Struct e4m3 

pub struct e4m3(/* private fields */);

A 8-bit floating point type with 4 exponent bits and 3 mantissa bits.

Follows table 1 of FP8 Formats for Deep Learning. E4M3 departs from IEEE 754 to widen its range: it has no infinities, and reserves only S.1111.111 for NaN. Reclaiming the rest of the special-value patterns is what puts its maximum at 448 rather than the 240 an IEEE-style reservation would give.

MAX, MIN, MAX_EXP and MANTISSA_DIGITS are spelled out here rather than delegated to float8, each for the reason given on the constant itself. Every other constant delegates and agrees. No infinity constant is exposed, because the format has none.

See also the minifloat overview.

Implementations

impl e4m3

pub const MAX: e4m3

Maximum representable value, S.1111.110 = 1.75 * 2^8 = 448.

Not taken from F8E4M3::MAX, which is 416 and one representable step low. E4M3 has no infinities and reserves only S.1111.111 for NaN, so 0x7E is finite. See table 1 of “FP8 Formats for Deep Learning” (arXiv:2209.05433), which also matches what from_f32 saturates to and what QuantValue::E4M3 bounds against.

pub const MIN: e4m3

Minimum representable value, the negation of MAX.

pub const EPSILON: e4m3

the difference between 1.0 and the next largest representable number.

pub const MIN_POSITIVE: e4m3

Minimum representable value

pub const DIGITS: u32 = F8E4M3::DIGITS

Approximate number of significant digits in base 10

pub const MANTISSA_DIGITS: u32 = 4

Number of mantissa digits, the 3 stored bits plus the implicit leading one.

F8E4M3::MANTISSA_DIGITS counts only the stored bits, where f32 and half::f16 both count the implicit one.

pub const MAX_10_EXP: i32 = F8E4M3::MAX_10_EXP

Maximum possible normal power of 10 exponent

pub const MAX_EXP: i32 = 9

One greater than the maximum possible normal power of 2 exponent, matching f32::MAX_EXP.

MAX is 1.75 * 2^8, so this is 9. F8E4M3::MAX_EXP is 7: one lower because it reserves an exponent for infinities this format does not have, and another because it does not add the one that f32 and half::f16 do.

pub const MIN_10_EXP: i32 = F8E4M3::MIN_10_EXP

Minimum possible normal power of 10 exponent

pub const MIN_EXP: i32 = F8E4M3::MIN_EXP

Minimum possible normal power of 2 exponent

pub const RADIX: u32 = 2

The radix, or base, of the floating-point representation.

pub const NAN: e4m3

nan

pub const ZERO: e4m3

Zero

pub const NEG_ZERO: e4m3

Negative Zero

pub const ONE: e4m3

One

pub const fn from_bits(bits: u8) -> e4m3

Constructs a e4m3 value from the raw bits.

pub const fn from_f32(value: f32) -> e4m3

Constructs a e4m3 value from a 32-bit floating point value.

This operation is lossy. Values too large to fit, infinities included, saturate to ±MAX, since the format has no infinities of its own. NaN values are preserved. Subnormal values that are too tiny to be represented will result in ±0. All other values are truncated and rounded to the nearest representable value.

pub const fn from_f64(value: f64) -> e4m3

Constructs a e4m3 value from a 64-bit floating point value.

This operation is lossy. Values too large to fit, infinities included, saturate to ±MAX, since the format has no infinities of its own. NaN values are preserved. 64-bit subnormal values are too tiny to be represented and result in ±0. Exponents that underflow the minimum exponent will result in subnormals or ±0. All other values are truncated and rounded to the nearest representable value.

pub const fn to_bits(self) -> u8

Converts a e4m3 into the underlying bit representation.

pub const fn to_f32(self) -> f32

Converts a e4m3 value into an f32 value.

This conversion is lossless as all values can be represented exactly in f32.

pub fn is_nan(self) -> bool

check if an e4m3 value is Nan

pub const fn to_f64(self) -> f64

Converts a e4m3 value into an f64 value.

This conversion is lossless as all values can be represented exactly in f64.

pub fn total_cmp(self, other: e4m3) -> Ordering

Compares e4m3 values

Trait Implementations

impl Add for e4m3

type Output = e4m3

The resulting type after applying the + operator.

fn add(self, rhs: e4m3) -> <e4m3 as Add>::Output

Performs the + operation.

impl AddAssign for e4m3

fn add_assign(&mut self, rhs: e4m3)

Performs the += operation.

impl Clone for e4m3

fn clone(&self) -> e4m3

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for e4m3

impl Debug for e4m3

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl Default for e4m3

fn default() -> e4m3

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for e4m3

fn deserialize<__D>( __deserializer: __D, ) -> Result<e4m3, <__D as Deserializer<'de>>::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for e4m3

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl Div for e4m3

type Output = e4m3

The resulting type after applying the / operator.

fn div(self, rhs: e4m3) -> <e4m3 as Div>::Output

Performs the / operation.

impl DivAssign for e4m3

fn div_assign(&mut self, rhs: e4m3)

Performs the /= operation.

impl From<F8E4M3> for e4m3

fn from(value: F8E4M3) -> e4m3

Converts to this type from the input type.

impl Mul for e4m3

type Output = e4m3

The resulting type after applying the * operator.

fn mul(self, rhs: e4m3) -> <e4m3 as Mul>::Output

Performs the * operation.

impl MulAssign for e4m3

fn mul_assign(&mut self, rhs: e4m3)

Performs the *= operation.

impl Neg for e4m3

type Output = e4m3

The resulting type after applying the - operator.

fn neg(self) -> <e4m3 as Neg>::Output

Performs the unary - operation.

impl Num for e4m3

type FromStrRadixErr = ParseFloatError

fn from_str_radix( src: &str, radix: u32, ) -> Result<e4m3, <e4m3 as Num>::FromStrRadixErr>

Convert from a string and radix (typically 2..=36).

impl NumCast for e4m3

fn from<T>(n: T) -> Option<e4m3>

where T: ToPrimitive,

Creates a number from another value that can be converted into a primitive via the ToPrimitive trait. If the source value cannot be represented by the target type, then None is returned.

impl One for e4m3

fn one() -> e4m3

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl PartialEq for e4m3

fn eq(&self, other: &e4m3) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl PartialOrd for e4m3

fn partial_cmp(&self, other: &e4m3) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Pod for e4m3

impl Rem for e4m3

type Output = e4m3

The resulting type after applying the % operator.

fn rem(self, rhs: e4m3) -> <e4m3 as Rem>::Output

Performs the % operation.

impl RemAssign for e4m3

fn rem_assign(&mut self, rhs: e4m3)

Performs the %= operation.

impl Serialize for e4m3

fn serialize<__S>( &self, __serializer: __S, ) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for e4m3

impl Sub for e4m3

type Output = e4m3

The resulting type after applying the - operator.

fn sub(self, rhs: e4m3) -> <e4m3 as Sub>::Output

Performs the - operation.

impl SubAssign for e4m3

fn sub_assign(&mut self, rhs: e4m3)

Performs the -= operation.

impl ToPrimitive for e4m3

fn to_i64(&self) -> Option<i64>

Converts the value of self to an i64. If the value cannot be represented by an i64, then None is returned.

fn to_u64(&self) -> Option<u64>

Converts the value of self to a u64. If the value cannot be represented by a u64, then None is returned.

fn to_f32(&self) -> Option<f32>

Converts the value of self to an f32. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f32.

fn to_f64(&self) -> Option<f64>

Converts the value of self to an f64. Overflows may map to positive or negative inifinity, otherwise None is returned if the value cannot be represented by an f64.

fn to_isize(&self) -> Option<isize>

Converts the value of self to an isize. If the value cannot be represented by an isize, then None is returned.

fn to_i8(&self) -> Option<i8>

Converts the value of self to an i8. If the value cannot be represented by an i8, then None is returned.

fn to_i16(&self) -> Option<i16>

Converts the value of self to an i16. If the value cannot be represented by an i16, then None is returned.

fn to_i32(&self) -> Option<i32>

Converts the value of self to an i32. If the value cannot be represented by an i32, then None is returned.

fn to_i128(&self) -> Option<i128>

Converts the value of self to an i128. If the value cannot be represented by an i128 (i64 under the default implementation), then None is returned.

fn to_usize(&self) -> Option<usize>

Converts the value of self to a usize. If the value cannot be represented by a usize, then None is returned.

fn to_u8(&self) -> Option<u8>

Converts the value of self to a u8. If the value cannot be represented by a u8, then None is returned.

fn to_u16(&self) -> Option<u16>

Converts the value of self to a u16. If the value cannot be represented by a u16, then None is returned.

fn to_u32(&self) -> Option<u32>

Converts the value of self to a u32. If the value cannot be represented by a u32, then None is returned.

fn to_u128(&self) -> Option<u128>

Converts the value of self to a u128. If the value cannot be represented by a u128 (u64 under the default implementation), then None is returned.

impl Zero for e4m3

fn zero() -> e4m3

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl Zeroable for e4m3

fn zeroed() -> Self

Calls zeroed.