/*                                                      md_ceil()
 *                                                      md_floor()
 *                                                      md_frexp()
 *                                                      md_ldexp()
 *                                                      signbit()
 *                                                      isnan()
 *                                                      isfinite()
 *
 *      Floating point numeric utilities
 *
 *
 *
 * SYNOPSIS:
 *
 * double md_ceil(), md_floor(), md_frexp(), md_ldexp();
 * int signbit(), isnan(), isfinite();
 * double x, y;
 * int expnt, n;
 *
 * y = md_floor(x);
 * y = md_ceil(x);
 * y = md_frexp( x, &expnt );
 * y = md_ldexp( x, n );
 * n = signbit(x);
 * n = isnan(x);
 * n = isfinite(x);
 *
 *
 *
 * DESCRIPTION:
 *
 * All four routines return a double precision floating point
 * result.
 *
 * md_floor() returns the largest integer less than or equal to x.
 * It truncates toward minus infinity.
 *
 * md_ceil() returns the smallest integer greater than or equal
 * to x.  It truncates toward plus infinity.
 *
 * md_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**md_expn.
 *
 * md_ldexp() multiplies x by 2**n.
 *
 * signbit(x) returns 1 if the sign bit of x is 1, else 0.
 *
 * 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 2.8:  June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier
*/
#include "mconf.h"
#ifdef UNK
/* md_ceil(), md_floor(), md_frexp(), md_ldexp() may need to be rewritten. */
#undef UNK
#if BIGENDIAN
#define MIEEE 1
#else
#define IBMPC 1
#endif
#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, NEGZERO;
#ifdef ANSIPROT
double md_floor ( double );
int isnan ( double );
int isfinite ( double );
double md_ldexp ( double, int );
#else
double md_floor();
int isnan(), isfinite();
double md_ldexp();
#endif
double md_ceil(x)
double x;
{
double y;
#ifdef UNK
mtherr( "md_ceil", DOMAIN );
return(0.0);
#endif
#ifdef NANS
if( isnan(x) )
        return( x );
#endif
#ifdef INFINITIES
if(!isfinite(x))
        return(x);
#endif
y = md_floor(x);
if( y < x )
        y += 1.0;
#ifdef MINUSZERO
if( y == 0.0 && x < 0.0 )
        return( NEGZERO );
#endif
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 md_floor(x)
double x;
{
union
        {
        double y;
        unsigned short sh[4];
        } u;
unsigned short *p;
int e;
#ifdef UNK
mtherr( "md_floor", DOMAIN );
return(0.0);
#endif
#ifdef NANS
if( isnan(x) )
        return( x );
#endif
#ifdef INFINITIES
if(!isfinite(x))
        return(x);
#endif
#ifdef MINUSZERO
if(x == 0.0L)
        return(x);
#endif
u.y = x;
/* find the exponent (power of 2) */
#ifdef DEC
p = (unsigned short *)&u.sh[0];
e = (( *p  >> 7) & 0377) - 0201;
p += 3;
#endif
#ifdef IBMPC
p = (unsigned short *)&u.sh[3];
e = (( *p >> 4) & 0x7ff) - 0x3ff;
p -= 3;
#endif
#ifdef MIEEE
p = (unsigned short *)&u.sh[0];
e = (( *p >> 4) & 0x7ff) - 0x3ff;
p += 3;
#endif
if( e < 0 )
        {
        if( u.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) && (u.y != x) )
        u.y -= 1.0;
return(u.y);
}
double md_frexp( x, pw2 )
double x;
int *pw2;
{
union
        {
        double y;
        unsigned short sh[4];
        } u;
int i;
#ifdef DENORMAL
int k;
#endif
short *q;
u.y = x;
#ifdef UNK
mtherr( "md_frexp", DOMAIN );
return(0.0);
#endif
#ifdef IBMPC
q = (short *)&u.sh[3];
#endif
#ifdef DEC
q = (short *)&u.sh[0];
#endif
#ifdef MIEEE
q = (short *)&u.sh[0];
#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(u.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;
#ifdef DENORMAL
#else
*pw2 = 0;
return(0.0);
#endif
#endif
#ifndef DEC
/* Number is denormal or zero */
#ifdef DENORMAL
if( u.y == 0.0 )
        {
        *pw2 = 0;
        return( 0.0 );
        }
/* Handle denormal number. */
do
        {
        u.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( u.y );
#endif
}
double md_ldexp( x, pw2 )
double x;
int pw2;
{
union
        {
        double y;
        unsigned short sh[4];
        } u;
short *q;
int e;
#ifdef UNK
mtherr( "md_ldexp", DOMAIN );
return(0.0);
#endif
u.y = x;
#ifdef DEC
q = (short *)&u.sh[0];
e  = ( *q >> 7) & 0377;
if( e == 0 )
        return(0.0);
#else
#ifdef IBMPC
q = (short *)&u.sh[3];
#endif
#ifdef MIEEE
q = (short *)&u.sh[0];
#endif
while( (e = (*q & 0x7ff0) >> 4) == 0 )
        {
        if( u.y == 0.0 )
                {
                return( 0.0 );
                }
/* Input is denormal. */
        if( pw2 > 0 )
                {
                u.y *= 2.0;
                pw2 -= 1;
                }
        if( pw2 < 0 )
                {
                if( pw2 < -53 )
                        return(0.0);
                u.y /= 2.0;
                pw2 += 1;
                }
        if( pw2 == 0 )
                return(u.y);
        }
#endif /* not DEC */
e += pw2;
/* Handle overflow */
#ifdef DEC
if( e > MEXP )
        return( MAXNUM );
#else
if( e >= MEXP )
        return( 2.0*MAXNUM );
#endif
/* Handle denormalized results */
if( e < 1 )
        {
#ifdef DENORMAL
        if( e < -53 )
                return(0.0);
        *q &= 0x800f;
        *q |= 0x10;
        /* For denormals, significant bits may be lost even
           when dividing by 2.  Construct 2^-(1-e) so the result
           is obtained with only one multiplication.  */
        u.y *= md_ldexp(1.0, e-1);
        return(u.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(u.y);
        }
}