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.

2 files changed, 91 insertions, 2 deletions

diff --git a/Userland/Libraries/LibCrypto/BigInt/SignedBigInteger.cpp b/Userland/Libraries/LibCrypto/BigInt/SignedBigInteger.cpp
index 48e56970a4..c4a49190e6 100644
--- a/Userland/Libraries/LibCrypto/BigInt/SignedBigInteger.cpp
+++ b/Userland/Libraries/LibCrypto/BigInt/SignedBigInteger.cpp
@@ -70,6 +70,8 @@ double SignedBigInteger::to_double() const
     double unsigned_value = m_unsigned_data.to_double();
     if (!m_sign)
         return unsigned_value;
+
+    VERIFY(!is_zero());
     return -unsigned_value;
 }
 
diff --git a/Userland/Libraries/LibCrypto/BigInt/UnsignedBigInteger.cpp b/Userland/Libraries/LibCrypto/BigInt/UnsignedBigInteger.cpp
index 23fcd2dde9..d9b8e7566d 100644
--- a/Userland/Libraries/LibCrypto/BigInt/UnsignedBigInteger.cpp
+++ b/Userland/Libraries/LibCrypto/BigInt/UnsignedBigInteger.cpp
@@ -115,8 +115,95 @@ u64 UnsignedBigInteger::to_u64() const
 
 double UnsignedBigInteger::to_double() const
 {
-    // FIXME: I am naive
-    return static_cast<double>(to_u64());
+    // NOTE: This function rounds toward zero!
+    // FIXME: Which is not exactly what we should do for JS when converting to number:
+    //        See: https://tc39.es/ecma262/#sec-number-constructor-number-value
+    //        Which has step 1.b If Type(prim) is BigInt, let n be 𝔽(ℝ(prim)).
+    //        Which then references: https://tc39.es/ecma262/#sec-ecmascript-language-types-number-type
+    //        Which is equivalent to (This procedure corresponds exactly to the behaviour of the IEEE 754-2019 roundTiesToEven mode.)
+
+    auto highest_bit = one_based_index_of_highest_set_bit();
+    if (highest_bit == 0)
+        return 0;
+    --highest_bit;
+
+    // Simple case if less than 2^53 since those number are all exactly representable in doubles
+    if (highest_bit < 53)
+        return static_cast<double>(to_u64());
+
+    constexpr u64 mantissa_size = 52;
+    constexpr u64 exponent_size = 11;
+    constexpr auto exponent_bias = (1 << (exponent_size - 1)) - 1;
+
+    // If it uses too many bit to represent in a double return infinity
+    if (highest_bit > exponent_bias)
+        return __builtin_huge_val();
+
+    // Otherwise we have to take the top 53 bits, use those as the mantissa,
+    // and the amount of bits as the exponent. Note that the mantissa has an implicit top bit of 1
+    // so we have to ignore the very top bit.
+
+    // Since we extract at most 53 bits it will take at most 3 words
+    static_assert(BITS_IN_WORD * 3 >= (mantissa_size + 1));
+    constexpr auto bits_in_u64 = 64;
+    static_assert(bits_in_u64 > mantissa_size + 1);
+
+    auto bits_to_read = min(mantissa_size + 1, highest_bit);
+
+    auto last_word_index = trimmed_length();
+    VERIFY(last_word_index > 0);
+
+    // Note that highest bit is 0-indexed at this point.
+    auto highest_bit_index_in_top_word = highest_bit % BITS_IN_WORD;
+
+    // Shift initial word until highest bit is just beyond top of u64.
+    u64 mantissa = static_cast<u64>(m_words[last_word_index - 1]) << (bits_in_u64 - highest_bit_index_in_top_word);
+
+    auto bits_written = highest_bit_index_in_top_word;
+
+    --last_word_index;
+
+    if (bits_written < bits_to_read && last_word_index > 0) {
+        // Second word can always just cleanly be shifted upto the final bit of the first word
+        // since the first has at most BIT_IN_WORD - 1, 31
+        u64 next_word = m_words[last_word_index - 1];
+        VERIFY((mantissa & (next_word << (bits_in_u64 - bits_written - BITS_IN_WORD))) == 0);
+        mantissa |= next_word << (bits_in_u64 - bits_written - BITS_IN_WORD);
+        bits_written += BITS_IN_WORD;
+        --last_word_index;
+
+        if (bits_written < bits_to_read && last_word_index > 0) {
+            // The final word has to be shifted down first to discard any excess bits.
+            u64 final_word = m_words[last_word_index - 1];
+
+            auto bits_to_write = bits_to_read - bits_written;
+
+            final_word >>= (BITS_IN_WORD - bits_to_write);
+
+            // Then move the bits right up to the lowest bits of the second word
+            VERIFY((mantissa & (final_word << (bits_in_u64 - bits_written - bits_to_write))) == 0);
+            mantissa |= final_word << (bits_in_u64 - bits_written - BITS_IN_WORD);
+        }
+    }
+
+    // Now the mantissa should be complete so shift it down
+    mantissa >>= bits_in_u64 - mantissa_size;
+
+    union FloatExtractor {
+        struct {
+            unsigned long long mantissa : mantissa_size;
+            unsigned exponent : exponent_size;
+            unsigned sign : 1;
+        };
+        double double_value = 0;
+    } extractor;
+
+    extractor.exponent = highest_bit + exponent_bias;
+
+    VERIFY((mantissa & 0xfff0000000000000) == 0);
+    extractor.mantissa = mantissa;
+
+    return extractor.double_value;
 }
 
 void UnsignedBigInteger::set_to_0()