fn fract(&self) -> Self;
}
- /// Defines constants and methods common to real numbers
- pub trait Real: Signed
- + Ord
- + Round
- + Div<Self,Self> {
- // Common Constants
- // FIXME (#5527): These should be associated constants
- fn pi() -> Self;
- fn two_pi() -> Self;
- fn frac_pi_2() -> Self;
- fn frac_pi_3() -> Self;
- fn frac_pi_4() -> Self;
- fn frac_pi_6() -> Self;
- fn frac_pi_8() -> Self;
- fn frac_1_pi() -> Self;
- fn frac_2_pi() -> Self;
- fn frac_2_sqrtpi() -> Self;
- fn sqrt2() -> Self;
- fn frac_1_sqrt2() -> Self;
- fn e() -> Self;
- fn log2_e() -> Self;
- fn log10_e() -> Self;
- fn ln_2() -> Self;
- fn ln_10() -> Self;
-
- // Fractional functions
-
- /// Take the reciprocal (inverse) of a number, `1/x`.
- fn recip(&self) -> Self;
-
- // Algebraic functions
- /// Raise a number to a power.
- fn powf(&self, n: &Self) -> Self;
-
- /// Take the square root of a number.
- fn sqrt(&self) -> Self;
- /// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`.
- fn rsqrt(&self) -> Self;
- /// Take the cubic root of a number.
- fn cbrt(&self) -> Self;
- /// Calculate the length of the hypotenuse of a right-angle triangle given
- /// legs of length `x` and `y`.
- fn hypot(&self, other: &Self) -> Self;
-
- // Trigonometric functions
-
- /// Computes the sine of a number (in radians).
- fn sin(&self) -> Self;
- /// Computes the cosine of a number (in radians).
- fn cos(&self) -> Self;
- /// Computes the tangent of a number (in radians).
- fn tan(&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 asin(&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 acos(&self) -> Self;
- /// Computes the arctangent of a number. Return value is in radians in the
- /// range [-pi/2, pi/2];
- fn atan(&self) -> Self;
- /// Computes the four quadrant arctangent of a number, `y`, and another
- /// number `x`. Return value is in radians in the range [-pi, pi].
- fn atan2(&self, other: &Self) -> Self;
- /// Simultaneously computes the sine and cosine of the number, `x`. Returns
- /// `(sin(x), cos(x))`.
- fn sin_cos(&self) -> (Self, Self);
-
- // Exponential functions
-
- /// Returns `e^(self)`, (the exponential function).
- fn exp(&self) -> Self;
- /// Returns 2 raised to the power of the number, `2^(self)`.
- fn exp2(&self) -> Self;
- /// Returns the natural logarithm of the number.
- fn ln(&self) -> Self;
- /// Returns the logarithm of the number with respect to an arbitrary base.
- fn log(&self, base: &Self) -> Self;
- /// Returns the base 2 logarithm of the number.
- fn log2(&self) -> Self;
- /// Returns the base 10 logarithm of the number.
- fn log10(&self) -> Self;
-
- // Hyperbolic functions
-
- /// Hyperbolic sine function.
- fn sinh(&self) -> Self;
- /// Hyperbolic cosine function.
- fn cosh(&self) -> Self;
- /// Hyperbolic tangent function.
- fn tanh(&self) -> Self;
- /// Inverse hyperbolic sine function.
- fn asinh(&self) -> Self;
- /// Inverse hyperbolic cosine function.
- fn acosh(&self) -> Self;
- /// Inverse hyperbolic tangent function.
- fn atanh(&self) -> Self;
-
- // Angular conversions
-
- /// Convert radians to degrees.
- fn to_degrees(&self) -> Self;
- /// Convert degrees to radians.
- fn to_radians(&self) -> Self;
- }
-
/// Raises a value to the power of exp, using exponentiation by squaring.
///
/// # Example
}
}
- /// Raise a number to a power.
- ///
- /// # Example
- ///
- /// ```rust
- /// use std::num;
- ///
- /// let sixteen: f64 = num::powf(2.0, 4.0);
- /// assert_eq!(sixteen, 16.0);
- /// ```
- #[inline(always)] pub fn powf<T: Real>(value: T, n: T) -> T { value.powf(&n) }
- /// Take the square root of a number.
- #[inline(always)] pub fn sqrt<T: Real>(value: T) -> T { value.sqrt() }
- /// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`.
- #[inline(always)] pub fn rsqrt<T: Real>(value: T) -> T { value.rsqrt() }
- /// Take the cubic root of a number.
- #[inline(always)] pub fn cbrt<T: Real>(value: T) -> T { value.cbrt() }
- /// Calculate the length of the hypotenuse of a right-angle triangle given legs of length `x` and
- /// `y`.
- #[inline(always)] pub fn hypot<T: Real>(x: T, y: T) -> T { x.hypot(&y) }
- /// Sine function.
- #[inline(always)] pub fn sin<T: Real>(value: T) -> T { value.sin() }
- /// Cosine function.
- #[inline(always)] pub fn cos<T: Real>(value: T) -> T { value.cos() }
- /// Tangent function.
- #[inline(always)] pub fn tan<T: Real>(value: T) -> T { value.tan() }
- /// Compute the arcsine of the number.
- #[inline(always)] pub fn asin<T: Real>(value: T) -> T { value.asin() }
- /// Compute the arccosine of the number.
- #[inline(always)] pub fn acos<T: Real>(value: T) -> T { value.acos() }
- /// Compute the arctangent of the number.
- #[inline(always)] pub fn atan<T: Real>(value: T) -> T { value.atan() }
- /// Compute the arctangent with 2 arguments.
- #[inline(always)] pub fn atan2<T: Real>(x: T, y: T) -> T { x.atan2(&y) }
- /// Simultaneously computes the sine and cosine of the number.
- #[inline(always)] pub fn sin_cos<T: Real>(value: T) -> (T, T) { value.sin_cos() }
- /// Returns `e^(value)`, (the exponential function).
- #[inline(always)] pub fn exp<T: Real>(value: T) -> T { value.exp() }
- /// Returns 2 raised to the power of the number, `2^(value)`.
- #[inline(always)] pub fn exp2<T: Real>(value: T) -> T { value.exp2() }
- /// Returns the natural logarithm of the number.
- #[inline(always)] pub fn ln<T: Real>(value: T) -> T { value.ln() }
- /// Returns the logarithm of the number with respect to an arbitrary base.
- #[inline(always)] pub fn log<T: Real>(value: T, base: T) -> T { value.log(&base) }
- /// Returns the base 2 logarithm of the number.
- #[inline(always)] pub fn log2<T: Real>(value: T) -> T { value.log2() }
- /// Returns the base 10 logarithm of the number.
- #[inline(always)] pub fn log10<T: Real>(value: T) -> T { value.log10() }
- /// Hyperbolic sine function.
- #[inline(always)] pub fn sinh<T: Real>(value: T) -> T { value.sinh() }
- /// Hyperbolic cosine function.
- #[inline(always)] pub fn cosh<T: Real>(value: T) -> T { value.cosh() }
- /// Hyperbolic tangent function.
- #[inline(always)] pub fn tanh<T: Real>(value: T) -> T { value.tanh() }
- /// Inverse hyperbolic sine function.
- #[inline(always)] pub fn asinh<T: Real>(value: T) -> T { value.asinh() }
- /// Inverse hyperbolic cosine function.
- #[inline(always)] pub fn acosh<T: Real>(value: T) -> T { value.acosh() }
- /// Inverse hyperbolic tangent function.
- #[inline(always)] pub fn atanh<T: Real>(value: T) -> T { value.atanh() }
-
pub trait Bounded {
// FIXME (#5527): These should be associated constants
fn min_value() -> Self;
+ BitXor<Self,Self>
+ Shl<Self,Self>
+ Shr<Self,Self> {
- /// Returns the number of bits set in the number.
+ /// Returns the number of ones in the binary representation of the number.
///
/// # Example
///
/// ```rust
/// use std::num::Bitwise;
///
- /// let n = 0b0101000u16;
- /// assert_eq!(n.population_count(), 2);
+ /// let n = 0b01001100u8;
+ /// assert_eq!(n.count_ones(), 3);
+ /// ```
+ fn count_ones(&self) -> Self;
+
+ /// Returns the number of zeros in the binary representation of the number.
+ ///
+ /// # Example
+ ///
+ /// ```rust
+ /// use std::num::Bitwise;
+ ///
+ /// let n = 0b01001100u8;
+ /// assert_eq!(n.count_zeros(), 5);
/// ```
- fn population_count(&self) -> Self;
- /// Returns the number of leading zeros in the number.
+ #[inline]
+ fn count_zeros(&self) -> Self {
+ (!*self).count_ones()
+ }
+
+ /// Returns the number of leading zeros in the in the binary representation
+ /// of the number.
///
/// # Example
///
/// assert_eq!(n.leading_zeros(), 10);
/// ```
fn leading_zeros(&self) -> Self;
- /// Returns the number of trailing zeros in the number.
+
+ /// Returns the number of trailing zeros in the in the binary representation
+ /// of the number.
///
/// # Example
///
}
/// Primitive floating point numbers
- pub trait Float: Real
- + Signed
+ pub trait Float: Signed
+ + Round
+ Primitive {
// FIXME (#5527): These should be associated constants
fn nan() -> Self;
fn next_after(&self, other: Self) -> Self;
fn integer_decode(&self) -> (u64, i16, i8);
+
+ // Common Mathematical Constants
+ // FIXME (#5527): These should be associated constants
+ fn pi() -> Self;
+ fn two_pi() -> Self;
+ fn frac_pi_2() -> Self;
+ fn frac_pi_3() -> Self;
+ fn frac_pi_4() -> Self;
+ fn frac_pi_6() -> Self;
+ fn frac_pi_8() -> Self;
+ fn frac_1_pi() -> Self;
+ fn frac_2_pi() -> Self;
+ fn frac_2_sqrtpi() -> Self;
+ fn sqrt2() -> Self;
+ fn frac_1_sqrt2() -> Self;
+ fn e() -> Self;
+ fn log2_e() -> Self;
+ fn log10_e() -> Self;
+ fn ln_2() -> Self;
+ fn ln_10() -> Self;
+
+ // Fractional functions
+
+ /// Take the reciprocal (inverse) of a number, `1/x`.
+ fn recip(&self) -> Self;
+
+ // Algebraic functions
+ /// Raise a number to a power.
+ fn powf(&self, n: &Self) -> Self;
+
+ /// Take the square root of a number.
+ fn sqrt(&self) -> Self;
+ /// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`.
+ fn rsqrt(&self) -> Self;
+ /// Take the cubic root of a number.
+ fn cbrt(&self) -> Self;
+ /// Calculate the length of the hypotenuse of a right-angle triangle given
+ /// legs of length `x` and `y`.
+ fn hypot(&self, other: &Self) -> Self;
+
+ // Trigonometric functions
+
+ /// Computes the sine of a number (in radians).
+ fn sin(&self) -> Self;
+ /// Computes the cosine of a number (in radians).
+ fn cos(&self) -> Self;
+ /// Computes the tangent of a number (in radians).
+ fn tan(&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 asin(&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 acos(&self) -> Self;
+ /// Computes the arctangent of a number. Return value is in radians in the
+ /// range [-pi/2, pi/2];
+ fn atan(&self) -> Self;
+ /// Computes the four quadrant arctangent of a number, `y`, and another
+ /// number `x`. Return value is in radians in the range [-pi, pi].
+ fn atan2(&self, other: &Self) -> Self;
+ /// Simultaneously computes the sine and cosine of the number, `x`. Returns
+ /// `(sin(x), cos(x))`.
+ fn sin_cos(&self) -> (Self, Self);
+
+ // Exponential functions
+
+ /// Returns `e^(self)`, (the exponential function).
+ fn exp(&self) -> Self;
+ /// Returns 2 raised to the power of the number, `2^(self)`.
+ fn exp2(&self) -> Self;
+ /// Returns the natural logarithm of the number.
+ fn ln(&self) -> Self;
+ /// Returns the logarithm of the number with respect to an arbitrary base.
+ fn log(&self, base: &Self) -> Self;
+ /// Returns the base 2 logarithm of the number.
+ fn log2(&self) -> Self;
+ /// Returns the base 10 logarithm of the number.
+ fn log10(&self) -> Self;
+
+ // Hyperbolic functions
+
+ /// Hyperbolic sine function.
+ fn sinh(&self) -> Self;
+ /// Hyperbolic cosine function.
+ fn cosh(&self) -> Self;
+ /// Hyperbolic tangent function.
+ fn tanh(&self) -> Self;
+ /// Inverse hyperbolic sine function.
+ fn asinh(&self) -> Self;
+ /// Inverse hyperbolic cosine function.
+ fn acosh(&self) -> Self;
+ /// Inverse hyperbolic tangent function.
+ fn atanh(&self) -> Self;
+
+ // Angular conversions
+
+ /// Convert radians to degrees.
+ fn to_degrees(&self) -> Self;
+ /// Convert degrees to radians.
+ fn to_radians(&self) -> Self;
}
/// Returns the exponential of the number, minus `1`, `exp(n) - 1`, in a way
/// architectures) than a separate multiplication operation followed by an add.
#[inline(always)] pub fn mul_add<T: Float>(a: T, b: T, c: T) -> T { a.mul_add(b, c) }
+ /// Raise a number to a power.
+ ///
+ /// # Example
+ ///
+ /// ```rust
+ /// use std::num;
+ ///
+ /// let sixteen: f64 = num::powf(2.0, 4.0);
+ /// assert_eq!(sixteen, 16.0);
+ /// ```
+ #[inline(always)] pub fn powf<T: Float>(value: T, n: T) -> T { value.powf(&n) }
+ /// Take the square root of a number.
+ #[inline(always)] pub fn sqrt<T: Float>(value: T) -> T { value.sqrt() }
+ /// Take the reciprocal (inverse) square root of a number, `1/sqrt(x)`.
+ #[inline(always)] pub fn rsqrt<T: Float>(value: T) -> T { value.rsqrt() }
+ /// Take the cubic root of a number.
+ #[inline(always)] pub fn cbrt<T: Float>(value: T) -> T { value.cbrt() }
+ /// Calculate the length of the hypotenuse of a right-angle triangle given legs
+ /// of length `x` and `y`.
+ #[inline(always)] pub fn hypot<T: Float>(x: T, y: T) -> T { x.hypot(&y) }
+ /// Sine function.
+ #[inline(always)] pub fn sin<T: Float>(value: T) -> T { value.sin() }
+ /// Cosine function.
+ #[inline(always)] pub fn cos<T: Float>(value: T) -> T { value.cos() }
+ /// Tangent function.
+ #[inline(always)] pub fn tan<T: Float>(value: T) -> T { value.tan() }
+ /// Compute the arcsine of the number.
+ #[inline(always)] pub fn asin<T: Float>(value: T) -> T { value.asin() }
+ /// Compute the arccosine of the number.
+ #[inline(always)] pub fn acos<T: Float>(value: T) -> T { value.acos() }
+ /// Compute the arctangent of the number.
+ #[inline(always)] pub fn atan<T: Float>(value: T) -> T { value.atan() }
+ /// Compute the arctangent with 2 arguments.
+ #[inline(always)] pub fn atan2<T: Float>(x: T, y: T) -> T { x.atan2(&y) }
+ /// Simultaneously computes the sine and cosine of the number.
+ #[inline(always)] pub fn sin_cos<T: Float>(value: T) -> (T, T) { value.sin_cos() }
+ /// Returns `e^(value)`, (the exponential function).
+ #[inline(always)] pub fn exp<T: Float>(value: T) -> T { value.exp() }
+ /// Returns 2 raised to the power of the number, `2^(value)`.
+ #[inline(always)] pub fn exp2<T: Float>(value: T) -> T { value.exp2() }
+ /// Returns the natural logarithm of the number.
+ #[inline(always)] pub fn ln<T: Float>(value: T) -> T { value.ln() }
+ /// Returns the logarithm of the number with respect to an arbitrary base.
+ #[inline(always)] pub fn log<T: Float>(value: T, base: T) -> T { value.log(&base) }
+ /// Returns the base 2 logarithm of the number.
+ #[inline(always)] pub fn log2<T: Float>(value: T) -> T { value.log2() }
+ /// Returns the base 10 logarithm of the number.
+ #[inline(always)] pub fn log10<T: Float>(value: T) -> T { value.log10() }
+ /// Hyperbolic sine function.
+ #[inline(always)] pub fn sinh<T: Float>(value: T) -> T { value.sinh() }
+ /// Hyperbolic cosine function.
+ #[inline(always)] pub fn cosh<T: Float>(value: T) -> T { value.cosh() }
+ /// Hyperbolic tangent function.
+ #[inline(always)] pub fn tanh<T: Float>(value: T) -> T { value.tanh() }
+ /// Inverse hyperbolic sine function.
+ #[inline(always)] pub fn asinh<T: Float>(value: T) -> T { value.asinh() }
+ /// Inverse hyperbolic cosine function.
+ #[inline(always)] pub fn acosh<T: Float>(value: T) -> T { value.acosh() }
+ /// Inverse hyperbolic tangent function.
+ #[inline(always)] pub fn atanh<T: Float>(value: T) -> T { value.atanh() }
+
/// A generic trait for converting a value to a number.
pub trait ToPrimitive {
/// Converts the value of `self` to an `int`.
projects / rust.git / commitdiff