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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.
This commit is contained in:
davidot
Linus Groh
parent
2290fbc2a0
commit
8b8cee3172
3 changed files with 241 additions and 71 deletions
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@ -659,96 +659,177 @@ TEST_CASE(test_negative_zero_is_not_allowed)
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EXPECT(!zero.is_negative());
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}
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TEST_CASE(double_comparisons)
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{
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TEST_CASE(double_comparisons) {
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#define EXPECT_LESS_THAN(bigint, double_value) EXPECT_EQ(bigint.compare_to_double(double_value), Crypto::SignedBigInteger::CompareResult::DoubleGreaterThanBigInt)
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#define EXPECT_GREATER_THAN(bigint, double_value) EXPECT_EQ(bigint.compare_to_double(double_value), Crypto::SignedBigInteger::CompareResult::DoubleLessThanBigInt)
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#define EXPECT_EQUAL_TO(bigint, double_value) EXPECT_EQ(bigint.compare_to_double(double_value), Crypto::SignedBigInteger::CompareResult::DoubleEqualsBigInt)
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{
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Crypto::SignedBigInteger zero { 0 };
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EXPECT_EQUAL_TO(zero, 0.0);
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EXPECT_EQUAL_TO(zero, -0.0);
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}
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{ Crypto::SignedBigInteger zero { 0 };
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EXPECT_EQUAL_TO(zero, 0.0);
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EXPECT_EQUAL_TO(zero, -0.0);
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}
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{
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Crypto::SignedBigInteger one { 1 };
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EXPECT_EQUAL_TO(one, 1.0);
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EXPECT_GREATER_THAN(one, -1.0);
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EXPECT_GREATER_THAN(one, 0.5);
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EXPECT_GREATER_THAN(one, -0.5);
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EXPECT_LESS_THAN(one, 1.000001);
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{
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Crypto::SignedBigInteger one { 1 };
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EXPECT_EQUAL_TO(one, 1.0);
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EXPECT_GREATER_THAN(one, -1.0);
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EXPECT_GREATER_THAN(one, 0.5);
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EXPECT_GREATER_THAN(one, -0.5);
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EXPECT_LESS_THAN(one, 1.000001);
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one.negate();
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auto const& negative_one = one;
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EXPECT_EQUAL_TO(negative_one, -1.0);
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EXPECT_LESS_THAN(negative_one, 1.0);
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EXPECT_LESS_THAN(one, 0.5);
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EXPECT_LESS_THAN(one, -0.5);
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EXPECT_GREATER_THAN(one, -1.5);
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EXPECT_LESS_THAN(one, 1.000001);
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EXPECT_GREATER_THAN(one, -1.000001);
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}
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one.negate();
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auto const& negative_one = one;
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EXPECT_EQUAL_TO(negative_one, -1.0);
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EXPECT_LESS_THAN(negative_one, 1.0);
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EXPECT_LESS_THAN(one, 0.5);
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EXPECT_LESS_THAN(one, -0.5);
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EXPECT_GREATER_THAN(one, -1.5);
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EXPECT_LESS_THAN(one, 1.000001);
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EXPECT_GREATER_THAN(one, -1.000001);
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}
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{
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double double_max_value = NumericLimits<double>::max();
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double double_below_max_value = nextafter(double_max_value, 0.0);
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VERIFY(double_below_max_value < double_max_value);
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VERIFY(double_below_max_value < (double_max_value - 1.0));
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auto max_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
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auto max_value_plus_one = max_value_in_bigint.plus(Crypto::SignedBigInteger { 1 });
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auto max_value_minus_one = max_value_in_bigint.minus(Crypto::SignedBigInteger { 1 });
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{
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double double_max_value = NumericLimits<double>::max();
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double double_below_max_value = nextafter(double_max_value, 0.0);
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VERIFY(double_below_max_value < double_max_value);
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VERIFY(double_below_max_value < (double_max_value - 1.0));
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auto max_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
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auto max_value_plus_one = max_value_in_bigint.plus(Crypto::SignedBigInteger { 1 });
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auto max_value_minus_one = max_value_in_bigint.minus(Crypto::SignedBigInteger { 1 });
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auto below_max_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "fffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
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auto below_max_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "fffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
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EXPECT_EQUAL_TO(max_value_in_bigint, double_max_value);
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EXPECT_LESS_THAN(max_value_minus_one, double_max_value);
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EXPECT_GREATER_THAN(max_value_plus_one, double_max_value);
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EXPECT_LESS_THAN(below_max_value_in_bigint, double_max_value);
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EXPECT_EQUAL_TO(max_value_in_bigint, double_max_value);
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EXPECT_LESS_THAN(max_value_minus_one, double_max_value);
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EXPECT_GREATER_THAN(max_value_plus_one, double_max_value);
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EXPECT_LESS_THAN(below_max_value_in_bigint, double_max_value);
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EXPECT_GREATER_THAN(max_value_in_bigint, double_below_max_value);
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EXPECT_GREATER_THAN(max_value_minus_one, double_below_max_value);
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EXPECT_GREATER_THAN(max_value_plus_one, double_below_max_value);
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EXPECT_EQUAL_TO(below_max_value_in_bigint, double_below_max_value);
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}
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EXPECT_GREATER_THAN(max_value_in_bigint, double_below_max_value);
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EXPECT_GREATER_THAN(max_value_minus_one, double_below_max_value);
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EXPECT_GREATER_THAN(max_value_plus_one, double_below_max_value);
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EXPECT_EQUAL_TO(below_max_value_in_bigint, double_below_max_value);
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}
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{
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double double_min_value = NumericLimits<double>::lowest();
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double double_above_min_value = nextafter(double_min_value, 0.0);
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VERIFY(double_above_min_value > double_min_value);
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VERIFY(double_above_min_value > (double_min_value + 1.0));
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auto min_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "-fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
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auto min_value_plus_one = min_value_in_bigint.plus(Crypto::SignedBigInteger { 1 });
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auto min_value_minus_one = min_value_in_bigint.minus(Crypto::SignedBigInteger { 1 });
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{
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double double_min_value = NumericLimits<double>::lowest();
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double double_above_min_value = nextafter(double_min_value, 0.0);
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VERIFY(double_above_min_value > double_min_value);
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VERIFY(double_above_min_value > (double_min_value + 1.0));
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auto min_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "-fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
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auto min_value_plus_one = min_value_in_bigint.plus(Crypto::SignedBigInteger { 1 });
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auto min_value_minus_one = min_value_in_bigint.minus(Crypto::SignedBigInteger { 1 });
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auto above_min_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "-fffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
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auto above_min_value_in_bigint = Crypto::SignedBigInteger::from_base(16, "-fffffffffffff000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv);
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EXPECT_EQUAL_TO(min_value_in_bigint, double_min_value);
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EXPECT_LESS_THAN(min_value_minus_one, double_min_value);
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EXPECT_GREATER_THAN(min_value_plus_one, double_min_value);
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EXPECT_GREATER_THAN(above_min_value_in_bigint, double_min_value);
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EXPECT_EQUAL_TO(min_value_in_bigint, double_min_value);
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EXPECT_LESS_THAN(min_value_minus_one, double_min_value);
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EXPECT_GREATER_THAN(min_value_plus_one, double_min_value);
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EXPECT_GREATER_THAN(above_min_value_in_bigint, double_min_value);
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EXPECT_LESS_THAN(min_value_in_bigint, double_above_min_value);
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EXPECT_LESS_THAN(min_value_minus_one, double_above_min_value);
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EXPECT_LESS_THAN(min_value_plus_one, double_above_min_value);
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EXPECT_EQUAL_TO(above_min_value_in_bigint, double_above_min_value);
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}
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EXPECT_LESS_THAN(min_value_in_bigint, double_above_min_value);
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EXPECT_LESS_THAN(min_value_minus_one, double_above_min_value);
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EXPECT_LESS_THAN(min_value_plus_one, double_above_min_value);
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EXPECT_EQUAL_TO(above_min_value_in_bigint, double_above_min_value);
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}
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{
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double just_above_255 = bit_cast<double>(0x406fe00000000001ULL);
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double just_below_255 = bit_cast<double>(0x406fdfffffffffffULL);
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double double_255 = 255.0;
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Crypto::SignedBigInteger bigint_255 { 255 };
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{
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double just_above_255 = bit_cast<double>(0x406fe00000000001ULL);
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double just_below_255 = bit_cast<double>(0x406fdfffffffffffULL);
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double double_255 = 255.0;
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Crypto::SignedBigInteger bigint_255 { 255 };
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EXPECT_EQUAL_TO(bigint_255, double_255);
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EXPECT_GREATER_THAN(bigint_255, just_below_255);
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EXPECT_LESS_THAN(bigint_255, just_above_255);
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}
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EXPECT_EQUAL_TO(bigint_255, double_255);
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EXPECT_GREATER_THAN(bigint_255, just_below_255);
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EXPECT_LESS_THAN(bigint_255, just_above_255);
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}
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#undef EXPECT_LESS_THAN
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#undef EXPECT_GREATER_THAN
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#undef EXPECT_EQUAL_TO
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}
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TEST_CASE(to_double)
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{
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#define EXPECT_TO_EQUAL_DOUBLE(bigint, double_value) \
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EXPECT_EQ((bigint).to_double(), double_value)
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EXPECT_TO_EQUAL_DOUBLE(Crypto::UnsignedBigInteger(0), 0.0);
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// Make sure we don't get negative zero!
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EXPECT_EQ(signbit(Crypto::UnsignedBigInteger(0).to_double()), 0);
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{
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Crypto::SignedBigInteger zero { 0 };
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EXPECT(!zero.is_negative());
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EXPECT_TO_EQUAL_DOUBLE(zero, 0.0);
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EXPECT_EQ(signbit(zero.to_double()), 0);
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zero.negate();
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EXPECT(!zero.is_negative());
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EXPECT_TO_EQUAL_DOUBLE(zero, 0.0);
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EXPECT_EQ(signbit(zero.to_double()), 0);
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}
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EXPECT_TO_EQUAL_DOUBLE(Crypto::UnsignedBigInteger(9682), 9682.0);
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EXPECT_TO_EQUAL_DOUBLE(Crypto::SignedBigInteger(-9660), -9660.0);
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double double_max_value = NumericLimits<double>::max();
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double infinity = INFINITY;
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::UnsignedBigInteger::from_base(16, "fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
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double_max_value);
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::UnsignedBigInteger::from_base(16, "ffffffffffffff00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
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double_max_value);
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::UnsignedBigInteger::from_base(16, "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"sv),
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double_max_value);
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::UnsignedBigInteger::from_base(16, "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
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infinity);
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::SignedBigInteger::from_base(16, "-fffffffffffff800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
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-double_max_value);
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::SignedBigInteger::from_base(16, "-ffffffffffffff00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
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-double_max_value);
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::SignedBigInteger::from_base(16, "-ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff"sv),
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-double_max_value);
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::SignedBigInteger::from_base(16, "-10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"sv),
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-infinity);
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::UnsignedBigInteger::from_base(16, "ffffffffffffffff"sv),
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18446744073709549568.0);
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::UnsignedBigInteger::from_base(16, "fffffffffffff800"sv),
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18446744073709549568.0);
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EXPECT_TO_EQUAL_DOUBLE(
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Crypto::UnsignedBigInteger::from_base(16, "fffffffffffff8ff"sv),
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18446744073709549568.0);
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EXPECT_TO_EQUAL_DOUBLE(Crypto::SignedBigInteger::from_base(10, "1234567890123456789"sv),
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1234567890123456800.0);
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EXPECT_TO_EQUAL_DOUBLE(Crypto::SignedBigInteger::from_base(10, "2345678901234567890"sv),
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2345678901234567680.0);
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EXPECT_EQ(1234567890123456800.0, 1234567890123456768.0);
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#undef EXPECT_TO_EQUAL_DOUBLE
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}
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namespace AK {
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template<>
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