module Math
Usage
import util::Math;
Dependencies
import List;
import Exception;
Synopsis
Mathematical functions.
Description
The Math library provides the following functions:
- E
- PI
- abs
- arbInt
- arbPrime
- arbRat
- arbReal
- arbSeed
- ceil
- cos
- denominator
- exp
- fitDouble
- fitFloat
- floor
- ln
- log
- log10
- log2
- max
- min
- nroot
- numerator
- percent
- pow
- precision
- primes
- remainder
- round
- scale
- setPrecision
- sin
- sqrt
- tan
- toInt
- toRat
- toReal
- toString
- unscaled
function abs
Synopsis
Absolute value of a number.
Description
Absolute value of the number n. The result type is equal to the type of the argument n.
Examples
rascal>import util::Math;
ok
rascal>abs(13)
int: 13
rascal>abs(-13)
int: 13
rascal>abs(3.14)
real: 3.14
rascal>abs(-3.14)
real: 3.14
&T <: num abs(&T <: num N)
function arbInt
Synopsis
Generate a random integer value.
Description
Return an arbitrary integer value. When the argument limit is given, the generated value is in the interval [0, limit),
i.e., the limit is exclusive.
Examples
rascal>import util::Math;
ok
rascal>arbInt();
int: 278168714
rascal>arbInt();
int: -274673295
rascal>arbInt();
int: -2059673550
rascal>arbInt(10);
int: 5
rascal>arbInt(10);
int: 6
rascal>arbInt(10);
int: 3
Benefits
arbInt is a convenient generator for pseudo-random integers.
int arbInt()
int arbInt(int limit)
function arbReal
Synopsis
Generate a random real value in the interval [0.0,1.0).
Description
Generates an arbitrary real value in the interval [0.0, 1.0].
Examples
rascal>import util::Math;
ok
rascal>arbReal();
real: 0.12089370589400783
rascal>arbReal();
real: 0.25707824065322293
rascal>arbReal();
real: 0.3612035851303099
real arbReal()
function arbSeed
Synopsis
Define the seed for the generation of arbitrary values.
Description
Define the seed for the generation of arbitrary values such as Arb Bool, Arb Int, Arb Real, Arb Rat, GetOneFrom,GetOneFrom, TakeOneFrom and TakeOneFrom. Arb Seed resets the random number generator that is used to choose arbitrary values. This can be used to generate a reproducible series of choices.
void arbSeed(int seed)
function arbRat
Synopsis
Generate an arbitrary rational value.
Examples
rascal>import util::Math;
ok
rascal>arbRat();
rat: -1642697521r1347435886
rascal>arbRat();
rat: 10999464r394171643
rascal>arbRat();
rat: -812056956r967938473
rascal>arbRat(10,100);
rat: 0r
rascal>arbRat(10,100);
rat: 5r11
rascal>arbRat(10,100);
rat: 1r51
rat arbRat()
rat arbRat(int limit1, int limit2)
function ceil
Synopsis
Compute the smallest integer that is larger than a given number.
Description
Computes the ceiling of a given number. Also see floor.
Examples
rascal>import util::Math;
ok
rascal>ceil(3.2);
int: 4
rascal>ceil(-3.2);
int: -3
int ceil(num x)
function cos
Synopsis
Calculate the cosine of a numeric value.
Description
The cosine of the number x.
Examples
rascal>import util::Math;
ok
rascal>cos(1.0)
real: 0.54030230588
rascal>cos(60 * PI() / 180)
real: 0.50000000000
real cos(num x)
function denominator
Synopsis
Return the denominator of a rational value.
int denominator(rat n)
function E
Synopsis
The constant E.
Examples
rascal>import util::Math;
ok
rascal>E();
real: 2.7182818285
real E()
function exp
Synopsis
Compute exp(x).
Description
Calculate ex.
real exp(num x)
function floor
Synopsis
Compute the largest integer that is smaller than a given number.
Description
Computes the floor of a given number. Also see ceil.
Examples
rascal>import util::Math;
ok
rascal>floor(3.2);
int: 3
rascal>floor(-3.2);
int: -4
int floor(num x)
function ln
Synopsis
Calculate the natural log of a numeric value.
Description
Calculate natural log of x.
Examples
rascal>import util::Math;
ok
rascal>ln(20.0)
real: 2.9957322736
rascal>ln(42.0)
real: 3.7376696183
real ln(num x)
function log
Synopsis
Calculate the logbase of a numeric value.
Description
Calculate logbase of x.
Examples
rascal>import util::Math;
ok
rascal>log(9.99999999, 10)
real: 0.999999999566
rascal>log(10, 10)
real: 1.
rascal>log(256.0, 2)
real: 7.99999999999
real log(num x, num base)
function log10
Synopsis
Compute the 10 based log(x).
real log10(num x)
function log2
Synopsis
Compute the 2 based log(x).
real log2(num x)
function max
Synopsis
Determine the largest of two numeric values.
Description
The largest of two numbers. The type of the result is the same as the type of the largest argument.
Examples
rascal>import util::Math;
ok
rascal>max(12, 13);
int: 13
rascal>max(12, 13.5);
num: 13.5
rascal>max(12, 11.5);
num: 12
&T <: num max(&T <: num N, &T <: num M)
function min
Synopsis
Determine the smallest of two numeric values.
Description
The smallest of two numbers. The type of the result is the same as the type of the smallest argument.
Examples
rascal>import util::Math;
ok
rascal>min(12, 13);
int: 12
rascal>min(12, -13);
int: -13
rascal>min(3.14, 4);
num: 3.14
&T <: num min(&T <: num N, &T <: num M)
function numerator
Synopsis
Return the numerator of a rational value.
int numerator(rat n)
function nroot
Synopsis
Calculate the nth root of a numeric value.
Description
Calculate n√x where n can only be a integer.
Examples
rascal>import util::Math;
ok
rascal>nroot(42 * 42, 2);
real: 42.0000000000
rascal>nroot(42 * 42 * 42, 3);
real: 42.0000000000
rascal>nroot(123456789012345678901234567890123456789.0, 100)
real: 2.4038930938
real nroot(num x, int n)
function PI
Synopsis
The constant pi.
Examples
rascal>import util::Math;
ok
rascal>PI();
real: 3.1415926536
real PI()
function pow
Synopsis
Calculate an arbitrary power of a numeric value.
Description
The calculate xy where y can only be a integer.
Examples
rascal>import util::Math;
ok
rascal>pow(sqrt(42), 2)
real: 41.99999999989811976256
rascal>pow(12345678901234567890.0, 1000)
real: 327323519862176629730082067574716643439462300540185122220961832511288805718030910484304325108222843885957688250811158315340566475836232001571619541935415038796348602192296984423155079801992333140052863080750492018420590783574245411031311510942905796189450351912614510641741094491709589411239576756065619918176653289948094430880732479266853021246187981170634861333302200580872985856560855518977488511675544145006801675791138351985746678734387422142342185164278661836498313416561398901718399810114596984172777042303963800096899625199810241300878005585014082782334502894938457546968837522885101157892509894692459561354313786780532679517827353604060468681961209174542267424246240853816845886755294209996435433895294269712878992262721644106226890031664370462222706979715904672586297266460593551184450504665032451235999357222433465060299295477020462819514888057483551478759508444976793225466736775132290553092049866427876353526626065630474037490603570383940996843823967040247622022658439400707006053650592894261198654836654639504753542843560398908885522596433160079097075880850067383018892541529465995345763588872837837593907229770700976597566733884202506653739605059379401347861288230399126563406134764726379055786459406660737522798066830604288612726394086519909309338994703718119693639450620275447776806553594104597194048560725083279242120977189767528195495335507571774589656293544257012451347889004221446663952536972136269481724663158860532924322053397767933001924701437115740854657082984585991651836842229921223742828990473127280082431920682100750955123993671834387994643422520721282979578784909325571258649149109201827243509225859052305726449746668735118920743230654106301983770403775061147939915240771494456634249374454345250552415101593382958143513116801567849013973694567642919070533812941570184136127617255991655186770210261385873186409485713856293174509996217914589400976889855958713421577335212662218393411619879901532201876563269347123972872344497080886637930441651259141049569049804413000150297629676129305940405487092640315363913091042956266173352666027423873096773031569220441623779694026871629405544513139993091183726122490006827751752741076885620415211542317496941956676394754879276979814511653516542017832996653484412313736356363305261532812972679430377759838879013873699720739033015759349473652785594888893377041014822677972342113818352300626995374712448170130314174419289739529982021437898597025566184922042135782017301373340541840251886826793222171028600662975155228812797443522045892690780164900156894217461209188361915847649443941189447229439906721259825215932223371314915787322490148065038149065584317884221248098894972346389635965334847844894296983317214252456367600733903894880305858451738209033898028888738089429510748290579293786966511702526421636839023818144487303883796157019333481281590182592242664434310787411848124503254182702718762286778744163663752419726010543539695902378784425822053579035604233167402979429162902604120869094779466506794967733027126798330733504515320709935121379216936936503517150761677018393050209847312382660928887004146016965681452309940614395990071269237730777211494402285973401134347314396249658064535813498390390228707068969712346028221844247394911352355219205653068923998044169246696199205931532280062594043451189765555574643899576685276356280338555983266720699445887933479778575910620051014501087647914152552526207935492180262761720164698382158135451840846941977075240573647713026577508324564964050461276723248623764128711424186543354565805827986611623687766424190141159982065651733888853975873295262987666051724164426176971670664220786382312628833993735024432664073367706606256513404081195840674289520710497921821809284330939220609778362882454615392304832328664341446921914422579024146155571399642339764786384745922769575752043854715925941119782659099976703423673050490970007943369522561413084390356583974592565338819090682096052094155857739238468257491510074355659857818999361006574913097067978865657382215313176814231120597124842183478696513677197512045290255088756641096724459645973492430801864900314570449211289319281689687528990384602371132230192221449626569380251208...
real pow(num x, int y)
real pow(num x, real y)
function precision
Synopsis
Return the precision of a real number.
int precision(num x)
real precision(num x, int p)
function setPrecision
Synopsis
Define the precision for numeric calculations; returns the previous precision.
int setPrecision(int p)
function scale
Synopsis
Return the scale of a real number.
int scale(num x)
function unscaled
Synopsis
Return the unscaled integer of a real.
int unscaled(real x)
function remainder
Synopsis
Return the remainder of dividing the numerator by the denominator.
int remainder(rat n)
function round
Synopsis
Round a number to the nearest multiple of a given number (default 1).
Examples
rascal>import util::Math;
ok
rascal>round(3.4);
int: 3
rascal>round(3.5);
int: 4
rascal>round(3.6);
int: 4
rascal>round(-3.4);
int: -3
rascal>round(-3.5);
int: -4
rascal>round(-3.6);
int: -4
rascal>round(13, 5);
int: 15
rascal>round(1.5,0.2);
real: 1.6
rascal>round(3r2,1r4);
rat: 3r2
int round(num d)
(&T <: num) round(&T <: num r, &T <: num nearest)
function fitFloat
.Synopsis push real value into a float using coercion and return the value represented by that float as a real
Description
The function fitFloat converts the unlimited precision real into a JVM float value.
Benefits
- This function comes in handy in combination with random real test values which have to
go through coercion in a Java library, like so:
bool test myTest(real r, real j) = fitFloat(r) + fitFloat(j) == fitFloat(r) + fitFloat(j);
Pitfalls
- If the real is smaller than the minimum float value or larger than the maximum float value, this function will throw an ArithmeticException.
real fitFloat(real r) throws ArithmeticException
function fitDouble
.Synopsis push real value into a JVM double using coercion and return the value represented by that float as a real
Description
The function fitDouble converts the unlimited precision real into a JVM double value.
Benefits
- This function comes in handy in combination with random real test values which have to
go through coercion in a Java library, like so:
bool test myTest(real r, real j) = fitDouble(r) + fitDouble(j) == fitDouble(r) + fitDouble(j);
Pitfalls
- If the real is smaller than the minimum double value or larger than the maximum double value, this function will throw an ArithmeticException.
real fitDouble(real r) throws ArithmeticException
function percent
Synopsis
Compute the ratio between two numbers as a percentage.
Examples
rascal>import util::Math;
ok
rascal>percent(1r4, 1);
int: 25
rascal>percent(13,250);
int: 5
rascal>percent(80.0,160.0);
int: 50
int percent(num part, num whole)
function sin
Synopsis
Calculate the sine of a numeric value.
Description
The sine of the number x.
Examples
rascal>import util::Math;
ok
rascal>sin(0)
real: 0.
rascal>sin(PI() / 2)
real: 1.00000000000
real sin(num x)
function sqrt
Synopsis
Calculate the square root of a numeric value.
Description
Calculate √x.
Examples
rascal>import util::Math;
ok
rascal>sqrt(42 * 42);
real: 42.0000000000
rascal>sqrt(12345678901234567890.5 * 12345678901234567890.5);
real: 12345678901234567890.5000000000
real sqrt(num x)
function tan
Synopsis
Calculate the tangent of a numeric value.
Description
The tangent of the number x.
Examples
rascal>import util::Math;
ok
rascal>tan(45 * PI() / 180)
real: 1.0000000000
real tan(num x)
function toInt
Synopsis
Convert a numeric value to an integer.
Description
Convert a number to an integer. If n is an integer, this is the identity. If n is a real value (implemented as BigDecimal) to an integer (implemented as BigInteger). This conversion is analogous to a narrowing primitive conversion from double to long as defined in the Java Language Specification: any fractional part of this BigDecimal will be discarded. Note that this conversion can loose information about the precision of the BigDecimal value.
Examples
rascal>import util::Math;
ok
rascal>toInt(13)
int: 13
rascal>toInt(13.5)
int: 13
int toInt(num N)
function toRat
Synopsis
Convert two numbers to a rational value (not supported on reals).
rat toRat(int numerator, int denominator)
function toReal
Synopsis
Convert a numeric value to a real.
Examples
rascal>import util::Math;
ok
rascal>toReal(12)
real: 12.
rascal>toReal(3.14)
real: 3.14
real toReal(num N)
function toString
Synopsis
Convert a numeric value to a string.
Examples
rascal>import util::Math;
ok
rascal>toString(12)
str: "12"
---
12
---
rascal>toString(3.14)
str: "3.14"
---
3.14
---
str toString(num N)
function primes
Synopsis
generate prime numbers up to a maximum
list[int] primes(int upTo)
function arbPrime
int arbPrime(int upTo)