🚀 go-pugleaf

My thanks to everybody who answered my last question.

I have an other question reguarding how much the
support of lower precision fp numbers is worth to
people buying supercomputers, where a supercomputer
is defined as any machine which attains 1 GFLOP
sustained while running "typical" code.

Suppose that somebody were designing a machine that
only directly supported a 2^N bit FP format and
2^N bit integers. Suppose that the amount of I/O
bandwidth (and blinking lights) have already been
fixed, but the designer believes that he/she
may be loosing a significant portion of the
market which uses 2^(N-1) and 2^(N-2) formats.

Without changing the cost at all, The designer
realizes that he/she can create machines with
the following five specifications.

Option 1: A 2^N bit FP      GFLOPS
          A 2^N bit Integer GOPS

Option 2: B     2^N     bit FP      GFLOPS
          B     2^N     bit Integer GOPS
          (2*B) 2^(N-1) bit Integer GOPS

Option 3: C     2^N     bit FP      GFLOPS
          C     2^N     bit Integer GOPS
          (2*C) 2^(N-1) bit FP      GFLOPS
          (2*C) 2^(N-1) bit Integer GOPS

Option 4: D     2^N     bit FP      GFLOPS
          D     2^N     bit Integer GOPS
          (2*D) 2^(N-1) bit Integer GOPS
          (4*D) 2^(N-2) bit Integer GOPS

Option 5: E     2^N     bit FP      GFLOPS
          E     2^N     bit Integer GOPS
          (2*E) 2^(N-1) bit FP      GFLOPS
          (2*E) 2^(N-1) bit Integer GOPS
          (4*E) 2^(N-2) bit FP      GFLOPS
          (4*E) 2^(N-2) bit Integer GOPS

Suppose that 2B>2C>A>B>C
             2D>B>D
             2E>C>E
             D>E

How high must B be for customers to prefer it
over A? How high must D be for customers to
prefer it over B? ect.

In other words, when it is possible to increase
tremendously the speed of lower precision
operations at the cost of higher precision
operations, AT WHAT POINT DOES THE GAIN IN
PERFORMANCE OF THE LOWER PRECISION OPERATIONS
JUSTIFY THE DECREASE IN HIGHER PRECISION
PERFORMANCE.

A corrolary question is:

If machine A gives X   GFLOPS of 64 bit power,
   machine B gives 2*Y GFLOPS of 32 bit power, and
   machine C gives 4*Z GFLOPS of 16 bit power, and

X = Y = Z, Which would you prefer?

If X = 1.1*Y = 1.2*Z, Would that still be the case?

Thanks, Jason W. Solinsky.