decimal-scaled 0.5.0

// SPDX-FileCopyrightText: 2026 John Moxley
// SPDX-License-Identifier: MIT OR Apache-2.0

//! Baked Newton-reciprocal table for the `/10^scale` rescale.
//!
//! `r(s) = floor(2^(64*k) / 10^s)`, `k = even(width + s/19 + 3)`, stored
//! little-endian u64 at the widest working width (96 u64 limbs = Int<96>,
//! the AGM working width). A narrower `w`-limb tier reads the HIGH
//! `k_w + 1` limbs: `r_w(s) = r_96(s) >> 64*(96 - w)` (an exact prefix —
//! the reciprocal of `10^s` is one number, truncated to fewer limbs at
//! narrower widths), so all tiers SHARE one per-scale reciprocal.
//!
//! Compile-time read-only data (architectural-review Class K — NOT a
//! runtime cache); size-local consumption via the width slice. GENERATED
//! by `scripts/gen_newton_recip_table.py` — do not edit by hand.

/// Widest baked working width, in u64 limbs (Int<96> = the AGM width).
#[cfg(any(feature = "x-wide", feature = "xx-wide"))]
pub(crate) const NEWTON_RECIP_MAX_W: usize = 132;
/// Highest baked scale (inclusive).
#[cfg(any(feature = "x-wide", feature = "xx-wide"))]
pub(crate) const NEWTON_RECIP_MAX_SCALE: u32 = 1850;

#[cfg(any(feature = "x-wide", feature = "xx-wide"))]
#[rustfmt::skip]
static NEWTON_RECIP: [&[u64]; 1851] = [
    &[0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000001],
    &[0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x9999999999999999, 0x1999999999999999, 0x0000000000000000],
    &[0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0xc28f5c28f5c28f5c, 0x5c28f5c28f5c28f5, 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0x028f5c28f5c28f5c, 0x0000000000000000],
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/// `floor(2^(64*k) / 10^scale)` little-endian for a `width_limbs`-limb
/// working integer (`k = even(width_limbs + scale/19 + 3)`), or `None` if
/// outside the baked range (`scale > MAX_SCALE` / `width > MAX_W`), where
/// the caller falls back to the runtime reciprocal / MgChain.
#[inline]
pub(crate) fn newton_recip_le(scale: u32, width_limbs: usize) -> Option<&'static [u64]> {
    // The table is gated behind the wide features (size-local: the narrow /
    // base build never reaches the wide rescale). Absent => `None` => the
    // caller falls back to the runtime reciprocal / MgChain.
    #[cfg(any(feature = "x-wide", feature = "xx-wide"))]
    {
        if scale <= NEWTON_RECIP_MAX_SCALE && width_limbs <= NEWTON_RECIP_MAX_W {
            // High `k_w + 1` limbs of the width-96 reciprocal (drop the low
            // `96 - width_limbs`): r_w = r_96 >> 64*(96 - width_limbs).
            return Some(&NEWTON_RECIP[scale as usize][NEWTON_RECIP_MAX_W - width_limbs..]);
        }
    }
    let _ = (scale, width_limbs);
    None
}