51  * of the approximation interval the logarithm equal 1/32
52  * and its relative error is about 1 lsb = 1.1e-19.  Hence
70  * pow underflow   x**y < 1/MAXNUM       0.0
82 /* log(1+x) =  x - .5x^2 + x^3 *  P(z)/Q(z)
83  * on the domain  2^(-1/32) - 1  <=  x  <=  2^(1/32) - 1
87  4.9000050881978028599627E-1L,
102  9.7857206208770013448287E-1L,
103  9.5760328069857364691013E-1L,
104  9.3708381705514995065011E-1L,
105  9.1700404320467123175367E-1L,
106  8.9735453750155359320742E-1L,
107  8.7812608018664974155474E-1L,
108  8.5930964906123895780165E-1L,
109  8.4089641525371454301892E-1L,
110  8.2287773907698242225554E-1L,
111  8.0524516597462715409607E-1L,
112  7.8799042255394324325455E-1L,
113  7.7110541270397041179298E-1L,
114  7.5458221379671136985669E-1L,
115  7.3841307296974965571198E-1L,
116  7.2259040348852331001267E-1L,
117  7.0710678118654752438189E-1L,
118  6.9195494098191597746178E-1L,
119  6.7712777346844636413344E-1L,
120  6.6261832157987064729696E-1L,
121  6.4841977732550483296079E-1L,
122  6.3452547859586661129850E-1L,
123  6.2092890603674202431705E-1L,
124  6.0762367999023443907803E-1L,
125  5.9460355750136053334378E-1L,
126  5.8186242938878875689693E-1L,
127  5.6939431737834582684856E-1L,
128  5.5719337129794626814472E-1L,
129  5.4525386633262882960438E-1L,
130  5.3357020033841180906486E-1L,
131  5.2213689121370692017331E-1L,
132  5.1094857432705833910408E-1L,
133  5.0000000000000000000000E-1L,
155 /* 2^x = 1 + x P(x),
156  * on the interval -1/32 <= x <= 0
164  2.4022650695910062854352E-1L,
165  6.9314718055994530931447E-1L,
173 /* log2(e) - 1 */
178 static const long double LOGE2L = 6.9314718055994530941723E-1L;
211 /* Set iyflg to 1 if y is an integer.  */  in powl()
214 /* flag = 1 if x is negative */  in powl()
221         ya = ldexpl(y, -1);  in powl()
237                 if (fabsl(x) < 1)  in powl()
241                 if (fabsl(x) < 1)  in powl()
247 /* y >= 2**80, infinity (x > 1) or zero (x < 1) */  in powl()
255 		return __math_oflowl(1);  in powl()
259 /* y <= -2**80, zero (x > 1) or infinity (x < 1) */  in powl()
346 i = 1;  in powl()
355 if( x >= douba(1) )  in powl()
356 	i = -1;  in powl()
357 i += 1;  in powl()
365  * log(x/a) = log(1+v),  v = x/a - 1 = (x-a)/a  in powl()
372 /* rational approximation for log(1+v):  in powl()
374  * log(1+v)  =  v  -  v**2/2  +  v**3 P(v) / Q(v)  in powl()
378 w = w - ldexpl( z, -1 );   /*  w - 0.5 * z  */  in powl()
381  * multiply by log2(e) = 1 + LOG2EA  in powl()
397  * and small part yb less than 1/NXT  in powl()
429 	e += 1;  in powl()
438 z = Hb * __polevll( Hb, R, 6 );  /*    z  =  2**Hb - 1    */  in powl()
440 /* Express e/NXT as an integer plus a negative number of (1/NXT)ths.  in powl()
446 	i = 1;  in powl()
450 z = w * z;      /*    2**-e * ( 1 + (2**Hb-1) )    */  in powl()
460 	w = ldexpl( y, -1 );  in powl()
462 	w = ldexpl( w, 1 );  in powl()
471 /* Find a multiple of 1/NXT that is within 1/NXT of x. */
516  *    IEEE        1,2     -1022,1023  20000       3.9e-17     7.6e-18
546 	asign = -1;  in powil()
555 	sign = -1;  in powil()
560 	sign = 1;  in powil()
569 e = (lx - 1)*n;  in powil()
572 	s = (s - 7.0710678118654752e-1L) / (s +  7.0710678118654752e-1L);  in powil()
581 	return __math_oflowl(asign < 0 && (nn & 1));		/* overflow */  in powil()
584 	return __math_uflowl(asign < 0 && (nn & 1));	/* underflow */  in powil()
597 if( n & 1 )  in powil()
607 n >>= 1;  in powil()
611 	if( n & 1 )	/* if that bit is set, then include in product */  in powil()
613 	n >>= 1;  in powil()