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FLOOR(3M)							     FLOOR(3M)

NAME
     floor, floorl, ffloor, floorf, ceil, ceill, fceil, ceilf, copysign,
     copysignl, drem, dreml, fmod, fmodl, fmodf, fabsl, fabs, fabsf,
     remainder, rint, rintl, trunc, truncl, ftrunc, truncf - floor, ceiling,
     remainder, absolute value, nearest integer, and truncation functions

SYNOPSIS
     #include <math.h>

     double floor (double x);
     long double floorl (long double x);
     float ffloor (float x);
     float floorf (float x);

     double ceil (double x);
     long double ceill (long double x);
     float fceil (float x);
     float ceilf (float x);

     double copysign (double x, double y);
     long double copysignl \
	       (long double x, long double y);

     double drem (double x, double y);
     long double dreml \
	       (long double x, long double y);

     double remainder (double x, double y);

     double trunc (double x);
     long double truncl (long double x);
     float ftrunc (float x);
     float truncf (float x);

     double fmod (double x, double y);
     long double fmodl \
	       (long double x, long double y);
     float fmodf (float x, float y);

     double fabs (double x);
     long double fabsl (long double x);
     float fabsf (float x);

     double rint (double x);
     long double rintl (long double x);

DESCRIPTION
     The fmod, fabs, and trunc functions listed above, as well as the long
     double and single-precision versions of the remaining functions, are only
     available in the standard math library, -lm, and in -lmx.

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FLOOR(3M)							     FLOOR(3M)

     The floor functions return the largest integer not greater than x.	 The
     argument x is double for floor, long double for floorl, and float for
     ffloor and its ANSI-named equivalent floorf.

     copysign(x,y) returns the number with the magnitude of x and the sign of
     y.	 copysignl is the long double counterpart of copysign.

     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.  remainder is an
     alternate entry point for drem.  dreml is the long double counterpart of
     drem.

     The ceil functions return the smallest integer not less than x.  The
     argument x is double for ceil, long double for ceill, and float for fceil
     and its ANSI-named equivalent ceilf.

     The trunc functions return the integer (represented as a floating-point
     number) of x with the fractional bits truncated.  The argument x is
     double for trunc, long double for truncl, and float for ftrunc.

     fabs returns the absolute value of the double x, |x|.  It also has
     counterparts of type long double and float, namely fabsl, and fabsf,
     respectively.

     rint returns the integer (represented as a double precision number)
     nearest its double argument x in the direction of the prevailing rounding
     mode.  rintl is the long double counterpart of rint.  rint has no
     counterpart which accepts an argument of type float.

     fmod returns the floating-point remainder of the division of its double
     arguments x by y.	It returns a number f with the same sign as x, such
     that x = iy + f for some integer i, and |f| < |y|.	 Hence both the
     invocations
	  fmod(2.5,1.0)
	  fmod(2.5,-1.0)
     yield 0.5, while the two invocations
	  fmod(-2.5,1.0)
	  fmod(-2.5,-1.0)
     yield -0.5.
     fmodl is the counterpart of fmod which accepts and returns values of type
     long double and fmodf is the counterpart of fmod which accepts and
     returns values of type float.

DIAGNOSTICS
     In the diagnostics below, functions in the standard math library libm.a,
     are referred to as -lm versions, those in math library libmx.a are
     referred to as -lmx versions, and those in the the BSD math library
     libm43.a are referred to as -lm43 versions.  The -lm and -lmx versions
     always return the default Quiet NaN and set errno to EDOM when a NaN is
     used as an argument.  A NaN argument usually causes the -lm43 versions to

									Page 2

FLOOR(3M)							     FLOOR(3M)

     return the same argument.	The -lm43 versions never set errno.  The value
     of HUGE_VAL is IEEE Infinity.

     If y (and, possibly, x) are zero, or if x is +/-HUGE_VAL, the fmod
     functions return a quiet NaN, and set errno to EDOM.

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

     A version of the double-precision fabs function exists in the C library
     as well.  The C library version may not behave correctly when the input
     is NaN.

NOTES
     Long double operations on this system are only supported in round to
     nearest rounding mode (the default).  The system must be in round to
     nearest rounding mode when calling any of the long double functions, or
     incorrect answers will result.

     Users concerned with portability to other computer systems should note
     that the long double and float versions of these functions are optional
     according to the ANSI C Programming Language Specification ISO/IEC 9899 :
     1990 (E).

     Long double functions have been renamed to be compliant with the ANSI-C
     standard, however to be backward compatible, they may still be called
     with the double precision function name prefixed with a q.	 (Exceptions:
     functions fabsl and fmodl may be called with names qabs and qmod, resp.)

     In the default rounding mode, round to nearest, rint(x) is the integer
     nearest x with the additional stipulation that if |rint(x)-x|=1/2 then
     rint(x) is even.  Other rounding modes can make rint act like floor, or
     like ceil, or round towards zero.

     Another way to obtain an integer near x is to declare (in C)
	  double x;	int k;	  k = x;
     The C compilers round x towards zero to get the integer k.	 Also note
     that, if x is larger than k can accommodate, the value of k and the
     presence or absence of an integer overflow are hard to detect.

     IEEE 754 requires copysign(x,Nan) = _x.  In this implementation of
     copysign, the sign of NaN is ignored.  Thus copysign(x,_NaN) = +x, and
     copysign(_NaN,x) = +NaN.

SEE ALSO
     abs(3C), math(3M), matherr(3M)

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