Trait FunctionsRealType

pub trait FunctionsRealType<T: NumKernel>:
    FunctionsGeneralType<T>
    + PartialEq
    + PartialEq<f64>
    + PartialOrd
    + PartialOrd<f64>
    + MulComplexRight<T>
    + One {
    // Required methods
    fn atan2_(self, other: &Self) -> Self;
    fn ceil_(self) -> Self;
    fn clamp_(self, min: &Self, max: &Self) -> Self;
    fn classify_(&self) -> FpCategory;
    fn copysign_(self, sign: &Self) -> Self;
    fn epsilon_() -> Self;
    fn exp_m1_(self) -> Self;
    fn floor_(self) -> Self;
    fn fract_(self) -> Self;
    fn hypot_(self, other: &Self) -> Self;
    fn infinity_() -> Self;
    fn is_sign_negative_(&self) -> bool;
    fn is_sign_positive_(&self) -> bool;
    fn ln_1p_(self) -> Self;
    fn neg_infinity_() -> Self;
    fn max_(self, other: &Self) -> Self;
    fn min_(self, other: &Self) -> Self;
    fn mul_add_mul_mut_(&mut self, mul: &Self, add_mul1: &Self, add_mul2: &Self);
    fn mul_sub_mul_mut_(&mut self, mul: &Self, sub_mul1: &Self, sub_mul2: &Self);
    fn negative_one_() -> Self;
    fn one_div_2_() -> Self;
    fn round_(self) -> Self;
    fn round_ties_even_(self) -> Self;
    fn signum_(self) -> Self;
    fn total_cmp_(&self, other: &Self) -> Ordering;
    fn try_from_f64_(value: f64) -> Result<Self, TryFromf64Errors>;
    fn trunc_(self) -> Self;
    fn two_() -> Self;

    // Provided methods
    fn pi_() -> Self { ... }
    fn pi_div_2_() -> Self { ... }
}

This trait represents the functions that can be applied on real numbers.

Required Methods

fn atan2_(self, other: &Self) -> Self

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

• x = 0, y = 0: 0
• x >= 0: arctan(y/x) -> [-pi/2, pi/2]
• y >= 0: arctan(y/x) + pi -> (pi/2, pi]
• y < 0: arctan(y/x) - pi -> (-pi, -pi/2)

fn ceil_(self) -> Self

Returns the smallest integer greater than or equal to self.

fn clamp_(self, min: &Self, max: &Self) -> Self

Clamp the value within the specified bounds.

Returns max if self is greater than max, and min if self is less than min. Otherwise this returns self.

Note that this function returns NaN if the initial value was NaN as well.

Panics

Panics if min > max, min is NaN, or max is NaN.

use ftl_numkernel::{FunctionsGeneralType, FunctionsRealType, IsNaN};

assert!((-3.0f64).clamp_(&-2.0, &1.0) == -2.0);
assert!((0.0f64).clamp_(&-2.0, &1.0) == 0.0);
assert!((2.0f64).clamp_(&-2.0, &1.0) == 1.0);
assert!((f64::NAN).clamp_(&-2.0, &1.0).is_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.

use ftl_numkernel::FunctionsRealType;
use std::num::FpCategory;

let num = 12.4_f64;
let inf = f64::INFINITY;

assert_eq!(num.classify_(), FpCategory::Normal);
assert_eq!(inf.classify_(), FpCategory::Infinite);

fn copysign_(self, sign: &Self) -> Self

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

fn epsilon_() -> Self

Machine epsilon value for Self.

This is the difference between 1.0 and the next larger representable number.

fn exp_m1_(self) -> Self

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

fn floor_(self) -> Self

Returns the largest integer smaller than or equal to self.

fn fract_(self) -> Self

Returns the fractional part of self.

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

Compute the distance between the origin and a point (self, other) on the Euclidean plane. Equivalently, compute the length of the hypotenuse of a right-angle triangle with other sides having length self.abs() and other.abs().

fn infinity_() -> Self

Returns the special value representing the positive infinity.

fn is_sign_negative_(&self) -> bool

Returns true if the value is negative, −0 or NaN with a negative sign.

fn is_sign_positive_(&self) -> bool

Returns true if the value is positive, +0 or NaN with a positive sign.

fn ln_1p_(self) -> Self

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

fn neg_infinity_() -> Self

Returns the special value representing the negative infinity.

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

Computes the maximum between self and other.

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

Computes the minimum between self and other.

fn mul_add_mul_mut_(&mut self, mul: &Self, add_mul1: &Self, add_mul2: &Self)

Multiplies two products and adds them in one fused operation, rounding to the nearest with only one rounding error. a.mul_add_mul_mut_(&b, &c, &d) produces a result like &a * &b + &c * &d, but stores the result in a using its precision.

fn mul_sub_mul_mut_(&mut self, mul: &Self, sub_mul1: &Self, sub_mul2: &Self)

Multiplies two products and subtracts them in one fused operation, rounding to the nearest with only one rounding error. a.mul_sub_mul_mut_(&b, &c, &d) produces a result like &a * &b - &c * &d, but stores the result in a using its precision.

fn negative_one_() -> Self

Build and return the (floating point) value -1. represented by the proper type.

fn one_div_2_() -> Self

Build and return the (floating point) value 0.5 represented by the proper type.

fn round_(self) -> Self

Rounds self to the nearest integer, rounding half-way cases away from zero.

fn round_ties_even_(self) -> Self

Returns the nearest integer to a number. Rounds half-way cases to the number with an even least significant digit.

This function always returns the precise result.

Examples

use ftl_numkernel::FunctionsRealType;

let f = 3.3_f64;
let g = -3.3_f64;
let h = 3.5_f64;
let i = 4.5_f64;

assert_eq!(f.round_ties_even_(), 3.0);
assert_eq!(g.round_ties_even_(), -3.0);
assert_eq!(h.round_ties_even_(), 4.0);
assert_eq!(i.round_ties_even_(), 4.0);

fn signum_(self) -> Self

Computes the signum.

The returned value is:

• 1.0 if the value is positive, +0.0 or +∞
• −1.0 if the value is negative, −0.0 or −∞
• NaN if the value is NaN

fn total_cmp_(&self, other: &Self) -> Ordering

fn try_from_f64_(value: f64) -> Result<Self, TryFromf64Errors>

Try to build a Self from a f64. The returned value is Ok if the input value is finite and can be exactly represented by T::RealType, otherwise the returned value is TryFromf64Errors.

fn trunc_(self) -> Self

Returns the integer part of self. This means that non-integer numbers are always truncated towards zero.

Examples

use ftl_numkernel::FunctionsRealType;

let f = 3.7_f64;
let g = 3.0_f64;
let h = -3.7_f64;

assert_eq!(f.trunc_(), 3.0);
assert_eq!(g.trunc_(), 3.0);
assert_eq!(h.trunc_(), -3.0);

fn two_() -> Self

Build and return the (floating point) value 1. represented by the proper type.

Provided Methods

fn pi_() -> Self

Build and return the (floating point) value π represented by the proper type.

fn pi_div_2_() -> Self

Build and return the (floating point) value π/2 represented by the proper type.

Dyn Compatibility

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementations on Foreign Types

impl FunctionsRealType<Native64> for f64

fn atan2_(self, other: &Self) -> Self

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

• x = 0, y = 0: 0
• x >= 0: arctan(y/x) -> [-pi/2, pi/2]
• y >= 0: arctan(y/x) + pi -> (pi/2, pi]
• y < 0: arctan(y/x) - pi -> (-pi, -pi/2)

use ftl_numkernel::{FunctionsGeneralType, FunctionsRealType};

let y = 3.0_f64;
let x = -4.0_f64;
let atan2 = y.atan2_(&x);
let expected = 2.4981_f64;
assert!((atan2 - expected).abs() < 0.0001);

fn ceil_(self) -> Self

Returns the smallest integer greater than or equal to self.

fn clamp_(self, min: &Self, max: &Self) -> Self

Clamp the value within the specified bounds.

Returns max if self is greater than max, and min if self is less than min. Otherwise this returns self.

Note that this function returns NaN if the initial value was NaN as well.

Panics

Panics if min > max, min is NaN, or max is NaN.

use ftl_numkernel::{FunctionsRealType, IsNaN};

assert!((-3.0f64).clamp_(&-2.0, &1.0) == -2.0);
assert!((0.0f64).clamp_(&-2.0, &1.0) == 0.0);
assert!((2.0f64).clamp_(&-2.0, &1.0) == 1.0);
assert!((f64::NAN).clamp_(&-2.0, &1.0).is_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.

use ftl_numkernel::FunctionsRealType;
use std::num::FpCategory;

let num = 12.4_f64;
let inf = f64::INFINITY;

assert_eq!(num.classify_(), FpCategory::Normal);
assert_eq!(inf.classify_(), FpCategory::Infinite);

fn copysign_(self, sign: &Self) -> Self

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

fn epsilon_() -> Self

Machine epsilon value for f64.

This is the difference between 1.0 and the next larger representable number.

fn exp_m1_(self) -> Self

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

fn floor_(self) -> Self

Returns the largest integer smaller than or equal to self.

fn fract_(self) -> Self

Returns the fractional part of self.

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

Compute the distance between the origin and a point (self, other) on the Euclidean plane. Equivalently, compute the length of the hypotenuse of a right-angle triangle with other sides having length self.abs() and other.abs().

fn infinity_() -> Self

Returns the special value representing the positive infinity.

fn is_sign_negative_(&self) -> bool

Returns true if the value is negative, −0 or NaN with a negative sign.

fn is_sign_positive_(&self) -> bool

Returns true if the value is positive, +0 or NaN with a positive sign.

fn ln_1p_(self) -> Self

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

fn neg_infinity_() -> Self

Returns the special value representing the negative infinity.

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

Computes the maximum between self and other.

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

Computes the minimum between self and other.

fn mul_add_mul_mut_(&mut self, mul: &Self, add_mul1: &Self, add_mul2: &Self)

Multiplies two products and adds them in one fused operation, rounding to the nearest with only one rounding error. a.mul_add_mul_mut_(&b, &c, &d) produces a result like &a * &b + &c * &d, but stores the result in a using its precision.

fn mul_sub_mul_mut_(&mut self, mul: &Self, sub_mul1: &Self, sub_mul2: &Self)

Multiplies two products and subtracts them in one fused operation, rounding to the nearest with only one rounding error. a.mul_sub_mul_mut_(&b, &c, &d) produces a result like &a * &b - &c * &d, but stores the result in a using its precision.

fn negative_one_() -> Self

Build and return the (floating point) value -1. represented by a f64.

fn one_div_2_() -> Self

Build and return the (floating point) value 0.5 represented by the proper type.

fn round_(self) -> Self

Rounds self to the nearest integer, rounding half-way cases away from zero.

fn round_ties_even_(self) -> Self

Returns the nearest integer to a number. Rounds half-way cases to the number with an even least significant digit.

This function always returns the precise result.

Examples

use ftl_numkernel::FunctionsRealType;

let f = 3.3_f64;
let g = -3.3_f64;
let h = 3.5_f64;
let i = 4.5_f64;

assert_eq!(f.round_ties_even_(), 3.0);
assert_eq!(g.round_ties_even_(), -3.0);
assert_eq!(h.round_ties_even_(), 4.0);
assert_eq!(i.round_ties_even_(), 4.0);

fn signum_(self) -> Self

Computes the signum.

The returned value is:

• 1.0 if the value is positive, +0.0 or +∞
• −1.0 if the value is negative, −0.0 or −∞
• NaN if the value is NaN

fn try_from_f64_(value: f64) -> Result<Self, TryFromf64Errors>

Try to build a f64 instance from a f64. The returned value is Ok if the input value is finite, otherwise the returned value is TryFromf64Errors.

fn trunc_(self) -> Self

Returns the integer part of self. This means that non-integer numbers are always truncated towards zero.

Examples

use ftl_numkernel::FunctionsRealType;

let f = 3.7_f64;
let g = 3.0_f64;
let h = -3.7_f64;

assert_eq!(f.trunc_(), 3.0);
assert_eq!(g.trunc_(), 3.0);
assert_eq!(h.trunc_(), -3.0);

fn two_() -> Self

Build and return the (floating point) value 2. represented by a f64.

fn total_cmp_(&self, other: &Self) -> Ordering

Implementors