dot notation with p for hexadecimal numeric literals in swift

Question

I'm working through the first basic playground in https://github.com/nettlep/learn-swift using XCode

What exactly is happening with this expression?

0xC.3p0 == 12.1875

I've learned about hexadecimal literals and the special "p" notation that indicates a power of 2.

0xF == 15

0xFp0 == 15   //  15 * 2^0

If I try 0xC.3 I get the error: Hexadecimal floating point literal must end with an exponent.

I found this nice overview of numeric literals and another deep explanation, but I didn't see something that explains what .3p0 does.

I've forked the code and upgraded this lesson to XCode 7 / Swift 2 -- here's the specific line.

Answer 1

This is Hexadecimal exponential notation.

By convention, the letter P (or p, for "power") represents times two raised to the power of ... The number after the P is decimal and represents the binary exponent.

...

Example: 1.3DEp42 represents hex(1.3DE) × dec(2^42).

For your example, we get:

0xC.3p0 represents 0xC.3 * 2^0 = 0xC.3 * 1 = hex(C.3) = 12.1875

where hex(C.3) = dec(12.{3/16}) = dec(12.1875)

As an example, you can try 0xC.3p1 (equals hex(C.3) * dec(2^1)), which yields double the value, i.e., 24.375.

You can also study the binary exponent growth in a playground for hex-value 1:

// ...
print(0x1p-3) // 1/8 (0.125)
print(0x1p-2) // 1/4 (0.25)
print(0x1p-1) // 1/2 (0.5)
print(0x1p1) // 2.0
print(0x1p2) // 4.0
print(0x1p3) // 8.0
// ...

---

Finally, this is also explained in Apple`s Language Reference - Lexical Types: Floating-Point Literals:

Hexadecimal floating-point literals consist of a 0x prefix, followed by an optional hexadecimal fraction, followed by a hexadecimal exponent. The hexadecimal fraction consists of a decimal point followed by a sequence of hexadecimal digits. The exponent consists of an upper- or lowercase p prefix followed by a sequence of decimal digits that indicates what power of 2 the value preceding the p is multiplied by. For example, 0xFp2 represents 15 x 2^2, which evaluates to 60. Similarly, 0xFp-2 represents 15 x 2^-2, which evaluates to 3.75.