自学教程：C++ GET_LOW_WORD函数代码示例

double__ieee754_exp10 (double arg){  int32_t lx;  double arg_high, arg_low;  double exp_high, exp_low;  if (!isfinite (arg))    return __ieee754_exp (arg);  if (arg < DBL_MIN_10_EXP - DBL_DIG - 10)    return DBL_MIN * DBL_MIN;  else if (arg > DBL_MAX_10_EXP + 1)    return DBL_MAX * DBL_MAX;  else if (fabs (arg) < 0x1p-56)    return 1.0;  GET_LOW_WORD (lx, arg);  lx &= 0xf8000000;  arg_high = arg;  SET_LOW_WORD (arg_high, lx);  arg_low = arg - arg_high;  exp_high = arg_high * log10_high;  exp_low = arg_high * log10_low + arg_low * M_LN10;  return __ieee754_exp (exp_high) * __ieee754_exp (exp_low);}

int__ieee754_ilogb (double x){  int32_t hx, lx, ix;  GET_HIGH_WORD (hx, x);  hx &= 0x7fffffff;  if (hx < 0x00100000)    {      GET_LOW_WORD (lx, x);      if ((hx | lx) == 0)	return FP_ILOGB0;               /* ilogb(0) = FP_ILOGB0 */      else                              /* subnormal x */      if (hx == 0)	{	  for (ix = -1043; lx > 0; lx <<= 1)	    ix -= 1;	}      else	{	  for (ix = -1022, hx <<= 11; hx > 0; hx <<= 1)	    ix -= 1;	}      return ix;    }  else if (hx < 0x7ff00000)    return (hx >> 20) - 1023;  else if (FP_ILOGBNAN != INT_MAX)

double atan(double x){	double w,s1,s2,z;	int32_t ix,hx,id;	GET_HIGH_WORD(hx, x);	ix = hx & 0x7fffffff;	if (ix >= 0x44100000) {   /* if |x| >= 2^66 */		uint32_t low;		GET_LOW_WORD(low, x);		if (ix > 0x7ff00000 ||		    (ix == 0x7ff00000 && low != 0))  /* NaN */			return x+x;		if (hx > 0)			return  atanhi[3] + *(volatile double *)&atanlo[3];		else			return -atanhi[3] - *(volatile double *)&atanlo[3];	}	if (ix < 0x3fdc0000) {    /* |x| < 0.4375 */		if (ix < 0x3e400000) {  /* |x| < 2^-27 */			/* raise inexact */			if (huge+x > 1.0)				return x;		}		id = -1;	} else {		x = fabs(x);		if (ix < 0x3ff30000) {  /* |x| < 1.1875 */			if (ix < 0x3fe60000) {  /*  7/16 <= |x| < 11/16 */				id = 0;				x = (2.0*x-1.0)/(2.0+x);			} else {                /* 11/16 <= |x| < 19/16 */				id = 1;				x = (x-1.0)/(x+1.0);			}		} else {			if (ix < 0x40038000) {  /* |x| < 2.4375 */				id = 2;				x = (x-1.5)/(1.0+1.5*x);			} else {                /* 2.4375 <= |x| < 2^66 */				id = 3;				x = -1.0/x;			}		}	}	/* end of argument reduction */	z = x*x;	w = z*z;	/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */	s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));	s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));	if (id < 0)		return x - x*(s1+s2);	z = atanhi[id] - (x*(s1+s2) - atanlo[id] - x);	return hx < 0 ? -z : z;}

double acos(double x){	double z, p, q, r, w, s, c, df;	s32_t hx, ix;	GET_HIGH_WORD(hx,x);	ix = hx & 0x7fffffff;	if (ix >= 0x3ff00000)	{		u32_t lx;		GET_LOW_WORD(lx,x);		if (((ix - 0x3ff00000) | lx) == 0)		{			if (hx > 0)				return 0.0;			else				return pi + 2.0 * pio2_lo;		}		return (x - x) / (x - x);	}	if (ix < 0x3fe00000)	{		if (ix <= 0x3c600000)			return pio2_hi + pio2_lo;		z = x * x;		p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));		q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));		r = p / q;		return pio2_hi - (x - (pio2_lo - x * r));	}	else if (hx < 0)	{		z = (one + x) * 0.5;		p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));		q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));		s = sqrt(z);		r = p / q;		w = r * s - pio2_lo;		return pi - 2.0 * (s + w);	}	else	{		z = (one - x) * 0.5;		s = sqrt(z);		df = s;		SET_LOW_WORD(df,0);		c = (z - df * df) / (s + df);		p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));		q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));		r = p / q;		w = r * s + c;		return 2.0 * (df + w);	}}

double__ieee754_cosh (double x){  double t, w;  int32_t ix;  u_int32_t lx;  /* High word of |x|. */  GET_HIGH_WORD (ix, x);  ix &= 0x7fffffff;  /* |x| in [0,22] */  if (ix < 0x40360000)    {      /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */      if (ix < 0x3fd62e43)	{	  if (ix < 0x3c800000)	    return one;                                   /* cosh(tiny) = 1 */	  t = __expm1 (fabs (x));	  w = one + t;	  return one + (t * t) / (w + w);	}      /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */      t = __ieee754_exp (fabs (x));      return half * t + half / t;    }  /* |x| in [22, log(maxdouble)] return half*exp(|x|) */  if (ix < 0x40862e42)    return half * __ieee754_exp (fabs (x));  /* |x| in [log(maxdouble), overflowthresold] */  GET_LOW_WORD (lx, x);  if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (u_int32_t) 0x8fb9f87d)))    {      w = __ieee754_exp (half * fabs (x));      t = half * w;      return t * w;    }  /* x is INF or NaN */  if (ix >= 0x7ff00000)    return x * x;  /* |x| > overflowthresold, cosh(x) overflow */  return huge * huge;}

doublecbrt(double x) {	int32_t	hx;	double r,s,t=0.0,w;	u_int32_t sign;	u_int32_t high,low;	GET_HIGH_WORD(hx,x);	sign=hx&0x80000000; 		/* sign= sign(x) */	hx  ^=sign;	if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */	GET_LOW_WORD(low,x);	if((hx|low)==0) 	    return(x);		/* cbrt(0) is itself */	SET_HIGH_WORD(x,hx);	/* x <- |x| */    /* rough cbrt to 5 bits */	if(hx<0x00100000) 		/* subnormal number */	  {SET_HIGH_WORD(t,0x43500000);	/* set t= 2**54 */	   t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);	  }	else	  SET_HIGH_WORD(t,hx/3+B1);    /* new cbrt to 23 bits, may be implemented in single precision */	r=t*t/x;	s=C+r*t;	t*=G+F/(s+E+D/s);	    /* chopped to 20 bits and make it larger than cbrt(x) */ 	GET_HIGH_WORD(high,t);	INSERT_WORDS(t,high+0x00000001,0);    /* one step newton iteration to 53 bits with error less than 0.667 ulps */	s=t*t;		/* t*t is exact */	r=x/s;	w=t+t;	r=(r-t)/(w+r);	/* r-s is exact */	t=t+t*r;    /* retore the sign bit */	GET_HIGH_WORD(high,t);	SET_HIGH_WORD(t,high|sign);	return(t);}

double asin(double x){	double t=0.0,w,p,q,c,r,s;	int32_t hx,ix;	GET_HIGH_WORD(hx, x);	ix = hx & 0x7fffffff;	if (ix >= 0x3ff00000) {           /* |x|>= 1 */		uint32_t lx;		GET_LOW_WORD(lx, x);		if ((ix-0x3ff00000 | lx) == 0)			/* asin(1) = +-pi/2 with inexact */			return x*pio2_hi + x*pio2_lo;		return (x-x)/(x-x);  /* asin(|x|>1) is NaN */	} else if (ix < 0x3fe00000) {  /* |x|<0.5 */		if (ix < 0x3e500000) {  /* if |x| < 2**-26 */			if (huge+x > 1.0)				return x; /* return x with inexact if x!=0*/		}		t = x*x;		p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));		q = 1.0+t*(qS1+t*(qS2+t*(qS3+t*qS4)));		w = p/q;		return x + x*w;	}	/* 1 > |x| >= 0.5 */	w = 1.0 - fabs(x);	t = w*0.5;	p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));	q = 1.0+t*(qS1+t*(qS2+t*(qS3+t*qS4)));	s = sqrt(t);	if (ix >= 0x3FEF3333) {  /* if |x| > 0.975 */		w = p/q;		t = pio2_hi-(2.0*(s+s*w)-pio2_lo);	} else {		w = s;		SET_LOW_WORD(w,0);		c = (t-w*w)/(s+w);		r = p/q;		p = 2.0*s*r-(pio2_lo-2.0*c);		q = pio4_hi - 2.0*w;		t = pio4_hi - (p-q);	}	if (hx > 0)		return t;	return -t;}

static double sin_pi(double x){	double y,z;	int n,ix;	GET_HIGH_WORD(ix, x);	ix &= 0x7fffffff;	if (ix < 0x3fd00000)		return __sin(pi*x, 0.0, 0);	y = -x;  /* negative x is assumed */	/*	 * argument reduction, make sure inexact flag not raised if input	 * is an integer	 */	z = floor(y);	if (z != y) {    /* inexact anyway */		y *= 0.5;		y  = 2.0*(y - floor(y));   /* y = |x| mod 2.0 */		n  = (int)(y*4.0);	} else {		if (ix >= 0x43400000) {			y = 0.0;    /* y must be even */			n = 0;		} else {			if (ix < 0x43300000)				z = y + two52;  /* exact */			GET_LOW_WORD(n, z);			n &= 1;			y = n;			n <<= 2;		}	}	switch (n) {	case 0:  y =  __sin(pi*y, 0.0, 0); break;	case 1:	case 2:  y =  __cos(pi*(0.5-y), 0.0); break;	case 3:	case 4:  y =  __sin(pi*(1.0-y), 0.0, 0); break;	case 5:	case 6:  y = -__cos(pi*(y-1.5), 0.0); break;	default: y =  __sin(pi*(y-2.0), 0.0, 0); break;	}	return -y;}

doubleexpm1(double x){	double y,hi,lo,c,t,e,hxs,hfx,r1,twopk;	int32_t k,xsb;	uint32_t hx;	GET_HIGH_WORD(hx,x);	xsb = hx&0x80000000;		/* sign bit of x */	hx &= 0x7fffffff;		/* high word of |x| */    /* filter out huge and non-finite argument */	if(hx >= 0x4043687A) {			/* if |x|>=56*ln2 */	    if(hx >= 0x40862E42) {		/* if |x|>=709.78... */                if(hx>=0x7ff00000) {		    uint32_t low;		    GET_LOW_WORD(low,x);		    if(((hx&0xfffff)|low)!=0)		         return x+x; 	 /* NaN */		    else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */	        }	        if(x > o_threshold) return huge*huge; /* overflow */	    }	    if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */		if(x+tiny<0.0)		/* raise inexact */		return tiny-one;	/* return -1 */	    }	}    /* argument reduction */	if(hx > 0x3fd62e42) {		/* if  |x| > 0.5 ln2 */	    if(hx < 0x3FF0A2B2) {	/* and |x| < 1.5 ln2 */		if(xsb==0)		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}		else		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}	    } else {		k  = invln2*x+((xsb==0)?0.5:-0.5);		t  = k;		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */		lo = t*ln2_lo;	    }	    STRICT_ASSIGN(double, x, hi - lo);	    c  = (hi-x)-lo;	}	else if(hx < 0x3c900000) {  	/* when |x|<2**-54, return x */

double__ieee754_acos(double x){	double z, p, q, r, w, s, c, df;	int32_t hx, ix;	GET_HIGH_WORD(hx, x);	ix = hx & 0x7fffffff;	if (ix >= 0x3ff00000) {	/* |x| >= 1 */		uint32_t lx;		GET_LOW_WORD(lx, x);		if (((ix - 0x3ff00000) | lx) == 0) {	/* |x|==1 */			if (hx>0) return 0.0;		/* acos(1) = 0  */			else return pi + 2.0*pio2_lo;	/* acos(-1)= pi */		}		return (x - x) / (x - x);		/* acos(|x|>1) is NaN */	}	if (ix<0x3fe00000) {	/* |x| < 0.5 */		if (ix <= 0x3c600000) return pio2_hi + pio2_lo;/*if|x|<2**-57*/		z = x*x;		p = z*(pS0 + z*(pS1 + z*(pS2 + z*(pS3 + z*(pS4 + z*pS5)))));		q = one + z*(qS1 + z*(qS2 + z*(qS3 + z*qS4)));		r = p / q;		return pio2_hi - (x - (pio2_lo - x*r));	}	else  if (hx<0) {		/* x < -0.5 */		z = (one + x)*0.5;		p = z*(pS0 + z*(pS1 + z*(pS2 + z*(pS3 + z*(pS4 + z*pS5)))));		q = one + z*(qS1 + z*(qS2 + z*(qS3 + z*qS4)));		s = sqrt(z);		r = p / q;		w = r*s - pio2_lo;		return pi - 2.0*(s + w);	}	else {			/* x > 0.5 */		z = (one - x)*0.5;		s = sqrt(z);		df = s;		SET_LOW_WORD(df, 0);		c = (z - df*df) / (s + df);		p = z*(pS0 + z*(pS1 + z*(pS2 + z*(pS3 + z*(pS4 + z*pS5)))));		q = one + z*(qS1 + z*(qS2 + z*(qS3 + z*qS4)));		r = p / q;		w = r*s + c;		return 2.0*(df + w);	}}

int ilogb(double x){	int32_t hx,lx,ix;	GET_HIGH_WORD(hx,x);	hx &= 0x7fffffff;	if(hx<0x00100000) {	    GET_LOW_WORD(lx,x);	    if((hx|lx)==0)		return 0x80000001;	/* ilogb(0) = 0x80000001 */	    else			/* subnormal x */		if(hx==0) {		    for (ix = -1043; lx>0; lx<<=1) ix -=1;		} else {		    for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1;		}	    return ix;	}	else if (hx<0x7ff00000) return (hx>>20)-1023;	else return 0x7fffffff;

double cosh(double x){	double t, w;	s32_t ix;	u32_t lx;	GET_HIGH_WORD(ix,x);	ix &= 0x7fffffff;	if (ix >= 0x7ff00000)		return x * x;	if (ix < 0x3fd62e43)	{		t = expm1(fabs(x));		w = one + t;		if (ix < 0x3c800000)			return w;		return one + (t * t) / (w + w);	}	if (ix < 0x40360000)	{		t = exp(fabs(x));		return half * t + half / t;	}	if (ix < 0x40862E42)		return half * exp(fabs(x));	GET_LOW_WORD(lx,x);	if (ix < 0x408633CE || ((ix == 0x408633ce)			&& (lx <= (u32_t) 0x8fb9f87d)))	{		w = exp(half * fabs(x));		t = half * w;		return t * w;	}	return huge * huge;}

double__ieee754_sinh(double x){	double t,w,h;	int32_t ix,jx;	uint32_t lx;    /* High word of |x|. */	GET_HIGH_WORD(jx,x);	ix = jx&0x7fffffff;    /* x is INF or NaN */	if(ix>=0x7ff00000) return x+x;	h = 0.5;	if (jx<0) h = -h;    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */	if (ix < 0x40360000) {		/* |x|<22 */	    if (ix<0x3e300000) 		/* |x|<2**-28 */		if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */	    t = expm1(fabs(x));	    if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));	    return h*(t+t/(t+one));	}    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */	if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));    /* |x| in [log(maxdouble), overflowthresold] */	GET_LOW_WORD(lx,x);	if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(uint32_t)0x8fb9f87d))) {	    w = __ieee754_exp(0.5*fabs(x));	    t = h*w;	    return t*w;	}    /* |x| > overflowthresold, sinh(x) overflow */	return x*shuge;}

	double __kernel_tan(double x, double y, int iy){	double z,r,v,w,s;	int32_t ix,hx;	GET_HIGH_WORD(hx,x);	ix = hx&0x7fffffff;	/* high word of |x| */	if(ix<0x3e300000)			/* x < 2**-28 */	    {if((int)x==0) {			/* generate inexact */		u_int32_t low;		GET_LOW_WORD(low,x);		if(((ix|low)|(iy+1))==0) return one/fabs(x);		else return (iy==1)? x: -one/x;	    }	    }	if(ix>=0x3FE59428) { 			/* |x|>=0.6744 */	    if(hx<0) {x = -x; y = -y;}	    z = pio4-x;	    w = pio4lo-y;	    x = z+w; y = 0.0;	}	z	=  x*x;	w 	=  z*z;    /* Break x^5*(T[1]+x^2*T[2]+...) into     *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +     *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))     */	r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));	v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));	s = z*x;	r = y + z*(s*(r+v)+y);	r += T[0]*s;	w = x+r;	if(ix>=0x3FE59428) {	    v = (double)iy;	    return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));	}

/* * exp2(x): compute the base 2 exponential of x * * Accuracy: Peak error < 0.503 ulp for normalized results. * * Method: (accurate tables) * *   Reduce x: *     x = 2**k + y, for integer k and |y| <= 1/2. *     Thus we have exp2(x) = 2**k * exp2(y). * *   Reduce y: *     y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE. *     Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]), *     with |z - eps[i]| <= 2**-9 + 2**-39 for the table used. * *   We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via *   a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61. *   The values in exp2t[] and eps[] are chosen such that *   exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such *   that exp2t[i] is accurate to 2**-64. * *   Note that the range of i is +-TBLSIZE/2, so we actually index the tables *   by i0 = i + TBLSIZE/2.  For cache efficiency, exp2t[] and eps[] are *   virtual tables, interleaved in the real table tbl[]. * *   This method is due to Gal, with many details due to Gal and Bachelis: * *      Gal, S. and Bachelis, B.  An Accurate Elementary Mathematical Library *      for the IEEE Floating Point Standard.  TOMS 17(1), 26-46 (1991). */double exp2(double x){	double r, t, z;	uint32_t hx, ix, i0;	union {uint32_t u; int32_t i;} k;	/* Filter out exceptional cases. */	GET_HIGH_WORD(hx, x);	ix = hx & 0x7fffffff;	if (ix >= 0x40900000) {        /* |x| >= 1024 */		if (ix >= 0x7ff00000) {			GET_LOW_WORD(ix, x);			if (hx == 0xfff00000 && ix == 0) /* -inf */				return 0;			return x;		}		if (x >= 1024) {			STRICT_ASSIGN(double, x, x * 0x1p1023);			return x;		}		if (x <= -1075) {			STRICT_ASSIGN(double, x, 0x1p-1000*0x1p-1000);			return x;		}

double__ieee754_hypot(double x, double y){	double a, b, t1, t2, y1, y2, w;	int32_t j, k, ha, hb;	GET_HIGH_WORD(ha, x);	ha &= 0x7fffffff;	GET_HIGH_WORD(hb, y);	hb &= 0x7fffffff;	if (hb > ha) { a = y; b = x; j = ha; ha = hb; hb = j; }	else { a = x; b = y; }	a = fabs(a);	b = fabs(b);	if ((ha - hb)>0x3c00000) { return a + b; } /* x/y > 2**60 */	k = 0;	if (ha > 0x5f300000) {	/* a>2**500 */		if (ha >= 0x7ff00000) {	/* Inf or NaN */			uint32_t low;			/* Use original arg order iff result is NaN; quieten sNaNs. */			w = fabs(x + 0.0) - fabs(y + 0.0);			GET_LOW_WORD(low, a);			if (((ha & 0xfffff) | low) == 0) w = a;			GET_LOW_WORD(low, b);			if (((hb ^ 0x7ff00000) | low) == 0) w = b;			return w;		}		/* scale a and b by 2**-600 */		ha -= 0x25800000; hb -= 0x25800000;	k += 600;		SET_HIGH_WORD(a, ha);		SET_HIGH_WORD(b, hb);	}	if (hb < 0x20b00000) {	/* b < 2**-500 */		if (hb <= 0x000fffff) {	/* subnormal b or 0 */			uint32_t low;			GET_LOW_WORD(low, b);			if ((hb | low) == 0) return a;			t1 = 0;			SET_HIGH_WORD(t1, 0x7fd00000);	/* t1=2^1022 */			b *= t1;			a *= t1;			k -= 1022;		}		else {		/* scale a and b by 2^600 */			ha += 0x25800000; 	/* a *= 2^600 */			hb += 0x25800000;	/* b *= 2^600 */			k -= 600;			SET_HIGH_WORD(a, ha);			SET_HIGH_WORD(b, hb);		}	}	/* medium size a and b */	w = a - b;	if (w>b) {		t1 = 0;		SET_HIGH_WORD(t1, ha);		t2 = a - t1;		w = sqrt(t1*t1 - (b*(-b) - t2*(a + t1)));	}	else {		a = a + a;		y1 = 0;		SET_HIGH_WORD(y1, hb);		y2 = b - y1;		t1 = 0;		SET_HIGH_WORD(t1, ha + 0x00100000);		t2 = a - t1;		w = sqrt(t1*y1 - (w*(-w) - (t1*y2 + t2*b)));	}	if (k != 0) {		uint32_t high;		t1 = 1.0;		GET_HIGH_WORD(high, t1);		SET_HIGH_WORD(t1, high + (k << 20));		return t1*w;	}	else return w;}

doubleexpm1(double x){	double y,hi,lo,c,t,e,hxs,hfx,r1;	int32_t k,xsb;	uint32_t hx;	c = 0;	GET_HIGH_WORD(hx,x);	xsb = hx&0x80000000;		/* sign bit of x */	if(xsb==0) y=x; else y= -x;	/* y = |x| */	hx &= 0x7fffffff;		/* high word of |x| */    /* filter out huge and non-finite argument */	if(hx >= 0x4043687A) {			/* if |x|>=56*ln2 */	    if(hx >= 0x40862E42) {		/* if |x|>=709.78... */                if(hx>=0x7ff00000) {		    uint32_t low;		    GET_LOW_WORD(low,x);		    if(((hx&0xfffff)|low)!=0)		         return x+x; 	 /* NaN */		    else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */	        }	        if(x > o_threshold) return huge*huge; /* overflow */	    }	    if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */		if(x+tiny<0.0)		/* raise inexact */		return tiny-one;	/* return -1 */	    }	}    /* argument reduction */	if(hx > 0x3fd62e42) {		/* if  |x| > 0.5 ln2 */	    if(hx < 0x3FF0A2B2) {	/* and |x| < 1.5 ln2 */		if(xsb==0)		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}		else		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}	    } else {		k  = invln2*x+((xsb==0)?0.5:-0.5);		t  = k;		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */		lo = t*ln2_lo;	    }	    x  = hi - lo;	    c  = (hi-x)-lo;	}	else if(hx < 0x3c900000) {  	/* when |x|<2**-54, return x */	    t = huge+x;	/* return x with inexact flags when x!=0 */	    return x - (t-(huge+x));	}	else k = 0;    /* x is now in primary range */	hfx = 0.5*x;	hxs = x*hfx;	r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));	t  = 3.0-r1*hfx;	e  = hxs*((r1-t)/(6.0 - x*t));	if(k==0) return x - (x*e-hxs);		/* c is 0 */	else {	    e  = (x*(e-c)-c);	    e -= hxs;	    if(k== -1) return 0.5*(x-e)-0.5;	    if(k==1)  {	       	if(x < -0.25) return -2.0*(e-(x+0.5));	       	else 	      return  one+2.0*(x-e);	    }	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */	        uint32_t high;	        y = one-(e-x);		GET_HIGH_WORD(high,y);		SET_HIGH_WORD(y,high+(k<<20));	/* add k to y's exponent */	        return y-one;	    }	    t = one;	    if(k<20) {	        uint32_t high;	        SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k));  /* t=1-2^-k */	       	y = t-(e-x);		GET_HIGH_WORD(high,y);		SET_HIGH_WORD(y,high+(k<<20));	/* add k to y's exponent */	   } else {

double__ieee754_hypot (double x, double y){  double a, b, t1, t2, y1, y2, w;  int32_t j, k, ha, hb;  GET_HIGH_WORD (ha, x);  ha &= 0x7fffffff;  GET_HIGH_WORD (hb, y);  hb &= 0x7fffffff;  if (hb > ha)    {      a = y; b = x; j = ha; ha = hb; hb = j;    }  else    {      a = x; b = y;    }  SET_HIGH_WORD (a, ha);        /* a <- |a| */  SET_HIGH_WORD (b, hb);        /* b <- |b| */  if ((ha - hb) > 0x3c00000)    {      return a + b;    }                                       /* x/y > 2**60 */  k = 0;  if (__glibc_unlikely (ha > 0x5f300000))                  /* a>2**500 */    {      if (ha >= 0x7ff00000)             /* Inf or NaN */	{	  u_int32_t low;	  w = a + b;                    /* for sNaN */	  GET_LOW_WORD (low, a);	  if (((ha & 0xfffff) | low) == 0)	    w = a;	  GET_LOW_WORD (low, b);	  if (((hb ^ 0x7ff00000) | low) == 0)	    w = b;	  return w;	}      /* scale a and b by 2**-600 */      ha -= 0x25800000; hb -= 0x25800000;  k += 600;      SET_HIGH_WORD (a, ha);      SET_HIGH_WORD (b, hb);    }  if (__builtin_expect (hb < 0x23d00000, 0))            /* b < 2**-450 */    {      if (hb <= 0x000fffff)             /* subnormal b or 0 */	{	  u_int32_t low;	  GET_LOW_WORD (low, b);	  if ((hb | low) == 0)	    return a;	  t1 = 0;	  SET_HIGH_WORD (t1, 0x7fd00000);       /* t1=2^1022 */	  b *= t1;	  a *= t1;	  k -= 1022;	  GET_HIGH_WORD (ha, a);	  GET_HIGH_WORD (hb, b);	  if (hb > ha)	    {	      t1 = a;	      a = b;	      b = t1;	      j = ha;	      ha = hb;	      hb = j;	    }	}      else                      /* scale a and b by 2^600 */	{	  ha += 0x25800000;             /* a *= 2^600 */	  hb += 0x25800000;             /* b *= 2^600 */	  k -= 600;	  SET_HIGH_WORD (a, ha);	  SET_HIGH_WORD (b, hb);	}    }  /* medium size a and b */  w = a - b;  if (w > b)    {      t1 = 0;      SET_HIGH_WORD (t1, ha);      t2 = a - t1;      w = __ieee754_sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1)));    }  else    {      a = a + a;      y1 = 0;      SET_HIGH_WORD (y1, hb);      y2 = b - y1;      t1 = 0;      SET_HIGH_WORD (t1, ha + 0x00100000);      t2 = a - t1;      w = __ieee754_sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));    }  if (k != 0)    {//.........这里部分代码省略.........

double expm1(double x){	double y, hi, lo, c=0, t, e, hxs, hfx, r1;	s32_t k, xsb;	u32_t hx;	GET_HIGH_WORD(hx,x);	xsb = hx & 0x80000000;	if (xsb == 0)		y = x;	else		y = -x;	hx &= 0x7fffffff;	if (hx >= 0x4043687A)	{		if (hx >= 0x40862E42)		{			if (hx >= 0x7ff00000)			{				u32_t low;				GET_LOW_WORD(low,x);				if (((hx & 0xfffff) | low) != 0)					return x + x;				else					return (xsb == 0) ? x : -1.0;			}			if (x > o_threshold)				return huge * huge;		}		if (xsb != 0)		{			if (x + tiny < 0.0)				return tiny - one;		}	}	if (hx > 0x3fd62e42)	{		if (hx < 0x3FF0A2B2)		{			if (xsb == 0)			{				hi = x - ln2_hi;				lo = ln2_lo;				k = 1;			}			else			{				hi = x + ln2_hi;				lo = -ln2_lo;				k = -1;			}		}		else		{			k = invln2 * x + ((xsb == 0) ? 0.5 : -0.5);			t = k;			hi = x - t * ln2_hi;			lo = t * ln2_lo;		}		x = hi - lo;		c = (hi - x) - lo;	}	else if (hx < 0x3c900000)	{		t = huge + x;		return x - (t - (huge + x));	}	else		k = 0;	hfx = 0.5 * x;	hxs = x * hfx;	r1 = one + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5))));	t = 3.0 - r1 * hfx;	e = hxs * ((r1 - t) / (6.0 - x * t));	if (k == 0)		return x - (x * e - hxs);	else	{		e = (x * (e - c) - c);		e -= hxs;		if (k == -1)			return 0.5 * (x - e) - 0.5;		if (k == 1)		{			if (x < -0.25)				return -2.0 * (e - (x + 0.5));			else				return one + 2.0 * (x - e);		}		if (k <= -2 || k > 56)		{			u32_t high;			y = one - (e - x);			GET_HIGH_WORD(high,y);			SET_HIGH_WORD(y,high+(k<<20));			return y - one;		}//.........这里部分代码省略.........

double attribute_hidden __ieee754_hypot(double x, double y){    double a=x,b=y,t1,t2,y1,y2,w;    int32_t j,k,ha,hb;    GET_HIGH_WORD(ha,x);    ha &= 0x7fffffff;    GET_HIGH_WORD(hb,y);    hb &= 0x7fffffff;    if(hb > ha) {        a=y;        b=x;        j=ha;        ha=hb;        hb=j;    }    else {        a=x;        b=y;    }    SET_HIGH_WORD(a,ha);	/* a <- |a| */    SET_HIGH_WORD(b,hb);	/* b <- |b| */    if((ha-hb)>0x3c00000) {        return a+b;   /* x/y > 2**60 */    }    k=0;    if(ha > 0x5f300000) {	/* a>2**500 */        if(ha >= 0x7ff00000) {	/* Inf or NaN */            u_int32_t low;            w = a+b;			/* for sNaN */            GET_LOW_WORD(low,a);            if(((ha&0xfffff)|low)==0) w = a;            GET_LOW_WORD(low,b);            if(((hb^0x7ff00000)|low)==0) w = b;            return w;        }        /* scale a and b by 2**-600 */        ha -= 0x25800000;        hb -= 0x25800000;        k += 600;        SET_HIGH_WORD(a,ha);        SET_HIGH_WORD(b,hb);    }    if(hb < 0x20b00000) {	/* b < 2**-500 */        if(hb <= 0x000fffff) {	/* subnormal b or 0 */            u_int32_t low;            GET_LOW_WORD(low,b);            if((hb|low)==0) return a;            t1=0;            SET_HIGH_WORD(t1,0x7fd00000);	/* t1=2^1022 */            b *= t1;            a *= t1;            k -= 1022;        } else {		/* scale a and b by 2^600 */            ha += 0x25800000; 	/* a *= 2^600 */            hb += 0x25800000;	/* b *= 2^600 */            k -= 600;            SET_HIGH_WORD(a,ha);            SET_HIGH_WORD(b,hb);        }    }    /* medium size a and b */    w = a-b;    if (w>b) {        t1 = 0;        SET_HIGH_WORD(t1,ha);        t2 = a-t1;        w  = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));    } else {        a  = a+a;        y1 = 0;        SET_HIGH_WORD(y1,hb);        y2 = b - y1;        t1 = 0;        SET_HIGH_WORD(t1,ha+0x00100000);        t2 = a - t1;        w  = __ieee754_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));    }    if(k!=0) {        u_int32_t high;        t1 = 1.0;        GET_HIGH_WORD(high,t1);        SET_HIGH_WORD(t1,high+(k<<20));        return t1*w;    } else return w;}