Struct TaylorDyn 

pub struct TaylorDyn<F: Float> { /* private fields */ }

Available on crate feature taylor only.

Dynamic Taylor coefficient variable.

Copy-friendly: stores only { value, index }. Coefficient vectors live in a thread-local TaylorArena.

value = coeffs[0] (primal), kept inline for comparisons/branching. index = arena slot, or CONSTANT sentinel for literals.

Implementations

impl<F: Float> TaylorDyn<F>

pub fn constant(value: F) -> Self

Create a constant (not stored in arena).

impl<F: Float + TaylorArenaLocal> TaylorDyn<F>

pub fn variable(val: F) -> Self

Create a variable: c₀ = val, c₁ = 1, rest zero.

pub fn from_coeffs(coeffs: &[F]) -> Self

Create from explicit coefficients (copies into arena).

pub fn value(&self) -> F

Primal value.

pub fn index(&self) -> u32

Get arena index.

pub fn coeffs(&self) -> Vec<F>

Read all coefficients (copies from arena).

pub fn derivative(&self, k: usize) -> F

Get the k-th derivative: k! × coeffs[k].

pub fn recip(self) -> Self

Reciprocal (1/x).

pub fn sqrt(self) -> Self

Square root.

pub fn cbrt(self) -> Self

Cube root.

pub fn powi(self, n: i32) -> Self

Integer power.

pub fn powf(self, n: Self) -> Self

Floating-point power.

pub fn exp(self) -> Self

Natural exponential (e^x).

pub fn exp2(self) -> Self

Base-2 exponential (2^x).

pub fn exp_m1(self) -> Self

e^x - 1, accurate near zero.

pub fn ln(self) -> Self

Natural logarithm.

pub fn log2(self) -> Self

Base-2 logarithm.

pub fn log10(self) -> Self

Base-10 logarithm.

pub fn ln_1p(self) -> Self

ln(1+x), accurate near zero.

pub fn log(self, base: Self) -> Self

Logarithm with given base.

pub fn sin(self) -> Self

Sine.

pub fn cos(self) -> Self

Cosine.

pub fn sin_cos(self) -> (Self, Self)

Simultaneous sine and cosine.

pub fn tan(self) -> Self

Tangent.

pub fn asin(self) -> Self

Arcsine.

pub fn acos(self) -> Self

Arccosine.

pub fn atan(self) -> Self

Arctangent.

pub fn atan2(self, other: Self) -> Self

Two-argument arctangent.

pub fn sinh(self) -> Self

Hyperbolic sine.

pub fn cosh(self) -> Self

Hyperbolic cosine.

pub fn tanh(self) -> Self

Hyperbolic tangent.

pub fn asinh(self) -> Self

Inverse hyperbolic sine.

pub fn acosh(self) -> Self

Inverse hyperbolic cosine.

pub fn atanh(self) -> Self

Inverse hyperbolic tangent.

pub fn abs(self) -> Self

Absolute value.

pub fn signum(self) -> Self

Sign function (zero derivative).

pub fn floor(self) -> Self

Floor (zero derivative).

pub fn ceil(self) -> Self

Ceiling (zero derivative).

pub fn round(self) -> Self

Round to nearest integer (zero derivative).

pub fn trunc(self) -> Self

Truncate toward zero (zero derivative).

pub fn fract(self) -> Self

Fractional part.

pub fn hypot(self, other: Self) -> Self

Euclidean distance: sqrt(self^2 + other^2).

pub fn max(self, other: Self) -> Self

Maximum of two values.

pub fn min(self, other: Self) -> Self

Minimum of two values.

Trait Implementations

impl Add<TaylorDyn<f32>> for f32

type Output = TaylorDyn<f32>

The resulting type after applying the + operator.

fn add(self, rhs: TaylorDyn<f32>) -> TaylorDyn<f32>

Performs the + operation.

impl Add<TaylorDyn<f64>> for f64

type Output = TaylorDyn<f64>

The resulting type after applying the + operator.

fn add(self, rhs: TaylorDyn<f64>) -> TaylorDyn<f64>

Performs the + operation.

impl Add<f32> for TaylorDyn<f32>

type Output = TaylorDyn<f32>

The resulting type after applying the + operator.

fn add(self, rhs: f32) -> TaylorDyn<f32>

Performs the + operation.

impl Add<f64> for TaylorDyn<f64>

type Output = TaylorDyn<f64>

The resulting type after applying the + operator.

fn add(self, rhs: f64) -> TaylorDyn<f64>

Performs the + operation.

impl<F: Float + TaylorArenaLocal> Add for TaylorDyn<F>

type Output = TaylorDyn<F>

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

Performs the + operation.

impl<F: Float + TaylorArenaLocal> AddAssign for TaylorDyn<F>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<F: Clone + Float> Clone for TaylorDyn<F>

fn clone(&self) -> TaylorDyn<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F: Debug + Float> Debug for TaylorDyn<F>

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

Formats the value using the given formatter.

impl<F: Float> Default for TaylorDyn<F>

fn default() -> Self

Returns the “default value” for a type.

impl<F: Float> Display for TaylorDyn<F>

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

Formats the value using the given formatter.

impl Div<TaylorDyn<f32>> for f32

type Output = TaylorDyn<f32>

The resulting type after applying the / operator.

fn div(self, rhs: TaylorDyn<f32>) -> TaylorDyn<f32>

Performs the / operation.

impl Div<TaylorDyn<f64>> for f64

type Output = TaylorDyn<f64>

The resulting type after applying the / operator.

fn div(self, rhs: TaylorDyn<f64>) -> TaylorDyn<f64>

Performs the / operation.

impl Div<f32> for TaylorDyn<f32>

type Output = TaylorDyn<f32>

The resulting type after applying the / operator.

fn div(self, rhs: f32) -> TaylorDyn<f32>

Performs the / operation.

impl Div<f64> for TaylorDyn<f64>

type Output = TaylorDyn<f64>

The resulting type after applying the / operator.

fn div(self, rhs: f64) -> TaylorDyn<f64>

Performs the / operation.

impl<F: Float + TaylorArenaLocal> Div for TaylorDyn<F>

type Output = TaylorDyn<F>

The resulting type after applying the / operator.

fn div(self, rhs: Self) -> Self

Performs the / operation.

impl<F: Float + TaylorArenaLocal> DivAssign for TaylorDyn<F>

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl<F: Float + TaylorArenaLocal> Float for TaylorDyn<F>

fn nan() -> Self

Returns the NaN value.

fn infinity() -> Self

Returns the infinite value.

fn neg_infinity() -> Self

Returns the negative infinite value.

fn neg_zero() -> Self

Returns -0.0.

fn min_value() -> Self

Returns the smallest finite value that this type can represent.

fn min_positive_value() -> Self

Returns the smallest positive, normalized value that this type can represent.

fn max_value() -> Self

Returns the largest finite value that this type can represent.

fn epsilon() -> Self

Returns epsilon, a small positive value.

fn is_nan(self) -> bool

Returns true if this value is NaN and false otherwise.

fn is_infinite(self) -> bool

Returns true if this value is positive infinity or negative infinity and false otherwise.

fn is_finite(self) -> bool

Returns true if this number is neither infinite nor NaN.

fn is_normal(self) -> bool

Returns true if the number is neither zero, infinite, subnormal, or NaN.

fn is_sign_positive(self) -> bool

Returns true if self is positive, including +0.0, Float::infinity(), and Float::nan().

fn is_sign_negative(self) -> bool

Returns true if self is negative, including -0.0, Float::neg_infinity(), and -Float::nan().

fn classify(self) -> FpCategory

Returns the floating point category of the number. If only one property is going to be tested, it is generally faster to use the specific predicate instead.

fn floor(self) -> Self

Returns the largest integer less than or equal to a number.

fn ceil(self) -> Self

Returns the smallest integer greater than or equal to a number.

fn round(self) -> Self

Returns the nearest integer to a number. Round half-way cases away from 0.0.

fn trunc(self) -> Self

Return the integer part of a number.

fn fract(self) -> Self

Returns the fractional part of a number.

fn abs(self) -> Self

Computes the absolute value of self. Returns Float::nan() if the number is Float::nan().

fn signum(self) -> Self

Returns a number that represents the sign of self.

fn mul_add(self, a: Self, b: Self) -> Self

Fused multiply-add. Computes (self * a) + b with only one rounding error, yielding a more accurate result than an unfused multiply-add.

fn recip(self) -> Self

Take the reciprocal (inverse) of a number, 1/x.

fn powi(self, n: i32) -> Self

Raise a number to an integer power.

fn powf(self, n: Self) -> Self

Raise a number to a floating point power.

fn sqrt(self) -> Self

Take the square root of a number.

fn cbrt(self) -> Self

Take the cubic root of a number.

fn exp(self) -> Self

Returns e^(self), (the exponential function).

fn exp2(self) -> Self

Returns 2^(self).

fn exp_m1(self) -> Self

Returns e^(self) - 1 in a way that is accurate even if the number is close to zero.

fn ln(self) -> Self

Returns the natural logarithm of the number.

fn log2(self) -> Self

Returns the base 2 logarithm of the number.

fn log10(self) -> Self

Returns the base 10 logarithm of the number.

fn ln_1p(self) -> Self

Returns ln(1+n) (natural logarithm) more accurately than if the operations were performed separately.

fn log(self, base: Self) -> Self

Returns the logarithm of the number with respect to an arbitrary base.

fn sin(self) -> Self

Computes the sine of a number (in radians).

fn cos(self) -> Self

Computes the cosine of a number (in radians).

fn tan(self) -> Self

Computes the tangent of a number (in radians).

fn sin_cos(self) -> (Self, Self)

Simultaneously computes the sine and cosine of the number, x. Returns (sin(x), cos(x)).

fn asin(self) -> Self

Computes the arcsine of a number. Return value is in radians in the range [-pi/2, pi/2] or NaN if the number is outside the range [-1, 1].

fn acos(self) -> Self

Computes the arccosine of a number. Return value is in radians in the range [0, pi] or NaN if the number is outside the range [-1, 1].

fn atan(self) -> Self

Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];

fn atan2(self, other: Self) -> Self

Computes the four quadrant arctangent of self (y) and other (x).

fn sinh(self) -> Self

Hyperbolic sine function.

fn cosh(self) -> Self

Hyperbolic cosine function.

fn tanh(self) -> Self

Hyperbolic tangent function.

fn asinh(self) -> Self

Inverse hyperbolic sine function.

fn acosh(self) -> Self

Inverse hyperbolic cosine function.

fn atanh(self) -> Self

Inverse hyperbolic tangent function.

fn hypot(self, other: Self) -> Self

Calculate the length of the hypotenuse of a right-angle triangle given legs of length x and y.

fn max(self, other: Self) -> Self

Returns the maximum of the two numbers.

fn min(self, other: Self) -> Self

Returns the minimum of the two numbers.

fn abs_sub(self, other: Self) -> Self

The positive difference of two numbers.

fn integer_decode(self) -> (u64, i16, i8)

Returns the mantissa, base 2 exponent, and sign as integers, respectively. The original number can be recovered by sign * mantissa * 2 ^ exponent.

fn to_degrees(self) -> Self

Converts radians to degrees.

fn to_radians(self) -> Self

Converts degrees to radians.

fn is_subnormal(self) -> bool

Returns true if the number is subnormal.

fn clamp(self, min: Self, max: Self) -> Self

Clamps a value between a min and max.

fn copysign(self, sign: Self) -> Self

Returns a number composed of the magnitude of self and the sign of sign.

impl<F: Float + TaylorArenaLocal> FloatConst for TaylorDyn<F>

fn E() -> Self

Return Euler’s number.

fn FRAC_1_PI() -> Self

Return 1.0 / π.

fn FRAC_1_SQRT_2() -> Self

Return 1.0 / sqrt(2.0).

fn FRAC_2_PI() -> Self

Return 2.0 / π.

fn FRAC_2_SQRT_PI() -> Self

Return 2.0 / sqrt(π).

fn FRAC_PI_2() -> Self

Return π / 2.0.

fn FRAC_PI_3() -> Self

Return π / 3.0.

fn FRAC_PI_4() -> Self

Return π / 4.0.

fn FRAC_PI_6() -> Self

Return π / 6.0.

fn FRAC_PI_8() -> Self

Return π / 8.0.

fn LN_10() -> Self

Return ln(10.0).

fn LN_2() -> Self

Return ln(2.0).

fn LOG10_E() -> Self

Return log10(e).

fn LOG2_E() -> Self

Return log2(e).

fn PI() -> Self

Return Archimedes’ constant π.

fn SQRT_2() -> Self

Return sqrt(2.0).

fn TAU() -> Self

Return the full circle constant τ.

fn LOG10_2() -> Self

Return log10(2.0).

fn LOG2_10() -> Self

Return log2(10.0).

impl<F: Float> FromPrimitive for TaylorDyn<F>

fn from_i64(n: i64) -> Option<Self>

Converts an i64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u64(n: u64) -> Option<Self>

Converts an u64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f32(n: f32) -> Option<Self>

Converts a f32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_f64(n: f64) -> Option<Self>

Converts a f64 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_isize(n: isize) -> Option<Self>

Converts an isize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i8(n: i8) -> Option<Self>

Converts an i8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i16(n: i16) -> Option<Self>

Converts an i16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i32(n: i32) -> Option<Self>

Converts an i32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_i128(n: i128) -> Option<Self>

Converts an i128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_usize(n: usize) -> Option<Self>

Converts a usize to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u8(n: u8) -> Option<Self>

Converts an u8 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u16(n: u16) -> Option<Self>

Converts an u16 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u32(n: u32) -> Option<Self>

Converts an u32 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

fn from_u128(n: u128) -> Option<Self>

Converts an u128 to return an optional value of this type. If the value cannot be represented by this type, then None is returned.

impl Mul<TaylorDyn<f32>> for f32

type Output = TaylorDyn<f32>

The resulting type after applying the * operator.

fn mul(self, rhs: TaylorDyn<f32>) -> TaylorDyn<f32>

Performs the * operation.

impl Mul<TaylorDyn<f64>> for f64

type Output = TaylorDyn<f64>

The resulting type after applying the * operator.

fn mul(self, rhs: TaylorDyn<f64>) -> TaylorDyn<f64>

Performs the * operation.

impl Mul<f32> for TaylorDyn<f32>

type Output = TaylorDyn<f32>

The resulting type after applying the * operator.

fn mul(self, rhs: f32) -> TaylorDyn<f32>

Performs the * operation.

impl Mul<f64> for TaylorDyn<f64>

type Output = TaylorDyn<f64>

The resulting type after applying the * operator.

fn mul(self, rhs: f64) -> TaylorDyn<f64>

Performs the * operation.

impl<F: Float + TaylorArenaLocal> Mul for TaylorDyn<F>

type Output = TaylorDyn<F>

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self

Performs the * operation.

impl<F: Float + TaylorArenaLocal> MulAssign for TaylorDyn<F>

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<F: Float + TaylorArenaLocal> Neg for TaylorDyn<F>

type Output = TaylorDyn<F>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<F: Float + TaylorArenaLocal> Num for TaylorDyn<F>

type FromStrRadixErr = <F as Num>::FromStrRadixErr

fn from_str_radix(str: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr>

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

impl<F: Float + TaylorArenaLocal> NumCast for TaylorDyn<F>

fn from<T: ToPrimitive>(n: T) -> Option<Self>

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<F: Float + TaylorArenaLocal> One for TaylorDyn<F>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

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

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<F: Float> PartialEq for TaylorDyn<F>

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

Tests for self and other values to be equal, and is used by ==.

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

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<F: Float> PartialOrd for TaylorDyn<F>

fn partial_cmp(&self, other: &Self) -> 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 Rem<TaylorDyn<f32>> for f32

type Output = TaylorDyn<f32>

The resulting type after applying the % operator.

fn rem(self, rhs: TaylorDyn<f32>) -> TaylorDyn<f32>

Performs the % operation.

impl Rem<TaylorDyn<f64>> for f64

type Output = TaylorDyn<f64>

The resulting type after applying the % operator.

fn rem(self, rhs: TaylorDyn<f64>) -> TaylorDyn<f64>

Performs the % operation.

impl Rem<f32> for TaylorDyn<f32>

type Output = TaylorDyn<f32>

The resulting type after applying the % operator.

fn rem(self, rhs: f32) -> TaylorDyn<f32>

Performs the % operation.

impl Rem<f64> for TaylorDyn<f64>

type Output = TaylorDyn<f64>

The resulting type after applying the % operator.

fn rem(self, rhs: f64) -> TaylorDyn<f64>

Performs the % operation.

impl<F: Float + TaylorArenaLocal> Rem for TaylorDyn<F>

type Output = TaylorDyn<F>

The resulting type after applying the % operator.

fn rem(self, rhs: Self) -> Self

Performs the % operation.

impl<F: Float + TaylorArenaLocal> RemAssign for TaylorDyn<F>

fn rem_assign(&mut self, rhs: Self)

Performs the %= operation.

impl<F: Float + TaylorArenaLocal> Scalar for TaylorDyn<F>

type Float = F

The underlying primitive float type.

fn from_f(val: F) -> Self

Lift a plain float to this scalar (constant — zero derivative).

fn value(&self) -> F

Extract the primal value.

impl<F: Float + TaylorArenaLocal> Signed for TaylorDyn<F>

fn abs(&self) -> Self

Computes the absolute value.

fn abs_sub(&self, other: &Self) -> Self

The positive difference of two numbers.

fn signum(&self) -> Self

Returns the sign of the number.

fn is_positive(&self) -> bool

Returns true if the number is positive and false if the number is zero or negative.

fn is_negative(&self) -> bool

Returns true if the number is negative and false if the number is zero or positive.

impl Sub<TaylorDyn<f32>> for f32

type Output = TaylorDyn<f32>

The resulting type after applying the - operator.

fn sub(self, rhs: TaylorDyn<f32>) -> TaylorDyn<f32>

Performs the - operation.

impl Sub<TaylorDyn<f64>> for f64

type Output = TaylorDyn<f64>

The resulting type after applying the - operator.

fn sub(self, rhs: TaylorDyn<f64>) -> TaylorDyn<f64>

Performs the - operation.

impl Sub<f32> for TaylorDyn<f32>

type Output = TaylorDyn<f32>

The resulting type after applying the - operator.

fn sub(self, rhs: f32) -> TaylorDyn<f32>

Performs the - operation.

impl Sub<f64> for TaylorDyn<f64>

type Output = TaylorDyn<f64>

The resulting type after applying the - operator.

fn sub(self, rhs: f64) -> TaylorDyn<f64>

Performs the - operation.

impl<F: Float + TaylorArenaLocal> Sub for TaylorDyn<F>

type Output = TaylorDyn<F>

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.

impl<F: Float + TaylorArenaLocal> SubAssign for TaylorDyn<F>

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<F: Float> ToPrimitive for TaylorDyn<F>

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<F: Float + TaylorArenaLocal> Zero for TaylorDyn<F>

fn zero() -> Self

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<F: Copy + Float> Copy for TaylorDyn<F>

impl<F: Float + TaylorArenaLocal> Float for TaylorDyn<F>