decimal-scaled 0.4.2

Const-generic base-10 fixed-point decimals (D9/D18/D38/D76/D153/D307) with integer-only transcendentals correctly rounded to within 0.5 ULP — exact at the type's last representable place. Deterministic across every platform; no_std-friendly.
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79

//! Bespoke narrow-`GUARD` `sinh_strict` / `cosh_strict` /
//! `tanh_strict` kernel slot for `D115<SCALE>` with `SCALE = 57`.
//!
//! Direct port of [`crate::algos::trig::lookup_d57_s18_22_hyper`].
//! Shares the Tang-style exp from
//! [`crate::algos::exp::lookup_d115_s57_tang`] and avoids the second
//! `exp_fixed` call via the `1/eˣ` reciprocal identity.
//!
//! ## Algorithm
//!
//! ```text
//! ex  = exp(v)
//! enx = 1 / ex          (exp(-v) identity)
//! sinh = (ex - enx) / 2
//! cosh = (ex + enx) / 2
//! tanh = (ex - enx) / (ex + enx)
//! ```
//!
//! ## Correctness
//!
//! Per-op error at working scale `w = SCALE + 8 = 65` is bounded by
//! ~15 LSB-of-w (one Tang exp ≤ ~12 LSB + reciprocal + add/sub +
//! /2 + final round). At w=65 that's `~1.5·10⁻⁶⁴`; storage half-ULP
//! at SCALE=57 is `5·10⁻⁵⁸`, so the budget closes with ~6 orders to
//! spare.

#![cfg(any(feature = "d115", feature = "wide"))]

use crate::types::widths::wide_trig_d115 as core;
use crate::support::rounding::RoundingMode;
use crate::wide_int::Int384;

/// Narrow guard for the SCALE = 57 hyperbolic slot. Matches the Tang
/// exp narrow guard so the `pow10_cached(w)` slot is shared.
const GUARD_NARROW: u32 = 8;

/// Joint `(ex, enx)` pair via one Tang exp + one reciprocal divide.
#[inline]
fn ex_enx(v: core::W, w: u32) -> (core::W, core::W) {
    let ex = crate::algos::exp::lookup_d115_s57_tang::tang_exp_fixed(v, w);
    let one_w = core::one(w);
    let enx = core::div(one_w, ex, w);
    (ex, enx)
}

/// `sinh_strict` for `D115<SCALE>` with `SCALE = 57`.
#[inline]
#[must_use]
pub(crate) fn sinh_strict<const SCALE: u32>(raw: Int384, mode: RoundingMode) -> Int384 {
    let w = SCALE + GUARD_NARROW;
    let v = core::to_work_w(raw, GUARD_NARROW);
    let (ex, enx) = ex_enx(v, w);
    let two = core::lit(2);
    let r = (ex - enx) / two;
    core::round_to_storage_with(r, w, SCALE, mode)
}

/// `cosh_strict` for `D115<SCALE>` with `SCALE = 57`.
#[inline]
#[must_use]
pub(crate) fn cosh_strict<const SCALE: u32>(raw: Int384, mode: RoundingMode) -> Int384 {
    let w = SCALE + GUARD_NARROW;
    let v = core::to_work_w(raw, GUARD_NARROW);
    let (ex, enx) = ex_enx(v, w);
    let two = core::lit(2);
    let r = (ex + enx) / two;
    core::round_to_storage_with(r, w, SCALE, mode)
}

/// `tanh_strict` for `D115<SCALE>` with `SCALE = 57`.
#[inline]
#[must_use]
pub(crate) fn tanh_strict<const SCALE: u32>(raw: Int384, mode: RoundingMode) -> Int384 {
    let w = SCALE + GUARD_NARROW;
    let v = core::to_work_w(raw, GUARD_NARROW);
    let (ex, enx) = ex_enx(v, w);
    let r = core::div(ex - enx, ex + enx, w);
    core::round_to_storage_with(r, w, SCALE, mode)
}