commit 559de8f5f0 redefined FLT_ROUNDS
to use an external function that can report the actual current
rounding mode, rather than always reporting round-to-nearest. however,
float.h did not include 'extern "C"' wrapping for C++, so C++ programs
using FLT_ROUNDS ended up with an unresolved reference to a
name-mangled C++ function __flt_rounds.
this is enough to produce the correct value even if the constant is
interpreted as 80-bit extended precision, which matters on archs with
excess precision (FLT_EVAL_METHOD==2) under at least some
interpretations of the C standard. the shorter representations, while
correct if converted to the nominal precision at translation time,
could produce an incorrect value at extended precision, yielding
results such as (double)DBL_MAX != DBL_MAX.
there was some question as to how many decimal places to use, since
one decimal place is always sufficient to identify the smallest
denormal uniquely. for now, I'm following the example in the C
standard which is consistent with the other min/max macros we already
had in place.
DECIMAL_DIG is not the same as LDBL_DIG
type_DIG is the maximimum number of decimal digits that can survive a
round trip from decimal to type and back to decimal.
DECIMAL_DIG is the minimum number of decimal digits required in order
for any floating point type to survive the round trip to decimal and
back, and it is generally larger than LDBL_DIG. since the exact
formula is non-trivial, and defining it larger than necessary may be
legal but wasteful, just define the right value in bits/float.h.
Rich Felker
Szabolcs Nagy