BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:44

IEEE 754 binary16 (half-precision) floating-point number.

Backed by a JS number; each operation rounds the result to half precision using round-to-nearest-even before storing it.

Range: ≈ ±65504; precision: ~3–4 significant decimal digits.

References:

IEEE 754-2019: https://en.wikipedia.org/wiki/IEEE_754
Half precision: https://en.wikipedia.org/wiki/Half-precision_floating-point_format

Extends

BinaryFpBase<BinaryFp16>

Implements

Constructors

Constructor

new BinaryFp16(value): BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:84

Parameters

value

number

Returns

BinaryFp16

Overrides

BinaryFpBase<BinaryFp16>.constructor

Properties

IEEE754

readonly static IEEE754: IeeeFormat = IEEE_FORMAT_BINARY16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:59

IEEE 754-2008 structural parameters for binary16. b=2, k=16, p=11, emax=15.

INFINITY

readonly static INFINITY: BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:72

IEEE 754 positive infinity.

MAX_VALUE

readonly static MAX_VALUE: BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:77

Max finite positive float16 (65504).

MIN_VALUE

readonly static MIN_VALUE: BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:79

Min positive normalised float16 (2^−14 ≈ 6.1035e-5).

NAN

readonly static NAN: BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:70

IEEE 754 Not-a-Number.

NEG_INFINITY

readonly static NEG_INFINITY: BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:74

IEEE 754 negative infinity.

ONE

readonly static ONE: BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:64

Multiplicative identity 1.0h.

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

BinaryFpBase.STRUCTURE

TAG

readonly static TAG: typeof TAG

Defined in: packages/math-numbers/src/num/binary-fp16.ts:53

Unique type tag used by the converter registry.

TEN

readonly static TEN: BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:68

The value 10.0h.

TWO

readonly static TWO: BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:66

The value 2.0h.

ZERO

readonly static ZERO: BinaryFp16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:62

Additive identity 0.0h.

Accessors

bitWidth

Get Signature

get bitWidth(): 16

Defined in: packages/math-numbers/src/num/binary-fp16.ts:48

Total width of the representation, in bits.

Returns

16

Overrides

BinaryFpBase.bitWidth

decimalPrecision

Get Signature

get decimalPrecision(): number

Defined in: packages/math-numbers/src/num/binary-fp16.ts:172

Number of significant decimal digits (~3–4 for float16).

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

  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)\<`BinaryFp16`\>

Defined in: packages/math-numbers/src/num/binary-fp16.ts:296

Fixed-precision format descriptor for IEEE 754 binary16.

##### Returns

[`FixedPrecisionInfo`](../type-aliases/FixedPrecisionInfo.md)\<`BinaryFp16`\>

#### Overrides

`BinaryFpBase.formatInfo`

***

### fractionalPrecision

#### Get Signature

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

Defined in: packages/math-numbers/src/num/binary-fp16.ts:186

Number of decimal digits in the fractional part.

##### 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-fp16.ts:177

Number of decimal digits in the integer part.

##### 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-fp16.ts:113

`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-fp16.ts:118

`true` if this value is +∞ or −∞.

##### Returns

`boolean`

***

### isNaN

#### Get Signature

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

Defined in: packages/math-numbers/src/num/binary-fp16.ts:108

`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"`

#### 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-fp16.ts:160

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**(): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:268

Absolute value `|x|`.

#### Returns

`BinaryFp16`

#### Overrides

`BinaryFpBase.abs`

***

### add()

> **add**(`other`): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:213

Returns `this + other`, rounded to float16.

#### Parameters

##### other

`BinaryFp16`

#### Returns

`BinaryFp16`

#### Overrides

`BinaryFpBase.add`

***

### bitAt()

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

Defined in: packages/math-numbers/src/num/binary-fp16.ts:316

Returns the bit at `position` in the IEEE 754 binary16 layout. Position `0`
is the least-significant bit; position `15` is the sign bit.

#### Parameters

##### position

`number`

#### Returns

`0` \| `1`

#### Throws

When `position` is outside `[0, 15]`.

#### Overrides

`BinaryFpBase.bitAt`

***

### clamp()

> **clamp**(`lower`, `upper`): `BinaryFp16`

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

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

#### Parameters

##### lower

`BinaryFp16`

##### upper

`BinaryFp16`

#### Returns

`BinaryFp16`

#### Inherited from

`BinaryFpBase.clamp`

***

### cmp()

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

Defined in: packages/math-numbers/src/num/binary-fp16.ts:255

Three-way comparison.

#### Parameters

##### other

`BinaryFp16`

#### Returns

`Sign`

#### Throws

When either value is NaN.

#### Overrides

`BinaryFpBase.cmp`

***

### div()

> **div**(`other`): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:242

Returns `this / other`, rounded to float16.

#### Parameters

##### other

`BinaryFp16`

#### Returns

`BinaryFp16`

#### Overrides

`BinaryFpBase.div`

***

### eq()

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

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

#### Parameters

##### other

`BinaryFp16`

#### Returns

`boolean`

#### Inherited from

`BinaryFpBase.eq`

***

### format()

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

Defined in: packages/math-numbers/src/num/binary-fp16.ts:143

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

`BinaryFp16`

#### Returns

`boolean`

#### Inherited from

`BinaryFpBase.gt`

***

### gte()

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

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

#### Parameters

##### other

`BinaryFp16`

#### Returns

`boolean`

#### Inherited from

`BinaryFpBase.gte`

***

### identity()

> **identity**(): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:204

Returns the multiplicative identity `1.0h`.

#### Returns

`BinaryFp16`

#### Overrides

`BinaryFpBase.identity`

***

### inv()

> **inv**(): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:237

Returns `1 / this`, rounded to float16.

#### Returns

`BinaryFp16`

#### Overrides

`BinaryFpBase.inv`

***

### lt()

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

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

#### Parameters

##### other

`BinaryFp16`

#### Returns

`boolean`

#### Inherited from

`BinaryFpBase.lt`

***

### lte()

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

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

#### Parameters

##### other

`BinaryFp16`

#### Returns

`boolean`

#### Inherited from

`BinaryFpBase.lte`

***

### max()

> **max**(`other`): `BinaryFp16`

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

The larger of the two operands under the total order.

#### Parameters

##### other

`BinaryFp16`

#### Returns

`BinaryFp16`

#### Inherited from

`BinaryFpBase.max`

***

### min()

> **min**(`other`): `BinaryFp16`

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

The smaller of the two operands under the total order.

#### Parameters

##### other

`BinaryFp16`

#### Returns

`BinaryFp16`

#### Inherited from

`BinaryFpBase.min`

***

### mul()

> **mul**(`other`): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:199

Returns `this × other`, rounded to float16.

#### Parameters

##### other

`BinaryFp16`

#### Returns

`BinaryFp16`

#### Overrides

`BinaryFpBase.mul`

***

### neg()

> **neg**(): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:223

Returns `−this`.

#### Returns

`BinaryFp16`

#### Overrides

`BinaryFpBase.neg`

***

### sign()

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

Defined in: packages/math-numbers/src/num/binary-fp16.ts:277

Sign of this value.

#### Returns

`Sign`

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

#### Overrides

`BinaryFpBase.sign`

***

### sqrt()

> **sqrt**(): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:287

Principal square root `√x`, rounded to float16. Returns `NaN` for negative
inputs.

#### Returns

`BinaryFp16`

#### Overrides

`BinaryFpBase.sqrt`

***

### sub()

> **sub**(`other`): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:228

Returns `this − other`, rounded to float16.

#### Parameters

##### other

`BinaryFp16`

#### Returns

`BinaryFp16`

#### Overrides

`BinaryFpBase.sub`

***

### toExponential()

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

Defined in: packages/math-numbers/src/num/binary-fp16.ts:135

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-fp16.ts:131

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-fp16.ts:139

`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-fp16.ts:127

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-fp16.ts:155

Returns the underlying `number` value (float16-rounded).

#### Returns

`number`

#### Implementation of

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

#### Overrides

`BinaryFpBase.valueOf`

***

### zero()

> **zero**(): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:218

Returns the additive identity `0.0h`.

#### Returns

`BinaryFp16`

#### Overrides

`BinaryFpBase.zero`

***

### from()

> `static` **from**(`value`): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:90

Creates a `BinaryFp16` from a `number` or parseable numeric string.

#### Parameters

##### value

`string` \| `number`

#### Returns

`BinaryFp16`

***

### fromBits()

> `static` **fromBits**(`bits`): `BinaryFp16`

Defined in: packages/math-numbers/src/num/binary-fp16.ts:99

Creates a `BinaryFp16` from a raw 16-bit IEEE 754 bit pattern.

#### Parameters

##### bits

`number`

16-bit unsigned integer bit pattern (values 0–65535).

#### Returns

`BinaryFp16`