri; a+=ai;
}//fend i
ctx.strokeStyle = clr; ctx.stroke();
}
</script></body></html>
|
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #jq | jq | def spiral($zero; $turns; $step):
def pi: 1 | atan * 4;
def p2: (. * 100 | round) / 100;
def svg:
400 as $width
| 400 as $height
| 2 as $swidth # stroke
| "blue" as $stroke
| (range($zero; $turns * 2 * pi; $step) as $theta
| (((($theta)|cos) * 2 * $theta + ($width/2)) |p2) as $x
| (((($theta)|sin) * 2 * $theta + ($height/2))|p2) as $y
| if $theta == $zero
then "<path fill='transparent' style='stroke:\($stroke); stroke-width:\($swidth)' d='M \($x) \($y)"
else " L \($x) \($y)"
end),
"' />";
"<svg width='100%' height='100%'
xmlns='http://www.w3.org/2000/svg'>",
svg,
"</svg>" ;
spiral(0; 10; 0.025)
|
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Julia | Julia | using UnicodePlots
spiral(θ, a=0, b=1) = @. b * θ * cos(θ + a), b * θ * sin(θ + a)
x, y = spiral(1:0.1:10)
println(lineplot(x, y)) |
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #AppleScript | AppleScript | set is_open to {}
repeat 100 times
set end of is_open to false
end
repeat with pass from 1 to 100
repeat with door from pass to 100 by pass
set item door of is_open to not item door of is_open
end
end
set open_doors to {}
repeat with door from 1 to 100
if item door of is_open then
set end of open_doors to door
end
end
set text item delimiters to ", "
display dialog "Open doors: " & open_doors |
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #ChucK | ChucK |
int array[0]; // instantiate int array
array << 1; // append item
array << 2 << 3; // append items
4 => array[3]; // assign element(4) to index(3)
5 => array.size; // resize
array.clear(); // clear elements
<<<array.size()>>>; // print in cosole array size
[1,2,3,4,5,6,7] @=> array;
array.popBack(); // Pop last element
|
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Groovy | Groovy | class Complex {
final Number real, imag
static final Complex i = [0,1] as Complex
Complex(Number r, Number i = 0) { (real, imag) = [r, i] }
Complex(Map that) { (real, imag) = [that.real ?: 0, that.imag ?: 0] }
Complex plus (Complex c) { [real + c.real, imag + c.imag] as Complex }
Complex plus (Number n) { [real + n, imag] as Complex }
Complex minus (Complex c) { [real - c.real, imag - c.imag] as Complex }
Complex minus (Number n) { [real - n, imag] as Complex }
Complex multiply (Complex c) { [real*c.real - imag*c.imag , imag*c.real + real*c.imag] as Complex }
Complex multiply (Number n) { [real*n , imag*n] as Complex }
Complex div (Complex c) { this * c.recip() }
Complex div (Number n) { this * (1/n) }
Complex negative () { [-real, -imag] as Complex }
/** the complex conjugate of this complex number. Overloads the bitwise complement (~) operator. */
Complex bitwiseNegate () { [real, -imag] as Complex }
/** the magnitude of this complex number. */
// could also use Math.sqrt( (this * (~this)).real )
Number getAbs() { Math.sqrt( real*real + imag*imag ) }
/** the magnitude of this complex number. */
Number abs() { this.abs }
/** the reciprocal of this complex number. */
Complex getRecip() { (~this) / (ρ**2) }
/** the reciprocal of this complex number. */
Complex recip() { this.recip }
/** derived polar angle θ (theta) for polar form. Normalized to 0 ≤ θ < 2π. */
Number getTheta() {
def θ = Math.atan2(imag,real)
θ = θ < 0 ? θ + 2 * Math.PI : θ
}
/** derived polar angle θ (theta) for polar form. Normalized to 0 ≤ θ < 2π. */
Number getΘ() { this.theta } // this is greek uppercase theta
/** derived polar magnitude ρ (rho) for polar form. */
Number getRho() { this.abs }
/** derived polar magnitude ρ (rho) for polar form. */
Number getΡ() { this.abs } // this is greek uppercase rho, not roman P
/** Runs Euler's polar-to-Cartesian complex conversion,
* converting [ρ, θ] inputs into a [real, imag]-based complex number */
static Complex fromPolar(Number ρ, Number θ) {
[ρ * Math.cos(θ), ρ * Math.sin(θ)] as Complex
}
/** Creates new complex with same magnitude ρ, but different angle θ */
Complex withTheta(Number θ) { fromPolar(this.rho, θ) }
/** Creates new complex with same magnitude ρ, but different angle θ */
Complex withΘ(Number θ) { fromPolar(this.rho, θ) }
/** Creates new complex with same angle θ, but different magnitude ρ */
Complex withRho(Number ρ) { fromPolar(ρ, this.θ) }
/** Creates new complex with same angle θ, but different magnitude ρ */
Complex withΡ(Number ρ) { fromPolar(ρ, this.θ) } // this is greek uppercase rho, not roman P
static Complex exp(Complex c) { fromPolar(Math.exp(c.real), c.imag) }
static Complex log(Complex c) { [Math.log(c.rho), c.theta] as Complex }
Complex power(Complex c) {
def zero = [0] as Complex
(this == zero && c != zero) \
? zero \
: c == 1 \
? this \
: exp( log(this) * c )
}
Complex power(Number n) { this ** ([n, 0] as Complex) }
boolean equals(that) {
that != null && (that instanceof Complex \
? [this.real, this.imag] == [that.real, that.imag] \
: that instanceof Number && [this.real, this.imag] == [that, 0])
}
int hashCode() { [real, imag].hashCode() }
String toString() {
def realPart = "${real}"
def imagPart = imag.abs() == 1 ? "i" : "${imag.abs()}i"
real == 0 && imag == 0 \
? "0" \
: real == 0 \
? (imag > 0 ? '' : "-") + imagPart \
: imag == 0 \
? realPart \
: realPart + (imag > 0 ? " + " : " - ") + imagPart
}
} |
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #jq | jq | # a and b are assumed to be non-zero integers
def gcd(a; b):
# subfunction expects [a,b] as input
# i.e. a ~ .[0] and b ~ .[1]
def rgcd: if .[1] == 0 then .[0]
else [.[1], .[0] % .[1]] | rgcd
end;
[a,b] | rgcd;
# To take advantage of gojq's support for accurate integer division:
def idivide($j):
. as $i
| ($i % $j) as $mod
| ($i - $mod) / $j ;
# To take advantage of gojq's arbitrary-precision integer arithmetic:
def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
# $p should be an integer or a rational
# $q should be a non-zero integer or a rational
# Output: a Rational: $p // $q
def r($p;$q):
def r: if type == "number" then {n: ., d: 1} else . end;
# The remaining subfunctions assume all args are Rational
def n: if .d < 0 then {n: -.n, d: -.d} else . end;
def rdiv($a;$b):
($a.d * $b.n) as $denom
| if $denom==0 then "r: division by 0" | error
else r($a.n * $b.d; $denom)
end;
if $q == 1 and ($p|type) == "number" then {n: $p, d: 1}
elif $q == 0 then "r: denominator cannot be 0" | error
else if ($p|type == "number") and ($q|type == "number")
then gcd($p;$q) as $g
| {n: ($p/$g), d: ($q/$g)} | n
else rdiv($p|r; $q|r)
end
end;
# Polymorphic (integers and rationals in general)
def requal($a; $b):
if $a | type == "number" and $b | type == "number" then $a == $b
else r($a;1) == r($b;1)
end;
# Input: a Rational
# Output: a Rational with a denominator that has no more than $digits digits
# and such that |rBefore - rAfter| < 1/(10|power($digits)
# where $digits should be a positive integer.
def rround($digits):
if .d | length > $digits
then (10|power($digits)) as $p
| .d as $d
| r($p * .n | idivide($d); $p)
else . end;
# Polymorphic; see also radd/0
def radd($a; $b):
def r: if type == "number" then {n: ., d: 1} else . end;
($a|r) as {n: $na, d: $da}
| ($b|r) as {n: $nb, d: $db}
| r( ($na * $db) + ($nb * $da); $da * $db );
# Polymorphic; see also rmult/0
def rmult($a; $b):
def r: if type == "number" then {n: ., d: 1} else . end;
($a|r) as {n: $na, d: $da}
| ($b|r) as {n: $nb, d: $db}
| r( $na * $nb; $da * $db ) ;
# Input: an array of rationals (integers and/or Rationals)
# Output: a Rational computed using left-associativity
def rmult:
if length == 0 then r(1;1)
elif length == 1 then r(.[0]; 1) # ensure the result is Rational
else .[0] as $first
| reduce .[1:][] as $x ($first; rmult(.; $x))
end;
# Input: an array of rationals (integers and/or Rationals)
# Output: a Rational computed using left-associativity
def radd:
if length == 0 then r(0;1)
elif length == 1 then r(.[0]; 1) # ensure the result is Rational
else .[0] as $first
| reduce .[1:][] as $x ($first; radd(. ; $x))
end;
def rabs: r(.;1) | r(.n|length; .d|length);
def rminus: r(-1 * .n; .d);
def rminus($a; $b): radd($a; rmult(-1; $b));
# Note that rinv does not check for division by 0
def rinv: r(1; .);
def rdiv($a; $b): r($a; $b);
# Input: an integer or a Rational, $p
# Output: $p < $q
def rlessthan($q):
# lt($b) assumes . and $b have the same sign
def lt($b):
. as $a
| ($a.n * $b.d) < ($b.n * $a.d);
if $q|type == "number" then rlessthan(r($q;1))
else if type == "number" then r(.;1) else . end
| if .n < 0
then if ($q.n >= 0) then true
else . as $p | ($q|rminus | rlessthan($p|rminus))
end
else lt($q)
end
end;
def rgreaterthan($q):
. as $p | $q | rlessthan($p);
def rlessthanOrEqual($q): requal(.;$q) or rlessthan($q);
def rgreaterthanOrEqual($q): requal(.;$q) or rgreaterthan($q);
# Input: non-negative integer or Rational
def rsqrt(precision):
r(.;1) as $n
| (precision + 1) as $digits
| def update: rmult( r(1;2); radd(.x; rdiv($n; .x))) | rround($digits);
| def update: rmult( r(1;2); radd(.x; rdiv($n; .x)));
r(1; 10|power(precision)) as $p
| { x: .}
| .root = update
| until( rminus(.root; .x) | rabs | rlessthan($p);
.x = .root
| .root = update )
| .root ;
# Use native floats
# q.v. r_to_decimal(precision)
def r_to_decimal: .n / .d;
# Input: a Rational, or {n, d} in general, or an integer.
# Output: a string representation of the input as a decimal number.
# If the input is a number, it is simply converted to a string.
# Otherwise, $precision determines the number of digits after the decimal point,
# obtained by truncating, but trailing 0s are omitted.
# Examples assuming $digits is 5:
# -0//1 => "0"
# 2//1 => "2"
# 1//2 => "0.5"
# 1//3 => "0.33333"
# 7//9 => "0.77777"
# 1//100 => "0.01"
# -1//10 => "-0.1"
# 1//1000000 => "0."
def r_to_decimal($digits):
if .n == 0 # captures the annoying case of -0
then "0"
elif type == "number" then tostring
elif .d < 0 then {n: -.n, d: -.d}|r_to_decimal($digits)
elif .n < 0
then "-" + ((.n = -.n) | r_to_decimal($digits))
else (10|power($digits)) as $p
| .d as $d
| if $d == 1 then .n|tostring
else ($p * .n | idivide($d) | tostring) as $n
| ($n|length) as $nlength
| (if $nlength > $digits then $n[0:$nlength-$digits] + "." + $n[$nlength-$digits:]
else "0." + ("0"*($digits - $nlength) + $n)
end) | sub("0+$";"")
end
end;
# pretty print ala Julia
def rpp: "\(.n) // \(.d)"; |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #Maxima | Maxima | agm(a, b) := %pi/4*(a + b)/elliptic_kc(((a - b)/(a + b))^2)$
agm(1, 1/sqrt(2)), bfloat, fpprec: 85;
/* 8.472130847939790866064991234821916364814459103269421850605793726597340048341347597232b-1 */ |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #.D0.9C.D0.9A-61.2F52 | МК-61/52 | П1 <-> П0 1 ВП 8 /-/ П2 ИП0 ИП1
- ИП2 - /-/ x<0 31 ИП1 П3 ИП0 ИП1
* КвКор П1 ИП0 ИП3 + 2 / П0 БП
08 ИП0 С/П |
http://rosettacode.org/wiki/Arithmetic_evaluation | Arithmetic evaluation | Create a program which parses and evaluates arithmetic expressions.
Requirements
An abstract-syntax tree (AST) for the expression must be created from parsing the input.
The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.)
The expression will be a string or list of symbols like "(1+3)*7".
The four symbols + - * / must be supported as binary operators with conventional precedence rules.
Precedence-control parentheses must also be supported.
Note
For those who don't remember, mathematical precedence is as follows:
Parentheses
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
C.f
24 game Player.
Parsing/RPN calculator algorithm.
Parsing/RPN to infix conversion.
| #Groovy | Groovy | enum Op {
ADD('+', 2),
SUBTRACT('-', 2),
MULTIPLY('*', 1),
DIVIDE('/', 1);
static {
ADD.operation = { a, b -> a + b }
SUBTRACT.operation = { a, b -> a - b }
MULTIPLY.operation = { a, b -> a * b }
DIVIDE.operation = { a, b -> a / b }
}
final String symbol
final int precedence
Closure operation
private Op(String symbol, int precedence) {
this.symbol = symbol
this.precedence = precedence
}
String toString() { symbol }
static Op fromSymbol(String symbol) {
Op.values().find { it.symbol == symbol }
}
}
interface Expression {
Number evaluate();
}
class Constant implements Expression {
Number value
Constant (Number value) { this.value = value }
Constant (String str) {
try { this.value = str as BigInteger }
catch (e) { this.value = str as BigDecimal }
}
Number evaluate() { value }
String toString() { "${value}" }
}
class Term implements Expression {
Op op
Expression left, right
Number evaluate() { op.operation(left.evaluate(), right.evaluate()) }
String toString() { "(${op} ${left} ${right})" }
}
void fail(String msg, Closure cond = {true}) {
if (cond()) throw new IllegalArgumentException("Cannot parse expression: ${msg}")
}
Expression parse(String expr) {
def tokens = tokenize(expr)
def elements = groupByParens(tokens, 0)
parse(elements)
}
List tokenize(String expr) {
def tokens = []
def constStr = ""
def captureConstant = { i ->
if (constStr) {
try { tokens << new Constant(constStr) }
catch (NumberFormatException e) { fail "Invalid constant '${constStr}' near position ${i}" }
constStr = ''
}
}
for(def i = 0; i<expr.size(); i++) {
def c = expr[i]
def constSign = c in ['+','-'] && constStr.empty && (tokens.empty || tokens[-1] != ')')
def isConstChar = { it in ['.'] + ('0'..'9') || constSign }
if (c in ([')'] + Op.values()*.symbol) && !constSign) { captureConstant(i) }
switch (c) {
case ~/\s/: break
case isConstChar: constStr += c; break
case Op.values()*.symbol: tokens << Op.fromSymbol(c); break
case ['(',')']: tokens << c; break
default: fail "Invalid character '${c}' at position ${i+1}"
}
}
captureConstant(expr.size())
tokens
}
List groupByParens(List tokens, int depth) {
def deepness = depth
def tokenGroups = []
for (def i = 0; i < tokens.size(); i++) {
def token = tokens[i]
switch (token) {
case '(':
fail("'(' too close to end of expression") { i+2 > tokens.size() }
def subGroup = groupByParens(tokens[i+1..-1], depth+1)
tokenGroups << subGroup[0..-2]
i += subGroup[-1] + 1
break
case ')':
fail("Unbalanced parens, found extra ')'") { deepness == 0 }
tokenGroups << i
return tokenGroups
default:
tokenGroups << token
}
}
fail("Unbalanced parens, unclosed groupings at end of expression") { deepness != 0 }
def n = tokenGroups.size()
fail("The operand/operator sequence is wrong") { n%2 == 0 }
(0..<n).each {
def i = it
fail("The operand/operator sequence is wrong") { (i%2 == 0) == (tokenGroups[i] instanceof Op) }
}
tokenGroups
}
Expression parse(List elements) {
while (elements.size() > 1) {
def n = elements.size()
fail ("The operand/operator sequence is wrong") { n%2 == 0 }
def groupLoc = (0..<n).find { i -> elements[i] instanceof List }
if (groupLoc != null) {
elements[groupLoc] = parse(elements[groupLoc])
continue
}
def opLoc = (0..<n).find { i -> elements[i] instanceof Op && elements[i].precedence == 1 } \
?: (0..<n).find { i -> elements[i] instanceof Op && elements[i].precedence == 2 }
if (opLoc != null) {
fail ("Operator out of sequence") { opLoc%2 == 0 }
def term = new Term(left:elements[opLoc-1], op:elements[opLoc], right:elements[opLoc+1])
elements[(opLoc-1)..(opLoc+1)] = [term]
continue
}
}
return elements[0] instanceof List ? parse(elements[0]) : elements[0]
} |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Kotlin | Kotlin | // version 1.1.0
import java.awt.*
import javax.swing.*
class ArchimedeanSpiral : JPanel() {
init {
preferredSize = Dimension(640, 640)
background = Color.white
}
private fun drawGrid(g: Graphics2D) {
g.color = Color(0xEEEEEE)
g.stroke = BasicStroke(2f)
val angle = Math.toRadians(45.0)
val w = width
val center = w / 2
val margin = 10
val numRings = 8
val spacing = (w - 2 * margin) / (numRings * 2)
for (i in 0 until numRings) {
val pos = margin + i * spacing
val size = w - (2 * margin + i * 2 * spacing)
g.drawOval(pos, pos, size, size)
val ia = i * angle
val x2 = center + (Math.cos(ia) * (w - 2 * margin) / 2).toInt()
val y2 = center - (Math.sin(ia) * (w - 2 * margin) / 2).toInt()
g.drawLine(center, center, x2, y2)
}
}
private fun drawSpiral(g: Graphics2D) {
g.stroke = BasicStroke(2f)
g.color = Color.magenta
val degrees = Math.toRadians(0.1)
val center = width / 2
val end = 360 * 2 * 10 * degrees
val a = 0.0
val b = 20.0
val c = 1.0
var theta = 0.0
while (theta < end) {
val r = a + b * Math.pow(theta, 1.0 / c)
val x = r * Math.cos(theta)
val y = r * Math.sin(theta)
plot(g, (center + x).toInt(), (center - y).toInt())
theta += degrees
}
}
private fun plot(g: Graphics2D, x: Int, y: Int) {
g.drawOval(x, y, 1, 1)
}
override fun paintComponent(gg: Graphics) {
super.paintComponent(gg)
val g = gg as Graphics2D
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
drawGrid(g)
drawSpiral(g)
}
}
fun main(args: Array<String>) {
SwingUtilities.invokeLater {
val f = JFrame()
f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
f.title = "Archimedean Spiral"
f.isResizable = false
f.add(ArchimedeanSpiral(), BorderLayout.CENTER)
f.pack()
f.setLocationRelativeTo(null)
f.isVisible = true
}
} |
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #Arbre | Arbre |
openshut(n):
for x in [1..n]
x%n==0
pass(n):
if n==100
openshut(n)
else
openshut(n) xor pass(n+1)
100doors():
pass(1) -> io
|
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #Clean | Clean | array :: {String}
array = {"Hello", "World"} |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Hare | Hare | use fmt;
use math::complex::{c128,addc128,mulc128,divc128,negc128,conjc128};
export fn main() void = {
let x: c128 = (1.0, 1.0);
let y: c128 = (3.14159265, 1.2);
// addition
let (re, im) = addc128(x, y);
fmt::printfln("{} + {}i", re, im)!;
// multiplication
let (re, im) = mulc128(x, y);
fmt::printfln("{} + {}i", re, im)!;
// inversion
let (re, im) = divc128((1.0, 0.0), x);
fmt::printfln("{} + {}i", re, im)!;
// negation
let (re, im) = negc128(x);
fmt::printfln("{} + {}i", re, im)!;
// conjugate
let (re, im) = conjc128(x);
fmt::printfln("{} + {}i", re, im)!;
}; |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Haskell | Haskell | import Data.Complex
main = do
let a = 1.0 :+ 2.0 -- complex number 1+2i
let b = 4 -- complex number 4+0i
-- 'b' is inferred to be complex because it's used in
-- arithmetic with 'a' below.
putStrLn $ "Add: " ++ show (a + b)
putStrLn $ "Subtract: " ++ show (a - b)
putStrLn $ "Multiply: " ++ show (a * b)
putStrLn $ "Divide: " ++ show (a / b)
putStrLn $ "Negate: " ++ show (-a)
putStrLn $ "Inverse: " ++ show (recip a)
putStrLn $ "Conjugate:" ++ show (conjugate a) |
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #Julia | Julia | using Primes
divisors(n) = foldl((a, (p, e)) -> vcat((a * [p^i for i in 0:e]')...), factor(n), init=[1])
isperfect(n) = sum(1 // d for d in divisors(n)) == 2
lo, hi = 2, 2^19
println("Perfect numbers between ", lo, " and ", hi, ": ", collect(filter(isperfect, lo:hi)))
|
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #Modula-2 | Modula-2 | MODULE AGM;
FROM EXCEPTIONS IMPORT AllocateSource,ExceptionSource,GetMessage,RAISE;
FROM LongConv IMPORT ValueReal;
FROM LongMath IMPORT sqrt;
FROM LongStr IMPORT RealToStr;
FROM Terminal IMPORT ReadChar,Write,WriteString,WriteLn;
VAR
TextWinExSrc : ExceptionSource;
PROCEDURE ReadReal() : LONGREAL;
VAR
buffer : ARRAY[0..63] OF CHAR;
i : CARDINAL;
c : CHAR;
BEGIN
i := 0;
LOOP
c := ReadChar();
IF ((c >= '0') AND (c <= '9')) OR (c = '.') THEN
buffer[i] := c;
Write(c);
INC(i)
ELSE
WriteLn;
EXIT
END
END;
buffer[i] := 0C;
RETURN ValueReal(buffer)
END ReadReal;
PROCEDURE WriteReal(r : LONGREAL);
VAR
buffer : ARRAY[0..63] OF CHAR;
BEGIN
RealToStr(r, buffer);
WriteString(buffer)
END WriteReal;
PROCEDURE AGM(a,g : LONGREAL) : LONGREAL;
CONST iota = 1.0E-16;
VAR a1, g1 : LONGREAL;
BEGIN
IF a * g < 0.0 THEN
RAISE(TextWinExSrc, 0, "arithmetic-geometric mean undefined when x*y<0")
END;
WHILE ABS(a - g) > iota DO
a1 := (a + g) / 2.0;
g1 := sqrt(a * g);
a := a1;
g := g1
END;
RETURN a
END AGM;
VAR
x, y, z: LONGREAL;
BEGIN
WriteString("Enter two numbers: ");
x := ReadReal();
y := ReadReal();
WriteReal(AGM(x, y));
WriteLn
END AGM. |
http://rosettacode.org/wiki/Zero_to_the_zero_power | Zero to the zero power | Some computer programming languages are not exactly consistent (with other computer programming languages)
when raising zero to the zeroth power: 00
Task
Show the results of raising zero to the zeroth power.
If your computer language objects to 0**0 or 0^0 at compile time, you may also try something like:
x = 0
y = 0
z = x**y
say 'z=' z
Show the result here.
And of course use any symbols or notation that is supported in your computer programming language for exponentiation.
See also
The Wiki entry: Zero to the power of zero.
The Wiki entry: History of differing points of view.
The MathWorld™ entry: exponent laws.
Also, in the above MathWorld™ entry, see formula (9):
x
0
=
1
{\displaystyle x^{0}=1}
.
The OEIS entry: The special case of zero to the zeroth power
| #11l | 11l | print(0 ^ 0) |
http://rosettacode.org/wiki/Arithmetic_evaluation | Arithmetic evaluation | Create a program which parses and evaluates arithmetic expressions.
Requirements
An abstract-syntax tree (AST) for the expression must be created from parsing the input.
The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.)
The expression will be a string or list of symbols like "(1+3)*7".
The four symbols + - * / must be supported as binary operators with conventional precedence rules.
Precedence-control parentheses must also be supported.
Note
For those who don't remember, mathematical precedence is as follows:
Parentheses
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
C.f
24 game Player.
Parsing/RPN calculator algorithm.
Parsing/RPN to infix conversion.
| #Haskell | Haskell | {-# LANGUAGE FlexibleContexts #-}
import Text.Parsec
import Text.Parsec.Expr
import Text.Parsec.Combinator
import Data.Functor
import Data.Function (on)
data Exp
= Num Int
| Add Exp
Exp
| Sub Exp
Exp
| Mul Exp
Exp
| Div Exp
Exp
expr
:: Stream s m Char
=> ParsecT s u m Exp
expr = buildExpressionParser table factor
where
table =
[ [op "*" Mul AssocLeft, op "/" Div AssocLeft]
, [op "+" Add AssocLeft, op "-" Sub AssocLeft]
]
op s f = Infix (f <$ string s)
factor = (between `on` char) '(' ')' expr <|> (Num . read <$> many1 digit)
eval
:: Integral a
=> Exp -> a
eval (Num x) = fromIntegral x
eval (Add a b) = eval a + eval b
eval (Sub a b) = eval a - eval b
eval (Mul a b) = eval a * eval b
eval (Div a b) = eval a `div` eval b
solution
:: Integral a
=> String -> a
solution = either (const (error "Did not parse")) eval . parse expr ""
main :: IO ()
main = print $ solution "(1+3)*7" |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Lua | Lua |
a=1
b=2
cycles=40
step=0.001
x=0
y=0
function love.load()
x = love.graphics.getWidth()/2
y = love.graphics.getHeight()/2
end
function love.draw()
love.graphics.print("a="..a,16,16)
love.graphics.print("b="..b,16,32)
for i=0,cycles*math.pi,step do
love.graphics.points(x+(a + b*i)*math.cos(i),y+(a + b*i)*math.sin(i))
end
end
|
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #M2000_Interpreter | M2000 Interpreter |
module Archimedean_spiral {
smooth on ' enable GDI+
def r(θ)=5+3*θ
cls #002222,0
pen #FFFF00
refresh 5000
every 1000 {
\\ redifine window (console width and height) and place it to center (symbol ;)
Window 12, random(10, 18)*1000, random(8, 12)*1000;
move scale.x/2, scale.y/2
let N=2, k1=pi/120, k=k1, op=5, op1=1
for i=1 to int(1200*min.data(scale.x, scale.y)/18000)
pen op
swap op, op1
Width 3 {draw angle k, r(k)*n}
k+=k1
next
refresh 5000
\\ press space to exit loop
if keypress(32) then exit
}
pen 14
cls 5
refresh 50
}
Archimedean_spiral
|
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #Argile | Argile | use std, array
close all doors
for each pass from 1 to 100
for (door = pass) (door <= 100) (door += pass)
toggle door
let int pass, door.
.: close all doors :. {memset doors 0 size of doors}
.:toggle <int door>:. { !!(doors[door - 1]) }
let doors be an array of 100 bool
for each door from 1 to 100
printf "#%.3d %s\n" door (doors[door - 1]) ? "[ ]", "[X]" |
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #Clipper | Clipper | // Declare and initialize two-dimensional array
Local arr1 := { { "NITEM","N",10,0 }, { "CONTENT","C",60,0} }
// Create an empty array
Local arr2 := {}
// Declare three-dimensional array
Local arr3[2,100,3]
// Create an array
Local arr4 := Array(50)
// Array can be dynamically resized:
arr4 := ASize( arr4, 80 ) |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Icon_and_Unicon | Icon and Unicon | procedure main()
SetupComplex()
a := complex(1,2)
b := complex(3,4)
c := complex(&pi,1.5)
d := complex(1)
e := complex(,1)
every v := !"abcde" do write(v," := ",cpxstr(variable(v)))
write("a+b := ", cpxstr(cpxadd(a,b)))
write("a-b := ", cpxstr(cpxsub(a,b)))
write("a*b := ", cpxstr(cpxmul(a,b)))
write("a/b := ", cpxstr(cpxdiv(a,b)))
write("neg(a) := ", cpxstr(cpxneg(a)))
write("inv(a) := ", cpxstr(cpxinv(a)))
write("conj(a) := ", cpxstr(cpxconj(a)))
write("abs(a) := ", cpxabs(a))
write("neg(1) := ", cpxstr(cpxneg(1)))
end |
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #Kotlin | Kotlin | // version 1.1.2
fun gcd(a: Long, b: Long): Long = if (b == 0L) a else gcd(b, a % b)
infix fun Long.ldiv(denom: Long) = Frac(this, denom)
infix fun Int.idiv(denom: Int) = Frac(this.toLong(), denom.toLong())
fun Long.toFrac() = Frac(this, 1)
fun Int.toFrac() = Frac(this.toLong(), 1)
class Frac : Comparable<Frac> {
val num: Long
val denom: Long
companion object {
val ZERO = Frac(0, 1)
val ONE = Frac(1, 1)
}
constructor(n: Long, d: Long) {
require(d != 0L)
var nn = n
var dd = d
if (nn == 0L) {
dd = 1
}
else if (dd < 0) {
nn = -nn
dd = -dd
}
val g = Math.abs(gcd(nn, dd))
if (g > 1) {
nn /= g
dd /= g
}
num = nn
denom = dd
}
constructor(n: Int, d: Int) : this(n.toLong(), d.toLong())
operator fun plus(other: Frac) =
Frac(num * other.denom + denom * other.num, other.denom * denom)
operator fun unaryPlus() = this
operator fun unaryMinus() = Frac(-num, denom)
operator fun minus(other: Frac) = this + (-other)
operator fun times(other: Frac) = Frac(this.num * other.num, this.denom * other.denom)
operator fun rem(other: Frac) = this - Frac((this / other).toLong(), 1) * other
operator fun inc() = this + ONE
operator fun dec() = this - ONE
fun inverse(): Frac {
require(num != 0L)
return Frac(denom, num)
}
operator fun div(other: Frac) = this * other.inverse()
fun abs() = if (num >= 0) this else -this
override fun compareTo(other: Frac): Int {
val diff = this.toDouble() - other.toDouble()
return when {
diff < 0.0 -> -1
diff > 0.0 -> +1
else -> 0
}
}
override fun equals(other: Any?): Boolean {
if (other == null || other !is Frac) return false
return this.compareTo(other) == 0
}
override fun hashCode() = num.hashCode() xor denom.hashCode()
override fun toString() = if (denom == 1L) "$num" else "$num/$denom"
fun toDouble() = num.toDouble() / denom
fun toLong() = num / denom
}
fun isPerfect(n: Long): Boolean {
var sum = Frac(1, n)
val limit = Math.sqrt(n.toDouble()).toLong()
for (i in 2L..limit) {
if (n % i == 0L) sum += Frac(1, i) + Frac(1, n / i)
}
return sum == Frac.ONE
}
fun main(args: Array<String>) {
var frac1 = Frac(12, 3)
println ("frac1 = $frac1")
var frac2 = 15 idiv 2
println("frac2 = $frac2")
println("frac1 <= frac2 is ${frac1 <= frac2}")
println("frac1 >= frac2 is ${frac1 >= frac2}")
println("frac1 == frac2 is ${frac1 == frac2}")
println("frac1 != frac2 is ${frac1 != frac2}")
println("frac1 + frac2 = ${frac1 + frac2}")
println("frac1 - frac2 = ${frac1 - frac2}")
println("frac1 * frac2 = ${frac1 * frac2}")
println("frac1 / frac2 = ${frac1 / frac2}")
println("frac1 % frac2 = ${frac1 % frac2}")
println("inv(frac1) = ${frac1.inverse()}")
println("abs(-frac1) = ${-frac1.abs()}")
println("inc(frac2) = ${++frac2}")
println("dec(frac2) = ${--frac2}")
println("dbl(frac2) = ${frac2.toDouble()}")
println("lng(frac2) = ${frac2.toLong()}")
println("\nThe Perfect numbers less than 2^19 are:")
// We can skip odd numbers as no known perfect numbers are odd
for (i in 2 until (1 shl 19) step 2) {
if (isPerfect(i.toLong())) print(" $i")
}
println()
} |
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #NetRexx | NetRexx | /* NetRexx */
options replace format comments java crossref symbols nobinary
numeric digits 18
parse arg a_ g_ .
if a_ = '' | a_ = '.' then a0 = 1
else a0 = a_
if g_ = '' | g_ = '.' then g0 = 1 / Math.sqrt(2)
else g0 = g_
say agm(a0, g0)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method agm(a0, g0) public static returns Rexx
a1 = a0
g1 = g0
loop while (a1 - g1).abs() >= Math.pow(10, -14)
temp = (a1 + g1) / 2
g1 = Math.sqrt(a1 * g1)
a1 = temp
end
return a1 + 0
|
http://rosettacode.org/wiki/Zero_to_the_zero_power | Zero to the zero power | Some computer programming languages are not exactly consistent (with other computer programming languages)
when raising zero to the zeroth power: 00
Task
Show the results of raising zero to the zeroth power.
If your computer language objects to 0**0 or 0^0 at compile time, you may also try something like:
x = 0
y = 0
z = x**y
say 'z=' z
Show the result here.
And of course use any symbols or notation that is supported in your computer programming language for exponentiation.
See also
The Wiki entry: Zero to the power of zero.
The Wiki entry: History of differing points of view.
The MathWorld™ entry: exponent laws.
Also, in the above MathWorld™ entry, see formula (9):
x
0
=
1
{\displaystyle x^{0}=1}
.
The OEIS entry: The special case of zero to the zeroth power
| #8th | 8th |
0 0 ^ .
|
http://rosettacode.org/wiki/Zero_to_the_zero_power | Zero to the zero power | Some computer programming languages are not exactly consistent (with other computer programming languages)
when raising zero to the zeroth power: 00
Task
Show the results of raising zero to the zeroth power.
If your computer language objects to 0**0 or 0^0 at compile time, you may also try something like:
x = 0
y = 0
z = x**y
say 'z=' z
Show the result here.
And of course use any symbols or notation that is supported in your computer programming language for exponentiation.
See also
The Wiki entry: Zero to the power of zero.
The Wiki entry: History of differing points of view.
The MathWorld™ entry: exponent laws.
Also, in the above MathWorld™ entry, see formula (9):
x
0
=
1
{\displaystyle x^{0}=1}
.
The OEIS entry: The special case of zero to the zeroth power
| #Action.21 | Action! | INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit
PROC Main()
REAL z,res
Put(125) PutE() ;clear the screen
IntToReal(0,z)
Power(z,z,res)
PrintR(z) Print("^")
PrintR(z) Print("=")
PrintRE(res)
RETURN |
http://rosettacode.org/wiki/Arithmetic_evaluation | Arithmetic evaluation | Create a program which parses and evaluates arithmetic expressions.
Requirements
An abstract-syntax tree (AST) for the expression must be created from parsing the input.
The AST must be used in evaluation, also, so the input may not be directly evaluated (e.g. by calling eval or a similar language feature.)
The expression will be a string or list of symbols like "(1+3)*7".
The four symbols + - * / must be supported as binary operators with conventional precedence rules.
Precedence-control parentheses must also be supported.
Note
For those who don't remember, mathematical precedence is as follows:
Parentheses
Multiplication/Division (left to right)
Addition/Subtraction (left to right)
C.f
24 game Player.
Parsing/RPN calculator algorithm.
Parsing/RPN to infix conversion.
| #Icon_and_Unicon | Icon and Unicon | procedure main() #: simple arithmetical parser / evaluator
write("Usage: Input expression = Abstract Syntax Tree = Value, ^Z to end.")
repeat {
writes("Input expression : ")
if not writes(line := read()) then break
if map(line) ? { (x := E()) & pos(0) } then
write(" = ", showAST(x), " = ", evalAST(x))
else
write(" rejected")
}
end
procedure evalAST(X) #: return the evaluated AST
local x
if type(X) == "list" then {
x := evalAST(get(X))
while x := get(X)(x, evalAST(get(X) | stop("Malformed AST.")))
}
return \x | X
end
procedure showAST(X) #: return a string representing the AST
local x,s
s := ""
every x := !X do
s ||:= if type(x) == "list" then "(" || showAST(x) || ")" else x
return s
end
########
# When you're writing a big parser, a few utility recognisers are very useful
#
procedure ws() # skip optional whitespace
suspend tab(many(' \t')) | ""
end
procedure digits()
suspend tab(many(&digits))
end
procedure radixNum(r) # r sets the radix
static chars
initial chars := &digits || &lcase
suspend tab(many(chars[1 +: r]))
end
########
global token
record HansonsDevice(precedence,associativity)
procedure opinfo()
static O
initial {
O := HansonsDevice([], table(&null)) # parsing table
put(O.precedence, ["+", "-"], ["*", "/", "%"], ["^"]) # Lowest to Highest precedence
every O.associativity[!!O.precedence] := 1 # default to 1 for LEFT associativity
O.associativity["^"] := 0 # RIGHT associativity
}
return O
end
procedure E(k) #: Expression
local lex, pL
static opT
initial opT := opinfo()
/k := 1
lex := []
if not (pL := opT.precedence[k]) then # this op at this level?
put(lex, F())
else {
put(lex, E(k + 1))
while ws() & put(lex, token := =!pL) do
put(lex, E(k + opT.associativity[token]))
}
suspend if *lex = 1 then lex[1] else lex # strip useless []
end
procedure F() #: Factor
suspend ws() & ( # skip optional whitespace, and ...
(="+" & F()) | # unary + and a Factor, or ...
(="-" || V()) | # unary - and a Value, or ...
(="-" & [-1, "*", F()]) | # unary - and a Factor, or ...
2(="(", E(), ws(), =")") | # parenthesized subexpression, or ...
V() # just a value
)
end
procedure V() #: Value
local r
suspend ws() & numeric( # skip optional whitespace, and ...
=(r := 1 to 36) || ="r" || radixNum(r) | # N-based number, or ...
digits() || (="." || digits() | "") || exponent() # plain number with optional fraction
)
end
procedure exponent()
suspend tab(any('eE')) || =("+" | "-" | "") || digits() | ""
end |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Maple | Maple |
plots[polarplot](1+2*theta, theta = 0 .. 6*Pi)
|
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #Mathematica.2FWolfram_Language | Mathematica/Wolfram Language | With[{a = 5, b = 4}, PolarPlot[a + b t, {t, 0, 10 Pi}]] |
http://rosettacode.org/wiki/Archimedean_spiral | Archimedean spiral |
The Archimedean spiral is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
r
=
a
+
b
θ
{\displaystyle \,r=a+b\theta }
with real numbers a and b.
Task
Draw an Archimedean spiral.
| #MATLAB | MATLAB | a = 1;
b = 1;
turns = 2;
theta = 0:0.1:2*turns*pi;
polarplot(theta, a + b*theta); |
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #ARM_Assembly | ARM Assembly |
/* ARM assembly Raspberry PI */
/* program 100doors.s */
/************************************/
/* Constantes */
/************************************/
.equ STDOUT, 1 @ Linux output console
.equ EXIT, 1 @ Linux syscall
.equ WRITE, 4 @ Linux syscall
.equ NBDOORS, 100
/*********************************/
/* Initialized data */
/*********************************/
.data
sMessResult: .ascii "The door "
sMessValeur: .fill 11, 1, ' ' @ size => 11
.asciz "is open.\n"
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
stTableDoors: .skip 4 * NBDOORS
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: @ entry of program
push {fp,lr} @ saves 2 registers
@ display first line
ldr r3,iAdrstTableDoors @ table address
mov r5,#1
1:
mov r4,r5
2: @ begin loop
ldr r2,[r3,r4,lsl #2] @ read doors index r4
cmp r2,#0
moveq r2,#1 @ if r2 = 0 1 -> r2
movne r2,#0 @ if r2 = 1 0 -> r2
str r2,[r3,r4,lsl #2] @ store value of doors
add r4,r5 @ increment r4 with r5 value
cmp r4,#NBDOORS @ number of doors ?
ble 2b @ no -> loop
add r5,#1 @ increment the increment !!
cmp r5,#NBDOORS @ number of doors ?
ble 1b @ no -> loop
@ loop display state doors
mov r4,#0
3:
ldr r2,[r3,r4,lsl #2] @ read state doors r4 index
cmp r2,#0
beq 4f
mov r0,r4 @ open -> display message
ldr r1,iAdrsMessValeur @ display value index
bl conversion10 @ call function
ldr r0,iAdrsMessResult
bl affichageMess @ display message
4:
add r4,#1
cmp r4,#NBDOORS
ble 3b @ loop
100: @ standard end of the program
mov r0, #0 @ return code
pop {fp,lr} @restaur 2 registers
mov r7, #EXIT @ request to exit program
svc #0 @ perform the system call
iAdrsMessValeur: .int sMessValeur
iAdrstTableDoors: .int stTableDoors
iAdrsMessResult: .int sMessResult
/******************************************************************/
/* display text with size calculation */
/******************************************************************/
/* r0 contains the address of the message */
affichageMess:
push {r0,r1,r2,r7,lr} @ save registres
mov r2,#0 @ counter length
1: @ loop length calculation
ldrb r1,[r0,r2] @ read octet start position + index
cmp r1,#0 @ if 0 its over
addne r2,r2,#1 @ else add 1 in the length
bne 1b @ and loop
@ so here r2 contains the length of the message
mov r1,r0 @ address message in r1
mov r0,#STDOUT @ code to write to the standard output Linux
mov r7, #WRITE @ code call system "write"
svc #0 @ call systeme
pop {r0,r1,r2,r7,lr} @ restaur des 2 registres */
bx lr @ return
/******************************************************************/
/* Converting a register to a decimal unsigned */
/******************************************************************/
/* r0 contains value and r1 address area */
/* r0 return size of result (no zero final in area) */
/* area size => 11 bytes */
.equ LGZONECAL, 10
conversion10:
push {r1-r4,lr} @ save registers
mov r3,r1
mov r2,#LGZONECAL
1: @ start loop
bl divisionpar10U @unsigned r0 <- dividende. quotient ->r0 reste -> r1
add r1,#48 @ digit
strb r1,[r3,r2] @ store digit on area
cmp r0,#0 @ stop if quotient = 0
subne r2,#1 @ else previous position
bne 1b @ and loop
// and move digit from left of area
mov r4,#0
2:
ldrb r1,[r3,r2]
strb r1,[r3,r4]
add r2,#1
add r4,#1
cmp r2,#LGZONECAL
ble 2b
// and move spaces in end on area
mov r0,r4 @ result length
mov r1,#' ' @ space
3:
strb r1,[r3,r4] @ store space in area
add r4,#1 @ next position
cmp r4,#LGZONECAL
ble 3b @ loop if r4 <= area size
100:
pop {r1-r4,lr} @ restaur registres
bx lr @return
/***************************************************/
/* division par 10 unsigned */
/***************************************************/
/* r0 dividende */
/* r0 quotient */
/* r1 remainder */
divisionpar10U:
push {r2,r3,r4, lr}
mov r4,r0 @ save value
//mov r3,#0xCCCD @ r3 <- magic_number lower @ for Raspberry pi 3
//movt r3,#0xCCCC @ r3 <- magic_number upper @ for Raspberry pi 3
ldr r3,iMagicNumber @ for Raspberry pi 1 2
umull r1, r2, r3, r0 @ r1<- Lower32Bits(r1*r0) r2<- Upper32Bits(r1*r0)
mov r0, r2, LSR #3 @ r2 <- r2 >> shift 3
add r2,r0,r0, lsl #2 @ r2 <- r0 * 5
sub r1,r4,r2, lsl #1 @ r1 <- r4 - (r2 * 2) = r4 - (r0 * 10)
pop {r2,r3,r4,lr}
bx lr @ leave function
iMagicNumber: .int 0xCCCCCCCD
|
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #Clojure | Clojure | ;clojure is a language built with immutable/persistent data structures. there is no concept of changing what a vector/list
;is, instead clojure creates a new array with an added value using (conj...)
;in the example below the my-list does not change.
user=> (def my-list (list 1 2 3 4 5))
user=> my-list
(1 2 3 4 5)
user=> (first my-list)
1
user=> (nth my-list 3)
4
user=> (conj my-list 100) ;adding to a list always adds to the head of the list
(100 1 2 3 4 5)
user=> my-list ;it is impossible to change the list pointed to by my-list
(1 2 3 4 5)
user=> (def my-new-list (conj my-list 100))
user=> my-new-list
(100 1 2 3 4 5)
user=> (cons 200 my-new-list) ;(cons makes a new list, (conj will make a new object of the same type as the one it is given
(200 100 1 2 3 4 5)
user=> (def my-vec [1 2 3 4 5 6])
user=> (conj my-vec 300) ;adding to a vector always adds to the end of the vector
[1 2 3 4 5 6 300] |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #IDL | IDL | x=complex(1,1)
y=complex(!pi,1.2)
print,x+y
( 4.14159, 2.20000)
print,x*y
( 1.94159, 4.34159)
print,-x
( -1.00000, -1.00000)
print,1/x
( 0.500000, -0.500000) |
http://rosettacode.org/wiki/Arithmetic/Rational | Arithmetic/Rational | Task
Create a reasonably complete implementation of rational arithmetic in the particular language using the idioms of the language.
Example
Define a new type called frac with binary operator "//" of two integers that returns a structure made up of the numerator and the denominator (as per a rational number).
Further define the appropriate rational unary operators abs and '-', with the binary operators for addition '+', subtraction '-', multiplication '×', division '/', integer division '÷', modulo division, the comparison operators (e.g. '<', '≤', '>', & '≥') and equality operators (e.g. '=' & '≠').
Define standard coercion operators for casting int to frac etc.
If space allows, define standard increment and decrement operators (e.g. '+:=' & '-:=' etc.).
Finally test the operators:
Use the new type frac to find all perfect numbers less than 219 by summing the reciprocal of the factors.
Related task
Perfect Numbers
| #Liberty_BASIC | Liberty BASIC |
n=2^19
for testNumber=1 to n
sum$=castToFraction$(0)
for factorTest=1 to sqr(testNumber)
if GCD(factorTest,testNumber)=factorTest then sum$=add$(sum$,add$(reciprocal$(castToFraction$(factorTest)),reciprocal$(castToFraction$(testNumber/factorTest))))
next factorTest
if equal(sum$,castToFraction$(2))=1 then print testNumber
next testNumber
end
function abs$(a$)
aNumerator=val(word$(a$,1,"/"))
aDenominator=val(word$(a$,2,"/"))
bNumerator=abs(aNumerator)
bDenominator=abs(aDenominator)
b$=str$(bNumerator)+"/"+str$(bDenominator)
abs$=simplify$(b$)
end function
function negate$(a$)
aNumerator=val(word$(a$,1,"/"))
aDenominator=val(word$(a$,2,"/"))
bNumerator=-1*aNumerator
bDenominator=aDenominator
b$=str$(bNumerator)+"/"+str$(bDenominator)
negate$=simplify$(b$)
end function
function add$(a$,b$)
aNumerator=val(word$(a$,1,"/"))
aDenominator=val(word$(a$,2,"/"))
bNumerator=val(word$(b$,1,"/"))
bDenominator=val(word$(b$,2,"/"))
cNumerator=(aNumerator*bDenominator+bNumerator*aDenominator)
cDenominator=aDenominator*bDenominator
c$=str$(cNumerator)+"/"+str$(cDenominator)
add$=simplify$(c$)
end function
function subtract$(a$,b$)
aNumerator=val(word$(a$,1,"/"))
aDenominator=val(word$(a$,2,"/"))
bNumerator=val(word$(b$,1,"/"))
bDenominator=val(word$(b$,2,"/"))
cNumerator=(aNumerator*bDenominator-bNumerator*aDenominator)
cDenominator=aDenominator*bDenominator
c$=str$(cNumerator)+"/"+str$(cDenominator)
subtract$=simplify$(c$)
end function
function multiply$(a$,b$)
aNumerator=val(word$(a$,1,"/"))
aDenominator=val(word$(a$,2,"/"))
bNumerator=val(word$(b$,1,"/"))
bDenominator=val(word$(b$,2,"/"))
cNumerator=aNumerator*bNumerator
cDenominator=aDenominator*bDenominator
c$=str$(cNumerator)+"/"+str$(cDenominator)
multiply$=simplify$(c$)
end function
function divide$(a$,b$)
divide$=multiply$(a$,reciprocal$(b$))
end function
function simplify$(a$)
aNumerator=val(word$(a$,1,"/"))
aDenominator=val(word$(a$,2,"/"))
gcd=GCD(aNumerator,aDenominator)
if aNumerator<0 and aDenominator<0 then gcd=-1*gcd
bNumerator=aNumerator/gcd
bDenominator=aDenominator/gcd
b$=str$(bNumerator)+"/"+str$(bDenominator)
simplify$=b$
end function
function reciprocal$(a$)
aNumerator=val(word$(a$,1,"/"))
aDenominator=val(word$(a$,2,"/"))
reciprocal$=str$(aDenominator)+"/"+str$(aNumerator)
end function
function equal(a$,b$)
if simplify$(a$)=simplify$(b$) then equal=1:else equal=0
end function
function castToFraction$(a)
do
exp=exp+1
a=a*10
loop until a=int(a)
castToFraction$=simplify$(str$(a)+"/"+str$(10^exp))
end function
function castToReal(a$)
aNumerator=val(word$(a$,1,"/"))
aDenominator=val(word$(a$,2,"/"))
castToReal=aNumerator/aDenominator
end function
function castToInt(a$)
castToInt=int(castToReal(a$))
end function
function GCD(a,b)
if a=0 then
GCD=1
else
if a>=b then
while b
c = a
a = b
b = c mod b
GCD = abs(a)
wend
else
GCD=GCD(b,a)
end if
end if
end function
|
http://rosettacode.org/wiki/Arithmetic-geometric_mean | Arithmetic-geometric mean |
This page uses content from Wikipedia. The original article was at Arithmetic-geometric mean. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)
Task
Write a function to compute the arithmetic-geometric mean of two numbers.
The arithmetic-geometric mean of two numbers can be (usefully) denoted as
a
g
m
(
a
,
g
)
{\displaystyle \mathrm {agm} (a,g)}
, and is equal to the limit of the sequence:
a
0
=
a
;
g
0
=
g
{\displaystyle a_{0}=a;\qquad g_{0}=g}
a
n
+
1
=
1
2
(
a
n
+
g
n
)
;
g
n
+
1
=
a
n
g
n
.
{\displaystyle a_{n+1}={\tfrac {1}{2}}(a_{n}+g_{n});\quad g_{n+1}={\sqrt {a_{n}g_{n}}}.}
Since the limit of
a
n
−
g
n
{\displaystyle a_{n}-g_{n}}
tends (rapidly) to zero with iterations, this is an efficient method.
Demonstrate the function by calculating:
a
g
m
(
1
,
1
/
2
)
{\displaystyle \mathrm {agm} (1,1/{\sqrt {2}})}
Also see
mathworld.wolfram.com/Arithmetic-Geometric Mean
| #NewLISP | NewLISP |
(define (a-next a g) (mul 0.5 (add a g)))
(define (g-next a g) (sqrt (mul a g)))
(define (amg a g tolerance)
(if (<= (sub a g) tolerance)
a
(amg (a-next a g) (g-next a g) tolerance)
)
)
(define quadrillionth 0.000000000000001)
(define root-reciprocal-2 (div 1.0 (sqrt 2.0)))
(println
"To the nearest one-quadrillionth, "
"the arithmetic-geometric mean of "
"1 and the reciprocal of the square root of 2 is "
(amg 1.0 root-reciprocal-2 quadrillionth)
)
|
http://rosettacode.org/wiki/Zero_to_the_zero_power | Zero to the zero power | Some computer programming languages are not exactly consistent (with other computer programming languages)
when raising zero to the zeroth power: 00
Task
Show the results of raising zero to the zeroth power.
If your computer language objects to 0**0 or 0^0 at compile time, you may also try something like:
x = 0
y = 0
z = x**y
say 'z=' z
Show the result here.
And of course use any symbols or notation that is supported in your computer programming language for exponentiation.
See also
The Wiki entry: Zero to the power of zero.
The Wiki entry: History of differing points of view.
The MathWorld™ entry: exponent laws.
Also, in the above MathWorld™ entry, see formula (9):
x
0
=
1
{\displaystyle x^{0}=1}
.
The OEIS entry: The special case of zero to the zeroth power
| #Ada | Ada | with Ada.Text_IO, Ada.Integer_Text_IO, Ada.Long_Integer_Text_IO,
Ada.Long_Long_Integer_Text_IO, Ada.Float_Text_IO, Ada.Long_Float_Text_IO,
Ada.Long_Long_Float_Text_IO;
use Ada.Text_IO, Ada.Integer_Text_IO, Ada.Long_Integer_Text_IO,
Ada.Long_Long_Integer_Text_IO, Ada.Float_Text_IO, Ada.Long_Float_Text_IO,
Ada.Long_Long_Float_Text_IO;
procedure Test5 is
I : Integer := 0;
LI : Long_Integer := 0;
LLI : Long_Long_Integer := 0;
F : Float := 0.0;
LF : Long_Float := 0.0;
LLF : Long_Long_Float := 0.0;
Zero : Natural := 0;
begin
Put ("Integer 0^0 = ");
Put (I ** Zero, 2); New_Line;
Put ("Long Integer 0^0 = ");
Put (LI ** Zero, 2); New_Line;
Put ("Long Long Integer 0^0 = ");
Put (LLI ** Zero, 2); New_Line;
Put ("Float 0.0^0 = ");
Put (F ** Zero); New_Line;
Put ("Long Float 0.0^0 = ");
Put (LF ** Zero); New_Line;
Put ("Long Long Float 0.0^0 = ");
Put (LLF ** Zero); New_Line;
end Test5;
|