`std/number`

Every numeric type of the language: Numeric, Signed, Bits and Real, the traits their operators go through; the sized integer types and the two floating-point types; Decimal; the conversions between all of them; and ByteSize, a number of bytes in its units.

Reach for Int, UInt or Float - the three default-width aliases - and only name a sized type (Int8, UInt32, ...) where a signature has to say exactly how wide a value is.

Modules

std/number/libEvery numeric type of the language: [Numeric], [Signed], [Bits] and [Real], the traits their operators go through; the sized integer types and the two floating-point types; [Decimal]; the conversions between all of them; and [ByteSize], a number of bytes in its units.

Everything

trait BitsThe bit operations of an integer, and the operators that are them: a & b is bitwiseAnd, a | b bitwiseOr, a ^ b bitwiseExclusiveOr, ~a bitwiseNot, a << n shiftedLeft(by:) and a >> n shiftedRight(by:).
type ByteSizeA number of bytes: the size of a memory, of a volume, of a limit.
type DecimalExact base-10 arithmetic: an unscaled whole number of any size and an Int32 scale, the value being the one divided by ten to the other (docs/design/DECIMAL.md).
extend DecimalThe zero and the one of a Decimal.
extend DecimalThe scale of a Decimal, and rounding to one.
extend Decimal with From<Int64>Every Int64 is a Decimal at scale 0.
extend Decimal with From<UInt64>Every UInt64 is a Decimal at scale 0.
extend Decimal with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a decimal number.
alias FloatThe default width for a floating-point number: Float64.
type Float32A 32-bit floating-point number: IEEE-754 binary32, rounded to the nearest one with ties to even after every operation, in both back ends and in a folded constant alike.
extend Float32The zero and the one of a Float32, its two infinities, and the one value for which == is never true.
extend Float32 with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a decimal number.
extend Float32 with TryFrom<Float64, NumberRangeError>The nearest Float32, ties to even: most Float64 values lose digits on the way.
type Float64A 64-bit floating-point number, and the type of a decimal literal.
extend Float64The constants and the operations of a Float64 that read as its own, not as a function of a value.
extend Float64 with RealFloat64 is the fast [Real]: the square root, the rounding and isCloseTo are its own methods already, and the trigonometry, the exponential and the logarithm are the runtime's thin wrappers over <math.h>.
extend Float64 with Power<Int64>x ** n for a whole exponent: 2.0 ** 10 and 10.0 ** -3.
extend Float64 with From<Int64>Every Int64 is representable as a Float64.
extend Float64 with From<Float32>Every Float32 widens to Float64 without loss.
extend Float64 with From<Decimal>The nearest Float64, a tie to even, as reading the decimal's text would give it.
extend Float64 with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a decimal number.
alias IntThe default width for a whole number: Int64.
type Int16A 16-bit signed integer, from [Int16.minimum] to [Int16.maximum].
extend Int16The range of an Int16, and its zero and one.
extend Int16 with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a whole number, or does not fit an Int16.
extend Int16 with TryFrom<Int64, NumberRangeError>Fails with a [NumberRangeError] when the Int64 does not fit an Int16.
type Int32A 32-bit signed integer, from [Int32.minimum] to [Int32.maximum].
extend Int32The range of an Int32, and its zero and one.
extend Int32 with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a whole number, or does not fit an Int32.
extend Int32 with TryFrom<Int64, NumberRangeError>Fails with a [NumberRangeError] when the Int64 does not fit an Int32.
type Int64A 64-bit signed integer, and the type of an integer literal.
extend Int64The range of an Int64, its zero and one, and reading digits in another base.
extend Int64 with From<Int8>A narrower signed integer always fits: Int.from(byte) for an Int8.
extend Int64 with From<Int16>A narrower signed integer always fits: Int.from(short) for an Int16.
extend Int64 with From<Int32>A narrower signed integer always fits: Int.from(word) for an Int32.
extend Int64 with From<UInt8>Every unsigned value below the width of an Int64 fits into it: Int.from(byte) for a byte of a String.
extend Int64 with From<UInt16>Every unsigned value below the width of an Int64 fits into it.
extend Int64 with From<UInt32>Every unsigned value below the width of an Int64 fits into it.
extend Int64 with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a whole number, or does not fit an Int64.
extend Int64 with TryFrom<UInt64, NumberRangeError>Fails with a [NumberRangeError] when the UInt64 is above the largest Int64.
extend Int64 with TryFrom<Float64, NumberRangeError>Fails with a [NumberRangeError] when the Float64 does not fit an Int64, e.g.
extend Int64 with TryFrom<Decimal, NumberRangeError>Fails with a [NumberRangeError] unless the Decimal is a whole number that fits an Int64: 19.00 converts and 19.5 does not.
extend Int64 with From<Char>The code point: Int.from('A') is 65.
extend Int64A [ByteSize] of this many bytes, in either family of units.
type Int8An 8-bit signed integer, from [Int8.minimum] to [Int8.maximum].
extend Int8The range of an Int8, and its zero and one.
extend Int8 with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a whole number, or does not fit an Int8.
extend Int8 with TryFrom<Int64, NumberRangeError>Fails with a [NumberRangeError] when the Int64 does not fit an Int8.
trait Integer[Numeric] of a whole number, with its range: [Integer.minimum], [Integer.maximum], and the arithmetic that answers None exactly where the operator would panic.
type NumberParseErrorWhat Int.tryFrom(text) fails with: the text is not a valid number.
type NumberRangeErrorWhat a narrowing conversion (Int8.tryFrom, Int64.tryFrom) fails with: the value does not fit the target type.
trait NumericThe arithmetic and comparison every number has: +, -, *, /, %, ==, <, reading one from text, and its zero and its one.
trait Real[Signed] plus the operations that need a root or an angle: the scalar of geometry, trigonometry and interpolation.
type RoundingHow a value is cut where a digit has to go: the mode of [Decimal.rounded] and [Decimal.divided].
trait Signed[Numeric] plus a sign: the unary - and [Signed.absolute].
alias UIntThe default width for a non-negative whole number: UInt64.
type UInt16A 16-bit unsigned integer, from 0 to [UInt16.maximum].
extend UInt16The range of a UInt16, and its zero and one.
extend UInt16 with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a non-negative whole number, or does not fit a UInt16.
extend UInt16 with TryFrom<Int64, NumberRangeError>Fails with a [NumberRangeError] when the Int64 is negative or does not fit a UInt16.
type UInt32A 32-bit unsigned integer, from 0 to [UInt32.maximum].
extend UInt32The range of a UInt32, and its zero and one.
extend UInt32 with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a non-negative whole number, or does not fit a UInt32.
extend UInt32 with TryFrom<Int64, NumberRangeError>Fails with a [NumberRangeError] when the Int64 is negative or does not fit a UInt32.
type UInt64A 64-bit unsigned integer, from 0 to [UInt64.maximum].
extend UInt64The range of a UInt64, its zero and one, and the two operations that wrap instead of panicking.
extend UInt64 with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a non-negative whole number, or does not fit a UInt64.
extend UInt64 with TryFrom<Int64, NumberRangeError>Fails with a [NumberRangeError] when the Int64 is negative: every other one fits a UInt64.
extend UInt64 with TryFrom<Decimal, NumberRangeError>Fails with a [NumberRangeError] unless the Decimal is a whole number that fits a UInt64.
type UInt8An 8-bit unsigned integer, from 0 to [UInt8.maximum].
extend UInt8The range of a UInt8, and its zero and one.
extend UInt8 with TryFrom<String, NumberParseError>Fails with a [NumberParseError] when the text is not a non-negative whole number, or does not fit a UInt8.
extend UInt8 with TryFrom<Int64, NumberRangeError>Fails with a [NumberRangeError] when the Int64 is negative or above 255: the one way from a number to a byte.