Use 128-bit integers for ExactValue integers

1 files changed, 612 insertions, 0 deletions

diff --git a/src/integer128.c b/src/integer128.c
new file mode 100644
index 000000000..70cf6bca0
--- /dev/null
+++ b/src/integer128.c
@@ -0,0 +1,612 @@
+typedef struct u128 {u64 lo; u64 hi;} u128;
+typedef struct i128 {u64 lo; i64 hi;} i128;
+
+#define BIT128_U64_HIGHBIT 0x8000000000000000ul
+#define BIT128_U64_BITS62  0x7ffffffffffffffful
+#define BIT128_U64_ALLBITS 0xfffffffffffffffful
+
+static u128 const U128_ZERO = {0, 0};
+static u128 const U128_ONE  = {1, 0};
+static i128 const I128_ZERO = {0, 0};
+static i128 const I128_ONE  = {1, 0};
+static u128 const U128_NEG_ONE = {BIT128_U64_ALLBITS, BIT128_U64_ALLBITS};
+static i128 const I128_NEG_ONE = {BIT128_U64_ALLBITS, BIT128_U64_ALLBITS};
+
+u128 u128_lo_hi      (u64 lo, u64 hi);
+u128 u128_from_u32   (u32 u);
+u128 u128_from_u64   (u64 u);
+u128 u128_from_i64   (i64 u);
+u128 u128_from_f32   (f32 f);
+u128 u128_from_f64   (f64 f);
+u128 u128_from_string(String string);
+
+i128 i128_lo_hi      (u64 lo, i64 hi);
+i128 i128_from_u32   (u32 u);
+i128 i128_from_u64   (u64 u);
+i128 i128_from_i64   (i64 u);
+i128 i128_from_f32   (f32 f);
+i128 i128_from_f64   (f64 f);
+i128 i128_from_string(String string);
+
+u64 u128_to_u64(u128 a);
+i64 u128_to_i64(u128 a);
+f64 u128_to_f64(u128 a);
+
+u64 i128_to_u64(i128 a);
+i64 i128_to_i64(i128 a);
+f64 i128_to_f64(i128 a);
+
+String u128_to_string(u128 a, char *buf, isize len);
+String i128_to_string(i128 a, char *buf, isize len);
+
+i32  u128_cmp    (u128 a, u128 b);
+bool u128_eq     (u128 a, u128 b);
+bool u128_ne     (u128 a, u128 b);
+bool u128_lt     (u128 a, u128 b);
+bool u128_gt     (u128 a, u128 b);
+bool u128_le     (u128 a, u128 b);
+bool u128_ge     (u128 a, u128 b);
+u128 u128_add    (u128 a, u128 b);
+u128 u128_not    (u128 a);
+u128 u128_neg    (u128 a);
+u128 u128_sub    (u128 a, u128 b);
+u128 u128_and    (u128 a, u128 b);
+u128 u128_or     (u128 a, u128 b);
+u128 u128_xor    (u128 a, u128 b);
+u128 u128_and_not(u128 a, u128 b);
+u128 u128_shl    (u128 a, u32 n);
+u128 u128_shr    (u128 a, u32 n);
+u128 u128_mul    (u128 a, u128 b);
+void u128_divide (u128 num, u128 den, u128 *quo, u128 *rem);
+u128 u128_quo    (u128 a, u128 b);
+u128 u128_mod    (u128 a, u128 b);
+
+i128 i128_abs    (i128 a);
+i32  i128_cmp    (i128 a, i128 b);
+bool i128_eq     (i128 a, i128 b);
+bool i128_ne     (i128 a, i128 b);
+bool i128_lt     (i128 a, i128 b);
+bool i128_gt     (i128 a, i128 b);
+bool i128_le     (i128 a, i128 b);
+bool i128_ge     (i128 a, i128 b);
+i128 i128_add    (i128 a, i128 b);
+i128 i128_not    (i128 a);
+i128 i128_neg    (i128 a);
+i128 i128_sub    (i128 a, i128 b);
+i128 i128_and    (i128 a, i128 b);
+i128 i128_or     (i128 a, i128 b);
+i128 i128_xor    (i128 a, i128 b);
+i128 i128_and_not(i128 a, i128 b);
+i128 i128_shl    (i128 a, u32 n);
+i128 i128_shr    (i128 a, u32 n);
+i128 i128_mul    (i128 a, i128 b);
+void i128_divide (i128 num, i128 den, i128 *quo, i128 *rem);
+i128 i128_quo    (i128 a, i128 b);
+i128 i128_mod    (i128 a, i128 b);
+
+
+////////////////////////////////////////////////////////////////
+
+
+u64 bit128__digit_value(Rune r) {
+	if ('0' <= r && r <= '9') {
+		return r - '0';
+	} else if ('a' <= r && r <= 'f') {
+		return r - 'a' + 10;
+	} else if ('A' <= r && r <= 'F') {
+		return r - 'A' + 10;
+	}
+	return 16; // NOTE(bill): Larger than highest possible
+}
+
+u128 u128_lo_hi(u64 lo, u64 hi) { return (u128){lo, hi}; }
+u128 u128_from_u32(u32 u)       { return u128_lo_hi(cast(u64)u, 0); }
+u128 u128_from_u64(u64 u)       { return u128_lo_hi(cast(u64)u, 0); }
+u128 u128_from_i64(i64 u)       { return u128_lo_hi(cast(u64)u, u < 0 ? -1 : 0); }
+u128 u128_from_f32(f32 f)       { return u128_lo_hi(cast(u64)f, 0); }
+u128 u128_from_f64(f64 f)       { return u128_lo_hi(cast(u64)f, 0); }
+u128 u128_from_string(String string) {
+	// TODO(bill): Allow for numbers with underscores in them
+	u64 base = 10;
+	bool has_prefix = false;
+	if (string.len > 2 && string.text[0] == '0') {
+		switch (string.text[1]) {
+		case 'b': base = 2;  has_prefix = true; break;
+		case 'o': base = 8;  has_prefix = true; break;
+		case 'd': base = 10; has_prefix = true; break;
+		case 'z': base = 12; has_prefix = true; break;
+		case 'x': base = 16; has_prefix = true; break;
+		}
+	}
+
+	u8 *text = string.text;
+	isize len = string.len;
+	if (has_prefix) {
+		text += 2;
+		len -= 2;
+	}
+
+	u128 base_ = u128_from_u64(base);
+
+	u128 result = {0};
+	for (isize i = 0; i < len; i++) {
+		Rune r = cast(Rune)text[i];
+		if (r == '_') {
+			continue;
+		}
+		u64 v = bit128__digit_value(r);
+		if (v >= base) {
+			break;
+		}
+		result = u128_mul(result, base_);
+		result = u128_add(result, u128_from_u64(v));
+	}
+	return result;
+}
+
+
+i128 i128_lo_hi(u64 lo, i64 hi) {
+	i128 i;
+	i.lo = lo;
+	i.hi = hi;
+	return i;
+}
+i128 i128_from_u32(u32 u)       { return i128_lo_hi(cast(u64)u, 0); }
+i128 i128_from_u64(u64 u)       { return i128_lo_hi(cast(u64)u, 0); }
+i128 i128_from_i64(i64 u)       { return i128_lo_hi(cast(u64)u, u < 0 ? -1 : 0); }
+i128 i128_from_f32(f32 f)       { return i128_lo_hi(cast(u64)f, 0); }
+i128 i128_from_f64(f64 f)       { return i128_lo_hi(cast(u64)f, 0); }
+i128 i128_from_string(String string) {
+	// TODO(bill): Allow for numbers with underscores in them
+	u64 base = 10;
+	bool has_prefix = false;
+	if (string.len > 2 && string.text[0] == '0') {
+		switch (string.text[1]) {
+		case 'b': base = 2;  has_prefix = true; break;
+		case 'o': base = 8;  has_prefix = true; break;
+		case 'd': base = 10; has_prefix = true; break;
+		case 'z': base = 12; has_prefix = true; break;
+		case 'x': base = 16; has_prefix = true; break;
+		}
+	}
+
+	u8 *text = string.text;
+	isize len = string.len;
+	if (has_prefix) {
+		text += 2;
+		len -= 2;
+	}
+
+	i128 base_ = i128_from_u64(base);
+
+	i128 result = {0};
+	for (isize i = 0; i < len; i++) {
+		Rune r = cast(Rune)text[i];
+		if (r == '_') {
+			continue;
+		}
+		u64 v = bit128__digit_value(r);
+		if (v >= base) {
+			break;
+		}
+		result = i128_mul(result, base_);
+		result = i128_add(result, i128_from_u64(v));
+	}
+
+	return result;
+}
+
+
+
+u64 u128_to_u64(u128 a) {
+	return (a.lo&BIT128_U64_BITS62) | (a.hi&BIT128_U64_HIGHBIT);
+}
+i64 u128_to_i64(u128 a) {
+	return a.lo;
+}
+f64 u128_to_f64(u128 a) {
+	if (a.hi >= 0) {
+		return (cast(f64)a.hi * 18446744073709551616.0) + cast(f64)a.lo;
+	}
+	i64 h = cast(i64)a.hi;
+	u64 l = a.lo;
+	h = ~h;
+	l = ~l;
+	l += 1;
+	if (l == 0) {
+		h += 1;
+	}
+
+	return -((cast(f64)h * 18446744073709551616.0) + cast(f64)l);
+}
+
+u64 i128_to_u64(i128 a) {
+	return (a.lo&BIT128_U64_BITS62) | (a.hi&BIT128_U64_HIGHBIT);
+}
+i64 i128_to_i64(i128 a) {
+	return cast(i64)a.lo;
+}
+f64 i128_to_f64(i128 a) {
+	if (a.hi >= 0) {
+		return (cast(f64)a.hi * 18446744073709551616.0) + cast(f64)a.lo;
+	}
+	i64 h = a.hi;
+	u64 l = a.lo;
+	h = ~h;
+	l = ~l;
+	l += 1;
+	if (l == 0) {
+		h += 1;
+	}
+
+	return -((cast(f64)h * 18446744073709551616.0) + cast(f64)l);
+}
+
+
+String u128_to_string(u128 a, char *out_buf, isize out_buf_len) {
+	char buf[200] = {0};
+	isize i = 0;
+
+	if (u128_ne(a, U128_ZERO)) {
+		u128 base = u128_from_u64(10);
+		while (u128_gt(a, U128_ZERO)) {
+			i64 digit = u128_to_i64(u128_mod(a, base));
+			buf[i++] = gb__num_to_char_table[digit];
+			a = u128_quo(a, base);
+		}
+	} else {
+		buf[i++] = '0';
+	}
+
+	gb_reverse(buf, i, 1);
+
+	isize len = gb_min(i, out_buf_len);
+	gb_memcopy(out_buf, &buf[0], len);
+	return make_string(cast(u8 *)out_buf, len);
+}
+String i128_to_string(i128 a, char *out_buf, isize out_buf_len) {
+	char buf[200] = {0};
+	isize i = 0;
+	bool negative = false;
+	if (i128_lt(a, I128_ZERO)) {
+		negative = true;
+		a = i128_neg(a);
+	}
+
+	if (i128_ne(a, I128_ZERO)) {
+		i128 base = i128_from_u64(10);
+		while (i128_gt(a, I128_ZERO)) {
+			i64 digit = i128_to_i64(i128_mod(a, base));
+			buf[i++] = gb__num_to_char_table[digit];
+			a = i128_quo(a, base);
+		}
+	} else {
+		buf[i++] = '0';
+	}
+
+	if (negative) {
+		buf[i++] = '-';
+	}
+
+	GB_ASSERT(i > 0);
+	for (isize j = 0; j < i/2; j++) {
+		char tmp = buf[j];
+		buf[j] = buf[i-1-j];
+		buf[i-1-j] = tmp;
+	}
+
+	isize len = gb_min(i, out_buf_len);
+	gb_memcopy(out_buf, &buf[0], len);
+	return make_string(cast(u8 *)out_buf, len);
+}
+
+
+
+////////////////////////////////////////////////////////////////
+
+i32 u128_cmp(u128 a, u128 b) {
+	if (a.hi == b.hi && b.lo == b.lo) {
+		return 0;
+	}
+	if (a.hi == b.hi) {
+		return a.lo < b.lo ? -1 : +1;
+	}
+	return a.hi < b.hi ? -1 : +1;
+}
+
+bool u128_eq(u128 a, u128 b) { return a.hi == b.hi && a.lo == b.lo; }
+bool u128_ne(u128 a, u128 b) { return !u128_eq(a, b); }
+bool u128_lt(u128 a, u128 b) { return a.hi == b.hi ? a.lo < b.lo : a.hi < b.hi; }
+bool u128_gt(u128 a, u128 b) { return a.hi == b.hi ? a.lo > b.lo : a.hi > b.hi; }
+bool u128_le(u128 a, u128 b) { return !u128_gt(a, b); }
+bool u128_ge(u128 a, u128 b) { return !u128_lt(a, b); }
+
+u128 u128_add(u128 a, u128 b) {
+	u128 old_a = a;
+	a.lo += b.lo;
+	a.hi += b.hi;
+	if (a.lo < old_a.lo) {
+		a.hi += 1;
+	}
+	return a;
+}
+u128 u128_not(u128 a) { return u128_lo_hi(~a.lo, ~a.hi); }
+
+u128 u128_neg(u128 a) {
+	return u128_add(u128_not(a), u128_from_u64(1));
+}
+u128 u128_sub(u128 a, u128 b) {
+	return u128_add(a, u128_neg(b));
+}
+u128 u128_and(u128 a, u128 b) { return u128_lo_hi(a.lo&b.lo, a.hi&b.hi); }
+u128 u128_or (u128 a, u128 b) { return u128_lo_hi(a.lo|b.lo, a.hi|b.hi); }
+u128 u128_xor(u128 a, u128 b) { return u128_lo_hi(a.lo^b.lo, a.hi^b.hi); }
+u128 u128_and_not(u128 a, u128 b) { return u128_lo_hi(a.lo&(~b.lo), a.hi&(~b.hi)); }
+
+
+u128 u128_shl(u128 a, u32 n) {
+	if (n >= 128) {
+		return u128_lo_hi(0, 0);
+	}
+
+	if (n >= 64) {
+		n -= 64;
+		a.hi = a.lo;
+		a.lo = 0;
+	}
+
+	if (n != 0) {
+		u64 mask = ~(BIT128_U64_ALLBITS >> n);
+
+		a.hi <<= n;
+		a.hi |= (a.lo&mask) >> (64 - n);
+		a.lo <<= n;
+	}
+	return a;
+}
+
+u128 u128_shr(u128 a, u32 n) {
+	if (n >= 128) {
+		return u128_lo_hi(0, 0);
+	}
+
+	if (n >= 64) {
+		n -= 64;
+		a.lo = a.hi;
+		a.hi = 0;
+	}
+
+	if (n != 0) {
+		u64 mask = ~(BIT128_U64_ALLBITS << n);
+		a.lo >>= n;
+		a.lo |= (a.hi&mask) << (64 - n);
+		a.hi >>= n;
+	}
+	return a;
+}
+
+
+u128 u128_mul(u128 a, u128 b) {
+	if (a.lo == 0 && a.hi == 0) {
+		return u128_from_u64(0);
+	} else if (b.lo == 0 && b.hi == 0) {
+		return u128_from_u64(0);
+	}
+	if (u128_eq(a, U128_ONE)) {
+		return b;
+	}
+	if (u128_eq(b, U128_ONE)) {
+		return a;
+	}
+
+	u128 res = {0};
+	u128 t = b;
+	for (u32 i = 0; i < 128; i++) {
+		if ((t.lo&1) != 0) {
+			res = u128_add(res, u128_shl(a, i));
+		}
+
+		t = u128_shr(t, 1);
+	}
+
+	return res;
+}
+
+void u128_divide(u128 num, u128 den, u128 *quo, u128 *rem) {
+	if (u128_eq(den, U128_ZERO)) {
+		if (quo) *quo = u128_from_u64(num.lo/den.lo);
+		if (rem) *rem = U128_ZERO;
+	} else {
+		u128 n = num;
+		u128 d = den;
+		u128 x = U128_ONE;
+		u128 r = U128_ZERO;
+
+		while (u128_ge(n, d) && ((u128_shr(d, 128-1).lo&1) == 0)) {
+			x = u128_shl(x, 1);
+			d = u128_shl(d, 1);
+		}
+
+		while (u128_ne(x, U128_ZERO)) {
+			if (u128_ge(n, d)) {
+				n = u128_sub(n, d);
+				r = u128_or(r, x);
+			}
+
+			x = u128_shr(x, 1);
+			d = u128_shr(d, 1);
+		}
+
+		if (quo) *quo = r;
+		if (rem) *rem = n;
+	}
+}
+
+u128 u128_quo(u128 a, u128 b) {
+	u128 res = {0};
+	u128_divide(a, b, &res, NULL);
+	return res;
+}
+u128 u128_mod(u128 a, u128 b) {
+	u128 res = {0};
+	u128_divide(a, b, NULL, &res);
+	return res;
+}
+
+////////////////////////////////////////////////////////////////
+
+i128 i128_abs(i128 a) {
+	if ((a.hi&BIT128_U64_HIGHBIT) != 0) {
+		return i128_neg(a);
+	}
+	return a;
+}
+
+i32 i128_cmp(i128 a, i128 b) {
+	if (a.hi == b.hi && b.lo == b.lo) {
+		return 0;
+	}
+	if (a.hi == b.hi) {
+		return a.lo < b.lo ? -1 : +1;
+	}
+	return a.hi < b.hi ? -1 : +1;
+}
+
+bool i128_eq(i128 a, i128 b) { return a.hi == b.hi && a.lo == b.lo; }
+bool i128_ne(i128 a, i128 b) { return !i128_eq(a, b); }
+bool i128_lt(i128 a, i128 b) { return a.hi == b.hi ? a.lo < b.lo : a.hi < b.hi; }
+bool i128_gt(i128 a, i128 b) { return a.hi == b.hi ? a.lo > b.lo : a.hi > b.hi; }
+bool i128_le(i128 a, i128 b) { return a.hi == b.hi ? a.lo <= b.lo : a.hi <= b.hi; }
+bool i128_ge(i128 a, i128 b) { return a.hi == b.hi ? a.lo >= b.lo : a.hi >= b.hi; }
+
+i128 i128_add(i128 a, i128 b) {
+	i128 old_a = a;
+	a.lo += b.lo;
+	a.hi += b.hi;
+	if (a.lo < old_a.lo) {
+		a.hi += 1;
+	}
+	return a;
+}
+i128 i128_not(i128 a) { return i128_lo_hi(~a.lo, ~a.hi); }
+
+i128 i128_neg(i128 a) {
+	return i128_add(i128_not(a), i128_from_u64(1));
+}
+i128 i128_sub(i128 a, i128 b) {
+	return i128_add(a, i128_neg(b));
+}
+i128 i128_and(i128 a, i128 b) { return i128_lo_hi(a.lo&b.lo, a.hi&b.hi); }
+i128 i128_or (i128 a, i128 b) { return i128_lo_hi(a.lo|b.lo, a.hi|b.hi); }
+i128 i128_xor(i128 a, i128 b) { return i128_lo_hi(a.lo^b.lo, a.hi^b.hi); }
+i128 i128_and_not(i128 a, i128 b) { return i128_lo_hi(a.lo&(~b.lo), a.hi&(~b.hi)); }
+
+
+i128 i128_shl(i128 a, u32 n) {
+	if (n >= 128) {
+		return i128_lo_hi(0, 0);
+	}
+
+	if (n >= 64) {
+		n -= 64;
+		a.hi = a.lo;
+		a.lo = 0;
+	}
+
+	if (n != 0) {
+		u64 mask = ~(BIT128_U64_ALLBITS >> n);
+
+		a.hi <<= n;
+		a.hi |= (a.lo&mask) >> (64 - n);
+		a.lo <<= n;
+	}
+	return a;
+}
+
+i128 i128_shr(i128 a, u32 n) {
+	if (n >= 128) {
+		return i128_lo_hi(0, 0);
+	}
+
+	if (n >= 64) {
+		n -= 64;
+		a.lo = a.hi;
+		a.hi = 0;
+	}
+
+	if (n != 0) {
+		u64 mask = ~(BIT128_U64_ALLBITS << n);
+		a.lo >>= n;
+		a.lo |= (a.hi&mask) << (64 - n);
+		a.hi >>= n;
+	}
+	return a;
+}
+
+
+i128 i128_mul(i128 a, i128 b) {
+	if (a.lo == 0 && a.hi == 0) {
+		return i128_from_u64(0);
+	} else if (b.lo == 0 && b.hi == 0) {
+		return i128_from_u64(0);
+	}
+	if (i128_eq(a, I128_ONE)) {
+		return b;
+	}
+	if (i128_eq(b, I128_ONE)) {
+		return a;
+	}
+
+	i128 res = {0};
+	i128 t = b;
+	for (u32 i = 0; i < 128; i++) {
+		if ((t.lo&1) != 0) {
+			res = i128_add(res, i128_shl(a, i));
+		}
+
+		t = i128_shr(t, 1);
+	}
+
+	return res;
+}
+
+void i128_divide(i128 num, i128 den, i128 *quo, i128 *rem) {
+	if (i128_eq(den, I128_ZERO)) {
+		if (quo) *quo = i128_from_u64(num.lo/den.lo);
+		if (rem) *rem = I128_ZERO;
+	} else {
+		i128 n = num;
+		i128 d = den;
+		i128 x = I128_ONE;
+		i128 r = I128_ZERO;
+
+		while (i128_ge(n, d) && ((i128_shr(d, 128-1).lo&1) == 0)) {
+			x = i128_shl(x, 1);
+			d = i128_shl(d, 1);
+		}
+
+		while (i128_ne(x, I128_ZERO)) {
+			if (i128_ge(n, d)) {
+				n = i128_sub(n, d);
+				r = i128_or(r, x);
+			}
+
+			x = i128_shr(x, 1);
+			d = i128_shr(d, 1);
+		}
+
+		if (quo) *quo = r;
+		if (rem) *rem = n;
+	}
+}
+
+i128 i128_quo(i128 a, i128 b) {
+	i128 res = {0};
+	i128_divide(a, b, &res, NULL);
+	return res;
+}
+i128 i128_mod(i128 a, i128 b) {
+	i128 res = {0};
+	i128_divide(a, b, NULL, &res);
+	return res;
+}