//! `f32` 单精度浮点类型专用的常量。
//!
//! *[See also the `f32` primitive type](primitive@f32).*
//!
//! `consts` 子模块中提供了数学上有效的数字。
//!
//! 对于直接在此模块中定义的常量 (不同于 `consts` 子模块中定义的常量)，新代码应改为使用直接在 `f32` 类型上定义的关联常量。
//!
//!
//!

#![stable(feature = "rust1", since = "1.0.0")]
#![allow(missing_docs)]

#[cfg(test)]
mod tests;

#[cfg(not(test))]
use crate::intrinsics;
#[cfg(not(test))]
use crate::sys::cmath;

#[stable(feature = "rust1", since = "1.0.0")]
#[allow(deprecated, deprecated_in_future)]
pub use core::f32::{
    consts, DIGITS, EPSILON, INFINITY, MANTISSA_DIGITS, MAX, MAX_10_EXP, MAX_EXP, MIN, MIN_10_EXP,
    MIN_EXP, MIN_POSITIVE, NAN, NEG_INFINITY, RADIX,
};

#[cfg(not(test))]
#[lang = "f32_runtime"]
impl f32 {
    /// 返回小于或等于数字的最大整数。
    ///
    /// # Examples
    ///
    /// ```
    /// let f = 3.7_f32;
    /// let g = 3.0_f32;
    /// let h = -3.7_f32;
    ///
    /// assert_eq!(f.floor(), 3.0);
    /// assert_eq!(g.floor(), 3.0);
    /// assert_eq!(h.floor(), -4.0);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn floor(self) -> f32 {
        unsafe { intrinsics::floorf32(self) }
    }

    /// 返回大于或等于数字的最小整数。
    ///
    /// # Examples
    ///
    /// ```
    /// let f = 3.01_f32;
    /// let g = 4.0_f32;
    ///
    /// assert_eq!(f.ceil(), 4.0);
    /// assert_eq!(g.ceil(), 4.0);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn ceil(self) -> f32 {
        unsafe { intrinsics::ceilf32(self) }
    }

    /// 返回最接近整数的数字。
    /// 远离 `0.0` 的圆形中途机箱。
    ///
    /// # Examples
    ///
    /// ```
    /// let f = 3.3_f32;
    /// let g = -3.3_f32;
    ///
    /// assert_eq!(f.round(), 3.0);
    /// assert_eq!(g.round(), -3.0);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn round(self) -> f32 {
        unsafe { intrinsics::roundf32(self) }
    }

    /// 返回数字的整数部分。
    ///
    /// # Examples
    ///
    /// ```
    /// let f = 3.7_f32;
    /// let g = 3.0_f32;
    /// let h = -3.7_f32;
    ///
    /// assert_eq!(f.trunc(), 3.0);
    /// assert_eq!(g.trunc(), 3.0);
    /// assert_eq!(h.trunc(), -3.0);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn trunc(self) -> f32 {
        unsafe { intrinsics::truncf32(self) }
    }

    /// 返回数字的小数部分。
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 3.6_f32;
    /// let y = -3.6_f32;
    /// let abs_difference_x = (x.fract() - 0.6).abs();
    /// let abs_difference_y = (y.fract() - (-0.6)).abs();
    ///
    /// assert!(abs_difference_x <= f32::EPSILON);
    /// assert!(abs_difference_y <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn fract(self) -> f32 {
        self - self.trunc()
    }

    /// 计算 `self` 的绝对值。
    /// 如果数字为 `NAN`，则返回 `NAN`。
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 3.5_f32;
    /// let y = -3.5_f32;
    ///
    /// let abs_difference_x = (x.abs() - x).abs();
    /// let abs_difference_y = (y.abs() - (-y)).abs();
    ///
    /// assert!(abs_difference_x <= f32::EPSILON);
    /// assert!(abs_difference_y <= f32::EPSILON);
    ///
    /// assert!(f32::NAN.abs().is_nan());
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn abs(self) -> f32 {
        unsafe { intrinsics::fabsf32(self) }
    }

    /// 返回一个表示 `self` 符号的数字。
    ///
    /// - `1.0` 如果数字为正，则为 `+0.0` 或 `INFINITY`
    /// - `-1.0` 如果数字为负，则 `-0.0` 或 `NEG_INFINITY`
    /// - `NAN` 如果数字是 `NAN`
    ///
    /// # Examples
    ///
    /// ```
    /// let f = 3.5_f32;
    ///
    /// assert_eq!(f.signum(), 1.0);
    /// assert_eq!(f32::NEG_INFINITY.signum(), -1.0);
    ///
    /// assert!(f32::NAN.signum().is_nan());
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn signum(self) -> f32 {
        if self.is_nan() { Self::NAN } else { 1.0_f32.copysign(self) }
    }

    /// 返回一个数字，该数字由 `self` 的大小和 `sign` 的符号组成。
    ///
    /// 如果 `self` 和 `sign` 的符号相同，则等于 `self`，否则等于 `-self`。
    /// 如果 `self` 是 `NAN`，则返回带有 `sign` 符号的 `NAN`。
    ///
    /// # Examples
    ///
    /// ```
    /// let f = 3.5_f32;
    ///
    /// assert_eq!(f.copysign(0.42), 3.5_f32);
    /// assert_eq!(f.copysign(-0.42), -3.5_f32);
    /// assert_eq!((-f).copysign(0.42), 3.5_f32);
    /// assert_eq!((-f).copysign(-0.42), -3.5_f32);
    ///
    /// assert!(f32::NAN.copysign(1.0).is_nan());
    /// ```
    ///
    ///
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[inline]
    #[stable(feature = "copysign", since = "1.35.0")]
    pub fn copysign(self, sign: f32) -> f32 {
        unsafe { intrinsics::copysignf32(self, sign) }
    }

    /// 融合乘法加法。
    /// 仅用一个舍入误差计算 `(self * a) + b`，比未融合的乘法加法产生更准确的结果。
    ///
    /// 如果目标体系结构具有专用的 `fma` CPU 指令，则使用 `mul_add` 的性能可能比未融合的乘加性能更高。
    ///
    /// 但是，这并不总是正确的，并且在很大程度上取决于设计算法时要考虑特定的目标硬件。
    ///
    /// # Examples
    ///
    /// ```
    /// let m = 10.0_f32;
    /// let x = 4.0_f32;
    /// let b = 60.0_f32;
    ///
    /// // 100.0
    /// let abs_difference = (m.mul_add(x, b) - ((m * x) + b)).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    ///
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn mul_add(self, a: f32, b: f32) -> f32 {
        unsafe { intrinsics::fmaf32(self, a, b) }
    }

    /// 计算欧几里得除法，即 `rem_euclid` 的匹配方法。
    ///
    /// 这将计算整数 `n`，如 `self = n * rhs + self.rem_euclid(rhs)`。
    /// 换句话说，结果是将 `self / rhs` 舍入为 `n` 的整数 `n`。
    ///
    ///
    /// # Examples
    ///
    /// ```
    /// let a: f32 = 7.0;
    /// let b = 4.0;
    /// assert_eq!(a.div_euclid(b), 1.0); // 7.0 > 4.0 * 1.0
    /// assert_eq!((-a).div_euclid(b), -2.0); // -7.0 >= 4.0 * -2.0
    /// assert_eq!(a.div_euclid(-b), -1.0); // 7.0 >= -4.0 * -1.0
    /// assert_eq!((-a).div_euclid(-b), 2.0); // -7.0 >= -4.0 * 2.0
    /// ```
    ///
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[inline]
    #[stable(feature = "euclidean_division", since = "1.38.0")]
    pub fn div_euclid(self, rhs: f32) -> f32 {
        let q = (self / rhs).trunc();
        if self % rhs < 0.0 {
            return if rhs > 0.0 { q - 1.0 } else { q + 1.0 };
        }
        q
    }

    /// 计算 `self (mod rhs)` 的最小非负余数。
    ///
    /// 特别地，在大多数情况下，返回值 `r` 满足 `0.0 <= r < rhs.abs()`。
    /// 但是，由于浮点舍入误差，如果 `self` 的幅值和 `self < 0.0` 远小于 `rhs.abs()`，则可能会导致 `r == rhs.abs()` 违反数学定义。
    /// 此结果不是函数共域的元素，但它是实数中最接近的浮点数，因此近似满足属性 `self == self.div_euclid(rhs) * rhs + self.rem_euclid(rhs)`。
    ///
    ///
    /// # Examples
    ///
    /// ```
    /// let a: f32 = 7.0;
    /// let b = 4.0;
    /// assert_eq!(a.rem_euclid(b), 3.0);
    /// assert_eq!((-a).rem_euclid(b), 1.0);
    /// assert_eq!(a.rem_euclid(-b), 3.0);
    /// assert_eq!((-a).rem_euclid(-b), 1.0);
    /// // 由于舍入误差而造成的限制
    /// assert!((-f32::EPSILON).rem_euclid(3.0) != 0.0);
    /// ```
    ///
    ///
    ///
    ///
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[inline]
    #[stable(feature = "euclidean_division", since = "1.38.0")]
    pub fn rem_euclid(self, rhs: f32) -> f32 {
        let r = self % rhs;
        if r < 0.0 { r + rhs.abs() } else { r }
    }

    /// 将数字提高到整数幂。
    ///
    /// 使用此函数通常比使用 `powf` 更快
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 2.0_f32;
    /// let abs_difference = (x.powi(2) - (x * x)).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn powi(self, n: i32) -> f32 {
        unsafe { intrinsics::powif32(self, n) }
    }

    /// 将数字加到浮点幂。
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 2.0_f32;
    /// let abs_difference = (x.powf(2.0) - (x * x)).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn powf(self, n: f32) -> f32 {
        unsafe { intrinsics::powf32(self, n) }
    }

    /// 返回数字的平方根。
    ///
    /// 如果 `self` 是 `-0.0` 以外的负数，则返回 NaN。
    ///
    /// # Examples
    ///
    /// ```
    /// let positive = 4.0_f32;
    /// let negative = -4.0_f32;
    /// let negative_zero = -0.0_f32;
    ///
    /// let abs_difference = (positive.sqrt() - 2.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// assert!(negative.sqrt().is_nan());
    /// assert!(negative_zero.sqrt() == negative_zero);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn sqrt(self) -> f32 {
        unsafe { intrinsics::sqrtf32(self) }
    }

    /// 返回 `e^(self)` (指数函数)。
    ///
    /// # Examples
    ///
    /// ```
    /// let one = 1.0f32;
    /// // e^1
    /// let e = one.exp();
    ///
    /// // ln(e) - 1 == 0
    /// let abs_difference = (e.ln() - 1.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn exp(self) -> f32 {
        unsafe { intrinsics::expf32(self) }
    }

    /// 返回 `2^(self)`。
    ///
    /// # Examples
    ///
    /// ```
    /// let f = 2.0f32;
    ///
    /// // 2^2 - 4 == 0
    /// let abs_difference = (f.exp2() - 4.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn exp2(self) -> f32 {
        unsafe { intrinsics::exp2f32(self) }
    }

    /// 返回数字的自然对数。
    ///
    /// # Examples
    ///
    /// ```
    /// let one = 1.0f32;
    /// // e^1
    /// let e = one.exp();
    ///
    /// // ln(e) - 1 == 0
    /// let abs_difference = (e.ln() - 1.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn ln(self) -> f32 {
        unsafe { intrinsics::logf32(self) }
    }

    /// 返回数字相对于任意基数的对数。
    ///
    /// 由于实现细节，结果可能无法正确舍入;
    /// `self.log2()` 可以针对基准 2 产生更准确的结果，而 `self.log10()` 可以针对基准 10 产生更准确的结果。
    ///
    ///
    /// # Examples
    ///
    /// ```
    /// let five = 5.0f32;
    ///
    /// // log5(5) - 1 == 0
    /// let abs_difference = (five.log(5.0) - 1.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn log(self, base: f32) -> f32 {
        self.ln() / base.ln()
    }

    /// 返回数字的以 2 为底的对数。
    ///
    /// # Examples
    ///
    /// ```
    /// let two = 2.0f32;
    ///
    /// // log2(2) - 1 == 0
    /// let abs_difference = (two.log2() - 1.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn log2(self) -> f32 {
        #[cfg(target_os = "android")]
        return crate::sys::android::log2f32(self);
        #[cfg(not(target_os = "android"))]
        return unsafe { intrinsics::log2f32(self) };
    }

    /// 返回数字的以 10 为底的对数。
    ///
    /// # Examples
    ///
    /// ```
    /// let ten = 10.0f32;
    ///
    /// // log10(10) - 1 == 0
    /// let abs_difference = (ten.log10() - 1.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn log10(self) -> f32 {
        unsafe { intrinsics::log10f32(self) }
    }

    /// 两个数字的正差。
    ///
    /// * 如果是 `self <= other`: `0:0`
    /// * Else: `self - other`
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 3.0f32;
    /// let y = -3.0f32;
    ///
    /// 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 <= f32::EPSILON);
    /// assert!(abs_difference_y <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    #[rustc_deprecated(
        since = "1.10.0",
        reason = "you probably meant `(self - other).abs()`: \
                  this operation is `(self - other).max(0.0)` \
                  except that `abs_sub` also propagates NaNs (also \
                  known as `fdimf` in C). If you truly need the positive \
                  difference, consider using that expression or the C function \
                  `fdimf`, depending on how you wish to handle NaN (please consider \
                  filing an issue describing your use-case too)."
    )]
    pub fn abs_sub(self, other: f32) -> f32 {
        unsafe { cmath::fdimf(self, other) }
    }

    /// 返回数字的立方根。
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 8.0f32;
    ///
    /// // x^(1/3) - 2 == 0
    /// let abs_difference = (x.cbrt() - 2.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn cbrt(self) -> f32 {
        unsafe { cmath::cbrtf(self) }
    }

    /// 给定长度为 `x` 和 `y` 的支路，计算直角三角形的斜边的长度。
    ///
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 2.0f32;
    /// let y = 3.0f32;
    ///
    /// // sqrt(x^2 + y^2)
    /// let abs_difference = (x.hypot(y) - (x.powi(2) + y.powi(2)).sqrt()).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn hypot(self, other: f32) -> f32 {
        unsafe { cmath::hypotf(self, other) }
    }

    /// 计算数字的正弦 (以弧度为单位)。
    ///
    /// # Examples
    ///
    /// ```
    /// let x = std::f32::consts::FRAC_PI_2;
    ///
    /// let abs_difference = (x.sin() - 1.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn sin(self) -> f32 {
        unsafe { intrinsics::sinf32(self) }
    }

    /// 计算数字的余弦 (以弧度为单位)。
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 2.0 * std::f32::consts::PI;
    ///
    /// let abs_difference = (x.cos() - 1.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn cos(self) -> f32 {
        unsafe { intrinsics::cosf32(self) }
    }

    /// 计算一个数的正切 (以弧度为单位)。
    ///
    /// # Examples
    ///
    /// ```
    /// let x = std::f32::consts::FRAC_PI_4;
    /// let abs_difference = (x.tan() - 1.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn tan(self) -> f32 {
        unsafe { cmath::tanf(self) }
    }

    /// 计算数字的反正弦。
    /// 如果数字超出 [-1, 1] 范围，则返回值的弧度范围为 [-pi/2, pi/2] 或 NaN。
    ///
    ///
    /// # Examples
    ///
    /// ```
    /// let f = std::f32::consts::FRAC_PI_2;
    ///
    /// // asin(sin(pi/2))
    /// let abs_difference = (f.sin().asin() - std::f32::consts::FRAC_PI_2).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn asin(self) -> f32 {
        unsafe { cmath::asinf(self) }
    }

    /// 计算数字的反余弦值。
    /// 如果数字超出 [-1, 1] 范围，则返回值的弧度范围为 [0, pi] 或 NaN。
    ///
    ///
    /// # Examples
    ///
    /// ```
    /// let f = std::f32::consts::FRAC_PI_4;
    ///
    /// // acos(cos(pi/4))
    /// let abs_difference = (f.cos().acos() - std::f32::consts::FRAC_PI_4).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn acos(self) -> f32 {
        unsafe { cmath::acosf(self) }
    }

    /// 计算数字的反正切。
    /// 返回值的弧度范围为 [-pi/2, pi/2];
    ///
    /// # Examples
    ///
    /// ```
    /// let f = 1.0f32;
    ///
    /// // atan(tan(1))
    /// let abs_difference = (f.tan().atan() - 1.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn atan(self) -> f32 {
        unsafe { cmath::atanf(self) }
    }

    /// 计算弧度 `self` (`y`) 和 `other` (`x`) 的四个象限反正切。
    ///
    /// * `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)`
    ///
    /// # Examples
    ///
    /// ```
    /// // 从正 x 轴 -pi/4 弧度逆时针测量的正角 (顺时针 45 度)
    /////
    /////
    /// let x1 = 3.0f32;
    /// let y1 = -3.0f32;
    ///
    /// // 3pi/4 弧度 (逆时针 135 度)
    /// let x2 = -3.0f32;
    /// let y2 = 3.0f32;
    ///
    /// let abs_difference_1 = (y1.atan2(x1) - (-std::f32::consts::FRAC_PI_4)).abs();
    /// let abs_difference_2 = (y2.atan2(x2) - (3.0 * std::f32::consts::FRAC_PI_4)).abs();
    ///
    /// assert!(abs_difference_1 <= f32::EPSILON);
    /// assert!(abs_difference_2 <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn atan2(self, other: f32) -> f32 {
        unsafe { cmath::atan2f(self, other) }
    }

    /// 同时计算数字的正弦和余弦， `x`.
    /// 返回 `(sin(x), cos(x))`。
    ///
    /// # Examples
    ///
    /// ```
    /// let x = std::f32::consts::FRAC_PI_4;
    /// 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 <= f32::EPSILON);
    /// assert!(abs_difference_1 <= f32::EPSILON);
    /// ```
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn sin_cos(self) -> (f32, f32) {
        (self.sin(), self.cos())
    }

    /// 即使数字接近零，也以准确的方式返回 `e^(self) - 1`。
    ///
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 1e-8_f32;
    ///
    /// // 对于非常小的 x，e^x 约为 1 + x + x^2 / 2
    /// let approx = x + x * x / 2.0;
    /// let abs_difference = (x.exp_m1() - approx).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn exp_m1(self) -> f32 {
        unsafe { cmath::expm1f(self) }
    }

    /// 与单独执行操作相比，返回 `ln(1+n)` (自然对数) 的准确性更高。
    ///
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 1e-8_f32;
    ///
    /// // 对于非常小的 x，ln(1 + x) 大约为 x - x^2 / 2
    /// let approx = x - x * x / 2.0;
    /// let abs_difference = (x.ln_1p() - approx).abs();
    ///
    /// assert!(abs_difference < 1e-10);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn ln_1p(self) -> f32 {
        unsafe { cmath::log1pf(self) }
    }

    /// 双曲正弦函数。
    ///
    /// # Examples
    ///
    /// ```
    /// let e = std::f32::consts::E;
    /// let x = 1.0f32;
    ///
    /// let f = x.sinh();
    /// // 将 sinh() 求解为 1 得到 `(e^2-1)/(2e)`
    /// let g = ((e * e) - 1.0) / (2.0 * e);
    /// let abs_difference = (f - g).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn sinh(self) -> f32 {
        unsafe { cmath::sinhf(self) }
    }

    /// 双曲余弦函数。
    ///
    /// # Examples
    ///
    /// ```
    /// let e = std::f32::consts::E;
    /// let x = 1.0f32;
    /// let f = x.cosh();
    /// // 将 cosh() 求解为 1 可得出此结果
    /// let g = ((e * e) + 1.0) / (2.0 * e);
    /// let abs_difference = (f - g).abs();
    ///
    /// // 结果相同
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn cosh(self) -> f32 {
        unsafe { cmath::coshf(self) }
    }

    /// 双曲正切函数。
    ///
    /// # Examples
    ///
    /// ```
    /// let e = std::f32::consts::E;
    /// let x = 1.0f32;
    ///
    /// let f = x.tanh();
    /// // 将 tanh() 求解为 1 得到 `(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 <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn tanh(self) -> f32 {
        unsafe { cmath::tanhf(self) }
    }

    /// 反双曲正弦函数。
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 1.0f32;
    /// let f = x.sinh().asinh();
    ///
    /// let abs_difference = (f - x).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn asinh(self) -> f32 {
        (self.abs() + ((self * self) + 1.0).sqrt()).ln().copysign(self)
    }

    /// 反双曲余弦函数。
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 1.0f32;
    /// let f = x.cosh().acosh();
    ///
    /// let abs_difference = (f - x).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn acosh(self) -> f32 {
        if self < 1.0 { Self::NAN } else { (self + ((self * self) - 1.0).sqrt()).ln() }
    }

    /// 反双曲正切函数。
    ///
    /// # Examples
    ///
    /// ```
    /// let e = std::f32::consts::E;
    /// let f = e.tanh().atanh();
    ///
    /// let abs_difference = (f - e).abs();
    ///
    /// assert!(abs_difference <= 1e-5);
    /// ```
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    pub fn atanh(self) -> f32 {
        0.5 * ((2.0 * self) / (1.0 - self)).ln_1p()
    }

    /// `start` 和 `end` 之间的线性插值。
    ///
    /// 这可以在 `start` 和 `end` 之间启用线性插值，其中开始由 `self == 0.0` 表示，`end` 由 `self == 1.0` 表示。
    /// 这是所有 "transition"、"easing" 或 "step" 函数的基础; 如果您以给定的速率将 `self` 从 0.0 更改为 1.0，结果将以相似的速率从 `start` 更改为 `end`。
    ///
    ///
    /// 允许低于 0.0 或高于 1.0 的值，允许您推断 `start` 到 `end` 范围之外的值。
    /// 这对于可能稍微移动到结尾或开始以获得所需效果的过渡函数也很有用。
    /// 在数学上，返回的值等同于 `start + self * (end - start)`，尽管我们做出了一些特别对线性插值有用的特定保证。
    ///
    /// 这些保证是:
    ///
    /// * 如果 `start` 和 `end` 为 [finite]，则 0.0 处的值始终为 `start`，1.0 处的值始终为 `end`。(exactness)
    /// * 如果 `start` 和 `end` 为 [finite]，则值将始终沿 `start` 到 `end` (monotonicity) 的方向移动
    /// * 如果 `self` 是 [finite] 和 `start == end`，则任何一点的值将始终为 `start == end`。(consistency)
    ///
    /// [finite]: #method.is_finite
    ///
    ///
    ///
    ///
    ///
    ///
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[unstable(feature = "float_interpolation", issue = "86269")]
    pub fn lerp(self, start: f32, end: f32) -> f32 {
        // consistent
        if start == end {
            start

        // exact/monotonic
        } else {
            self.mul_add(end, (-self).mul_add(start, start))
        }
    }
}