Math constants and functions

From Rosetta Code

Show how to use the following math constants and functions in your language (if not available, note it):

• e (Euler's number)
• pi
• square root
• logarithm (any base allowed)
• exponential (e^x)
• absolute value (a.k.a. "magnitude")
• floor (largest integer less than or equal to this number--not the same as truncate or int)
• ceiling (smallest integer not less than this number--not the same as round up)
• power (x^y)

See also Trigonometric Functions

Contents 1 Ada 2 BASIC 3 C 4 D 5 E 6 Forth 7 Fortran 8 Haskell 9 J 10 Java 11 JavaScript 12 MAXScript 13 Logo 14 OCaml 15 Perl 16 PHP 17 Pop11 18 Python 19 Scheme

[edit] Ada

Most of the constants and functions used in this task are defined in the pre-defined Ada package Ada.Numerics.Elementary_Functions.

 
Ada.Numerics.e  -- Euler's number
Ada.Numerics.pi -- pi
sqrt(x)         -- square root
log(x, base)    -- logarithm to any specified base
exp(x)          -- exponential
abs(x)          -- absolute value
S'floor(x)      -- Produces the floor of an instance of subtype S
S'ceiling(x)    -- Produces the ceiling of an instance of subtype S
x**y            -- x raised to the y power
 

[edit] BASIC

Works with: QuickBasic version 4.5

ABS(x) 'absolute value
SQR(x) 'square root
EXP(x) 'exponential
LOG(x) 'natural logarithm
x ^ y 'power
'floor, ceiling, e, and pi not available

[edit] C

Most of the following functions take a double.

#include <math.h>
 
M_E; /* e - not standard but offered by most implementations */
M_PI; /* pi - not standard but offered by most implementations */
sqrt(x); /* square root--cube root also available in C99 (cbrt) */
log(x); /* natural logarithm--log base 10 also available (log10) */
exp(x); /* exponential */
abs(x); /* absolute value (for integers) */
fabs(x); /* absolute value (for doubles) */
floor(x); /* floor */
ceil(x); /* ceiling */
pow(x,y); /* power */

[edit] D

import std.math ; // need to import this module
E        // Euler's number
PI       // pi constant
sqrt(x)  // square root
log(x)   // natural logarithm
log10(x) // logarithm base 10
log2(x)  // logarithm base 2
exp(x)   // exponential
abs(x)   // absolute value (= magnitude for complex)
floor(x) // floor
ceil(x)  // ceiling
pow(x,y) // power

[edit] E

? 1.0.exp()
# value: 2.7182818284590455

? 0.0.acos() * 2
# value: 3.141592653589793

? 2.0.sqrt()
# value: 1.4142135623730951

? 2.0.log()
# value: 0.6931471805599453

? 5.0.exp()
# value: 148.4131591025766

? (-5).abs()
# value: 5

? 1.2.floor()
# value: 1

? 1.2.ceil()
# value: 2

? 10 ** 6
# value: 1000000

[edit] Forth

1e fexp fconstant e
0e facos 2e f* fconstant pi  \ predefined in gforth
fsqrt ( f -- f )
fln ( f -- f )   \ flog for base 10
fexp ( f -- f )
fabs ( f -- f )
floor ( f -- f )  \ round towards -inf
: ceil ( f -- f ) fnegate floor fnegate ; \ not standard, though fround is available
f** ( f e -- f^e )

[edit] Fortran

e          ! Not available. Can be calculated EXP(1)
pi         ! Not available. Can be calculated 4.0*ATAN(1.0)
SQRT(x)    ! square root
LOG(x)     ! natural logarithm
LOG10(x)   ! logarithm to base 10
EXP(x)     ! exponential
ABS(x)     ! absolute value
FLOOR(x)   ! floor - Fortran 90 or later only
CEILING(x) ! ceiling - Fortran 90 or later only
x**y       ! x raised to the y power

[edit] Haskell

The operations are defined for the various numeric typeclasses, as defined in their type signature.

exp 1     -- Euler number
pi        -- pi
sqrt x    -- square root
log x     -- natural logarithm
exp x     -- exponential
abs x     -- absolute value
floor x   -- floor
ceiling x -- ceiling
x ** y    -- power (e.g. floating-point exponentiation)
x ^ y     -- power (e.g. integer exponentiation, positive y only)
x ^^ y    -- power (e.g. rational exponentiation, also negative y)

[edit] J

The examples below require arguments (x and y) to be numeric nouns.

e =. 1x1   NB. Euler's number, specified as a numeric literal.
e =. ^ 1   NB. Euler's number, computed by exponentiation.
pi=. 1p1   NB. pi, specified as a numeric literal.
pi=. o.1   NB. pi, computed trigonometrically.
magnitude_of_x   =. |x
floor_of_x       =. <.x
ceiling_of_x     =. >.x
natural_log_of_x =. ^.x
base_x_log_of_y  =. x^.y
x_squared        =. *:x     NB. special form
x_squared        =. x^2     NB. exponential form
square_root_of_x =. %:x     NB. special form
square_root_of_x =. x^0.5   NB. exponential form
x_to_the_y_power =. x^y

[edit] Java

All of these functions are in Java's Math class which, does not require any imports:

Math.E; //e
Math.PI; //pi
Math.sqrt(x); //square root--cube root also available (cbrt)
Math.log(x); //natural logarithm--log base 10 also available (log10)
Math.exp(x); //exponential
Math.abs(x); //absolute value
Math.floor(x); //floor
Math.ceil(x); //ceiling
Math.pow(x,y); //power

[edit] JavaScript

Math.E
Math.PI
Math.sqrt(x)
Math.log(x)
Math.exp(x)
Math.abs(x)
Math.floor(x)
Math.ceil(x)
Math.pow(x,y)

[edit] MAXScript

e       -- Euler's number
pi      -- pi
log x   -- natural logarithm
log10 x -- log base 10
exp x   -- exponantial
abs x   -- absolute value
floor x -- floor
ceil x  -- ceiling
pow x y -- power

[edit] Logo

Works with: UCB Logo

make "e exp 1
make "pi 2*(RADARCTAN 0 1)
sqrt :x
ln :x
exp :x
; there is no standard abs, floor, or ceiling; only INT and ROUND.
power :x :y

[edit] OCaml

Unless otherwise noted, the following functions are for floats only:

sqrt x;; (* square root *)
log x;; (* natural logarithm--log base 10 also available (log10) *)
exp x;; (* exponential *)
abs_float x;; (* absolute value *)
abs x;; (* absolute value (for integers) *)
floor x;; (* floor *)
ceil x;; (* ceiling *)
x ** y; (* power *)

[edit] Perl

use POSIX;
 
exp(1); # e
4 * atan2(1, 1); # pi
sqrt($x); # square root
log($x); # natural logarithm
exp($x); # exponential
abs($x); # absolute value
POSIX::floor($x); # floor
POSIX::ceil($x); # ceiling
$x**$y; # power

[edit] PHP

M_E; //e
M_PI; //pi
sqrt(x); //square root
log(x); //natural logarithm--log base 10 also available (log10)
exp(x); //exponential
abs(x); //absolute value
floor(x); //floor
ceil(x); //ceiling
pow(x,y); //power

[edit] Pop11

pi        ;;; Number Pi
sqrt(x)   ;;; Square root
log(x)    ;;; Natural logarithm
exp(x)    ;;; Exponential function
abs(x)    ;;; Absolute value
x ** y    ;;; x to the power y

The number e is not provided directly, one has to compute 'exp(1)' instead. Also, floor and ceiling are not provided, one can define them using integer part:

define floor(x);
    if x < 0 then
        -intof(x);
    else
        intof(x);
    endif;
enddefine;

define ceiling(x);
    -floor(-x);
enddefine;

[edit] Python

import math
 
math.e #e
math.pi #pi
math.sqrt(x) #square root
math.log(x) #natural logarithm--log base 10 also available (math.log10)
math.exp(x) #exponential
abs(x) #absolute value
math.floor(x) #floor
math.ceil(x) #ceiling
x ** y #power

[edit] Scheme

(sqrt x) ;square root
(log x) ;natural logarithm
(exp x) ;exponential
(abs x) ;absolute value
(floor x) ;floor
(ceiling x) ;ceiling
(expt x y) ;power