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gawk: Numeric Functions

 9.1.2 Numeric Functions
 The following list describes all of the built-in functions that work
 with numbers.  Optional parameters are enclosed in square
 brackets ([ ]):
 'atan2(Y, X)'
      Return the arctangent of 'Y / X' in radians.  You can use 'pi =
      atan2(0, -1)' to retrieve the value of pi.
      Return the cosine of X, with X in radians.
      Return the exponential of X ('e ^ X') or report an error if X is
      out of range.  The range of values X can have depends on your
      machine's floating-point representation.
      Return the nearest integer to X, located between X and zero and
      truncated toward zero.  For example, 'int(3)' is 3, 'int(3.9)' is
      3, 'int(-3.9)' is -3, and 'int(-3)' is -3 as well.
      Return the natural logarithm of X, if X is positive; otherwise,
      return 'NaN' ("not a number") on IEEE 754 systems.  Additionally,
      'gawk' prints a warning message when 'x' is negative.
      Return a random number.  The values of 'rand()' are uniformly
      distributed between zero and one.  The value could be zero but is
      never one.(1)
      Often random integers are needed instead.  Following is a
      user-defined function that can be used to obtain a random
      nonnegative integer less than N:
           function randint(n)
               return int(n * rand())
      The multiplication produces a random number greater than or equal
      to zero and less than 'n'.  Using 'int()', this result is made into
      an integer between zero and 'n' - 1, inclusive.
      The following example uses a similar function to produce random
      integers between one and N.  This program prints a new random
      number for each input record:
           # Function to roll a simulated die.
           function roll(n) { return 1 + int(rand() * n) }
           # Roll 3 six-sided dice and
           # print total number of points.
               printf("%d points\n", roll(6) + roll(6) + roll(6))
           CAUTION: In most 'awk' implementations, including 'gawk',
           'rand()' starts generating numbers from the same starting
           number, or "seed", each time you run 'awk'.(2)  Thus, a
           program generates the same results each time you run it.  The
           numbers are random within one 'awk' run but predictable from
           run to run.  This is convenient for debugging, but if you want
           a program to do different things each time it is used, you
           must change the seed to a value that is different in each run.
           To do this, use 'srand()'.
      Return the sine of X, with X in radians.
      Return the positive square root of X.  'gawk' prints a warning
      message if X is negative.  Thus, 'sqrt(4)' is 2.
      Set the starting point, or seed, for generating random numbers to
      the value X.
      Each seed value leads to a particular sequence of random
      numbers.(3)  Thus, if the seed is set to the same value a second
      time, the same sequence of random numbers is produced again.
           CAUTION: Different 'awk' implementations use different
           random-number generators internally.  Don't expect the same
           'awk' program to produce the same series of random numbers
           when executed by different versions of 'awk'.
      If the argument X is omitted, as in 'srand()', then the current
      date and time of day are used for a seed.  This is the way to get
      random numbers that are truly unpredictable.
      The return value of 'srand()' is the previous seed.  This makes it
      easy to keep track of the seeds in case you need to consistently
      reproduce sequences of random numbers.
      POSIX does not specify the initial seed; it differs among 'awk'
    ---------- Footnotes ----------
    (1) The C version of 'rand()' on many Unix systems is known to
 produce fairly poor sequences of random numbers.  However, nothing
 requires that an 'awk' implementation use the C 'rand()' to implement
 the 'awk' version of 'rand()'.  In fact, 'gawk' uses the BSD 'random()'
 function, which is considerably better than 'rand()', to produce random
    (2) 'mawk' uses a different seed each time.
    (3) Computer-generated random numbers really are not truly random.
 They are technically known as "pseudorandom".  This means that although
 the numbers in a sequence appear to be random, you can in fact generate
 the same sequence of random numbers over and over again.
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