Base conversion refers to the transformation of a number represented in one base to a number represented in another base. I/O routines such as printf and scanf in C and read, write, and print in Fortran involve base conversion between numbers represented in bases 2 and 10:
Base conversion from base 10 to base 2 occurs when reading in a number in conventional decimal notation and storing it in internal binary format.
Base conversion from base 2 to base 10 occurs when printing an internal binary value as an ASCII string of decimal digits.
In the Oracle Solaris environment, the fundamental routines for base conversion in all languages are contained in the standard C library, libc. These routines use table-driven algorithms that yield correctly rounded conversion between any input and output formats subject to modest restrictions on the lengths of the strings of decimal digits involved. In addition to their accuracy, table-driven algorithms reduce the worst-case times for correctly rounded base conversion.
The 1985 IEEE standard requires correct rounding for typical numbers whose magnitudes range from 10–44 to 10+44 but permits slightly incorrect rounding for larger exponents. See section 5.6 of IEEE Standard 754. The libc table-driven algorithms round correctly throughout the entire range of single, double, and double extended formats, as required by the revised 754-2008.
In C, conversions between decimal strings and binary floating-point values are always rounded correctly in accordance with IEEE 754: the converted result is the number representable in the result's format that is nearest to the original value in the direction specified by the current rounding mode. When the rounding mode is round-to-nearest and the original value lies exactly halfway between two representable numbers in the result format, the converted result is the one whose least significant digit is even. These rules apply to conversions of constants in source code performed by the compiler as well as to conversions of data performed by the program using standard library routines.
In Fortran, conversions between decimal strings and binary floating-point values are rounded correctly following the same rules as C by default. For I/O conversions, the “round-ties-to-even” rule in round-to-nearest mode can be overridden, either by using the ROUNDING= specifier in the program or by compiling with the –iorounding flag. See the Oracle Solaris Studio 12.4: Fortran User’s Guide and the f95(1) man page for more information.
See Appendix F, References for references on base conversion, particularly Coonen's thesis and Sterbenz's book.