Category : C Source Code
Archive   : CEPHES22.ZIP
Filename : FLOOR.C

/* ceil()
* floor()
* frexp()
* ldexp()
*
* Floating point numeric utilities
*
*
*
* SYNOPSIS:
*
* double x, y;
* double ceil(), floor(), frexp(), ldexp();
* int expnt, n;
*
* y = floor(x);
* y = ceil(x);
* y = frexp( x, &expnt );
* y = ldexp( x, n );
*
*
*
* DESCRIPTION:
*
* All four routines return a double precision floating point
* result.
*
* floor() returns the largest integer less than or equal to x.
* It truncates toward minus infinity.
*
* ceil() returns the smallest integer greater than or equal
* to x. It truncates toward plus infinity.
*
* frexp() extracts the exponent from x. It returns an integer
* power of two to expnt and the significand between 0.5 and 1
* to y. Thus x = y * 2**expn.
*
* ldexp() multiplies x by 2**n.
*
* These functions are part of the standard C run time library
* for many but not all C compilers. The ones supplied are
* written in C for either DEC or IEEE arithmetic. They should
* be used only if your compiler library does not already have
* them.
*
* The IEEE versions assume that denormal numbers are implemented
* in the arithmetic. Some modifications will be required if
* the arithmetic has abrupt rather than gradual underflow.
*/


/*
Cephes Math Library Release 2.1: December, 1988
Copyright 1984, 1987, 1988 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/


#include "mconf.h"
#define DENORMAL 1

#ifdef UNK
char *unkmsg = "ceil(), floor(), frexp(), ldexp() must be rewritten!\n";
#endif

#ifdef DEC
#define EXPMSK 0x807f
#define MEXP 255
#define NBITS 56
#endif

#ifdef IBMPC
#define EXPMSK 0x800f
#define MEXP 0x7ff
#define NBITS 53
#endif

#ifdef MIEEE
#define EXPMSK 0x800f
#define MEXP 0x7ff
#define NBITS 53
#endif

extern double MAXNUM;





double ceil(x)
double x;
{
double y;
double floor();

#ifdef UNK
mtherr( "ceil", DOMAIN );
return(0.0);
#endif

y = floor(x);
if( y < x )
y += 1.0;
return(y);
}




/* Bit clearing masks: */

static unsigned short bmask[] = {
0xffff,
0xfffe,
0xfffc,
0xfff8,
0xfff0,
0xffe0,
0xffc0,
0xff80,
0xff00,
0xfe00,
0xfc00,
0xf800,
0xf000,
0xe000,
0xc000,
0x8000,
0x0000,
};




double floor(x)
double x;
{
unsigned short *p;
double y;
int e, i;

#ifdef UNK
mtherr( "floor", DOMAIN );
return(0.0);
#endif

y = x;
/* find the exponent (power of 2) */
#ifdef DEC
p = (unsigned short *)&y;
e = (( *p >> 7) & 0377) - 0201;
p += 3;
#endif

#ifdef IBMPC
p = (unsigned short *)&y + 3;
e = (( *p >> 4) & 0x7ff) - 0x3ff;
p -= 3;
#endif

#ifdef MIEEE
p = (unsigned short *)&y;
e = (( *p >> 4) & 0x7ff) - 0x3ff;
p += 3;
#endif

if( e < 0 )
{
if( y < 0.0 )
return( -1.0 );
else
return( 0.0 );
}

e = (NBITS -1) - e;
/* clean out 16 bits at a time */
while( e >= 16 )
{
#ifdef IBMPC
*p++ = 0;
#endif

#ifdef DEC
*p-- = 0;
#endif

#ifdef MIEEE
*p-- = 0;
#endif
e -= 16;
}

/* clear the remaining bits */
if( e > 0 )
*p &= bmask[e];

if( (x < 0) && (y != x) )
y -= 1.0;

return(y);
}



double frexp( x, pw2 )
double x;
int *pw2;
{
double y;
int i, k;
short *q;

y = x;

#ifdef UNK
mtherr( "frexp", DOMAIN );
return(0.0);
#endif

#ifdef IBMPC
q = (short *)&y + 3;
#endif

#ifdef DEC
q = (short *)&y;
#endif

#ifdef MIEEE
q = (short *)&y;
#endif

/* find the exponent (power of 2) */
#ifdef DEC
i = ( *q >> 7) & 0377;
if( i == 0 )
{
*pw2 = 0;
return(0.0);
}
i -= 0200;
*pw2 = i;
*q &= 0x807f; /* strip all exponent bits */
*q |= 040000; /* mantissa between 0.5 and 1 */
return(y);
#endif

#ifdef IBMPC
i = ( *q >> 4) & 0x7ff;
if( i != 0 )
goto ieeedon;
#endif

#ifdef MIEEE
i = *q >> 4;
i &= 0x7ff;
if( i != 0 )
goto ieeedon;
#if DENORMAL

#else
*pw2 = 0;
return(0.0);
#endif

#endif


#ifndef DEC
/* Number is denormal or zero */
#if DENORMAL
if( y == 0.0 )
{
iszero:
*pw2 = 0;
return( 0.0 );
}


/* Handle denormal number. */
do
{
y *= 2.0;
i -= 1;
k = ( *q >> 4) & 0x7ff;
}
while( k == 0 );
i = i + k;
#endif /* DENORMAL */

ieeedon:

i -= 0x3fe;
*pw2 = i;
*q &= 0x800f;
*q |= 0x3fe0;
return( y );
#endif
}






double ldexp( x, pw2 )
double x;
int pw2;
{
double y;
short *q;
int e;

#ifdef UNK
mtherr( "ldexp", DOMAIN );
return(0.0);
#endif

y = x;
#ifdef DEC
q = (short *)&y;
e = ( *q >> 7) & 0377;
if( e == 0 )
return(0.0);
#else

#ifdef IBMPC
q = (short *)&y + 3;
#endif
#ifdef MIEEE
q = (short *)&y;
#endif
while( (e = (*q & 0x7ff0) >> 4) == 0 )
{
if( y == 0.0 )
{
return( 0.0 );
}
/* Input is denormal. */
if( pw2 > 0 )
{
y *= 2.0;
pw2 -= 1;
}
if( pw2 < 0 )
{
if( pw2 < -53 )
return(0.0);
y /= 2.0;
pw2 += 1;
}
if( pw2 == 0 )
return(y);
}
#endif /* not DEC */

e += pw2;

/* Handle overflow */
if( e > MEXP )
{
return( MAXNUM );
}

/* Handle denormalized results */
if( e < 1 )
{
#if DENORMAL
if( e < -53 )
return(0.0);
*q &= 0x800f;
*q |= 0x10;
while( e < 1 )
{
y /= 2.0;
e += 1;
}
return(y);
#else
return(0.0);
#endif
}
else
{
#ifdef DEC
*q &= 0x807f; /* strip all exponent bits */
*q |= (e & 0xff) << 7;
#else
*q &= 0x800f;
*q |= (e & 0x7ff) << 4;
#endif
return(y);
}
}