ieee man page on 4.4BSD

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IEEE(3)			 BSD Library Functions Manual		       IEEE(3)

NAME
     copysign, drem, finite, logb, scalb — IEEE 754 floating point support

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 -∞ < x < +∞; other‐
     wise a zero is returned (when |x| = ∞ 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| = ∞ or x
     lies between 0 and the Underflow Threshold.  (See below under BUGS.)

     The scalb() function 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(∞, y) to be invalid
     operations that produce a NaN.  On the VAX, drem(x, 0) generates a
     reserved operand fault.  No ∞ exists on a VAX.

     IEEE 754 defines logb(±∞) = ∞ and logb(0) = -∞, 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, ∞ 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	 June 4, 1993	     4.3 Berkeley Distribution
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