[bigint] Implement comparisons with Numbers/Strings

This patch provides "Abstract Comparison" functions on the BigInt
class for comparing BigInts to Numbers and Strings.
The functionality is not exposed to JavaScript yet.

Bug: v8:6791
Change-Id: I835f290203a31f363970b1edb359e19af6dabc5d
Reviewed-on: https://chromium-review.googlesource.com/722324
Commit-Queue: Georg Neis <neis@chromium.org>
Reviewed-by: Andreas Haas <ahaas@chromium.org>
Cr-Commit-Position: refs/heads/master@{#48718}

src/conversions.h

@@ -113,7 +113,8 @@ MaybeHandle<BigInt> StringToBigInt(Isolate* isolate, Handle<String> string,
 //   0x -> hex
 //   0o -> octal
 //   0b -> binary
-MaybeHandle<BigInt> StringToBigInt(Isolate* isolate, const char* string);
+V8_EXPORT_PRIVATE MaybeHandle<BigInt> StringToBigInt(Isolate* isolate,
+                                                     const char* string);
 
 const int kDoubleToCStringMinBufferSize = 100;
 

src/objects.cc

@@ -627,7 +627,7 @@ bool Object::StrictEquals(Object* that) {
     return String::cast(this)->Equals(String::cast(that));
   } else if (this->IsBigInt()) {
     if (!that->IsBigInt()) return false;
-    return BigInt::Equal(BigInt::cast(this), BigInt::cast(that));
+    return BigInt::EqualToBigInt(BigInt::cast(this), BigInt::cast(that));
   }
   return this == that;
 }
@@ -2437,7 +2437,7 @@ bool Object::SameValue(Object* other) {
     return String::cast(this)->Equals(String::cast(other));
   }
   if (IsBigInt() && other->IsBigInt()) {
-    return BigInt::Equal(BigInt::cast(this), BigInt::cast(other));
+    return BigInt::EqualToBigInt(BigInt::cast(this), BigInt::cast(other));
   }
   return false;
 }
@@ -2457,7 +2457,7 @@ bool Object::SameValueZero(Object* other) {
     return String::cast(this)->Equals(String::cast(other));
   }
   if (IsBigInt() && other->IsBigInt()) {
-    return BigInt::Equal(BigInt::cast(this), BigInt::cast(other));
+    return BigInt::EqualToBigInt(BigInt::cast(this), BigInt::cast(other));
   }
   return false;
 }

src/objects/bigint.cc

@@ -19,6 +19,7 @@
 
 #include "src/objects/bigint.h"
 
+#include "src/double.h"
 #include "src/objects-inl.h"
 
 namespace v8 {
@@ -165,15 +166,37 @@ MaybeHandle<BigInt> BigInt::UnsignedRightShift(Handle<BigInt> x,
                   BigInt);
 }
 
-bool BigInt::LessThan(Handle<BigInt> x, Handle<BigInt> y) {
-  if (x->sign() == y->sign()) {
+namespace {
+
+// Produces comparison result for {left_negative} == sign(x) != sign(y).
+ComparisonResult UnequalSign(bool left_negative) {
+  return left_negative ? ComparisonResult::kLessThan
+                       : ComparisonResult::kGreaterThan;
+}
+// Produces result for |x| > |y|, with {both_negative} == sign(x) == sign(y);
+ComparisonResult AbsoluteGreater(bool both_negative) {
+  return both_negative ? ComparisonResult::kLessThan
+                       : ComparisonResult::kGreaterThan;
+}
+// Produces result for |x| < |y|, with {both_negative} == sign(x) == sign(y).
+ComparisonResult AbsoluteLess(bool both_negative) {
+  return both_negative ? ComparisonResult::kGreaterThan
+                       : ComparisonResult::kLessThan;
+}
+
+}  // namespace
+
+ComparisonResult BigInt::CompareToBigInt(Handle<BigInt> x, Handle<BigInt> y) {
+  bool x_sign = x->sign();
+  if (x_sign != y->sign()) return UnequalSign(x_sign);
+
   int result = AbsoluteCompare(x, y);
-    return x->sign() ? (result > 0) : (result < 0);
-  }
-  return x->sign();
+  if (result > 0) return AbsoluteGreater(x_sign);
+  if (result < 0) return AbsoluteLess(x_sign);
+  return ComparisonResult::kEqual;
 }
 
-bool BigInt::Equal(BigInt* x, BigInt* y) {
+bool BigInt::EqualToBigInt(BigInt* x, BigInt* y) {
   if (x->sign() != y->sign()) return false;
   if (x->length() != y->length()) return false;
   for (int i = 0; i < x->length(); i++) {
@@ -279,6 +302,173 @@ MaybeHandle<BigInt> BigInt::Decrement(Handle<BigInt> x) {
   return result;
 }
 
+bool BigInt::EqualToString(Handle<BigInt> x, Handle<String> y) {
+  Isolate* isolate = x->GetIsolate();
+  // a. Let n be StringToBigInt(y).
+  MaybeHandle<BigInt> maybe_n = StringToBigInt(isolate, y, 10);
+  // b. If n is NaN, return false.
+  Handle<BigInt> n;
+  if (!maybe_n.ToHandle(&n)) {
+    DCHECK(isolate->has_pending_exception());
+    isolate->clear_pending_exception();
+    return false;
+  }
+  // c. Return the result of x == n.
+  return EqualToBigInt(*x, *n);
+}
+
+bool BigInt::EqualToNumber(Handle<BigInt> x, Handle<Object> y) {
+  DCHECK(y->IsNumber());
+  // a. If x or y are any of NaN, +∞, or -∞, return false.
+  // b. If the mathematical value of x is equal to the mathematical value of y,
+  //    return true, otherwise return false.
+  if (y->IsSmi()) {
+    int value = Smi::ToInt(*y);
+    if (value == 0) return x->is_zero();
+    // Any multi-digit BigInt is bigger than a Smi.
+    STATIC_ASSERT(sizeof(digit_t) >= sizeof(value));
+    return (x->length() == 1) && (x->sign() == (value < 0)) &&
+           (x->digit(0) ==
+            static_cast<digit_t>(std::abs(static_cast<int64_t>(value))));
+  }
+  DCHECK(y->IsHeapNumber());
+  double value = Handle<HeapNumber>::cast(y)->value();
+  return CompareToDouble(x, value) == ComparisonResult::kEqual;
+}
+
+ComparisonResult BigInt::CompareToNumber(Handle<BigInt> x, Handle<Object> y) {
+  DCHECK(y->IsNumber());
+  if (y->IsSmi()) {
+    bool x_sign = x->sign();
+    int y_value = Smi::ToInt(*y);
+    bool y_sign = (y_value < 0);
+    if (x_sign != y_sign) return UnequalSign(x_sign);
+
+    if (x->is_zero()) {
+      DCHECK(!y_sign);
+      return y_value == 0 ? ComparisonResult::kEqual
+                          : ComparisonResult::kLessThan;
+    }
+    // Any multi-digit BigInt is bigger than a Smi.
+    STATIC_ASSERT(sizeof(digit_t) >= sizeof(y_value));
+    if (x->length() > 1) return AbsoluteGreater(x_sign);
+
+    digit_t abs_value = std::abs(static_cast<int64_t>(y_value));
+    digit_t x_digit = x->digit(0);
+    if (x_digit > abs_value) return AbsoluteGreater(x_sign);
+    if (x_digit < abs_value) return AbsoluteLess(x_sign);
+    return ComparisonResult::kEqual;
+  }
+  DCHECK(y->IsHeapNumber());
+  double value = Handle<HeapNumber>::cast(y)->value();
+  return CompareToDouble(x, value);
+}
+
+ComparisonResult BigInt::CompareToDouble(Handle<BigInt> x, double y) {
+  if (std::isnan(y)) return ComparisonResult::kUndefined;
+  if (y == V8_INFINITY) return ComparisonResult::kLessThan;
+  if (y == -V8_INFINITY) return ComparisonResult::kGreaterThan;
+  bool x_sign = x->sign();
+  // Note that this is different from the double's sign bit for -0. That's
+  // intentional because -0 must be treated like 0.
+  bool y_sign = (y < 0);
+  if (x_sign != y_sign) return UnequalSign(x_sign);
+  if (y == 0) {
+    DCHECK(!x_sign);
+    return x->is_zero() ? ComparisonResult::kEqual
+                        : ComparisonResult::kGreaterThan;
+  }
+  if (x->is_zero()) {
+    DCHECK(!y_sign);
+    return ComparisonResult::kLessThan;
+  }
+  uint64_t double_bits = bit_cast<uint64_t>(y);
+  int raw_exponent =
+      static_cast<int>(double_bits >> Double::kPhysicalSignificandSize) & 0x7FF;
+  uint64_t mantissa = double_bits & Double::kSignificandMask;
+  // Non-finite doubles are handled above.
+  DCHECK_NE(raw_exponent, 0x7FF);
+  int exponent = raw_exponent - 0x3FF;
+  if (exponent < 0) {
+    // The absolute value of the double is less than 1. Only 0n has an
+    // absolute value smaller than that, but we've already covered that case.
+    DCHECK(!x->is_zero());
+    return AbsoluteGreater(x_sign);
+  }
+  int x_length = x->length();
+  digit_t x_msd = x->digit(x_length - 1);
+  int msd_leading_zeros = base::bits::CountLeadingZeros(x_msd);
+  int x_bitlength = x_length * kDigitBits - msd_leading_zeros;
+  int y_bitlength = exponent + 1;
+  if (x_bitlength < y_bitlength) return AbsoluteLess(x_sign);
+  if (x_bitlength > y_bitlength) return AbsoluteGreater(x_sign);
+
+  // At this point, we know that signs and bit lengths (i.e. position of
+  // the most significant bit in exponent-free representation) are identical.
+  // {x} is not zero, {y} is finite and not denormal.
+  // Now we virtually convert the double to an integer by shifting its
+  // mantissa according to its exponent, so it will align with the BigInt {x},
+  // and then we compare them bit for bit until we find a difference or the
+  // least significant bit.
+  //                    <----- 52 ------> <-- virtual trailing zeroes -->
+  // y / mantissa:     1yyyyyyyyyyyyyyyyy 0000000000000000000000000000000
+  // x / digits:    0001xxxx xxxxxxxx xxxxxxxx ...
+  //                    <-->          <------>
+  //              msd_topbit         kDigitBits
+  //
+  mantissa |= Double::kHiddenBit;
+  const int kMantissaTopBit = 52;  // 0-indexed.
+  // 0-indexed position of {x}'s most significant bit within the {msd}.
+  int msd_topbit = kDigitBits - 1 - msd_leading_zeros;
+  DCHECK_EQ(msd_topbit, (x_bitlength - 1) % kDigitBits);
+  // Shifted chunk of {mantissa} for comparing with {digit}.
+  digit_t compare_mantissa;
+  // Number of unprocessed bits in {mantissa}. We'll keep them shifted to
+  // the left (i.e. most significant part) of the underlying uint64_t.
+  int remaining_mantissa_bits = 0;
+
+  // First, compare the most significant digit against the beginning of
+  // the mantissa.
+  if (msd_topbit < kMantissaTopBit) {
+    remaining_mantissa_bits = (kMantissaTopBit - msd_topbit);
+    compare_mantissa = mantissa >> remaining_mantissa_bits;
+    mantissa = mantissa << (64 - remaining_mantissa_bits);
+  } else {
+    DCHECK(msd_topbit >= kMantissaTopBit);
+    compare_mantissa = mantissa << (msd_topbit - kMantissaTopBit);
+    mantissa = 0;
+  }
+  if (x_msd > compare_mantissa) return AbsoluteGreater(x_sign);
+  if (x_msd < compare_mantissa) return AbsoluteLess(x_sign);
+
+  // Then, compare additional digits against any remaining mantissa bits.
+  for (int digit_index = x_length - 2; digit_index >= 0; digit_index--) {
+    if (remaining_mantissa_bits > 0) {
+      remaining_mantissa_bits -= kDigitBits;
+      if (sizeof(mantissa) != sizeof(x_msd)) {
+        compare_mantissa = mantissa >> (64 - kDigitBits);
+        // "& 63" to appease compilers. kDigitBits is 32 here anyway.
+        mantissa = mantissa << (kDigitBits & 63);
+      } else {
+        compare_mantissa = mantissa;
+        mantissa = 0;
+      }
+    } else {
+      compare_mantissa = 0;
+    }
+    digit_t digit = x->digit(digit_index);
+    if (digit > compare_mantissa) return AbsoluteGreater(x_sign);
+    if (digit < compare_mantissa) return AbsoluteLess(x_sign);
+  }
+
+  // Integer parts are equal; check whether {y} has a fractional part.
+  if (mantissa != 0) {
+    DCHECK(remaining_mantissa_bits > 0);
+    return AbsoluteLess(x_sign);
+  }
+  return ComparisonResult::kEqual;
+}
+
 MaybeHandle<String> BigInt::ToString(Handle<BigInt> bigint, int radix) {
   Isolate* isolate = bigint->GetIsolate();
   if (bigint->is_zero()) {

src/objects/bigint.h

@@ -17,7 +17,7 @@ namespace internal {
 
 // UNDER CONSTRUCTION!
 // Arbitrary precision integers in JavaScript.
-class BigInt : public HeapObject {
+class V8_EXPORT_PRIVATE BigInt : public HeapObject {
  public:
   // Implementation of the Spec methods, see:
   // https://tc39.github.io/proposal-bigint/#sec-numeric-types
@@ -36,22 +36,29 @@ class BigInt : public HeapObject {
                                               Handle<BigInt> y);
   static MaybeHandle<BigInt> UnsignedRightShift(Handle<BigInt> x,
                                                 Handle<BigInt> y);
-  static bool LessThan(Handle<BigInt> x, Handle<BigInt> y);
-  static bool Equal(BigInt* x, BigInt* y);
+  // More convenient version of "bool LessThan(x, y)".
+  static ComparisonResult CompareToBigInt(Handle<BigInt> x, Handle<BigInt> y);
+  static bool EqualToBigInt(BigInt* x, BigInt* y);
   static Handle<BigInt> BitwiseAnd(Handle<BigInt> x, Handle<BigInt> y);
   static Handle<BigInt> BitwiseXor(Handle<BigInt> x, Handle<BigInt> y);
   static Handle<BigInt> BitwiseOr(Handle<BigInt> x, Handle<BigInt> y);
 
+  // Other parts of the public interface.
   static MaybeHandle<BigInt> Increment(Handle<BigInt> x);
   static MaybeHandle<BigInt> Decrement(Handle<BigInt> x);
 
-  // Other parts of the public interface.
   bool ToBoolean() { return !is_zero(); }
   uint32_t Hash() {
     // TODO(jkummerow): Improve this. At least use length and sign.
     return is_zero() ? 0 : ComputeIntegerHash(static_cast<uint32_t>(digit(0)));
   }
 
+  static bool EqualToString(Handle<BigInt> x, Handle<String> y);
+  static bool EqualToNumber(Handle<BigInt> x, Handle<Object> y);
+  static ComparisonResult CompareToNumber(Handle<BigInt> x, Handle<Object> y);
+  // Exposed for tests, do not call directly. Use CompareToNumber() instead.
+  static ComparisonResult CompareToDouble(Handle<BigInt> x, double y);
+
   DECL_CAST(BigInt)
   DECL_VERIFIER(BigInt)
   DECL_PRINTER(BigInt)

src/runtime/runtime-bigint.cc

@@ -19,7 +19,7 @@ RUNTIME_FUNCTION(Runtime_BigIntEqual) {
   CONVERT_ARG_HANDLE_CHECKED(Object, lhs, 0);
   CONVERT_ARG_HANDLE_CHECKED(Object, rhs, 1);
   bool result = lhs->IsBigInt() && rhs->IsBigInt() &&
-                BigInt::Equal(BigInt::cast(*lhs), BigInt::cast(*rhs));
+                BigInt::EqualToBigInt(BigInt::cast(*lhs), BigInt::cast(*rhs));
   return *isolate->factory()->ToBoolean(result);
 }
 

test/unittests/BUILD.gn

@@ -63,6 +63,7 @@ v8_source_set("unittests_sources") {
     "base/sys-info-unittest.cc",
     "base/template-utils-unittest.cc",
     "base/utils/random-number-generator-unittest.cc",
+    "bigint-unittest.cc",
     "cancelable-tasks-unittest.cc",
     "char-predicates-unittest.cc",
     "code-stub-assembler-unittest.cc",

test/unittests/bigint-unittest.cc

+// Copyright 2017 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#include <cmath>
+
+#include "src/conversions.h"
+#include "src/factory.h"
+#include "src/isolate.h"
+#include "src/objects-inl.h"
+#include "src/objects/bigint-inl.h"
+#include "test/unittests/test-utils.h"
+
+#include "testing/gtest/include/gtest/gtest.h"
+
+namespace v8 {
+namespace internal {
+
+typedef TestWithIsolate BigIntWithIsolate;
+
+void Compare(Handle<BigInt> x, double value, ComparisonResult expected) {
+  CHECK_EQ(expected, BigInt::CompareToDouble(x, value));
+}
+
+TEST_F(BigIntWithIsolate, CompareToDouble) {
+  Factory* factory = isolate()->factory();
+  Handle<BigInt> zero = factory->NewBigIntFromInt(0);
+  Handle<BigInt> one = factory->NewBigIntFromInt(1);
+  Handle<BigInt> minus_one = factory->NewBigIntFromInt(-1);
+
+  // Non-finite doubles.
+  Compare(zero, std::nan(""), ComparisonResult::kUndefined);
+  Compare(one, INFINITY, ComparisonResult::kLessThan);
+  Compare(one, -INFINITY, ComparisonResult::kGreaterThan);
+
+  // Unequal sign.
+  Compare(one, -1, ComparisonResult::kGreaterThan);
+  Compare(minus_one, 1, ComparisonResult::kLessThan);
+
+  // Cases involving zero.
+  Compare(zero, 0, ComparisonResult::kEqual);
+  Compare(zero, -0, ComparisonResult::kEqual);
+  Compare(one, 0, ComparisonResult::kGreaterThan);
+  Compare(minus_one, 0, ComparisonResult::kLessThan);
+  Compare(zero, 1, ComparisonResult::kLessThan);
+  Compare(zero, -1, ComparisonResult::kGreaterThan);
+
+  // Small doubles.
+  Compare(zero, 0.25, ComparisonResult::kLessThan);
+  Compare(one, 0.5, ComparisonResult::kGreaterThan);
+  Compare(one, -0.5, ComparisonResult::kGreaterThan);
+  Compare(zero, -0.25, ComparisonResult::kGreaterThan);
+  Compare(minus_one, -0.5, ComparisonResult::kLessThan);
+
+  // Different bit lengths.
+  Handle<BigInt> four = factory->NewBigIntFromInt(4);
+  Handle<BigInt> minus_five = factory->NewBigIntFromInt(-5);
+  Compare(four, 3.9, ComparisonResult::kGreaterThan);
+  Compare(four, 1.5, ComparisonResult::kGreaterThan);
+  Compare(four, 8, ComparisonResult::kLessThan);
+  Compare(four, 16, ComparisonResult::kLessThan);
+  Compare(minus_five, -4.9, ComparisonResult::kLessThan);
+  Compare(minus_five, -4, ComparisonResult::kLessThan);
+  Compare(minus_five, -25, ComparisonResult::kGreaterThan);
+
+  // Same bit length, difference in first digit.
+  double big_double = 4428155326412785451008.0;
+  Handle<BigInt> big =
+      StringToBigInt(isolate(), "0xF10D00000000000000").ToHandleChecked();
+  Compare(big, big_double, ComparisonResult::kGreaterThan);
+  big = StringToBigInt(isolate(), "0xE00D00000000000000").ToHandleChecked();
+  Compare(big, big_double, ComparisonResult::kLessThan);
+
+  double other_double = -13758438578910658560.0;
+  Handle<BigInt> other =
+      StringToBigInt(isolate(), "-0xBEEFC1FE00000000").ToHandleChecked();
+  Compare(other, other_double, ComparisonResult::kGreaterThan);
+  other = StringToBigInt(isolate(), "-0xBEEFCBFE00000000").ToHandleChecked();
+  Compare(other, other_double, ComparisonResult::kLessThan);
+
+  // Same bit length, difference in non-first digit.
+  big = StringToBigInt(isolate(), "0xF00D00000000000001").ToHandleChecked();
+  Compare(big, big_double, ComparisonResult::kGreaterThan);
+  big = StringToBigInt(isolate(), "0xF00A00000000000000").ToHandleChecked();
+  Compare(big, big_double, ComparisonResult::kLessThan);
+
+  other = StringToBigInt(isolate(), "-0xBEEFCAFE00000001").ToHandleChecked();
+  Compare(other, other_double, ComparisonResult::kLessThan);
+
+  // Same bit length, difference in fractional part.
+  Compare(one, 1.5, ComparisonResult::kLessThan);
+  Compare(minus_one, -1.25, ComparisonResult::kGreaterThan);
+  big = factory->NewBigIntFromInt(0xF00D00);
+  Compare(big, 15731968.125, ComparisonResult::kLessThan);
+  Compare(big, 15731967.875, ComparisonResult::kGreaterThan);
+  big = StringToBigInt(isolate(), "0x123456789ab").ToHandleChecked();
+  Compare(big, 1250999896491.125, ComparisonResult::kLessThan);
+
+  // Equality!
+  Compare(one, 1, ComparisonResult::kEqual);
+  Compare(minus_one, -1, ComparisonResult::kEqual);
+  big = StringToBigInt(isolate(), "0xF00D00000000000000").ToHandleChecked();
+  Compare(big, big_double, ComparisonResult::kEqual);
+
+  Handle<BigInt> two_52 =
+      StringToBigInt(isolate(), "0x10000000000000").ToHandleChecked();
+  Compare(two_52, 4503599627370496.0, ComparisonResult::kEqual);
+}
+
+}  // namespace internal
+}  // namespace v8

test/unittests/unittests.gyp

@@ -36,6 +36,7 @@
       'base/sys-info-unittest.cc',
       'base/template-utils-unittest.cc',
       'base/utils/random-number-generator-unittest.cc',
+      'bigint-unittest.cc',
       'cancelable-tasks-unittest.cc',
       'char-predicates-unittest.cc',
       "code-stub-assembler-unittest.cc",