(feat) Add u256 multiplication (#84)

assembly/__tests__/u256.spec.ts

@@ -1,3 +1,4 @@
+import { u128 } from '../integer/u128';
 import { u256 } from '../integer/u256';
 
 describe("String Conversion", () => {
@@ -348,4 +349,94 @@ describe("Basic Operations", () => {
     var r = new u256(3, 4, 6, 8);
     expect(a - b).toStrictEqual(r);
   });
+
+  it("Should multiply two u256 numbers", () => {
+    var a = u256.from(3);
+    var b = u256.from(3);
+    var r = u256.from(9);
+
+    expect(a * b).toStrictEqual(r);
+    expect(b * a).toStrictEqual(r);
+  });
+
+  it("Should multiply two u256 numbers", () => {
+    var a = u256.from(43545453452);
+    var b = u256.from(2353454354);
+    var r = new u256(10248516654965971928, 5);
+
+    expect(a * b).toStrictEqual(r);
+    expect(b * a).toStrictEqual(r);
+  });
+
+  it("Should multiply two u256 numbers - 2", () => {
+    var a = u256.from(11);
+    var b = new u256(0, 2);
+    var r = new u256(0, 22);
+
+    expect(a * b).toStrictEqual(r);
+    expect(b * a).toStrictEqual(r);
+  });
+
+  it("Should multiply two u256 numbers - 3", () => {
+    var a = new u256(0, 3);
+    var b = new u256(0, 0,3);
+    var r = new u256(0, 0,0,9);
+
+    expect(a * b).toStrictEqual(r);
+    expect(b * a).toStrictEqual(r);
+  });
+
+  it("Should multiply two u256 numbers - 4", () => {
+    var a = u256.from(new u128(14083847773837265618, 6692605942));
+    var b = u256.from(new u128(18444665141527514289, 5354084802));
+    var r = new u256(5659639222556316466, 4474720309748468391, 17386035696907167262, 1);
+
+    expect(a * b).toStrictEqual(r);
+    expect(b * a).toStrictEqual(r);
+  });
+
+  it("Should multiply u256 numbers by 1", () => {
+    var a = u256.Max;
+    var b = u256.One;
+    var r = a;
+    expect(a * b).toStrictEqual(r);
+    expect(b * a).toStrictEqual(r);
+  });
+
+  it("Should multiply u256 numbers by 0", () => {
+    var a = new u256(5656466, 447478468391, 17386907167262, 1);
+    var b = u256.Zero;
+    var r = b;
+    expect(a * b).toStrictEqual(r);
+    expect(b * a).toStrictEqual(r);
+  });
+
+  it("Should multiply two u256 numbers with overflow", () => {
+    var a = new u256(0, 0, 1);
+    expect(a * a).toStrictEqual(u256.Zero);
+  });
+
+  it("Should multiply two u256 numbers with overflow - 2", () => {
+    var a = new u256(1, 0, 1);
+    expect(a * a).toStrictEqual(new u256(1, 0, 2));
+  });
+
+  it("Should multiply two u256 numbers with overflow - 3", () => {
+    var a = new u256(6, 0, 0, 420);
+    var b = new u256(0, 7, 0, 0);
+    var r = new u256(0, 42, 0, 0);
+
+    expect(a * b).toStrictEqual(r);
+    expect(b * a).toStrictEqual(r);
+  });
+
+  it("Should multiply two u256 numbers with overflow - 3", () => {
+    var a = new u256(2, 666, 666, 666);
+    var b = new u256(0, 0, 0, 3);
+    var r = new u256(0, 0, 0, 6);
+
+    expect(a * b).toStrictEqual(r);
+    expect(b * a).toStrictEqual(r);
+  });
+
 });

assembly/globals.ts

@@ -1,3 +1,4 @@
+import { u256 } from './integer';
 import { u128 } from './integer/u128';
 
 // used for returning quotient and reminder from __divmod128
@@ -7,6 +8,8 @@ import { u128 } from './integer/u128';
 
 // used for returning low and high part of __mulq64, __multi3 etc
 @lazy export var __res128_hi: u64 = 0;
+// used for returning 0 or 1
+@lazy export var __carry: u64 = 0;
 
 /**
  * Convert 128-bit unsigned integer to 64-bit float
@@ -75,14 +78,74 @@ export function __umulq64(a: u64, b: u64): u64 {
 
   var uv = u * v;
   var w0 = uv & 0xFFFFFFFF;
-      uv = a * v + (uv >> 32);
+  uv = a * v + (uv >> 32);
   var w1 = uv >> 32;
-      uv = u * b + (uv & 0xFFFFFFFF);
+  uv = u * b + (uv & 0xFFFFFFFF);
 
   __res128_hi = a * b + w1 + (uv >> 32);
   return (uv << 32) | w0;
 }
 
+// __umul64Hop computes (hi * 2^64 + lo) = z + (x * y)
+// @ts-ignore: decorator
+@inline
+export function __umul64Hop(z: u64, x: u64, y: u64): u64 {
+  var lo = __umulq64(x, y);
+  lo = __uadd64(lo, z);
+  var hi = __res128_hi +__carry;
+  __res128_hi = hi;
+  return lo
+}
+
+// __umul64Step computes (hi * 2^64 + lo) = z + (x * y) + carry.
+// @ts-ignore: decorator
+@inline
+export function __umul64Step(z: u64, x: u64, y: u64, carry: u64): u64 {
+  var lo = __umulq64(x, y)
+  lo = __uadd64(lo, carry);
+  var hi = __uadd64(__res128_hi, 0, __carry);
+  lo = __uadd64(lo, z);
+  hi += __carry;
+  __res128_hi = hi;
+  return lo
+}
+
+// __uadd64 returns the sum with carry of x, y and carry: sum = x + y + carry.
+// The carry input must be 0 or 1; otherwise the behavior is undefined.
+// The carryOut output is guaranteed to be 0 or 1.
+// @ts-ignore: decorator
+@inline
+export function __uadd64(x: u64, y: u64, carry: u64 = 0): u64 {
+  var sum = x + y + carry
+  // // The sum will overflow if both top bits are set (x & y) or if one of them
+  // // is (x | y), and a carry from the lower place happened. If such a carry
+  // // happens, the top bit will be 1 + 0 + 1 = 0 (& ~sum).
+  __carry = ((x & y) | ((x | y) & ~sum)) >>> 63
+  return sum;
+
+}
+
+// u256 * u256 => u256 implemented from https://github.com/holiman/uint256
+// @ts-ignore: decorator
+@global
+export function __mul256(x0: u64, x1: u64, x2: u64, x3: u64, y0: u64, y1: u64, y2: u64, y3: u64): u256 {
+  var lo1 = __umulq64(x0, y0);
+  var res1 = __umul64Hop(__res128_hi, x1, y0);
+  var res2 = __umul64Hop(__res128_hi, x2, y0);
+  var res3 = x3 * y0 + __res128_hi;
+
+  var lo2 = __umul64Hop(res1, x0, y1);
+  res2 = __umul64Step(res2, x1, y1, __res128_hi);
+  res3 += x2 * y1 + __res128_hi;
+
+  var hi1 = __umul64Hop(res2, x0, y2);
+  res3 += x1 * y2 + __res128_hi
+
+  var hi2 = __umul64Hop(res3, x0, y3);
+
+  return new u256(lo1, lo2, hi1, hi2);
+}
+
 // @ts-ignore: decorator
 @global
 export function __multi3(al: u64, ah: u64, bl: u64, bh: u64): u64 {

assembly/integer/u256.ts

@@ -1,6 +1,7 @@
 import { i128 } from './i128';
 import { u128 } from './u128';
 import { u256toDecimalString } from "../utils";
+import { __mul256 } from '../globals';
 
 @lazy const HEX_CHARS = '0123456789abcdef';
 
@@ -141,6 +142,31 @@ export class u256 {
     return new u256(<u64>value, mask, mask, mask);
   }
 
+  /**
+ * Create 256-bit unsigned integer from generic type T
+ * @param  value
+ * @returns 256-bit unsigned integer
+ */
+  @inline
+  static from<T>(value: T): u256 {
+    if (value instanceof bool) return u256.fromU64(<u64>value);
+    else if (value instanceof i8) return u256.fromI64(<i64>value);
+    else if (value instanceof u8) return u256.fromU64(<u64>value);
+    else if (value instanceof i16) return u256.fromI64(<i64>value);
+    else if (value instanceof u16) return u256.fromU64(<u64>value);
+    else if (value instanceof i32) return u256.fromI64(<i64>value);
+    else if (value instanceof u32) return u256.fromU64(<u64>value);
+    else if (value instanceof i64) return u256.fromI64(<i64>value);
+    else if (value instanceof u64) return u256.fromU64(<u64>value);
+    else if (value instanceof f32) return u256.fromF64(<f64>value);
+    else if (value instanceof f64) return u256.fromF64(<f64>value);
+    else if (value instanceof u128) return u256.fromU128(<u128>value);
+    else if (value instanceof u256) return u256.fromU256(<u256>value);
+    else if (value instanceof u8[]) return u256.fromBytes(<u8[]>value);
+    else if (value instanceof Uint8Array) return u256.fromBytes(<Uint8Array>value);
+    else throw new TypeError("Unsupported generic type");
+  }
+
   // TODO
   // static fromString(str: string): u256
 
@@ -431,6 +457,12 @@ export class u256 {
     return !u256.lt(a, b);
   }
 
+  // mul: u256 x u256 = u256
+  @inline @operator('*')
+  static mul(a: u256, b: u256): u256 {
+    return __mul256(a.lo1, a.lo2, a.hi1, a.hi2, b.lo1, b.lo2, b.hi1, b.hi2)
+  }
+
   @inline
   static popcnt(value: u256): i32 {
     var count = popcnt(value.lo1);