#include <asm/atomic.h> // for a_clz_64
#include <float.h>	// for FLT_MIN, DBL_MIN
#include <math.h>	// for fma, scalbn, double_t
#include <stdint.h>	// for uint64_t, int64_t, uint32_t

#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 = (int)(ix >> 52);
	int sign = e & 0x800;
	e &= 0x7ff;
	if (!e) {
		ix = ASUINT64(x * 0x1p63);
		e = (int)(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;
		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 = (int64_t)rhi; /* i is in [1<<62,(1<<63)-1] */
	if (sign)
		i = -i;
	double r = (double)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 = (float)(0x0.ffffff8p-63) *
					       FLT_MIN * (float)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 = (int64_t)(rhi >> 1 | (rhi & 1) |
					      1ull << 62);
				if (sign)
					i = -i;
				r = (double)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);
				}
			}
		} else {
			/* only round once when scaled */
			d = 10;
			i = (int64_t)((rhi >> d | !!(rhi << (64 - d))) << d);
			if (sign)
				i = -i;
			r = (double)i;
		}
	}
	return scalbn(r, e);
}