IEEE

Section: Mathematical Library (3M)
Updated: May 12, 1986
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NAME

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

SYNOPSIS

#include <math.h>

double copysign(x,y)
double x,y;

double drem(x,y)
double x,y;

int finite(x)
double x;

double logb(x)
double x;

double scalb(x,n)
double x;
int n;

DESCRIPTION

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

Copysign(x,y) returns x with its sign changed to y's.

Drem(x,y) 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.

Finite(x) = 1 just when -infinity < x < +infinity,= 0 otherwise(when |x| = infinity or x is NaN or

Logb(x) 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".

Scalb(x,n) = x*(2**n) computed, for integer n, without first computing 2**n.

DIAGNOSTICS

IEEE 754 defines drem(x,0) and drem(infinity,y) to be invalid operations that produce a NaN.

IEEE 754 defines logb(±infinity) = +infinity and logb(0) = -infinity, requires the latter to signal Division-by-Zero.

AUTHOR

Kwok-Choi Ng

BUGS

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?

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