biggest integer that can be stored in a double

Question

What is the biggest \"no-floating\" integer that can be stored in an IEEE 754 double type without losing precision ?

Answer 1

The largest integer that can be represented in IEEE 754 double (64-bit) is the same as the largest value that the type can represent, since that value is itself an integer.

This is represented as 0x7FEFFFFFFFFFFFFF, which is made up of:

• The sign bit 0 (positive) rather than 1 (negative)
• The maximum exponent 0x7FE (2046 which represents 1023 after the bias is subtracted) rather than 0x7FF (2047 which indicates a NaN or infinity).
• The maximum mantissa 0xFFFFFFFFFFFFF which is 52 bits all 1.

In binary, the value is the implicit 1 followed by another 52 ones from the mantissa, then 971 zeros (1023 - 52 = 971) from the exponent.

The exact decimal value is:

179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368

This is approximately 1.8 x 10³⁰⁸.