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//! The engine's arbitrary-precision signed integer — the foundation for a
//! conformant `BigInt`.
//!
//! This is a thin wrapper over [`puremp::Int`] (the Karpelès Lab pure-Rust
//! multi-precision maths crate), preserving a small, `BigInt`-focused API so the
//! rest of the engine is decoupled from the backend. `puremp::Int` provides the
//! semantically-critical operations directly: truncated (toward-zero) division
//! (`div_rem`), two's-complement bitwise ops, and radix I/O. No `unsafe`, no
//! foreign code; `no_std` + `alloc`.
use alloc::string::String;
use core::cmp::Ordering;
use puremp::Int;
/// An arbitrary-precision signed integer.
#[derive(Clone, PartialEq, Eq, Debug, Default)]
pub struct BigInt(Int);
impl BigInt {
/// Zero.
#[must_use]
pub fn zero() -> Self {
Self(Int::from(0i32))
}
/// Whether this is zero.
#[must_use]
pub fn is_zero(&self) -> bool {
self.0.is_zero()
}
/// Whether this is strictly negative.
#[must_use]
pub fn is_negative(&self) -> bool {
self.0.is_negative()
}
/// Builds from an `i128`.
#[must_use]
pub fn from_i128(v: i128) -> Self {
Self(Int::from_i128(v))
}
/// Converts to the nearest `f64` (overflowing to ±∞ for huge magnitudes),
/// with correct round-to-nearest-even. For any value that fits in an `i128`
/// (magnitude < 2^127) we route through Rust's `i128 as f64`, which is IEEE
/// correctly-rounded; the backend's own conversion can round the wrong way at
/// a tie's neighbour (e.g. `Number(8692288669465520373761n)`), so it is only a
/// fallback for the rare > 2^127 magnitudes.
#[must_use]
pub fn to_f64(&self) -> f64 {
match self.to_i128() {
Some(v) => v as f64,
None => self.0.to_f64(),
}
}
/// Converts to an `i128` if it fits, else `None`.
#[must_use]
pub fn to_i128(&self) -> Option<i128> {
i128::try_from(&self.0).ok()
}
/// The low 64 bits of the value in two's-complement, regardless of magnitude
/// (the `BigInt64Array`/`BigUint64Array` element encoding: `ToBigInt64` /
/// `ToBigUint64` keep only the low 64 bits). For a negative value this is the
/// wrapped two's-complement bit pattern (`(-1n) -> 0xFFFF_FFFF_FFFF_FFFF`).
#[must_use]
pub fn to_u64_wrapping(&self) -> u64 {
// `mod_2k(64)` is the non-negative residue mod 2^64 — exactly the
// two's-complement low 64 bits — so it always fits a `u64`.
u64::try_from(&self.0.mod_2k(64)).unwrap_or(0)
}
/// Returns `self + other`.
#[must_use]
pub fn add(&self, other: &Self) -> Self {
Self(self.0.add(&other.0))
}
/// Returns `-self`.
#[must_use]
pub fn neg(&self) -> Self {
Self(self.0.neg())
}
/// Returns `self - other`.
#[must_use]
pub fn sub(&self, other: &Self) -> Self {
Self(self.0.sub(&other.0))
}
/// Returns `self * other`.
#[must_use]
pub fn mul(&self, other: &Self) -> Self {
Self(self.0.mul(&other.0))
}
/// Returns `(quotient, remainder)` with truncated (toward-zero) division;
/// the remainder takes the dividend's sign. Returns `None` on divide-by-zero.
#[must_use]
pub fn divmod(&self, other: &Self) -> Option<(Self, Self)> {
// `div_rem` is truncated (toward-zero): the remainder takes the
// dividend's sign, matching BigInt `/` and `%`. `None` on divide-by-zero.
self.0.div_rem(&other.0).map(|(q, r)| (Self(q), Self(r)))
}
/// Bitwise AND (two's-complement).
#[must_use]
pub fn bitand(&self, other: &Self) -> Self {
Self(self.0.bitand(&other.0))
}
/// Bitwise OR (two's-complement).
#[must_use]
pub fn bitor(&self, other: &Self) -> Self {
Self(self.0.bitor(&other.0))
}
/// Bitwise XOR (two's-complement).
#[must_use]
pub fn bitxor(&self, other: &Self) -> Self {
Self(self.0.bitxor(&other.0))
}
/// The number of bits in the magnitude (0 for zero) — i.e.
/// `floor(log2(|n|)) + 1`. Used to bound the projected size of a `pow`/shift
/// result before growing it, so an attacker exponent cannot drive an OOM.
#[must_use]
pub fn bit_len(&self) -> u64 {
u64::from(self.0.bit_len())
}
/// Like [`pow`](Self::pow), but refuses to build a result larger than
/// `max_bits` bits, returning `None` instead. The result of `self ** exp`
/// has roughly `bit_len(self) * exp` bits, so this rejects the allocation
/// up front — a defense-in-depth guard so no caller can trigger a
/// multi-gigabyte allocation bomb (MEM-6). Computes `pow(exp)` when within
/// bounds.
#[must_use]
pub fn try_pow(&self, exp: u64, max_bits: u64) -> Option<Self> {
if self.bit_len().saturating_mul(exp) > max_bits {
return None;
}
Some(self.pow(exp))
}
/// Returns `self ** exp` (non-negative exponent) by binary exponentiation.
#[must_use]
pub fn pow(&self, exp: u64) -> Self {
// `puremp::Int::pow` takes a `u32`; a `u64` exponent large enough to
// overflow it is always rejected by `try_pow`'s `max_bits` guard first,
// but fall back to binary exponentiation so any exponent stays correct.
if let Ok(e) = u32::try_from(exp) {
return Self(self.0.pow(e));
}
let mut result = Self::from_i128(1);
let mut base = self.clone();
let mut exp = exp;
while exp > 0 {
if exp & 1 == 1 {
result = result.mul(&base);
}
exp >>= 1;
if exp > 0 {
base = base.mul(&base);
}
}
result
}
/// Renders in `radix` (2..=36), with a leading `-` when negative.
#[must_use]
pub fn to_str_radix(&self, radix: u32) -> String {
debug_assert!((2..=36).contains(&radix));
let mut s = String::new();
// `write_radix` into a `String` is infallible.
let _ = self.0.write_radix(&mut s, radix);
s
}
/// Parses `s` in `radix` (2..=36); an optional leading `-`/`+` is allowed.
/// Returns `None` on an invalid digit.
#[must_use]
pub fn from_str_radix(s: &str, radix: u32) -> Option<Self> {
Int::from_str_radix(s.trim(), radix).ok().map(Self)
}
}
impl Ord for BigInt {
/// Signed comparison.
fn cmp(&self, other: &Self) -> Ordering {
self.0.cmp(&other.0)
}
}
impl PartialOrd for BigInt {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl core::fmt::Display for BigInt {
fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
write!(f, "{}", self.0)
}
}
#[cfg(test)]
mod tests {
use super::BigInt;
use alloc::string::ToString;
fn b(s: &str) -> BigInt {
BigInt::from_str_radix(s, 10).unwrap()
}
#[test]
fn roundtrips_decimal() {
for s in [
"0",
"1",
"-1",
"42",
"-42",
"1000000000000000000000000000000",
] {
assert_eq!(b(s).to_string(), s);
}
}
#[test]
fn add_and_sub() {
assert_eq!(b("10").add(&b("20")).to_string(), "30");
assert_eq!(b("-5").add(&b("3")).to_string(), "-2");
assert_eq!(b("5").add(&b("-5")).to_string(), "0");
assert_eq!(b("100").sub(&b("250")).to_string(), "-150");
// Carries across a limb boundary.
assert_eq!(b("4294967295").add(&b("1")).to_string(), "4294967296");
}
#[test]
fn multiply_beyond_i128() {
// 2^127 * 2^127 = 2^254, which overflows i128.
let big = b("170141183460469231731687303715884105728"); // 2^127
assert_eq!(
big.mul(&big).to_string(),
"28948022309329048855892746252171976963317496166410141009864396001978282409984"
);
}
#[test]
fn divmod_truncates_toward_zero() {
assert_eq!(b("17").divmod(&b("5")).unwrap().0.to_string(), "3");
assert_eq!(b("17").divmod(&b("5")).unwrap().1.to_string(), "2");
assert_eq!(b("-17").divmod(&b("5")).unwrap().1.to_string(), "-2");
assert_eq!(
b("1000000000000000000000")
.divmod(&b("7"))
.unwrap()
.0
.to_string(),
"142857142857142857142"
);
assert!(b("1").divmod(&b("0")).is_none());
}
#[test]
fn pow_and_radix() {
assert_eq!(
b("2").pow(100).to_string(),
"1267650600228229401496703205376"
);
assert_eq!(b("255").to_str_radix(16), "ff");
assert_eq!(BigInt::from_str_radix("ff", 16).unwrap().to_string(), "255");
assert_eq!(
BigInt::from_str_radix("-1010", 2).unwrap().to_string(),
"-10"
);
}
#[test]
fn bitwise_twos_complement() {
assert_eq!(b("12").bitand(&b("10")).to_string(), "8");
assert_eq!(b("12").bitor(&b("10")).to_string(), "14");
assert_eq!(b("12").bitxor(&b("10")).to_string(), "6");
// Negative operands follow two's-complement semantics.
assert_eq!(b("-1").bitand(&b("12")).to_string(), "12"); // -1 is all ones
assert_eq!(b("-12").bitor(&b("10")).to_string(), "-2");
assert_eq!(b("-5").bitxor(&b("3")).to_string(), "-8");
// Beyond i128 width.
let big = b("2").pow(200);
assert_eq!(big.bitor(&BigInt::from_i128(1)).sub(&big).to_string(), "1");
}
#[test]
fn i128_roundtrip() {
for v in [0i128, 1, -1, i128::MAX, i128::MIN, 123456789] {
assert_eq!(BigInt::from_i128(v).to_i128(), Some(v));
}
// A value beyond i128 has no i128 form.
assert_eq!(b("2").pow(200).to_i128(), None);
}
#[test]
fn to_u64_wrapping_twos_complement() {
assert_eq!(BigInt::from_i128(0).to_u64_wrapping(), 0);
assert_eq!(BigInt::from_i128(1).to_u64_wrapping(), 1);
assert_eq!(BigInt::from_i128(-1).to_u64_wrapping(), u64::MAX);
assert_eq!(BigInt::from_i128(255).to_u64_wrapping(), 255);
// Only the low 64 bits survive.
assert_eq!(b("18446744073709551617").to_u64_wrapping(), 1); // 2^64 + 1
}
}