Utility functions for built in types
************************************

   Files `builtin.h' and corresponding `.cc' implementation files
contain various convenient inline and non-inline utility functions.
These include useful enumeration types, such as `TRUE', `FALSE' ,the
type definition for pointers to libg++ error handling functions, and
the following functions.

`long abs(long x); double abs(double x);'
     inline versions of abs. Note that the standard libc.a version,
     `int abs(int)' is *not* declared as inline.

`void clearbit(long& x, long b);'
     clears the b'th bit of x (inline).

`void setbit(long& x, long b);'
     sets the b'th bit of x (inline)

`int testbit(long x, long b);'
     returns the b'th bit of x (inline).

`int even(long y);'
     returns true if x is even (inline).

`int odd(long y);'
     returns true is x is odd (inline).

`int sign(long x); int sign(double x);'
     returns -1, 0, or 1, indicating whether x is less than, equal to,
     or greater than zero (inline).

`long gcd(long x, long y);'
     returns the greatest common divisor of x and y.

`long lcm(long x, long y);'
     returns the least common multiple of x and y.

`long lg(long x);'
     returns the floor of the base 2 log of x.

`long pow(long x, long y); double pow(double x, long y);'
     returns x to the integer power y using via the iterative O(log y)
     "Russian peasant" method.

`long sqr(long x); double sqr(double x);'
     returns x squared (inline).

`long sqrt(long y);'
     returns the floor of the square root of x.

`unsigned int hashpjw(const char* s);'
     a hash function for null-terminated char* strings using the method
     described in Aho, Sethi, & Ullman, p 436.

`unsigned int multiplicativehash(int x);'
     a hash function for integers that returns the lower bits of
     multiplying x by the golden ratio times pow(2, 32).  See Knuth,
     Vol 3, p 508.

`unsigned int foldhash(double x);'
     a hash function for doubles that exclusive-or's the first and
     second words of x, returning the result as an integer.

`double start_timer()'
     Starts a process timer.

`double return_elapsed_time(double last_time)'
     Returns the process time since last_time.  If last_time == 0
     returns the time since the last start_timer.  Returns -1 if
     start_timer was not first called.

   File `Maxima.h' includes versions of `MAX, MIN' for builtin types.

   File `compare.h' includes versions of `compare(x, y)' for builtin
types. These return negative if the first argument is less than the
second, zero for equal, and positive for greater.