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BinaryFp64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:43

IEEE 754 binary64 (double-precision) floating-point number.

Backed directly by the native JS number type — all arithmetic is performed by the JavaScript engine with hardware double-precision semantics.

Role in the type hierarchy:

  • BinaryFp16 and BinaryFp32 are backed by a number too, rounding to their narrower precision after each operation.
  • For software-emulated wide formats (binary128+), use BinaryFp.

References:

Extends

Section titled “Extends”
  • BinaryFpBase<BinaryFp64>

Implements

Section titled “Implements”

Constructors

Section titled “Constructors”

Constructor

Section titled “Constructor”

new BinaryFp64(value): BinaryFp64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:75

Parameters

Section titled “Parameters”
value
Section titled “value”

number

Returns

Section titled “Returns”

BinaryFp64

Overrides

Section titled “Overrides”

BinaryFpBase<BinaryFp64>.constructor

Properties

Section titled “Properties”

IEEE754

Section titled “IEEE754”

readonly static IEEE754: IeeeFormat = IEEE_FORMAT_BINARY64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:58

IEEE 754-2008 structural parameters for binary64. b=2, k=64, p=53, emax=1023.

INFINITY

Section titled “INFINITY”

readonly static INFINITY: BinaryFp64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:71

IEEE 754 positive infinity.

NAN

Section titled “NAN”

readonly static NAN: BinaryFp64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:69

IEEE 754 Not-a-Number.

NEG_INFINITY

Section titled “NEG_INFINITY”

readonly static NEG_INFINITY: BinaryFp64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:73

IEEE 754 negative infinity.

ONE

Section titled “ONE”

readonly static ONE: BinaryFp64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:63

Multiplicative identity 1.0.

STRUCTURE

Section titled “STRUCTURE”

readonly static STRUCTURE: AlgebraicStructure = APPROXIMATE_ORDERED_FIELD

Defined in: packages/math-numbers/src/num/_binary-fp-base.ts:41

Binary floating point is not a field: every operation rounds, so associativity and distributivity fail.

Inherited from

Section titled “Inherited from”

BinaryFpBase.STRUCTURE

TAG

Section titled “TAG”

readonly static TAG: typeof TAG

Defined in: packages/math-numbers/src/num/binary-fp64.ts:52

Unique type tag used by the converter registry.

TEN

Section titled “TEN”

readonly static TEN: BinaryFp64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:67

The value 10.0.

TWO

Section titled “TWO”

readonly static TWO: BinaryFp64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:65

The value 2.0.

ZERO

Section titled “ZERO”

readonly static ZERO: BinaryFp64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:61

Additive identity 0.0.

Accessors

Section titled “Accessors”

bitWidth

Section titled “bitWidth”

Get Signature

Section titled “Get Signature”

get bitWidth(): 64

Defined in: packages/math-numbers/src/num/binary-fp64.ts:47

Total width of the representation, in bits.

Returns
Section titled “Returns”

64

Total width of the representation, in bits.

Implementation of

Section titled “Implementation of”

IFixedPrecision.bitWidth

Overrides

Section titled “Overrides”

BinaryFpBase.bitWidth

decimalPrecision

Section titled “decimalPrecision”

Get Signature

Section titled “Get Signature”

get decimalPrecision(): number

Defined in: packages/math-numbers/src/num/binary-fp64.ts:152

Number of significant decimal digits in this value’s string representation. Returns DBL_DIG (15) for NaN/±∞.

Returns
Section titled “Returns”

number

Total number of significant decimal digits needed to exactly represent this value.

Returns Number.POSITIVE_INFINITY for values with non-terminating decimal expansions (e.g. Fraction(1, 3), √2).

Example

Section titled “Example”
  Integer.from(12345n).decimalPrecision; // → 5
  Decimal.from("3.14").decimalPrecision; // → 3
  Fraction.from(1n, 3n).decimalPrecision; // → Infinity
  ```;


#### Implementation of


[`INum`](../interfaces/INum.md).[`decimalPrecision`](../interfaces/INum.md#decimalprecision)


#### Overrides


`BinaryFpBase.decimalPrecision`


***


### formatInfo


#### Get Signature


> **get** **formatInfo**(): [`FixedPrecisionInfo`](../type-aliases/FixedPrecisionInfo.md)\<`BinaryFp64`\>


Defined in: packages/math-numbers/src/num/binary-fp64.ts:287


Fixed-precision format descriptor for IEEE 754 binary64.


##### Returns


[`FixedPrecisionInfo`](../type-aliases/FixedPrecisionInfo.md)\<`BinaryFp64`\>


#### Overrides


`BinaryFpBase.formatInfo`


***


### fractionalPrecision


#### Get Signature


> **get** **fractionalPrecision**(): `number`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:174


Number of decimal digits in the fractional part of `|value|`. `0` for
integer-valued doubles.


##### Returns


`number`


Number of decimal digits in the fractional part of `|value|`. `0` for exact
integers. Returns `Number.POSITIVE_INFINITY` for non-terminating decimal
expansions.


#### Example


```ts
  Integer.from(42n).fractionalPrecision; // → 0
  Decimal.from("3.14").fractionalPrecision; // → 2
  Fraction.from(1n, 3n).fractionalPrecision; // → Infinity
  ```;


#### Implementation of


[`INum`](../interfaces/INum.md).[`fractionalPrecision`](../interfaces/INum.md#fractionalprecision)


#### Overrides


`BinaryFpBase.fractionalPrecision`


***


### integralPrecision


#### Get Signature


> **get** **integralPrecision**(): `number`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:162


Number of decimal digits in the integer part of `|value|`. Always at least
`1`.


##### Returns


`number`


Number of decimal digits in the integer (integral) part of `|value|`.
Always at least `1` (the digit `0` for values with `|value| < 1`).


#### Example


```ts
  Integer.from(123n).integralPrecision; // → 3
  Decimal.from("0.5").integralPrecision; // → 1  (the leading '0')
  Decimal.from("3.14").integralPrecision; // → 1
  ```;


#### Implementation of


[`INum`](../interfaces/INum.md).[`integralPrecision`](../interfaces/INum.md#integralprecision)


#### Overrides


`BinaryFpBase.integralPrecision`


***


### isFinite


#### Get Signature


> **get** **isFinite**(): `boolean`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:94


`true` if this value is finite (not NaN and not ±∞).


##### Returns


`boolean`


***


### isInfinite


#### Get Signature


> **get** **isInfinite**(): `boolean`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:99


`true` if this value is +∞ or −∞.


##### Returns


`boolean`


***


### isNaN


#### Get Signature


> **get** **isNaN**(): `boolean`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:89


`true` if this value is IEEE 754 NaN.


##### Returns


`boolean`


***


### precisionKind


#### Get Signature


> **get** **precisionKind**(): `"fixed"`


Defined in: packages/math-numbers/src/num/\_binary-fp-base.ts:30


##### Returns


`"fixed"`


#### Implementation of


[`IFixedPrecision`](../interfaces/IFixedPrecision.md).[`precisionKind`](../interfaces/IFixedPrecision.md#precisionkind)


#### Inherited from


`BinaryFpBase.precisionKind`


***


### radix


#### Get Signature


> **get** **radix**(): `2`


Defined in: packages/math-numbers/src/num/\_binary-fp-base.ts:33


##### Returns


`2`


#### Implementation of


[`IBinaryEncoded`](../interfaces/IBinaryEncoded.md).[`radix`](../interfaces/IBinaryEncoded.md#radix)


#### Inherited from


`BinaryFpBase.radix`


## Methods


### \[toPrimitive\]()


> **\[toPrimitive\]**(`hint`): `string` \| `number` \| `bigint`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:137


Coerces to a JS primitive.


#### Parameters


##### hint


`"string"` \| `"number"` \| `"default"`


#### Returns


`string` \| `number` \| `bigint`


#### Implementation of


[`INum`](../interfaces/INum.md).[`[toPrimitive]`](../interfaces/INum.md#toprimitive)


#### Overrides


`BinaryFpBase.[toPrimitive]`


***


### abs()


> **abs**(): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:257


Absolute value `|x|`.


#### Returns


`BinaryFp64`


#### Overrides


`BinaryFpBase.abs`


***


### add()


> **add**(`other`): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:201


Returns `this + other`.


#### Parameters


##### other


`BinaryFp64`


#### Returns


`BinaryFp64`


#### Overrides


`BinaryFpBase.add`


***


### bitAt()


> **bitAt**(`position`): `0` \| `1`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:310


Returns the bit at `position` in the IEEE 754 binary64 layout of this
value. Position `0` is the least-significant bit; position `63` is the sign
bit.


Reference: https://en.wikipedia.org/wiki/IEEE_754#Formats


#### Parameters


##### position


`number`


#### Returns


`0` \| `1`


#### Throws


When `position` is outside `[0, 63]`.


#### Overrides


`BinaryFpBase.bitAt`


***


### clamp()


> **clamp**(`lower`, `upper`): `BinaryFp64`


Defined in: packages/math-algebra/src/\_ordered-defaults.ts:69


Restricts the value to `[lower, upper]`.


#### Parameters


##### lower


`BinaryFp64`


##### upper


`BinaryFp64`


#### Returns


`BinaryFp64`


#### Inherited from


`BinaryFpBase.clamp`


***


### cmp()


> **cmp**(`other`): `Sign`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:244


Three-way comparison.


#### Parameters


##### other


`BinaryFp64`


#### Returns


`Sign`


#### Throws


When either value is NaN (NaN is unordered in IEEE
  754).


#### Overrides


`BinaryFpBase.cmp`


***


### div()


> **div**(`other`): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:230


Returns `this / other` (IEEE 754 semantics).


#### Parameters


##### other


`BinaryFp64`


#### Returns


`BinaryFp64`


#### Overrides


`BinaryFpBase.div`


***


### eq()


> **eq**(`other`): `boolean`


Defined in: packages/math-algebra/src/\_ordered-defaults.ts:45


#### Parameters


##### other


`BinaryFp64`


#### Returns


`boolean`


#### Inherited from


`BinaryFpBase.eq`


***


### format()


> **format**(`locales?`, `options?`): `string`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:124


This value rendered for a human, by `Intl.NumberFormat`.


The parameters are `new Intl.NumberFormat(locales, options)`'s own,
unchanged — including the default, which is the ambient locale. Ask for
`"en-US"` with `useGrouping: false` when the output has to be
machine-readable.


#### Parameters


##### locales?


`LocalesArgument`


##### options?


`NumberFormatOptions`


#### Returns


`string`


#### Implementation of


[`INum`](../interfaces/INum.md).[`format`](../interfaces/INum.md#format)


#### Overrides


`BinaryFpBase.format`


***


### gt()


> **gt**(`other`): `boolean`


Defined in: packages/math-algebra/src/\_ordered-defaults.ts:57


#### Parameters


##### other


`BinaryFp64`


#### Returns


`boolean`


#### Inherited from


`BinaryFpBase.gt`


***


### gte()


> **gte**(`other`): `boolean`


Defined in: packages/math-algebra/src/\_ordered-defaults.ts:73


#### Parameters


##### other


`BinaryFp64`


#### Returns


`boolean`


#### Inherited from


`BinaryFpBase.gte`


***


### identity()


> **identity**(): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:192


Returns the multiplicative identity `1.0`.


#### Returns


`BinaryFp64`


#### Overrides


`BinaryFpBase.identity`


***


### inv()


> **inv**(): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:225


Returns `1 / this`. Returns ±∞ when `this` is zero (IEEE 754 semantics).


#### Returns


`BinaryFp64`


#### Overrides


`BinaryFpBase.inv`


***


### lt()


> **lt**(`other`): `boolean`


Defined in: packages/math-algebra/src/\_ordered-defaults.ts:49


#### Parameters


##### other


`BinaryFp64`


#### Returns


`boolean`


#### Inherited from


`BinaryFpBase.lt`


***


### lte()


> **lte**(`other`): `boolean`


Defined in: packages/math-algebra/src/\_ordered-defaults.ts:53


#### Parameters


##### other


`BinaryFp64`


#### Returns


`boolean`


#### Inherited from


`BinaryFpBase.lte`


***


### max()


> **max**(`other`): `BinaryFp64`


Defined in: packages/math-algebra/src/\_ordered-defaults.ts:65


The larger of the two operands under the total order.


#### Parameters


##### other


`BinaryFp64`


#### Returns


`BinaryFp64`


#### Inherited from


`BinaryFpBase.max`


***


### min()


> **min**(`other`): `BinaryFp64`


Defined in: packages/math-algebra/src/\_ordered-defaults.ts:61


The smaller of the two operands under the total order.


#### Parameters


##### other


`BinaryFp64`


#### Returns


`BinaryFp64`


#### Inherited from


`BinaryFpBase.min`


***


### mul()


> **mul**(`other`): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:187


Returns `this × other`.


#### Parameters


##### other


`BinaryFp64`


#### Returns


`BinaryFp64`


#### Overrides


`BinaryFpBase.mul`


***


### neg()


> **neg**(): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:211


Returns `−this`.


#### Returns


`BinaryFp64`


#### Overrides


`BinaryFpBase.neg`


***


### sign()


> **sign**(): `Sign`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:266


Sign of this value.


#### Returns


`Sign`


`-1` for negative, `0` for zero/NaN, `+1` for positive.


#### Overrides


`BinaryFpBase.sign`


***


### sqrt()


> **sqrt**(): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:278


Principal square root `√x`. Returns `NaN` for negative inputs (IEEE 754
semantics).


Reference: https://en.wikipedia.org/wiki/Square_root


#### Returns


`BinaryFp64`


#### Overrides


`BinaryFpBase.sqrt`


***


### sub()


> **sub**(`other`): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:216


Returns `this − other`.


#### Parameters


##### other


`BinaryFp64`


#### Returns


`BinaryFp64`


#### Overrides


`BinaryFpBase.sub`


***


### toExponential()


> **toExponential**(`fractionDigits?`): `string`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:116


Exponential notation: one digit before the point, `fractionDigits` after,
and an `e±` exponent. Omitting the count shows as many as the value has,
matching `Number.prototype.toExponential`.


#### Parameters


##### fractionDigits?


`number`


#### Returns


`string`


#### Implementation of


[`INum`](../interfaces/INum.md).[`toExponential`](../interfaces/INum.md#toexponential)


#### Overrides


`BinaryFpBase.toExponential`


***


### toFixed()


> **toFixed**(`fractionDigits?`): `string`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:112


Fixed-point notation with exactly `fractionDigits` places, padded with
zeros where the value has fewer — `Number.prototype.toFixed`, without its
cap of 100. A type that can hold more places can show them.


#### Parameters


##### fractionDigits?


`number` = `0`


#### Returns


`string`


#### Implementation of


[`INum`](../interfaces/INum.md).[`toFixed`](../interfaces/INum.md#tofixed)


#### Overrides


`BinaryFpBase.toFixed`


***


### toPrecision()


> **toPrecision**(`precision`): `string`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:120


`precision` significant digits, switching to exponential notation at the
same thresholds `Number.prototype.toPrecision` does.


#### Parameters


##### precision


`number`


#### Returns


`string`


#### Implementation of


[`INum`](../interfaces/INum.md).[`toPrecision`](../interfaces/INum.md#toprecision)


#### Overrides


`BinaryFpBase.toPrecision`


***


### toString()


> **toString**(`radix?`): `string`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:108


The shortest numeral that round-trips, or `radix` when given.


#### Parameters


##### radix?


`number`


#### Returns


`string`


#### Implementation of


[`INum`](../interfaces/INum.md).[`toString`](../interfaces/INum.md#tostring)


#### Overrides


`BinaryFpBase.toString`


***


### valueOf()


> **valueOf**(): `number`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:132


Returns the underlying `number` value.


#### Returns


`number`


#### Implementation of


[`INum`](../interfaces/INum.md).[`valueOf`](../interfaces/INum.md#valueof)


#### Overrides


`BinaryFpBase.valueOf`


***


### zero()


> **zero**(): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:206


Returns the additive identity `0.0`.


#### Returns


`BinaryFp64`


#### Overrides


`BinaryFpBase.zero`


***


### from()


> `static` **from**(`value`): `BinaryFp64`


Defined in: packages/math-numbers/src/num/binary-fp64.ts:80


Creates a `BinaryFp64` from a `number` or parseable numeric string.


#### Parameters


##### value


`string` \| `number`


#### Returns


`BinaryFp64`