is iPhone 5S 2-times faster than iPhone 5 at Graphics Task (like Gaming) due to 64-bit CPU? Phil Schiller talked about "iPhone 5S"


  This is the first-ever 64-bit processor in a phone of any kind. I
  don’t think the other guys are even talking about it yet. Why go
  through all this? The benefits are huge. The A7 is up to twice as fast
  as the previous-generation system at CPU tasks, and up to twice as
  fast at graphics tasks, too. 


—Phil Schiller, Apple keynote at 4
 Infinite Loop on September 10, 2013
(source: Wikipedia)

Since Memory is only 1GB for "iPhone 5S" then
How is 64 bit CPU faster than 32 bit CPU?

I heard that, in desktop enviroment, to ultilise 64 bit architecture we need more than 4GB memory.

Very confused?
This covers pretty much everything you need to know about benefits of Apple switching to ARM64.

https://www.mikeash.com/pyblog/friday-qa-2013-09-27-arm64-and-you.html

tl;dr conclusion/answer from the link


  It's also important to point out the things that "64-bit" does not refer to, as there's a lot of confusion in this area as well. In particular, "64-bit" does not include:
  
  
  Physical RAM address size. The number of bits used to actually talk to RAM (and therefore the amount of RAM the hardware can support) is decoupled from the question of CPU bitness. ARM CPUs have ranged from 26 bits to 40 bits, and this can be changed independently from the rest.
  Data bus size. The amount of data fetched from RAM or cache is likewise decoupled. Individual CPU instructions may request a certain amount of data, but the amount of data actually fetched can be independent, either by splitting the fetch into smaller parts, or fetching more than is necessary. The iPhone 5 already fetches data from memory in 64-bit chunks, and chunk sizes of up to 192 bits exist in the PC world.
  Anything related to floating-point. FPU register size and internal design is independent, and ARM CPUs have had 64-bit FPU registers since well before ARM64.
  
  
  "64-bit" A7 is not just a marketing gimmic, but neither is it an amazing breakthrough that enables a new class of applications. The truth, as happens often, lies in between.
  
  The simple fact of moving to 64-bit does little. It makes for slightly faster computations in some cases, somewhat higher memory usage for most programs, and makes certain programming techniques more viable. Overall, it's not hugely significant.
  
  The ARM architecture changed a bunch of other things in its transition to 64-bit. An increased number of registers and a revised, streamlined instruction set make for a nice performance gain over 32-bit ARM.
  
  Apple took advantage of the transition to make some changes of their own. The biggest change is an inline retain count, which eliminates the need to perform a costly hash table lookup for retain and release operations in the common case. Since those operations are so common in most Objective-C code, this is a big win. Per-object resource cleanup flags make object deallocation quite a bit faster in certain cases. All in all, the cost of creating and destroying an object is roughly cut in half. Tagged pointers also make for a nice performance win as well as reduced memory use.


tl;dr tl;dr


RAM(Memory) is decoupled from CPU bitness and has no play in it's performance
64-bit does not give 2x boost by itself
Due to transition to 64-bit Apple managed introduce some clever ways to improve performance