Researching 128bit integers

big_int.cpp

@@ -1,6 +1,195 @@
+/*
+We use two's complement
 
-#if COMPILER_CLANG
-typedef __int128 int128;
-#else
-#error "Need big int implementation"
-#endif
+Adding the value
+Adding a positive number to a negative number is actually subtracting the value.
+Last bit is a biggest possible negative number for that bit range.
+0111 1111 => 127
+1111 1111 => -128 - 127 = 1
+
+1000 0000 => -128
+if we add 4 we get
+1000 0100 => -124
+
+Negating the value
+1000 0001 => -127
+flip bits
+0111 1110 => 126
+we need to add 1
+0111 1111 -> 127
+
+*/
+
+struct S128{U64 hi, lo;};
+
+function S64
+is_negative(S128 v){
+  S64 result = v.hi >> 63;
+  return result;
+}
+
+function S64
+sign(S128 val){
+  S64 result = is_negative(val) ? -1 : 1;
+  return result;
+}
+
+function S128
+s128(S64 value){
+  S128 result = {value < 0 ? ~0 : 0ull, (U64)value};
+  return result;
+}
+
+function S128
+s128_from_u64(U64 value){
+  S128 result = {0, value};
+  return result;
+}
+
+function S128
+operator+(S128 a, S128 b){
+  U64 lo = a.lo + b.lo;
+  U64 hi = a.hi + b.hi + (a.lo > lo); // (a.lo > lo) is carry
+  return {hi,lo};
+}
+
+function S128
+operator-(S128 a, S128 b){
+  U64 lo = a.lo - b.lo;
+  U64 hi = a.hi - b.hi - (a.lo < lo); // (a.lo < lo) is carry
+  return {hi,lo};
+}
+
+force_inline U64 lo32(U64 a){return a & 0xffffffff;}
+force_inline U64 hi32(U64 a){return a >> 32;}
+force_inline S128 operator~(S128 a){return {~a.hi, ~a.lo};}
+force_inline S128 operator^(S128 a, S128 b){return {a.hi ^ b.hi, a.lo ^ b.lo};}
+force_inline S128 operator&(S128 a, S128 b){return {a.hi & b.hi, a.lo & b.lo};}
+force_inline S128 operator|(S128 a, S128 b){return {a.hi | b.hi, a.lo | b.lo};}
+
+function S128
+operator-(S128 a){
+  a = (~a) + s128(1);
+  return a;
+}
+
+/*
+U64 u1 = lo32(u);
+U64 v1 = lo32(v);
+
+U64 t = u1 * v1;
+U64 w3 = lo32(t);
+U64 k = hi32(t);
+
+u >>= 32;
+t = u * v1 + k;
+k = lo32(t);
+U64 w1 = hi32(t);
+
+v >>= 32;
+t = u1 * v + k;
+
+return { (u * v) + w1 + hi32(t), (t << 32) + w3 };
+*/
+
+void mult64to128(U64 u, U64 v, U64& h, U64 &l)
+{
+    U64 u1 = (u & 0xffffffff);
+    U64 v1 = (v & 0xffffffff);
+    U64 t = (u1 * v1);
+    U64 w3 = (t & 0xffffffff); // w3 = t1_lo
+    U64 k = (t >> 32); // k = t1_hi
+
+    u >>= 32; // u_hi
+    t = (u * v1) + k; // t2 = (u_hi * v_lo) + t1_hi
+    k = (t & 0xffffffff); // t2_lo
+    U64 w1 = (t >> 32); // t2_hi
+
+    v >>= 32;
+    t = (u1 * v) + k; // t3 = (u_lo * v_hi) + t2_lo
+    k = (t >> 32); // t3_hi
+
+    h = (u * v) + w1 + k;
+    l = (t << 32) + w3;
+}
+
+function S128
+u64_mul(U64 u, U64 v){
+  U64 u_lo = lo32(u);
+  U64 v_lo = lo32(v);
+  U64 u_hi = hi32(u);
+  U64 v_hi = hi32(v);
+
+  U64 t1 = u_lo * v_lo;
+  U64 t1_lo = lo32(t1);
+  U64 t1_hi = hi32(t1);
+
+  U64 t2 = (u_hi * v_lo) + t1_hi;
+  U64 t2_lo = lo32(t2);
+  U64 t2_hi = hi32(t2);
+
+  U64 t3 = (u_lo * v_hi) + t2_lo;
+  U64 t3_hi = hi32(t3);
+
+  U64 lo = (t3 << 32) + t1_lo;
+  U64 hi = (u_hi * v_hi) + t2_hi + t3_hi;
+  return {hi,lo};
+}
+
+function S128
+operator*(S128 a, S128 b){
+  S128 c = u64_mul(a.lo, b.lo);
+  c.hi += (a.hi * b.lo) + (a.lo * b.hi);
+  return c;
+}
+
+function void
+test_big_int(){
+  S128 v1 = s128(-1);
+  assert(v1.hi == U64MAX && v1.lo == U64MAX);
+  assert(is_negative(v1));
+  assert(sign(v1) == -1);
+
+  S128 v2 = s128_from_u64(U64MAX) + s128_from_u64(1);
+  assert(v2.lo == 0 && v2.hi == 1);
+
+  S128 v3 = s128_from_u64(U64MAX) + s128_from_u64(100);
+  assert(v3.lo == 99 && v3.hi == 1);
+
+  // S64 s64_max = S64MAX;
+  S128 v4 = s128(S64MIN) + s128_from_u64(100);
+  assert((v4.lo - S64MAX) == 101); // 101 cause S64MIN is larher by 1
+
+  S128 v5 = {1, 0};
+  S128 v6 = v5 - s128(1);
+  assert(v6.lo == U64MAX && v6.hi == 0);
+
+  {
+    S128 v7 = u64_mul(S64MAX, S64MAX);
+    U64 a,b;
+    mult64to128(S64MAX,S64MAX,a,b);
+    assert(v7.hi == a && v7.lo == b);
+  }
+
+  {
+    S128 v7 = u64_mul(S64MIN, S64MIN);
+    U64 a,b;
+    mult64to128(S64MIN,S64MIN,a,b);
+    assert(v7.hi == a && v7.lo == b);
+  }
+
+  {
+    S128 v7 = u64_mul(15125125, -1424124);
+    U64 a,b;
+    mult64to128(15125125,-1424124,a,b);
+    assert(v7.hi == a && v7.lo == b);
+  }
+
+  {
+    S128 v7 = u64_mul(52242, 2);
+    U64 a,b;
+    mult64to128(52242, 2,a,b);
+    assert(v7.hi == a && v7.lo == b);
+    assert(v7.lo == 52242*2);
+  }
+}

main.cpp

@@ -92,7 +92,6 @@ For now I don't thing it should be overloadable.
 
 #include "base.cpp"
 #include "base_unicode.cpp"
-#include "big_int.cpp"
 #include "new_lex.cpp"
 #include "types.h"
 #include "new_ast.cpp"
@@ -100,7 +99,10 @@ For now I don't thing it should be overloadable.
 #include "typecheck.h"
 #include "typecheck.cpp"
 #include "ccodegen.cpp"
+
+#include "big_int.cpp"
 int main(){
+  test_big_int();
 
   test_os_memory();
   thread_ctx_init();

new_ast.cpp

@@ -330,6 +330,7 @@ ast_int(Token *pos, U64 integer){
   AST_NEW(Atom, VALUE, pos, AST_EXPR | AST_ATOM);
   result->type = untyped_int;
   result->int_val = integer;
+  // result->big_int = big_int(pctx->perm, integer); // @todo: int arena??
   return result;
 }
 

typecheck.h

@@ -208,6 +208,7 @@ operand_int(S64 int_val){
   Operand result = {};
   result.type = type_int;
   result.int_val = int_val;
+  // result.big_int = int_val;
   result.is_const = true;
   result.is_lvalue = false;
   return result;