Trait std::num::FloatStable
[-] [+]
[src]
pub trait Float: Copy + Clone + NumCast + PartialOrd + PartialEq + Neg<Output=Self> + Add<Output=Self> + Sub<Output=Self> + Mul<Output=Self> + Div<Output=Self> + Rem<Output=Self> {
fn nan() -> Self;
fn infinity() -> Self;
fn neg_infinity() -> Self;
fn zero() -> Self;
fn neg_zero() -> Self;
fn one() -> Self;
fn mantissa_digits(unused_self: Option<Self>) -> usize;
fn digits(unused_self: Option<Self>) -> usize;
fn epsilon() -> Self;
fn min_exp(unused_self: Option<Self>) -> isize;
fn max_exp(unused_self: Option<Self>) -> isize;
fn min_10_exp(unused_self: Option<Self>) -> isize;
fn max_10_exp(unused_self: Option<Self>) -> isize;
fn min_value() -> Self;
fn min_pos_value(unused_self: Option<Self>) -> Self;
fn max_value() -> Self;
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 integer_decode(self) -> (u64, i16, i8);
fn floor(self) -> Self;
fn ceil(self) -> Self;
fn round(self) -> Self;
fn trunc(self) -> Self;
fn fract(self) -> Self;
fn abs(self) -> Self;
fn signum(self) -> Self;
fn is_positive(self) -> bool;
fn is_negative(self) -> bool;
fn mul_add(self, a: Self, b: Self) -> Self;
fn recip(self) -> Self;
fn powi(self, n: i32) -> Self;
fn powf(self, n: Self) -> Self;
fn sqrt(self) -> Self;
fn rsqrt(self) -> Self;
fn exp(self) -> Self;
fn exp2(self) -> Self;
fn ln(self) -> Self;
fn log(self, base: Self) -> Self;
fn log2(self) -> Self;
fn log10(self) -> Self;
fn to_degrees(self) -> Self;
fn to_radians(self) -> Self;
fn ldexp(x: Self, exp: isize) -> Self;
fn frexp(self) -> (Self, isize);
fn next_after(self, other: Self) -> Self;
fn max(self, other: Self) -> Self;
fn min(self, other: Self) -> Self;
fn abs_sub(self, other: Self) -> Self;
fn cbrt(self) -> Self;
fn hypot(self, other: Self) -> Self;
fn sin(self) -> Self;
fn cos(self) -> Self;
fn tan(self) -> Self;
fn asin(self) -> Self;
fn acos(self) -> Self;
fn atan(self) -> Self;
fn atan2(self, other: Self) -> Self;
fn sin_cos(self) -> (Self, Self);
fn exp_m1(self) -> Self;
fn ln_1p(self) -> Self;
fn sinh(self) -> Self;
fn cosh(self) -> Self;
fn tanh(self) -> Self;
fn asinh(self) -> Self;
fn acosh(self) -> Self;
fn atanh(self) -> Self;
}Mathematical operations on primitive floating point numbers.
Required Methods
fn nan() -> Self
Returns the NaN value.
use std::num::Float; let nan: f32 = Float::nan(); assert!(nan.is_nan());
fn infinity() -> Self
Returns the infinite value.
fn main() { use std::num::Float; use std::f32; let infinity: f32 = Float::infinity(); assert!(infinity.is_infinite()); assert!(!infinity.is_finite()); assert!(infinity > f32::MAX); }use std::num::Float; use std::f32; let infinity: f32 = Float::infinity(); assert!(infinity.is_infinite()); assert!(!infinity.is_finite()); assert!(infinity > f32::MAX);
fn neg_infinity() -> Self
Returns the negative infinite value.
fn main() { use std::num::Float; use std::f32; let neg_infinity: f32 = Float::neg_infinity(); assert!(neg_infinity.is_infinite()); assert!(!neg_infinity.is_finite()); assert!(neg_infinity < f32::MIN); }use std::num::Float; use std::f32; let neg_infinity: f32 = Float::neg_infinity(); assert!(neg_infinity.is_infinite()); assert!(!neg_infinity.is_finite()); assert!(neg_infinity < f32::MIN);
fn zero() -> Self
Returns 0.0.
use std::num::Float; let inf: f32 = Float::infinity(); let zero: f32 = Float::zero(); let neg_zero: f32 = Float::neg_zero(); assert_eq!(zero, neg_zero); assert_eq!(7.0f32/inf, zero); assert_eq!(zero * 10.0, zero);
fn neg_zero() -> Self
Returns -0.0.
use std::num::Float; let inf: f32 = Float::infinity(); let zero: f32 = Float::zero(); let neg_zero: f32 = Float::neg_zero(); assert_eq!(zero, neg_zero); assert_eq!(7.0f32/inf, zero); assert_eq!(zero * 10.0, zero);
fn one() -> Self
Returns 1.0.
use std::num::Float; let one: f32 = Float::one(); assert_eq!(one, 1.0f32);
fn mantissa_digits(unused_self: Option<Self>) -> usize
Deprecated: use std::f32::MANTISSA_DIGITS or std::f64::MANTISSA_DIGITS
instead.
fn digits(unused_self: Option<Self>) -> usize
Deprecated: use std::f32::DIGITS or std::f64::DIGITS instead.
fn epsilon() -> Self
Deprecated: use std::f32::EPSILON or std::f64::EPSILON instead.
fn min_exp(unused_self: Option<Self>) -> isize
Deprecated: use std::f32::MIN_EXP or std::f64::MIN_EXP instead.
fn max_exp(unused_self: Option<Self>) -> isize
Deprecated: use std::f32::MAX_EXP or std::f64::MAX_EXP instead.
fn min_10_exp(unused_self: Option<Self>) -> isize
Deprecated: use std::f32::MIN_10_EXP or std::f64::MIN_10_EXP instead.
fn max_10_exp(unused_self: Option<Self>) -> isize
Deprecated: use std::f32::MAX_10_EXP or std::f64::MAX_10_EXP instead.
fn min_value() -> Self
Returns the smallest finite value that this type can represent.
fn main() { use std::num::Float; use std::f64; let x: f64 = Float::min_value(); assert_eq!(x, f64::MIN); }use std::num::Float; use std::f64; let x: f64 = Float::min_value(); assert_eq!(x, f64::MIN);
fn min_pos_value(unused_self: Option<Self>) -> Self
Returns the smallest normalized positive number that this type can represent.
fn max_value() -> Self
Returns the largest finite value that this type can represent.
fn main() { use std::num::Float; use std::f64; let x: f64 = Float::max_value(); assert_eq!(x, f64::MAX); }use std::num::Float; use std::f64; let x: f64 = Float::max_value(); assert_eq!(x, f64::MAX);
fn is_nan(self) -> bool
Returns true if this value is NaN and false otherwise.
use std::num::Float; use std::f64; let nan = f64::NAN; let f = 7.0; assert!(nan.is_nan()); assert!(!f.is_nan());
fn is_infinite(self) -> bool
Returns true if this value is positive infinity or negative infinity and
false otherwise.
use std::num::Float; use std::f32; let f = 7.0f32; let inf: f32 = Float::infinity(); let neg_inf: f32 = Float::neg_infinity(); let nan: f32 = f32::NAN; assert!(!f.is_infinite()); assert!(!nan.is_infinite()); assert!(inf.is_infinite()); assert!(neg_inf.is_infinite());
fn is_finite(self) -> bool
Returns true if this number is neither infinite nor NaN.
use std::num::Float; use std::f32; let f = 7.0f32; let inf: f32 = Float::infinity(); let neg_inf: f32 = Float::neg_infinity(); let nan: f32 = f32::NAN; assert!(f.is_finite()); assert!(!nan.is_finite()); assert!(!inf.is_finite()); assert!(!neg_inf.is_finite());
fn is_normal(self) -> bool
Returns true if the number is neither zero, infinite,
subnormal, or NaN.
use std::num::Float; use std::f32; let min = f32::MIN_POSITIVE; // 1.17549435e-38f32 let max = f32::MAX; let lower_than_min = 1.0e-40_f32; let zero = 0.0f32; assert!(min.is_normal()); assert!(max.is_normal()); assert!(!zero.is_normal()); assert!(!f32::NAN.is_normal()); assert!(!f32::INFINITY.is_normal()); // Values between `0` and `min` are Subnormal. assert!(!lower_than_min.is_normal());
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 main() { use std::num::{Float, FpCategory}; use std::f32; let num = 12.4f32; let inf = f32::INFINITY; assert_eq!(num.classify(), FpCategory::Normal); assert_eq!(inf.classify(), FpCategory::Infinite); }use std::num::{Float, FpCategory}; use std::f32; let num = 12.4f32; let inf = f32::INFINITY; assert_eq!(num.classify(), FpCategory::Normal); assert_eq!(inf.classify(), FpCategory::Infinite);
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.
The floating point encoding is documented in the Reference.
use std::num::Float; let num = 2.0f32; // (8388608u64, -22i16, 1i8) let (mantissa, exponent, sign) = num.integer_decode(); let sign_f = sign as f32; let mantissa_f = mantissa as f32; let exponent_f = num.powf(exponent as f32); // 1 * 8388608 * 2^(-22) == 2 let abs_difference = (sign_f * mantissa_f * exponent_f - num).abs(); assert!(abs_difference < 1e-10);
fn floor(self) -> Self
Returns the largest integer less than or equal to a number.
fn main() { use std::num::Float; let f = 3.99; let g = 3.0; assert_eq!(f.floor(), 3.0); assert_eq!(g.floor(), 3.0); }use std::num::Float; let f = 3.99; let g = 3.0; assert_eq!(f.floor(), 3.0); assert_eq!(g.floor(), 3.0);
fn ceil(self) -> Self
Returns the smallest integer greater than or equal to a number.
fn main() { use std::num::Float; let f = 3.01; let g = 4.0; assert_eq!(f.ceil(), 4.0); assert_eq!(g.ceil(), 4.0); }use std::num::Float; let f = 3.01; let g = 4.0; assert_eq!(f.ceil(), 4.0); assert_eq!(g.ceil(), 4.0);
fn round(self) -> Self
Returns the nearest integer to a number. Round half-way cases away from
0.0.
use std::num::Float; let f = 3.3; let g = -3.3; assert_eq!(f.round(), 3.0); assert_eq!(g.round(), -3.0);
fn trunc(self) -> Self
Return the integer part of a number.
fn main() { use std::num::Float; let f = 3.3; let g = -3.7; assert_eq!(f.trunc(), 3.0); assert_eq!(g.trunc(), -3.0); }use std::num::Float; let f = 3.3; let g = -3.7; assert_eq!(f.trunc(), 3.0); assert_eq!(g.trunc(), -3.0);
fn fract(self) -> Self
Returns the fractional part of a number.
fn main() { use std::num::Float; let x = 3.5; let y = -3.5; let abs_difference_x = (x.fract() - 0.5).abs(); let abs_difference_y = (y.fract() - (-0.5)).abs(); assert!(abs_difference_x < 1e-10); assert!(abs_difference_y < 1e-10); }use std::num::Float; let x = 3.5; let y = -3.5; let abs_difference_x = (x.fract() - 0.5).abs(); let abs_difference_y = (y.fract() - (-0.5)).abs(); assert!(abs_difference_x < 1e-10); assert!(abs_difference_y < 1e-10);
fn abs(self) -> Self
Computes the absolute value of self. Returns Float::nan() if the
number is Float::nan().
use std::num::Float; use std::f64; let x = 3.5; let y = -3.5; let abs_difference_x = (x.abs() - x).abs(); let abs_difference_y = (y.abs() - (-y)).abs(); assert!(abs_difference_x < 1e-10); assert!(abs_difference_y < 1e-10); assert!(f64::NAN.abs().is_nan());
fn signum(self) -> Self
Returns a number that represents the sign of self.
1.0if the number is positive,+0.0orFloat::infinity()-1.0if the number is negative,-0.0orFloat::neg_infinity()Float::nan()if the number isFloat::nan()
use std::num::Float; use std::f64; let f = 3.5; assert_eq!(f.signum(), 1.0); assert_eq!(f64::NEG_INFINITY.signum(), -1.0); assert!(f64::NAN.signum().is_nan());
fn is_positive(self) -> bool
Returns true if self is positive, including +0.0 and
Float::infinity().
use std::num::Float; use std::f64; let nan: f64 = f64::NAN; let f = 7.0; let g = -7.0; assert!(f.is_positive()); assert!(!g.is_positive()); // Requires both tests to determine if is `NaN` assert!(!nan.is_positive() && !nan.is_negative());
fn is_negative(self) -> bool
Returns true if self is negative, including -0.0 and
Float::neg_infinity().
use std::num::Float; use std::f64; let nan = f64::NAN; let f = 7.0; let g = -7.0; assert!(!f.is_negative()); assert!(g.is_negative()); // Requires both tests to determine if is `NaN`. assert!(!nan.is_positive() && !nan.is_negative());
fn mul_add(self, a: Self, b: Self) -> Self
Fused multiply-add. Computes (self * a) + b with only one rounding
error. This produces a more accurate result with better performance than
a separate multiplication operation followed by an add.
use std::num::Float; let m = 10.0; let x = 4.0; let b = 60.0; // 100.0 let abs_difference = (m.mul_add(x, b) - (m*x + b)).abs(); assert!(abs_difference < 1e-10);
fn recip(self) -> Self
Take the reciprocal (inverse) of a number, 1/x.
use std::num::Float; let x = 2.0; let abs_difference = (x.recip() - (1.0/x)).abs(); assert!(abs_difference < 1e-10);
fn powi(self, n: i32) -> Self
Raise a number to an integer power.
Using this function is generally faster than using powf
use std::num::Float; let x = 2.0; let abs_difference = (x.powi(2) - x*x).abs(); assert!(abs_difference < 1e-10);
fn powf(self, n: Self) -> Self
Raise a number to a floating point power.
fn main() { use std::num::Float; let x = 2.0; let abs_difference = (x.powf(2.0) - x*x).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; let x = 2.0; let abs_difference = (x.powf(2.0) - x*x).abs(); assert!(abs_difference < 1e-10);
fn sqrt(self) -> Self
Take the square root of a number.
Returns NaN if self is a negative number.
use std::num::Float; let positive = 4.0; let negative = -4.0; let abs_difference = (positive.sqrt() - 2.0).abs(); assert!(abs_difference < 1e-10); assert!(negative.sqrt().is_nan());
fn rsqrt(self) -> Self
Take the reciprocal (inverse) square root of a number, 1/sqrt(x).
use std::num::Float; let f = 4.0; let abs_difference = (f.rsqrt() - 0.5).abs(); assert!(abs_difference < 1e-10);
fn exp(self) -> Self
Returns e^(self), (the exponential function).
use std::num::Float; let one = 1.0; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn exp2(self) -> Self
Returns 2^(self).
use std::num::Float; let f = 2.0; // 2^2 - 4 == 0 let abs_difference = (f.exp2() - 4.0).abs(); assert!(abs_difference < 1e-10);
fn ln(self) -> Self
Returns the natural logarithm of the number.
fn main() { use std::num::Float; let one = 1.0; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; let one = 1.0; // e^1 let e = one.exp(); // ln(e) - 1 == 0 let abs_difference = (e.ln() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn log(self, base: Self) -> Self
Returns the logarithm of the number with respect to an arbitrary base.
fn main() { use std::num::Float; let ten = 10.0; let two = 2.0; // log10(10) - 1 == 0 let abs_difference_10 = (ten.log(10.0) - 1.0).abs(); // log2(2) - 1 == 0 let abs_difference_2 = (two.log(2.0) - 1.0).abs(); assert!(abs_difference_10 < 1e-10); assert!(abs_difference_2 < 1e-10); }use std::num::Float; let ten = 10.0; let two = 2.0; // log10(10) - 1 == 0 let abs_difference_10 = (ten.log(10.0) - 1.0).abs(); // log2(2) - 1 == 0 let abs_difference_2 = (two.log(2.0) - 1.0).abs(); assert!(abs_difference_10 < 1e-10); assert!(abs_difference_2 < 1e-10);
fn log2(self) -> Self
Returns the base 2 logarithm of the number.
fn main() { use std::num::Float; let two = 2.0; // log2(2) - 1 == 0 let abs_difference = (two.log2() - 1.0).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; let two = 2.0; // log2(2) - 1 == 0 let abs_difference = (two.log2() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn log10(self) -> Self
Returns the base 10 logarithm of the number.
fn main() { use std::num::Float; let ten = 10.0; // log10(10) - 1 == 0 let abs_difference = (ten.log10() - 1.0).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; let ten = 10.0; // log10(10) - 1 == 0 let abs_difference = (ten.log10() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn to_degrees(self) -> Self
Convert radians to degrees.
fn main() { use std::num::Float; use std::f64::consts; let angle = consts::PI; let abs_difference = (angle.to_degrees() - 180.0).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; use std::f64::consts; let angle = consts::PI; let abs_difference = (angle.to_degrees() - 180.0).abs(); assert!(abs_difference < 1e-10);
fn to_radians(self) -> Self
Convert degrees to radians.
fn main() { use std::num::Float; use std::f64::consts; let angle = 180.0; let abs_difference = (angle.to_radians() - consts::PI).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; use std::f64::consts; let angle = 180.0; let abs_difference = (angle.to_radians() - consts::PI).abs(); assert!(abs_difference < 1e-10);
fn ldexp(x: Self, exp: isize) -> Self
Constructs a floating point number of x*2^exp.
use std::num::Float; // 3*2^2 - 12 == 0 let abs_difference = (Float::ldexp(3.0, 2) - 12.0).abs(); assert!(abs_difference < 1e-10);
fn frexp(self) -> (Self, isize)
Breaks the number into a normalized fraction and a base-2 exponent, satisfying:
self = x * 2^exp0.5 <= abs(x) < 1.0
use std::num::Float; let x = 4.0; // (1/2)*2^3 -> 1 * 8/2 -> 4.0 let f = x.frexp(); let abs_difference_0 = (f.0 - 0.5).abs(); let abs_difference_1 = (f.1 as f64 - 3.0).abs(); assert!(abs_difference_0 < 1e-10); assert!(abs_difference_1 < 1e-10);
fn next_after(self, other: Self) -> Self
Returns the next representable floating-point value in the direction of
other.
use std::num::Float; let x = 1.0f32; let abs_diff = (x.next_after(2.0) - 1.00000011920928955078125_f32).abs(); assert!(abs_diff < 1e-10);
fn max(self, other: Self) -> Self
Returns the maximum of the two numbers.
fn main() { use std::num::Float; let x = 1.0; let y = 2.0; assert_eq!(x.max(y), y); }use std::num::Float; let x = 1.0; let y = 2.0; assert_eq!(x.max(y), y);
fn min(self, other: Self) -> Self
Returns the minimum of the two numbers.
fn main() { use std::num::Float; let x = 1.0; let y = 2.0; assert_eq!(x.min(y), x); }use std::num::Float; let x = 1.0; let y = 2.0; assert_eq!(x.min(y), x);
fn abs_sub(self, other: Self) -> Self
The positive difference of two numbers.
- If
self <= other:0:0 - Else:
self - other
use std::num::Float; let x = 3.0; let y = -3.0; let abs_difference_x = (x.abs_sub(1.0) - 2.0).abs(); let abs_difference_y = (y.abs_sub(1.0) - 0.0).abs(); assert!(abs_difference_x < 1e-10); assert!(abs_difference_y < 1e-10);
fn cbrt(self) -> Self
Take the cubic root of a number.
fn main() { use std::num::Float; let x = 8.0; // x^(1/3) - 2 == 0 let abs_difference = (x.cbrt() - 2.0).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; let x = 8.0; // x^(1/3) - 2 == 0 let abs_difference = (x.cbrt() - 2.0).abs(); assert!(abs_difference < 1e-10);
fn hypot(self, other: Self) -> Self
Calculate the length of the hypotenuse of a right-angle triangle given
legs of length x and y.
use std::num::Float; let x = 2.0; let y = 3.0; // sqrt(x^2 + y^2) let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs(); assert!(abs_difference < 1e-10);
fn sin(self) -> Self
Computes the sine of a number (in radians).
fn main() { use std::num::Float; use std::f64; let x = f64::consts::PI/2.0; let abs_difference = (x.sin() - 1.0).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; use std::f64; let x = f64::consts::PI/2.0; let abs_difference = (x.sin() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn cos(self) -> Self
Computes the cosine of a number (in radians).
fn main() { use std::num::Float; use std::f64; let x = 2.0*f64::consts::PI; let abs_difference = (x.cos() - 1.0).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; use std::f64; let x = 2.0*f64::consts::PI; let abs_difference = (x.cos() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn tan(self) -> Self
Computes the tangent of a number (in radians).
fn main() { use std::num::Float; use std::f64; let x = f64::consts::PI/4.0; let abs_difference = (x.tan() - 1.0).abs(); assert!(abs_difference < 1e-14); }use std::num::Float; use std::f64; let x = f64::consts::PI/4.0; let abs_difference = (x.tan() - 1.0).abs(); assert!(abs_difference < 1e-14);
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 main() { use std::num::Float; use std::f64; let f = f64::consts::PI / 2.0; // asin(sin(pi/2)) let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; use std::f64; let f = f64::consts::PI / 2.0; // asin(sin(pi/2)) let abs_difference = (f.sin().asin() - f64::consts::PI / 2.0).abs(); assert!(abs_difference < 1e-10);
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 main() { use std::num::Float; use std::f64; let f = f64::consts::PI / 4.0; // acos(cos(pi/4)) let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; use std::f64; let f = f64::consts::PI / 4.0; // acos(cos(pi/4)) let abs_difference = (f.cos().acos() - f64::consts::PI / 4.0).abs(); assert!(abs_difference < 1e-10);
fn atan(self) -> Self
Computes the arctangent of a number. Return value is in radians in the range [-pi/2, pi/2];
fn main() { use std::num::Float; let f = 1.0; // atan(tan(1)) let abs_difference = (f.tan().atan() - 1.0).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; let f = 1.0; // atan(tan(1)) let abs_difference = (f.tan().atan() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn atan2(self, other: Self) -> Self
Computes the four quadrant arctangent of self (y) and other (x).
x = 0,y = 0:0x >= 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 std::num::Float; use std::f64; let pi = f64::consts::PI; // All angles from horizontal right (+x) // 45 deg counter-clockwise let x1 = 3.0; let y1 = -3.0; // 135 deg clockwise let x2 = -3.0; let y2 = 3.0; let abs_difference_1 = (y1.atan2(x1) - (-pi/4.0)).abs(); let abs_difference_2 = (y2.atan2(x2) - 3.0*pi/4.0).abs(); assert!(abs_difference_1 < 1e-10); assert!(abs_difference_2 < 1e-10);
fn sin_cos(self) -> (Self, Self)
Simultaneously computes the sine and cosine of the number, x. Returns
(sin(x), cos(x)).
use std::num::Float; use std::f64; let x = f64::consts::PI/4.0; let f = x.sin_cos(); let abs_difference_0 = (f.0 - x.sin()).abs(); let abs_difference_1 = (f.1 - x.cos()).abs(); assert!(abs_difference_0 < 1e-10); assert!(abs_difference_0 < 1e-10);
fn exp_m1(self) -> Self
Returns e^(self) - 1 in a way that is accurate even if the
number is close to zero.
use std::num::Float; let x = 7.0; // e^(ln(7)) - 1 let abs_difference = (x.ln().exp_m1() - 6.0).abs(); assert!(abs_difference < 1e-10);
fn ln_1p(self) -> Self
Returns ln(1+n) (natural logarithm) more accurately than if
the operations were performed separately.
use std::num::Float; use std::f64; let x = f64::consts::E - 1.0; // ln(1 + (e - 1)) == ln(e) == 1 let abs_difference = (x.ln_1p() - 1.0).abs(); assert!(abs_difference < 1e-10);
fn sinh(self) -> Self
Hyperbolic sine function.
fn main() { use std::num::Float; use std::f64; let e = f64::consts::E; let x = 1.0; let f = x.sinh(); // Solving sinh() at 1 gives `(e^2-1)/(2e)` let g = (e*e - 1.0)/(2.0*e); let abs_difference = (f - g).abs(); assert!(abs_difference < 1e-10); }use std::num::Float; use std::f64; let e = f64::consts::E; let x = 1.0; let f = x.sinh(); // Solving sinh() at 1 gives `(e^2-1)/(2e)` let g = (e*e - 1.0)/(2.0*e); let abs_difference = (f - g).abs(); assert!(abs_difference < 1e-10);
fn cosh(self) -> Self
Hyperbolic cosine function.
fn main() { use std::num::Float; use std::f64; let e = f64::consts::E; let x = 1.0; let f = x.cosh(); // Solving cosh() at 1 gives this result let g = (e*e + 1.0)/(2.0*e); let abs_difference = (f - g).abs(); // Same result assert!(abs_difference < 1.0e-10); }use std::num::Float; use std::f64; let e = f64::consts::E; let x = 1.0; let f = x.cosh(); // Solving cosh() at 1 gives this result let g = (e*e + 1.0)/(2.0*e); let abs_difference = (f - g).abs(); // Same result assert!(abs_difference < 1.0e-10);
fn tanh(self) -> Self
Hyperbolic tangent function.
fn main() { use std::num::Float; use std::f64; let e = f64::consts::E; let x = 1.0; let f = x.tanh(); // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))` let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2)); let abs_difference = (f - g).abs(); assert!(abs_difference < 1.0e-10); }use std::num::Float; use std::f64; let e = f64::consts::E; let x = 1.0; let f = x.tanh(); // Solving tanh() at 1 gives `(1 - e^(-2))/(1 + e^(-2))` let g = (1.0 - e.powi(-2))/(1.0 + e.powi(-2)); let abs_difference = (f - g).abs(); assert!(abs_difference < 1.0e-10);
fn asinh(self) -> Self
Inverse hyperbolic sine function.
fn main() { use std::num::Float; let x = 1.0; let f = x.sinh().asinh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10); }use std::num::Float; let x = 1.0; let f = x.sinh().asinh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10);
fn acosh(self) -> Self
Inverse hyperbolic cosine function.
fn main() { use std::num::Float; let x = 1.0; let f = x.cosh().acosh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10); }use std::num::Float; let x = 1.0; let f = x.cosh().acosh(); let abs_difference = (f - x).abs(); assert!(abs_difference < 1.0e-10);
fn atanh(self) -> Self
Inverse hyperbolic tangent function.
fn main() { use std::num::Float; use std::f64; let e = f64::consts::E; let f = e.tanh().atanh(); let abs_difference = (f - e).abs(); assert!(abs_difference < 1.0e-10); }use std::num::Float; use std::f64; let e = f64::consts::E; let f = e.tanh().atanh(); let abs_difference = (f - e).abs(); assert!(abs_difference < 1.0e-10);