tract-linalg 0.23.7

#![allow(clippy::excessive_precision)]
use tract_data::internal::*;

/// The input clamp of the f32 sigmoid fit, shared by [`ssigmoid`] and by the SiLU kernels
/// built on the same coefficients.
///
/// It alone holds the result inside `[0, 1]`, so a SiLU kernel needs it as the floor of
/// the factor its sigmoid multiplies. See [`ssigmoid`] for what fixes its value.
pub const LOW: f32 = -14.5;

/// f32 sigmoid, as a rational minimax fit of `sigmoid(x) - 0.5` over `[LOW, HIGH]`.
///
/// The clamp keeps the `[0, 1]` range consumers rely on without an output clamp: on either
/// tail `p / q` approaches ±0.5 and the `+ 0.5` cancels against it, so the cancellation
/// has to stay above the ~6e-8 f32 rounding error of `p / q` rather than run down to zero.
/// At `±14.5` the sum keeps six f32 steps of margin at both ends for every f32 input. It
/// costs the tails their last few ulps — a saturated input returns `1 - 4.8e-7` or
/// `4.8e-7`, not exactly 1 or 0. NaN propagates.
///
/// Raising the clamp voids this: `1 - sigmoid(16.29)` is already under the rounding error,
/// so the sum crosses 1 at scattered inputs from there up. `14.5` rather than something
/// nearer 16 because the value is shared, and `armv7neon_sigmoid_f32_4n` crosses from
/// 15.92 — it refines a `vrecpe` estimate instead of dividing.
pub fn ssigmoid(x: f32) -> f32 {
    const HIGH: f32 = -LOW;

    const ALPHA_13: f32 = -4.433153405e-18;
    const ALPHA_11: f32 = 1.169974371e-14;
    const ALPHA_9: f32 = -1.875289645e-11;
    const ALPHA_7: f32 = 4.257889523e-8;
    const ALPHA_5: f32 = 0.00004811817576;
    const ALPHA_3: f32 = 0.008163842030;
    const ALPHA_1: f32 = 0.2499999971;
    const BETA_6: f32 = 3.922935744e-6;
    const BETA_4: f32 = 0.001524872358;
    const BETA_2: f32 = 0.1159886749;
    const BETA_0: f32 = 1.0;

    let x = x.clamp(LOW, HIGH);

    let x2 = x * x;

    let p = ALPHA_13;
    let p = x2 * p + ALPHA_11;
    let p = x2 * p + ALPHA_9;
    let p = x2 * p + ALPHA_7;
    let p = x2 * p + ALPHA_5;
    let p = x2 * p + ALPHA_3;
    let p = x2 * p + ALPHA_1;
    let p = p * x;

    let q = BETA_6;
    let q = x2 * q + BETA_4;
    let q = x2 * q + BETA_2;
    let q = x2 * q + BETA_0;

    p / q + 0.5
}

/// f16 sigmoid, as a rational minimax fit of `sigmoid(x) - 0.5` over `[LOW, HIGH]`.
///
/// Needs no output clamp, like [`ssigmoid`]: the `+ 0.5` cancellation stays inside
/// (0, 1) for every non-NaN f16 input, whatever the clamp.
pub fn hsigmoid(x: f16) -> f16 {
    /*
     * (x (0.249895 + x^2 (0.00400222 - 0.0000124702 x^2)))
     * /
     * (1. + 0.098734 x^2)
     */

    const LOW: f16 = f16::from_f32_const(-6.92);
    const HIGH: f16 = f16::from_f32_const(6.92);

    const ALPHA_5: f16 = f16::from_f32_const(-0.0000124702);
    const ALPHA_3: f16 = f16::from_f32_const(0.00400222);
    const ALPHA_1: f16 = f16::from_f32_const(0.249895);

    const BETA_2: f16 = f16::from_f32_const(0.098734);
    const BETA_0: f16 = f16::from_f32_const(1.0);

    let x = x.clamp(LOW, HIGH);

    let x2 = x * x;

    let p = ALPHA_5;
    let p = x2 * p + ALPHA_3;
    let p = x2 * p + ALPHA_1;
    let p = p * x;

    let q = BETA_2;
    let q = x2 * q + BETA_0;

    p / q + f16::from_f32_const(0.5)
}

routine_ew_rust!(generic;
    f32,
    generic_sigmoid_f32_4n,
    4,
    4,
    fn run(x: &mut [f32], _: ()) {
        debug_assert!(x.len() % Self::nr() == 0);
        debug_assert!(x.as_ptr() as usize % Self::alignment_bytes() == 0);
        x.iter_mut().for_each(|px| *px = ssigmoid(*px))
    },
    func(Sigmoid)
);

routine_ew_rust!(generic;
    f16,
    generic_sigmoid_f16_8n,
    8,
    8,
    fn run(x: &mut [f16], _: ()) {
        debug_assert!(x.len() % Self::nr() == 0);
        debug_assert!(x.as_ptr() as usize % Self::alignment_bytes() == 0);
        x.iter_mut().for_each(|px| *px = hsigmoid(*px))
    },
    func(Sigmoid)
);