Exponentials and logarithms v0.1.0

Powers of e and two, and logarithms in base e, two and ten.

`Exp`

pub func Exp(x: float64) -> float64
pub func Exp(x: float32) -> float32

Computes e raised to x. The error is at most one ulp. Positive infinity returns positive infinity, negative infinity returns +0.0, and a NaN remains a NaN. Finite results overflow to infinity or underflow to zero when required by float64.

Overload	Summary
`pub func Exp(x: float64) -> float64`	Computes `e` raised to `x`.
`pub func Exp(x: float32) -> float32`	Computes `e` raised to `x` at `float32` precision.

Source

Parameters

Name	Type	Description
`x`	`float64` / `float32`	exponent

Returns: e raised to x

`Exp2`

pub func Exp2(x: float64) -> float64
pub func Exp2(x: float32) -> float32

Computes two raised to x. The error is at most one ulp, and an in-range integer exponent is exact. Positive infinity returns positive infinity, negative infinity returns zero, and a NaN remains a NaN.

Overload	Summary
`pub func Exp2(x: float64) -> float64`	Computes two raised to `x`.
`pub func Exp2(x: float32) -> float32`	Computes two raised to `x` at `float32` precision.

Source

Parameters

Name	Type	Description
`x`	`float64` / `float32`	binary exponent

Returns: two raised to x

`Expm1`

pub func Expm1(x: float64) -> float64
pub func Expm1(x: float32) -> float32

Computes Exp(x) - 1 without losing precision near zero. The error is at most one ulp and remains small relative to the result as x approaches zero. A signed zero returns itself, positive infinity returns positive infinity, negative infinity returns -1.0, and a NaN remains a NaN.

Overload	Summary
`pub func Expm1(x: float64) -> float64`	Computes `Exp(x) - 1` without losing precision near zero.
`pub func Expm1(x: float32) -> float32`	Computes `Exp(x) - 1` at `float32` precision without losing precision near zero.

Source

Parameters

Name	Type	Description
`x`	`float64` / `float32`	exponent

Returns: e raised to x, minus one

`Log`

pub func Log(x: float64) -> float64
pub func Log(x: float32) -> float32

Computes the natural logarithm of x. The error is at most one ulp. Either signed zero returns negative infinity, a negative value returns a NaN, positive infinity returns itself, and a NaN remains a NaN.

Overload	Summary
`pub func Log(x: float64) -> float64`	Computes the natural logarithm of `x`.
`pub func Log(x: float32) -> float32`	Computes the natural logarithm of `x` at `float32` precision.

Source

Parameters

Name	Type	Description
`x`	`float64` / `float32`	positive value whose logarithm is computed

Returns: the base-e logarithm of x

`Log10`

pub func Log10(x: float64) -> float64
pub func Log10(x: float32) -> float32

Computes the base-ten logarithm of x. The error is at most one ulp, and an exact power of ten returns its exact exponent. Either signed zero returns negative infinity, a negative value returns a NaN, positive infinity returns itself, and a NaN remains a NaN.

Overload	Summary
`pub func Log10(x: float64) -> float64`	Computes the base-ten logarithm of `x`.
`pub func Log10(x: float32) -> float32`	Computes the base-ten logarithm of `x` at `float32` precision.

Source

Parameters

Name	Type	Description
`x`	`float64` / `float32`	positive value whose logarithm is computed

Returns: the base-ten logarithm of x

`Log1p`

pub func Log1p(x: float64) -> float64
pub func Log1p(x: float32) -> float32

Computes Log(1 + x) without losing precision near zero. Log1p(0.0) is zero with the argument's sign, Log1p(-1.0) is negative infinity, and an argument below -1 has no real logarithm and gives a NaN.

Overload	Summary
`pub func Log1p(x: float64) -> float64`	Computes `Log(1 + x)` without losing precision near zero.
`pub func Log1p(x: float32) -> float32`	Computes `Log(1 + x)` at `float32` precision without losing precision near zero.

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Parameters

Name	Type	Description
`x`	`float64` / `float32`	value added to one before taking the logarithm

Returns: the natural logarithm of 1 + x

`Log2`

pub func Log2(x: float64) -> float64
pub func Log2(x: float32) -> float32

Computes the base-two logarithm of x. The error is at most one ulp, and an exact power of two returns its exact exponent. Either signed zero returns negative infinity, a negative value returns a NaN, positive infinity returns itself, and a NaN remains a NaN.

Overload	Summary
`pub func Log2(x: float64) -> float64`	Computes the base-two logarithm of `x`.
`pub func Log2(x: float32) -> float32`	Computes the base-two logarithm of `x` at `float32` precision.

Source

Parameters

Name	Type	Description
`x`	`float64` / `float32`	positive value whose logarithm is computed

Returns: the base-two logarithm of x

Classification and special values

Telling NaNs, infinities, zeros, subnormals and normal values apart, and making the special ones.

Floating-point representation

Signs, exponents, neighbouring values and ulp distances of floating-point values.

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