rapier/src/utils.rs

//! Miscellaneous utilities.

use na::{
    Matrix1, Matrix2, Matrix3, Point2, Point3, RowVector2, Scalar, SimdRealField, UnitComplex,
    UnitQuaternion, Vector1, Vector2, Vector3,
};
use num::Zero;
use simba::simd::SimdValue;
use std::ops::IndexMut;

use parry::utils::SdpMatrix3;
use {
    crate::math::{Real, SimdReal},
    na::SimdPartialOrd,
    num::One,
};

/// The trait for real numbers used by Rapier.
///
/// This includes `f32`, `f64` and their related SIMD types.
pub trait SimdRealCopy: SimdRealField<Element = Real> + Copy {}
impl SimdRealCopy for Real {}
impl SimdRealCopy for SimdReal {}

const INV_EPSILON: Real = 1.0e-20;

pub(crate) fn inv(val: Real) -> Real {
    if (-INV_EPSILON..=INV_EPSILON).contains(&val) {
        0.0
    } else {
        1.0 / val
    }
}

pub(crate) fn simd_inv<N: SimdRealCopy>(val: N) -> N {
    let eps = N::splat(INV_EPSILON);
    N::zero().select(val.simd_gt(-eps) & val.simd_lt(eps), N::one() / val)
}

/// Trait to copy the sign of each component of one scalar/vector/matrix to another.
pub trait SimdSign<Rhs>: Sized {
    // See SIMD implementations of copy_sign there: https://stackoverflow.com/a/57872652
    /// Copy the sign of each component of `self` to the corresponding component of `to`.
    fn copy_sign_to(self, to: Rhs) -> Rhs;
}

impl SimdSign<Real> for Real {
    fn copy_sign_to(self, to: Self) -> Self {
        const MINUS_ZERO: Real = -0.0;
        let signbit = MINUS_ZERO.to_bits();
        Real::from_bits((signbit & self.to_bits()) | ((!signbit) & to.to_bits()))
    }
}

impl<N: Scalar + Copy + SimdSign<N>> SimdSign<Vector2<N>> for N {
    fn copy_sign_to(self, to: Vector2<N>) -> Vector2<N> {
        Vector2::new(self.copy_sign_to(to.x), self.copy_sign_to(to.y))
    }
}

impl<N: Scalar + Copy + SimdSign<N>> SimdSign<Vector3<N>> for N {
    fn copy_sign_to(self, to: Vector3<N>) -> Vector3<N> {
        Vector3::new(
            self.copy_sign_to(to.x),
            self.copy_sign_to(to.y),
            self.copy_sign_to(to.z),
        )
    }
}

impl<N: Scalar + Copy + SimdSign<N>> SimdSign<Vector2<N>> for Vector2<N> {
    fn copy_sign_to(self, to: Vector2<N>) -> Vector2<N> {
        Vector2::new(self.x.copy_sign_to(to.x), self.y.copy_sign_to(to.y))
    }
}

impl<N: Scalar + Copy + SimdSign<N>> SimdSign<Vector3<N>> for Vector3<N> {
    fn copy_sign_to(self, to: Vector3<N>) -> Vector3<N> {
        Vector3::new(
            self.x.copy_sign_to(to.x),
            self.y.copy_sign_to(to.y),
            self.z.copy_sign_to(to.z),
        )
    }
}

impl SimdSign<SimdReal> for SimdReal {
    fn copy_sign_to(self, to: SimdReal) -> SimdReal {
        to.simd_copysign(self)
    }
}

pub(crate) trait SimdComponent: Sized {
    type Element;

    fn min_component(self) -> Self::Element;
    fn max_component(self) -> Self::Element;
}

impl SimdComponent for Real {
    type Element = Real;

    fn min_component(self) -> Self::Element {
        self
    }
    fn max_component(self) -> Self::Element {
        self
    }
}

impl SimdComponent for SimdReal {
    type Element = Real;

    fn min_component(self) -> Self::Element {
        self.simd_horizontal_min()
    }
    fn max_component(self) -> Self::Element {
        self.simd_horizontal_max()
    }
}

/// Trait to compute the orthonormal basis of a vector.
pub trait SimdBasis: Sized {
    /// The type of the array of orthonormal vectors.
    type Basis;
    /// Computes the vectors which, when combined with `self`, form an orthonormal basis.
    fn orthonormal_basis(self) -> Self::Basis;
    /// Computes a vector orthogonal to `self` with a unit length (if `self` has a unit length).
    fn orthonormal_vector(self) -> Self;
}

impl<N: SimdRealCopy> SimdBasis for Vector2<N> {
    type Basis = [Vector2<N>; 1];
    fn orthonormal_basis(self) -> [Vector2<N>; 1] {
        [Vector2::new(-self.y, self.x)]
    }
    fn orthonormal_vector(self) -> Vector2<N> {
        Vector2::new(-self.y, self.x)
    }
}

impl<N: SimdRealCopy + SimdSign<N>> SimdBasis for Vector3<N> {
    type Basis = [Vector3<N>; 2];
    // Robust and branchless implementation from Pixar:
    // https://graphics.pixar.com/library/OrthonormalB/paper.pdf
    fn orthonormal_basis(self) -> [Vector3<N>; 2] {
        let sign = self.z.copy_sign_to(N::one());
        let a = -N::one() / (sign + self.z);
        let b = self.x * self.y * a;

        [
            Vector3::new(
                N::one() + sign * self.x * self.x * a,
                sign * b,
                -sign * self.x,
            ),
            Vector3::new(b, sign + self.y * self.y * a, -self.y),
        ]
    }

    fn orthonormal_vector(self) -> Vector3<N> {
        let sign = self.z.copy_sign_to(N::one());
        let a = -N::one() / (sign + self.z);
        let b = self.x * self.y * a;
        Vector3::new(b, sign + self.y * self.y * a, -self.y)
    }
}

pub(crate) trait SimdVec: Sized {
    type Element;

    fn horizontal_inf(&self) -> Self::Element;
    fn horizontal_sup(&self) -> Self::Element;
}

impl<N: Scalar + Copy + SimdComponent> SimdVec for Vector2<N>
where
    N::Element: Scalar,
{
    type Element = Vector2<N::Element>;

    fn horizontal_inf(&self) -> Self::Element {
        Vector2::new(self.x.min_component(), self.y.min_component())
    }

    fn horizontal_sup(&self) -> Self::Element {
        Vector2::new(self.x.max_component(), self.y.max_component())
    }
}

impl<N: Scalar + Copy + SimdComponent> SimdVec for Point2<N>
where
    N::Element: Scalar,
{
    type Element = Point2<N::Element>;

    fn horizontal_inf(&self) -> Self::Element {
        Point2::new(self.x.min_component(), self.y.min_component())
    }

    fn horizontal_sup(&self) -> Self::Element {
        Point2::new(self.x.max_component(), self.y.max_component())
    }
}

impl<N: Scalar + Copy + SimdComponent> SimdVec for Vector3<N>
where
    N::Element: Scalar,
{
    type Element = Vector3<N::Element>;

    fn horizontal_inf(&self) -> Self::Element {
        Vector3::new(
            self.x.min_component(),
            self.y.min_component(),
            self.z.min_component(),
        )
    }

    fn horizontal_sup(&self) -> Self::Element {
        Vector3::new(
            self.x.max_component(),
            self.y.max_component(),
            self.z.max_component(),
        )
    }
}

impl<N: Scalar + Copy + SimdComponent> SimdVec for Point3<N>
where
    N::Element: Scalar,
{
    type Element = Point3<N::Element>;

    fn horizontal_inf(&self) -> Self::Element {
        Point3::new(
            self.x.min_component(),
            self.y.min_component(),
            self.z.min_component(),
        )
    }

    fn horizontal_sup(&self) -> Self::Element {
        Point3::new(
            self.x.max_component(),
            self.y.max_component(),
            self.z.max_component(),
        )
    }
}

pub(crate) trait SimdCrossMatrix: Sized {
    type CrossMat;
    type CrossMatTr;

    fn gcross_matrix(self) -> Self::CrossMat;
    fn gcross_matrix_tr(self) -> Self::CrossMatTr;
}

impl<N: SimdRealCopy> SimdCrossMatrix for Vector3<N> {
    type CrossMat = Matrix3<N>;
    type CrossMatTr = Matrix3<N>;

    #[inline]
    #[rustfmt::skip]
    fn gcross_matrix(self) -> Self::CrossMat {
        Matrix3::new(
            N::zero(), -self.z, self.y,
            self.z, N::zero(), -self.x,
            -self.y, self.x, N::zero(),
        )
    }

    #[inline]
    #[rustfmt::skip]
    fn gcross_matrix_tr(self) -> Self::CrossMatTr {
        Matrix3::new(
            N::zero(), self.z, -self.y,
            -self.z, N::zero(), self.x,
            self.y, -self.x, N::zero(),
        )
    }
}

impl<N: SimdRealCopy> SimdCrossMatrix for Vector2<N> {
    type CrossMat = RowVector2<N>;
    type CrossMatTr = Vector2<N>;

    #[inline]
    fn gcross_matrix(self) -> Self::CrossMat {
        RowVector2::new(-self.y, self.x)
    }
    #[inline]
    fn gcross_matrix_tr(self) -> Self::CrossMatTr {
        Vector2::new(-self.y, self.x)
    }
}
impl SimdCrossMatrix for Real {
    type CrossMat = Matrix2<Real>;
    type CrossMatTr = Matrix2<Real>;

    #[inline]
    fn gcross_matrix(self) -> Matrix2<Real> {
        Matrix2::new(0.0, -self, self, 0.0)
    }

    #[inline]
    fn gcross_matrix_tr(self) -> Matrix2<Real> {
        Matrix2::new(0.0, self, -self, 0.0)
    }
}

impl SimdCrossMatrix for SimdReal {
    type CrossMat = Matrix2<SimdReal>;
    type CrossMatTr = Matrix2<SimdReal>;

    #[inline]
    fn gcross_matrix(self) -> Matrix2<SimdReal> {
        Matrix2::new(SimdReal::zero(), -self, self, SimdReal::zero())
    }

    #[inline]
    fn gcross_matrix_tr(self) -> Matrix2<SimdReal> {
        Matrix2::new(SimdReal::zero(), self, -self, SimdReal::zero())
    }
}

pub(crate) trait SimdCross<Rhs>: Sized {
    type Result;
    fn gcross(&self, rhs: Rhs) -> Self::Result;
}

impl SimdCross<Vector3<Real>> for Vector3<Real> {
    type Result = Self;

    fn gcross(&self, rhs: Vector3<Real>) -> Self::Result {
        self.cross(&rhs)
    }
}

impl SimdCross<Vector2<Real>> for Vector2<Real> {
    type Result = Real;

    fn gcross(&self, rhs: Vector2<Real>) -> Self::Result {
        self.x * rhs.y - self.y * rhs.x
    }
}

impl SimdCross<Vector2<Real>> for Real {
    type Result = Vector2<Real>;

    fn gcross(&self, rhs: Vector2<Real>) -> Self::Result {
        Vector2::new(-rhs.y * *self, rhs.x * *self)
    }
}

pub(crate) trait SimdDot<Rhs>: Sized {
    type Result;
    fn gdot(&self, rhs: Rhs) -> Self::Result;
}

impl<N: SimdRealCopy> SimdDot<Vector3<N>> for Vector3<N> {
    type Result = N;

    fn gdot(&self, rhs: Vector3<N>) -> Self::Result {
        self.x * rhs.x + self.y * rhs.y + self.z * rhs.z
    }
}

impl<N: SimdRealCopy> SimdDot<Vector2<N>> for Vector2<N> {
    type Result = N;

    fn gdot(&self, rhs: Vector2<N>) -> Self::Result {
        self.x * rhs.x + self.y * rhs.y
    }
}

impl<N: SimdRealCopy> SimdDot<Vector1<N>> for N {
    type Result = N;

    fn gdot(&self, rhs: Vector1<N>) -> Self::Result {
        *self * rhs.x
    }
}

impl<N: SimdRealCopy> SimdDot<N> for N {
    type Result = N;

    fn gdot(&self, rhs: N) -> Self::Result {
        *self * rhs
    }
}

impl<N: SimdRealCopy> SimdDot<N> for Vector1<N> {
    type Result = N;

    fn gdot(&self, rhs: N) -> Self::Result {
        self.x * rhs
    }
}

impl SimdCross<Vector3<SimdReal>> for Vector3<SimdReal> {
    type Result = Vector3<SimdReal>;

    fn gcross(&self, rhs: Self) -> Self::Result {
        self.cross(&rhs)
    }
}

impl SimdCross<Vector2<SimdReal>> for SimdReal {
    type Result = Vector2<SimdReal>;

    fn gcross(&self, rhs: Vector2<SimdReal>) -> Self::Result {
        Vector2::new(-rhs.y * *self, rhs.x * *self)
    }
}

impl SimdCross<Vector2<SimdReal>> for Vector2<SimdReal> {
    type Result = SimdReal;

    fn gcross(&self, rhs: Self) -> Self::Result {
        let yx = Vector2::new(rhs.y, rhs.x);
        let prod = self.component_mul(&yx);
        prod.x - prod.y
    }
}

/// Trait implemented by quaternions.
pub trait SimdQuat<N> {
    /// The result of quaternion differentiation.
    type Result;

    /// Compute the differential of `inv(q1) * q2`.
    fn diff_conj1_2(&self, rhs: &Self) -> Self::Result;
}

impl<N: SimdRealCopy> SimdQuat<N> for UnitComplex<N> {
    type Result = Matrix1<N>;

    fn diff_conj1_2(&self, rhs: &Self) -> Self::Result {
        let two: N = N::splat(2.0);
        Matrix1::new((self.im * rhs.im + self.re * rhs.re) * two)
    }
}

impl<N: SimdRealCopy> SimdQuat<N> for UnitQuaternion<N> {
    type Result = Matrix3<N>;

    fn diff_conj1_2(&self, rhs: &Self) -> Self::Result {
        let half = N::splat(0.5);
        let v1 = self.imag();
        let v2 = rhs.imag();
        let w1 = self.w;
        let w2 = rhs.w;

        // TODO: this can probably be optimized a lot by unrolling the ops.
        (v1 * v2.transpose() + Matrix3::from_diagonal_element(w1 * w2)
            - (v1 * w2 + v2 * w1).cross_matrix()
            + v1.cross_matrix() * v2.cross_matrix())
            * half
    }
}

pub(crate) trait SimdAngularInertia<N> {
    type AngVector;
    type LinVector;
    type AngMatrix;
    fn inverse(&self) -> Self;
    fn transform_lin_vector(&self, pt: Self::LinVector) -> Self::LinVector;
    fn transform_vector(&self, pt: Self::AngVector) -> Self::AngVector;
    fn squared(&self) -> Self;
    fn transform_matrix(&self, mat: &Self::AngMatrix) -> Self::AngMatrix;
    fn into_matrix(self) -> Self::AngMatrix;
}

impl<N: SimdRealCopy> SimdAngularInertia<N> for N {
    type AngVector = N;
    type LinVector = Vector2<N>;
    type AngMatrix = N;

    fn inverse(&self) -> Self {
        simd_inv(*self)
    }

    fn transform_lin_vector(&self, pt: Vector2<N>) -> Vector2<N> {
        pt * *self
    }
    fn transform_vector(&self, pt: N) -> N {
        pt * *self
    }

    fn squared(&self) -> N {
        *self * *self
    }

    fn transform_matrix(&self, mat: &Self::AngMatrix) -> Self::AngMatrix {
        *mat * *self
    }

    fn into_matrix(self) -> Self::AngMatrix {
        self
    }
}

impl SimdAngularInertia<Real> for SdpMatrix3<Real> {
    type AngVector = Vector3<Real>;
    type LinVector = Vector3<Real>;
    type AngMatrix = Matrix3<Real>;

    fn inverse(&self) -> Self {
        let minor_m12_m23 = self.m22 * self.m33 - self.m23 * self.m23;
        let minor_m11_m23 = self.m12 * self.m33 - self.m13 * self.m23;
        let minor_m11_m22 = self.m12 * self.m23 - self.m13 * self.m22;

        let determinant =
            self.m11 * minor_m12_m23 - self.m12 * minor_m11_m23 + self.m13 * minor_m11_m22;

        if determinant.is_zero() {
            Self::zero()
        } else {
            SdpMatrix3 {
                m11: minor_m12_m23 / determinant,
                m12: -minor_m11_m23 / determinant,
                m13: minor_m11_m22 / determinant,
                m22: (self.m11 * self.m33 - self.m13 * self.m13) / determinant,
                m23: (self.m13 * self.m12 - self.m23 * self.m11) / determinant,
                m33: (self.m11 * self.m22 - self.m12 * self.m12) / determinant,
            }
        }
    }

    fn squared(&self) -> Self {
        SdpMatrix3 {
            m11: self.m11 * self.m11 + self.m12 * self.m12 + self.m13 * self.m13,
            m12: self.m11 * self.m12 + self.m12 * self.m22 + self.m13 * self.m23,
            m13: self.m11 * self.m13 + self.m12 * self.m23 + self.m13 * self.m33,
            m22: self.m12 * self.m12 + self.m22 * self.m22 + self.m23 * self.m23,
            m23: self.m12 * self.m13 + self.m22 * self.m23 + self.m23 * self.m33,
            m33: self.m13 * self.m13 + self.m23 * self.m23 + self.m33 * self.m33,
        }
    }

    fn transform_lin_vector(&self, v: Vector3<Real>) -> Vector3<Real> {
        self.transform_vector(v)
    }

    fn transform_vector(&self, v: Vector3<Real>) -> Vector3<Real> {
        let x = self.m11 * v.x + self.m12 * v.y + self.m13 * v.z;
        let y = self.m12 * v.x + self.m22 * v.y + self.m23 * v.z;
        let z = self.m13 * v.x + self.m23 * v.y + self.m33 * v.z;
        Vector3::new(x, y, z)
    }

    #[rustfmt::skip]
    fn into_matrix(self) -> Matrix3<Real> {
        Matrix3::new(
            self.m11, self.m12, self.m13,
            self.m12, self.m22, self.m23,
            self.m13, self.m23, self.m33,
        )
    }

    #[rustfmt::skip]
    fn transform_matrix(&self, m: &Matrix3<Real>) -> Matrix3<Real> {
        *self * *m
    }
}

impl SimdAngularInertia<SimdReal> for SdpMatrix3<SimdReal> {
    type AngVector = Vector3<SimdReal>;
    type LinVector = Vector3<SimdReal>;
    type AngMatrix = Matrix3<SimdReal>;

    fn inverse(&self) -> Self {
        let minor_m12_m23 = self.m22 * self.m33 - self.m23 * self.m23;
        let minor_m11_m23 = self.m12 * self.m33 - self.m13 * self.m23;
        let minor_m11_m22 = self.m12 * self.m23 - self.m13 * self.m22;

        let determinant =
            self.m11 * minor_m12_m23 - self.m12 * minor_m11_m23 + self.m13 * minor_m11_m22;

        let zero = <SimdReal>::zero();
        let is_zero = determinant.simd_eq(zero);
        let inv_det = (<SimdReal>::one() / determinant).select(is_zero, zero);

        SdpMatrix3 {
            m11: minor_m12_m23 * inv_det,
            m12: -minor_m11_m23 * inv_det,
            m13: minor_m11_m22 * inv_det,
            m22: (self.m11 * self.m33 - self.m13 * self.m13) * inv_det,
            m23: (self.m13 * self.m12 - self.m23 * self.m11) * inv_det,
            m33: (self.m11 * self.m22 - self.m12 * self.m12) * inv_det,
        }
    }

    fn transform_lin_vector(&self, v: Vector3<SimdReal>) -> Vector3<SimdReal> {
        self.transform_vector(v)
    }

    fn transform_vector(&self, v: Vector3<SimdReal>) -> Vector3<SimdReal> {
        let x = self.m11 * v.x + self.m12 * v.y + self.m13 * v.z;
        let y = self.m12 * v.x + self.m22 * v.y + self.m23 * v.z;
        let z = self.m13 * v.x + self.m23 * v.y + self.m33 * v.z;
        Vector3::new(x, y, z)
    }

    fn squared(&self) -> Self {
        SdpMatrix3 {
            m11: self.m11 * self.m11 + self.m12 * self.m12 + self.m13 * self.m13,
            m12: self.m11 * self.m12 + self.m12 * self.m22 + self.m13 * self.m23,
            m13: self.m11 * self.m13 + self.m12 * self.m23 + self.m13 * self.m33,
            m22: self.m12 * self.m12 + self.m22 * self.m22 + self.m23 * self.m23,
            m23: self.m12 * self.m13 + self.m22 * self.m23 + self.m23 * self.m33,
            m33: self.m13 * self.m13 + self.m23 * self.m23 + self.m33 * self.m33,
        }
    }

    #[rustfmt::skip]
    fn into_matrix(self) -> Matrix3<SimdReal> {
        Matrix3::new(
            self.m11, self.m12, self.m13,
            self.m12, self.m22, self.m23,
            self.m13, self.m23, self.m33,
        )
    }

    #[rustfmt::skip]
    fn transform_matrix(&self, m: &Matrix3<SimdReal>) -> Matrix3<SimdReal> {
        let x0 = self.m11 * m.m11 + self.m12 * m.m21 + self.m13 * m.m31;
        let y0 = self.m12 * m.m11 + self.m22 * m.m21 + self.m23 * m.m31;
        let z0 = self.m13 * m.m11 + self.m23 * m.m21 + self.m33 * m.m31;

        let x1 = self.m11 * m.m12 + self.m12 * m.m22 + self.m13 * m.m32;
        let y1 = self.m12 * m.m12 + self.m22 * m.m22 + self.m23 * m.m32;
        let z1 = self.m13 * m.m12 + self.m23 * m.m22 + self.m33 * m.m32;

        let x2 = self.m11 * m.m13 + self.m12 * m.m23 + self.m13 * m.m33;
        let y2 = self.m12 * m.m13 + self.m22 * m.m23 + self.m23 * m.m33;
        let z2 = self.m13 * m.m13 + self.m23 * m.m23 + self.m33 * m.m33;

        Matrix3::new(
            x0, x1, x2,
            y0, y1, y2,
            z0, z1, z2,
        )
    }
}

// This is an RAII structure that enables flushing denormal numbers
// to zero, and automatically reseting previous flags once it is dropped.
#[derive(Clone, Debug, PartialEq, Eq)]
pub(crate) struct FlushToZeroDenormalsAreZeroFlags {
    original_flags: u32,
}

impl FlushToZeroDenormalsAreZeroFlags {
    #[cfg(not(all(
        not(feature = "enhanced-determinism"),
        any(target_arch = "x86_64", target_arch = "x86"),
        target_feature = "sse"
    )))]
    pub fn flush_denormal_to_zero() -> Self {
        Self { original_flags: 0 }
    }

    #[cfg(all(
        not(feature = "enhanced-determinism"),
        any(target_arch = "x86", target_arch = "x86_64"),
        target_feature = "sse"
    ))]
    #[allow(deprecated)] // will address that later.
    pub fn flush_denormal_to_zero() -> Self {
        unsafe {
            #[cfg(target_arch = "x86")]
            use std::arch::x86::{_mm_getcsr, _mm_setcsr, _MM_FLUSH_ZERO_ON};
            #[cfg(target_arch = "x86_64")]
            use std::arch::x86_64::{_mm_getcsr, _mm_setcsr, _MM_FLUSH_ZERO_ON};

            // Flush denormals & underflows to zero as this as a significant impact on the solver's performances.
            // To enable this we need to set the bit 15 (given by _MM_FLUSH_ZERO_ON) and the bit 6 (for denormals-are-zero).
            // See https://software.intel.com/content/www/us/en/develop/articles/x87-and-sse-floating-point-assists-in-ia-32-flush-to-zero-ftz-and-denormals-are-zero-daz.html
            let original_flags = _mm_getcsr();
            _mm_setcsr(original_flags | _MM_FLUSH_ZERO_ON | (1 << 6));
            Self { original_flags }
        }
    }
}

#[cfg(all(
    not(feature = "enhanced-determinism"),
    any(target_arch = "x86", target_arch = "x86_64"),
    target_feature = "sse"
))]
impl Drop for FlushToZeroDenormalsAreZeroFlags {
    #[allow(deprecated)] // will address that later.
    fn drop(&mut self) {
        #[cfg(target_arch = "x86")]
        unsafe {
            std::arch::x86::_mm_setcsr(self.original_flags)
        }
        #[cfg(target_arch = "x86_64")]
        unsafe {
            std::arch::x86_64::_mm_setcsr(self.original_flags)
        }
    }
}

/// This is an RAII structure that disables floating point exceptions while
/// it is alive, so that operations which generate NaNs and infinite values
/// intentionally will not trip an exception when debugging problematic
/// code that is generating NaNs and infinite values erroneously.
#[derive(Clone, Debug, PartialEq, Eq)]
pub(crate) struct DisableFloatingPointExceptionsFlags {
    #[cfg(feature = "debug-disable-legitimate-fe-exceptions")]
    // We can't get a precise size for this, because it's of type
    // `fenv_t`, which is a definition that doesn't exist in rust
    // (not even in the libc crate, as of the time of writing.)
    // But since the state is intended to be stored on the stack,
    // 256 bytes should be more than enough.
    original_flags: [u8; 256],
}

#[cfg(feature = "debug-disable-legitimate-fe-exceptions")]
extern "C" {
    fn feholdexcept(env: *mut std::ffi::c_void);
    fn fesetenv(env: *const std::ffi::c_void);
}

impl DisableFloatingPointExceptionsFlags {
    #[cfg(not(feature = "debug-disable-legitimate-fe-exceptions"))]
    #[allow(dead_code)]
    /// Disables floating point exceptions as long as this object is not dropped.
    pub fn disable_floating_point_exceptions() -> Self {
        Self {}
    }

    #[cfg(feature = "debug-disable-legitimate-fe-exceptions")]
    /// Disables floating point exceptions as long as this object is not dropped.
    pub fn disable_floating_point_exceptions() -> Self {
        unsafe {
            let mut original_flags = [0; 256];
            feholdexcept(original_flags.as_mut_ptr() as *mut _);
            Self { original_flags }
        }
    }
}

#[cfg(feature = "debug-disable-legitimate-fe-exceptions")]
impl Drop for DisableFloatingPointExceptionsFlags {
    fn drop(&mut self) {
        unsafe {
            fesetenv(self.original_flags.as_ptr() as *const _);
        }
    }
}

pub(crate) fn select_other<T: PartialEq>(pair: (T, T), elt: T) -> T {
    if pair.0 == elt {
        pair.1
    } else {
        pair.0
    }
}

/// Methods for simultaneously indexing a container with two distinct indices.
pub trait IndexMut2<I>: IndexMut<I> {
    /// Gets mutable references to two distinct elements of the container.
    ///
    /// Panics if `i == j`.
    fn index_mut2(&mut self, i: usize, j: usize) -> (&mut Self::Output, &mut Self::Output);

    /// Gets a mutable reference to one element, and immutable reference to a second one.
    ///
    /// Panics if `i == j`.
    #[inline]
    fn index_mut_const(&mut self, i: usize, j: usize) -> (&mut Self::Output, &Self::Output) {
        let (a, b) = self.index_mut2(i, j);
        (a, &*b)
    }
}

impl<T> IndexMut2<usize> for Vec<T> {
    #[inline]
    fn index_mut2(&mut self, i: usize, j: usize) -> (&mut T, &mut T) {
        assert!(i != j, "Unable to index the same element twice.");
        assert!(i < self.len() && j < self.len(), "Index out of bounds.");

        unsafe {
            let a = &mut *(self.get_unchecked_mut(i) as *mut _);
            let b = &mut *(self.get_unchecked_mut(j) as *mut _);
            (a, b)
        }
    }
}

impl<T> IndexMut2<usize> for [T] {
    #[inline]
    fn index_mut2(&mut self, i: usize, j: usize) -> (&mut T, &mut T) {
        assert!(i != j, "Unable to index the same element twice.");
        assert!(i < self.len() && j < self.len(), "Index out of bounds.");

        unsafe {
            let a = &mut *(self.get_unchecked_mut(i) as *mut _);
            let b = &mut *(self.get_unchecked_mut(j) as *mut _);
            (a, b)
        }
    }
}

/// Calculate the difference with smallest absolute value between the two given values.
pub fn smallest_abs_diff_between_sin_angles<N: SimdRealCopy>(a: N, b: N) -> N {
    // Select the smallest path among the two angles to reach the target.
    let s_err = a - b;
    let sgn = s_err.simd_signum();
    let s_err_complement = s_err - sgn * N::splat(2.0);
    let s_err_is_smallest = s_err.simd_abs().simd_lt(s_err_complement.simd_abs());
    s_err.select(s_err_is_smallest, s_err_complement)
}

/// Calculate the difference with smallest absolute value between the two given angles.
pub fn smallest_abs_diff_between_angles<N: SimdRealCopy>(a: N, b: N) -> N {
    // Select the smallest path among the two angles to reach the target.
    let s_err = a - b;
    let sgn = s_err.simd_signum();
    let s_err_complement = s_err - sgn * N::simd_two_pi();
    let s_err_is_smallest = s_err.simd_abs().simd_lt(s_err_complement.simd_abs());
    s_err.select(s_err_is_smallest, s_err_complement)
}