Math

Overview
Installation
How to use
FAQ
License
Contributing

Overview

Arbitrary-precision numbers for PHP, where arithmetic is exact and rounding is explicit.

Addition, subtraction and multiplication never round. Division returns a BigRational, so it is exact for every pair of operands and raises only on a zero divisor. Rounding happens where you ask for it, by naming both a scale and a RoundingMode. There is no ambient precision context, no process-global scale, and no default rounding mode to forget.

The arithmetic runs through a single integer engine, and every value type is a thin facade over it. The engine is the bcmath extension when it is loaded, and a pure PHP backend when it is not, so the library has no required extension and no Composer dependency. Both produce identical results, so bcmath buys speed rather than correctness. On money values the pure PHP backend stays within roughly an order of magnitude on arithmetic, rounding, comparison, allocation and division. Square roots are the outlier, several dozen times slower. The gap widens with operand size, so install the extension where wide operands meet throughput. Nothing in the library routes a number through float.

Pairs with tiny-blocks/currency, whose Currency::getFractionDigits() is exactly the scale toScale wants. The library has no Composer dependencies of its own.

Installation

composer require tiny-blocks/math

How to use

Every numeric type is immutable, and every operation returns a new instance.

Number

The contract BigInteger, BigDecimal and BigRational share. Every method below works across all three, so a function can take a Number and compare or convert whatever arrives.

Comparison is exact whatever the pair of types. Two numbers of the same type are compared on their own representation. Across types the comparison goes through BigRational, the only form every number has exactly, which is what keeps the contract to one method instead of one per pair of types.

Method	Returns	Notes
`compareTo(Number $other)`	`int`	Negative, zero, or positive. Exact across types.
`isEqualTo(Number $other)`	`bool`	Arithmetic, so `1.0` equals `1.00`.
`isLessThan(Number $other)`	`bool`
`isGreaterThan(Number $other)`	`bool`
`isLessThanOrEqualTo(Number $other)`	`bool`
`isGreaterThanOrEqualTo(Number $other)`	`bool`
`isZero()`	`bool`
`isNegative()`	`bool`	Strictly less than zero.
`isPositive()`	`bool`	Strictly greater than zero.
`negated()`	`Number`
`absolute()`	`Number`
`toBigRational()`	`BigRational`
`toString()`	`string`	Round-trips through the type's own factory.
`hashCode()`	`string`	Agrees with the type's own `equals`.
`jsonSerialize()`	`string`	A JSON string, never a JSON number.

Each implementation adds an equals of its own, typed to its exact class: BigDecimal::equals(BigDecimal $other), BigInteger::equals(BigInteger $other), BigRational::equals(BigRational $other). That one is structural, so 1.0 does not equal 1.00, and comparing across types is a type error rather than a silent false. isEqualTo and equals answer different questions on purpose, and FAQ 02 explains why.

<?phpdeclare(strict_types=1);
useTinyBlocks\Math\BigDecimal;
useTinyBlocks\Math\BigInteger;
BigInteger::of(value: 5)->isEqualTo(other: BigDecimal::of(value: '5.00'));
# true

Percentage and Ratio are not Number instances: a rate and a proportion are not quantities you add to an amount. Percentage carries the same comparison predicates typed against Percentage. Percentage converts with rate() or toRatio(), and Ratio with toBigRational() or toPercentage().

BigDecimal

An arbitrary-precision decimal, held as an unscaled integer and a non-negative scale.

<?phpdeclare(strict_types=1);
useTinyBlocks\Math\BigDecimal;
useTinyBlocks\Math\Percentage;
useTinyBlocks\Math\RoundingMode;
$price = BigDecimal::of(value: '19.99');
$final = Percentage::of(value: '12.5')->decrease(amount: $price);
$final->toScale(scale: 2, rounding: RoundingMode::HalfEven);
# 17.49

Method	Returns	Result scale
`of(string\|int $value)`	`BigDecimal`	The scale of the literal.
`one()`	`BigDecimal`	0.
`zero()`	`BigDecimal`	0.
`fromFloat(float $value)`	`BigDecimal`	The shortest round-trip.
`ofUnscaledValue(int $scale, BigInteger $unscaled)`	`BigDecimal`	`$scale`.
`plus(BigDecimal $addend)`	`BigDecimal`	`max(a, b)`.
`minus(BigDecimal $subtrahend)`	`BigDecimal`	`max(a, b)`.
`multipliedBy(BigDecimal $multiplier)`	`BigDecimal`	`a + b`.
`dividedBy(BigDecimal $divisor)`	`BigRational`	Not applicable.
`power(int $exponent)`	`BigDecimal`	`a × exponent`.
`squareRoot(int $scale, RoundingMode $rounding)`	`BigDecimal`	`$scale`.
`toScale(int $scale, RoundingMode $rounding)`	`BigDecimal`	`$scale`.
`toScaleExact(int $scale)`	`BigDecimal`	`$scale`.
`withoutTrailingZeros()`	`BigDecimal`	The smallest possible.
`allocate(int $scale, BigDecimals $weights)`	`BigDecimals`	`$scale`.
`negated()`	`BigDecimal`	Unchanged.
`absolute()`	`BigDecimal`	Unchanged.
`scale()`	`int`	Not applicable.
`unscaledValue()`	`BigInteger`	Not applicable.
`integralPart()`	`BigInteger`	Not applicable.
`fractionalPart()`	`BigDecimal`	Unchanged.
`toBigInteger()`	`BigInteger`	Not applicable.
`toBigRational()`	`BigRational`	Not applicable.
`toFloat()`	`float`	Not applicable.
`toString()`	`string`	Not applicable.

Scale propagation matches Java's BigDecimal, so nothing here surprises a reader who knows it.

allocate splits an amount so that the parts sum back to it exactly. Each part is the exact share truncated toward negative infinity at the given scale, and the units left over are handed out one at a time in descending order of the discarded remainder, ties broken by position. Plain rounding cannot preserve the total, which is why this exists.

<?phpdeclare(strict_types=1);
useTinyBlocks\Math\BigDecimal;
useTinyBlocks\Math\BigDecimals;
$parts = BigDecimal::of(value: '100.00')->allocate(scale: 2, weights: BigDecimals::of('1', '1', '1'));
$parts->sum()->toString();
# 100.00, and the parts are 33.34, 33.33, 33.33

BigInteger

An arbitrary-precision integer, for problems that have no scale.

<?phpdeclare(strict_types=1);
useTinyBlocks\Math\BigInteger;
BigInteger::of(value: '9007199254740993')
->multipliedBy(multiplier: BigInteger::of(value: '9007199254740993'))
->toString();
# 81129638414606699710187514626049

Method	Returns	Notes
`of(string\|int $value)`	`BigInteger`	A zero fractional part is accepted.
`one()`	`BigInteger`
`zero()`	`BigInteger`
`fromBase(int $base, string $value)`	`BigInteger`	Base 2 to 36, case-insensitive.
`plus(BigInteger $addend)`	`BigInteger`
`minus(BigInteger $subtrahend)`	`BigInteger`
`multipliedBy(BigInteger $multiplier)`	`BigInteger`
`dividedBy(BigInteger $divisor)`	`BigRational`	Exact, never rounds.
`quotient(BigInteger $divisor)`	`BigInteger`	Truncated toward zero.
`remainder(BigInteger $divisor)`	`BigInteger`	Sign follows the dividend.
`modulo(BigInteger $modulus)`	`BigInteger`	Never negative.
`power(int $exponent)`	`BigInteger`	Rejects a negative exponent.
`squareRoot()`	`BigInteger`	Floor.
`greatestCommonDivisor(BigInteger $other)`	`BigInteger`	Never negative.
`isEven()`	`bool`
`isOdd()`	`bool`
`toBase(int $base)`	`string`	Lowercase for bases above ten.
`toBigDecimal()`	`BigDecimal`	Scale zero.
`toBigRational()`	`BigRational`	Denominator one.
`toInt()`	`int`	Raises outside the native range.
`toString()`	`string`

remainder and modulo are separate methods because the two conventions genuinely differ: bcmod follows the dividend's sign while gmp_mod never returns a negative. Hiding both behind one name is how a backend swap silently changes answers.

BigRational

An exact fraction, always in lowest terms with a strictly positive denominator. This is the type that lets division stay total.

<?phpdeclare(strict_types=1);
useTinyBlocks\Math\BigDecimal;
useTinyBlocks\Math\RoundingMode;
$share = BigDecimal::of(value: '100.00')->dividedBy(divisor: BigDecimal::of(value: '3'));
$share->toDecimal(scale: 2, rounding: RoundingMode::HalfEven)->toString();
# 33.33

Method	Returns	Notes
`of(string\|int $value)`	`BigRational`	Accepts `3/4`, `0.75`, and `3`.
`ofFraction(BigInteger $numerator, BigInteger $denominator)`	`BigRational`	Reduced on construction.
`one()`	`BigRational`
`zero()`	`BigRational`
`plus(BigRational $addend)`	`BigRational`	Exact.
`minus(BigRational $subtrahend)`	`BigRational`	Exact.
`multipliedBy(BigRational $multiplier)`	`BigRational`	Exact.
`dividedBy(BigRational $divisor)`	`BigRational`	Exact.
`power(int $exponent)`	`BigRational`	Negative exponents supported.
`reciprocal()`	`BigRational`	Raises on zero.
`numerator()`	`BigInteger`	Carries the sign.
`denominator()`	`BigInteger`	Always positive.
`hasTerminatingDecimal()`	`bool`	True when the denominator is 2^a·5^b.
`toDecimal(int $scale, RoundingMode $rounding)`	`BigDecimal`
`toDecimalExact()`	`BigDecimal`	Raises when the expansion repeats.
`toBigInteger()`	`BigInteger`	Raises when the denominator is not one.
`toFloat()`	`float`
`toString()`	`string`	`3/4`, or `3` when the denominator is one.

hasTerminatingDecimal() is the cheap way to ask before converting, instead of calling toDecimalExact() and catching the failure.

Percentage

A rate expressed per hundred, held as a BigDecimal. Applying it to an amount is a multiplication and therefore exact, so no rounding decision is forced until the result is presented.

<?phpdeclare(strict_types=1);
useTinyBlocks\Math\BigDecimal;
useTinyBlocks\Math\Percentage;
useTinyBlocks\Math\RoundingMode;
Percentage::of(value: '12.5')
->increase(amount: BigDecimal::of(value: '19.99'))
->toScale(scale: 2, rounding: RoundingMode::HalfEven)
->toString();
# 22.49

Method	Returns	Notes
`of(string\|int $value)`	`Percentage`	`'12.5'` is twelve and a half percent. A trailing `%` is accepted.
`zero()`	`Percentage`
`fromRatio(Ratio $ratio, int $scale, RoundingMode $rounding)`	`Percentage`	A scale is required, a ratio may not terminate.
`rate()`	`BigDecimal`	`0.125` for twelve and a half percent.
`applyTo(BigDecimal $amount)`	`BigDecimal`	Exact.
`increase(BigDecimal $amount)`	`BigDecimal`	Exact.
`decrease(BigDecimal $amount)`	`BigDecimal`	Exact.
`toRatio()`	`Ratio`	In lowest terms.
`isZero()`	`bool`
`isNegative()`	`bool`	A negative rate is legal.
`isPositive()`	`bool`
`isEqualTo(Percentage $other)`	`bool`	Arithmetic, so the scale plays no part.
`isLessThan(Percentage $other)`	`bool`
`isGreaterThan(Percentage $other)`	`bool`
`isLessThanOrEqualTo(Percentage $other)`	`bool`
`isGreaterThanOrEqualTo(Percentage $other)`	`bool`
`toString()`	`string`	`12.5%`.
`equals(Percentage $other)`	`bool`	Structural, so `'10'` does not equal `'10.0'`.
`hashCode()`	`string`	Agrees with `equals`.
`jsonSerialize()`	`string`	A JSON string, `12.5%`, which reads back through `of`.

Rates above one hundred and below zero are legal, because a one hundred and fifty percent increase and a negative growth rate are both real.

Ratio

An exact proportion between two quantities, written antecedent to consequent.

<?phpdeclare(strict_types=1);
useTinyBlocks\Math\Ratio;
useTinyBlocks\Math\RoundingMode;
Ratio::of(antecedent: 16, consequent: 9)
->toPercentage(scale: 2, rounding: RoundingMode::HalfEven)
->toString();
# 177.78%

Method	Returns	Notes
`of(int\|string $antecedent, int\|string $consequent)`	`Ratio`	Reduced on construction.
`from(string $value)`	`Ratio`	Reads the `16:9` form back.
`between(Number $antecedent, Number $consequent)`	`Ratio`	Exact, so no scale is involved.
`applyTo(Number $amount)`	`BigRational`	Exact.
`inverted()`	`Ratio`	Swaps the terms.
`antecedent()`	`BigInteger`	Carries the sign.
`consequent()`	`BigInteger`	Always positive.
`toPercentage(int $scale, RoundingMode $rounding)`	`Percentage`
`toBigRational()`	`BigRational`
`toString()`	`string`	`16:9`.
`equals(Ratio $other)`	`bool`	Structural, and a ratio is always in lowest terms.
`hashCode()`	`string`	Agrees with `equals`.
`jsonSerialize()`	`string`	A JSON string, `16:9`, which reads back through `from`.

BigDecimals

An immutable, ordered collection of decimals. It carries the weights handed to allocate and the parts it produces.

<?phpdeclare(strict_types=1);
useTinyBlocks\Math\BigDecimal;
useTinyBlocks\Math\BigDecimals;
BigDecimal::of(value: '100.00')
->allocate(scale: 2, weights: BigDecimals::of('1', '1', '1'))
->sum()
->toString();
# 100.00

Method	Returns	Notes
`of(string\|int ...$values)`	`BigDecimals`	`BigDecimals::of('1', '1', '1')`.
`from(BigDecimal ...$values)`	`BigDecimals`
`sum()`	`BigDecimal`	Exact, at the largest scale in the set.
`all()`	`list<BigDecimal>`	In order.
`count()`	`int`	The collection is `Countable`.
`getIterator()`	`Traversable`	The collection is iterable with `foreach`.
`jsonSerialize()`	`list<string>`	A JSON array of strings, which reads back through `of`.

RoundingMode

Eight cases. A mode decides one thing: whether the discarded fraction pushes the kept digit away from zero, given how that fraction compares with one half, the sign of the value, and the parity of the digit being kept. That is the definition Java's RoundingMode javadoc gives each constant, and it is what roundsAwayFromZero() implements. The table below rounds -2.345 to two decimal places, and matches Java's published rounding table.

<?phpdeclare(strict_types=1);
useTinyBlocks\Math\BigDecimal;
useTinyBlocks\Math\RoundingMode;
BigDecimal::of(value: '-2.345')->toScale(scale: 2, rounding: RoundingMode::HalfEven)->toString();
# -2.34

Case	Backing value	Native equivalent	Result
`Up`	`up`	`AwayFromZero`	`-2.35`
`Down`	`down`	`TowardsZero`	`-2.34`
`Floor`	`floor`	`NegativeInfinity`	`-2.35`
`HalfUp`	`half-up`	`HalfAwayFromZero`	`-2.35`
`Ceiling`	`ceiling`	`PositiveInfinity`	`-2.34`
`HalfOdd`	`half-odd`	`HalfOdd`	`-2.35`
`HalfDown`	`half-down`	`HalfTowardsZero`	`-2.34`
`HalfEven`	`half-even`	`HalfEven`	`-2.34`

fromNativeRoundingMode() and toNativeRoundingMode() convert to and from PHP's native RoundingMode enum, for consumers holding one from configuration or Intl. The library does not use them internally, so a replacement calculation backend is never bypassed. There is no case meaning "do not round": that path is toScaleExact() and toDecimalExact(), which raise instead of guessing.

Failures

Every failure implements MathFailure, so one catch clause covers the library. The interface exists because PHP splits Error and Exception at the root and a zero divisor genuinely belongs under DivisionByZeroError.

<?phpdeclare(strict_types=1);
useTinyBlocks\Math\BigDecimal;
useTinyBlocks\Math\Exceptions\MathFailure;
try {
BigDecimal::of(value: '1.00')->dividedBy(divisor: BigDecimal::zero());
} catch (MathFailure$failure) {
$failure->getMessage();
# Cannot divide <1> by zero.
}

Class	Extends	Raised when
`NumberNotWellFormed`	`InvalidArgumentException`	A literal is not a number, the empty string included.
`DivisionByZero`	`DivisionByZeroError`	A zero divisor, denominator, or reciprocal.
`NonTerminatingDecimal`	`DomainException`	An exact decimal was demanded of a repeating expansion.
`InexactConversion`	`DomainException`	An exact conversion would discard digits.
`ScaleOutOfRange`	`InvalidArgumentException`	A scale is negative or beyond the supported range.
`NegativeExponent`	`InvalidArgumentException`	An integer or decimal was raised to a negative power.
`ExponentOutOfRange`	`InvalidArgumentException`	An exponent is beyond the supported magnitude.
`NegativeRoot`	`DomainException`	The square root of a negative value.
`NegativeWeight`	`InvalidArgumentException`	An allocation weight is negative.
`BaseOutOfRange`	`InvalidArgumentException`	A positional base is outside 2 to 36.
`IntegerOverflow`	`OverflowException`	A conversion leaves the native integer or float range.
`CalculatorNotAvailable`	`RuntimeException`	The calculation backend cannot run in this process.

NonTerminatingDecimal and InexactConversion are separate on purpose. The first cannot be fixed by asking for more digits, the second can.

Calculation backend

Calculator is the integer engine every value type runs on. The contract is integer only, because that is the boundary every candidate backend shares: GMP has no fractional type, and a decimal is an integer plus a scale. Scale bookkeeping therefore stays inside the library and two backends cannot disagree about a result.

Two backends ship. Resolution takes the first that can run: BCMath when the extension is loaded, otherwise a pure PHP backend that needs nothing beyond 64-bit integers. The pure PHP backend is verified against libbcmath over a corpus that crosses every limb boundary and both signs, so the two agree digit for digit and the extension is a speed decision rather than a correctness one.

The gap is worth planning for. Measured on the project image, 2000 scale-2 money operations take about 280 ms on BCMath and about 3.4 s on the pure PHP backend, and 200 exact divisions take about 60 ms against about 15 s. Division is the widest gap because each quotient digit costs a full-width multiply and compare. Install ext-bcmath on any host that does real volume, and treat the pure PHP backend as the guarantee that the library still runs where you cannot.

A registered backend always wins over the resolved one, and it is checked when it is registered rather than when it is used, so a bootstrap mistake surfaces at bootstrap. When a GMP backend is added it goes at the front.

A backend implements nine methods. Every operand is a plain decimal integer string: an optional leading minus, then digits, with no leading zero and no decimal point.

Method	Returns	Notes
`add(string $left, string $right)`	`string`
`subtract(string $minuend, string $subtrahend)`	`string`
`multiply(string $left, string $right)`	`string`
`quotient(string $numerator, string $denominator)`	`string`	Truncated toward zero.
`remainder(string $numerator, string $denominator)`	`string`	Sign follows the numerator.
`power(string $base, int $exponent)`	`string`	The exponent is never negative.
`squareRoot(string $radicand)`	`string`	Truncated. The radicand is never negative.
`compare(string $left, string $right)`	`int`	Exactly `-1`, `0`, or `1`.
`isAvailable()`	`bool`	Whether this backend can run in this process.

Calculators is the resolution surface.

Method	Returns	Notes
`active()`	`Calculator`	Resolves on first call, then caches.
`register(Calculator $calculator)`	`void`	Bootstrap only. Raises when the backend is unavailable.
`reset()`	`void`	Returns to automatic resolution.

Calculators::register(calculator: newGmpCalculator());

register is bootstrap-only. What it replaces is a stateless, pure engine, so a replacement changes how fast a result is produced and never what the result is.

FAQ

01. Why does division return a BigRational instead of a BigDecimal?

Because the exact answer always exists as a fraction, and hiding that costs the caller something either way. Libraries that return a decimal must round silently, demand a scale at every division site, or raise when the quotient repeats. A fraction is none of those: dividedBy has one signature on all three numeric types, takes one argument, and raises only on a zero divisor. You leave exactness behind when you are ready, by naming a scale and a rounding mode, or by asking for toDecimalExact() and handling the case where no exact decimal exists.

02. Why is `equals` different from `isEqualTo`?

isEqualTo is arithmetic and lives on Number, so 1.0 and 1.00 are equal and a BigDecimal can be compared with a BigInteger. equals is structural and lives on each concrete type, typed to that exact type, so the same pair is not equal because the scales differ and a cross-type call does not compile. Both notions are useful and both are wrong as the only one on offer, so each has its own name.

Oracle, java.math.BigDecimal Javadoc (Oracle, 2024), "Note: this class has a natural ordering that is inconsistent with equals".

03. Why is scale part of the value at all?

Because USD 3.00 is not USD 3. A model based on significant digits cannot express the difference, and loses it on ordinary addition: in decimal.js at precision: 5, new Decimal('100000').plus('0.0001') is 100000. Fixed scale survives addition, which is what money needs.

04. Why does `jsonSerialize` emit a string rather than a number?

A JSON number is read back as an IEEE-754 double by every JavaScript consumer, which discards exactly what this library preserves. json_encode(BigDecimal::of(value: '1.50')) is "1.50".

05. Why is there no `__toString`?

The ecosystem's phpcs ruleset places magic methods after every other method, while the member ordering convention places methods by name length. The two cannot both be satisfied for __toString, so the magic method is absent and toString() is the single canonical string form.

06. Why does `fromFloat` exist if floats are the problem?

Because real programs receive floats from JSON and from other libraries, and refusing them only moves the conversion somewhere less careful. It is the one lossy entry point, it is named so, and it reads the shortest decimal that round-trips to the same float, so 0.1 becomes '0.1' rather than its exact binary expansion. Prefer a string literal whenever one is available.

License

Math is licensed under MIT.

Contributing

Please follow the contributing guidelines to contribute to the project.

Name		Name	Last commit message	Last commit date
.github		.github
docs/specs		docs/specs
src		src
tests/Unit		tests/Unit
.editorconfig		.editorconfig
.gitattributes		.gitattributes
.gitignore		.gitignore
LICENSE		LICENSE
Makefile		Makefile
README.md		README.md
SECURITY.md		SECURITY.md
UPGRADE.md		UPGRADE.md
composer.json		composer.json
infection.json.dist		infection.json.dist
phpcs.xml		phpcs.xml
phpstan.neon.dist		phpstan.neon.dist
phpunit.xml		phpunit.xml

Navigation Menu

Uh oh!

Repository files navigation

Math

Overview

Installation

How to use

Number

BigDecimal

BigInteger

BigRational

Percentage

Ratio

BigDecimals

RoundingMode

Failures

Calculation backend

FAQ

01. Why does division return a BigRational instead of a BigDecimal?

02. Why is `equals` different from `isEqualTo`?

03. Why is scale part of the value at all?

04. Why does `jsonSerialize` emit a string rather than a number?

05. Why is there no `__toString`?

06. Why does `fromFloat` exist if floats are the problem?

License

Contributing

About

Releases

Packages

Used by

Contributors

Languages

Uh oh!

Latest commit

History

Folders and files

Repository files navigation

Math

Overview

Installation

How to use

Number

BigDecimal

BigInteger

BigRational

Percentage

Ratio

BigDecimals

RoundingMode

Failures

Calculation backend

FAQ

01. Why does division return a BigRational instead of a BigDecimal?

02. Why is equals different from isEqualTo?

03. Why is scale part of the value at all?

04. Why does jsonSerialize emit a string rather than a number?

05. Why is there no __toString?

06. Why does fromFloat exist if floats are the problem?

License

Contributing

About

Topics

Resources

Security policy

Stars

Watchers

Forks

Releases

Packages

Used by

Contributors

Languages

02. Why is `equals` different from `isEqualTo`?

04. Why does `jsonSerialize` emit a string rather than a number?

05. Why is there no `__toString`?

06. Why does `fromFloat` exist if floats are the problem?