JIT: implement frsqrte

Mostly a straightforward translation of the interpreter code, with a few
tricksy optimizations and fallbacks for rare paths.

Source/Core/Common/MathUtil.cpp

@@ -90,6 +90,84 @@ u32 ClassifyFloat(float fvalue)
 	}
 }
 
+const int frsqrte_expected_base[] =
+{
+	0x3ffa000, 0x3c29000, 0x38aa000, 0x3572000,
+	0x3279000, 0x2fb7000, 0x2d26000, 0x2ac0000,
+	0x2881000, 0x2665000, 0x2468000, 0x2287000,
+	0x20c1000, 0x1f12000, 0x1d79000, 0x1bf4000,
+	0x1a7e800, 0x17cb800, 0x1552800, 0x130c000,
+	0x10f2000, 0x0eff000, 0x0d2e000, 0x0b7c000,
+	0x09e5000, 0x0867000, 0x06ff000, 0x05ab800,
+	0x046a000, 0x0339800, 0x0218800, 0x0105800,
+};
+const int frsqrte_expected_dec[] =
+{
+	0x7a4, 0x700, 0x670, 0x5f2,
+	0x584, 0x524, 0x4cc, 0x47e,
+	0x43a, 0x3fa, 0x3c2, 0x38e,
+	0x35e, 0x332, 0x30a, 0x2e6,
+	0x568, 0x4f3, 0x48d, 0x435,
+	0x3e7, 0x3a2, 0x365, 0x32e,
+	0x2fc, 0x2d0, 0x2a8, 0x283,
+	0x261, 0x243, 0x226, 0x20b,
+};
+
+double ApproximateReciprocalSquareRoot(double val)
+{
+	union
+	{
+		double valf;
+		s64 vali;
+	};
+	valf = val;
+	s64 mantissa = vali & ((1LL << 52) - 1);
+	s64 sign = vali & (1ULL << 63);
+	s64 exponent = vali & (0x7FFLL << 52);
+
+	// Special case 0
+	if (mantissa == 0 && exponent == 0)
+		return sign ? -std::numeric_limits<double>::infinity() :
+		std::numeric_limits<double>::infinity();
+	// Special case NaN-ish numbers
+	if (exponent == (0x7FFLL << 52))
+	{
+		if (mantissa == 0)
+		{
+			if (sign)
+				return std::numeric_limits<double>::quiet_NaN();
+
+			return 0.0;
+		}
+
+		return 0.0 + valf;
+	}
+
+	// Negative numbers return NaN
+	if (sign)
+		return std::numeric_limits<double>::quiet_NaN();
+
+	if (!exponent)
+	{
+		// "Normalize" denormal values
+		do
+		{
+			exponent -= 1LL << 52;
+			mantissa <<= 1;
+		} while (!(mantissa & (1LL << 52)));
+		mantissa &= (1LL << 52) - 1;
+		exponent += 1LL << 52;
+	}
+
+	bool odd_exponent = !(exponent & (1LL << 52));
+	exponent = ((0x3FFLL << 52) - ((exponent - (0x3FELL << 52)) / 2)) & (0x7FFLL << 52);
+
+	int i = (int)(mantissa >> 37);
+	vali = sign | exponent;
+	int index = i / 2048 + (odd_exponent ? 16 : 0);
+	vali |= (s64)(frsqrte_expected_base[index] - frsqrte_expected_dec[index] * (i % 2048)) << 26;
+	return valf;
+}
 
 }  // namespace