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{{task|Basic language learning}} [[Category:Arithmetic operations]] [[Category:Simple]]
;Task: Show how to use the following math constants and functions in your language (if not available, note it): :* ''e'' (base of the natural logarithm) :* :* 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'' )
;Related task:
- [[Trigonometric Functions]]
ACL2
Only the last three are available as built in functions.
(floor 15 2) ;; This is the floor of 15/2
(ceiling 15 2)
(expt 15 2) ;; 15 squared
ActionScript
Actionscript has all the functions and constants mentioned in the task, available in the Math class.
Math.E; //e
Math.PI; //pi
Math.sqrt(u); //square root of u
Math.log(u); //natural logarithm of u
Math.exp(u); //e to the power of u
Math.abs(u); //absolute value of u
Math.floor(u);//floor of u
Math.ceil(u); //ceiling of u
Math.pow(u,v);//u to the power of v
The Math class also contains several other constants.
Math.LN10; // natural logarithm of 10
Math.LN2; // natural logarithm of 2
Math.LOG10E; // base-10 logarithm of e
Math.LOG2E; // base-2 logarithm of e
Math.SQRT1_2;// square root of 1/2
Math.SQRT2; //square root of 2
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
Aime
# e
exp(1);
# pi
2 * asin(1);
sqrt(x);
log(x);
exp(x);
fabs(x);
floor(x);
ceil(x);
pow(x, y);
ALGOL 68
REAL x:=exp(1), y:=4*atan(1);
printf(($g(-8,5)"; "$,
exp(1), # e #
pi, # pi #
sqrt(x), # square root #
log(x), # logarithm base 10 #
ln(x), # natural logarithm #
exp(x), # exponential #
ABS x, # absolute value #
ENTIER x, # floor #
-ENTIER -x, # ceiling #
x ** y # power #
))
{{out}}
2.71828; 3.14159; 1.64872; 0.43429; 1.00000; 15.15426; 2.71828; 2.00000; 3.00000; 23.14069;
''ALGOL 68'' also includes assorted long, short and complex versions of the above, eg: ''long exp'', ''long long exp'', ''short exp'', ''complex exp'' etc.
And assorted trig functions: ''sin(x)'', ''arcsin(x)'', ''cos(x)'', ''arccos(x)'', ''tan(x)'', ''arctan(x)'', ''arctan2(x,y)'', ''sinh(x)'', ''arcsinh(x)'', ''cosh(x)'', ''arccosh(x)'', ''tanh(x)'' AND ''arctanh(x)''.
ALGOL W
begin
real t, u;
t := 10;
u := -2.3;
i_w := 4; s_w := 0; r_format := "A"; r_d := 4; r_w := 9; % set output format %
write( " e: ", exp( 1 ) ); % e %
write( " pi: ", pi ); % pi %
write( " root t: ", sqrt( t ) ); % square root %
write( " log t: ", log( t ) ); % log base 10 %
write( " ln t: ", ln( t ) ); % log base e %
write( " exp u: ", exp( u ) ); % exponential %
write( " abs u: ", abs u ); % absolute value %
write( " floor pi: ", entier( pi ) ); % floor %
write( "ceiling pi: ", - entier( - pi ) ); % ceiling %
% the raise-to-the-power operator is "**" - it only allows integers for the power %
write( " pi cubed: ", pi ** 3 ) % use exp( ln( x ) * y ) for general x^y %
end.
ARM Assembly
{{omit from|ARM Assembly}}
## AutoHotkey
The following math functions are built into AutoHotkey:
```autohotkey
Sqrt(Number) ; square root
Log(Number) ; logarithm (base 10)
Ln(Number) ; natural logarithm (base e)
Exp(N) ; e to the power N
Abs(Number) ; absolute value
Floor(Number) ; floor
Ceil(Number) ; ceiling
x**y ; x to the power y
No mathematical constants are built-in, but they can all be calculated:
e:=exp(1)
pi:=2*asin(1)
The following are additional trigonometric functions that are built into the AutoHotkey language:
Sin(Number) ; sine
Cos(Number) ; cosine
Tan(Number) ; tangent
ASin(Number) ; arcsine
ACos(Number) ; arccosine
ATan(Number) ; arctangent
AWK
Awk has square root, logarithm, exponential and power.
BEGIN {
print sqrt(2) # square root
print log(2) # logarithm base e
print exp(2) # exponential
print 2 ^ -3.4 # power
}
# outputs 1.41421, 0.693147, 7.38906, 0.0947323
'''Power's note:''' With [[nawk]] or [[gawk]],2 ** -3.4acts like2 ^ -3.4. With [[mawk]],2 ** -3.4is a syntax error. Nawk allows**, but its manual page only has^. Gawk's manual warns, ''"The POSIX standard only specifies the use of `^' for exponentiation. For maximum portability, do not use the `**' operator."''
Awk misses e, pi, absolute value, floor and ceiling; but these are all easy to implement:
BEGIN {
E = exp(1)
PI = atan2(0, -1)
}
function abs(x) {
return x < 0 ? -x : x
}
function floor(x) {
y = int(x)
return y > x ? y - 1 : y
}
function ceil(x) {
y = int(x)
return y < x ? y + 1 : y
}
BEGIN {
print E
print PI
print abs(-3.4) # absolute value
print floor(-3.4) # floor
print ceil(-3.4) # ceiling
}
# outputs 2.71828, 3.14159, 3.4, -4, -3
Axe
In general, Axe does not support many operations on real numbers. However, there are a few special cases that it does support.
To take the square root of an integer X:
√(X)
To take the square root of an 8.8 fixed-point number Y:
√(Y)ʳ
To take the base-2 logarithm of an integer X:
ln(X)
To take 2 raised to an integer X: (Note that the base is not Euler's number)
e^(X)
To take the absolute value of a signed integer X:
abs(X)
BASIC
{{works with|QuickBasic|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
==={{header|IS-BASIC}}===
=
## Sinclair ZX81 BASIC
=
Arguments to built-in functions may be placed in parentheses, but are not required to be.
Base of the natural logarithm:
```basic>EXP 1</lang
<math>\pi</math>:
```basic>PI</lang
Square root:
```basic>SQR X</lang
Natural logarithm:
```basic>LN X</lang
Exponential:
```basic>EXP X</lang
Absolute value:
```basic>ABS X</lang
Floor:
```basic>INT X</lang
(NB. Although this function is called <code>INT</code>, it corresponds to <code>floor</code>: e.g. <code>INT -3.1</code> returns -4 not -3.)
Ceiling:
not provided as a built-in function.
Power:
```basic
X**Y
NB. Both and can be real numbers.
=
BBC BASIC
=
e = EXP(1)
Pi = PI
Sqr2 = SQR(2)
Ln2 = LN(2)
Log2 = LOG(2) : REM Base 10
Exp2 = EXP(2)
Abs2 = ABS(-2)
Floor = INT(1.234)
Ceil = FNceil(1.234)
Power = 1.23^4
END
DEF FNceil(n) = INT(n) - (INT(n) <> n)
bc
The language has square root and power, but power only works if the exponent is an integer.
scale = 6
sqrt(2) /* 1.414213 square root */
4.3 ^ -2 /* .054083 power (integer exponent) */
The standard library has natural logarithm and exponential functions. It can calculate e and pi: e comes from the exponential function, while pi is four times the arctangent of one. The usual formulas can calculate the powers with fractional exponents, and the logarithms with any base.
{{libheader|bc -l}}
scale = 6
l(2) /* .693147 natural logarithm */
e(2) /* 7.389056 exponential */
p = 4 * a(1)
e = e(1)
p /* 3.141592 pi to 6 fractional digits */
e /* 2.178281 e to 6 fractional digits */
e(l(2) * -3.4) /* .094734 2 to the power of -3.4 */
l(1024) / l(2) /* 10.000001 logarithm base 2 of 1024 */
The missing functions are absolute value, floor and ceiling. You can implement these functions, if you know what to do.
{{trans|AWK}}
/* absolute value */
define v(x) {
if (x < 0) return (-x)
return (x)
}
/* floor */
define f(x) {
auto s, y
s = scale
scale = 0
y = x / 1
scale = s
if (y > x) return (y - 1)
return (y)
}
/* ceiling */
define g(x) {
auto s, y
s = scale
scale = 0
y = x / 1
scale = s
if (y < x) return (y + 1)
return (y)
}
v(-3.4) /* 3.4 absolute value */
f(-3.4) /* -4 floor */
g(-3.4) /* -3 ceiling */
blz
The constant e
{e}
The constant pi
{pi}
Square root
x ** 0.5
Logarithm (base n)
x __ n
Exponential
{e} ** x
Absolute Value
abs(x)
Floor
floor(x)
Ceiling
ceil(x)
Power x to the y
x ** y
Bracmat
Bracmat has no real number type, but the constants e and pi, together with i can be used as symbols with the intended mathematical meaning in exponential functions.
For example, differentiation 10^x to x
x \D (10^x) { \D is the differentiation operator }
has the result
10^x*e\L10 { \L is the logarithm operator }
Likewise e^(ipi) evaluates to -1 and e^(1/2i*pi) evaluates to i.
When taking the square root of a (rational) number, and nominator and denominator are not too big (convertible to 32 or 64 bit integers, depending on platform), Bracmat resolves the number in prime factors and halves the exponents of each of the prime factors.
Bracmat handles logarithms in any base, except real numbers that are not rational. Example: 24/7 \L 119/9 evaluates to 2+24/7\L5831/5184.
Bracmat does not attempt to compute the numerical value of the exponential function, except for a the special case where the result is a rational number.
Thus e^0 evaluates to 1.
Bracmat has no built-in functions for computing the absolute value, floor or ceiling. For real numbers that are rational such functions can be written.
If the result of taking the power of a rational number to another rational number is rational, Bracmat can in many compute it, if needed using prime factorization. See root above. Example:
243/1024^2/5 evaluates to 9/16.
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 */
To access the M_PI, etc. constants in Visual Studio, you may need to add the line #define _USE_MATH_DEFINES before the #include <math.h>.
C++
#include <iostream>
#include <cmath>
#ifdef M_E
static double euler_e = M_E;
#else
static double euler_e = std::exp(1); // standard fallback
#endif
#ifdef M_PI
static double pi = M_PI;
#else
static double pi = std::acos(-1);
#endif
int main()
{
std::cout << "e = " << euler_e
<< "\npi = " << pi
<< "\nsqrt(2) = " << std::sqrt(2.0)
<< "\nln(e) = " << std::log(e)
<< "\nlg(100) = " << std::log10(100.0)
<< "\nexp(3) = " << std::exp(3.0)
<< "\n|-4.5| = " << std::abs(-4.5) // or std::fabs(4.0); both work in C++
<< "\nfloor(4.5) = " << std::floor(4.5)
<< "\nceiling(4.5) = " << std::ceil(4.5)
<< "\npi^2 = " << std::pow(pi,2.0) << std::endl;
}
C#
using System;
class Program {
static void Main(string[] args) {
Console.WriteLine(Math.E); //E
Console.WriteLine(Math.PI); //PI
Console.WriteLine(Math.Sqrt(10)); //Square Root
Console.WriteLine(Math.Log(10)); // Logarithm
Console.WriteLine(Math.Log10(10)); // Base 10 Logarithm
Console.WriteLine(Math.Exp(10)); // Exponential
Console.WriteLine(Math.Abs(10)); //Absolute value
Console.WriteLine(Math.Floor(10.0)); //Floor
Console.WriteLine(Math.Ceiling(10.0)); //Ceiling
Console.WriteLine(Math.Pow(2, 5)); // Exponentiation
}
}
Chef
See [[Basic integer arithmetic#Chef]] for powers.
Clojure
{{trans|Java}} which is directly available.
(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
Clojure does provide arbitrary precision versions as well:
(ns user (:require [clojure.contrib.math :as math]))
(math/sqrt x)
(math/abs x)
(math/floor x)
(math/ceil x)
(math/expt x y)
.. and as multimethods that can be defined for any type (e.g. complex numbers).
(ns user (:require [clojure.contrib.generic.math-functions :as generic]))
(generic/sqrt x)
(generic/log x)
(generic/exp x)
(generic/abs x)
(generic/floor x)
(generic/ceil x)
(generic/pow x y)
COBOL
Everything that follows can take any number (except for SQRT which expects a non-negative number).
The task constants and (intrinsic) functions:
E *> e
PI *> Pi
SQRT(n) *> Sqaure root
LOG(n) *> Natural logarithm
LOG10(n) *> Logarithm (base 10)
EXP(n) *> e to the nth power
ABS(n) *> Absolute value
INTEGER(n) *> While not a proper floor function, it is implemented in the same way.
*> There is no ceiling function. However, it could be implemented like so:
ADD 1 TO N
MOVE INTEGER(N) TO Result
*> There is no pow function, although the COMPUTE verb does have an exponention operator.
COMPUTE Result = N ** 2
COBOL also has the following extra mathematical functions:
FACTORIAL(n) *> Factorial
EXP10(n) *> 10 to the nth power
*> Trigonometric functions, including inverse ones, named as would be expected.
Common Lisp
In Lisp we should really be talking about numbers rather than the type real. The types real and complex are subtypes of number. Math operations that accept or produce complex numbers generally do.
(exp 1) ; e (Euler's number)
pi ; pi constant
(sqrt x) ; square root: works for negative reals and complex
(log x) ; natural logarithm: works for negative reals and complex
(log x 10) ; logarithm base 10
(exp x) ; exponential
(abs x) ; absolute value: result exact if input exact: (abs -1/3) -> 1/3.
(floor x) ; floor: restricted to real, two valued (second value gives residue)
(ceiling x) ; ceiling: restricted to real, two valued (second value gives residue)
(expt x y) ; power
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
Delphi
Log, Floor, Ceil and Power functions defined in Math.pas.
Exp(1); // e (Euler's number)
Pi; // π (Pi)
Sqrt(x); // square root
LogN(BASE, x) // log of x for a specified base
Log2(x) // log of x for base 2
Log10(x) // log of x for base 10
Ln(x); // natural logarithm (for good measure)
Exp(x); // exponential
Abs(x); // absolute value (a.k.a. "magnitude")
Floor(x); // floor
Ceil(x); // ceiling
Power(x, y); // power
DWScript
See [[Real_constants_and_functions#Delphi|Delphi]].
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
Elena
ELENA 4.x :
import system'math;
import extensions;
public program()
{
console.printLine(E_value); //E
console.printLine(Pi_value); //PI
console.printLine(10.sqrt()); //Square Root
console.printLine(10.ln()); //Logarithm
console.printLine(10.log10()); // Base 10 Logarithm
console.printLine(10.exp()); //Exponential
console.printLine(10.Absolute); //Absolute value
console.printLine(10.0r.floor()); //Floor
console.printLine(10.0r.ceil()); //Ceiling
console.printLine(2.power(5)); //Exponentiation
}
Elixir
defmodule Real_constants_and_functions do
def main do
IO.puts :math.exp(1) # e
IO.puts :math.pi # pi
IO.puts :math.sqrt(16) # square root
IO.puts :math.log(10) # natural logarithm
IO.puts :math.log10(10) # base 10 logarithm
IO.puts :math.exp(2) # e raised to the power of x
IO.puts abs(-2.24) # absolute value
IO.puts Float.floor(3.1423) # floor
IO.puts Float.ceil(20.125) # ceiling
IO.puts :math.pow(3,2) # exponentiation
end
end
Real_constants_and_functions.main
Elm
The following are all in the Basics module, which is imported by default:
e -- e
pi -- pi
sqrt x -- square root
logBase 3 9 -- logarithm (any base)
e^x -- exponential
abs x -- absolute value
floor x -- floor
ceiling x -- ceiling
2 ^ 3 -- power
Erlang
% Implemented by Arjun Sunel
-module(math_constants).
-export([main/0]).
main() ->
io:format("~p~n", [math:exp(1)] ), % e
io:format("~p~n", [math:pi()] ), % pi
io:format("~p~n", [math:sqrt(16)] ), % square root
io:format("~p~n", [math:log(10)] ), % natural logarithm
io:format("~p~n", [math:log10(10)] ), % base 10 logarithm
io:format("~p~n", [math:exp(2)] ), % e raised to the power of x
io:format("~p~n", [abs(-2.24)] ), % absolute value
io:format("~p~n", [floor(3.1423)] ), % floor
io:format("~p~n", [ceil(20.125)] ), % ceiling
io:format("~p~n", [math:pow(3,2)] ). % exponentiation
floor(X) when X < 0 ->
T = trunc(X),
case X - T == 0 of
true -> T;
false -> T - 1
end;
floor(X) ->
trunc(X).
ceil(X) when X < 0 ->
trunc(X);
ceil(X) ->
T = trunc(X),
case X - T == 0 of
true -> T;
false -> T + 1
end.
{{out}}
2.718281828459045
3.141592653589793
4.0
2.302585092994046
1.0
7.38905609893065
2.24
3
21
9.0
ok
ERRE
PROGRAM R_C_F
FUNCTION CEILING(X)
CEILING=INT(X)-(X-INT(X)>0)
END FUNCTION
FUNCTION FLOOR(X)
FLOOR=INT(X)
END FUNCTION
BEGIN
PRINT(EXP(1)) ! e not available
PRINT(π) ! pi is available or ....
PRINT(4*ATN(1)) ! .... equal to
X=12.345
Y=1.23
PRINT(SQR(X),X^0.5) ! square root
PRINT(LOG(X)) ! natural logarithm base e
PRINT(LOG(X)/LOG(10)) ! base 10 logarithm
PRINT(LOG(X)/LOG(Y)) ! arbitrary base logarithm (y>0)
PRINT(EXP(X)) ! exponential
PRINT(ABS(X)) ! absolute value
PRINT(FLOOR(X)) ! floor
PRINT(CEILING(X)) ! ceiling
PRINT(X^Y) ! power
END PROGRAM
{{out}}
2.718282
3.141592653589793
3.141593
3.513545 3.513545
2.513251
1.091491
12.14048
229808.1
12.345
12
13
22.00564
=={{header|F Sharp|F#}}== {{trans|C#|C sharp}}
open System
let main _ =
Console.WriteLine(Math.E); // e
Console.WriteLine(Math.PI); // Pi
Console.WriteLine(Math.Sqrt(10.0)); // Square Root
Console.WriteLine(Math.Log(10.0)); // Logarithm
Console.WriteLine(Math.Log10(10.0)); // Base 10 Logarithm
Console.WriteLine(Math.Exp(10.0)); // Exponential
Console.WriteLine(Math.Abs(10)); // Absolute value
Console.WriteLine(Math.Floor(10.0)); // Floor
Console.WriteLine(Math.Ceiling(10.0)); // Ceiling
Console.WriteLine(Math.Pow(2.0, 5.0)); // Exponentiation
0
Factor
e ! e
pi ! π
sqrt ! square root
log ! natural logarithm
exp ! exponentiation
abs ! absolute value
floor ! greatest whole number smaller than or equal
ceiling ! smallest whole number greater than or equal
truncate ! remove the fractional part (i.e. round towards 0)
round ! round to next whole number
^ ! power
Fantom
The Float class holds 64-bit floating point numbers, and contains most of the useful mathematical functions. A floating point number must be specified when entered with the suffix 'f', e.g. 9f
Float.e
Float.pi
9f.sqrt
9f.log // natural logarithm
9f.log10 // logarithm to base 10
9f.exp // exponentiation
(-3f).abs // absolute value, note bracket
3.2f.floor // nearest Int smaller than this number
3.2f.ceil // nearest Int bigger than this number
3.2f.round // nearest Int
3f.pow(2f) // power
Note, . binds more tightly than -, so use brackets around negative numbers:
> -3f.pow(2f)
-9
> (-3f).pow(2f)
9
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 )
Fortran
e ! Not available. Can be calculated EXP(1.0)
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
4ATAN(1.0) will be calculated in single precision, likewise EXP(1.0) (not EXP(1), because 1 is an integer) and although double precision functions can be named explicitly, 4DATAN(1.0) will be rejected because 1.0 is in single precision and DATAN expects double. Thus, 4DATAN(1.0D0) or 4DATAN(1D0) will do, as the D in the exponent form specifies double precision. Whereupon, the generic names can be returned to: 4*ATAN(1D0). Some systems go further and offer quadruple precision. Others allow that all constants will be deemed double precision as a compiler option.
The 4 need not be named as 4.0, or 4D0, as 4 the integer will be converted by the compiler to double precision, because it is to meet a known double precision value in simple multiplication and so will be promoted. Hopefully, at compile time.
FreeBASIC
' FB 1.05.0 Win64
#Include "crt/math.bi"
Print M_E '' constant "e" from C runtime library
Print M_PI '' constant "pi" from C runtime library
Print Sqr(2) '' square root function built into FB
Print Log(M_E) '' log to base "e" built into FB
Print log10(10) '' log to base 10 from C runtime library
Print Exp(1) '' exponential function built into FB
Print Abs(-1) '' absolute value function (integers or floats) built into FB
Print Int(-2.5) '' floor function built into FB
Print ceil(-2.5) '' ceiling function from C runtime library
Print 2.5 ^ 3.5 '' exponentiation operator built into FB
Sleep
{{out}}
2.718281828459045
3.141592653589793
1.414213562373095
1
1
2.718281828459045
1
-3
-2
24.70529422006547
Frink
All of the following operations work for any numerical type, including rational numbers, complex numbers and intervals of real numbers.
e
pi, π // Unicode can also be written in ASCII programs as \u03C0
sqrt[x]
ln[x] // Natural log
log[x] // Log to base 10
exp[x], e^x
abs[x]
floor[x] // Except for complex numbers where there's no good interpretation.
ceil[x] // Except for complex numbers where there's no good interpretation.
x^y
FutureBasic
include "ConsoleWindow"
// Set width of tab
def tab 8
print "exp:", exp(1)
print "pi:", pi
print "sqr:", sqr(2)
print "log:", log(2)
print "log2:", log2(2)
print "log10", log10(2)
print "abs:", abs(-2)
print "floor:", int(1.534)
print "ceil:", val( using"###"; 1.534 )
print "power:", 1.23 ^ 4
Output:
exp: 2.7182818285
pi: 3.1415926536
sqr: 1.4142135624
log: 0.6931471806
log2: 1
log10 0.3010299957
abs: 2
floor: 2
ceil: 2
power: 2.28886641
Go
package main
import (
"fmt"
"math"
"math/big"
)
func main() {
// e and pi defined as constants.
// In Go, that means they are not of a specific data type and can be used
// as float32 or float64. Println takes the float64 values.
fmt.Println("float64 values:")
fmt.Println("e:", math.E)
fmt.Println("π:", math.Pi)
// The following functions all take and return the float64 data type.
// square root. cube root also available (math.Cbrt)
fmt.Println("square root(1.44):", math.Sqrt(1.44))
// natural logarithm--log base 10, 2 also available (math.Log10, math.Log2)
// also available is log1p, the log of 1+x. (using log1p can be more
// accurate when x is near zero.)
fmt.Println("ln(e):", math.Log(math.E))
// exponential. also available are exp base 10, 2 (math.Pow10, math.Exp2)
fmt.Println("exponential(1):", math.Exp(1))
fmt.Println("absolute value(-1.2):", math.Abs(-1.2))
fmt.Println("floor(-1.2):", math.Floor(-1.2))
fmt.Println("ceiling(-1.2):", math.Ceil(-1.2))
fmt.Println("power(1.44, .5):", math.Pow(1.44, .5))
// Equivalent functions for the float32 type are not in the standard
// library. Here are the constants e and π as float32s however.
fmt.Println("\nfloat32 values:")
fmt.Println("e:", float32(math.E))
fmt.Println("π:", float32(math.Pi))
// The standard library has an arbitrary precision floating point type but
// provides only the most basic methods. Also while the constants math.E
// and math.Pi are provided to over 80 decimal places, there is no
// convenient way of loading these numbers (with their full precision)
// into a big.Float. A hack is cutting and pasting into a string, but
// of course if you're going to do that you are free to cut and paste from
// any other source. (The documentation cites OEIS as its source.)
pi := "3.141592653589793238462643383279502884197169399375105820974944"
π, _, _ := big.ParseFloat(pi, 10, 200, 0)
fmt.Println("\nbig.Float values:")
fmt.Println("π:", π)
// Of functions requested by the task, only absolute value is provided.
x := new(big.Float).Neg(π)
y := new(big.Float)
fmt.Println("x:", x)
fmt.Println("abs(x):", y.Abs(x))
}
{{out}}
float64 values:
e: 2.718281828459045
π: 3.141592653589793
square root(1.44): 1.2
ln(e): 1
exponential(1): 2.718281828459045
absolute value(-1.2): 1.2
floor(-1.2): -2
ceiling(-1.2): -1
power(1.44, .5): 1.2
float32 values:
e: 2.7182817
π: 3.1415927
big.Float values:
π: 3.141592653589793238462643383279502884197169399375105820974944
x: -3.141592653589793238462643383279502884197169399375105820974944
abs(x): 3.141592653589793238462643383279502884197169399375105820974944
Groovy
Math constants and functions are as outlined in the [[#Java|Java]] example, except as follows:
'''Absolute Value'''
In addition to the java.lang.Math.abs() method, each numeric type has an abs() method, which can be invoked directly on the number:
println ((-22).abs())
{{out}}
22
'''Power'''
In addition to the java.lang.Math.pow() method, each numeric type works with the power operator (**), which can be invoked as an in-fix operator between two numbers:
println 22**3.5
{{out}}
49943.547010599876
Power results are not defined for all possible pairs of operands. Any power operation that does not have a result returns a 64-bit IEEE NaN (Not a Number) value.
println ((-22)**3.5)
{{out}}
NaN
Also note that at the moment (07:00, 19 March 2011 (UTC)) Groovy (1.7.7) gives a mathematically incorrect result for "0**0". The correct result should be "NaN", but the Groovy operation result is "1".
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, nonnegative y only)
x ^^ y -- power (e.g. integer exponentiation of rationals, also negative y)
HicEst
Except for x^y, this is identical to Fortran:
e ! Not available. Can be calculated EXP(1)
pi ! Not available. Can be calculated 4.0*ATAN(1.0)
x^0.5 ! square root
LOG(x) ! natural logarithm
LOG(x, 10) ! logarithm to base 10
EXP(x) ! exponential
ABS(x) ! absolute value
FLOOR(x) ! floor
CEILING(x) ! ceiling
x**y ! x raised to the y power
x^y ! same as x**y
== {{header|Icon}} and {{header|Unicon}} ==
link numbers # for floor and ceil
procedure main()
write("e=",&e)
write("pi=",&pi)
write("phi=",&phi)
write("sqrt(2)=",sqrt(2.0))
write("log(e)=",log(&e))
write("log(100.,10)=",log(100,10))
write("exp(1)=",exp(1.0))
write("abs(-2)=",abs(-2))
write("floor(-2.2)=",floor(-2.2))
write("ceil(-2.2)=",ceil(-2.2))
write("power: 3^3=",3^3)
end
{{libheader|Icon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/procs/numbers.icn numbers provides floor and ceiling]
{{out}}
e=2.718281828459045
pi=3.141592653589793
phi=1.618033988749895
sqrt(2)=1.414213562373095
log(e)=1.0
log(100.,10)=2.0
exp(1)=2.718281828459045
abs(-2)=2
floor(-2.2)=-2
ceil(-2.2)=-3
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
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
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)
jq
The mathematical functions available in jq are defined as 0-arity filters, so to evaluate the sqrt of 4, one writes 4|sqrt. In jq, "." refers to the output coming from the left in the pipeline.
In the following, comments appear after the "#":
1 | exp # i.e. e
1 | atan * 4 # i.e. π
sqrt
log # Naperian log
exp
if . < 0 then -. else . end # absolute value
floor
# jq does not currently have a ceiling function
# jq does not currently have a function to compute x^y
Jsish
/* real constants and functions, in JSI */
var x, y;
;Math.E;
;Math.PI;
;x = 100.0;
;Math.sqrt(x);
;Math.log(x);
;x = 2.0;
;Math.exp(x);
;x = -x;
;Math.abs(x);
;x = 42.42;
;Math.floor(x);
;Math.ceil(x);
;x = 10.0;
;y = 5;
;Math.pow(x,y);
/*
=!EXPECTSTART!=
Math.E ==> 2.718281828459045
Math.PI ==> 3.141592653589793
x = 100.0 ==> 100
Math.sqrt(x) ==> 10
Math.log(x) ==> 4.605170185988092
x = 2.0 ==> 2
Math.exp(x) ==> 7.38905609893065
x = -x ==> -2
Math.abs(x) ==> 2
x = 42.42 ==> 42.42
Math.floor(x) ==> 42
Math.ceil(x) ==> 43
x = 10.0 ==> 10
y = 5 ==> 5
Math.pow(x,y) ==> 100000
=!EXPECTEND!=
*/
{{out}}
prompt$ jsish --U real-constants.jsi
Math.E ==> 2.718281828459045
Math.PI ==> 3.141592653589793
x = 100.0 ==> 100
Math.sqrt(x) ==> 10
Math.log(x) ==> 4.605170185988092
x = 2.0 ==> 2
Math.exp(x) ==> 7.38905609893065
x = -x ==> -2
Math.abs(x) ==> 2
x = 42.42 ==> 42.42
Math.floor(x) ==> 42
Math.ceil(x) ==> 43
x = 10.0 ==> 10
y = 5 ==> 5
Math.pow(x,y) ==> 100000
# Run the unit tests
prompt$ jsish -u real-constants.jsi
[PASS] real-constants.jsi
Julia
e
π, pi
sqrt(x)
log(x)
exp(x)
abs(x)
floor(x)
ceil(x)
x^y
Note that Julia supports Unicode identifiers, and allows either π or pi for that constant.
Also, mathematical constants like e and π in Julia are of a special type that is automatically converted to the correct precision when used in aritmetic operations. So, for example, BigFloat(2) * π computes 2π in arbitrary precision arithmetic.
Kotlin
// version 1.0.6
fun main(args: Array<String>) {
println(Math.E) // e
println(Math.PI) // pi
println(Math.sqrt(2.0)) // square root
println(Math.log(Math.E)) // log to base e
println(Math.log10(10.0)) // log to base 10
println(Math.exp(1.0)) // exponential
println(Math.abs(-1)) // absolute value
println(Math.floor(-2.5)) // floor
println(Math.ceil(-2.5)) // ceiling
println(Math.pow(2.5, 3.5)) // power
}
{{out}}
2.718281828459045
3.141592653589793
1.4142135623730951
1.0
1.0
2.718281828459045
1
-3.0
-2.0
24.705294220065465
Lasso
//e
define e => 2.7182818284590452
//π
define pi => 3.141592653589793
e
pi
9.0->sqrt
1.64->log
1.64->log10
1.64->exp
1.64->abs
1.64->floor
1.64->ceil
1.64->pow(10.0)
Liberty BASIC
Ceiling and floor easily implemented as functions.
sqr( is the LB function for square root.
e & pi not available- calculate as shown.
print exp( 1) ' e not available
print 4 *atn( 1) ' pi not available
x =12.345: y =1.23
print sqr( x), x^0.5 ' square root- NB the unusual name
print log( x) ' natural logarithm base e
print log( x) /2.303 ' base 10 logarithm
print log( x) /log( y) ' arbitrary base logarithm
print exp( x) ' exponential
print abs( x) ' absolute value
print floor( x) ' floor
print ceiling( x) ' ceiling
print x^y ' power
end
function floor( x)
if x >0 then
floor =int( x)
else
if x <>int( x) then floor =int( x) -1 else floor =int( x)
end if
end function
function ceiling( x)
if x <0 then
ceiling =int( x)
else
ceiling =int( x) +1
end if
end function
Lingo
the floatPrecision = 8
-- e (base of the natural logarithm)
put exp(1)
-- 2.71828183
-- pi
put PI
-- 3.14159265
-- square root
put sqrt(2.0)
-- 1.41421356
-- logarithm (any base allowed)
x = 100
put log(x) -- calculate log for base e
-- 4.60517019
put log(x)/log(10) -- calculate log for base 10
-- 2.00000000
-- exponential (ex)
put exp(3)
-- 20.08553692
-- absolute value (a.k.a. "magnitude")
put abs(-1)
-- 1
-- floor (largest integer less than or equal to this number--not the same as truncate or int)
n = 23.536
put bitOr(n, 0) -- calculates floor
-- 23
-- ceiling (smallest integer not less than this number--not the same as round up)
n = 23.536
-- calculates ceil
floor = bitOr(n, 0)
if (floor >= n) then put floor
else put floor+1
-- 24
-- power
put power(2, 8)
-- 256.00000000
LiveCode
LC 7.1+, prior to this floor & ceil were not built-in.
e: exp(1)
pi: pi
square root: sqrt(x)
logarithm: log(x)
exponential (ex): exp(x)
absolute value: abs(x)
floor: floor(x)
ceiling: ceil(x)
power: x^y
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
Logtalk
:- object(constants_and_functions).
:- public(show/0).
show :-
write('e = '), E is e, write(E), nl,
write('pi = '), PI is pi, write(PI), nl,
write('sqrt(2) = '), SQRT is sqrt(2), write(SQRT), nl,
% only base e logorithm is avaialable as a standard built-in function
write('log(2) = '), LOG is log(2), write(LOG), nl,
write('exp(2) = '), EXP is exp(2), write(EXP), nl,
write('abs(-1) = '), ABS is abs(-1), write(ABS), nl,
write('floor(-3.4) = '), FLOOR is floor(-3.4), write(FLOOR), nl,
write('ceiling(-3.4) = '), CEILING is ceiling(-3.4), write(CEILING), nl,
write('2 ** -3.4 = '), POWER is 2 ** -3.4, write(POWER), nl.
:- end_object.
{{out}}
| ?- constants_and_functions::show.
e = 2.718281828459045
pi = 3.141592653589793
sqrt(2) = 1.4142135623730951
log(2) = 0.6931471805599453
exp(2) = 7.38905609893065
abs(-1) = 1
floor(-3.4) = -4
ceiling(-3.4) = -3
2 ** -3.4 = 0.09473228540689989
yes
Lua
math.exp(1)
math.pi
math.sqrt(x)
math.log(x)
math.log10(x)
math.exp(x)
math.abs(x)
math.floor(x)
math.ceil(x)
x^y
M2000 Interpreter
Module Checkit {
Def exp(x)= 2.71828182845905^x
Print Ln(exp(1))==1
Print Log(10^5)==5
Print Sgn(-5)=-1
Print Abs(-2.10#)=2.1#
Def exptype$(x)=type$(x)
Print exptype$(Abs(-2.1#))="Currency"
Print exptype$(Abs(-2.1~))="Single"
Print exptype$(Abs(-2.1@))="Decimal"
Print exptype$(Abs(-2&))="Long"
Print exptype$(Abs(-2%))="Integer"
Print exptype$(Abs(-2.212e34))="Double"
Print exptype$(Sgn(-2.1#))="Integer"
\\ Sgn return integer type
Print exptype$(Sgn(-2.212e34))="Integer"
\\ Log, Len return double
Print exptype$(Log(1000))="Double"
Print exptype$(exp(1%))="Double"
Print exptype$(Ln(1212%))="Double"
\\ power return type Double
Print exptype$(2&^2&)="Double"
Print exptype$(2&**2&)="Double"
Print exptype$(2&*2&)="Long"
Print 2**2=4, 2^2=4, 2^2^2=16, 2**2**2=16
\\ floor() and Int() is the same
Print Int(-2.7)=-3, Int(2.7)=2
Print Floor(-2.7)=-3, Floor(2.7)=2
Print Ceil(-2.7)=-2, Ceil(2.7)=3
Print Sqrt(4)=2
}
Checkit
Maple
abs(ceil(floor(ln(exp(1)^sqrt(exp(Pi*I)+1)))));
0
Mathematica
E
Pi
Sqrt[x]
Log[x]
Log[b,x]
Exp[x]
Abs[x]
Floor[x]
Ceiling[x]
Power[x, y]
Where x is the number, and b the base. Exp[x] can also be inputted as E^x or Ex and Power[x,y] can be also inputted as x^y or xy. All functions work with symbols, integers, floats and can be complex. Abs giving the modulus (|x|) if the argument is a complex number. Constant like E and Pi are kep unevaluated until someone explicitly tells it to give a numerical approximation: N[Pi,n] gives Pi to n-digit precision. Functions given an exact argument will be kept unevaluated if the answer can't be written more compact, approximate arguments will always be evaluated:
Log[1.23] => 0.207014
Log[10] => Log[10]
Log[10,100] => 2
Log[E^4] => 4
Log[1 + I] => Log[1+I]
Log[1. + I] => 0.346574 + 0.785398 I
Ceiling[Pi] => 4
Floor[Pi] => 3
Sqrt[2] => Sqrt[2]
Sqrt[4] => 2
Sqrt[9/2] => 3/Sqrt[2]
Sqrt[3.5] => 1.87083
Sqrt[-5 + 12 I] => 2 + 3 I
Sqrt[-4] => 2I
Exp[2] => E^2
Exp[Log[4]] => 4
=={{header|MATLAB}} / {{header|Octave}}==
exp(1) % e
pi % pi
sqrt(x) % square root
log(x) % natural logarithm
log2(x) % logarithm base 2
log10(x) % logarithm base 10
exp(x) % exponential
abs(-x) % absolute value
floor(x) % floor
ceil(x) % ceiling
x^y % power
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
Mercury
Metafont
show mexp(256); % outputs e; since MF uses mexp(x) = exp(x/256)
show 3.14159; % no pi constant built in; of course we can define it
% in several ways... even computing
% C/2r (which would be funny since MF handles paths,
% and a circle is a path...)
show sqrt2; % 1.41422, or in general sqrt(a)
show mexp(256*x); % see e.
show abs(x); % returns |x| (the absolute value of the number x, or
% the length of the vector x); it is the same as
% length(x); plain Metafont in fact says:
% let abs = length;
show floor(x); % floor
show ceiling(x); % ceiling
show x**y; % ** is not a built in: it is defined in the basic macros
% set for Metafont (plain Metafont) as a primarydef
min
{{works with|min|0.19.3}}
e ; e
pi ; π
sqrt ; square root
log10 ; common logarithm
log2 ; binary logarithm
; no exponential
; no absolute value
floor ; greatest whole number smaller than or equal
ceil ; smallest whole number greater than or equal
trunc ; remove the fractional part (i.e. round towards 0)
round ; round number to nth decimal place
pow ; power
=={{header|MK-61/52}}==
пи С/П
КвКор С/П
lg С/П
e^x С/П
|x| С/П
П0 ^ [x] П1 - x=0 09 ИП0 С/П ЗН x>=0 14 ИП1 С/П ИП1 1 - С/П
П0 ^ [x] П1 - x=0 09 ИП0 С/П ЗН x<0 14 ИП1 С/П ИП1 1 + С/П
x^y С/П
=={{header|Modula-3}}==
Modula-3 uses a module that is a wrapper around [[C]]'s <tt>math.h</tt>.
Note that all of these procedures (except the built ins) take <tt>LONGREAL</tt>s as their argument, and return <tt>LONGREAL</tt>s.
```modula3
Math.E;
Math.Pi;
Math.sqrt(x);
Math.log(x);
Math.exp(x);
ABS(x); (* Built in function. *)
FLOOR(x); (* Built in function. *)
CEILING(x); (* Built in function. *)
Math.pow(x, y);
Neko
/**
Real constants and functions, in Neko
Tectonics:
nekoc real-constants.neko
neko real-constants
*/
var euler = $loader.loadprim("std@math_exp", 1)(1)
var pi = $loader.loadprim("std@math_pi", 0)()
var math_sqrt = $loader.loadprim("std@math_sqrt", 1)
var math_log = $loader.loadprim("std@math_log", 1)
var math_exp = $loader.loadprim("std@math_exp", 1)
var math_abs = $loader.loadprim("std@math_abs", 1)
var math_floor = $loader.loadprim("std@math_floor", 1)
var math_ceil = $loader.loadprim("std@math_ceil", 1)
var math_pow = $loader.loadprim("std@math_pow", 2)
$print("Euler : ", euler, "\n")
$print("Pi : ", pi, "\n")
$print("Sqrt(2) : ", math_sqrt(2), "\n")
$print("Log(10) : ", math_log(10), "\n")
$print("Exp(1) : ", math_pow(euler, 1), "\n")
$print("Abs(-2.2) : ", math_abs(-2.2), "\n")
$print("Floor(-2.2): ", math_floor(-2.2), "\n")
$print("Ceil(-2.2) : ", math_ceil(-2.2), "\n")
$print("Pow(2, 8) : ", math_pow(2, 8), "\n")
{{out}}
prompt$ nekoc real-contstants.neko
prompt$ neko real-contstants.n
Euler : 2.71828182845905
Pi : 3.14159265358979
Sqrt(2) : 1.4142135623731
Log(10) : 2.30258509299405
Exp(1) : 2.71828182845905
Abs(-2.2) : 2.2
Floor(-2.2): -3
Ceil(-2.2) : -2
Pow(2, 8) : 256
NetRexx
All the required constants and functions (and more) are in [[Java|Java's]] Math class. NetRexx also provides a limited set of built in numeric manipulation functions for it's Rexx object.
/* NetRexx */
options replace format comments java crossref symbols nobinary utf8
numeric digits 30
x = 2.5
y = 3
pad = 40
say
say 'Java Math constants & functions:'
say Rexx(' Euler''s number (e):').left(pad) Math.E
say Rexx(' Pi:').left(pad) Math.PI
say Rexx(' Square root of' x':').left(pad) Math.sqrt(x)
say Rexx(' Log(e) of' x':').left(pad) Math.log(x)
say Rexx(' Log(e) of e:').left(pad) Math.log(Math.E)
say Rexx(' Log(10) of' x':').left(pad) Math.log10(x)
say Rexx(' Log(10) of 10:').left(pad) Math.log10(10)
say Rexx(' Exponential (e**x) of' x':').left(pad) Math.exp(x)
say Rexx(' Exponential (e**x) of log(e)' x':').left(pad) Math.exp(Math.log(x))
say Rexx(' Abs of' x':').left(pad) Math.abs(x.todouble)
say Rexx(' Abs of' (-x)':').left(pad) Math.abs((-x).todouble)
say Rexx(' Floor of' x':').left(pad) Math.floor(x)
say Rexx(' Floor of' (-x)':').left(pad) Math.floor((-x))
say Rexx(' Ceiling of' x':').left(pad) Math.ceil(x)
say Rexx(' Ceiling of' (-x)':').left(pad) Math.ceil((-x))
say Rexx(' ' x 'to the power of' y':').left(pad) Math.pow(x, y)
say Rexx(' ' x 'to the power of' 1 / y':').left(pad) Math.pow(x, 1 / y)
say Rexx(' 10 to the power of log10' x':').left(pad) Math.pow(10, Math.log10(x))
-- Extras
say Rexx(' Cube root of' x':').left(pad) Math.cbrt(x)
say Rexx(' Hypotenuse of' 3 'x' 4 'right triangle:').left(pad) Math.hypot(3, 4)
say Rexx(' Max of' (-x) '&' x':').left(pad) Math.max((-x).todouble, x)
say Rexx(' Min of' (-x) '&' x':').left(pad) Math.min((-x).todouble, x)
say Rexx(' Signum of' x':').left(pad) Math.signum((x).todouble)
say Rexx(' Signum of' x '-' x':').left(pad) Math.signum((x - x).todouble)
say Rexx(' Signum of' (-x)':').left(pad) Math.signum((-x).todouble)
say
say 'NetRexx built-in support for numeric data:'
say Rexx(' Abs of' x':').left(pad) x.abs()
say Rexx(' Abs of' (-x)':').left(pad) (-x).abs()
say Rexx(' Sign of' x':').left(pad) x.sign()
say Rexx(' Sign of' x '-' x':').left(pad) (x - x).sign()
say Rexx(' Sign of' (-x)':').left(pad) (-x).sign()
say Rexx(' Max of' (-x) '&' x':').left(pad) (-x).max(x)
say Rexx(' Min of' (-x) '&' x':').left(pad) (-x).min(x)
say Rexx(' Truncate' x 'by' y':').left(pad) x.trunc(y)
say Rexx(' Format (with rounding)' x 'by' y':').left(pad) x.format(y, 0)
{{out}}
Java Math constants & functions:
Euler's number (e): 2.718281828459045
Pi: 3.141592653589793
Square root of 2.5: 1.58113883008419
Log(e) of 2.5: 0.9162907318741551
Log(e) of e: 1
Log(10) of 2.5: 0.3979400086720376
Log(10) of 10: 1
Exponential (e**x) of 2.5: 12.18249396070347
Exponential (e**x) of log(e) 2.5: 2.5
Abs of 2.5: 2.5
Abs of -2.5: 2.5
Floor of 2.5: 2
Floor of -2.5: -3
Ceiling of 2.5: 3
Ceiling of -2.5: -2
2.5 to the power of 3: 15.625
2.5 to the power of 0.3333333333333333 1.357208808297453
10 to the power of log10 2.5: 2.5
Cube root of 2.5: 1.357208808297453
Hypotenuse of 3 x 4 right triangle: 5
Max of -2.5 & 2.5: 2.5
Min of -2.5 & 2.5: -2.5
Signum of 2.5: 1
Signum of 2.5 - 2.5: 0
Signum of -2.5: -1
NetRexx built-in support for numeric data:
Abs of 2.5: 2.5
Abs of -2.5: 2.5
Sign of 2.5: 1
Sign of 2.5 - 2.5: 0
Sign of -2.5: -1
Max of -2.5 & 2.5: 2.5
Min of -2.5 & 2.5: -2.5
Truncate 2.5 by 3: 2.500
Format (with rounding) 2.5 by 3: 3
Nim
import math
var x, y = 12.5
echo E
echo Pii
echo sqrt(x)
echo ln(x)
echo log10(x)
echo exp(x)
echo abs(x)
echo floor(x)
echo ceil(x)
echo pow(x, y)
Objeck
Float->Pi();
Float->E();
4.0->SquareRoot();
1.5->Log();
# exponential is not supported
3.99->Abs();
3.99->Floor();
3.99->Ceiling();
4.5->Ceiling(2.0);
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 *)
-. x (* negation for floats *)
Octave
e % e
pi % pi
sqrt(pi) % square root
log(e) % natural logarithm
exp(pi) % exponential
abs(-e) % absolute value
floor(pi) % floor
ceil(pi) % ceiling
e**pi % power
Oforth
import: math
: testReal
E println
Pi println
9 sqrt println
2 ln println
2 exp println
-3.4 abs println
3.4 exp println
2.4 floor println
3.9 floor println
5.5 floor println
-2.4 floor println
-3.9 floor println
-5.5 floor println
2.4 ceil println
3.9 ceil println
5.5 ceil println
-2.4 ceil println
-3.9 ceil println
-5.5 ceil println ;
ooRexx
{{trans|NetRexx}} {{uses from|OoRexx|RxMath}}
/* Rexx */
-- MathLoadFuncs & MathDropFuncs are no longer needed and are effectively NOPs
-- but MathLoadFuncs does return its copyright statement when given a string argument
RxMathCopyright = MathLoadFuncs('')
say RxMathCopyright
numeric digits 16
x = 2.5
y = 3
pad = 40
digs = digits()
say
say 'Working with precision' digs
say 'Math constants & functions:'
say (' Euler''s number (e):')~left(pad) RxCalcExp(1, digs)
say (' Pi:')~left(pad) RxCalcPi(digs)
say (' Square root of' x':')~left(pad) RxCalcSqrt(x, digs)
say (' Log(e) of' x':')~left(pad) RxCalcLog(x, digs)
say (' Log(e) of e:')~left(pad) RxCalcLog(RxCalcExp(1, digs), digs)
say (' Log(10) of' x':')~left(pad) RxCalcLog10(x, digs)
say (' Log(10) of 10:')~left(pad) RxCalcLog10(10, digs)
say (' Exponential (e**x) of' x':')~left(pad) RxCalcExp(x, digs)
say (' Exponential (e**x) of log(e)' x':')~left(pad) RxCalcExp(RxCalcLog(x, digs), digs)
say (' ' x 'to the power of' y':')~left(pad) RxCalcPower(x, y, digs)
say (' ' x 'to the power of 1/'y':')~left(pad) RxCalcPower(x, 1 / y, digs)
say (' 10 to the power of log10' x':')~left(pad) RxCalcPower(10, RxCalcLog10(x), digs)
say
say 'Rexx built-in support for numeric data:'
say (' Abs of' x':')~left(pad) x~abs()
say (' Abs of' (-x)':')~left(pad) (-x)~abs()
say (' Sign of' x':')~left(pad) x~sign()
say (' Sign of' x '-' x':')~left(pad) (x - x)~sign()
say (' Sign of' (-x)':')~left(pad) (-x)~sign()
say (' Max of' (-x) '&' x':')~left(pad) (-x)~max(x)
say (' Min of' (-x) '&' x':')~left(pad) (-x)~min(x)
say (' Truncate' x 'by' y':')~left(pad) x~trunc(y)
say (' Format (with rounding)' x 'by' y':')~left(pad) x~format(y, 0)
say
say 'Use RYO functions for floor & ceiling:'
say (' Floor of' x':')~left(pad) floor(x)
say (' Floor of' (-x)':')~left(pad) floor((-x))
say (' Ceiling of' x':')~left(pad) ceiling(x)
say (' Ceiling of' (-x)':')~left(pad) ceiling((-x))
return
-- floor and ceiling functions are not part of ooRexx
floor: procedure
return arg(1)~trunc() - (arg(1) < 0) * (arg(1) \= arg(1)~trunc())
ceiling: procedure
return arg(1)~trunc() + (arg(1) > 0) * (arg(1) \= arg(1)~trunc())
::requires 'RxMath' library
{{out}}
rxmath 1.1 - REXX mathematical function package
(c) Copyright RexxLanguage Association 2005.
All Rights Reserved.
Working with precision 16
Math constants & functions:
Euler's number (e): 2.718281828459045
Pi: 3.141592653589793
Square root of 2.5: 1.581138830084190
Log(e) of 2.5: 0.9162907318741551
Log(e) of e: 1
Log(10) of 2.5: 0.3979400086720376
Log(10) of 10: 1
Exponential (e**x) of 2.5: 12.18249396070347
Exponential (e**x) of log(e) 2.5: 2.5
2.5 to the power of 3: 15.625
2.5 to the power of 1/3: 1.357208808297453
10 to the power of log10 2.5: 2.5
Rexx built-in support for numeric data:
Abs of 2.5: 2.5
Abs of -2.5: 2.5
Sign of 2.5: 1
Sign of 2.5 - 2.5: 0
Sign of -2.5: -1
Max of -2.5 & 2.5: 2.5
Min of -2.5 & 2.5: -2.5
Truncate 2.5 by 3: 2.500
Format (with rounding) 2.5 by 3: 3
Use RYO functions for floor & ceiling:
Floor of 2.5: 2
Floor of -2.5: -3
Ceiling of 2.5: 3
Ceiling of -2.5: -2
Oz
{ForAll
[
{Exp 1.} %% 2.7183 Euler's number: not predefined
4. * {Atan2 1. 1.} %% 3.1416 pi: not predefined
{Sqrt 81.} %% 9.0 square root; expects a float
{Log 2.7183} %% 1.0 natural logarithm
{Abs ~1} %% 1 absolute value; expects a float or an integer
{Floor 1.999} %% 1.0 floor; expects and returns a float
{Ceil 1.999} %% 2.0 ceiling; expects and returns a float
{Pow 2 3} %% 8 power; both arguments must be of the same type
]
Show}
PARI/GP
[exp(1), Pi, sqrt(2), log(2), abs(2), floor(2), ceil(2), 2^3]
Pascal
See [[Real_constants_and_functions#Delphi | Delphi]]
Perl
use POSIX; # for floor() and ceil()
exp(1); # e
4 * atan2(1, 1); # pi
sqrt($x); # square root
log($x); # natural logarithm; log10() available in POSIX module
exp($x); # exponential
abs($x); # absolute value
floor($x); # floor
ceil($x); # ceiling
$x ** $y; # power
use Math::Trig;
pi; # alternate way to get pi
use Math::Complex;
pi; # alternate way to get pi
Perl 6
say e; # e
say π; # or pi # pi
say τ; # or tau # tau
# Common mathmatical function are availble
# as subroutines and as numeric methods.
# It is a matter of personal taste and
# programming style as to which is used.
say sqrt 2; # Square root
say 2.sqrt; # Square root
# If you omit a base, does natural logarithm
say log 2; # Natural logarithm
say 2.log; # Natural logarithm
# Specify a base if other than e
say log 4, 10; # Base 10 logarithm
say 4.log(10); # Base 10 logarithm
say 4.log10; # Convenience, base 10 only logarithm
say exp 7; # Exponentiation base e
say 7.exp; # Exponentiation base e
# Specify a base if other than e
say exp 7, 4; # Exponentiation
say 7.exp(4); # Exponentiation
say 4 ** 7; # Exponentiation
say abs -2; # Absolute value
say (-2).abs; # Absolute value
say floor -3.5; # Floor
say (-3.5).floor; # Floor
say ceiling pi; # Ceiling
say pi.ceiling; # Ceiling
say e ** π\i + 1 ≅ 0; # :-)
Phix
?E -- Euler number
?PI -- pi
?log(E) -- natural logarithm
?log10(10) -- base 10 logarithm
?exp(log(5)) -- exponential
?sqrt(5) -- square root
?abs(-1.2) -- absolute value
?floor(-1.2) -- floor, -2
?ceil(-1.2) -- ceiling, -1
?round(-1.8) -- rounded, -2
?trunc(-1.8) -- truncate, -1
?power(E,log(5)) -- displays 5.0
?power(10,log10(5)) -- displays 5.0
?INVLN10 -- displays 0.434..
?exp(1/INVLN10) -- displays 10.0
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
PL/I
/* e not available other than by using exp(1q0).*/
/* pi not available other than by using a trig function such as: pi=4*atan(1) */
y = sqrt(x);
y = log(x);
y = log2(x);
y = log10(x);
y = exp(x);
y = abs(x);
y = floor(x);
y = ceil(x);
a = x**y; /* power */
/* extra functions: */
y = erf(x); /* the error function. */
y = erfc(x); /* the error function complemented. */
y = gamma (x);
y = loggamma (x);
PicoLisp
PicoLisp has only limited floating point support (scaled bignum arithmetics). It can handle real numbers with as many positions after the decimal point as desired, but is practically limited by the precision of the C-library functions (about 16 digits). The default precision is six, and can be changed with '[http://software-lab.de/doc/refS.html#scl scl]':
(scl 12) # 12 places after decimal point
(load "@lib/math.l")
(prinl (format (exp 1.0) *Scl)) # e, exp
(prinl (format pi *Scl)) # pi
(prinl (format (pow 2.0 0.5) *Scl)) # sqare root
(prinl (format (sqrt 2.0 1.0) *Scl))
(prinl (format (log 2.0) *Scl)) # logarithm
(prinl (format (exp 4.0) *Scl)) # exponential
(prinl (format (abs -7.2) *Scl)) # absolute value
(prinl (abs -123))
(prinl (format (pow 3.0 4.0) *Scl)) # power
{{out}}
2.718281828459
3.141592653590
1.414213562373
1.414213562373
0.693147180560
54.598150033144
7.200000000000
123
81.000000000000
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, f/math>)
See also [[Trigonometric Functions]]
ACL2
Only the last three are available as built in functions.
loor 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;
PowerShell
Since PowerShell has access to .NET all this can be achieved using the .NET Base Class Library:
Write-Host ([Math]::E)
Write-Host ([Math]::Pi)
Write-Host ([Math]::Sqrt(2))
Write-Host ([Math]::Log(2))
Write-Host ([Math]::Exp(2))
Write-Host ([Math]::Abs(-2))
Write-Host ([Math]::Floor(3.14))
Write-Host ([Math]::Ceiling(3.14))
Write-Host ([Math]::Pow(2, 3))
PureBasic
Debug #E
Debug #PI
Debug Sqr(f)
Debug Log(f)
Debug Exp(f)
Debug Log10(f)
Debug Abs(f)
Debug Pow(f,f)
Python
import math
math.e # e
math.pi # pi
math.sqrt(x) # square root (Also commonly seen as x ** 0.5 to obviate importing the math module)
math.log(x) # natural logarithm
math.log10(x) # base 10 logarithm
math.exp(x) # e raised to the power of x
abs(x) # absolute value
math.floor(x) # floor
math.ceil(x) # ceiling
x ** y # exponentiation
pow(x, y[, n]) # exponentiation [, modulo n (useful in certain encryption/decryption algorithms)]
# The math module constants and functions can, of course, be imported directly by:
# from math import e, pi, sqrt, log, log10, exp, floor, ceil
R
exp(1) # e
pi # pi
sqrt(x) # square root
log(x) # natural logarithm
log10(x) # base 10 logarithm
log(x, y) # arbitrary base logarithm
exp(x) # exponential
abs(x) # absolute value
floor(x) # floor
ceiling(x) # ceiling
x^y # power
Racket
(exp 1) ; e
pi ; pi
(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
REXX
REXX has no built-in functions for trig functions, square root, pi, exponential ('''e''' raised to a power), logarithms and other similar functions.
REXX doesn't have any built-in (math) constants.
abs
a=abs(y) /*takes the absolute value of y.*/
===exponentiation (**)===
r=x**y /*REXX only supports integer powers.*/
/*Y may be negative, zero, positive.*/
/*X may be any real number. */
ceiling
A ceiling function for REXX:
ceiling: procedure; parse arg x; t=trunc(x); return t+(x>0)*(x\=t)
floor
A floor function for REXX:
floor: procedure; parse arg x; t=trunc(x); return t-(x<0)-(x\=t)
===sqrt (optimized)=== A [principal] square root (SQRT) function for REXX (with arbitrary precision):
/*──────────────────────────────────SQRT subroutine───────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0 /*handle 0 case.*/
if \datatype(x,'N') then return '[n/a]' /*Not Applicable ───if not numeric.*/
i=; if x<0 then do; x=-x; i='i'; end /*handle complex numbers if X is < 0.*/
d=digits() /*get the current numeric precision. */
m.=9 /*technique uses just enough digits. */
h=d+6 /*use extra decimal digits for accuracy*/
numeric digits 9 /*use "small" precision at first. */
numeric form /*force scientific form of the number. */
if fuzz()\==0 then numeric fuzz 0 /*just in case invoker has a FUZZ set.*/
parse value format(x,2,1,,0) 'E0' with g 'E' _ . /*get the X's exponent.*/
g=(g * .5) || 'e' || (_ % 2) /*1st guesstimate for the square root. */
/* g= g * .5 'e' (_ % 2) */ /*a shorter & concise version of above.*/
/*Note: to insure enough accuracy for */
/* the result, the precision during */
/* the SQRT calculations is increased */
/* by two extra decimal digits. */
do j=0 while h>9; m.j=h; h=h%2+1 /*compute the sizes (digs) of precision*/
end /*j*/ /* [↑] precisions are stored in M. */
/*now, we start to do the heavy lifting*/
do k=j+5 to 0 by -1 /*compute the √ with increasing digs.*/
numeric digits m.k /*each iteration, increase the digits. */
g=(g+x/g) * .5 /*perform the nitty-gritty calculations*/
end /*k*/ /* [↑] * .5 is faster than / 2 */
/* [↓] normalize √ ──► original digits*/
numeric digits d /* [↓] make answer complex if X < 0. */
return (g/1)i /*normalize, and add possible I suffix.*/
╔════════════════════════════════════════════════════════════════════╗
╔═╝ __ ╚═╗
║ √ ║
║ ║
║ While the above REXX code seems like it's doing a lot of extra work, ║
║ it saves a substantial amount of processing time when the precision ║
║ (DIGITs) is a lot greater than the default (default is nine digits). ║
║ ║
║ Indeed, when computing square roots in the hundreds (even thousands) ║
║ of digits, this technique reduces the amount of CPU processing time ║
║ by keeping the length of the computations to a minimum (due to a large ║
║ precision), while the accuracy at the beginning isn't important for ║
║ calculating the (first) guesstimate (the running square root guess). ║
║ ║
║ Each iteration of K (approximately) doubles the number of digits, ║
║ but takes almost four times longer to compute (actually, around 3.8). ║
║ ║
║ The REXX code could be streamlined (pruned) by removing the ║
║ The NUMERIC FUZZ 0 statement can be removed if it is known ║
║ that it is already set to zero. (which is the default). ║
║ ║
║ Also, the NUMERIC FORM statement can be removed if it is known ║
║ that the form is SCIENTIFIC (which is the default). ║
║ __ ║
╚═╗ √ ╔═╝
╚════════════════════════════════════════════════════════════════════╝
===sqrt (simple)===
/*──────────────────────────────────SQRT subroutine─────────────────────*/
sqrt: procedure; arg x /*a simplistic SQRT subroutine.*/
if x=0 then return 0 /*handle special case of zero. */
d=digits() /*get the current precision (dig)*/
numeric digits d+2 /*ensure extra precision (2 digs)*/
g=x/4 /*try get a so-so 1st guesstimate*/
old=0 /*set OLD guess to zero. */
do forever /*keep at it 'til G (guess)=old.*/
g=(g+x/g) / 2 /*do the nitty-gritty calculation*/
if g=old then leave /*if G is the same as old, quit. */
old=g /*save OLD for next iteration. */
end /*forever*/ /* [↑] ···'til we run out of digs*/
numeric digits d /*restore the original precision.*/
return g/1 /*normalize to old precision (d).*/
other
Other mathematical-type functions supported are:
numeric digits ddd /*sets the current precision to DDD */
numeric fuzz fff /*arithmetic comparisons with FFF fuzzy*/
numeric form kkk /*exponential: scientific | engineering*/
low=min(a,b,c,d,e,f,g, ...) /*finds the min of specified arguments.*/
big=min(a,b,c,d,e,f,g, ...) /*finds the max of specified arguments.*/
rrr=random(low,high) /*gets a random integer from LOW-->HIGH*/
arr=random(low,high,seed) /* ... with a seed (to make repeatable)*/
mzp=sign(x) /*finds the sign of x (-1, 0, +1). */
fs=format(x) /*formats X with the current DIGITS() */
fb=format(x,bbb) /* BBB digs before decimal*/
fa=format(x,bbb,aaa) /* AAA digs after decimal*/
fa=format(x,,0) /* rounds X to an integer.*/
fe=format(x,,eee) /* exponent has eee places. */
ft=format(x,,eee,ttt) /*if x exceeds TTT digits, force exp. */
hh=b2x(bbb) /*converts binary/bits to hexadecimal. */
dd=c2d(ccc) /*converts character to decimal. */
hh=c2x(ccc) /*converts character to hexadecimal. */
cc=d2c(ddd) /*converts decimal to character. */
hh=d2x(ddd) /*converts decimal to hexadecimal. */
bb=x2b(hhh) /*converts hexadecimal to binary (bits)*/
cc=x2c(hhh) /*converts hexadecimal to character. */
dd=x2d(hhh) /*converts hexadecimal to decimal. */
Ring
See "Mathematical Functions" + nl
See "Sin(0) = " + sin(0) + nl
See "Sin(90) radians = " + sin(90) + nl
See "Sin(90) degree = " + sin(90*3.14/180) + nl
See "Cos(0) = " + cos(0) + nl
See "Cos(90) radians = " + cos(90) + nl
See "Cos(90) degree = " + cos(90*3.14/180) + nl
See "Tan(0) = " + tan(0) + nl
See "Tan(90) radians = " + tan(90) + nl
See "Tan(90) degree = " + tan(90*3.14/180) + nl
See "asin(0) = " + asin(0) + nl
See "acos(0) = " + acos(0) + nl
See "atan(0) = " + atan(0) + nl
See "atan2(1,1) = " + atan2(1,1) + nl
See "sinh(0) = " + sinh(0) + nl
See "sinh(1) = " + sinh(1) + nl
See "cosh(0) = " + cosh(0) + nl
See "cosh(1) = " + cosh(1) + nl
See "tanh(0) = " + tanh(0) + nl
See "tanh(1) = " + tanh(1) + nl
See "exp(0) = " + exp(0) + nl
See "exp(1) = " + exp(1) + nl
See "log(1) = " + log(1) + nl
See "log(2) = " + log(2) + nl
See "log10(1) = " + log10(1) + nl
See "log10(2) = " + log10(2) + nl
See "log10(10) = " + log10(10) + nl
See "Ceil(1.12) = " + Ceil(1.12) + nl
See "Ceil(1.72) = " + Ceil(1.72) + nl
See "Floor(1.12) = " + floor(1.12) + nl
See "Floor(1.72) = " + floor(1.72) + nl
See "fabs(1.12) = " + fabs(1.12) + nl
See "fabs(1.72) = " + fabs(1.72) + nl
See "pow(2,3) = " + pow(2,3) + nl
see "sqrt(16) = " + sqrt(16) + nl
RLaB
Mathematical Constants
RLaB has a number of mathematical constants built-in within the list ''const''. These facilities are provided through the Gnu Science Library [[http://www.gnu.org/software/gsl]].
const
e euler ln10 ln2 lnpi
log10e log2e pi pihalf piquarter
rpi sqrt2 sqrt2r sqrt3 sqrtpi
tworpi
Physical Constants
Another list of physical constants and unit conversion factors exists and is called ''mks''. Here the conversion goes between that particular unit and the equivalent unit in, one and only, metric system.
mks
F G J L N
Na R0 Ry Tsp V0
a a0 acre alpha atm
au bar barn btu c
cal cgal cm cm2 cm3
ct cup curie day dm
dm2 dm3 dyne e eV
eps0 erg fathom floz ft
ftcan ftlam g gal gauss
gf h ha hbar hour
hp in inH2O inHg kSB
kb kcal km km2 km3
kmh knot kpf lam lb
lumen lux ly mHg mSun
me micron mil mile min
mm mm2 mm3 mmu mn
mp mph mu0 mub mue
mun mup nmi oz pal
parsec pf phot poise psi
rad roe stilb stokes tcs
therm tntton ton torr toz
tsp uam ukgal ukton uston
week yd
Elementary Functions
x = rand()
>> sqrt(x)
2.23606798
>> log(x)
1.60943791
>> log10(x)
0.698970004
>> exp(x)
148.413159
>> abs(x)
5
>> floor(x)
5
>> ceil(x)
5
>> x .^ 2
25
Ruby
x.abs #absolute value
x.magnitude #absolute value
x.floor #floor
x.ceil #ceiling
x ** y #power
include Math
E #e
PI #pi
sqrt(x) #square root
log(x) #natural logarithm
log(x, y) #logarithm base y
log10(x) #base 10 logarithm
exp(x) #exponential
Run BASIC
print "exp:";chr$(9); EXP(1)
print "PI:";chr$(9); 22/7
print "Sqr2:";chr$(9); SQR(2)
print "Log2:";chr$(9); LOG(2) : REM Base 10
print "Exp2:";chr$(9); EXP(2)
print "Abs2:";chr$(9); ABS(-2)
print "Floor:";chr$(9); INT(1.534)
print "ceil:";chr$(9); val(using("###",1.534))
print "Power:";chr$(9); 1.23^4
exp: 2.71828183
PI: 3.14285707
Sqr2: 1.41421356
Log2: 0.693147181
Exp2: 7.3890561
Abs2: 2
Floor: 1
ceil: 2
Power: 2.28886641
Rust
use std::f64::consts::*;
fn main() {
// e (base of the natural logarithm)
let mut x = E;
// π
x += PI;
// square root
x = x.sqrt();
// logarithm (any base allowed)
x = x.ln();
// ceiling (smallest integer not less than this number--not the same as round up)
x = x.ceil();
// exponential (ex)
x = x.exp();
// absolute value (a.k.a. "magnitude")
x = x.abs();
// floor (largest integer less than or equal to this number--not the same as truncate or int)
x = x.floor();
// power (xy)
x = x.powf(x);
assert_eq!(x, 4.0);
}
Scala
object RealConstantsFunctions extends App{
println(math.E) // e
println(math.Pi) // pi
println(math.sqrt(2.0)) // square root
println(math.log(math.E)) // log to base e
println(math.log10(10.0)) // log to base 10
println(math.exp(1.0)) // exponential
println(math.abs(-1)) // absolute value
println(math.floor(-2.5)) // floor
println(math.ceil(-2.5)) // ceiling
println(math.pow(2.5, 3.5)) // power
}
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
Seed7
The [http://seed7.sourceforge.net/libraries/math.htm math.s7i] library defines: {| class="wikitable" style="text-align:left" | [http://seed7.sourceforge.net/libraries/math.htm#E E] || # e (Euler's number) |- | [http://seed7.sourceforge.net/libraries/math.htm#PI PI] || # Pi |- | [http://seed7.sourceforge.net/libraries/math.htm#sqrt%28ref_float%29 sqrt(x)] || # square root |- | [http://seed7.sourceforge.net/libraries/math.htm#log%28ref_float%29 log(x)] || # natural logarithm - log base 10 is also available: [http://seed7.sourceforge.net/libraries/math.htm#log10%28ref_float%29 log10(x)]) |- | [http://seed7.sourceforge.net/libraries/math.htm#exp%28ref_float%29 exp(x)] || # exponential |- | [http://seed7.sourceforge.net/libraries/math.htm#abs%28ref_float%29 abs(x)] || # absolute value |- | [http://seed7.sourceforge.net/libraries/math.htm#floor%28ref_float%29 floor(x)] || # floor |- | [http://seed7.sourceforge.net/libraries/math.htm#ceil%28ref_float%29 ceil(x)] || # ceiling |}
The [http://seed7.sourceforge.net/libraries/float.htm float.s7i] library defines: {| class="wikitable" style="text-align:left" | [http://seed7.sourceforge.net/libraries/float.htm#%28ref_float%29**%28ref_integer%29 x ** y] || # power with [http://seed7.sourceforge.net/libraries/integer.htm integer] exponent |- | [http://seed7.sourceforge.net/libraries/float.htm#%28ref_float%29**%28ref_float%29 x ** y] || # power with float exponent |}
Sidef
Num.e # e
Num.pi # pi
x.sqrt # square root
x.log # natural logarithm
x.log10 # base 10 logarithm
x.exp # e raised to the power of x
x.abs # absolute value
x.floor # floor
x.ceil # ceiling
x**y # exponentiation
Slate
numerics E.
numerics Pi.
n sqrt.
n log10. "base 10 logarithm"
n ln. "natural logarithm"
n log: m. "arbitrary base logarithm"
n exp. "exponential"
n abs. "absolute value"
n floor.
n ceiling.
n raisedTo: anotherNumber
Smalltalk
Float e.
Float pi.
aNumber sqrt.
aNumber log. "base 10 logarithm"
aNumber ln. "natural logarithm"
aNumber exp. "exponential"
aNumber abs. "absolute value"
aNumber floor.
aNumber ceiling.
aNumber raisedTo: anotherNumber
Sparkling
// e:
print(M_E);
// π:
print(M_PI);
// square root:
let five = sqrt(25);
// logarithm
// natural:
let one = log(M_E);
// base-2:
let six = log2(64);
// base-10
let three = log10(1000);
// exponential
let e_cubed = exp(3);
// absolute value
let ten = abs(-10);
// floor
let seven = floor(7.8);
// ceiling
let four = ceil(3.2);
// power
let eighty_one = pow(3, 4);
Standard ML
Math.e; (* e *)
Math.pi; (* pi *)
Math.sqrt x; (* square root *)
Math.ln x; (* natural logarithm--log base 10 also available (Math.log10) *)
Math.exp x; (* exponential *)
abs x; (* absolute value *)
floor x; (* floor *)
ceil x; (* ceiling *)
Math.pow (x, y); (* power *)
~ x; (* negation *)
Stata
scalar x=2
scalar y=3
di exp(1)
di _pi
di c(pi)
di sqrt(x)
di log(x)
di log10(x)
di exp(x)
di abs(x)
di floor(x)
di ceil(x)
di x^y
Swift
import Darwin
M_E // e
M_PI // pi
sqrt(x) // square root--cube root also available (cbrt)
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
Tcl
expr {exp(1)} ;# e
expr {4 * atan(1)} ;# pi -- also, simpler: expr acos(-1)
expr {sqrt($x)} ;# square root
expr {log($x)} ;# natural logarithm, also log10
expr {exp($x)} ;# exponential
expr {abs($x)} ;# absolute value
expr {floor($x)} ;# floor
expr {ceil($x)} ;# ceiling
expr {$x**$y} ;# power, also pow($x,$y)
The constants and are also available with high precision in a support library. {{tcllib|math::constants}}
package require math::constants
math::constants::constants e pi
puts "e = $e, pi = $pi"
=={{header|TI-89 BASIC}}==
{|
|-
! Mathematical !! TI-89 !! Notes
|-
| || ℯ || (U+212F SCRIPT SMALL E)
|-
| || π || (U+03C0 GREEK SMALL LETTER PI)
|-
| || √(x) || (U+221A SQUARE ROOT)
|-
| || ln(x)
|-
| || log(x)
|-
| || log(b, x) || The optional base argument comes ''first''
|-
| || floor(x)
|-
| || ceiling(x)
|-
| || x^y
|}
UNIX Shell
{{works with|ksh93}} ksh93 exposes math functions from the C math library
echo $(( exp(1) )) # e
echo $(( acos(-1) )) # PI
x=5
echo $(( sqrt(x) )) # square root
echo $(( log(x) )) # logarithm base e
echo $(( log2(x) )) # logarithm base 2
echo $(( log10(x) )) # logarithm base 10
echo $(( exp(x) )) # exponential
x=-42
echo $(( abs(x) )) # absolute value
x=-5.5
echo $(( floor(x) )) # floor
echo $(( ceil(x) )) # ceiling
x=10 y=3
echo $(( pow(x,y) )) # power
{{out}}
2.71828182845904524
3.14159265358979324
2.2360679774997897
1.60943791243410037
2.32192809488736235
0.698970004336018805
148.413159102576603
42
-6
-5
1000
XPL0
include c:\cxpl\codes; \intrinsic 'code' declarations
func real Power(X, Y); \X raised to the Y power
real X, Y;
return Exp(Y*Ln(X));
real E, Pi;
[Format(4, 16); \places shown before and after .
E:= Exp(1.0);
RlOut(0, E); CrLf(0);
RlOut(0, Ln(E)); CrLf(0);
CrLf(0);
Pi:= ATan2(0.0, -1.0); \Pi is also a defined constant
RlOut(0, Pi); CrLf(0);
RlOut(0, Cos(Pi)); CrLf(0);
CrLf(0);
RlOut(0, Sqrt(2.0)); CrLf(0); \Sqrt is a call to an intrinsic
RlOut(0, Log(100.0)); CrLf(0);
RlOut(0, Ln(Exp(123.456789))); CrLf(0);
CrLf(0);
RlOut(0, abs(-1234.5)); CrLf(0); \abs works for both reals & ints
CrLf(0);
RlOut(0, float(fix(1.999-0.5))); CrLf(0); \floor rounds toward -infinity
RlOut(0, float(fix(1.001+0.5))); CrLf(0); \ceiling rounds toward +infinity
RlOut(0, Power(sqrt(2.0), 4.0)); CrLf(0); \sqrt is an inline function and
] \ can be used for both reals & ints
{{out}}
2.7182818284590500
1.0000000000000000
3.1415926535897900
-1.0000000000000000
1.4142135623731000
2.0000000000000000
123.4567890000000000
1234.5000000000000000
1.0000000000000000
2.0000000000000000
4.0000000000000000
zkl
(0.0).e // Euler's number, a property of all floats
(0.0).e.pi // pi, yep, all floats
(2.0).sqrt() // square root
(2.0).log() // natural (base e) logarithm
(2.0).log10() // log base 10
(0.0).e.pow(x) // e^x
(-10.0).abs() // absolute value, both floats and ints
x.pow(y) // x raised to the y power
x.ceil() // ceiling
x.floor() // floor
{{omit from|GUISS}} {{omit from|M4}} {{omit from|ML/I}}