/*-
 * ====================================================
 * 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 <float.h>
#include <stdint.h>

#include "fpmath.h"
#include "math.h"
#include "math_private.h"

#define BIAS (LDBL_MAX_EXP - 1)

#if LDBL_MANL_SIZE > 32
typedef uint64_t manl_t;
#else
typedef uint32_t manl_t;
#endif

#if LDBL_MANH_SIZE > 32
typedef uint64_t manh_t;
#else
typedef uint32_t manh_t;
#endif

/*
 * 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 SET_NBIT(hx)    ((hx) | (1ULL << LDBL_MANH_SIZE))
#define HFRAC_BITS      LDBL_MANH_SIZE
#else
#define SET_NBIT(hx)    (hx)
#define HFRAC_BITS      (LDBL_MANH_SIZE - 1)
#endif

#define MANL_SHIFT      (LDBL_MANL_SIZE - 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)
{
        union IEEEl2bits ux, uy;
        int64_t hx,hz;  /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
        manh_t hy;
        manl_t lx,ly,lz;
        int ix,iy,n,q,sx,sxy;

        ux.e = x;
        uy.e = y;
        sx = ux.bits.sign;
        sxy = sx ^ uy.bits.sign;
        ux.bits.sign = 0;       /* |x| */
        uy.bits.sign = 0;       /* |y| */

    /* purge off exception values */
        if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
           (ux.bits.exp == BIAS + LDBL_MAX_EXP) ||       /* or x not finite */
           (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
            ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
            return nan_mix_op(x, y, *)/nan_mix_op(x, y, *);
        if(ux.bits.exp<=uy.bits.exp) {
            if((ux.bits.exp<uy.bits.exp) ||
               (ux.bits.manh<=uy.bits.manh &&
                (ux.bits.manh<uy.bits.manh ||
                 ux.bits.manl<uy.bits.manl))) {
                q = 0;
                goto fixup;     /* |x|<|y| return x or x-y */
            }
            if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
                *quo = (sxy ? -1 : 1);
                return Zero[sx];        /* |x|=|y| return x*0*/
            }
        }

    /* determine ix = ilogb(x) */
        if(ux.bits.exp == 0) {  /* subnormal x */
            ux.e *= 0x1.0p512;
            ix = ux.bits.exp - (BIAS + 512);
        } else {
            ix = ux.bits.exp - BIAS;
        }

    /* determine iy = ilogb(y) */
        if(uy.bits.exp == 0) {  /* subnormal y */
            uy.e *= 0x1.0p512;
            iy = uy.bits.exp - (BIAS + 512);
        } else {
            iy = uy.bits.exp - BIAS;
        }

    /* set up {hx,lx}, {hy,ly} and align y to x */
        hx = SET_NBIT(ux.bits.manh);
        hy = SET_NBIT(uy.bits.manh);
        lx = ux.bits.manl;
        ly = uy.bits.manl;

    /* 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 */
            q &= 0x7fffffff;
            *quo = (sxy ? -q : q);
            return Zero[sx];
        }
        while(hx<(1ULL<<HFRAC_BITS)) {  /* normalize x */
            hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
            iy -= 1;
        }
        ux.bits.manh = hx; /* The integer bit is truncated here if needed. */
        ux.bits.manl = lx;
        if (iy < LDBL_MIN_EXP) {
            ux.bits.exp = iy + (BIAS + 512);
            ux.e *= 0x1p-512;
        } else {
            ux.bits.exp = iy + BIAS;
        }
fixup:
        x = ux.e;               /* |x| */
        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;
        }
        ux.e = x;
        ux.bits.sign ^= sx;
        x = ux.e;
        q &= 0x7fffffff;
        *quo = (sxy ? -q : q);
        return x;
}