Trait malachite_base::num::basic::floats::PrimitiveFloat

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pub trait PrimitiveFloat: 'static + Abs<Output = Self> + AbsAssign + Add<Output = Self> + AddAssign<Self> + AddMul<Output = Self> + AddMulAssign<Self, Self> + Ceiling<Output = Self> + CeilingAssign + CeilingLogBase2<Output = i64> + CeilingLogBasePowerOf2<u64, Output = i64> + CheckedFrom<u8> + CheckedFrom<u16> + CheckedFrom<u32> + CheckedFrom<u64> + CheckedFrom<u128> + CheckedFrom<usize> + CheckedFrom<i8> + CheckedFrom<i16> + CheckedFrom<i32> + CheckedFrom<i64> + CheckedFrom<i128> + CheckedFrom<isize> + CheckedInto<u8> + CheckedInto<u16> + CheckedInto<u32> + CheckedInto<u64> + CheckedInto<u128> + CheckedInto<usize> + CheckedInto<i8> + CheckedInto<i16> + CheckedInto<i32> + CheckedInto<i64> + CheckedInto<i128> + CheckedInto<isize> + CheckedLogBase2<Output = i64> + CheckedLogBasePowerOf2<u64, Output = i64> + ConvertibleFrom<u8> + ConvertibleFrom<u16> + ConvertibleFrom<u32> + ConvertibleFrom<u64> + ConvertibleFrom<u128> + ConvertibleFrom<usize> + ConvertibleFrom<i8> + ConvertibleFrom<i16> + ConvertibleFrom<i32> + ConvertibleFrom<i64> + ConvertibleFrom<i128> + ConvertibleFrom<isize> + Copy + Debug + Default + Display + Div<Output = Self> + DivAssign + Display + Floor<Output = Self> + FloorAssign + FloorLogBase2<Output = i64> + FloorLogBasePowerOf2<u64, Output = i64> + FmtRyuString + From<f32> + FromStr + IntegerMantissaAndExponent<u64, i64> + Into<f64> + IsInteger + IsPowerOf2 + Iverson + LowerExp + Min + Max + Mul<Output = Self> + MulAssign<Self> + Named + Neg<Output = Self> + NegAssign + NegativeOne + NextPowerOf2<Output = Self> + NextPowerOf2Assign + One + PartialEq<Self> + PartialOrd<Self> + Pow<i64, Output = Self> + Pow<Self, Output = Self> + PowAssign<i64> + PowAssign<Self> + PowerOf2<i64> + Product + RawMantissaAndExponent<u64, u64> + Rem<Output = Self> + RemAssign<Self> + RoundingFrom<u8> + RoundingFrom<u16> + RoundingFrom<u32> + RoundingFrom<u64> + RoundingFrom<u128> + RoundingFrom<usize> + RoundingFrom<i8> + RoundingFrom<i16> + RoundingFrom<i32> + RoundingFrom<i64> + RoundingFrom<i128> + RoundingFrom<isize> + RoundingInto<u8> + RoundingInto<u16> + RoundingInto<u32> + RoundingInto<u64> + RoundingInto<u128> + RoundingInto<usize> + RoundingInto<i8> + RoundingInto<i16> + RoundingInto<i32> + RoundingInto<i64> + RoundingInto<i128> + RoundingInto<isize> + SciMantissaAndExponent<Self, i64> + Sign + Sized + Sqrt<Output = Self> + SqrtAssign + Square<Output = Self> + SquareAssign + Sub<Output = Self> + SubAssign<Self> + SubMul<Output = Self> + SubMulAssign<Self, Self> + Sum<Self> + Two + UpperExp + Zero {
Show 16 associated constants and 16 methods
    const WIDTH: u64;
    const MANTISSA_WIDTH: u64;
    const MIN_POSITIVE_SUBNORMAL: Self;
    const MAX_SUBNORMAL: Self;
    const MIN_POSITIVE_NORMAL: Self;
    const MAX_FINITE: Self;
    const NEGATIVE_ZERO: Self;
    const POSITIVE_INFINITY: Self;
    const NEGATIVE_INFINITY: Self;
    const NAN: Self;
    const SMALLEST_UNREPRESENTABLE_UINT: u64;
    const LARGEST_ORDERED_REPRESENTATION: u64;
    const EXPONENT_WIDTH: u64 = Self::WIDTH - Self::MANTISSA_WIDTH - 1;
    const MIN_NORMAL_EXPONENT: i64 = -(1 << (Self::EXPONENT_WIDTH - 1)) + 2;
    const MIN_EXPONENT: i64 = Self::MIN_NORMAL_EXPONENT - (Self::MANTISSA_WIDTH as i64);
    const MAX_EXPONENT: i64 = (1 << (Self::EXPONENT_WIDTH - 1)) - 1;

    fn is_nan(self) -> bool;
    fn is_infinite(self) -> bool;
    fn is_finite(self) -> bool;
    fn is_normal(self) -> bool;
    fn classify(self) -> FpCategory;
    fn to_bits(self) -> u64;
    fn from_bits(v: u64) -> Self;

    fn is_negative_zero(self) -> bool { ... }
    fn abs_negative_zero(self) -> Self { ... }
    fn abs_negative_zero_assign(&mut self) { ... }
    fn next_higher(self) -> Self { ... }
    fn next_lower(self) -> Self { ... }
    fn to_ordered_representation(self) -> u64 { ... }
    fn from_ordered_representation(n: u64) -> Self { ... }
    fn precision(self) -> u64 { ... }
    fn max_precision_for_sci_exponent(exponent: i64) -> u64 { ... }
}

Expand description

This trait defines functions on primitive float types: f32 and f64.

Many of the functions here concern exponents and mantissas. We define three ways to express a float, each with its own exponent and mantissa. In the following, let $x$ be an arbitrary positive, finite, non-zero, non-NaN float. Let $M$ and $E$ be the mantissa width and exponent width of the floating point type; for f32s, this is 23 and 8, and for f64s it’s 52 and 11.

In the following we assume that $x$ is positive, but you can easily extend these definitions to negative floats by first taking their absolute value.

raw form

The raw exponent and raw mantissa are the actual bit patterns used to represent the components of $x$. The raw exponent $e_r$ is an integer in $[0, 2^E-2]$ and the raw mantissa $m_r$ is an integer in $[0, 2^M-1]$. Since we are dealing with a nonzero $x$, we forbid $e_r$ and $m_r$ from both being zero. We have $$ x = \begin{cases} 2^{2-2^{E-1}-M}m_r & \text{if} \quad e_r = 0, \\ 2^{e_r-2^{E-1}+1}(2^{-M}m_r+1) & \textrm{otherwise}, \end{cases} $$ $$ e_r = \begin{cases} 0 & \text{if} \quad x < 2^{2-2^{E-1}}, \\ \lfloor \log_2 x \rfloor + 2^{E-1} - 1 & \textrm{otherwise}, \end{cases} $$ $$ m_r = \begin{cases} 2^{M+2^{E-1}-2}x & \text{if} \quad x < 2^{2-2^{E-1}}, \\ 2^M \left ( \frac{x}{2^{\lfloor \log_2 x \rfloor}}-1\right ) & \textrm{otherwise}. \end{cases} $$

scientific form

We can write $x = 2^{e_s}m_s$, where $e_s$ is an integer and $m_s$ is a rational number with $1 \leq m_s < 2$. If $x$ is a valid float, the scientific mantissa $m_s$ is always exactly representable as a float of the same type. We have $$ x = 2^{e_s}m_s, $$ $$ e_s = \lfloor \log_2 x \rfloor, $$ $$ m_s = \frac{x}{2^{\lfloor \log_2 x \rfloor}}. $$

integer form

We can also write $x = 2^{e_i}m_i$, where $e_i$ is an integer and $m_i$ is an odd integer. We have $$ x = 2^{e_i}m_i, $$ $e_i$ is the unique integer such that $x/2^{e_i}$is an odd integer, and $$ m_i = \frac{x}{2^{e_i}}. $$

Trait malachite_base::num::basic::floats::PrimitiveFloat

Required Associated Constants

const WIDTH: u64

const MANTISSA_WIDTH: u64

const MIN_POSITIVE_SUBNORMAL: Self

const MAX_SUBNORMAL: Self

const MIN_POSITIVE_NORMAL: Self

const MAX_FINITE: Self

const NEGATIVE_ZERO: Self

const POSITIVE_INFINITY: Self

const NEGATIVE_INFINITY: Self

const NAN: Self

const SMALLEST_UNREPRESENTABLE_UINT: u64

const LARGEST_ORDERED_REPRESENTATION: u64

Provided Associated Constants

const EXPONENT_WIDTH: u64 = Self::WIDTH - Self::MANTISSA_WIDTH - 1

const MIN_NORMAL_EXPONENT: i64 = -(1 << (Self::EXPONENT_WIDTH - 1)) + 2

const MIN_EXPONENT: i64 = Self::MIN_NORMAL_EXPONENT - (Self::MANTISSA_WIDTH as i64)

const MAX_EXPONENT: i64 = (1 << (Self::EXPONENT_WIDTH - 1)) - 1

Required Methods

fn is_nan(self) -> bool

fn is_infinite(self) -> bool

fn is_finite(self) -> bool

fn is_normal(self) -> bool

fn classify(self) -> FpCategory

fn to_bits(self) -> u64

fn from_bits(v: u64) -> Self

Provided Methods

fn is_negative_zero(self) -> bool

fn abs_negative_zero(self) -> Self

fn abs_negative_zero_assign(&mut self)

fn next_higher(self) -> Self

fn next_lower(self) -> Self

fn to_ordered_representation(self) -> u64

fn from_ordered_representation(n: u64) -> Self

fn precision(self) -> u64

fn max_precision_for_sci_exponent(exponent: i64) -> u64

Implementations on Foreign Types

impl PrimitiveFloat for f32

const WIDTH: u64 = 32u64

const MANTISSA_WIDTH: u64 = 23u64

const POSITIVE_INFINITY: Self = +Inff32

const NEGATIVE_INFINITY: Self = -Inff32

const NEGATIVE_ZERO: Self = -0f32

const NAN: Self = NaNf32

const MAX_FINITE: Self = 3.40282347E+38f32

const MIN_POSITIVE_SUBNORMAL: Self = 1.40129846E-45f32

const MAX_SUBNORMAL: Self = 1.17549421E-38f32

const MIN_POSITIVE_NORMAL: Self = 1.17549435E-38f32

const SMALLEST_UNREPRESENTABLE_UINT: u64 = 16_777_217u64

const LARGEST_ORDERED_REPRESENTATION: u64 = 4_278_190_081u64

fn is_nan(self) -> bool

fn is_infinite(self) -> bool

fn is_finite(self) -> bool

fn is_normal(self) -> bool

fn classify(self) -> FpCategory

fn to_bits(self) -> u64

fn from_bits(v: u64) -> f32

impl PrimitiveFloat for f64

const WIDTH: u64 = 64u64

const MANTISSA_WIDTH: u64 = 52u64

const POSITIVE_INFINITY: Self = +Inff64

const NEGATIVE_INFINITY: Self = -Inff64

const NEGATIVE_ZERO: Self = -0f64

const NAN: Self = NaNf64

const MAX_FINITE: Self = 1.7976931348623157E+308f64

const MIN_POSITIVE_SUBNORMAL: Self = 4.9406564584124654E-324f64

const MAX_SUBNORMAL: Self = 2.2250738585072009E-308f64

const MIN_POSITIVE_NORMAL: Self = 2.2250738585072014E-308f64

const SMALLEST_UNREPRESENTABLE_UINT: u64 = 9_007_199_254_740_993u64

const LARGEST_ORDERED_REPRESENTATION: u64 = 18_437_736_874_454_810_625u64

fn is_nan(self) -> bool

fn is_infinite(self) -> bool

fn is_finite(self) -> bool

fn is_normal(self) -> bool

fn classify(self) -> FpCategory

fn to_bits(self) -> u64

fn from_bits(v: u64) -> f64

Implementors