g_math 0.6.4

#!/usr/bin/env python3
"""References for the Q64.64 wide tier and the exact decimal-literal parser
(tests/data/wide_q64_refs.rs).

  - exp / ln / sin / cos: Q64.64 inputs and the nearest Q64.64 integer to the
    true result, computed with mpmath at 120 significant digits. sin/cos inputs
    are grouped in magnitude bands, because range reduction by a 64-bit pi/2
    loses accuracy as |x| grows.
  - decimal literals: strings (plain, exponent notation, constructed ties,
    range edges) and the raw each must parse to, `floor(v * 2^F + 1/2)` of
    the exact rational value (nearest, ties toward +infinity), or None where
    it does not fit. Wide (i128) cases for several F; storage cases for every
    profile, realtime at FRAC_BITS 16 and 10.
  - rms_norm_factor_eps_wide: 1 / sqrt(eps_c) for an all-zero vector, eps_c
    the Q64.64 epsilon rounded to each profile's compute tier.
Deterministic: fixed seed; no floating-point arithmetic in the references.

Usage: python3 scripts/generate_wide_refs.py
"""
import random
from fractions import Fraction

from mpmath import mp, mpf, exp, log, sin, cos, sqrt, nint

mp.dps = 120
SEED = 20260924
ONE = 1 << 64

PROFILES = [
    # (name, storage width W, fraction bits F); realtime: every GMATH_FRAC_BITS
    *[(f"REALTIME_F{F}", 32, F) for F in range(2, 31)],
    ("COMPACT", 64, 32),
    ("EMBEDDED", 128, 64),
    ("BALANCED", 256, 128),
    ("SCIENTIFIC", 512, 256),
]
WIDE_FRAC_BITS = [0, 1, 10, 16, 20, 32, 52, 64, 100, 126, 127]


def q64(v):
    return int(nint(v * ONE))


def nearest_up(v, f):
    """floor(v * 2^f + 1/2) for a Fraction v: nearest, ties toward +inf."""
    t = v * (1 << f) + Fraction(1, 2)
    return t.numerator // t.denominator


def decimal_of(v):
    """Exact decimal string of a Fraction whose denominator is 2^a 5^b."""
    sign = "-" if v < 0 else ""
    v = abs(v)
    digits = 0
    while (v * 10 ** digits).denominator != 1:
        digits += 1
    n = int(v * 10 ** digits)
    if digits == 0:
        return f"{sign}{n}"
    s = str(n).rjust(digits + 1, "0")
    return f"{sign}{s[:-digits]}.{s[-digits:]}"


def literal_value(s):
    """Exact Fraction of a literal in the parser grammar."""
    s = s.strip()
    mant, _, e = s.replace("E", "e").partition("e")
    neg = mant.startswith("-")
    mant = mant.lstrip("+-")
    ip, _, fp = mant.partition(".")
    v = Fraction(int((ip or "0") + (fp or "")), 10 ** len(fp))
    v *= Fraction(10) ** int(e or "0")
    return -v if neg else v


def random_literal(rng, max_int_digits):
    int_len = rng.randint(0, max_int_digits)
    frac_len = rng.randint(0, 45)
    ip = "".join(rng.choice("0123456789") for _ in range(int_len))
    fp = "".join(rng.choice("0123456789") for _ in range(frac_len))
    if not ip and not fp:
        ip = "0"
    form = rng.randint(0, 5)
    if form == 0 and ip:
        body = f"{ip}."
    elif form == 1 and fp:
        body = f".{fp}"
    else:
        body = f"{ip or '0'}.{fp}" if fp else (ip or "0")
    if rng.random() < 0.3:
        e = rng.randint(-40, 3)
        body += rng.choice("eE") + (str(e) if e < 0 else rng.choice(["", "+"]) + str(e))
    return rng.choice(["", "", "-", "+"]) + body


def literal_cases(rng, width, f, count):
    """(literal, expected raw or None) for a width-bit raw with f frac bits."""
    lo, hi = -(1 << (width - 1)), (1 << (width - 1)) - 1
    int_digits = max(1, (width - 1 - f) * 30103 // 100000)
    lits = [random_literal(rng, int_digits) for _ in range(count)]
    half = Fraction(1, 1 << (f + 1))
    ulp = Fraction(1, 1 << f)
    tiny = Fraction(1, 10 ** (f + 10))
    for _ in range(12):
        k = rng.randrange(0, 1 << min(width - 2, 40))
        tie = k * ulp + half
        for v in (tie, -tie, tie + tiny, tie - tiny, -tie - tiny, -tie + tiny):
            lits.append(decimal_of(v) if (v * 10 ** (f + 11)).denominator == 1 else None)
        # the exact tie with trailing zeros and in exponent form
        lits.append(decimal_of(tie) + "000")
        d = decimal_of(tie)
        if "." in d:
            ip, fp = d.split(".")
            lits.append(f"{ip}{fp}e-{len(fp)}")
    top = Fraction(hi, 1 << f)
    bottom = Fraction(lo, 1 << f)
    for v in (top, top + half, top + half - tiny, bottom, bottom - half, bottom - half - tiny):
        lits.append(decimal_of(v) if (v * 10 ** (f + 11)).denominator == 1 else None)
    lits += ["0", "-0", "0.0", "-0.000", "00012.5000", "  1.5  ", "1e400", "-1e400", "1e-400", "-1e-400",
             "1e-06", "1e-05", "1E6", "6.283185307179586476925286766559"]
    out = []
    for s in lits:
        if s is None:
            continue
        r = nearest_up(literal_value(s), f)
        out.append((s, r if lo <= r <= hi else None))
    return out


def rust_i128(v):
    return f"{v}" if v >= 0 else f"-{-v}"


def main():
    rng = random.Random(SEED)
    lines = [
        "// Generated by scripts/generate_wide_refs.py - do not edit.",
        "// mpmath 120 significant digits (transcendentals); exact fractions.Fraction",
        "// (literals: nearest, ties toward +infinity).",
        "",
    ]

    # ---- exp -------------------------------------------------------------
    xs = [rng.randrange(-40 * ONE, 41 * ONE) for _ in range(600)]
    xs += [rng.randrange(-ONE, ONE) >> rng.randint(0, 60) for _ in range(150)]
    xs += [k * ONE + d for k in range(-40, 41, 7) for d in (-1, 1, 1 << 40)]
    xs = [x for x in xs if -40 * ONE <= x < 41 * ONE]
    lines.append("/// (x, nearest Q64.64 of e^x), x in [-40, 41).")
    lines.append("pub const EXP: &[(i128, i128)] = &[")
    for x in xs:
        lines.append(f"    ({rust_i128(x)}, {rust_i128(q64(exp(mpf(x) / ONE)))}),")
    lines.append("];\n")

    # ---- ln --------------------------------------------------------------
    xs = []
    for _ in range(700):
        bits = rng.randint(1, 127)
        xs.append(rng.randrange(1 << (bits - 1), (1 << bits) if bits < 127 else (1 << 127) - 1))
    xs += [1, 2, ONE - 1, ONE + 1, (1 << 127) - 1]
    lines.append("/// (x, nearest Q64.64 of ln x), x > 0.")
    lines.append("pub const LN: &[(i128, i128)] = &[")
    for x in xs:
        lines.append(f"    ({rust_i128(x)}, {rust_i128(q64(log(mpf(x) / ONE)))}),")
    lines.append("];\n")

    # ---- sin / cos -------------------------------------------------------
    bands = [
        ("SINCOS_0_2PI", 0, q64(2 * mp.pi)),
        ("SINCOS_2PI_2P12", q64(2 * mp.pi), 1 << (64 + 12)),
        ("SINCOS_2P12_2P20", 1 << (64 + 12), 1 << (64 + 20)),
        ("SINCOS_2P20_2P32", 1 << (64 + 20), 1 << (64 + 32)),
        ("SINCOS_2P32_2P62", 1 << (64 + 32), 1 << (64 + 62)),
    ]
    for name, lo, hi in bands:
        lines.append(f"/// (x, nearest Q64.64 of sin x, of cos x), |x| in [{name}).")
        lines.append(f"pub const {name}: &[(i128, i128, i128)] = &[")
        for _ in range(300):
            x = rng.randrange(lo, hi) * rng.choice([1, -1])
            v = mpf(x) / ONE
            lines.append(f"    ({rust_i128(x)}, {rust_i128(q64(sin(v)))}, {rust_i128(q64(cos(v)))}),")
        lines.append("];\n")

    # ---- literals: wide ----------------------------------------------------
    lines.append("/// (literal, frac_bits, i128 raw or None = TierOverflow).")
    lines.append("pub const LITERALS_WIDE: &[(&str, u32, Option<i128>)] = &[")
    for f in WIDE_FRAC_BITS:
        for s, r in literal_cases(rng, 128, f, 250):
            lines.append(f"    ({s!r}, {f}, {'None' if r is None else f'Some({rust_i128(r)})'}),".replace("'", '"'))
    lines.append("];\n")

    # ---- literals: storage -------------------------------------------------
    lines.append("/// (literal, raw as (negative, hex magnitude), or None = TierOverflow).")
    lines.append("pub type Storage = (&'static str, Option<(bool, &'static str)>);\n")
    for name, width, f in PROFILES:
        lines.append(f"pub const {name}_LITERALS: &[Storage] = &[")
        for s, r in literal_cases(rng, width, f, 250):
            ref = "None" if r is None else f'Some(({"true" if r < 0 else "false"}, "{abs(r):x}"))'
            lines.append(f'    ("{s}", {ref}),')
        lines.append("];\n")

    # ---- rms_norm_factor_eps_wide on an all-zero vector ---------------------
    eps_q64 = {e: nearest_up(Fraction(e), 64) for e in ("1e-5", "1e-6")}
    lines.append("/// Q64.64 epsilons (nearest, ties toward +inf).")
    for e, v in eps_q64.items():
        lines.append(f"pub const EPS_{e.replace('-', '_M').upper().replace('.', '_')}_Q64: i128 = {v};")
    lines.append("")
    lines.append("/// (epsilon literal, exact 1/sqrt(eps_c) at 100 digits) per profile, eps_c the")
    lines.append("/// Q64.64 epsilon rounded to the compute tier (2F bits, nearest ties toward +inf).")
    for name, width, f in PROFILES:
        cf = 2 * f
        lines.append(f"pub const {name}_RMS_ZERO: &[(&str, &str)] = &[")
        for e, v in eps_q64.items():
            if cf < 64:
                t = Fraction(v, 1 << (64 - cf)) + Fraction(1, 2)
                eps_c = Fraction(t.numerator // t.denominator, 1 << cf)
            else:
                eps_c = Fraction(v, 1 << 64)
            if eps_c == 0:
                # the epsilon rounds to zero at the compute tier: no 1/sqrt
                lines.append(f'    ("{e}", "DivisionByZero"),')
                continue
            r = 1 / sqrt(mpf(eps_c.numerator) / eps_c.denominator)
            lines.append(f'    ("{e}", "{mp.nstr(r, 100, strip_zeros=False)}"),')
        lines.append("];\n")

    arms = " ".join(f"{F} => REALTIME_F{F}_LITERALS," for F in range(2, 31))
    lines.append("/// The realtime literal table for the build's split.")
    lines.append(f"pub const REALTIME_LITERALS: &[Storage] = match g_math::fixed_point::frac_config::FRAC_BITS {{ {arms} _ => &[] }};")
    arms = " ".join(f"{F} => REALTIME_F{F}_RMS_ZERO," for F in range(2, 31))
    lines.append("/// The realtime rms table for the build's split.")
    lines.append(f"pub const REALTIME_RMS_ZERO: &[(&str, &str)] = match g_math::fixed_point::frac_config::FRAC_BITS {{ {arms} _ => &[] }};")
    lines.append("")
    with open("tests/data/wide_q64_refs.rs", "w") as fh:
        fh.write("\n".join(lines))


if __name__ == "__main__":
    main()