A double value is stored in computers using the into a 64 bit double-precision floating-point format according to the IEEE754 standard. This means that a double like

6.62607015e-34

is stored internally as

0x 39 0B 86 0B DE 02 31 11

It is stored as a 1.xxxxx number times a power of 2 so the above number will be stored as

1.7202261612138196*2^-111

This is a swift implementation of how a computer might handle doubles under the hood. It therefor uses bit operations only.

The following operations are supported: <, >, +, -, *, /, sqrt, sin, cos, tan, log, exp, pow and atan

For clarity reasons, the code is deliberately written without focus on rounding errors, overflow situations, NaN, Inf or efficiency, it's just to show how calculations with doubles could be done with bit operations only.

This is an example of what you can do with it:

let f = DoubleByBit(1.234)
let g = DoubleByBit(-1.99)
let h = DoubleByBit.pow(f, g)
print(h.doubleValue)         // 0.6580862733673336

It also provides an initializer for strings so this will also work:

let f = DoubleByBit("1.234")
let g = DoubleByBit("-1.99")
let h = DoubleByBit.pow(f, g)
print(h.doubleValue)         // 0.6580862733673336

There is some validation on the input string so in case of invalid input it will fail with a Parse error.

Valid examples include:

• 299792458
• 00299792458.0000
• 2.99792458e8
• +2.99792458e+8
• 0000.0000299792458000e+0013
• -6.62607015e-34
• -0.00e+10