g_math 0.4.27

Multi-domain fixed-point arithmetic with geometric extension: Lie groups, manifolds, ODE solvers, tensors, fiber bundles — pure Rust, zero-float, deterministic
Documentation 
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#!/usr/bin/env python3
"""Generate gMath decimal contract-validation golden tables.

Independent mpmath oracle for gMath's DecimalFixed<SCALE> domain. Emits the
same mode-agnostic format used by mootable/decimal-scaled so a single Rust
grader handles both this (oracle #1) and that corpus (oracle #2):

    <input_raw>\t<floor_raw>\t<cls>

  input_raw  storage integer; mathematical value x = input_raw / 10**SCALE.
  floor_raw  floor(f(x) * 10**SCALE), toward negative infinity (sign here).
  cls        fractional class of f(x)*10**SCALE - floor_raw, in [0, 1):
               Z exact, L below-half, E exact-half-tie, G above-half.

NO floats cross the boundary: mpmath computes at high guard precision and we
emit exact integer strings. The Rust side is pure integer arithmetic.

Deterministic: fixed seed, sorted inputs -> byte-identical reruns.

Usage:  python3 scripts/gen_decimal_golden.py
"""
from __future__ import annotations

import random
from pathlib import Path

from mpmath import mp, mpf, floor as mp_floor, exp, ln, sqrt, sin

# Scale 28 lands on decimal-scaled's d38_s28 grid point (both i128), so the
# phase-2 second-oracle comparison is apples-to-apples at the same grid cell.
SCALE = 28
SCALE_POW = 10 ** SCALE
I128_MAX = (1 << 127) - 1
# Stay clear of the i128 edge so neither input_raw nor floor_raw overflows.
RANGE_LIMIT = mpf(I128_MAX) / mpf(SCALE_POW) * mpf("0.95")  # ~1.6e10

# Guard precision: far wider than the storage scale so L/E/G is unambiguous.
mp.dps = 2 * SCALE + 80

OUT_DIR = Path(__file__).resolve().parent.parent / "tests" / "oracle_golden"
PER_FUNC = 64


def floor_and_class(value: mpf) -> tuple[int, str] | None:
    """(floor_raw, cls) for value at SCALE, or None if it leaves i128 range."""
    scaled = value * mpf(SCALE_POW)
    if abs(scaled) >= mpf(I128_MAX):
        return None
    floor_int = int(mp_floor(scaled))
    frac = scaled - mpf(floor_int)
    half = mpf("0.5")
    if frac == 0:
        cls = "Z"
    elif frac < half:
        cls = "L"
    elif frac == half:
        cls = "E"
    else:
        cls = "G"
    return floor_int, cls


def to_raw(x: mpf) -> int:
    """Storage integer for input value x (round to nearest, ties away)."""
    scaled = x * mpf(SCALE_POW)
    floor_int = int(mp_floor(scaled))
    frac = scaled - mpf(floor_int)
    return floor_int + 1 if frac >= mpf("0.5") else floor_int


def gen_inputs(name: str, rng: random.Random) -> list[mpf]:
    """In-range, well-conditioned input values for one function."""
    xs: list[mpf] = []
    if name == "exp":
        # output exp(x) must stay < RANGE_LIMIT  ->  x < ln(RANGE_LIMIT) ~ 23.5
        hi = float(ln(RANGE_LIMIT))
        xs += [mpf(rng.uniform(-hi, hi)) for _ in range(PER_FUNC - 4)]
        xs += [mpf(0), mpf("0.5"), mpf(-1), mpf(1)]
    elif name == "ln":
        # x in (0, RANGE_LIMIT); output ln(x) within range for x > ~5e-9
        lo, hi = -20.0, float(ln(RANGE_LIMIT))
        xs += [exp(mpf(rng.uniform(lo, hi))) for _ in range(PER_FUNC - 3)]
        xs += [mpf(1), mpf(2), mpf("0.5")]
    elif name == "sqrt":
        hi = float(RANGE_LIMIT)
        xs += [mpf(rng.uniform(0, hi)) for _ in range(PER_FUNC - 4)]
        # perfect squares -> exact (Z) coverage
        xs += [mpf(4), mpf(9), mpf("2.25"), mpf(0)]
    elif name == "sin":
        xs += [mpf(rng.uniform(-20.0, 20.0)) for _ in range(PER_FUNC - 3)]
        xs += [mpf(0), mpf(1), mpf(-1)]
    else:
        raise ValueError(name)
    return xs


FUNCS = {"exp": exp, "ln": ln, "sqrt": sqrt, "sin": sin}


def main() -> None:
    OUT_DIR.mkdir(parents=True, exist_ok=True)
    for name, fn in FUNCS.items():
        rng = random.Random(f"gmath-decimal-golden-{name}-s{SCALE}")
        rows: list[tuple[int, int, str]] = []
        seen: set[int] = set()
        for x in gen_inputs(name, rng):
            raw = to_raw(x)
            if raw in seen:
                continue
            seen.add(raw)
            xv = mpf(raw) / mpf(SCALE_POW)
            if name in ("ln", "sqrt") and xv < 0:
                continue
            if name == "ln" and xv == 0:
                continue
            res = floor_and_class(fn(xv))
            if res is None:
                continue  # out of representable range; skip
            floor_raw, cls = res
            rows.append((raw, floor_raw, cls))
        rows.sort()
        path = OUT_DIR / f"{name}_s{SCALE}.txt"
        with path.open("w") as f:
            f.write("# gMath decimal contract golden table (oracle #1)\n")
            f.write("# generated by scripts/gen_decimal_golden.py\n")
            f.write(f"# function={name}  scale={SCALE}  guard_dps={mp.dps}\n")
            f.write("# each line: <input_raw>\\t<floor_raw>\\t<cls>\n")
            f.write("# value x = input_raw / 10**scale; "
                    "floor_raw = floor(f(x)*10**scale) toward -inf;\n")
            f.write("# cls: Z exact, L below-half, E half-tie, G above-half.\n")
            for raw, floor_raw, cls in rows:
                f.write(f"{raw}\t{floor_raw}\t{cls}\n")
        print(f"{path.name}: {len(rows)} rows")


if __name__ == "__main__":
    main()