/* @(#)e_fmod.c 1.3 95/01/18 */
/*-
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#include <sys/types.h>
#include <machine/ieee.h>

#include <float.h>
#include <math.h>
#include <stdint.h>

#include "math_private.h"

#define BIAS (LDBL_MAX_EXP - 1)

/*
 * These macros add and remove an explicit integer bit in front of the
 * fractional mantissa, if the architecture doesn't have such a bit by
 * default already.
 */
#ifdef LDBL_IMPLICIT_NBIT
#define LDBL_NBIT       0
#define SET_NBIT(hx)    ((hx) | (1ULL << LDBL_MANH_SIZE))
#define HFRAC_BITS      EXT_FRACHBITS
#else
#define LDBL_NBIT       0x80000000
#define SET_NBIT(hx)    (hx)
#define HFRAC_BITS      (EXT_FRACHBITS - 1)
#endif

#define MANL_SHIFT      (EXT_FRACLBITS - 1)

static const long double Zero[] = {0.0L, -0.0L};

/*
 * Return the IEEE remainder and set *quo to the last n bits of the
 * quotient, rounded to the nearest integer.  We choose n=31 because
 * we wind up computing all the integer bits of the quotient anyway as
 * a side-effect of computing the remainder by the shift and subtract
 * method.  In practice, this is far more bits than are needed to use
 * remquo in reduction algorithms.
 *
 * Assumptions:
 * - The low part of the mantissa fits in a manl_t exactly.
 * - The high part of the mantissa fits in an int64_t with enough room
 *   for an explicit integer bit in front of the fractional bits.
 */
long double
remquol(long double x, long double y, int *quo)
{
        int64_t hx,hz;  /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
        uint32_t hy;
        uint32_t lx,ly,lz;
        uint32_t esx, esy;
        int ix,iy,n,q,sx,sxy;

        GET_LDOUBLE_WORDS(esx,hx,lx,x);
        GET_LDOUBLE_WORDS(esy,hy,ly,y);
        sx = esx & 0x8000;
        sxy = sx ^ (esy & 0x8000);
        esx &= 0x7fff;                          /* |x| */
        esy &= 0x7fff;                          /* |y| */
        SET_LDOUBLE_EXP(x,esx);
        SET_LDOUBLE_EXP(y,esy);

    /* purge off exception values */
        if((esy|hy|ly)==0 ||                    /* y=0 */
           (esx == BIAS + LDBL_MAX_EXP) ||      /* or x not finite */
           (esy == BIAS + LDBL_MAX_EXP &&
            ((hy&~LDBL_NBIT)|ly)!=0))           /* or y is NaN */
            return (x*y)/(x*y);
        if(esx<=esy) {
            if((esx<esy) ||
               (hx<=hy &&
                (hx<hy ||
                 lx<ly))) {
                q = 0;
                goto fixup;                     /* |x|<|y| return x or x-y */
            }
            if(hx==hy && lx==ly) {
                *quo = 1;
                return Zero[sx!=0];             /* |x|=|y| return x*0*/
            }
        }

    /* determine ix = ilogb(x) */
        if(esx == 0) {                          /* subnormal x */
            x *= 0x1.0p512;
            GET_LDOUBLE_WORDS(esx,hx,lx,x);
            ix = esx - (BIAS + 512);
        } else {
            ix = esx - BIAS;
        }

    /* determine iy = ilogb(y) */
        if(esy == 0) {                          /* subnormal y */
            y *= 0x1.0p512;
            GET_LDOUBLE_WORDS(esy,hy,ly,y);
            iy = esy - (BIAS + 512);
        } else {
            iy = esy - BIAS;
        }

    /* set up {hx,lx}, {hy,ly} and align y to x */
        hx = SET_NBIT(hx);
        lx = SET_NBIT(lx);

    /* fix point fmod */
        n = ix - iy;
        q = 0;

        while(n--) {
            hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
            if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
            else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;}
            q <<= 1;
        }
        hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
        if(hz>=0) {hx=hz;lx=lz;q++;}

    /* convert back to floating value and restore the sign */
        if((hx|lx)==0) {                        /* return sign(x)*0 */
            *quo = (sxy ? -q : q);
            return Zero[sx!=0];
        }
        while(hx<(1ULL<<HFRAC_BITS)) {  /* normalize x */
            hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
            iy -= 1;
        }
        if (iy < LDBL_MIN_EXP) {
            esx = (iy + BIAS + 512) & 0x7fff;
            SET_LDOUBLE_WORDS(x,esx,hx,lx);
            x *= 0x1p-512;
            GET_LDOUBLE_WORDS(esx,hx,lx,x);
        } else {
            esx = (iy + BIAS) & 0x7fff;
        }
        SET_LDOUBLE_WORDS(x,esx,hx,lx);
fixup:
        y = fabsl(y);
        if (y < LDBL_MIN * 2) {
            if (x+x>y || (x+x==y && (q & 1))) {
                q++;
                x-=y;
            }
        } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
            q++;
            x-=y;
        }

        GET_LDOUBLE_EXP(esx,x);
        esx ^= sx;
        SET_LDOUBLE_EXP(x,esx);

        q &= 0x7fffffff;
        *quo = (sxy ? -q : q);
        return x;
}
DEF_STD(remquol);