Start of core:math/bigint

We have:
- `init` to create a new `Int`
- `init(from_integer)` to create a new `Int` and set it to `from_integer`.
- `set(Int, from_integer)` to set an `Int` to `from_integer`
- `add(dest, a, b)` to add `a` and `b` into `dest`.
- `sub(dest, a, b)` to subtract `b` from `a` and put the result in `dest`.

And a few helper functions, like:
- `is_zero`, `is_negative`, ...
- `grow`, `shrink`, `clear`, `zero`

core/math/bigint/basic.odin

@@ -0,0 +1,196 @@
+package bigint
+
+/*
+	Copyright 2021 Jeroen van Rijn <nom@duclavier.com>.
+	Made available under Odin's BSD-2 license.
+
+	A BigInt implementation in Odin.
+	For the theoretical underpinnings, see Knuth's The Art of Computer Programming, Volume 2, section 4.3.
+	The code started out as an idiomatic source port of libTomMath, which is in the public domain, with thanks.
+*/
+
+import "core:mem"
+import "core:intrinsics"
+
+/*
+	High-level addition. Handles sign.
+*/
+add :: proc(dest, a, b: ^Int) -> (err: Error) {
+	dest := dest; x := a; y := b;
+	_panic_if_uninitialized(a); _panic_if_uninitialized(b); _panic_if_uninitialized(dest);
+
+	/*
+		Handle both negative or both positive.
+	*/
+	if x.sign == y.sign {
+		dest.sign = x.sign;
+		return _add(dest, x, y);
+	}
+
+	/*
+    	One positive, the other negative.
+    	Subtract the one with the greater magnitude from the other.
+    	The result gets the sign of the one with the greater magnitude.
+    */
+    if cmp_mag(x, y) == .Less_Than {
+    	x, y = y, x;
+    }
+
+    dest.sign = x.sign;
+    return _sub(dest, x, y);
+}
+
+/*
+	Low-level addition, unsigned.
+	Handbook of Applied Cryptography, algorithm 14.7.
+*/
+_add :: proc(dest, a, b: ^Int) -> (err: Error) {
+	dest := dest; x := a; y := b;
+	_panic_if_uninitialized(a); _panic_if_uninitialized(b); _panic_if_uninitialized(dest);
+
+	old_used, min_used, max_used, i: int;
+
+	if x.used < y.used {
+		x, y = y, x;
+	}
+
+	min_used = x.used;
+	max_used = y.used;
+	old_used = dest.used;
+
+	err = grow(dest, max(max_used + 1, _DEFAULT_DIGIT_COUNT));
+	if err != .OK {
+		return err;
+	}
+	dest.used = max_used + 1;
+
+	/* Zero the carry */
+	carry := DIGIT(0);
+
+	for i = 0; i < min_used; i += 1 {
+		/*
+			Compute the sum one _DIGIT at a time.
+			dest[i] = a[i] + b[i] + carry;
+		*/
+		dest.digit[i] = x.digit[i] + y.digit[i] + carry;
+
+		/*
+			Compute carry
+		*/
+		carry = dest.digit[i] >> _DIGIT_BITS;
+		/*
+			Mask away carry from result digit.
+		*/
+		dest.digit[i] &= _MASK;
+	}
+
+	if min_used != max_used {
+		/*
+			Now copy higher words, if any, in A+B.
+			If A or B has more digits, add those in.
+		*/
+		for ; i < max_used; i += 1 {
+			dest.digit[i] = x.digit[i] + carry;
+			/*
+				Compute carry
+			*/
+			carry = dest.digit[i] >> _DIGIT_BITS;
+			/*
+				Mask away carry from result digit.
+			*/
+			dest.digit[i] &= _MASK;
+		}
+	}
+	/*
+		Add remaining carry.
+	*/
+	dest.digit[i] = carry;
+
+	zero_count := old_used - dest.used;
+	/*
+		Zero remainder.
+	*/
+	if zero_count > 0 {
+		mem.zero_slice(dest.digit[dest.used:][:zero_count]);
+	}
+	/*
+		Adjust dest.used based on leading zeroes.
+	*/
+	clamp(dest);
+
+	return .OK;
+}
+
+
+/*
+	Low-level subtraction. Assumes |a| > |b|.
+	Handbook of Applied Cryptography, algorithm 14.9.
+*/
+_sub :: proc(dest, a, b: ^Int) -> (err: Error) {
+	dest := dest; x := a; y := b;
+	_panic_if_uninitialized(a); _panic_if_uninitialized(b); _panic_if_uninitialized(dest);
+
+	for n in 0..=12 {
+		dest.digit[n] = DIGIT(n);
+		dest.used = n+1;
+	}
+
+	old_used := dest.used;
+	min_used := y.used;
+	max_used := a.used;
+	i: int;
+
+	err = grow(dest, max(max_used, _DEFAULT_DIGIT_COUNT));
+	if err != .OK {
+		return err;
+	}
+	dest.used = max_used;
+
+	borrow := DIGIT(0);
+
+	for i = 0; i < min_used; i += 1 {
+		dest.digit[i] = (x.digit[i] - y.digit[i] - borrow);
+		/*
+			borrow = carry bit of dest[i]
+			Note this saves performing an AND operation since if a carry does occur,
+			it will propagate all the way to the MSB.
+			As a result a single shift is enough to get the carry.
+		*/
+		borrow = dest.digit[i] >> (_DIGIT_BITS - 1);
+		/*
+			Clear borrow from dest[i].
+		*/
+		dest.digit[i] &= _MASK;
+	}
+
+	/*
+		Now copy higher words if any, e.g. if A has more digits than B
+	*/
+	for ; i < max_used; i += 1 {
+		dest.digit[i] = x.digit[i] - borrow;
+		/*
+			borrow = carry bit of dest[i]
+			Note this saves performing an AND operation since if a carry does occur,
+			it will propagate all the way to the MSB.
+			As a result a single shift is enough to get the carry.
+		*/
+		borrow = dest.digit[i] >> (_DIGIT_BITS - 1);
+		/*
+			Clear borrow from dest[i].
+		*/
+		dest.digit[i] &= _MASK;
+	}
+
+	zero_count := old_used - dest.used;
+	/*
+		Zero remainder.
+	*/
+	if zero_count > 0 {
+		mem.zero_slice(dest.digit[dest.used:][:zero_count]);
+	}
+	/*
+		Adjust dest.used based on leading zeroes.
+	*/
+	clamp(dest);
+   	return .OK;
+}