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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)
$\pi$
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 )

Related task

Trigonometric Functions

11l

Translation of: Python

<lang 11l>math:e // e math:pi // pi sqrt(x) // square root log(x) // natural logarithm log10(x) // base 10 logarithm exp(x) // e raised to the power of x abs(x) // absolute value floor(x) // floor ceil(x) // ceiling x ^ y // exponentiation</lang>

6502 Assembly

None of these are built-in, irrational constants are best implemented with lookup tables. Absolute value can be handled like so:

<lang 6502asm>GetAbs: ;assumes value we want to abs() is loaded into accumulator eor #$ff clc adc #1 rts</lang>

ACL2

Only the last three are available as built in functions.

<lang Lisp>(floor 15 2) ;; This is the floor of 15/2 (ceiling 15 2) (expt 15 2) ;; 15 squared</lang> ==ACL2== Only the last three are available as built in functions.

loor and ceiling are not provided, one can define them using integer part:

<lang pop11>define floor(x);

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

enddefine;

define ceiling(x);

   -floor(-x);

enddefine;</lang>

Action!

Part of the solution can be find in REALMATH.ACT.

Library: Action! Tool Kit

Library: Action! Real Math

<lang Action!>INCLUDE "H6:REALMATH.ACT"

PROC Euler(REAL POINTER e)

 REAL x

 IntToReal(1,x)
 Exp(x,e)

RETURN

PROC Main()

 REAL a,b,c
 INT i

 Put(125) PutE() ;clear screen
 MathInit()

 Euler(a)
 Print("e=") PrintR(a)
 PrintE(" by Exp(1)")

 ValR("2",a)
 Sqrt(a,b)
 Print("Sqrt(") PrintR(a)
 Print(")=") PrintR(b)
 Print(" by Power(") PrintR(a)
 PrintE(",0.5)")

 ValR("2.5",a)
 Ln(a,b)
 Print("Ln(") PrintR(a)
 Print(")=") PrintRE(b)

 ValR("14.2",a)
 Log10(a,b)
 Print("Log10(") PrintR(a)
 Print(")=") PrintRE(b)

 ValR("-3.7",a)
 Exp(a,b)
 Print("Exp(") PrintR(a)
 Print(")=") PrintRE(b)

 ValR("2.6",a)
 Exp10(a,b)
 Print("Exp10(") PrintR(a)
 Print(")=") PrintRE(b)

 ValR("25.3",a)
 ValR("1.3",b)
 Power(a,b,c)
 Print("Power(") PrintR(a)
 Print(",") PrintR(b)
 Print(")=") PrintRE(c)

 ValR("-32.5",a)
 RealAbs(a,b)
 Print("Abs(") PrintR(a)
 Print(")=") PrintR(b)
 PrintE(" by bit manipulation")

 ValR("23.15",a)
 i=Floor(a)
 Print("Floor(") PrintR(a)
 PrintF(")=%I by own function%E",i)

 ValR("-23.15",a)
 i=Floor(a)
 Print("Floor(") PrintR(a)
 PrintF(")=%I by own function%E",i)

 ValR("23.15",a)
 i=Ceiling(a)
 Print("Ceiling(") PrintR(a)
 PrintF(")=%I by own function%E",i)

 ValR("-23.15",a)
 i=Ceiling(a)
 Print("Ceiling(") PrintR(a)
 PrintF(")=%I by own function%E",i)

 PutE()
 PrintE("There is no support in Action! for pi.")

RETURN</lang>

Output:

Screenshot from Atari 8-bit computer

e=2.71828179 by Exp(1)
Sqrt(2)=1.41421355 by Power(2,0.5)
Ln(2.5)=.9162907319
Log10(14.2)=1.15228834
Exp(-3.7)=.0247235365
Exp10(2.6)=398.106988
Power(25.3,1.3)=66.6893784
Abs(-32.5)=32.5 by bit manipulation
Floor(23.15)=23 by own function
Floor(-23.15)=-24 by own function
Ceiling(23.15)=24 by own function
Ceiling(-23.15)=-23 by own function

There is no support in Action! for pi.

ActionScript

Actionscript has all the functions and constants mentioned in the task, available in the Math class. <lang ActionScript>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</lang> The Math class also contains several other constants. <lang ActionScript>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</lang>

Ada

Most of the constants and functions used in this task are defined in the pre-defined Ada package Ada.Numerics.Elementary_Functions. <lang ada>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</lang>

Aime

<lang aime># e exp(1);

pi

2 * asin(1);

sqrt(x); log(x); exp(x); fabs(x); floor(x); ceil(x); pow(x, y);</lang>

ALGOL 68

<lang algol68>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 #

))</lang>

Output:

 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

<lang algolw>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.</lang>

ARM Assembly

<lang> /* functions not availables */ </lang>

Arturo

<lang rebol>print ["Euler:" e] print ["Pi:" pi]

print ["sqrt 2.0:" sqrt 2.0] print ["ln 100:" ln 100] print ["log(10) 100:" log 100 10] print ["exp 3:" exp 3] print ["abs -1:" abs neg 1] print ["floor 23.536:" floor 23.536] print ["ceil 23.536:" ceil 23.536] print ["2 ^ 8:" 2 ^ 8]</lang>

Output:

Euler: 2.718281828459045 
Pi: 3.141592653589793 
sqrt 2.0: 1.414213562373095 
ln 100: 4.605170185988092 
log(10) 100: 2.0 
exp 3: 20.08553692318767 
abs -1: 1 
floor 23.536: 23 
ceil 23.536: 24 
2 ^ 8: 256

Asymptote

<lang Asymptote>real e = exp(1); // e not available write("e = ", e); write("pi = ", pi);

real x = 12.345; real y = 1.23;

write("sqrt = ", sqrt(2)); // square root write("ln = ", log(e)); // natural logarithm base e write("log = ", log10(x)); // base 10 logarithm write("log1p = ", log1p(x)); // log (1+x) write("exp = ", exp(e)); // exponential write("abs = ", abs(-1)); // absolute value write("fabs = ", fabs(-1)); // absolute value write("floor = ", floor(-e)); // floor write("ceil = ", ceil(-e)); // ceiling write("power = ", x ^ y); // power write("power = ", x ** y); // power</lang>

Output:

e     = 2.71828182845905
pi    = 3.14159265358979
sqrt  = 1.4142135623731
ln    = 1
log   = 1.09149109426795
log1p = 2.59114178285649
exp   = 15.1542622414793
abs   = 1
fabs   = 1
floor = -3
ceil  = -2
power = 22.0056421323763
power = 22.0056421323763

AutoHotkey

The following math functions are built into AutoHotkey: <lang 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</lang> No mathematical constants are built-in, but they can all be calculated: <lang autohotkey>e:=exp(1) pi:=2*asin(1)</lang> The following are additional trigonometric functions that are built into the AutoHotkey language: <lang autohotkey>Sin(Number) ; sine Cos(Number) ; cosine Tan(Number) ; tangent ASin(Number) ; arcsine ACos(Number) ; arccosine ATan(Number) ; arctangent</lang>

AWK

Awk has square root, logarithm, exponential and power.

<lang awk>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</lang>

Power's note:
With nawk or gawk, 2 ** -3.4 acts like 2 ^ -3.4. With mawk, 2 ** -3.4 is 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:

<lang awk>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</lang>

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: <lang axe>√(X)</lang>

To take the square root of an 8.8 fixed-point number Y: <lang axe>√(Y)ʳ</lang>

To take the base-2 logarithm of an integer X: <lang axe>ln(X)</lang>

To take 2 raised to an integer X: (Note that the base is not Euler's number) <lang axe>e^(X)</lang>

To take the absolute value of a signed integer X: <lang axe>abs(X)</lang>

BASIC

Works with: QuickBasic version 4.5

<lang qbasic>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</lang>

IS-BASIC

<lang IS-BASIC>100 LET X=2:LET Y=5 110 PRINT EXP(1) ! value of e 120 PRINT PI ! value of Pi 130 PRINT ROUND(PI,3) ! rounds Pi to 3 decimal places 140 PRINT TRUNCATE(PI,3) ! cuts 3 decimal places from Pi 150 PRINT SQR(X) ! square root of x 160 PRINT LOG(X) ! the natural logarithm of number x 170 PRINT LOG2(X) ! logarithm of x to base 2 180 PRINT LOG10(X) ! logarithm of x to base 10 190 PRINT EXP(X) ! exponential 200 PRINT ABS(X) ! the absolute value of a number 210 PRINT INT(X) ! the largest whole number not bigger than x 220 PRINT IP(X) ! the integer part of x 230 PRINT FP(X) ! stands for fractorial part 240 PRINT CEIL(X) ! ceiling: gives the smallest whole number not less than x 250 PRINT X^Y ! power 260 PRINT MIN(X,Y) ! the smaller number of x and y 270 PRINT MAX(X,Y) ! the bigger number of x and y 280 PRINT EPS(X) ! the smallest quantity that can be added to or subtracted from x to make the interpreter register a change in the value of x 290 PRINT INF ! The largest positive number the tinterpreter can handle. This number is 9.999999999*10^62</lang>

Sinclair ZX81 BASIC

Arguments to built-in functions may be placed in parentheses, but are not required to be.

Base of the natural logarithm: <lang basic>EXP 1</lang>

$\pi$ : <lang basic>PI</lang>

Square root: <lang basic>SQR X</lang>

Natural logarithm: <lang basic>LN X</lang>

Exponential: <lang basic>EXP X</lang>

Absolute value: <lang basic>ABS X</lang>

Floor: <lang basic>INT X</lang> (NB. Although this function is called INT, it corresponds to floor: e.g. INT -3.1 returns -4 not -3.)

Ceiling:
not provided as a built-in function.

Power: <lang basic>X**Y</lang> NB. Both $x$ and $y$ can be real numbers.

BBC BASIC

<lang bbcbasic> 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)

</lang>

BASIC256

<lang basic256>e = exp(1) # e not available print "e = "; e print "PI = "; PI

x = 12.345 y = 1.23

print "sqrt = "; sqr(x) # square root print "ln = "; log(e) # natural logarithm base e print "log10 = "; log10(e) # base 10 logarithm print "log = "; log(x)/log(y) # arbitrary base logarithm print "exp = "; exp(e) # exponential print "abs = "; abs(-1) # absolute value print "floor = "; floor(-e) # floor print "ceil = "; ceil(-e) # ceiling print "power = "; x ^ y # power</lang>

Output:

e     = 2.71828182846
PI    = 3.14159265359
sqrt  = 3.51354521815
ln    = 1.0
log10 = 0.4342944819
log   = 12.1404787425
exp   = 15.1542622415
abs   = 1
floor = -3
ceil  = -2
power = 22.0056421324

bc

The language has square root and power, but power only works if the exponent is an integer.

<lang bc>scale = 6 sqrt(2) /* 1.414213 square root */ 4.3 ^ -2 /* .054083 power (integer exponent) */</lang>

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.

Library: bc -l

<lang bc>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 */</lang>

The missing functions are absolute value, floor and ceiling. You can implement these functions, if you know what to do.

Translation of: AWK

<lang bc>/* 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 */</lang>

blz

The constant e <lang blz>{e}</lang>

The constant pi <lang blz>{pi}</lang>

Square root <lang blz>x ** 0.5</lang>

Logarithm (base n) <lang blz>x __ n</lang>

Exponential <lang blz>{e} ** x</lang>

Absolute Value <lang blz>abs(x)</lang>

Floor <lang blz>floor(x)</lang>

Ceiling <lang blz>ceil(x)</lang>

Power x to the y <lang blz>x ** y</lang>

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 <lang bracmat>x \D (10^x) { \D is the differentiation operator }</lang> has the result <lang bracmat>10^x*e\L10 { \L is the logarithm operator }</lang> Likewise e^(i*pi) evaluates to -1 and e^(1/2*i*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. <lang c>#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 */</lang>

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#

<lang csharp>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
   }

}</lang>

C++

using Math macros

<lang cpp>#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(euler_e)
           << "\nlg(100) = " << std::log10(100.0)
           << "\nexp(3) = " << std::exp(3.0)
           << "\n|-4.5| = " << std::abs(-4.5)   // or std::fabs(-4.5); 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;

}</lang>

using Boost

Library: Boost

<lang cpp>#include <iostream>

include <iomanip>
include <cmath>
include <boost/math/constants/constants.hpp>

int main() {

   using namespace boost::math::double_constants;
   std::cout << "e = " << std::setprecision(18) << e
             << "\ne³ = " << std::exp(3.0)
             << "\nπ = " << pi
             << "\nπ² = " << pi_sqr
             << "\n√2 = " << root_two
             << "\nln(e) = " << std::log(e)
             << "\nlg(100) = " << std::log10(100.0)
             << "\n|-4.5| = " << std::abs(-4.5)
             << "\nfloor(4.5) = " << std::floor(4.5)
             << "\nceiling(4.5) = " << std::ceil(4.5) << std::endl;

}</lang>

Output:

e = 2.71828182845904509
e³ = 20.0855369231876679
π = 3.14159265358979312
π² = 9.86960440108935799
√2 = 1.41421356237309515
ln(e) = 1
lg(100) = 2
|-4.5| = 4.5
floor(4.5) = 4
ceiling(4.5) = 5

Chef

See Basic integer arithmetic#Chef for powers.

Clojure

Translation of: Java

which is directly available.

<lang lisp>(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</lang>

Clojure does provide arbitrary precision versions as well:

<lang lisp>(ns user (:require [clojure.contrib.math :as math])) (math/sqrt x) (math/abs x) (math/floor x) (math/ceil x) (math/expt x y) </lang>

.. and as multimethods that can be defined for any type (e.g. complex numbers).

<lang lisp>(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)</lang>

COBOL

Everything that follows can take any number (except for SQRT which expects a non-negative number). The task constants and (intrinsic) functions: <lang cobol>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 </lang> COBOL also has the following extra mathematical functions: <lang cobol>FACTORIAL(n) *> Factorial EXP10(n) *> 10 to the nth power

> Trigonometric functions, including inverse ones, named as would be expected.</lang>

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. <lang lisp> (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 </lang>

Crystal

<lang ruby>x = 3.25 y = 4

puts x.abs # absolute value puts x.floor # floor puts x.ceil # ceiling puts x ** y # power puts

include Math # without including

puts E # puts Math::E -- exponential constant puts PI # puts Math::PI -- Archimedes circle constant puts TAU # puts Math::TAU -- the correct circle constant, >= version 0.36 puts sqrt(x) # puts Math.sqrt(x) -- real square root puts log(x) # puts Math.log(x) -- natural logarithm puts log10(x) # puts Math.log10(x) -- base 10 logarithm puts log(x, y) # puts Math.log(x, y) -- logarithm x base y puts exp(x) # puts Math.exp(x) -- exponential puts E**x # puts Math::E**x -- same </lang>

Template:0ut

3.25
3.0
4.0
111.56640625

2.718281828459045
3.141592653589793
6.283185307179586
1.8027756377319946
1.1786549963416462
0.5118833609788744
0.8502198590705461
25.790339917193062
25.79033991719306

D

<lang 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</lang>

Delphi

Log, Floor, Ceil and Power functions defined in Math.pas.

<lang Delphi>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</lang>

DWScript

See Delphi.

E

<lang 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</lang>

Elena

ELENA 4.x : <lang elena>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

}</lang>

Elixir

<lang 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</lang>

Elm

The following are all in the Basics module, which is imported by default: <lang elm>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</lang>

Erlang

<lang 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. </lang>

Output:

2.718281828459045
3.141592653589793
4.0
2.302585092994046
1.0
7.38905609893065
2.24
3
21
9.0
ok

ERRE

<lang 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</lang>

Output:

 2.718282
 3.141592653589793
 3.141593
 3.513545      3.513545
 2.513251
 1.091491
 12.14048
 229808.1
 12.345
 12
 13
 22.00564

F#

Translation of: C# – C sharp

<lang fsharp>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</lang>

Factor

<lang 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</lang>

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

<lang fantom> 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 </lang>

Note, . binds more tightly than -, so use brackets around negative numbers:

> -3f.pow(2f)
-9
> (-3f).pow(2f)
9

Forth

<lang 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 )</lang>

Fortran

<lang 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</lang>

4*ATAN(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, 4*DATAN(1.0) will be rejected because 1.0 is in single precision and DATAN expects double. Thus, 4*DATAN(1.0D0) or 4*DATAN(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

<lang 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 </lang>

Output:

 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. <lang frink> 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 </lang>

FutureBasic

<lang 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 </lang> 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

<lang 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))

}</lang>

Output:

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 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: <lang groovy>println ((-22).abs())</lang>

Output:

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: <lang groovy>println 22**3.5</lang>

Output:

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. <lang groovy>println ((-22)**3.5)</lang>

Output:

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. <lang haskell>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)</lang>

HicEst

Except for x^y, this is identical to Fortran: <lang HicEst>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</lang>

Icon and Unicon

<lang Icon>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</lang>

Library: Icon Programming Library

numbers provides floor and ceiling

Output:

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. <lang j>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</lang>

Java

All of these functions are in Java's Math class which, does not require any imports: <lang java>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</lang>

JavaScript

<lang 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)</lang>

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 "#":<lang jq> 1 | exp # i.e. e 1 | atan * 4 # i.e. π sqrt log # Naperian log exp length # absolute value if the argument is numeric floor ceil # requires jq >= 1.5 pow(x; y) # requires jq >= 1.5</lang>

Jsish

<lang javascript>/* 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!

/</lang>

Output:

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

<lang julia>e π, pi sqrt(x) log(x) exp(x) abs(x) floor(x) ceil(x) x^y</lang> 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

<lang scala>// 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

}</lang>

Output:

2.718281828459045
3.141592653589793
1.4142135623730951
1.0
1.0
2.718281828459045
1
-3.0
-2.0
24.705294220065465

Lambdatalk

<lang scheme> {E} -> 2.718281828459045 {PI} -> 3.141592653589793 {sqrt 2} -> 1.4142135623730951 {log {E}} -> 1 {exp 1} -> 2.718281828459045 {abs -1} -> 1 {floor -2.5} -> -3 {ceil -2.5} -> -2 {pow 2.5 3.5} -> 24.705294220065465 </lang>

Lasso

<lang 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)</lang>

Liberty BASIC

Ceiling and floor easily implemented as functions.
sqr( is the LB function for square root.
e & pi not available- calculate as shown. <lang lb> 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 </lang>

Lingo

<lang 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</lang>

LiveCode

LC 7.1+, prior to this floor & ceil were not built-in. <lang LiveCode>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</lang>

Logo

Works with: UCB Logo

<lang 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</lang>

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.

</lang>

Output:

| ?- 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

<lang 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</lang>

M2000 Interpreter

<lang 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 round(-2.7, 0)=-3, round(2.7, 0)=3
     Print round(-2.2, 0)=-2, round(2.2, 0)=2

     Print Sqrt(4)=2

} Checkit </lang>

Maple

<lang Maple>> abs(ceil(floor(ln(exp(1)^sqrt(exp(Pi*I)+1)))));

                                  0</lang>

Mathematica/Wolfram Language

<lang Mathematica>E Pi Sqrt[x] Log[x] Log[b,x] Exp[x] Abs[x] Floor[x] Ceiling[x] Power[x, y]</lang> Where x is the number, and b the base. Exp[x] can also be inputted as E^x or E^x and Power[x,y] can be also inputted as x^y or x^y. 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: <lang Mathematica>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</lang>

MATLAB / Octave

<lang MATLAB>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</lang>

MAXScript

<lang 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</lang>

Mercury

<lang> math.pi % Pi. math.e % Euler's number. math.sqrt(X) % Square root of X. math.ln(X) % Natural logarithm of X. math.log10(X) % Logarithm to the base 10 of X. math.log2(X) % Logarithm to the base 2 of X. math.log(B, X) % Logarithm to the base B of X. math.exp(X) % e raised to the power of X. float.abs(X) % Absolute value of X. math.floor(X) % Floor of X. math.ceiling(X) % Ceiling of X. math.pow(X, Y) % X raised to the power of Y.</lang>

Metafont

<lang 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</lang>

min

Works with: min version 0.19.3

<lang min>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</lang>

МК-61/52

<lang>1 e^x С/П

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</lang>

Modula-3

Modula-3 uses a module that is a wrapper around C's math.h.

Note that all of these procedures (except the built ins) take LONGREALs as their argument, and return LONGREALs. <lang 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);</lang>

Neko

<lang ActionScript>/**

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")</lang>

Output:

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's Math class. NetRexx also provides a limited set of built in numeric manipulation functions for it's Rexx object. <lang NetRexx>/* 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(' Eulers 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) </lang>

Output:

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

<lang nim>import math

var x, y = 12.5

echo E echo PI 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)</lang>

Objeck

<lang 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);</lang>

OCaml

Unless otherwise noted, the following functions are for floats only: <lang ocaml>Float.pi (* pi *) 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 *)</lang>

Octave

<lang 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</lang>

Oforth

<lang 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 ;</lang>

ooRexx

Translation of: NetRexx

Uses: RxMath

<lang ooRexx>/* 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 (' Eulers 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</lang>

Output:

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

<lang 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}</lang>

PARI/GP

<lang parigp>[exp(1), Pi, sqrt(2), log(2), abs(2), floor(2), ceil(2), 2^3]</lang>

Pascal

See Delphi

Perl

<lang 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</lang>

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

<lang 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</lang>

Picat

 println(math.e),
 println(math.pi),
 nl,
 
 println(sqrt(2)),
 nl,
 
 println(log(10)),                % base e
 println(log(math.pi,10)),        % some base, here pi
 println(log2(10)),               % base 2
 println(exp(2.302585092994046)),
 nl,
 
 println(abs(- math.e)),
 nl,
 println(floor(sqrt(101))),
 println(ceiling(sqrt(101))),
 nl,
 println(math.pi**math.e),        % power
 println(pow(math.pi,math.e)),    % power  
 nl.</lang>

Output:

2.718281828459045
3.141592653589793

1.414213562373095

2.302585092994046
2.011465867588061
3.321928094887362
10.000000000000002

2.718281828459045

10
11

22.459157718361041
22.459157718361041

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 'scl': <lang PicoLisp>(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</lang>

Output:

2.718281828459
3.141592653590
1.414213562373
1.414213562373
0.693147180560
54.598150033144
7.200000000000
123
81.000000000000

PL/I

<lang pli>/* 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);</lang>

Pop11

<lang 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</lang>

The number e is not provided directly, one has to compute 'exp(1)' instead. Also, f/math>)

PowerShell

Since PowerShell has access to .NET all this can be achieved using the .NET Base Class Library: <lang powershell>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))</lang>

PureBasic

<lang PureBasic>Debug #E Debug #PI Debug Sqr(f) Debug Log(f) Debug Exp(f) Debug Log10(f) Debug Abs(f) Debug Pow(f,f)</lang>

Python

<lang 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</lang>

R

<lang 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</lang>

Racket

<lang 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</lang>

Raku

(formerly Perl 6) <lang perl6>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; # :-)</lang>

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

<lang rexx>a=abs(y) /*takes the absolute value of y.*/</lang>

exponentiation (**)

<lang rexx>r=x**y /*REXX only supports integer powers.*/

                              /*Y may be negative, zero, positive.*/
                              /*X may be any real number.         */</lang>

ceiling

A ceiling function for REXX: <lang rexx> ceiling: procedure; parse arg x; t=trunc(x); return t+(x>0)*(x\=t) </lang>

floor

A floor function for REXX: <lang rexx> floor: procedure; parse arg x; t=trunc(x); return t-(x<0)-(x\=t) </lang>

sqrt (optimized)

A [principal] square root (SQRT) function for REXX (with arbitrary precision): <lang rexx>/*──────────────────────────────────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.*/</lang> <lang rexx> ╔════════════════════════════════════════════════════════════════════╗ ╔═╝ __ ╚═╗ ║ √ ║ ║ ║ ║ 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). ║ ║ __ ║ ╚═╗ √ ╔═╝

 ╚════════════════════════════════════════════════════════════════════╝</lang>

sqrt (simple)

<lang rexx>/*──────────────────────────────────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).*/</lang>

other

Other mathematical-type functions supported are: <lang rexx>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. */</lang>

Ring

<lang 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 </lang>

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 [[1]]. <lang RLaB>>> const

  e                    euler           ln10            ln2             lnpi
  log10e               log2e           pi              pihalf          piquarter
  rpi                  sqrt2           sqrt2r          sqrt3           sqrtpi
  tworpi</lang>

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. <lang RLaB>>> 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</lang>

Elementary Functions

<lang RLaB>>> x = rand() >> sqrt(x)

 2.23606798

>> log(x)

 1.60943791

>> log10(x)

0.698970004

>> exp(x)

 148.413159

>> abs(x)

>> floor(x)

>> ceil(x)

>> x .^ 2

 25</lang>

Ruby

<lang 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 </lang>

Run BASIC

<lang runbasic>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</lang>

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

<lang 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);

}</lang>

Scala

<lang 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

}</lang>

Scheme

<lang 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</lang>

Seed7

The math.s7i library defines:

E	# e (Euler's number)
PI	# Pi
sqrt(x)	# square root
log(x)	# natural logarithm - log base 10 is also available: log10(x))
exp(x)	# exponential
abs(x)	# absolute value
floor(x)	# floor
ceil(x)	# ceiling

The float.s7i library defines:

x ** y	# power with integer exponent
x ** y	# power with float exponent

Sidef

<lang ruby>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</lang>

Slate

<lang 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</lang>

Smalltalk

<lang 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</lang>

Sparkling

<lang 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);</lang>

Standard ML

<lang sml>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 *)</lang>

Stata

<lang 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</lang>

Swift

<lang 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</lang>

Tcl

<lang 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)</lang> The constants $e$ and $\pi$ are also available with high precision in a support library.

Library: Tcllib (Package: math::constants)

<lang tcl>package require math::constants math::constants::constants e pi puts "e = $e, pi = $pi"</lang>

TI-89 BASIC

Mathematical	TI-89	Notes
$e$	`ℯ`	(U+212F SCRIPT SMALL E)
$\pi$	`π`	(U+03C0 GREEK SMALL LETTER PI)
${\sqrt {x}}$	`√(x)`	(U+221A SQUARE ROOT)
$\log _{e}(x)$	`ln(x)`
$\log _{10}(x)$	`log(x)`
$\log _{b}(x)$	`log(b, x)`	The optional base argument comes first
$\lfloor x\rfloor$	`floor(x)`
$\lceil x\rceil$	`ceiling(x)`
$x^{y}$	`x^y`

True BASIC

<lang qbasic>FUNCTION floor(x)

   IF x > 0 THEN
      LET floor = INT(x)
   ELSE
      IF x <> INT(x) THEN LET floor = INT(x) - 1 ELSE LET floor = INT(x)
   END IF

END FUNCTION

PRINT "e = "; exp(1) ! e not available PRINT "PI = "; PI

LET x = 12.345 LET y = 1.23

PRINT "sqrt = "; SQR(x), x^0.5 ! square root- NB the unusual name PRINT "ln = "; LOG(x) ! natural logarithm base e PRINT "log2 = "; LOG2(x) ! base 2 logarithm PRINT "log10 = "; LOG10(x) ! base 10 logarithm PRINT "log = "; LOG(x)/LOG(y) ! arbitrary base logarithm PRINT "exp = "; EXP(x) ! exponential PRINT "abs = "; ABS(-1) ! absolute value PRINT "floor = "; floor(x) ! floor easily implemented as functions PRINT "ceil = "; CEIL(x) ! ceiling PRINT "power = "; x ^ y ! power END</lang>

UNIX Shell

Works with: ksh93

ksh93 exposes math functions from the C math library <lang bash>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</lang>

Output:

2.71828182845904524
3.14159265358979324
2.2360679774997897
1.60943791243410037
2.32192809488736235
0.698970004336018805
148.413159102576603
42
-6
-5
1000

Wren

<lang ecmascript>var e = 1.exp

System.print("e = %(e)") System.print("pi = %(Num.pi)") System.print("sqrt(2) = %(2.sqrt)") System.print("ln(3) = %(3.log)") // log base e System.print("exp(2) = %(2.exp)") System.print("abs(-e) = %((-e).abs)") System.print("floor(e) = %(e.floor)") System.print("ceil(e) = %(e.ceil)") System.print("pow(e, 2) = %(e.pow(2))")</lang>

Output:

e         = 2.718281828459
pi        = 3.1415926535898
sqrt(2)   = 1.4142135623731
ln(3)     = 1.0986122886681
exp(2)    = 7.3890560989307
abs(-e)   = 2.718281828459
floor(e)  = 2
ceil(e)   = 3
pow(e, 2) = 7.3890560989306

XPL0

<lang 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</lang>

Output:

   2.7182818284590500
   1.0000000000000000

   3.1415926535897900
  -1.0000000000000000

   1.4142135623731000
   2.0000000000000000
 123.4567890000000000

1234.5000000000000000

   1.0000000000000000
   2.0000000000000000
   4.0000000000000000

Yabasic

<lang yabasic>print "e = ", euler print "pi = ", pi

x = 12.345 y = 1.23

print "sqrt = ", sqrt(2) // square root print "ln = ", log(euler) // natural logarithm base e print "log = ", log(x, y) // arbitrary base y logarithm print "exp = ", exp(euler) // exponential print "abs = ", abs(-1) // absolute value print "floor = ", floor(-euler) // floor print "ceil = ", ceil(-euler) // ceiling print "power = ", x ^ y, " ", x ** y // power end</lang>

Output:

e     = 2.71828
pi    = 3.14159
sqrt  = 1.41421
ln    = 1
log   = 12.1405
exp   = 15.1543
abs   = 1
floor = -3
ceil  = -2
power = 22.0056  22.0056

Zig

<lang zig>const std = @import("std");

pub fn main() void {

   var x: f64 = -1.2345;
   std.debug.print("e = {d}\n", .{std.math.e});
   std.debug.print("pi = {d}\n", .{std.math.pi});
   std.debug.print("sqrt(4) = {d}\n", .{std.math.sqrt(4)});
   std.debug.print("ln(e) = {d}\n", .{std.math.ln(std.math.e)});
   std.debug.print("exp(x) = {d}\n", .{std.math.exp(x)});
   std.debug.print("abs(x) = {d}\n", .{std.math.absFloat(x)});
   std.debug.print("floor(x) = {d}\n", .{std.math.floor(x)});
   std.debug.print("ceil(x) = {d}\n", .{std.math.ceil(x)});
   std.debug.print("pow(f64, -x, x) = {d}\n", .{std.math.pow(f64, -x, x)});

}</lang>

zkl

<lang 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</lang>