Why does Double reach `Double.infinity` BEFORE Double Max is reached?

I wrote a tiny Swift programme to add a number to the previous number until it reached infinity. However, infinity is reached BEFORE the Double Maximum is reached.

• Double limit is 1.79769313486232e+308
• Distance to limit is 4.90703911098917e+307
• Yet, 8.07763763215622e+307 + 1.3069892237634e+308 reached infinity

Why is this? (I answered this below.)

Run it for yourselves:

import Foundation
import Darwin

var current: Double = 1
var previous: Double = 0
var register: Double = 0

var infinity = Double.infinity
var isInfinite = infinity.isInfinite

var n = 1
while current < infinity {

    register = current
    current = previous + register
    print("\(n): \(current)")

    guard current != infinity else { break }

    previous = register

    n += 1
}

print("\n")
print("Double limit is \(DBL_MAX)")
print("Distance to limit is \(DBL_MAX - register)")
print("Yet, \(previous) + \(register) reached infinity")

After adding:

    print((DBL_MAX - register) - previous)

to the end of my code, I realised my error is not fully grasping e+ notation.

Thus, the above prints out:

-3.17059852116705e+307

showing that Double Max is over-shot in the final calculation, proving as to why infinity is reached.

Well, I've done my learning in public now!