//! `f32` 单精度浮点类型的常量。
//!
//! *[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))]
impl f32 {
    /// 返回小于或等于 `self` 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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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 `self` 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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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 `self` 的整数。
    /// 如果值介于两个整数之间，则舍入 `0.0`。
    ///
    /// # Examples
    ///
    /// ```
    /// let f = 3.3_f32;
    /// let g = -3.3_f32;
    /// let h = -3.7_f32;
    /// let i = 3.5_f32;
    /// let j = 4.5_f32;
    ///
    /// assert_eq!(f.round(), 3.0);
    /// assert_eq!(g.round(), -3.0);
    /// assert_eq!(h.round(), -4.0);
    /// assert_eq!(i.round(), 4.0);
    /// assert_eq!(j.round(), 5.0);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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) }
    }

    /// 返回最接近整数的数字。
    /// 将中途个案四舍五入到具有最低有效数字的数字。
    ///
    /// # Examples
    ///
    /// ```
    /// #![feature(round_ties_even)]
    ///
    /// let f = 3.3_f32;
    /// let g = -3.3_f32;
    /// let h = 3.5_f32;
    /// let i = 4.5_f32;
    ///
    /// 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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[unstable(feature = "round_ties_even", issue = "96710")]
    #[inline]
    pub fn round_ties_even(self) -> f32 {
        unsafe { intrinsics::rintf32(self) }
    }

    /// 返回 `self` 的整数部分。
    /// 这意味着非整数总是被截断为零。
    ///
    /// # 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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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 `self` 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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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。
    ///
    /// # 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());
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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` 如果数字是正数，`+0.0` 或 `INFINITY`
    /// - `-1.0` 如果数字是负数，`-0.0` 或 `NEG_INFINITY`
    /// - 如果数字为 NaN，则为 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());
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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，则返回符号位为 `sign` 的 NaN。
    /// 但是请注意，通常不能保证在算术运算中保留 NaN 上的符号位。
    ///
    /// 有关详细信息，请参见 [将 NaN 解释为特殊值](primitive@f32)。
    ///
    /// # 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());
    /// ```
    ///
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    ///
    #[rustc_allow_incoherent_impl]
    #[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
    /// ```
    ///
    #[rustc_allow_incoherent_impl]
    #[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。
    /// 此结果不是函数的余域的元素，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);
    /// ```
    ///
    ///
    ///
    ///
    #[rustc_allow_incoherent_impl]
    #[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。
    ///
    /// 使用这个函数通常比使用 `powf` 更快。
    /// 它可能具有与 `powf` 不同的舍入操作序列，因此不能保证结果一致。
    ///
    ///
    /// # Examples
    ///
    /// ```
    /// let x = 2.0_f32;
    /// let abs_difference = (x.powi(2) - (x * x)).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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，结果可能无法正确四舍五入；
    /// `self.log2()` 可以为基数 2 生成更准确的结果，而 `self.log10()` 可以为基数 10 生成更准确的结果。
    ///
    ///
    /// # Examples
    ///
    /// ```
    /// let five = 5.0f32;
    ///
    /// // log5(5) - 1 == 0
    /// let abs_difference = (five.log(5.0) - 1.0).abs();
    ///
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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 `self <= other`: `0:0`
    /// * 否则: `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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[must_use = "method returns a new number and does not mutate the original value"]
    #[stable(feature = "rust1", since = "1.0.0")]
    #[inline]
    #[deprecated(
        since = "1.10.0",
        note = "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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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) }
    }

    /// 计算原点与欧几里德平面上的点 (`x`, `y`) 之间的距离。
    /// 等价地，计算直角三角形的斜边长度，其他边的长度分别为 `x.abs()` 和 `y.abs()`。
    ///
    ///
    /// # 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);
    /// ```
    ///
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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。
    /// 返回值以弧度为单位，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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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 轴逆时针测量的正角度 -pi/4 弧度 (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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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 `x` 的正弦和余弦。
    /// 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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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();
    ///
    /// // 同样的结果
    /// assert!(abs_difference <= f32::EPSILON);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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 {
        let ax = self.abs();
        let ix = 1.0 / ax;
        (ax + (ax / (Self::hypot(1.0, ix) + ix))).ln_1p().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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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 - 1.0).sqrt() * (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);
    /// ```
    #[rustc_allow_incoherent_impl]
    #[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()
    }
}