IEEE(3)                   386BSD Programmer's Manual                   IEEE(3)

NAME
     copysign, drem, finite, logb, scalb copysign, remainder, - exponent
     manipulations

SYNOPSIS
     #include <math.h>

     double
     copysign(double x, double y)

     double
     drem(double x, double y)

     int
     finite(double x)

     double
     logb(double x)

     double
     scalb(double x, int n)

DESCRIPTION
     These functions are required for, or recommended by the IEEE standard 754
     for floating-point arithmetic.

     The copysign() function returns x with its sign changed to y's.

     The drem() function returns the remainder r := x - n*y where n is the
     integer nearest the exact value of x/y; moreover if |n - x/y| = 1/2 then
     n is even.  Consequently the remainder is computed exactly and |r| <=
     |y|/2. But drem(x, 0) is exceptional.  (See below under DIAGNOSTICS.)

     The finite() function returns the value 1 just when -infinity < x <
     +infinity; otherwise a zero is returned (when |x| = infinity or x is NaN
     or is the VAX's reserved operand).

     The logb() function returns x's exponent n, a signed integer converted to
     double-precision floating-point and so chosen that 1 (<= |x|2**n < 2
     unless x = 0 or (only on machines that conform to IEEE 754) |x| =
     infinity or x lies between 0 and the Underflow Threshold.  (See below
     under BUGS.)

     The Fn calb returns x*(2**n) computed, for integer n, without first
     computing 2*n.

RETURN VALUES
     The IEEE standard 754 defines drem(x, 0) and drem(infinity, y) to be
     invalid operations that produce a NaN.  On the VAX, drem(x, 0) generates
     a reserved operand fault.  No infinity exists on a VAX.

     IEEE 754 defines logb(+-infinity) = infinity and logb(0) = -infinity, and
     requires the latter to signal Division-by-Zero.  But on a VAX, logb(0) =
     1.0 - 2.0**31 = -2,147,483,647.0.  And if the correct value of scalb()
     would overflow on a VAX, it generates a reserved operand fault and sets
     the global variable errno to ERANGE.

SEE ALSO
     floor(3),  math(3),  infnan(3)

HISTORY
     The ieee functions appeared in 4.3BSD.

BUGS
     Should drem(x, 0) and logb(0) on a VAX signal invalidity by setting errno
     = EDOM ? Should logb(0) return  -1.7e38?

     IEEE 754 currently specifies that logb(denormalized no.) = logb(tiniest
     normalized no. > 0) but the consensus has changed to the specification in
     the new proposed IEEE standard p854, namely that logb(x) satisfy

           1 <= scalb(|x|, -logb(x)) < Radix  ... = 2 for IEEE 754

     for every x except 0, infinity and NaN.  Almost every program that
     assumes 754's specification will work correctly if logb() follows 854's
     specification instead.

     IEEE 754 requires copysign(x, NaN)) = +-x but says nothing else about the
     sign of a NaN.  A NaN Not a Number) is similar in spirit to the VAX's
     reserved operand, but very different in important details.  Since the
     sign bit of a reserved operand makes it look negative,

           copysign(x, reserved operand) = -x;

     should this return the reserved operand instead?

4.3 Berkeley Distribution         May 6, 1991                                2