module util::Math

rascal-0.40.16

Mathematical functions.

Usage

import util::Math;

Dependencies

import List;
import Exception;

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

Absolute value of a number.

&T <: num abs(&T <: num N)

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

function arbInt

Generate a random integer value.

int arbInt()

int arbInt(int limit)

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: 1762992961
rascal>arbInt();
int: -2078635996
rascal>arbInt();
int: 459128808
rascal>arbInt(10);
int: 9
rascal>arbInt(10);
int: 3
rascal>arbInt(10);
int: 9

Benefits

arbInt is a convenient generator for pseudo-random integers.

function arbReal

Generate a random real value in the interval [0.0,1.0).

real arbReal()

Generates an arbitrary real value in the interval [0.0, 1.0].

Examples

rascal>import util::Math;
ok
rascal>arbReal();
real: 0.22313173943455145
rascal>arbReal();
real: 0.1904051573142883
rascal>arbReal();
real: 0.2779615773742464

function arbSeed

Define the seed for the generation of arbitrary values.

void arbSeed(int seed)

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.

function arbRat

Generate an arbitrary rational value.

rat arbRat()

rat arbRat(int limit1, int limit2)

Examples

rascal>import util::Math;
ok
rascal>arbRat();
rat: 1275897562r404230305
rascal>arbRat();
rat: -1156511503r1289299555
rascal>arbRat();
rat: -298301089r433299798
rascal>arbRat(10,100);
rat: 1r13
rascal>arbRat(10,100);
rat: 3r74
rascal>arbRat(10,100);
rat: 2r23

function ceil

Compute the smallest integer that is larger than a given number.

int ceil(num x)

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

function cos

Calculate the cosine of a numeric value.

real cos(num x)

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

function denominator

Return the denominator of a rational value.

int denominator(rat n)

function E

The constant E.

real E()

Examples

rascal>import util::Math;
ok
rascal>E();
real: 2.7182818285

function exp

Compute exp(x).

real exp(num x)

Calculate ex.

function floor

Compute the largest integer that is smaller than a given number.

int floor(num x)

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

function ln

Calculate the natural log of a numeric value.

real ln(num x)

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

function log

Calculate the log_base of a numeric value.

real log(num x, num base)

Calculate log_base 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

function log10

Compute the 10 based log(x).

real log10(num x)

function log2

Compute the 2 based log(x).

real log2(num x)

function max

Determine the largest of two numeric values.

&T <: num max(&T <: num N, &T <: num M)

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

function min

Determine the smallest of two numeric values.

&T <: num min(&T <: num N, &T <: num M)

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

function numerator

Return the numerator of a rational value.

int numerator(rat n)

function nroot

Calculate the n^th root of a numeric value.

real nroot(num x, int n)

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

function PI

The constant pi.

real PI()

Examples

rascal>import util::Math;
ok
rascal>PI();
real: 3.1415926536

function pow

Calculate an arbitrary power of a numeric value.

real pow(num x, int y)

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...

function pow

Calculate an arbitrary power of a numeric value.

real pow(num x, real y)

The calculate xy where y can be any real value.

Examples

rascal>import util::Math;
ok
rascal>pow(sqrt(42), 2.3)
real: 73.57608648260
rascal>pow(12345678901234567890.0, 100.2)
real: 93282615968788129056780000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.000000000000000000000

function precision

Return the precision of a real number.

int precision(num x)

function precision

Return a real number with given precision.

real precision(num x, int p)

function setPrecision

Define the precision for numeric calculations; returns the previous precision.

int setPrecision(int p)

function scale

Return the scale of a real number.

int scale(num x)

function unscaled

Return the unscaled integer of a real.

int unscaled(real x)

function remainder

Return the remainder of dividing the numerator by the denominator.

int remainder(rat n)

function round

Round a number to the nearest multiple of a given number (default 1).

int round(num d)

(&T <: num) round(&T <: num r, &T <: num nearest)

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

function fitFloat

P Push real value into a float using coercion and return the value represented by that float as a real.

real fitFloat(real r) throws ArithmeticException

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.

function fitDouble

Push real value into a JVM double using coercion and return the value represented by that float as a real.

real fitDouble(real r) throws ArithmeticException

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.

function percent

Compute the ratio between two numbers as a percentage.

int percent(num part, num whole)

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

function sin

Calculate the sine of a numeric value.

real sin(num x)

The sine of the number x.

Examples

rascal>import util::Math;
ok
rascal>sin(0)
real: 0.
rascal>sin(PI() / 2)
real: 1.00000000000

function sqrt

Calculate the square root of a numeric value.

real sqrt(num x)

Calculate √x.

Examples

rascal>import util::Math;
ok
rascal>sqrt(42 * 42);
real: 42.0000000000
rascal>sqrt(12345678901234567890.5 * 12345678901234567890.5);
real: 12345678901234567890.5000000000

function tan

Calculate the tangent of a numeric value.

real tan(num x)

The tangent of the number x.

Examples

rascal>import util::Math;
ok
rascal>tan(45 * PI() / 180)
real: 1.0000000000

function toInt

Convert a numeric value to an integer.

int toInt(num N)

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

function toRat

Convert two numbers to a rational value (not supported on reals).

rat toRat(int numerator, int denominator)

function toReal

Convert a numeric value to a real.

real toReal(num N)

Examples

rascal>import util::Math;
ok
rascal>toReal(12)
real: 12.
rascal>toReal(3.14)
real: 3.14

function toString

Convert a numeric value to a string.

str toString(num N)

Examples

rascal>import util::Math;
ok
rascal>toString(12)
str: "12"
---
12
---
rascal>toString(3.14)
str: "3.14"
---
3.14
---

function primes

Generate prime numbers up to a maximum.

list[int] primes(int upTo)

function arbPrime

int arbPrime(int upTo)