source: asp3_tinet_ecnl_arm/trunk/musl-1.1.18/src/math/fma.c@ 352

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

#define ASUINT64(x) ((union {double f; uint64_t i;}){x}).i
#define ZEROINFNAN (0x7ff-0x3ff-52-1)

struct num { uint64_t m; int e; int sign; };

static struct num normalize(double x)
{
        uint64_t ix = ASUINT64(x);
        int e = ix>>52;
        int sign = e & 0x800;
        e &= 0x7ff;
        if (!e) {
                ix = ASUINT64(x*0x1p63);
                e = ix>>52 & 0x7ff;
                e = e ? e-63 : 0x800;
        }
        ix &= (1ull<<52)-1;
        ix |= 1ull<<52;
        ix <<= 1;
        e -= 0x3ff + 52 + 1;
        return (struct num){ix,e,sign};
}

static void mul(uint64_t *hi, uint64_t *lo, uint64_t x, uint64_t y)
{
        uint64_t t1,t2,t3;
        uint64_t xlo = (uint32_t)x, xhi = x>>32;
        uint64_t ylo = (uint32_t)y, yhi = y>>32;

        t1 = xlo*ylo;
        t2 = xlo*yhi + xhi*ylo;
        t3 = xhi*yhi;
        *lo = t1 + (t2<<32);
        *hi = t3 + (t2>>32) + (t1 > *lo);
}

double fma(double x, double y, double z)
{
        #pragma STDC FENV_ACCESS ON

        /* normalize so top 10bits and last bit are 0 */
        struct num nx, ny, nz;
        nx = normalize(x);
        ny = normalize(y);
        nz = normalize(z);

        if (nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN)
                return x*y + z;
        if (nz.e >= ZEROINFNAN) {
                if (nz.e > ZEROINFNAN) /* z==0 */
                        return x*y + z;
                return z;
        }

        /* mul: r = x*y */
        uint64_t rhi, rlo, zhi, zlo;
        mul(&rhi, &rlo, nx.m, ny.m);
        /* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */

        /* align exponents */
        int e = nx.e + ny.e;
        int d = nz.e - e;
        /* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
        if (d > 0) {
                if (d < 64) {
                        zlo = nz.m<<d;
                        zhi = nz.m>>64-d;
                } else {
                        zlo = 0;
                        zhi = nz.m;
                        e = nz.e - 64;
                        d -= 64;
                        if (d == 0) {
                        } else if (d < 64) {
                                rlo = rhi<<64-d | rlo>>d | !!(rlo<<64-d);
                                rhi = rhi>>d;
                        } else {
                                rlo = 1;
                                rhi = 0;
                        }
                }
        } else {
                zhi = 0;
                d = -d;
                if (d == 0) {
                        zlo = nz.m;
                } else if (d < 64) {
                        zlo = nz.m>>d | !!(nz.m<<64-d);
                } else {
                        zlo = 1;
                }
        }

        /* add */
        int sign = nx.sign^ny.sign;
        int samesign = !(sign^nz.sign);
        int nonzero = 1;
        if (samesign) {
                /* r += z */
                rlo += zlo;
                rhi += zhi + (rlo < zlo);
        } else {
                /* r -= z */
                uint64_t t = rlo;
                rlo -= zlo;
                rhi = rhi - zhi - (t < rlo);
                if (rhi>>63) {
                        rlo = -rlo;
                        rhi = -rhi-!!rlo;
                        sign = !sign;
                }
                nonzero = !!rhi;
        }

        /* set rhi to top 63bit of the result (last bit is sticky) */
        if (nonzero) {
                e += 64;
                d = a_clz_64(rhi)-1;
                /* note: d > 0 */
                rhi = rhi<<d | rlo>>64-d | !!(rlo<<d);
        } else if (rlo) {
                d = a_clz_64(rlo)-1;
                if (d < 0)
                        rhi = rlo>>1 | (rlo&1);
                else
                        rhi = rlo<<d;
        } else {
                /* exact +-0 */
                return x*y + z;
        }
        e -= d;

        /* convert to double */
        int64_t i = rhi; /* i is in [1<<62,(1<<63)-1] */
        if (sign)
                i = -i;
        double r = i; /* |r| is in [0x1p62,0x1p63] */

        if (e < -1022-62) {
                /* result is subnormal before rounding */
                if (e == -1022-63) {
                        double c = 0x1p63;
                        if (sign)
                                c = -c;
                        if (r == c) {
                                /* min normal after rounding, underflow depends
                                   on arch behaviour which can be imitated by
                                   a double to float conversion */
                                float fltmin = 0x0.ffffff8p-63*FLT_MIN * r;
                                return DBL_MIN/FLT_MIN * fltmin;
                        }
                        /* one bit is lost when scaled, add another top bit to
                           only round once at conversion if it is inexact */
                        if (rhi << 53) {
                                i = rhi>>1 | (rhi&1) | 1ull<<62;
                                if (sign)
                                        i = -i;
                                r = i;
                                r = 2*r - c; /* remove top bit */

                                /* raise underflow portably, such that it
                                   cannot be optimized away */
                                {
                                        double_t tiny = DBL_MIN/FLT_MIN * r;
                                        r += (double)(tiny*tiny) * (r-r);
                                }
                        }
                } else {
                        /* only round once when scaled */
                        d = 10;
                        i = ( rhi>>d | !!(rhi<<64-d) ) << d;
                        if (sign)
                                i = -i;
                        r = i;
                }
        }
        return scalbn(r, e);
}