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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.
| #Component_Pascal | Component Pascal |
MODULE Complex;
IMPORT StdLog;
TYPE
Complex* = POINTER TO ComplexDesc;
ComplexDesc = RECORD
r-,i-: REAL;
END;
VAR
r,x,y: Complex;
PROCEDURE New(x,y: REAL): Complex;
VAR
r: Complex;
BEGIN
NEW(r);r.r := x;r.i := y;
RETURN r
END New;
PROCEDURE (x: Complex) Add*(y: Complex): Complex,NEW;
BEGIN
RETURN New(x.r + y.r,x.i + y.i)
END Add;
PROCEDURE ( x: Complex) Sub*( y: Complex): Complex, NEW;
BEGIN
RETURN New(x.r - y.r,x.i - y.i)
END Sub;
PROCEDURE ( x: Complex) Mul*( y: Complex): Complex, NEW;
BEGIN
RETURN New(x.r*y.r - x.i*y.i,x.r*y.i + x.i*y.r)
END Mul;
PROCEDURE ( x: Complex) Div*( y: Complex): Complex, NEW;
VAR
d: REAL;
BEGIN
d := y.r * y.r + y.i * y.i;
RETURN New((x.r*y.r + x.i*y.i)/d,(x.i*y.r - x.r*y.i)/d)
END Div;
(* Reciprocal *)
PROCEDURE (x: Complex) Rec*(): Complex,NEW;
VAR
d: REAL;
BEGIN
d := x.r * x.r + x.i * x.i;
RETURN New(x.r/d,(-1.0 * x.i)/d);
END Rec;
(* Conjugate *)
PROCEDURE (x: Complex) Con*(): Complex,NEW;
BEGIN
RETURN New(x.r, (-1.0) * x.i);
END Con;
PROCEDURE (x: Complex) Out(),NEW;
BEGIN
StdLog.String("Complex(");
StdLog.Real(x.r);StdLog.String(',');StdLog.Real(x.i);
StdLog.String("i );")
END Out;
PROCEDURE Do*;
BEGIN
x := New(1.5,3);
y := New(1.0,1.0);
StdLog.String("x: ");x.Out();StdLog.Ln;
StdLog.String("y: ");y.Out();StdLog.Ln;
r := x.Add(y);
StdLog.String("x + y: ");r.Out();StdLog.Ln;
r := x.Sub(y);
StdLog.String("x - y: ");r.Out();StdLog.Ln;
r := x.Mul(y);
StdLog.String("x * y: ");r.Out();StdLog.Ln;
r := x.Div(y);
StdLog.String("x / y: ");r.Out();StdLog.Ln;
r := y.Rec();
StdLog.String("1 / y: ");r.Out();StdLog.Ln;
r := x.Con();
StdLog.String("x': ");r.Out();StdLog.Ln;
END Do;
END Complex.
|
http://rosettacode.org/wiki/Arena_storage_pool | Arena storage pool | Dynamically allocated objects take their memory from a heap.
The memory for an object is provided by an allocator which maintains the storage pool used for the heap.
Often a call to allocator is denoted as
P := new T
where T is the type of an allocated object, and P is a reference to the object.
The storage pool chosen by the allocator can be determined by either:
the object type T
the type of pointer P
In the former case objects can be allocated only in one storage pool.
In the latter case objects of the type can be allocated in any storage pool or on the stack.
Task
The task is to show how allocators and user-defined storage pools are supported by the language.
In particular:
define an arena storage pool. An arena is a pool in which objects are allocated individually, but freed by groups.
allocate some objects (e.g., integers) in the pool.
Explain what controls the storage pool choice in the language.
| #Wren | Wren | var arena = List.filled(5, 0) // allocate memory for 5 integers
for (i in 0..4) arena[i] = i // insert some integers
System.print(arena) // print them
arena = null // make arena eligible for garbage collection
System.gc() // request immediate garbage collection |
http://rosettacode.org/wiki/Arena_storage_pool | Arena storage pool | Dynamically allocated objects take their memory from a heap.
The memory for an object is provided by an allocator which maintains the storage pool used for the heap.
Often a call to allocator is denoted as
P := new T
where T is the type of an allocated object, and P is a reference to the object.
The storage pool chosen by the allocator can be determined by either:
the object type T
the type of pointer P
In the former case objects can be allocated only in one storage pool.
In the latter case objects of the type can be allocated in any storage pool or on the stack.
Task
The task is to show how allocators and user-defined storage pools are supported by the language.
In particular:
define an arena storage pool. An arena is a pool in which objects are allocated individually, but freed by groups.
allocate some objects (e.g., integers) in the pool.
Explain what controls the storage pool choice in the language.
| #zkl | zkl | var pool=List(); // pool could be any mutable container
pool.append(Data(0,1234)); // allocate mem blob and add to pool
pool=Void; // free the pool and everything in it. |
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
| #Elisa | Elisa | component RationalNumbers;
type Rational;
Rational(Numerator = integer, Denominater = integer) -> Rational;
Rational + Rational -> Rational;
Rational - Rational -> Rational;
Rational * Rational -> Rational;
Rational / Rational -> Rational;
Rational == Rational -> boolean;
Rational <> Rational -> boolean;
Rational >= Rational -> boolean;
Rational <= Rational -> boolean;
Rational > Rational -> boolean;
Rational < Rational -> boolean;
+ Rational -> Rational;
- Rational -> Rational;
abs(Rational) -> Rational;
Rational(integer) -> Rational;
Numerator(Rational) -> integer;
Denominator(Rational) -> integer;
begin
Rational(A,B) = Rational:[A;B];
R1 + R2 = Normalize( R1.A * R2.B + R1.B * R2.A, R1.B * R2.B);
R1 - R2 = Normalize( R1.A * R2.B - R1.B * R2.A, R1.B * R2.B);
R1 * R2 = Normalize( R1.A * R2.A, R1.B * R2.B);
R1 / R2 = Normalize( R1.A * R2.B, R1.B * R2.A);
R1 == R2 = [ R = (R1 - R2); R.A == 0];
R1 <> R2 = [ R = (R1 - R2); R.A <> 0];
R1 >= R2 = [ R = (R1 - R2); R.A >= 0];
R1 <= R2 = [ R = (R1 - R2); R.A <= 0];
R1 > R2 = [ R = (R1 - R2); R.A > 0];
R1 < R2 = [ R = (R1 - R2); R.A < 0];
+ R = R;
- R = Rational(-R.A, R.B);
abs(R) = Rational(abs(R.A), abs(R.B));
Rational(I) = Rational (I, 1);
Numerator(R) = R.A;
Denominator(R) = R.B;
<< internal definitions >>
Normalize (A = integer, B = integer) -> Rational;
Normalize (A, B) = [ exception( B == 0, "Illegal Rational Number");
Common = GCD(abs(A), abs(B));
if B < 0 then Rational(-A / Common, -B / Common)
else Rational( A / Common, B / Common) ];
GCD (A = integer, B = integer) -> integer;
GCD (A, B) = [ if A == 0 then return(B);
if B == 0 then return(A);
if A > B then GCD (B, mod(A,B))
else GCD (A, mod(B,A)) ];
end component RationalNumbers; |
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
| #EchoLisp | EchoLisp |
(lib 'math)
(define (agm a g)
(if (~= a g) a
(agm (// (+ a g ) 2) (sqrt (* a g)))))
(math-precision)
→ 0.000001 ;; default
(agm 1 (/ 1 (sqrt 2)))
→ 0.8472130848351929
(math-precision 1.e-15)
→ 1e-15
(agm 1 (/ 1 (sqrt 2)))
→ 0.8472130847939792
|
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.
| #Verilog | Verilog | module main;
integer a, b;
integer suma, resta, producto;
integer division, resto, expo;
initial begin
a = -12;
b = 7;
suma = a + b;
resta = a - b;
producto = a * b;
division = a / b;
resto = a % b;
expo = a ** b;
$display("Siendo dos enteros a = -12 y b = 7");
$display(" suma de a + b = ", suma);
$display(" resta de a - b = ", resta);
$display(" producto de a * b = ", producto);
$display(" división de a / b = ", division);
$display(" resto de a mod b = ", resto);
$display("exponenciación a ^ b = ", expo);
$finish ;
end
endmodule |
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.
| #ALGOL_68 | ALGOL 68 | INT base=10;
MODE FIXED = LONG REAL; # numbers in the format 9,999.999 #
#IF build abstract syntax tree and then EVAL tree #
MODE AST = UNION(NODE, FIXED);
MODE NUM = REF AST;
MODE NODE = STRUCT(NUM a, PROC (FIXED,FIXED)FIXED op, NUM b);
OP EVAL = (NUM ast)FIXED:(
CASE ast IN
(FIXED num): num,
(NODE fork): (op OF fork)(EVAL( a OF fork), EVAL (b OF fork))
ESAC
);
OP + = (NUM a,b)NUM: ( HEAP AST := NODE(a, (FIXED a,b)FIXED:a+b, b) );
OP - = (NUM a,b)NUM: ( HEAP AST := NODE(a, (FIXED a,b)FIXED:a-b, b) );
OP * = (NUM a,b)NUM: ( HEAP AST := NODE(a, (FIXED a,b)FIXED:a*b, b) );
OP / = (NUM a,b)NUM: ( HEAP AST := NODE(a, (FIXED a,b)FIXED:a/b, b) );
OP **= (NUM a,b)NUM: ( HEAP AST := NODE(a, (FIXED a,b)FIXED:a**b, b) );
#ELSE simply use REAL arithmetic with no abstract syntax tree at all # CO
MODE NUM = FIXED, AST = FIXED;
OP EVAL = (FIXED num)FIXED: num;
#FI# END CO
MODE LEX = PROC (TOK)NUM;
MODE MONADIC =PROC (NUM)NUM;
MODE DIADIC = PROC (NUM,NUM)NUM;
MODE TOK = CHAR;
MODE ACTION = UNION(STACKACTION, LEX, MONADIC, DIADIC);
MODE OPVAL = STRUCT(INT prio, ACTION action);
MODE OPITEM = STRUCT(TOK token, OPVAL opval);
[256]STACKITEM stack;
MODE STACKITEM = STRUCT(NUM value, OPVAL op);
MODE STACKACTION = PROC (REF STACKITEM)VOID;
PROC begin = (REF STACKITEM top)VOID: prio OF op OF top -:= +10;
PROC end = (REF STACKITEM top)VOID: prio OF op OF top -:= -10;
OP ** = (COMPL a,b)COMPL: complex exp(complex ln(a)*b);
[8]OPITEM op list :=(
# OP PRIO ACTION #
("^", (8, (NUM a,b)NUM: a**b)),
("*", (7, (NUM a,b)NUM: a*b)),
("/", (7, (NUM a,b)NUM: a/b)),
("+", (6, (NUM a,b)NUM: a+b)),
("-", (6, (NUM a,b)NUM: a-b)),
("(",(+10, begin)),
(")",(-10, end)),
("?", (9, LEX:SKIP))
);
PROC op dict = (TOK op)REF OPVAL:(
# This can be unrolled to increase performance #
REF OPITEM candidate;
FOR i TO UPB op list WHILE
candidate := op list[i];
# WHILE # op /= token OF candidate DO
SKIP
OD;
opval OF candidate
);
PROC build ast = (STRING expr)NUM:(
INT top:=0;
PROC compress ast stack = (INT prio, NUM in value)NUM:(
NUM out value := in value;
FOR loc FROM top BY -1 TO 1 WHILE
REF STACKITEM stack top := stack[loc];
# WHILE # ( top >= LWB stack | prio <= prio OF op OF stack top | FALSE ) DO
top := loc - 1;
out value :=
CASE action OF op OF stack top IN
(MONADIC op): op(value OF stack top), # not implemented #
(DIADIC op): op(value OF stack top,out value)
ESAC
OD;
out value
);
NUM value := NIL;
FIXED num value;
INT decimal places;
FOR i TO UPB expr DO
TOK token = expr[i];
REF OPVAL this op := op dict(token);
CASE action OF this op IN
(STACKACTION action):(
IF prio OF thisop = -10 THEN
value := compress ast stack(0, value)
FI;
IF top >= LWB stack THEN
action(stack[top])
FI
),
(LEX):( # a crude lexer #
SHORT INT digit = ABS token - ABS "0";
IF 0<= digit AND digit < base THEN
IF NUM(value) IS NIL THEN # first digit #
decimal places := 0;
value := HEAP AST := num value := digit
ELSE
NUM(value) := num value := IF decimal places = 0
THEN
num value * base + digit
ELSE
decimal places *:= base;
num value + digit / decimal places
FI
FI
ELIF token = "." THEN
decimal places := 1
ELSE
SKIP # and ignore spaces and any unrecognised characters #
FI
),
(MONADIC): SKIP, # not implemented #
(DIADIC):(
value := compress ast stack(prio OF this op, value);
IF top=UPB stack THEN index error FI;
stack[top+:=1]:=STACKITEM(value, this op);
value:=NIL
)
ESAC
OD;
compress ast stack(-max int, value)
);
test:(
printf(($" euler's number is about: "g(-long real width,long real width-2)l$,
EVAL build ast("1+1+(1+(1+(1+(1+(1+(1+(1+(1+(1+(1+(1+(1+(1+1/15)/14)/13)/12)/11)/10)/9)/8)/7)/6)/5)/4)/3)/2")));
SKIP EXIT
index error:
printf(("Stack over flow"))
) |
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.
| #8th | 8th |
\ Array of doors; init to empty; accessing a non-extant member will return
\ 'null', which is treated as 'false', so we don't need to initialize it:
[] var, doors
\ given a door number, get the value and toggle it:
: toggle-door \ n --
doors @ over a:@
not rot swap a:! drop ;
\ print which doors are open:
: .doors
(
doors @ over a:@ nip
if . space else drop then
) 1 100 loop ;
\ iterate over the doors, skipping 'n':
: main-pass \ n --
0
true
repeat
drop
dup toggle-door
over n:+
dup 101 <
while 2drop drop ;
\ calculate the first 100 doors:
' main-pass 1 100 loop
\ print the results:
.doors cr bye
|
http://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi | Arithmetic-geometric mean/Calculate Pi | Almkvist Berndt 1988 begins with an investigation of why the agm is such an efficient algorithm, and proves that it converges quadratically. This is an efficient method to calculate
π
{\displaystyle \pi }
.
With the same notations used in Arithmetic-geometric mean, we can summarize the paper by writing:
π
=
4
a
g
m
(
1
,
1
/
2
)
2
1
−
∑
n
=
1
∞
2
n
+
1
(
a
n
2
−
g
n
2
)
{\displaystyle \pi ={\frac {4\;\mathrm {agm} (1,1/{\sqrt {2}})^{2}}{1-\sum \limits _{n=1}^{\infty }2^{n+1}(a_{n}^{2}-g_{n}^{2})}}}
This allows you to make the approximation, for any large N:
π
≈
4
a
N
2
1
−
∑
k
=
1
N
2
k
+
1
(
a
k
2
−
g
k
2
)
{\displaystyle \pi \approx {\frac {4\;a_{N}^{2}}{1-\sum \limits _{k=1}^{N}2^{k+1}(a_{k}^{2}-g_{k}^{2})}}}
The purpose of this task is to demonstrate how to use this approximation in order to compute a large number of decimals of
π
{\displaystyle \pi }
.
| #Ruby | Ruby | # Calculate Pi using the Arithmetic Geometric Mean of 1 and 1/sqrt(2)
#
#
# Nigel_Galloway
# March 8th., 2012.
#
require 'flt'
Flt::BinNum.Context.precision = 8192
a = n = 1
g = 1 / Flt::BinNum(2).sqrt
z = 0.25
(0..17).each{
x = [(a + g) * 0.5, (a * g).sqrt]
var = x[0] - a
z -= var * var * n
n += n
a = x[0]
g = x[1]
}
puts a * a / z |
http://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi | Arithmetic-geometric mean/Calculate Pi | Almkvist Berndt 1988 begins with an investigation of why the agm is such an efficient algorithm, and proves that it converges quadratically. This is an efficient method to calculate
π
{\displaystyle \pi }
.
With the same notations used in Arithmetic-geometric mean, we can summarize the paper by writing:
π
=
4
a
g
m
(
1
,
1
/
2
)
2
1
−
∑
n
=
1
∞
2
n
+
1
(
a
n
2
−
g
n
2
)
{\displaystyle \pi ={\frac {4\;\mathrm {agm} (1,1/{\sqrt {2}})^{2}}{1-\sum \limits _{n=1}^{\infty }2^{n+1}(a_{n}^{2}-g_{n}^{2})}}}
This allows you to make the approximation, for any large N:
π
≈
4
a
N
2
1
−
∑
k
=
1
N
2
k
+
1
(
a
k
2
−
g
k
2
)
{\displaystyle \pi \approx {\frac {4\;a_{N}^{2}}{1-\sum \limits _{k=1}^{N}2^{k+1}(a_{k}^{2}-g_{k}^{2})}}}
The purpose of this task is to demonstrate how to use this approximation in order to compute a large number of decimals of
π
{\displaystyle \pi }
.
| #Rust | Rust | /// calculate pi with algebraic/geometric mean
pub fn pi(n: usize) -> f64 {
let mut a : f64 = 1.0;
let two : f64= 2.0;
let mut g = 1.0 / two.sqrt();
let mut s = 0.0;
let mut k = 1;
while k<=n {
let a1 = (a+g)/two;
let g1 = (a*g).sqrt();
a = a1;
g = g1;
s += (a.powi(2)-g.powi(2)) * two.powi((k+1) as i32);
k += 1;
}
4.0 * a.powi(2) / (1.0-s)
}
|
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)
| #Babel | Babel | [1 2 3] |
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.
| #D | D | import std.stdio, std.complex;
void main() {
auto x = complex(1, 1); // complex of doubles on default
auto y = complex(3.14159, 1.2);
writeln(x + y); // addition
writeln(x * y); // multiplication
writeln(1.0 / x); // inversion
writeln(-x); // negation
} |
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
| #Elixir | Elixir | defmodule Rational do
import Kernel, except: [div: 2]
defstruct numerator: 0, denominator: 1
def new(numerator), do: %Rational{numerator: numerator, denominator: 1}
def new(numerator, denominator) do
sign = if numerator * denominator < 0, do: -1, else: 1
{numerator, denominator} = {abs(numerator), abs(denominator)}
gcd = gcd(numerator, denominator)
%Rational{numerator: sign * Kernel.div(numerator, gcd),
denominator: Kernel.div(denominator, gcd)}
end
def add(a, b) do
{a, b} = convert(a, b)
new(a.numerator * b.denominator + b.numerator * a.denominator,
a.denominator * b.denominator)
end
def sub(a, b) do
{a, b} = convert(a, b)
new(a.numerator * b.denominator - b.numerator * a.denominator,
a.denominator * b.denominator)
end
def mult(a, b) do
{a, b} = convert(a, b)
new(a.numerator * b.numerator, a.denominator * b.denominator)
end
def div(a, b) do
{a, b} = convert(a, b)
new(a.numerator * b.denominator, a.denominator * b.numerator)
end
defp convert(a), do: if is_integer(a), do: new(a), else: a
defp convert(a, b), do: {convert(a), convert(b)}
defp gcd(a, 0), do: a
defp gcd(a, b), do: gcd(b, rem(a, b))
end
defimpl Inspect, for: Rational do
def inspect(r, _opts) do
"%Rational<#{r.numerator}/#{r.denominator}>"
end
end
Enum.each(2..trunc(:math.pow(2,19)), fn candidate ->
sum = 2 .. round(:math.sqrt(candidate))
|> Enum.reduce(Rational.new(1, candidate), fn factor,sum ->
if rem(candidate, factor) == 0 do
Rational.add(sum, Rational.new(1, factor))
|> Rational.add(Rational.new(1, div(candidate, factor)))
else
sum
end
end)
if sum.denominator == 1 do
:io.format "Sum of recipr. factors of ~6w = ~w exactly ~s~n",
[candidate, sum.numerator, (if sum.numerator == 1, do: "perfect!", else: "")]
end
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
| #Elixir | Elixir | defmodule ArithhGeom do
def mean(a,g,tol) when abs(a-g) <= tol, do: a
def mean(a,g,tol) do
mean((a+g)/2,:math.pow(a*g, 0.5),tol)
end
end
IO.puts ArithhGeom.mean(1,1/:math.sqrt(2),0.0000000001) |
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
| #Erlang | Erlang | %% Arithmetic Geometric Mean of 1 and 1 / sqrt(2)
%% Author: Abhay Jain
-module(agm_calculator).
-export([find_agm/0]).
-define(TOLERANCE, 0.0000000001).
find_agm() ->
A = 1,
B = 1 / (math:pow(2, 0.5)),
AGM = agm(A, B),
io:format("AGM = ~p", [AGM]).
agm (A, B) when abs(A-B) =< ?TOLERANCE ->
A;
agm (A, B) ->
A1 = (A+B) / 2,
B1 = math:pow(A*B, 0.5),
agm(A1, B1). |
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.
| #Vim_Script | Vim Script | let a = float2nr(input("Number 1: ") + 0)
let b = float2nr(input("Number 2: ") + 0)
echo "\nSum: " . (a + b)
echo "Difference: " . (a - b)
echo "Product: " . (a * b)
" The result of an integer division is truncated
echo "Quotient: " . (a / b)
" The sign of the result of the remainder operation matches the sign of
" the first operand
echo "Remainder: " . (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.
| #AutoHotkey | AutoHotkey | /*
hand coded recursive descent parser
expr : term ( ( PLUS | MINUS ) term )* ;
term : factor ( ( MULT | DIV ) factor )* ;
factor : NUMBER | '(' expr ')';
*/
calcLexer := makeCalcLexer()
string := "((3+4)*(7*9)+3)+4"
tokens := tokenize(string, calcLexer)
msgbox % printTokens(tokens)
ast := expr()
msgbox % printTree(ast)
msgbox % expression := evalTree(ast)
filedelete expression.ahk
fileappend, % "msgbox % " expression, expression.ahk
run, expression.ahk
return
expr()
{
global tokens
ast := object(1, "expr")
if node := term()
ast._Insert(node)
loop
{
if peek("PLUS") or peek("MINUS")
{
op := getsym()
newop := object(1, op.type, 2, op.value)
node := term()
ast._Insert(newop)
ast._Insert(node)
}
Else
Break
}
return ast
}
term()
{
global tokens
tree := object(1, "term")
if node := factor()
tree._Insert(node)
loop
{
if peek("MULT") or peek("DIV")
{
op := getsym()
newop := object(1, op.type, 2, op.value)
node := factor()
tree._Insert(newop)
tree._Insert(node)
}
else
Break
}
return tree
}
factor()
{
global tokens
if peek("NUMBER")
{
token := getsym()
tree := object(1, token.type, 2, token.value)
return tree
}
else if peek("OPEN")
{
getsym()
tree := expr()
if peek("CLOSE")
{
getsym()
return tree
}
else
error("miss closing parentheses ")
}
else
error("no factor found")
}
peek(type, n=1)
{
global tokens
if (tokens[n, "type"] == type)
return 1
}
getsym(n=1)
{
global tokens
return token := tokens._Remove(n)
}
error(msg)
{
global tokens
msgbox % msg " at:`n" printToken(tokens[1])
}
printTree(ast)
{
if !ast
return
n := 0
loop
{
n += 1
if !node := ast[n]
break
if !isobject(node)
treeString .= node
else
treeString .= printTree(node)
}
return ("(" treeString ")" )
}
evalTree(ast)
{
if !ast
return
n := 1
loop
{
n += 1
if !node := ast[n]
break
if !isobject(node)
treeString .= node
else
treeString .= evalTree(node)
}
if (n == 3)
return treeString
return ("(" treeString ")" )
}
#include calclex.ahk |
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.
| #AArch64_Assembly | AArch64 Assembly |
/* ARM assembly AARCH64 Raspberry PI 3B */
/* program 100doors64.s */
/*******************************************/
/* Constantes file */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly*/
.include "../includeConstantesARM64.inc"
.equ NBDOORS, 100
/*********************************/
/* Initialized data */
/*********************************/
.data
sMessResult: .asciz "The door @ is open.\n"
/*********************************/
/* UnInitialized data */
/*********************************/
.bss
stTableDoors: .skip 8 * NBDOORS
sZoneConv: .skip 24
/*********************************/
/* code section */
/*********************************/
.text
.global main
main: // entry of program
// display first line
ldr x3,qAdrstTableDoors // table address
mov x5,1
1:
mov x4,x5
2: // begin loop
ldr x2,[x3,x4,lsl #3] // read doors index x4
cmp x2,#0
cset x2,eq
//moveq x2,#1 // if x2 = 0 1 -> x2
//movne x2,#0 // if x2 = 1 0 -> x2
str x2,[x3,x4,lsl #3] // store value of doors
add x4,x4,x5 // increment x4 with x5 value
cmp x4,NBDOORS // number of doors ?
ble 2b // no -> loop
add x5,x5,#1 // increment the increment !!
cmp x5,NBDOORS // number of doors ?
ble 1b // no -> loop
// loop display state doors
mov x4,#0
3:
ldr x2,[x3,x4,lsl #3] // read state doors x4 index
cmp x2,#0
beq 4f
mov x0,x4 // open -> display message
ldr x1,qAdrsZoneConv // display value index
bl conversion10 // call function
ldr x0,qAdrsMessResult
ldr x1,qAdrsZoneConv
bl strInsertAtCharInc // insert result at first @ character
bl affichageMess // display message
4:
add x4,x4,1
cmp x4,NBDOORS
ble 3b // loop
100: // standard end of the program
mov x0,0 // return code
mov x8,EXIT // request to exit program
svc 0 // perform the system call
qAdrstTableDoors: .quad stTableDoors
qAdrsMessResult: .quad sMessResult
qAdrsZoneConv: .quad sZoneConv
/***********************************************/
/* File Include fonctions */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
|
http://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi | Arithmetic-geometric mean/Calculate Pi | Almkvist Berndt 1988 begins with an investigation of why the agm is such an efficient algorithm, and proves that it converges quadratically. This is an efficient method to calculate
π
{\displaystyle \pi }
.
With the same notations used in Arithmetic-geometric mean, we can summarize the paper by writing:
π
=
4
a
g
m
(
1
,
1
/
2
)
2
1
−
∑
n
=
1
∞
2
n
+
1
(
a
n
2
−
g
n
2
)
{\displaystyle \pi ={\frac {4\;\mathrm {agm} (1,1/{\sqrt {2}})^{2}}{1-\sum \limits _{n=1}^{\infty }2^{n+1}(a_{n}^{2}-g_{n}^{2})}}}
This allows you to make the approximation, for any large N:
π
≈
4
a
N
2
1
−
∑
k
=
1
N
2
k
+
1
(
a
k
2
−
g
k
2
)
{\displaystyle \pi \approx {\frac {4\;a_{N}^{2}}{1-\sum \limits _{k=1}^{N}2^{k+1}(a_{k}^{2}-g_{k}^{2})}}}
The purpose of this task is to demonstrate how to use this approximation in order to compute a large number of decimals of
π
{\displaystyle \pi }
.
| #Scala | Scala | import java.math.MathContext
import scala.annotation.tailrec
import scala.compat.Platform.currentTime
import scala.math.BigDecimal
object Calculate_Pi extends App {
val precision = new MathContext(32768 /*65536*/)
val (bigZero, bigOne, bigTwo, bigFour) =
(BigDecimal(0, precision), BigDecimal(1, precision), BigDecimal(2, precision), BigDecimal(4, precision))
def bigSqrt(bd: BigDecimal) = {
@tailrec
def iter(x0: BigDecimal, x1: BigDecimal): BigDecimal =
if (x0 == x1) x1 else iter(x1, (bd / x1 + x1) / bigTwo)
iter(bigZero, BigDecimal(Math.sqrt(bd.toDouble), precision))
}
@tailrec
private def loop(a: BigDecimal, g: BigDecimal, sum: BigDecimal, pow: BigDecimal): BigDecimal = {
if (a == g) (bigFour * (a * a)) / (bigOne - sum)
else {
val (_a, _g, _pow) = ((a + g) / bigTwo, bigSqrt(a * g), pow * bigTwo)
loop(_a, _g, sum + ((_a * _a - (_g * _g)) * _pow), _pow)
}
}
println(precision)
val pi = loop(bigOne, bigOne / bigSqrt(bigTwo), bigZero, bigTwo)
println(s"This are ${pi.toString.length - 1} digits of π:")
val lines = pi.toString().sliding(103, 103).mkString("\n")
println(lines)
println(s"Successfully completed without errors. [total ${currentTime - executionStart} ms]")
} |
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #BaCon | BaCon |
DATA "January", "February", "March", "April", "May", "June", "July"
DATA "August", "September", "October", "November", "December"
LOCAL dat$[11]
FOR i = 0 TO 11
READ dat$[i]
PRINT dat$[i]
NEXT
|
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.
| #Dart | Dart |
class complex {
num real=0;
num imag=0;
complex(num r,num i){
this.real=r;
this.imag=i;
}
complex add(complex b){
return new complex(this.real + b.real, this.imag + b.imag);
}
complex mult(complex b){
//FOIL of (a+bi)(c+di) with i*i = -1
return new complex(this.real * b.real - this.imag * b.imag, this.real * b.imag + this.imag * b.real);
}
complex inv(){
//1/(a+bi) * (a-bi)/(a-bi) = 1/(a+bi) but it's more workable
num denom = real * real + imag * imag;
double r =real/denom;
double i= -imag/denom;
return new complex( r,-i);
}
complex neg(){
return new complex(-real, -imag);
}
complex conj(){
return new complex(real, -imag);
}
String toString(){
return this.real.toString()+' + '+ this.imag.toString()+'*i';
}
}
void main() {
var cl= new complex(1,2);
var cl2= new complex(3,-1);
print(cl.toString());
print(cl2.toString());
print(cl.inv().toString());
print(cl2.mult(cl).toString());
}
|
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
| #ERRE | ERRE | PROGRAM RATIONAL_ARITH
!
! for rosettacode.org
!
TYPE RATIONAL=(NUM,DEN)
DIM SUM:RATIONAL,ONE:RATIONAL,KF:RATIONAL
DIM A:RATIONAL,B:RATIONAL
PROCEDURE ABS(A.->A.)
A.NUM=ABS(A.NUM)
END PROCEDURE
PROCEDURE NEG(A.->A.)
A.NUM=-A.NUM
END PROCEDURE
PROCEDURE ADD(A.,B.->A.)
LOCAL T
T=A.DEN*B.DEN
A.NUM=A.NUM*B.DEN+B.NUM*A.DEN
A.DEN=T
END PROCEDURE
PROCEDURE SUB(A.,B.->A.)
LOCAL T
T=A.DEN*B.DEN
A.NUM=A.NUM*B.DEN-B.NUM*A.DEN
A.DEN=T
END PROCEDURE
PROCEDURE MULT(A.,B.->A.)
A.NUM*=B.NUM A.DEN*=B.DEN
END PROCEDURE
PROCEDURE DIVIDE(A.,B.->A.)
A.NUM*=B.DEN
A.DEN*=B.NUM
END PROCEDURE
PROCEDURE EQ(A.,B.->RES%)
RES%=A.NUM*B.DEN=B.NUM*A.DEN
END PROCEDURE
PROCEDURE LT(A.,B.->RES%)
RES%=A.NUM*B.DEN<B.NUM*A.DEN
END PROCEDURE
PROCEDURE GT(A.,B.->RES%)
RES%=A.NUM*B.DEN>B.NUM*A.DEN
END PROCEDURE
PROCEDURE NE(A.,B.->RES%)
RES%=A.NUM*B.DEN<>B.NUM*A.DEN
END PROCEDURE
PROCEDURE LE(A.,B.->RES%)
RES%=A.NUM*B.DEN<=B.NUM*A.DEN
END PROCEDURE
PROCEDURE GE(A.,B.->RES%)
RES%=A.NUM*B.DEN>=B.NUM*A.DEN
END PROCEDURE
PROCEDURE NORMALIZE(A.->A.)
LOCAL A,B,T
A=A.NUM B=A.DEN
WHILE B<>0 DO
T=A
A=B
B=T-B*INT(T/B)
END WHILE
A.NUM/=A A.DEN/=A
IF A.DEN<0 THEN A.NUM*=-1 A.DEN*=-1 END IF
END PROCEDURE
BEGIN
ONE.NUM=1 ONE.DEN=1
FOR N=2 TO 2^19-1 DO
SUM.NUM=1 SUM.DEN=N
FOR K=2 TO SQR(N) DO
IF N=K*INT(N/K) THEN
KF.NUM=1 KF.DEN=K
ADD(SUM.,KF.->SUM.)
NORMALIZE(SUM.->SUM.)
KF.DEN=INT(N/K)
ADD(SUM.,KF.->SUM.)
NORMALIZE(SUM.->SUM.)
END IF
END FOR
EQ(SUM.,ONE.->RES%)
IF RES% THEN PRINT(N;" is perfect") END IF
END FOR
END PROGRAM |
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
| #ERRE | ERRE |
PROGRAM AGM
!
! for rosettacode.org
!
!$DOUBLE
PROCEDURE AGM(A,G->A)
LOCAL TA
REPEAT
TA=A
A=(A+G)/2
G=SQR(TA*G)
UNTIL A=TA
END PROCEDURE
BEGIN
AGM(1.0,1/SQR(2)->A)
PRINT(A)
END PROGRAM
|
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
| #F.23 | F# | let rec agm a g precision =
if precision > abs(a - g) then a else
agm (0.5 * (a + g)) (sqrt (a * g)) precision
printfn "%g" (agm 1. (sqrt(0.5)) 1e-15) |
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.
| #Visual_Basic_.NET | Visual Basic .NET | Imports System.Console
Module Module1
Sub Main
Dim a = CInt(ReadLine)
Dim b = CInt(ReadLine)
WriteLine("Sum " & a + b)
WriteLine("Difference " & a - b)
WriteLine("Product " & a - b)
WriteLine("Quotient " & a / b)
WriteLine("Integer Quotient " & a \ b)
WriteLine("Remainder " & a Mod b)
WriteLine("Exponent " & a ^ b)
End Sub
End Module |
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.
| #BBC_BASIC | BBC BASIC | Expr$ = "1 + 2 * (3 + (4 * 5 + 6 * 7 * 8) - 9) / 10"
PRINT "Input = " Expr$
AST$ = FNast(Expr$)
PRINT "AST = " AST$
PRINT "Value = " ;EVAL(AST$)
END
DEF FNast(RETURN in$)
LOCAL ast$, oper$
REPEAT
ast$ += FNast1(in$)
WHILE ASC(in$)=32 in$ = MID$(in$,2) : ENDWHILE
oper$ = LEFT$(in$,1)
IF oper$="+" OR oper$="-" THEN
ast$ += oper$
in$ = MID$(in$,2)
ELSE
EXIT REPEAT
ENDIF
UNTIL FALSE
= "(" + ast$ + ")"
DEF FNast1(RETURN in$)
LOCAL ast$, oper$
REPEAT
ast$ += FNast2(in$)
WHILE ASC(in$)=32 in$ = MID$(in$,2) : ENDWHILE
oper$ = LEFT$(in$,1)
IF oper$="*" OR oper$="/" THEN
ast$ += oper$
in$ = MID$(in$,2)
ELSE
EXIT REPEAT
ENDIF
UNTIL FALSE
= "(" + ast$ + ")"
DEF FNast2(RETURN in$)
LOCAL ast$
WHILE ASC(in$)=32 in$ = MID$(in$,2) : ENDWHILE
IF ASC(in$)<>40 THEN = FNnumber(in$)
in$ = MID$(in$,2)
ast$ = FNast(in$)
in$ = MID$(in$,2)
= ast$
DEF FNnumber(RETURN in$)
LOCAL ch$, num$
REPEAT
ch$ = LEFT$(in$,1)
IF INSTR("0123456789.", ch$) THEN
num$ += ch$
in$ = MID$(in$,2)
ELSE
EXIT REPEAT
ENDIF
UNTIL FALSE
= num$ |
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.
| #C | C | #include <boost/spirit.hpp>
#include <boost/spirit/tree/ast.hpp>
#include <string>
#include <cassert>
#include <iostream>
#include <istream>
#include <ostream>
using boost::spirit::rule;
using boost::spirit::parser_tag;
using boost::spirit::ch_p;
using boost::spirit::real_p;
using boost::spirit::tree_node;
using boost::spirit::node_val_data;
// The grammar
struct parser: public boost::spirit::grammar<parser>
{
enum rule_ids { addsub_id, multdiv_id, value_id, real_id };
struct set_value
{
set_value(parser const& p): self(p) {}
void operator()(tree_node<node_val_data<std::string::iterator,
double> >& node,
std::string::iterator begin,
std::string::iterator end) const
{
node.value.value(self.tmp);
}
parser const& self;
};
mutable double tmp;
template<typename Scanner> struct definition
{
rule<Scanner, parser_tag<addsub_id> > addsub;
rule<Scanner, parser_tag<multdiv_id> > multdiv;
rule<Scanner, parser_tag<value_id> > value;
rule<Scanner, parser_tag<real_id> > real;
definition(parser const& self)
{
using namespace boost::spirit;
addsub = multdiv
>> *((root_node_d[ch_p('+')] | root_node_d[ch_p('-')]) >> multdiv);
multdiv = value
>> *((root_node_d[ch_p('*')] | root_node_d[ch_p('/')]) >> value);
value = real | inner_node_d[('(' >> addsub >> ')')];
real = leaf_node_d[access_node_d[real_p[assign_a(self.tmp)]][set_value(self)]];
}
rule<Scanner, parser_tag<addsub_id> > const& start() const
{
return addsub;
}
};
};
template<typename TreeIter>
double evaluate(TreeIter const& i)
{
double op1, op2;
switch (i->value.id().to_long())
{
case parser::real_id:
return i->value.value();
case parser::value_id:
case parser::addsub_id:
case parser::multdiv_id:
op1 = evaluate(i->children.begin());
op2 = evaluate(i->children.begin()+1);
switch(*i->value.begin())
{
case '+':
return op1 + op2;
case '-':
return op1 - op2;
case '*':
return op1 * op2;
case '/':
return op1 / op2;
default:
assert(!"Should not happen");
}
default:
assert(!"Should not happen");
}
return 0;
}
// the read/eval/write loop
int main()
{
parser eval;
std::string line;
while (std::cout << "Expression: "
&& std::getline(std::cin, line)
&& !line.empty())
{
typedef boost::spirit::node_val_data_factory<double> factory_t;
boost::spirit::tree_parse_info<std::string::iterator, factory_t> info =
boost::spirit::ast_parse<factory_t>(line.begin(), line.end(),
eval, boost::spirit::space_p);
if (info.full)
{
std::cout << "Result: " << evaluate(info.trees.begin()) << std::endl;
}
else
{
std::cout << "Error in expression." << std::endl;
}
}
}; |
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.
| #ABAP | ABAP | form open_doors_unopt.
data: lv_door type i,
lv_count type i value 1.
data: lt_doors type standard table of c initial size 100.
field-symbols: <wa_door> type c.
do 100 times.
append initial line to lt_doors assigning <wa_door>.
<wa_door> = 'X'.
enddo.
while lv_count < 100.
lv_count = lv_count + 1.
lv_door = lv_count.
while lv_door < 100.
read table lt_doors index lv_door assigning <wa_door>.
if <wa_door> = ' '.
<wa_door> = 'X'.
else.
<wa_door> = ' '.
endif.
add lv_count to lv_door.
endwhile.
endwhile.
loop at lt_doors assigning <wa_door>.
if <wa_door> = 'X'.
write : / 'Door', (4) sy-tabix right-justified, 'is open' no-gap.
endif.
endloop.
endform. |
http://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi | Arithmetic-geometric mean/Calculate Pi | Almkvist Berndt 1988 begins with an investigation of why the agm is such an efficient algorithm, and proves that it converges quadratically. This is an efficient method to calculate
π
{\displaystyle \pi }
.
With the same notations used in Arithmetic-geometric mean, we can summarize the paper by writing:
π
=
4
a
g
m
(
1
,
1
/
2
)
2
1
−
∑
n
=
1
∞
2
n
+
1
(
a
n
2
−
g
n
2
)
{\displaystyle \pi ={\frac {4\;\mathrm {agm} (1,1/{\sqrt {2}})^{2}}{1-\sum \limits _{n=1}^{\infty }2^{n+1}(a_{n}^{2}-g_{n}^{2})}}}
This allows you to make the approximation, for any large N:
π
≈
4
a
N
2
1
−
∑
k
=
1
N
2
k
+
1
(
a
k
2
−
g
k
2
)
{\displaystyle \pi \approx {\frac {4\;a_{N}^{2}}{1-\sum \limits _{k=1}^{N}2^{k+1}(a_{k}^{2}-g_{k}^{2})}}}
The purpose of this task is to demonstrate how to use this approximation in order to compute a large number of decimals of
π
{\displaystyle \pi }
.
| #Sidef | Sidef | func agm_pi(digits) {
var acc = (digits + 8);
local Num!PREC = 4*digits;
var an = 1;
var bn = sqrt(0.5);
var tn = 0.5**2;
var pn = 1;
while (pn < acc) {
var prev_an = an;
an = (bn+an / 2);
bn = sqrt(bn * prev_an);
prev_an -= an;
tn -= (pn * prev_an**2);
pn *= 2;
}
((an+bn)**2 / 4*tn).to_s
}
say agm_pi(100); |
http://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi | Arithmetic-geometric mean/Calculate Pi | Almkvist Berndt 1988 begins with an investigation of why the agm is such an efficient algorithm, and proves that it converges quadratically. This is an efficient method to calculate
π
{\displaystyle \pi }
.
With the same notations used in Arithmetic-geometric mean, we can summarize the paper by writing:
π
=
4
a
g
m
(
1
,
1
/
2
)
2
1
−
∑
n
=
1
∞
2
n
+
1
(
a
n
2
−
g
n
2
)
{\displaystyle \pi ={\frac {4\;\mathrm {agm} (1,1/{\sqrt {2}})^{2}}{1-\sum \limits _{n=1}^{\infty }2^{n+1}(a_{n}^{2}-g_{n}^{2})}}}
This allows you to make the approximation, for any large N:
π
≈
4
a
N
2
1
−
∑
k
=
1
N
2
k
+
1
(
a
k
2
−
g
k
2
)
{\displaystyle \pi \approx {\frac {4\;a_{N}^{2}}{1-\sum \limits _{k=1}^{N}2^{k+1}(a_{k}^{2}-g_{k}^{2})}}}
The purpose of this task is to demonstrate how to use this approximation in order to compute a large number of decimals of
π
{\displaystyle \pi }
.
| #Tcl | Tcl | package require math::bigfloat
namespace import math::bigfloat::*
proc agm/π {N {precision 8192}} {
set 1 [int2float 1 $precision]
set 2 [int2float 2 $precision]
set n 1
set a $1
set g [div $1 [sqrt $2]]
set z [div $1 [int2float 4 $precision]]
for {set i 0} {$i <= $N} {incr i} {
set x0 [div [add $a $g] $2]
set x1 [sqrt [mul $a $g]]
set var [sub $x0 $a]
set z [sub $z [mul [mul $var $n] $var]]
incr n $n
set a $x0
set g $x1
}
return [tostr [div [mul $a $a] $z]]
}
puts [agm/π 17] |
http://rosettacode.org/wiki/Arrays | Arrays | This task is about arrays.
For hashes or associative arrays, please see Creating an Associative Array.
For a definition and in-depth discussion of what an array is, see Array.
Task
Show basic array syntax in your language.
Basically, create an array, assign a value to it, and retrieve an element (if available, show both fixed-length arrays and
dynamic arrays, pushing a value into it).
Please discuss at Village Pump: Arrays.
Please merge code in from these obsolete tasks:
Creating an Array
Assigning Values to an Array
Retrieving an Element of an Array
Related tasks
Collections
Creating an Associative Array
Two-dimensional array (runtime)
| #BASIC | BASIC | OPTION BASE 1
DIM myArray(100) AS INTEGER |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #Delphi | Delphi |
program Arithmetic_Complex;
{$APPTYPE CONSOLE}
uses
System.SysUtils,
System.VarCmplx;
var
a, b: Variant;
begin
a := VarComplexCreate(5, 3);
b := VarComplexCreate(0.5, 6.0);
writeln(format('(%s) + (%s) = %s',[a,b, a+b]));
writeln(format('(%s) * (%s) = %s',[a,b, a*b]));
writeln(format('-(%s) = %s',[a,- a]));
writeln(format('1/(%s) = %s',[a,1/a]));
writeln(format('conj(%s) = %s',[a,VarComplexConjugate(a)]));
Readln;
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
| #F.23 | F# | type frac = Microsoft.FSharp.Math.BigRational
let perf n = 1N = List.fold (+) 0N (List.map (fun i -> if n % i = 0 then 1N/frac.FromInt(i) else 0N) [2..n])
for i in 1..(1<<<19) do if (perf i) then printfn "%i is perfect" i |
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
| #Factor | Factor | USING: kernel math math.functions prettyprint ;
IN: rosetta-code.arithmetic-geometric-mean
: agm ( a g -- a' g' ) 2dup [ + 0.5 * ] 2dip * sqrt ;
1 1 2 sqrt / [ 2dup - 1e-15 > ] [ agm ] while drop . |
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
| #Forth | Forth | : agm ( a g -- m )
begin
fover fover f+ 2e f/
frot frot f* fsqrt
fover fover 1e-15 f~
until
fdrop ;
1e 2e -0.5e f** agm f. \ 0.847213084793979 |
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.
| #Vlang | Vlang | // Arithmetic-integer in V
// Tectonics: v run arithmetic-integer.v
module main
import math
import os
// starts here
pub fn main() {
mut a := 0
mut b := 0
// get numbers from console
print("Enter two integer numbers, separated by a space: ")
text := os.get_raw_line()
values := text.split(' ')
a = values[0].int()
b = values[1].int()
// 4 basics, remainder, no exponentiation operator
println("values: a $a, b $b")
println("sum: a + b = ${a + b}")
println("difference: a - b = ${a - b}")
println("product: a * b = ${a * b}")
println("integer quotient: a / b = ${a / b}, truncation")
println("remainder: a % b = ${a % b}, sign follows dividend")
println("no exponentiation operator")
println(" math.pow: pow(a,b) = ${math.pow(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.
| #C.2B.2B | C++ | #include <boost/spirit.hpp>
#include <boost/spirit/tree/ast.hpp>
#include <string>
#include <cassert>
#include <iostream>
#include <istream>
#include <ostream>
using boost::spirit::rule;
using boost::spirit::parser_tag;
using boost::spirit::ch_p;
using boost::spirit::real_p;
using boost::spirit::tree_node;
using boost::spirit::node_val_data;
// The grammar
struct parser: public boost::spirit::grammar<parser>
{
enum rule_ids { addsub_id, multdiv_id, value_id, real_id };
struct set_value
{
set_value(parser const& p): self(p) {}
void operator()(tree_node<node_val_data<std::string::iterator,
double> >& node,
std::string::iterator begin,
std::string::iterator end) const
{
node.value.value(self.tmp);
}
parser const& self;
};
mutable double tmp;
template<typename Scanner> struct definition
{
rule<Scanner, parser_tag<addsub_id> > addsub;
rule<Scanner, parser_tag<multdiv_id> > multdiv;
rule<Scanner, parser_tag<value_id> > value;
rule<Scanner, parser_tag<real_id> > real;
definition(parser const& self)
{
using namespace boost::spirit;
addsub = multdiv
>> *((root_node_d[ch_p('+')] | root_node_d[ch_p('-')]) >> multdiv);
multdiv = value
>> *((root_node_d[ch_p('*')] | root_node_d[ch_p('/')]) >> value);
value = real | inner_node_d[('(' >> addsub >> ')')];
real = leaf_node_d[access_node_d[real_p[assign_a(self.tmp)]][set_value(self)]];
}
rule<Scanner, parser_tag<addsub_id> > const& start() const
{
return addsub;
}
};
};
template<typename TreeIter>
double evaluate(TreeIter const& i)
{
double op1, op2;
switch (i->value.id().to_long())
{
case parser::real_id:
return i->value.value();
case parser::value_id:
case parser::addsub_id:
case parser::multdiv_id:
op1 = evaluate(i->children.begin());
op2 = evaluate(i->children.begin()+1);
switch(*i->value.begin())
{
case '+':
return op1 + op2;
case '-':
return op1 - op2;
case '*':
return op1 * op2;
case '/':
return op1 / op2;
default:
assert(!"Should not happen");
}
default:
assert(!"Should not happen");
}
return 0;
}
// the read/eval/write loop
int main()
{
parser eval;
std::string line;
while (std::cout << "Expression: "
&& std::getline(std::cin, line)
&& !line.empty())
{
typedef boost::spirit::node_val_data_factory<double> factory_t;
boost::spirit::tree_parse_info<std::string::iterator, factory_t> info =
boost::spirit::ast_parse<factory_t>(line.begin(), line.end(),
eval, boost::spirit::space_p);
if (info.full)
{
std::cout << "Result: " << evaluate(info.trees.begin()) << std::endl;
}
else
{
std::cout << "Error in expression." << std::endl;
}
}
}; |
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.
| #ACL2 | ACL2 | (defun rep (n x)
(if (zp n)
nil
(cons x
(rep (- n 1) x))))
(defun toggle-every-r (n i bs)
(if (endp bs)
nil
(cons (if (zp i)
(not (first bs))
(first bs))
(toggle-every-r n (mod (1- i) n) (rest bs)))))
(defun toggle-every (n bs)
(toggle-every-r n (1- n) bs))
(defun 100-doors (i doors)
(if (zp i)
doors
(100-doors (1- i) (toggle-every i doors)))) |
http://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi | Arithmetic-geometric mean/Calculate Pi | Almkvist Berndt 1988 begins with an investigation of why the agm is such an efficient algorithm, and proves that it converges quadratically. This is an efficient method to calculate
π
{\displaystyle \pi }
.
With the same notations used in Arithmetic-geometric mean, we can summarize the paper by writing:
π
=
4
a
g
m
(
1
,
1
/
2
)
2
1
−
∑
n
=
1
∞
2
n
+
1
(
a
n
2
−
g
n
2
)
{\displaystyle \pi ={\frac {4\;\mathrm {agm} (1,1/{\sqrt {2}})^{2}}{1-\sum \limits _{n=1}^{\infty }2^{n+1}(a_{n}^{2}-g_{n}^{2})}}}
This allows you to make the approximation, for any large N:
π
≈
4
a
N
2
1
−
∑
k
=
1
N
2
k
+
1
(
a
k
2
−
g
k
2
)
{\displaystyle \pi \approx {\frac {4\;a_{N}^{2}}{1-\sum \limits _{k=1}^{N}2^{k+1}(a_{k}^{2}-g_{k}^{2})}}}
The purpose of this task is to demonstrate how to use this approximation in order to compute a large number of decimals of
π
{\displaystyle \pi }
.
| #Visual_Basic_.NET | Visual Basic .NET | Imports System, System.Numerics
Module Program
Function IntSqRoot(ByVal valu As BigInteger, ByVal guess As BigInteger) As BigInteger
Dim term As BigInteger : Do
term = valu / guess
If BigInteger.Abs(term - guess) <= 1 Then Exit Do
guess += term : guess >>= 1
Loop While True : Return guess
End Function
Function ISR(ByVal term As BigInteger, ByVal guess As BigInteger) As BigInteger
Dim valu As BigInteger = term * guess : Do
If BigInteger.Abs(term - guess) <= 1 Then Exit Do
guess += term : guess >>= 1 : term = valu / guess
Loop While True : Return guess
End Function
Function CalcAGM(ByVal lam As BigInteger, ByVal gm As BigInteger, ByRef z As BigInteger,
ByVal ep As BigInteger) As BigInteger
Dim am, zi As BigInteger : Dim n As ULong = 1 : Do
am = (lam + gm) >> 1 : gm = ISR(lam, gm)
Dim v As BigInteger = am - lam
zi = v * v * n : If zi < ep Then Exit Do
z -= zi : n <<= 1 : lam = am
Loop While True : Return am
End Function
Function BIP(ByVal exp As Integer, ByVal Optional man As ULong = 1) As BigInteger
Dim rv As BigInteger = BigInteger.Pow(10, exp) : Return If(man = 1, rv, man * rv)
End Function
Sub Main(args As String())
Dim d As Integer = 25000
If args.Length > 0 Then
Integer.TryParse(args(0), d)
If d < 1 OrElse d > 999999 Then d = 25000
End If
Dim st As DateTime = DateTime.Now
Dim am As BigInteger = BIP(d),
gm As BigInteger = IntSqRoot(BIP(d + d - 1, 5),
BIP(d - 15, Math.Sqrt(0.5) * 1.0E+15)),
z As BigInteger = BIP(d + d - 2, 25),
agm As BigInteger = CalcAGM(am, gm, z, BIP(d + 1)),
pi As BigInteger = agm * agm * BIP(d - 2) / z
Console.WriteLine("Computation time: {0:0.0000} seconds ",
(DateTime.Now - st).TotalMilliseconds / 1000)
If args.Length > 1 OrElse d <= 1000 Then
Dim s As String = pi.ToString()
Console.WriteLine("{0}.{1}", s(0), s.Substring(1))
End If
If Diagnostics.Debugger.IsAttached Then Console.ReadKey()
End Sub
End Module
|
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)
| #BASIC256 | BASIC256 | # numeric array
dim numbers(10)
for t = 0 to 9
numbers[t] = t + 1
next t
# string array
dim words$(10)
# assigning an array with a list
words$ = {"one","two","three","four","five","six","seven","eight","nine","ten"}
gosub display
# resize arrays (always preserves values if larger)
redim numbers(11)
redim words$(11)
numbers[10] = 11
words$[10] = "eleven"
gosub display
end
display:
# display arrays
# using ? to get size of array
for t = 0 to numbers[?]-1
print numbers[t] + "=" + words$[t]
next t
return |
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.
| #EchoLisp | EchoLisp |
(define a 42+666i) → a
(define b 1+i) → b
(- a) → -42-666i ; negate
(+ a b) → 43+667i ; add
(* a b) → -624+708i ; multiply
(/ b) → 0.5-0.5i ; invert
(conjugate b) → 1-i
(angle b) → 0.7853981633974483 ; = PI/4
(magnitude b) → 1.4142135623730951 ; = sqrt(2)
(exp (* I PI)) → -1+0i ; Euler = e^(I*PI) = -1
|
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
| #Factor | Factor | USING: generalizations io kernel math math.functions
math.primes.factors math.ranges prettyprint sequences ;
IN: rosetta-code.arithmetic-rational
2/5 ! literal syntax 2/5
2/4 ! automatically simplifies to 1/2
5/1 ! automatically coerced to 5
26/5 ! mixed fraction 5+1/5
13/178 >fraction ! get the numerator and denominator 13 178
8 recip ! get the reciprocal 1/8
! ratios can be any size
12417829731289312/61237812937138912735712
8 ndrop ! clear the stack
! arithmetic works the same as any other number.
: perfect? ( n -- ? )
divisors rest [ recip ] map-sum 1 = ;
"Perfect numbers <= 2^19: " print
2 19 ^ [1,b] [ perfect? ] filter . |
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
| #Fortran | Fortran | function agm(a,b)
implicit none
double precision agm,a,b,eps,c
parameter(eps=1.0d-15)
10 c=0.5d0*(a+b)
b=sqrt(a*b)
a=c
if(a-b.gt.eps*a) go to 10
agm=0.5d0*(a+b)
end
program test
implicit none
double precision agm
print*,agm(1.0d0,1.0d0/sqrt(2.0d0))
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
| #FreeBASIC | FreeBASIC | ' version 16-09-2015
' compile with: fbc -s console
Function agm(a As Double, g As Double) As Double
Dim As Double t_a
Do
t_a = (a + g) / 2
g = Sqr(a * g)
Swap a, t_a
Loop Until a = t_a
Return a
End Function
' ------=< MAIN >=------
Print agm(1, 1 / Sqr(2) )
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End |
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.
| #Wart | Wart | a <- (read)
b <- (read)
prn "sum: " a+b
prn "difference: " a-b
prn "product: " a*b
prn "quotient: " a/b
prn "integer quotient: " (int a/b)
prn "remainder: " a%b
prn "exponent: " a^b |
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.
| #Wren | Wren | import "io" for Stdin, Stdout
System.write("first number: ")
Stdout.flush()
var a = Num.fromString(Stdin.readLine())
System.write("second number: ")
Stdout.flush()
var b = Num.fromString(Stdin.readLine())
System.print("sum: %(a + b)")
System.print("difference: %(a - b)")
System.print("product: %(a * b)")
System.print("integer quotient: %((a / b).floor)")
System.print("remainder: %(a % b)")
System.print("exponentiation: %(a.pow(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.
| #Clojure | Clojure | (def precedence '{* 0, / 0
+ 1, - 1})
(defn order-ops
"((A x B) y C) or (A x (B y C)) depending on precedence of x and y"
[[A x B y C & more]]
(let [ret (if (<= (precedence x)
(precedence y))
(list (list A x B) y C)
(list A x (list B y C)))]
(if more
(recur (concat ret more))
ret)))
(defn add-parens
"Tree walk to add parens. All lists are length 3 afterwards."
[s]
(clojure.walk/postwalk
#(if (seq? %)
(let [c (count %)]
(cond (even? c) (throw (Exception. "Must be an odd number of forms"))
(= c 1) (first %)
(= c 3) %
(>= c 5) (order-ops %)))
%)
s))
(defn make-ast
"Parse a string into a list of numbers, ops, and lists"
[s]
(-> (format "'(%s)" s)
(.replaceAll , "([*+-/])" " $1 ")
load-string
add-parens))
(def ops {'* *
'+ +
'- -
'/ /})
(def eval-ast
(partial clojure.walk/postwalk
#(if (seq? %)
(let [[a o b] %]
((ops o) a b))
%)))
(defn evaluate [s]
"Parse and evaluate an infix arithmetic expression"
(eval-ast (make-ast s)))
user> (evaluate "1 + 2*(3 - 2*(3 - 2)*((2 - 4)*5 - 22/(7 + 2*(3 - 1)) - 1)) + 1")
60 |
http://rosettacode.org/wiki/100_doors | 100 doors | There are 100 doors in a row that are all initially closed.
You make 100 passes by the doors.
The first time through, visit every door and toggle the door (if the door is closed, open it; if it is open, close it).
The second time, only visit every 2nd door (door #2, #4, #6, ...), and toggle it.
The third time, visit every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door.
Task
Answer the question: what state are the doors in after the last pass? Which are open, which are closed?
Alternate:
As noted in this page's discussion page, the only doors that remain open are those whose numbers are perfect squares.
Opening only those doors is an optimization that may also be expressed;
however, as should be obvious, this defeats the intent of comparing implementations across programming languages.
| #Action.21 | Action! | DEFINE COUNT="100"
PROC Main()
BYTE ARRAY doors(COUNT+1)
BYTE door,pass
FOR door=1 TO COUNT
DO
doors(door)=0
OD
PrintE("Following doors are open:")
FOR pass=1 TO COUNT
DO
FOR door=pass TO COUNT STEP pass
DO
doors(door)==!$FF
OD
IF doors(pass)=$FF THEN
PrintB(pass) Put(32)
FI
OD
RETURN |
http://rosettacode.org/wiki/Arithmetic-geometric_mean/Calculate_Pi | Arithmetic-geometric mean/Calculate Pi | Almkvist Berndt 1988 begins with an investigation of why the agm is such an efficient algorithm, and proves that it converges quadratically. This is an efficient method to calculate
π
{\displaystyle \pi }
.
With the same notations used in Arithmetic-geometric mean, we can summarize the paper by writing:
π
=
4
a
g
m
(
1
,
1
/
2
)
2
1
−
∑
n
=
1
∞
2
n
+
1
(
a
n
2
−
g
n
2
)
{\displaystyle \pi ={\frac {4\;\mathrm {agm} (1,1/{\sqrt {2}})^{2}}{1-\sum \limits _{n=1}^{\infty }2^{n+1}(a_{n}^{2}-g_{n}^{2})}}}
This allows you to make the approximation, for any large N:
π
≈
4
a
N
2
1
−
∑
k
=
1
N
2
k
+
1
(
a
k
2
−
g
k
2
)
{\displaystyle \pi \approx {\frac {4\;a_{N}^{2}}{1-\sum \limits _{k=1}^{N}2^{k+1}(a_{k}^{2}-g_{k}^{2})}}}
The purpose of this task is to demonstrate how to use this approximation in order to compute a large number of decimals of
π
{\displaystyle \pi }
.
| #Wren | Wren | import "/big" for BigRat
var digits = 500
var an = BigRat.one
var bn = BigRat.half.sqrt(digits)
var tn = BigRat.half.square
var pn = BigRat.one
while (pn <= digits) {
var prevAn = an
an = (bn + an) * BigRat.half
bn = (bn * prevAn).sqrt(digits)
prevAn = prevAn - an
tn = tn - (prevAn.square * pn)
pn = pn + pn
}
var pi = (an + bn).square / (tn * 4)
System.print(pi.toDecimal(digits, false)) |
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)
| #Batch_File | Batch File | ::arrays.cmd
@echo off
setlocal ENABLEDELAYEDEXPANSION
set array.1=1
set array.2=2
set array.3=3
set array.4=4
for /L %%i in (1,1,4) do call :showit array.%%i !array.%%i!
set c=-27
call :mkarray marry 5 6 7 8
for /L %%i in (-27,1,-24) do call :showit "marry^&%%i" !marry^&%%i!
endlocal
goto :eof
:mkarray
set %1^&%c%=%2
set /a c += 1
shift /2
if "%2" neq "" goto :mkarray
goto :eof
:showit
echo %1 = %2
goto :eof
|
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.
| #Elixir | Elixir | defmodule Complex do
import Kernel, except: [abs: 1, div: 2]
defstruct real: 0, imag: 0
def new(real, imag) do
%__MODULE__{real: real, imag: imag}
end
def add(a, b) do
{a, b} = convert(a, b)
new(a.real + b.real, a.imag + b.imag)
end
def sub(a, b) do
{a, b} = convert(a, b)
new(a.real - b.real, a.imag - b.imag)
end
def mul(a, b) do
{a, b} = convert(a, b)
new(a.real*b.real - a.imag*b.imag, a.imag*b.real + a.real*b.imag)
end
def div(a, b) do
{a, b} = convert(a, b)
divisor = abs2(b)
new((a.real*b.real + a.imag*b.imag) / divisor,
(a.imag*b.real - a.real*b.imag) / divisor)
end
def neg(a) do
a = convert(a)
new(-a.real, -a.imag)
end
def inv(a) do
a = convert(a)
divisor = abs2(a)
new(a.real / divisor, -a.imag / divisor)
end
def conj(a) do
a = convert(a)
new(a.real, -a.imag)
end
def abs(a) do
:math.sqrt(abs2(a))
end
defp abs2(a) do
a = convert(a)
a.real*a.real + a.imag*a.imag
end
defp convert(a) when is_number(a), do: new(a, 0)
defp convert(%__MODULE__{} = a), do: a
defp convert(a, b), do: {convert(a), convert(b)}
def task do
a = new(1, 3)
b = new(5, 2)
IO.puts "a = #{a}"
IO.puts "b = #{b}"
IO.puts "add(a,b): #{add(a, b)}"
IO.puts "sub(a,b): #{sub(a, b)}"
IO.puts "mul(a,b): #{mul(a, b)}"
IO.puts "div(a,b): #{div(a, b)}"
IO.puts "div(b,a): #{div(b, a)}"
IO.puts "neg(a) : #{neg(a)}"
IO.puts "inv(a) : #{inv(a)}"
IO.puts "conj(a) : #{conj(a)}"
end
end
defimpl String.Chars, for: Complex do
def to_string(%Complex{real: real, imag: imag}) do
if imag >= 0, do: "#{real}+#{imag}j",
else: "#{real}#{imag}j"
end
end
Complex.task |
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.
| #Erlang | Erlang | %% Task: Complex Arithmetic
%% Author: Abhay Jain
-module(complex_number).
-export([calculate/0]).
-record(complex, {real, img}).
calculate() ->
A = #complex{real=1, img=3},
B = #complex{real=5, img=2},
Sum = add (A, B),
print (Sum),
Product = multiply (A, B),
print (Product),
Negation = negation (A),
print (Negation),
Inversion = inverse (A),
print (Inversion),
Conjugate = conjugate (A),
print (Conjugate).
add (A, B) ->
RealPart = A#complex.real + B#complex.real,
ImgPart = A#complex.img + B#complex.img,
#complex{real=RealPart, img=ImgPart}.
multiply (A, B) ->
RealPart = (A#complex.real * B#complex.real) - (A#complex.img * B#complex.img),
ImgPart = (A#complex.real * B#complex.img) + (B#complex.real * A#complex.img),
#complex{real=RealPart, img=ImgPart}.
negation (A) ->
#complex{real=-A#complex.real, img=-A#complex.img}.
inverse (A) ->
C = conjugate (A),
Mod = (A#complex.real * A#complex.real) + (A#complex.img * A#complex.img),
RealPart = C#complex.real / Mod,
ImgPart = C#complex.img / Mod,
#complex{real=RealPart, img=ImgPart}.
conjugate (A) ->
RealPart = A#complex.real,
ImgPart = -A#complex.img,
#complex{real=RealPart, img=ImgPart}.
print (A) ->
if A#complex.img < 0 ->
io:format("Ans = ~p~pi~n", [A#complex.real, A#complex.img]);
true ->
io:format("Ans = ~p+~pi~n", [A#complex.real, A#complex.img])
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
| #Fermat | Fermat |
for n=2 to 2^19 by 2 do
s:=3/n;
m:=1;
while m<=n/3 do
if Divides(m,n) then s:=s+1/m; fi;
m:=m+1;
od;
if s=2 then !!n fi;
od; |
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
| #Futhark | Futhark |
import "futlib/math"
fun agm(a: f64, g: f64): f64 =
let eps = 1.0E-16
loop ((a,g)) = while f64.abs(a-g) > eps do
((a+g) / 2.0,
f64.sqrt (a*g))
in a
fun main(x: f64, y: f64): f64 =
agm(x,y)
|
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
| #Go | Go | package main
import (
"fmt"
"math"
)
const ε = 1e-14
func agm(a, g float64) float64 {
for math.Abs(a-g) > math.Abs(a)*ε {
a, g = (a+g)*.5, math.Sqrt(a*g)
}
return a
}
func main() {
fmt.Println(agm(1, 1/math.Sqrt2))
} |
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.
| #x86_Assembly | x86 Assembly | arithm: mov cx, a
mov bx, b
xor dx, dx
mov ax, cx
add ax, bx
mov sum, ax
mov ax, cx
imul bx
mov product, ax
mov ax, cx
sub ax, bx
mov difference, ax
mov ax, cx
idiv bx
mov quotient, ax
mov remainder, dx
ret |
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.
| #Common_Lisp | Common Lisp | (defun tokenize-stream (stream)
(labels ((whitespace-p (char)
(find char #(#\space #\newline #\return #\tab)))
(consume-whitespace ()
(loop while (whitespace-p (peek-char nil stream nil #\a))
do (read-char stream)))
(read-integer ()
(loop while (digit-char-p (peek-char nil stream nil #\space))
collect (read-char stream) into digits
finally (return (parse-integer (coerce digits 'string))))))
(consume-whitespace)
(let* ((c (peek-char nil stream nil nil)))
(token (case c
(nil nil)
(#\( :lparen)
(#\) :rparen)
(#\* '*)
(#\/ '/)
(#\+ '+)
(#\- '-)
(otherwise
(unless (digit-char-p c)
(cerror "Skip it." "Unexpected character ~w." c)
(read-char stream)
(return-from tokenize-stream
(tokenize-stream stream)))
(read-integer)))))
(unless (or (null token) (integerp token))
(read-char stream))
token)))
(defun group-parentheses (tokens &optional (delimited nil))
(do ((new-tokens '()))
((endp tokens)
(when delimited
(cerror "Insert it." "Expected right parenthesis."))
(values (nreverse new-tokens) '()))
(let ((token (pop tokens)))
(case token
(:lparen
(multiple-value-bind (group remaining-tokens)
(group-parentheses tokens t)
(setf new-tokens (cons group new-tokens)
tokens remaining-tokens)))
(:rparen
(if (not delimited)
(cerror "Ignore it." "Unexpected right parenthesis.")
(return (values (nreverse new-tokens) tokens))))
(otherwise
(push token new-tokens))))))
(defun group-operations (expression)
(flet ((gop (exp) (group-operations exp)))
(if (integerp expression)
expression
(destructuring-bind (a &optional op1 b op2 c &rest others)
expression
(unless (member op1 '(+ - * / nil))
(error "syntax error: in expr ~a expecting operator, not ~a"
expression op1))
(unless (member op2 '(+ - * / nil))
(error "syntax error: in expr ~a expecting operator, not ~a"
expression op2))
(cond
((not op1) (gop a))
((not op2) `(,(gop a) ,op1 ,(gop b)))
(t (let ((a (gop a)) (b (gop b)) (c (gop c)))
(if (and (member op1 '(+ -)) (member op2 '(* /)))
(gop `(,a ,op1 (,b ,op2 ,c) ,@others))
(gop `((,a ,op1 ,b) ,op2 ,c ,@others))))))))))
(defun infix-to-prefix (expression)
(if (integerp expression)
expression
(destructuring-bind (a op b) expression
`(,op ,(infix-to-prefix a) ,(infix-to-prefix b)))))
(defun evaluate (string)
(with-input-from-string (in string)
(eval
(infix-to-prefix
(group-operations
(group-parentheses
(loop for token = (tokenize-stream in)
until (null token)
collect token))))))) |
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.
| #Action.21 | Action! | INT ARRAY SinTab=[
0 4 9 13 18 22 27 31 36 40 44 49 53 58 62 66 71 75 79 83
88 92 96 100 104 108 112 116 120 124 128 132 136 139 143
147 150 154 158 161 165 168 171 175 178 181 184 187 190
193 196 199 202 204 207 210 212 215 217 219 222 224 226
228 230 232 234 236 237 239 241 242 243 245 246 247 248
249 250 251 252 253 254 254 255 255 255 256 256 256 256]
INT FUNC Sin(INT a)
WHILE a<0 DO a==+360 OD
WHILE a>360 DO a==-360 OD
IF a<=90 THEN
RETURN (SinTab(a))
ELSEIF a<=180 THEN
RETURN (SinTab(180-a))
ELSEIF a<=270 THEN
RETURN (-SinTab(a-180))
ELSE
RETURN (-SinTab(360-a))
FI
RETURN (0)
INT FUNC Cos(INT a)
RETURN (Sin(a-90))
PROC DrawSpiral(INT x0,y0)
INT angle,radius,x,y
Plot(x0,y0)
FOR angle=0 TO 1800 STEP 5
DO
radius=angle/20
x=radius*Cos(angle)/256+x0
y=radius*Sin(angle)/256+y0
DrawTo(x,y)
OD
RETURN
PROC Main()
BYTE CH=$02FC,COLOR1=$02C5,COLOR2=$02C6
Graphics(8+16)
Color=1
COLOR1=$0C
COLOR2=$02
DrawSpiral(160,96)
DO UNTIL CH#$FF OD
CH=$FF
RETURN |
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.
| #ActionScript | ActionScript | package {
import flash.display.Sprite;
public class Doors extends Sprite {
public function Doors() {
// Initialize the array
var doors:Array = new Array(100);
for (var i:Number = 0; i < 100; i++) {
doors[i] = false;
// Do the work
for (var pass:Number = 0; pass < 100; pass++) {
for (var j:Number = pass; j < 100; j += (pass+1)) {
doors[j] = !doors[j];
}
}
trace(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)
| #BBC_BASIC | BBC BASIC | REM Declare arrays, dimension is maximum index:
DIM array(6), array%(6), array$(6)
REM Entire arrays may be assigned in one statement:
array() = 0.1, 1.2, 2.3, 3.4, 4.5, 5.6, 6.7
array%() = 0, 1, 2, 3, 4, 5, 6
array$() = "Zero", "One", "Two", "Three", "Four", "Five", "Six"
REM Or individual elements may be assigned:
array(2) = PI
array%(3) = RND
array$(4) = "Hello world!"
REM Print out sample array elements:
PRINT array(2) TAB(16) array(3) TAB(32) array(4)
PRINT array%(2) TAB(16) array%(3) TAB(32) array%(4)
PRINT array$(2) TAB(16) array$(3) TAB(32) array$(4) |
http://rosettacode.org/wiki/Arithmetic/Complex | Arithmetic/Complex | A complex number is a number which can be written as:
a
+
b
×
i
{\displaystyle a+b\times i}
(sometimes shown as:
b
+
a
×
i
{\displaystyle b+a\times i}
where
a
{\displaystyle a}
and
b
{\displaystyle b}
are real numbers, and
i
{\displaystyle i}
is √ -1
Typically, complex numbers are represented as a pair of real numbers called the "imaginary part" and "real part", where the imaginary part is the number to be multiplied by
i
{\displaystyle i}
.
Task
Show addition, multiplication, negation, and inversion of complex numbers in separate functions. (Subtraction and division operations can be made with pairs of these operations.)
Print the results for each operation tested.
Optional: Show complex conjugation.
By definition, the complex conjugate of
a
+
b
i
{\displaystyle a+bi}
is
a
−
b
i
{\displaystyle a-bi}
Some languages have complex number libraries available. If your language does, show the operations. If your language does not, also show the definition of this type.
| #ERRE | ERRE |
PROGRAM COMPLEX_ARITH
TYPE COMPLEX=(REAL#,IMAG#)
DIM X:COMPLEX,Y:COMPLEX,Z:COMPLEX
!
! complex arithmetic routines
!
DIM A:COMPLEX,B:COMPLEX,C:COMPLEX
PROCEDURE ADD(A.,B.->C.)
C.REAL#=A.REAL#+B.REAL#
C.IMAG#=A.IMAG#+B.IMAG#
END PROCEDURE
PROCEDURE INV(A.->B.)
LOCAL DENOM#
DENOM#=A.REAL#^2+A.IMAG#^2
B.REAL#=A.REAL#/DENOM#
B.IMAG#=-A.IMAG#/DENOM#
END PROCEDURE
PROCEDURE MULT(A.,B.->C.)
C.REAL#=A.REAL#*B.REAL#-A.IMAG#*B.IMAG#
C.IMAG#=A.REAL#*B.IMAG#+A.IMAG#*B.REAL#
END PROCEDURE
PROCEDURE NEG(A.->B.)
B.REAL#=-A.REAL#
B.IMAG#=-A.IMAG#
END PROCEDURE
BEGIN
PRINT(CHR$(12);) !CLS
X.REAL#=1
X.IMAG#=1
Y.REAL#=2
Y.IMAG#=2
ADD(X.,Y.->Z.)
PRINT(Z.REAL#;" + ";Z.IMAG#;"i")
MULT(X.,Y.->Z.)
PRINT(Z.REAL#;" + ";Z.IMAG#;"i")
INV(X.->Z.)
PRINT(Z.REAL#;" + ";Z.IMAG#;"i")
NEG(X.->Z.)
PRINT(Z.REAL#;" + ";Z.IMAG#;"i")
END PROGRAM
|
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.
| #Euler_Math_Toolbox | Euler Math Toolbox |
>a=1+4i; b=5-3i;
>a+b
6+1i
>a-b
-4+7i
>a*b
17+17i
>a/b
-0.205882352941+0.676470588235i
>fraction a/b
-7/34+23/34i
>conj(a)
1-4i
|
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
| #Forth | Forth | \ Rationals can use any double cell operations: 2!, 2@, 2dup, 2swap, etc.
\ Uses the stack convention of the built-in "*/" for int * frac -> int
: numerator drop ;
: denominator nip ;
: s>rat 1 ; \ integer to rational (n/1)
: rat>s / ; \ integer
: rat>frac mod ; \ fractional part
: rat>float swap s>f s>f f/ ;
: rat. swap 1 .r [char] / emit . ;
\ normalize: factors out gcd and puts sign into numerator
: gcd ( a b -- gcd ) begin ?dup while tuck mod repeat ;
: rat-normalize ( rat -- rat ) 2dup gcd tuck / >r / r> ;
: rat-abs swap abs swap ;
: rat-negate swap negate swap ;
: 1/rat over 0< if negate swap negate else swap then ;
: rat+ ( a b c d -- ad+bc bd )
rot 2dup * >r
rot * >r * r> +
r> rat-normalize ;
: rat- rat-negate rat+ ;
: rat* ( a b c d -- ac bd )
rot * >r * r> rat-normalize ;
: rat/ swap rat* ;
: rat-equal d= ;
: rat-less ( a b c d -- ad<bc )
-rot * >r * r> < ;
: rat-more 2swap rat-less ;
: rat-inc tuck + swap ;
: rat-dec tuck - swap ; |
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
| #Groovy | Groovy | double agm (double a, double g) {
double an = a, gn = g
while ((an-gn).abs() >= 10.0**-14) { (an, gn) = [(an+gn)*0.5, (an*gn)**0.5] }
an
} |
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
| #Haskell | Haskell | -- Return an approximation to the arithmetic-geometric mean of two numbers.
-- The result is considered accurate when two successive approximations are
-- sufficiently close, as determined by "eq".
agm :: (Floating a) => a -> a -> ((a, a) -> Bool) -> a
agm a g eq = snd $ until eq step (a, g)
where
step (a, g) = ((a + g) / 2, sqrt (a * g))
-- Return the relative difference of the pair. We assume that at least one of
-- the values is far enough from 0 to not cause problems.
relDiff :: (Fractional a) => (a, a) -> a
relDiff (x, y) =
let n = abs (x - y)
d = (abs x + abs y) / 2
in n / d
main :: IO ()
main = do
let equal = (< 0.000000001) . relDiff
print $ agm 1 (1 / sqrt 2) equal |
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.
| #XLISP | XLISP | (DEFUN INTEGER-ARITHMETIC ()
(DISPLAY "Enter two integers separated by a space.")
(NEWLINE)
(DISPLAY "> ")
(DEFINE A (READ))
(DEFINE B (READ))
(DISPLAY `(SUM ,(+ A B)))
(NEWLINE)
(DISPLAY `(DIFFERENCE ,(- A B)))
(NEWLINE)
(DISPLAY `(PRODUCT ,(* A B)))
(NEWLINE)
(DISPLAY `(QUOTIENT ,(QUOTIENT A B))) ; truncates towards zero
(NEWLINE)
(DISPLAY `(REMAINDER ,(REM A B))) ; takes sign of first operand
(NEWLINE)
(DISPLAY `(EXPONENTIATION ,(EXPT A B)))) |
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.
| #XPL0 | XPL0 | include c:\cxpl\codes;
int A, B;
[A:= IntIn(0);
B:= IntIn(0);
IntOut(0, A+B); CrLf(0);
IntOut(0, A-B); CrLf(0);
IntOut(0, A*B); CrLf(0);
IntOut(0, A/B); CrLf(0); \truncates toward zero
IntOut(0, rem(0)); CrLf(0); \remainder's sign matches first operand (A)
] |
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.
| #D | D | import std.stdio, std.string, std.ascii, std.conv, std.array,
std.exception, std.traits;
struct Stack(T) {
T[] data;
alias data this;
void push(T top) pure nothrow @safe { data ~= top; }
T pop(bool discard = true)() pure @nogc @safe {
immutable static exc = new immutable(Exception)("Stack Empty");
if (data.empty)
throw exc;
auto top = data[$ - 1];
static if (discard)
data.popBack;
return top;
}
}
enum Type { Num, OBkt, CBkt, Add, Sub, Mul, Div }
immutable opChar = ["#", "(", ")", "+", "-", "*", "/"];
immutable opPrec = [ 0, -9, -9, 1, 1, 2, 2];
abstract class Visitor { void visit(XP e) pure @safe; }
final class XP {
immutable Type type;
immutable string str;
immutable int pos; // Optional, to display AST struct.
XP LHS, RHS;
this(string s=")", int p = -1) pure nothrow @safe {
str = s;
pos = p;
auto localType = Type.Num;
foreach_reverse (immutable t; [EnumMembers!Type[1 .. $]])
if (opChar[t] == s)
localType = t;
this.type = localType;
}
override int opCmp(Object other) pure @safe {
auto rhs = cast(XP)other;
enforce(rhs !is null);
return opPrec[type] - opPrec[rhs.type];
}
void accept(Visitor v) pure @safe { v.visit(this); }
}
final class AST {
XP root;
Stack!XP opr, num;
string xpr, token;
int xpHead, xpTail;
void joinXP(XP x) pure @safe {
x.RHS = num.pop;
x.LHS = num.pop;
num.push(x);
}
string nextToken() pure @safe {
while (xpHead < xpr.length && xpr[xpHead] == ' ')
xpHead++; // Skip spc.
xpTail = xpHead;
if (xpHead < xpr.length) {
token = xpr[xpTail .. xpTail + 1];
switch (token) {
case "(", ")", "+", "-", "*", "/": // Valid non-number.
xpTail++;
return token;
default: // Should be number.
if (token[0].isDigit) {
while (xpTail < xpr.length && xpr[xpTail].isDigit())
xpTail++;
return xpr[xpHead .. xpTail];
} // Else may be error.
} // End switch.
}
if (xpTail < xpr.length)
throw new Exception("Invalid Char <" ~ xpr[xpTail] ~ ">");
return null;
} // End nextToken.
AST parse(in string s) /*@safe*/ {
bool expectingOP;
xpr = s;
try {
xpHead = xpTail = 0;
num = opr = null;
root = null;
opr.push(new XP); // CBkt, prevent evaluate null OP precedence.
while ((token = nextToken) !is null) {
XP tokenXP = new XP(token, xpHead);
if (expectingOP) { // Process OP-alike XP.
switch (token) {
case ")":
while (opr.pop!false.type != Type.OBkt)
joinXP(opr.pop);
opr.pop;
expectingOP = true;
break;
case "+", "-", "*", "/":
while (tokenXP <= opr.pop!false)
joinXP(opr.pop());
opr.push(tokenXP);
expectingOP = false;
break;
default:
throw new Exception("Expecting Operator or ), not <"
~ token ~ ">");
}
} else { // Process Num-alike XP.
switch (token) {
case "+", "-", "*", "/", ")":
throw new Exception("Expecting Number or (, not <"
~ token ~ ">");
case "(":
opr.push(tokenXP);
expectingOP = false;
break;
default: // Number.
num.push(tokenXP);
expectingOP = true;
}
}
xpHead = xpTail;
} // End while.
while (opr.length > 1) // Join pending Op.
joinXP(opr.pop);
} catch(Exception e) {
writefln("%s\n%s\n%s^", e.msg, xpr, " ".replicate(xpHead));
root = null;
return this;
}
if (num.length != 1) { // Should be one XP left.
"Parse Error...".writefln;
root = null;
} else {
root = num.pop;
}
return this;
} // End Parse.
} // End class AST.
// To display AST fancy struct.
void ins(ref char[][] s, in string v, in int p, in int l)
pure nothrow @safe {
if (l + 1 > s.length)
s.length++;
while (s[l].length < p + v.length + 1)
s[l] ~= " ";
s[l][p .. p + v.length] = v[];
}
final class CalcVis : Visitor {
int result, level;
string resultStr;
char[][] Tree;
static void opCall(AST a) @safe {
if (a && a.root) {
auto c = new CalcVis;
a.root.accept(c);
foreach (immutable i; 1 .. c.Tree.length) { // More fancy.
bool flipflop = false;
enum char mk = '.';
foreach (immutable j; 0 .. c.Tree[i].length) {
while (j >= c.Tree[i - 1].length)
c.Tree[i - 1] ~= " ";
immutable c1 = c.Tree[i][j];
immutable c2 = c.Tree[i - 1][j];
if (flipflop && (c1 == ' ') && c2 == ' ')
c.Tree[i - 1][j] = mk;
if (c1 != mk && c1 != ' ' &&
(j == 0 || !isDigit(c.Tree[i][j - 1])))
flipflop = !flipflop;
}
}
foreach (const t; c.Tree)
t.writefln;
writefln("\n%s ==>\n%s = %s", a.xpr, c.resultStr, c.result);
} else
"Evalute invalid or null Expression.".writefln;
}
// Calc. the value, display AST struct and eval order.
override void visit(XP xp) @safe {
ins(Tree, xp.str, xp.pos, level);
level++;
if (xp.type == Type.Num) {
resultStr ~= xp.str;
result = xp.str.to!int;
} else {
resultStr ~= "(";
xp.LHS.accept(this);
immutable int lhs = result;
resultStr ~= opChar[xp.type];
xp.RHS.accept(this);
resultStr ~= ")";
switch (xp.type) {
case Type.Add: result = lhs + result; break;
case Type.Sub: result = lhs - result; break;
case Type.Mul: result = lhs * result; break;
case Type.Div: result = lhs / result; break;
default: throw new Exception("Invalid type");
}
}
level--;
}
}
void main(string[] args) /*@safe*/ {
immutable exp0 = "1 + 2*(3 - 2*(3 - 2)*((2 - 4)*5" ~
" - 22/(7 + 2*(3 - 1)) - 1)) + 1";
immutable exp = (args.length > 1) ? args[1 .. $].join(' ') : exp0;
new AST().parse(exp).CalcVis; // Should be 60.
} |
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.
| #Ada | Ada | with Ada.Numerics.Elementary_Functions;
with SDL.Video.Windows.Makers;
with SDL.Video.Renderers.Makers;
with SDL.Events.Events;
procedure Archimedean_Spiral is
Width : constant := 800;
Height : constant := 800;
A : constant := 4.2;
B : constant := 3.2;
T_First : constant := 4.0;
T_Last : constant := 100.0;
Window : SDL.Video.Windows.Window;
Renderer : SDL.Video.Renderers.Renderer;
Event : SDL.Events.Events.Events;
procedure Draw_Archimedean_Spiral is
use type SDL.C.int;
use Ada.Numerics.Elementary_Functions;
Pi : constant := Ada.Numerics.Pi;
Step : constant := 0.002;
T : Float;
R : Float;
begin
T := T_First;
loop
R := A + B * T;
Renderer.Draw
(Point => (X => Width / 2 + SDL.C.int (R * Cos (T, 2.0 * Pi)),
Y => Height / 2 - SDL.C.int (R * Sin (T, 2.0 * Pi))));
exit when T >= T_Last;
T := T + Step;
end loop;
end Draw_Archimedean_Spiral;
procedure Wait is
use type SDL.Events.Event_Types;
begin
loop
while SDL.Events.Events.Poll (Event) loop
if Event.Common.Event_Type = SDL.Events.Quit then
return;
end if;
end loop;
end loop;
end Wait;
begin
if not SDL.Initialise (Flags => SDL.Enable_Screen) then
return;
end if;
SDL.Video.Windows.Makers.Create (Win => Window,
Title => "Archimedean spiral",
Position => SDL.Natural_Coordinates'(X => 10, Y => 10),
Size => SDL.Positive_Sizes'(Width, Height),
Flags => 0);
SDL.Video.Renderers.Makers.Create (Renderer, Window.Get_Surface);
Renderer.Set_Draw_Colour ((0, 0, 0, 255));
Renderer.Fill (Rectangle => (0, 0, Width, Height));
Renderer.Set_Draw_Colour ((0, 220, 0, 255));
Draw_Archimedean_Spiral;
Window.Update_Surface;
Wait;
Window.Finalize;
SDL.Finalise;
end 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.
| #Acurity_Architect | Acurity Architect | Using #HASH-OFF, OPTION OICC ="^" , CICC ="^"
|
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)
| #bc | bc | /* Put the value 42 into array g at index 3 */
g[3] = 42
/* Look at some other elements in g */
g[2]
0
g[4342]
0
/* Look at the elements of another array */
a[543]
0
/* Array names don't conflict with names of ordinary (scalar) identifiers */
g
0
g = 123
g
123
g[3]
42 |
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.
| #Euphoria | Euphoria | constant REAL = 1, IMAG = 2
type complex(sequence s)
return length(s) = 2 and atom(s[REAL]) and atom(s[IMAG])
end type
function add(complex a, complex b)
return a + b
end function
function mult(complex a, complex b)
return {a[REAL] * b[REAL] - a[IMAG] * b[IMAG],
a[REAL] * b[IMAG] + a[IMAG] * b[REAL]}
end function
function inv(complex a)
atom denom
denom = a[REAL] * a[REAL] + a[IMAG] * a[IMAG]
return {a[REAL] / denom, -a[IMAG] / denom}
end function
function neg(complex a)
return -a
end function
function scomplex(complex a)
sequence s
if a[REAL] != 0 then
s = sprintf("%g",a)
else
s = {}
end if
if a[IMAG] != 0 then
if a[IMAG] = 1 then
s &= "+i"
elsif a[IMAG] = -1 then
s &= "-i"
else
s &= sprintf("%+gi",a[IMAG])
end if
end if
if length(s) = 0 then
return "0"
else
return s
end if
end function
complex a, b
a = { 1.0, 1.0 }
b = { 3.14159, 1.2 }
printf(1,"a = %s\n",{scomplex(a)})
printf(1,"b = %s\n",{scomplex(b)})
printf(1,"a+b = %s\n",{scomplex(add(a,b))})
printf(1,"a*b = %s\n",{scomplex(mult(a,b))})
printf(1,"1/a = %s\n",{scomplex(inv(a))})
printf(1,"-a = %s\n",{scomplex(neg(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
| #Fortran | Fortran | module module_rational
implicit none
private
public :: rational
public :: rational_simplify
public :: assignment (=)
public :: operator (//)
public :: operator (+)
public :: operator (-)
public :: operator (*)
public :: operator (/)
public :: operator (<)
public :: operator (<=)
public :: operator (>)
public :: operator (>=)
public :: operator (==)
public :: operator (/=)
public :: abs
public :: int
public :: modulo
type rational
integer :: numerator
integer :: denominator
end type rational
interface assignment (=)
module procedure assign_rational_int, assign_rational_real
end interface
interface operator (//)
module procedure make_rational
end interface
interface operator (+)
module procedure rational_add
end interface
interface operator (-)
module procedure rational_minus, rational_subtract
end interface
interface operator (*)
module procedure rational_multiply
end interface
interface operator (/)
module procedure rational_divide
end interface
interface operator (<)
module procedure rational_lt
end interface
interface operator (<=)
module procedure rational_le
end interface
interface operator (>)
module procedure rational_gt
end interface
interface operator (>=)
module procedure rational_ge
end interface
interface operator (==)
module procedure rational_eq
end interface
interface operator (/=)
module procedure rational_ne
end interface
interface abs
module procedure rational_abs
end interface
interface int
module procedure rational_int
end interface
interface modulo
module procedure rational_modulo
end interface
contains
recursive function gcd (i, j) result (res)
integer, intent (in) :: i
integer, intent (in) :: j
integer :: res
if (j == 0) then
res = i
else
res = gcd (j, modulo (i, j))
end if
end function gcd
function rational_simplify (r) result (res)
type (rational), intent (in) :: r
type (rational) :: res
integer :: g
g = gcd (r % numerator, r % denominator)
res = r % numerator / g // r % denominator / g
end function rational_simplify
function make_rational (numerator, denominator) result (res)
integer, intent (in) :: numerator
integer, intent (in) :: denominator
type (rational) :: res
res = rational (numerator, denominator)
end function make_rational
subroutine assign_rational_int (res, i)
type (rational), intent (out), volatile :: res
integer, intent (in) :: i
res = i // 1
end subroutine assign_rational_int
subroutine assign_rational_real (res, x)
type (rational), intent(out), volatile :: res
real, intent (in) :: x
integer :: x_floor
real :: x_frac
x_floor = floor (x)
x_frac = x - x_floor
if (x_frac == 0) then
res = x_floor // 1
else
res = (x_floor // 1) + (1 // floor (1 / x_frac))
end if
end subroutine assign_rational_real
function rational_add (r, s) result (res)
type (rational), intent (in) :: r
type (rational), intent (in) :: s
type (rational) :: res
res = r % numerator * s % denominator + r % denominator * s % numerator // &
& r % denominator * s % denominator
end function rational_add
function rational_minus (r) result (res)
type (rational), intent (in) :: r
type (rational) :: res
res = - r % numerator // r % denominator
end function rational_minus
function rational_subtract (r, s) result (res)
type (rational), intent (in) :: r
type (rational), intent (in) :: s
type (rational) :: res
res = r % numerator * s % denominator - r % denominator * s % numerator // &
& r % denominator * s % denominator
end function rational_subtract
function rational_multiply (r, s) result (res)
type (rational), intent (in) :: r
type (rational), intent (in) :: s
type (rational) :: res
res = r % numerator * s % numerator // r % denominator * s % denominator
end function rational_multiply
function rational_divide (r, s) result (res)
type (rational), intent (in) :: r
type (rational), intent (in) :: s
type (rational) :: res
res = r % numerator * s % denominator // r % denominator * s % numerator
end function rational_divide
function rational_lt (r, s) result (res)
type (rational), intent (in) :: r
type (rational), intent (in) :: s
type (rational) :: r_simple
type (rational) :: s_simple
logical :: res
r_simple = rational_simplify (r)
s_simple = rational_simplify (s)
res = r_simple % numerator * s_simple % denominator < &
& s_simple % numerator * r_simple % denominator
end function rational_lt
function rational_le (r, s) result (res)
type (rational), intent (in) :: r
type (rational), intent (in) :: s
type (rational) :: r_simple
type (rational) :: s_simple
logical :: res
r_simple = rational_simplify (r)
s_simple = rational_simplify (s)
res = r_simple % numerator * s_simple % denominator <= &
& s_simple % numerator * r_simple % denominator
end function rational_le
function rational_gt (r, s) result (res)
type (rational), intent (in) :: r
type (rational), intent (in) :: s
type (rational) :: r_simple
type (rational) :: s_simple
logical :: res
r_simple = rational_simplify (r)
s_simple = rational_simplify (s)
res = r_simple % numerator * s_simple % denominator > &
& s_simple % numerator * r_simple % denominator
end function rational_gt
function rational_ge (r, s) result (res)
type (rational), intent (in) :: r
type (rational), intent (in) :: s
type (rational) :: r_simple
type (rational) :: s_simple
logical :: res
r_simple = rational_simplify (r)
s_simple = rational_simplify (s)
res = r_simple % numerator * s_simple % denominator >= &
& s_simple % numerator * r_simple % denominator
end function rational_ge
function rational_eq (r, s) result (res)
type (rational), intent (in) :: r
type (rational), intent (in) :: s
logical :: res
res = r % numerator * s % denominator == s % numerator * r % denominator
end function rational_eq
function rational_ne (r, s) result (res)
type (rational), intent (in) :: r
type (rational), intent (in) :: s
logical :: res
res = r % numerator * s % denominator /= s % numerator * r % denominator
end function rational_ne
function rational_abs (r) result (res)
type (rational), intent (in) :: r
type (rational) :: res
res = sign (r % numerator, r % denominator) // r % denominator
end function rational_abs
function rational_int (r) result (res)
type (rational), intent (in) :: r
integer :: res
res = r % numerator / r % denominator
end function rational_int
function rational_modulo (r) result (res)
type (rational), intent (in) :: r
integer :: res
res = modulo (r % numerator, r % denominator)
end function rational_modulo
end module module_rational |
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
| #Icon_and_Unicon | Icon and Unicon | procedure main(A)
a := real(A[1]) | 1.0
g := real(A[2]) | (1 / 2^0.5)
epsilon := real(A[3])
write("agm(",a,",",g,") = ",agm(a,g,epsilon))
end
procedure agm(an, gn, e)
/e := 1e-15
while abs(an-gn) > e do {
ap := (an+gn)/2.0
gn := (an*gn)^0.5
an := ap
}
return an
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
| #J | J | mean=: +/ % #
(mean , */ %:~ #)^:_] 1,%%:2
0.8472130847939792 0.8472130847939791 |
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.
| #XSLT | XSLT | <xsl:template name="arithmetic">
<xsl:param name="a">5</xsl:param>
<xsl:param name="b">2</xsl:param>
<fo:block>a + b = <xsl:value-of select="$a + $b"/></fo:block>
<fo:block>a - b = <xsl:value-of select="$a - $b"/></fo:block>
<fo:block>a * b = <xsl:value-of select="$a * $b"/></fo:block>
<fo:block>a / b = <xsl:value-of select="round($a div $b)"/></fo:block>
<fo:block>a mod b = <xsl:value-of select="$a mod $b"/></fo:block>
</xsl:template> |
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.
| #Delphi | Delphi | type Expr = Bin(op, Expr left, Expr right) or Literal(Float val)
with Lookup
type Token(val, Char kind) with Lookup
func Token.ToString() => this.val.ToString()
func tokenize(str) {
func isSep(c) =>
c is '+' or '-' or '*' or '/' or ' ' or '\t' or '\n' or '\r' or '(' or ')' or '\0'
var idx = -1
let len = str.Length()
let tokens = []
func next() {
idx += 1
return '\0' when idx >= len
str[idx]
}
while true {
let c = next()
match c {
'\0' => { break },
'+' => tokens.Add(Token(c, '+')),
'-' => tokens.Add(Token(c, '-')),
'*' => tokens.Add(Token(c, '*')),
'/' => tokens.Add(Token(c, '/')),
'(' => tokens.Add(Token(c, '(')),
')' => tokens.Add(Token(c, ')')),
_ => {
let i = idx
while !isSep(next()) { }
idx -= 1
tokens.Add(Token(Float.Parse(str[i..idx]), 'F'))
}
}
}
tokens
}
func parse(tokens) {
var idx = -1
let len = tokens.Length()
let eol = Token(val: nil, kind: 'E')
func pop() {
idx += 1
return eol when idx == len
tokens[idx]
}
func peek() {
let t = pop()
idx -=1
t
}
func expect(kind) {
peek().kind == kind
}
var add_or_sub1
func literal() {
return false when !expect('F')
Expr.Literal(pop().val)
}
func group() {
return false when !expect('(')
pop()
var ret = add_or_sub1()
throw "Invalid group" when !expect(')')
pop()
ret
}
func mul_or_div() {
var fst = group()
fst = literal() when !fst
return fst when !expect('*') && !expect('/')
let op = pop().val
var snd = group()
snd = literal() when !snd
Expr.Bin(op, fst, snd)
}
func add_or_sub() {
let fst = mul_or_div()
return fst when !expect('+') && !expect('-')
let op = pop().val
let snd = mul_or_div()
Expr.Bin(op, fst, snd)
}
add_or_sub1 = add_or_sub
add_or_sub()
}
func exec(ast) {
match ast {
Bin(op, left, right) => {
return exec(left) + exec(right) when op == '+'
return exec(left) - exec(right) when op == '-'
return exec(left) * exec(right) when op == '*'
return exec(left) / exec(right) when op == '/'
},
Literal(value) => value
}
}
func eval(str) {
let tokens = tokenize(str)
let ast = parse(tokens)
exec(ast)
}
print( eval("(1+33.23)*7") )
print( eval("1+33.23*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.
| #ALGOL_W | ALGOL W | begin % draw an Archimedian spiral %
% Translation of AWK which was a trnslation of Applesoft Basic program %
integer procedure max ( integer x, y ) ; begin if x > y then x else y end;
integer procedure min ( integer x, y ) ; begin if x < y then x else y end;
integer x_min, y_min, x_max, y_max, a, b, x, y;
string(255) array arr ( 1 :: 255 );
real h, w, m, s, t;
x_min := y_min := 9999;
x_max := y_max := 0;
h := 96;
w := h + h / 2;
a := 1;
b := 1;
m := 6 * PI;
s := .02;
t := s;
while t <= m do begin % build spiral %
real r;
r := a + b * t;
x := round(r * cos(t) + w);
y := round(r * sin(t) + h);
if x <= 0 or y <= 0 then begin end
else if x >= 280 then begin end
else if y >= 192 then begin end
else begin
arr( x )( y // 1 ) := "*";
x_min := min(x_min,x);
x_max := max(x_max,x);
y_min := min(y_min,y);
y_max := max(y_max,y);
t := t + s
end if__various_x_and_y_values__
end while__t_le_m ;
for i := x_min until x_max do begin
for j := y_min until y_max do begin
string(1) c;
c := arr( i )( j // 1 );
writeon( c, c )
end for_j ;
write()
end for_i
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.
| #APL | APL | 'InitCauseway' 'View' ⎕CY 'sharpplot'
InitCauseway ⍬ ⍝ initialise current namespace
sp←⎕NEW Causeway.SharpPlot
sp.DrawPolarChart {⍵(360|⍵)}⌽⍳720
View sp |
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.
| #AutoHotkey | AutoHotkey | if !pToken := Gdip_Startup()
{
MsgBox, 48, gdiplus error!, Gdiplus failed to start. Please ensure you have gdiplus on your system
ExitApp
}
OnExit, Exit
SysGet, MonitorPrimary, MonitorPrimary
SysGet, WA, MonitorWorkArea, %MonitorPrimary%
WAWidth := WARight-WALeft
WAHeight := WABottom-WATop
Gui, 1: -Caption +E0x80000 +LastFound +AlwaysOnTop +ToolWindow +OwnDialogs
Gui, 1: Show, NA
hwnd1 := WinExist()
hbm := CreateDIBSection(WAWidth, WAHeight)
hdc := CreateCompatibleDC()
obm := SelectObject(hdc, hbm)
G := Gdip_GraphicsFromHDC(hdc)
Gdip_SetSmoothingMode(G, 4)
pPen := Gdip_CreatePen(0xffff0000, 3)
;--------------------------------
a := 1, b := 4, th := 0.1, step := 0.1
loop, 720
{
th += step
r := a + b * th
x1 := r * Cos(th)
y1 := r * Sin(th)
x1 += A_ScreenWidth/2
y1 += A_ScreenHeight/2
if (x2 && y2)
Gdip_DrawLine(G, pPen, x1, y1, x2, y2)
x2 := x1, y2 := y1
if GetKeyState("Esc", "P")
break
; next two lines are optional to watch it draw
; Sleep 10
; UpdateLayeredWindow(hwnd1, hdc, WALeft, WATop, WAWidth, WAHeight)
}
UpdateLayeredWindow(hwnd1, hdc, WALeft, WATop, WAWidth, WAHeight)
;--------------------------------
return
Exit:
Gdip_DeletePen(pPen)
SelectObject(hdc, obm)
DeleteObject(hbm)
DeleteDC(hdc)
Gdip_DeleteGraphics(G)
Gdip_Shutdown(pToken)
ExitApp
Return |
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.
| #Ada | Ada | with Ada.Text_Io; use Ada.Text_Io;
procedure Doors is
type Door_State is (Closed, Open);
type Door_List is array(Positive range 1..100) of Door_State;
The_Doors : Door_List := (others => Closed);
begin
for I in 1..100 loop
for J in The_Doors'range loop
if J mod I = 0 then
if The_Doors(J) = Closed then
The_Doors(J) := Open;
else
The_Doors(J) := Closed;
end if;
end if;
end loop;
end loop;
for I in The_Doors'range loop
Put_Line(Integer'Image(I) & " is " & Door_State'Image(The_Doors(I)));
end loop;
end 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)
| #BML | BML |
% Define an array(containing the numbers 1-3) named arr in the group $
in $ let arr hold 1 2 3
% Replace the value at index 0 in array to "Index 0"
set $arr index 0 to "Index 0"
% Will display "Index 0"
display $arr index 0
% There is no automatic garbage collection
delete $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.
| #Excel | Excel |
=IMSUM(A1;B1)
|
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.
| #F.23 | F# |
> open Microsoft.FSharp.Math;;
> let a = complex 1.0 1.0;;
val a : complex = 1r+1i
> let b = complex 3.14159 1.25;;
val b : complex = 3.14159r+1.25i
> a + b;;
val it : Complex = 4.14159r+2.25i {Conjugate = 4.14159r-2.25i;
ImaginaryPart = 2.25;
Magnitude = 4.713307515;
Phase = 0.497661247;
RealPart = 4.14159;
i = 2.25;
r = 4.14159;}
> a * b;;
val it : Complex = 1.89159r+4.39159i {Conjugate = 1.89159r-4.39159i;
ImaginaryPart = 4.39159;
Magnitude = 4.781649868;
Phase = 1.164082262;
RealPart = 1.89159;
i = 4.39159;
r = 1.89159;}
> a / b;;
val it : Complex =
0.384145932435901r+0.165463215905043i
{Conjugate = 0.384145932435901r-0.165463215905043i;
ImaginaryPart = 0.1654632159;
Magnitude = 0.418265673;
Phase = 0.4067140652;
RealPart = 0.3841459324;
i = 0.1654632159;
r = 0.3841459324;}
> -a;;
val it : complex = -1r-1i {Conjugate = -1r+1i;
ImaginaryPart = -1.0;
Magnitude = 1.414213562;
Phase = -2.35619449;
RealPart = -1.0;
i = -1.0;
r = -1.0;}
|
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
| #Frink | Frink |
1/2 + 2/3
// 7/6 (approx. 1.1666666666666667)
1/2 + 1/2
// 1
5/sextillion + 3/quadrillion
// 600001/200000000000000000000 (exactly 3.000005e-15)
8^(1/3)
// 2 (note the exact integer result.)
|
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
| #Java | Java | /*
* Arithmetic-Geometric Mean of 1 & 1/sqrt(2)
* Brendan Shaklovitz
* 5/29/12
*/
public class ArithmeticGeometricMean {
public static double agm(double a, double g) {
double a1 = a;
double g1 = g;
while (Math.abs(a1 - g1) >= 1.0e-14) {
double arith = (a1 + g1) / 2.0;
double geom = Math.sqrt(a1 * g1);
a1 = arith;
g1 = geom;
}
return a1;
}
public static void main(String[] args) {
System.out.println(agm(1.0, 1.0 / Math.sqrt(2.0)));
}
} |
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.
| #Yabasic | Yabasic | input "ingrese un numero? " a
input "ingrese otro numero? " b
print "suma ", a, " + ", b, " = ", (a + b)
print "resta ", a, " - ", b, " = ", (a - b)
print "producto ", a, " * ", b, " = ", (a * b)
print "division ", a, " \ ", b, " = ", int(a / b)
print "modulo ", a, " % ", b, " = ", mod(a, b)
print "potencia ", a, " ^ ", b, " = ", (a ^ b)
end |
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.
| #Yorick | Yorick | x = y = 0;
read, x, y;
write, "x + y =", x + y;
write, "x - y =", x - y;
write, "x * y =", x * y;
write, "x / y =", x / y; // rounds toward zero
write, "x % y =", x % y; // remainder; matches sign of first operand when operands' signs differ
write, "x ^ y =", x ^ y; // exponentiation |
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.
| #Dyalect | Dyalect | type Expr = Bin(op, Expr left, Expr right) or Literal(Float val)
with Lookup
type Token(val, Char kind) with Lookup
func Token.ToString() => this.val.ToString()
func tokenize(str) {
func isSep(c) =>
c is '+' or '-' or '*' or '/' or ' ' or '\t' or '\n' or '\r' or '(' or ')' or '\0'
var idx = -1
let len = str.Length()
let tokens = []
func next() {
idx += 1
return '\0' when idx >= len
str[idx]
}
while true {
let c = next()
match c {
'\0' => { break },
'+' => tokens.Add(Token(c, '+')),
'-' => tokens.Add(Token(c, '-')),
'*' => tokens.Add(Token(c, '*')),
'/' => tokens.Add(Token(c, '/')),
'(' => tokens.Add(Token(c, '(')),
')' => tokens.Add(Token(c, ')')),
_ => {
let i = idx
while !isSep(next()) { }
idx -= 1
tokens.Add(Token(Float.Parse(str[i..idx]), 'F'))
}
}
}
tokens
}
func parse(tokens) {
var idx = -1
let len = tokens.Length()
let eol = Token(val: nil, kind: 'E')
func pop() {
idx += 1
return eol when idx == len
tokens[idx]
}
func peek() {
let t = pop()
idx -=1
t
}
func expect(kind) {
peek().kind == kind
}
var add_or_sub1
func literal() {
return false when !expect('F')
Expr.Literal(pop().val)
}
func group() {
return false when !expect('(')
pop()
var ret = add_or_sub1()
throw "Invalid group" when !expect(')')
pop()
ret
}
func mul_or_div() {
var fst = group()
fst = literal() when !fst
return fst when !expect('*') && !expect('/')
let op = pop().val
var snd = group()
snd = literal() when !snd
Expr.Bin(op, fst, snd)
}
func add_or_sub() {
let fst = mul_or_div()
return fst when !expect('+') && !expect('-')
let op = pop().val
let snd = mul_or_div()
Expr.Bin(op, fst, snd)
}
add_or_sub1 = add_or_sub
add_or_sub()
}
func exec(ast) {
match ast {
Bin(op, left, right) => {
return exec(left) + exec(right) when op == '+'
return exec(left) - exec(right) when op == '-'
return exec(left) * exec(right) when op == '*'
return exec(left) / exec(right) when op == '/'
},
Literal(value) => value
}
}
func eval(str) {
let tokens = tokenize(str)
let ast = parse(tokens)
exec(ast)
}
print( eval("(1+33.23)*7") )
print( eval("1+33.23*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.
| #AWK | AWK |
# syntax: GAWK -f ARCHIMEDEAN_SPIRAL.AWK
# converted from Applesoft BASIC
BEGIN {
x_min = y_min = 9999
x_max = y_max = 0
h = 96
w = h + h / 2
a = 1
b = 1
m = 6 * 3.1415926
step = .02
for (t=step; t<=m; t+=step) { # build spiral
r = a + b * t
x = int(r * cos(t) + w)
y = int(r * sin(t) + h)
if (x <= 0 || y <= 0) { continue }
if (x >= 280 ) { continue }
if (y >= 192) { continue }
arr[x,y] = "*"
x_min = min(x_min,x)
x_max = max(x_max,x)
y_min = min(y_min,y)
y_max = max(y_max,y)
}
for (i=x_min; i<=x_max; i++) { # print spiral
rec = ""
for (j=y_min; j<=y_max; j++) {
rec = sprintf("%s%1s",rec,arr[i,j])
}
printf("%s\n",rec)
}
exit(0)
}
function max(x,y) { return((x > y) ? x : y) }
function min(x,y) { return((x < y) ? x : y) }
|
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.
| #BASIC | BASIC | a=1.5
b=1.5
pi=3.141592
PSET (320,100)
FOR t=0 TO 40*pi STEP .1
r=a+b*t
LINE -(320+2*r*SIN(t),100+r*COS(t))
NEXT |
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.
| #Agena | Agena | # find the first few squares via the unoptimised door flipping method
scope
local doorMax := 100;
local door;
create register door( doorMax );
# set all doors to closed
for i to doorMax do door[ i ] := false od;
# repeatedly flip the doors
for i to doorMax do
for j from i to doorMax by i do door[ j ] := not door[ j ] od
od;
# display the results
for i to doorMax do if door[ i ] then write( " ", i ) fi od; print()
epocs |
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)
| #Boo | Boo |
myArray as (int) = (1, 2, 3) // Size based on initialization
fixedArray as (int) = array(int, 1) // Given size(1 in this case)
myArray[0] = 10
myArray = myArray + fixedArray // Append arrays
print myArray[0]
|
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.
| #Factor | Factor | USING: combinators kernel math math.functions prettyprint ;
C{ 1 2 } C{ 0.9 -2.78 } {
[ + . ] ! addition
[ - . ] ! subtraction
[ * . ] ! multiplication
[ / . ] ! division
[ ^ . ] ! power
} 2cleave
C{ 1 2 } {
[ neg . ] ! negation
[ recip . ] ! multiplicative inverse
[ conjugate . ] ! complex conjugate
[ sin . ] ! sine
[ log . ] ! natural logarithm
[ sqrt . ] ! square root
} cleave |
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
| #GAP | GAP | 2/3 in Rationals;
# true
2/3 + 3/4;
# 17/12 |
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
| #JavaScript | JavaScript | function agm(a0, g0) {
var an = (a0 + g0) / 2,
gn = Math.sqrt(a0 * g0);
while (Math.abs(an - gn) > tolerance) {
an = (an + gn) / 2, gn = Math.sqrt(an * gn)
}
return an;
}
agm(1, 1 / Math.sqrt(2)); |
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.
| #zkl | zkl | x,y:=ask("Two ints: ").split(" ").apply("toInt");
println("x+y = ",x + y);
println("x-y = ",x - y);
println("x*y = ",x * y);
println("x/y = ",x / y); // rounds toward zero
println("x%y = ",x % y); // remainder; matches sign of first operand when operands' signs differ
println("x.divr(y) = ",x.divr(y)); // (x/y,remainder); sign as above |
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.
| #zonnon | zonnon |
module Main;
var
i,j: integer;
begin
write("A integer?:");readln(i);
write("another?: ");readln(j);
writeln("sum: ",i + j);
writeln("difference: ", i - j);
writeln("product: ", i * j);
writeln("quotient: ", i div j);
writeln("remainder: ", i mod j);
end Main.
|
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.
| #E | E | def eParser := <elang:syntax.makeEParser>
def LiteralExpr := <elang:evm.makeLiteralExpr>.asType()
def arithEvaluate(expr :String) {
def ast := eParser(expr)
def evalAST(ast) {
return switch (ast) {
match e`@a + @b` { evalAST(a) + evalAST(b) }
match e`@a - @b` { evalAST(a) - evalAST(b) }
match e`@a * @b` { evalAST(a) * evalAST(b) }
match e`@a / @b` { evalAST(a) / evalAST(b) }
match e`-@a` { -(evalAST(a)) }
match l :LiteralExpr { l.getValue() }
}
}
return evalAST(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.
| #BQN | BQN | {(•math.Sin •Plot○(⊢×↕∘≠) •math.Cos) -(2×π) × 𝕩⥊(↕÷-⟜1)100} |