[libm] / src / math / remquol.c

/* origin: FreeBSD /usr/src/lib/msun/src/s_remquol.c */
/*-
 * ====================================================
 * 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 "libm.h"
#if LD64
long double remquol(long double x, long double y, int *quo)
{
        return remquo(x, y, quo);
}
#elif LD80 || LD128

#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| */
        x = ux.e;

        /* 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 (x*y)/(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 = 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 */
                *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;
        }
        ux.bits.sign = 0;
        x = ux.e;
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;
        }

        ux.e = x;
        ux.bits.sign ^= sx;
        x = ux.e;

        q &= 0x7fffffff;
        *quo = sxy ? -q : q;
        return x;
}
#endif