LibCrypto: Implement a (mostly) proper to_double for UnsignedBigInteger

SignedBigInteger can immediately use this by just negating the double if
the sign bit is set.
For simple cases (below 2^53) we can just convert via an u64, however
above that we need to extract the top 53 bits and use those as the
mantissa.

This function currently does not behave exactly as the JS spec specifies
however it is much less naive than the previous implementation.

1 files changed, 158 insertions, 77 deletions

diff --git a/Tests/LibCrypto/TestBigInteger.cpp b/Tests/LibCrypto/TestBigInteger.cpp
index 308ef61fc9..117f5e1891 100644
--- a/Tests/LibCrypto/TestBigInteger.cpp
+++ b/Tests/LibCrypto/TestBigInteger.cpp
@@ -659,96 +659,177 @@ TEST_CASE(test_negative_zero_is_not_allowed)
     EXPECT(!zero.is_negative());
 }
 
-TEST_CASE(double_comparisons)
-{
+TEST_CASE(double_comparisons) {
 #define EXPECT_LESS_THAN(bigint, double_value) EXPECT_EQ(bigint.compare_to_double(double_value), Crypto::SignedBigInteger::CompareResult::DoubleGreaterThanBigInt)
 #define EXPECT_GREATER_THAN(bigint, double_value) EXPECT_EQ(bigint.compare_to_double(double_value), Crypto::SignedBigInteger::CompareResult::DoubleLessThanBigInt)
 #define EXPECT_EQUAL_TO(bigint, double_value) EXPECT_EQ(bigint.compare_to_double(double_value), Crypto::SignedBigInteger::CompareResult::DoubleEqualsBigInt)
-    {
-        Crypto::SignedBigInteger zero { 0 };
-        EXPECT_EQUAL_TO(zero, 0.0);
-        EXPECT_EQUAL_TO(zero, -0.0);
-    }
+    { Crypto::SignedBigInteger zero { 0 };
+EXPECT_EQUAL_TO(zero, 0.0);
+EXPECT_EQUAL_TO(zero, -0.0);
+}
 
-    {
-        Crypto::SignedBigInteger one { 1 };
-        EXPECT_EQUAL_TO(one, 1.0);
-        EXPECT_GREATER_THAN(one, -1.0);
-        EXPECT_GREATER_THAN(one, 0.5);
-        EXPECT_GREATER_THAN(one, -0.5);
-        EXPECT_LESS_THAN(one, 1.000001);
-
-        one.negate();
-        auto const& negative_one = one;
-        EXPECT_EQUAL_TO(negative_one, -1.0);
-        EXPECT_LESS_THAN(negative_one, 1.0);
-        EXPECT_LESS_THAN(one, 0.5);
-        EXPECT_LESS_THAN(one, -0.5);
-        EXPECT_GREATER_THAN(one, -1.5);
-        EXPECT_LESS_THAN(one, 1.000001);
-        EXPECT_GREATER_THAN(one, -1.000001);
-    }
+{
+    Crypto::SignedBigInteger one { 1 };
+    EXPECT_EQUAL_TO(one, 1.0);
+    EXPECT_GREATER_THAN(one, -1.0);
+    EXPECT_GREATER_THAN(one, 0.5);
+    EXPECT_GREATER_THAN(one, -0.5);
+    EXPECT_LESS_THAN(one, 1.000001);
 
-    {
-        double double_max_value = NumericLimits<double>::max();
-        double double_below_max_value = nextafter(double_max_value, 0.0);
-        VERIFY(double_below_max_value < double_max_value);
-        VERIFY(double_below_max_value < (double_max_value - 1.0));
-        auto max_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
-        auto max_value_plus_one = max_value_in_bigint.plus(Crypto::SignedBigInteger { 1 });
-        auto max_value_minus_one = max_value_in_bigint.minus(Crypto::SignedBigInteger { 1 });
-
-        auto below_max_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "fffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
-
-        EXPECT_EQUAL_TO(max_value_in_bigint, double_max_value);
-        EXPECT_LESS_THAN(max_value_minus_one, double_max_value);
-        EXPECT_GREATER_THAN(max_value_plus_one, double_max_value);
-        EXPECT_LESS_THAN(below_max_value_in_bigint, double_max_value);
-
-        EXPECT_GREATER_THAN(max_value_in_bigint, double_below_max_value);
-        EXPECT_GREATER_THAN(max_value_minus_one, double_below_max_value);
-        EXPECT_GREATER_THAN(max_value_plus_one, double_below_max_value);
-        EXPECT_EQUAL_TO(below_max_value_in_bigint, double_below_max_value);
-    }
+    one.negate();
+    auto const& negative_one = one;
+    EXPECT_EQUAL_TO(negative_one, -1.0);
+    EXPECT_LESS_THAN(negative_one, 1.0);
+    EXPECT_LESS_THAN(one, 0.5);
+    EXPECT_LESS_THAN(one, -0.5);
+    EXPECT_GREATER_THAN(one, -1.5);
+    EXPECT_LESS_THAN(one, 1.000001);
+    EXPECT_GREATER_THAN(one, -1.000001);
+}
 
-    {
-        double double_min_value = NumericLimits<double>::lowest();
-        double double_above_min_value = nextafter(double_min_value, 0.0);
-        VERIFY(double_above_min_value > double_min_value);
-        VERIFY(double_above_min_value > (double_min_value + 1.0));
-        auto min_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "-fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
-        auto min_value_plus_one = min_value_in_bigint.plus(Crypto::SignedBigInteger { 1 });
-        auto min_value_minus_one = min_value_in_bigint.minus(Crypto::SignedBigInteger { 1 });
-
-        auto above_min_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "-fffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
-
-        EXPECT_EQUAL_TO(min_value_in_bigint, double_min_value);
-        EXPECT_LESS_THAN(min_value_minus_one, double_min_value);
-        EXPECT_GREATER_THAN(min_value_plus_one, double_min_value);
-        EXPECT_GREATER_THAN(above_min_value_in_bigint, double_min_value);
-
-        EXPECT_LESS_THAN(min_value_in_bigint, double_above_min_value);
-        EXPECT_LESS_THAN(min_value_minus_one, double_above_min_value);
-        EXPECT_LESS_THAN(min_value_plus_one, double_above_min_value);
-        EXPECT_EQUAL_TO(above_min_value_in_bigint, double_above_min_value);
-    }
+{
+    double double_max_value = NumericLimits<double>::max();
+    double double_below_max_value = nextafter(double_max_value, 0.0);
+    VERIFY(double_below_max_value < double_max_value);
+    VERIFY(double_below_max_value < (double_max_value - 1.0));
+    auto max_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
+    auto max_value_plus_one = max_value_in_bigint.plus(Crypto::SignedBigInteger { 1 });
+    auto max_value_minus_one = max_value_in_bigint.minus(Crypto::SignedBigInteger { 1 });
 
-    {
-        double just_above_255 = bit_cast<double>(0x406fe00000000001ULL);
-        double just_below_255 = bit_cast<double>(0x406fdfffffffffffULL);
-        double double_255 = 255.0;
-        Crypto::SignedBigInteger bigint_255 { 255 };
-
-        EXPECT_EQUAL_TO(bigint_255, double_255);
-        EXPECT_GREATER_THAN(bigint_255, just_below_255);
-        EXPECT_LESS_THAN(bigint_255, just_above_255);
-    }
+    auto below_max_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "fffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
+
+    EXPECT_EQUAL_TO(max_value_in_bigint, double_max_value);
+    EXPECT_LESS_THAN(max_value_minus_one, double_max_value);
+    EXPECT_GREATER_THAN(max_value_plus_one, double_max_value);
+    EXPECT_LESS_THAN(below_max_value_in_bigint, double_max_value);
+
+    EXPECT_GREATER_THAN(max_value_in_bigint, double_below_max_value);
+    EXPECT_GREATER_THAN(max_value_minus_one, double_below_max_value);
+    EXPECT_GREATER_THAN(max_value_plus_one, double_below_max_value);
+    EXPECT_EQUAL_TO(below_max_value_in_bigint, double_below_max_value);
+}
+
+{
+    double double_min_value = NumericLimits<double>::lowest();
+    double double_above_min_value = nextafter(double_min_value, 0.0);
+    VERIFY(double_above_min_value > double_min_value);
+    VERIFY(double_above_min_value > (double_min_value + 1.0));
+    auto min_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "-fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
+    auto min_value_plus_one = min_value_in_bigint.plus(Crypto::SignedBigInteger { 1 });
+    auto min_value_minus_one = min_value_in_bigint.minus(Crypto::SignedBigInteger { 1 });
+
+    auto above_min_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "-fffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
+
+    EXPECT_EQUAL_TO(min_value_in_bigint, double_min_value);
+    EXPECT_LESS_THAN(min_value_minus_one, double_min_value);
+    EXPECT_GREATER_THAN(min_value_plus_one, double_min_value);
+    EXPECT_GREATER_THAN(above_min_value_in_bigint, double_min_value);
+
+    EXPECT_LESS_THAN(min_value_in_bigint, double_above_min_value);
+    EXPECT_LESS_THAN(min_value_minus_one, double_above_min_value);
+    EXPECT_LESS_THAN(min_value_plus_one, double_above_min_value);
+    EXPECT_EQUAL_TO(above_min_value_in_bigint, double_above_min_value);
+}
+
+{
+    double just_above_255 = bit_cast<double>(0x406fe00000000001ULL);
+    double just_below_255 = bit_cast<double>(0x406fdfffffffffffULL);
+    double double_255 = 255.0;
+    Crypto::SignedBigInteger bigint_255 { 255 };
+
+    EXPECT_EQUAL_TO(bigint_255, double_255);
+    EXPECT_GREATER_THAN(bigint_255, just_below_255);
+    EXPECT_LESS_THAN(bigint_255, just_above_255);
+}
 
 #undef EXPECT_LESS_THAN
 #undef EXPECT_GREATER_THAN
 #undef EXPECT_EQUAL_TO
 }
 
+TEST_CASE(to_double)
+{
+#define EXPECT_TO_EQUAL_DOUBLE(bigint, double_value) \
+    EXPECT_EQ((bigint).to_double(), double_value)
+
+    EXPECT_TO_EQUAL_DOUBLE(Crypto::UnsignedBigInteger(0), 0.0);
+    // Make sure we don't get negative zero!
+    EXPECT_EQ(signbit(Crypto::UnsignedBigInteger(0).to_double()), 0);
+    {
+        Crypto::SignedBigInteger zero { 0 };
+
+        EXPECT(!zero.is_negative());
+        EXPECT_TO_EQUAL_DOUBLE(zero, 0.0);
+        EXPECT_EQ(signbit(zero.to_double()), 0);
+
+        zero.negate();
+
+        EXPECT(!zero.is_negative());
+        EXPECT_TO_EQUAL_DOUBLE(zero, 0.0);
+        EXPECT_EQ(signbit(zero.to_double()), 0);
+    }
+
+    EXPECT_TO_EQUAL_DOUBLE(Crypto::UnsignedBigInteger(9682), 9682.0);
+    EXPECT_TO_EQUAL_DOUBLE(Crypto::SignedBigInteger(-9660), -9660.0);
+
+    double double_max_value = NumericLimits<double>::max();
+    double infinity = INFINITY;
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::UnsignedBigInteger::from_base(16, "fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
+        double_max_value);
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::UnsignedBigInteger::from_base(16, "ffffffffffffff00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
+        double_max_value);
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::UnsignedBigInteger::from_base(16, "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"sv),
+        double_max_value);
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::UnsignedBigInteger::from_base(16, "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
+        infinity);
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::SignedBigInteger::from_base(16, "-fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
+        -double_max_value);
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::SignedBigInteger::from_base(16, "-ffffffffffffff00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
+        -double_max_value);
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::SignedBigInteger::from_base(16, "-ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"sv),
+        -double_max_value);
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::SignedBigInteger::from_base(16, "-10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
+        -infinity);
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::UnsignedBigInteger::from_base(16, "ffffffffffffffff"sv),
+        18446744073709549568.0);
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::UnsignedBigInteger::from_base(16, "fffffffffffff800"sv),
+        18446744073709549568.0);
+
+    EXPECT_TO_EQUAL_DOUBLE(
+        Crypto::UnsignedBigInteger::from_base(16, "fffffffffffff8ff"sv),
+        18446744073709549568.0);
+
+    EXPECT_TO_EQUAL_DOUBLE(Crypto::SignedBigInteger::from_base(10, "1234567890123456789"sv),
+        1234567890123456800.0);
+
+    EXPECT_TO_EQUAL_DOUBLE(Crypto::SignedBigInteger::from_base(10, "2345678901234567890"sv),
+        2345678901234567680.0);
+
+    EXPECT_EQ(1234567890123456800.0, 1234567890123456768.0);
+
+#undef EXPECT_TO_EQUAL_DOUBLE
+}
+
 namespace AK {
 
 template<>