Largest positive integer which can be represented in Julia using Float64

user_1418618 0
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I am trying to view the bitstring of the largest positive integer that can be exactly represented using Julia. Wikipedia says that 2^1024 * (1-2^(-53)) is the integer. However, when I try using Julia, the bitstring is all zeros.

julia> bitstring(Float64( 2^1024  - 2^971  ))
"0000000000000000000000000000000000000000000000000000000000000000"

The bitstring I am expecting is

0 11111111110 1111111111111111111111111111111111111111111111111111

Can you please help me clarify why this discrepancy happens?

julia floating-point
2 Answers

2^1024 - 2^971 overflows before you convert to Float64. Instead you can do

julia> bitstring(prevfloat(typemax(Float64)))
 "0111111111101111111111111111111111111111111111111111111111111111"

There are a few advantages over the big approach: You don't have to know what the max representable value is -- 2^1024 - 2^971; it works for many different types (you could do the same with Float32, etc); and it's faster.

For integer type T you would do

bitstring(typemax(T))

The reason for using prevfloat with floats, is that typemax(Float64) is Inf;

user_27498650

Those powers of integers overflow to zero integers before becoming floats. You can work in BigInt, though:

julia> 2^1024  - 2^971
0

julia> big"2"^1024  - big"2"^971
179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368

julia> Float64(big"2"^1024  - big"2"^971)
1.7976931348623157e308

julia> bitstring(ans)
"0111111111101111111111111111111111111111111111111111111111111111"

Or alternatively convert the input integers to floats already.

user_13462760
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