(libc.info.gz) Math Error Reporting

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 20.5.4 Error Reporting by Mathematical Functions
 ------------------------------------------------
 
 Many of the math functions are defined only over a subset of the real or
 complex numbers.  Even if they are mathematically defined, their result
 may be larger or smaller than the range representable by their return
 type without loss of accuracy.  These are known as "domain errors",
 "overflows", and "underflows", respectively.  Math functions do several
 things when one of these errors occurs.  In this manual we will refer to
 the complete response as "signalling" a domain error, overflow, or
 underflow.
 
    When a math function suffers a domain error, it raises the invalid
 exception and returns NaN. It also sets ERRNO to 'EDOM'; this is for
 compatibility with old systems that do not support IEEE 754 exception
 handling.  Likewise, when overflow occurs, math functions raise the
 overflow exception and, in the default rounding mode, return oo or -oo
 as appropriate (in other rounding modes, the largest finite value of the
 appropriate sign is returned when appropriate for that rounding mode).
 They also set ERRNO to 'ERANGE' if returning oo or -oo; ERRNO may or may
 not be set to 'ERANGE' when a finite value is returned on overflow.
 When underflow occurs, the underflow exception is raised, and zero
 (appropriately signed) or a subnormal value, as appropriate for the
 mathematical result of the function and the rounding mode, is returned.
 ERRNO may be set to 'ERANGE', but this is not guaranteed; it is intended
 that the GNU C Library should set it when the underflow is to an
 appropriately signed zero, but not necessarily for other underflows.
 
    Some of the math functions are defined mathematically to result in a
 complex value over parts of their domains.  The most familiar example of
 this is taking the square root of a negative number.  The complex math
 functions, such as 'csqrt', will return the appropriate complex value in
 this case.  The real-valued functions, such as 'sqrt', will signal a
 domain error.
 
    Some older hardware does not support infinities.  On that hardware,
 overflows instead return a particular very large number (usually the
 largest representable number).  'math.h' defines macros you can use to
 test for overflow on both old and new hardware.
 
  -- Macro: double HUGE_VAL
  -- Macro: float HUGE_VALF
  -- Macro: long double HUGE_VALL
      An expression representing a particular very large number.  On
      machines that use IEEE 754 floating point format, 'HUGE_VAL' is
      infinity.  On other machines, it's typically the largest positive
      number that can be represented.
 
      Mathematical functions return the appropriately typed version of
      'HUGE_VAL' or '-HUGE_VAL' when the result is too large to be
      represented.
 

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