The largest number representable in 64 bits

>>tromp+(OP)
IEEE754 64-bit representation already has infinity:

    uint64_t x = 0x7ff0000000000000ULL;
    printf("%f\n", *(double *)&x);

output:

inf

But you could use a representation where 0 is 0, and 1 is infinity, saving 63 bits...

>>matja+5c6
> But you could use a representation where 0 is 0, and 1 is infinity, saving 63 bits...

Reminds me of the hilarious and brilliant: http://tom7.org/nand/

>>loxias+4H6
Floating format 1:1:0:1's 8 possible values:

    000: +0
    001: +1 ( denormal: (-1)^0 * 0.5 * 2^(-0+1) )
    010: +inf
    011: +qnan
    100: -0
    101: -1 ( denormal: (-1)^1 * 0.5 * 2^(-0+1) )
    110: -inf
    111: -qnan

=== Floating point crib sheet ===

--- Format ---

Sign:exponent:stored explicit mantissa leading bit:mantissa fraction:

       binary16 = 1:5:0:10
       bfloat16 = 1:8:0:7
    TensorFloat = 1:8:0:10
           fp24 = 1:7:0:16
       binary32 = 1:8:0:23 
       binary64 = 1:11:0:52
           8087 = 1:11:1:67
      binary128 = 1:15:0:112

--- Interpretation ---

leading bit = (exponent != 0) ? 1 : 0 when implicit (not stored)

bias = 2^(exponent bits - 1) - 1

value = (-1)^sign * 0 when zero

value = (-1)^sign * {{leading bit}}.{{mantissa fraction}}b * 2^(exponent - bias) when normal

value = (-1)^sign * 0.{{mantissa fraction}}b * 2^(-bias+1) when denormal

--- Classification ---

zero = exponent == 0 && mantissa fraction == 0

denormal = exponent == 0 && mantissa fraction != 0

normal = exponent != 0 && exponent != ~0

inf = exponent == ~0 && mantissa fraction == 0

nan = exponent == ~0 && mantissa fraction != 0

snan = nan && msb(mantissa fraction) == 0

qnan = nan && msb(mantissa fraction) == 1

PS: It often takes fewer gates to implement a simpler microcoded microarchitecture than to implement a single hardwired macroarchitecture. Microcoded architectures are theoretically slower than hardwired but this is often not the case in reality because of the costs of gate fanout and extra gates for clock distribution that ameliorate gains of fully specified and decoded in hardware.

zlacker