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Rounding Modes
==============

   Floating-point calculations are carried out internally with extra
precision, and then rounded to fit into the destination type.  This
ensures that results are as precise as the input data.  IEEE 754
defines four possible rounding modes:

Round to nearest.
     This is the default mode.  It should be used unless there is a
     specific need for one of the others.  In this mode results are
     rounded to the nearest representable value.  If the result is
     midway between two representable values, the even representable is
     chosen. "Even" here means the lowest-order bit is zero.  This
     rounding mode prevents statistical bias and guarantees numeric
     stability: round-off errors in a lengthy calculation will remain
     smaller than half of `FLT_EPSILON'.

Round toward plus Infinity.
     All results are rounded to the smallest representable value which
     is greater than the result.

Round toward minus Infinity.
     All results are rounded to the largest representable value which
     is less than the result.

Round toward zero.
     All results are rounded to the largest representable value whose
     magnitude is less than that of the result.  In other words, if the
     result is negative it is rounded up; if it is positive, it is
     rounded down.

`fenv.h' defines constants which you can use to refer to the various
rounding modes.  Each one will be defined if and only if the FPU
supports the corresponding rounding mode.

`FE_TONEAREST'
     Round to nearest.

`FE_UPWARD'
     Round toward +oo.

`FE_DOWNWARD'
     Round toward -oo.

`FE_TOWARDZERO'
     Round toward zero.

   Underflow is an unusual case.  Normally, IEEE 754 floating point
numbers are always normalized (Note: Floating Point Concepts).
Numbers smaller than 2^r (where r is the minimum exponent,
`FLT_MIN_RADIX-1' for FLOAT) cannot be represented as normalized
numbers.  Rounding all such numbers to zero or 2^r would cause some
algorithms to fail at 0.  Therefore, they are left in denormalized
form.  That produces loss of precision, since some bits of the mantissa
are stolen to indicate the decimal point.

   If a result is too small to be represented as a denormalized number,
it is rounded to zero.  However, the sign of the result is preserved; if
the calculation was negative, the result is "negative zero".  Negative
zero can also result from some operations on infinity, such as 4/-oo.
Negative zero behaves identically to zero except when the `copysign' or
`signbit' functions are used to check the sign bit directly.

   At any time one of the above four rounding modes is selected.  You
can find out which one with this function:

 - Function: int fegetround (void)
     Returns the currently selected rounding mode, represented by one
     of the values of the defined rounding mode macros.

To change the rounding mode, use this function:

 - Function: int fesetround (int ROUND)
     Changes the currently selected rounding mode to ROUND.  If ROUND
     does not correspond to one of the supported rounding modes nothing
     is changed.  `fesetround' returns zero if it changed the rounding
     mode, a nonzero value if the mode is not supported.

   You should avoid changing the rounding mode if possible.  It can be
an expensive operation; also, some hardware requires you to compile your
program differently for it to work.  The resulting code may run slower.
See your compiler documentation for details.