Patrick - 4 months ago 21

C Question

Will

`printf('%.9e', value)`

`value`

`value`

Will the same hold for

`printf('%.17e', value)`

`value`

If not, how can I?

It appears that

`printf('%.17f', value)`

`printf('%.17g', value)`

Answer

Will printf('%.9e', value) always print the exact base10 representation?

No. Consider 0.5, 0.25, 0.125, 0.0625 .... Each value is one-half the preceding and needs another decimal place for each decremented power of 2.

`float`

, often binary32 can represent values about `pow(2,-127)`

and sub-normals even smaller. It would take 127+ decimal places to represent those exactly. Even counting only *significant* digits, then number is 89+. Example `FLT_MIN`

on one machine is *exactly*

`0.000000000000000000000000000000000000011754943508222875079687365372222456778186655567720875215087517062784172594547271728515625`

`FLT_TRUE_MIN`

, the smallest non-zero sub-normal is 151 digits:

`0.00000000000000000000000000000000000000000000140129846432481707092372958328991613128026194187651577175706828388979108268586060148663818836212158203125`

By comparison, `FLT_MAX`

only takes 39 digits.

`340282346638528859811704183484516925440`

Rarely are *exact* decimal representation of `float`

needed. Printing them to `FLT_DECIMAL_DIG`

(typically 9) significant digits is sufficient to uniquely display them. Many systems do not print exact decimal representation beyond a few dozen significant digits.

Vast majority of systems I have used printed `float/double`

exactly to at least `DBL_DIG`

significant digits (typically 15+). Most systems do so at least to `DBL_DECIMAL_DIG`

(typically 17+) significant digits.

Printf width specifier to maintain precision of floating-point value gets into these issues.

`printf('%.*e', FLT_DECIMAL_DIG - 1, value)`

will print a `float`

to enough decimals places to scan it back and get the same value - (round-trip).