1 /*
2 * ====================================================
3 * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Permission to use, copy, modify, and distribute this
6 * software is freely granted, provided that this notice
7 * is preserved.
8 * ====================================================
9 */
10
11 #include "bsd_private.h"
12
bsd__ieee754_pow(double x,double y)13 double bsd__ieee754_pow(double x, double y)
14 {
15 double z,ax,z_h,z_l,p_h,p_l;
16 double y1,t1,t2,r,s,t,u,v,w;
17 int32_t i,j,k,yisint,n;
18 int32_t hx,hy,ix,iy;
19 u_int32_t lx,ly;
20
21 EXTRACT_WORDS(hx,lx,x);
22 EXTRACT_WORDS(hy,ly,y);
23 ix = hx&0x7fffffff; iy = hy&0x7fffffff;
24
25 /* y==zero: x**0 = 1 */
26 if((iy|ly)==0) return one;
27
28 /* x==1: 1**y = 1, even if y is NaN */
29 if (hx==0x3ff00000 && lx == 0) return one;
30
31 /* y!=zero: result is NaN if either arg is NaN */
32 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
33 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
34 return (x+0.0)+(y+0.0);
35
36 /* determine if y is an odd int when x < 0
37 * yisint = 0 ... y is not an integer
38 * yisint = 1 ... y is an odd int
39 * yisint = 2 ... y is an even int
40 */
41 yisint = 0;
42 if (hx<0) {
43 if (iy>=0x43400000) yisint = 2; /* even integer y */
44 else if (iy>=0x3ff00000) {
45 k = (iy>>20)-0x3ff; /* exponent */
46 if(k>20) {
47 j = ly>>(52-k);
48 if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1);
49 } else if(ly==0) {
50 j = iy>>(20-k);
51 if((j<<(20-k))==iy) yisint = 2-(j&1);
52 }
53 }
54 }
55
56 /* special value of y */
57 if(ly==0) {
58 if (iy==0x7ff00000) { /* y is +-inf */
59 if(((ix-0x3ff00000)|lx)==0)
60 return one; /* (-1)**+-inf is NaN */
61 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
62 return (hy>=0)? y: zero;
63 else /* (|x|<1)**-,+inf = inf,0 */
64 return (hy<0)?-y: zero;
65 }
66 if(iy==0x3ff00000) { /* y is +-1 */
67 if(hy<0) return one/x; else return x;
68 }
69 if(hy==0x40000000) return x*x; /* y is 2 */
70 if(hy==0x3fe00000) { /* y is 0.5 */
71 if(hx>=0) /* x >= +0 */
72 return sqrt(x);
73 }
74 }
75
76 ax = fabs(x);
77 /* special value of x */
78 if(lx==0) {
79 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
80 z = ax; /*x is +-0,+-inf,+-1*/
81 if(hy<0) z = one/z; /* z = (1/|x|) */
82 if(hx<0) {
83 if(((ix-0x3ff00000)|yisint)==0) {
84 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
85 } else if(yisint==1)
86 z = -z; /* (x<0)**odd = -(|x|**odd) */
87 }
88 return z;
89 }
90 }
91
92 /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be
93 n = (hx>>31)+1;
94 but ANSI C says a right shift of a signed negative quantity is
95 implementation defined. */
96 n = ((u_int32_t)hx>>31)-1;
97
98 /* (x<0)**(non-int) is NaN */
99 if((n|yisint)==0) return (x-x)/(x-x);
100
101 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
102 if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
103
104 /* |y| is huge */
105 if(iy>0x41e00000) { /* if |y| > 2**31 */
106 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
107 if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
108 if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
109 }
110 /* over/underflow if x is not close to one */
111 if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
112 if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
113 /* now |1-x| is tiny <= 2**-20, suffice to compute
114 log(x) by x-x^2/2+x^3/3-x^4/4 */
115 t = ax-one; /* t has 20 trailing zeros */
116 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
117 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
118 v = t*ivln2_l-w*ivln2;
119 t1 = u+v;
120 SET_LOW_WORD(t1,0);
121 t2 = v-(t1-u);
122 } else {
123 double ss,s2,s_h,s_l,t_h,t_l;
124 n = 0;
125 /* take care subnormal number */
126 if(ix<0x00100000)
127 {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
128 n += ((ix)>>20)-0x3ff;
129 j = ix&0x000fffff;
130 /* determine interval */
131 ix = j|0x3ff00000; /* normalize ix */
132 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
133 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
134 else {k=0;n+=1;ix -= 0x00100000;}
135 SET_HIGH_WORD(ax,ix);
136
137 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
138 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
139 v = one/(ax+bp[k]);
140 ss = u*v;
141 s_h = ss;
142 SET_LOW_WORD(s_h,0);
143 /* t_h=ax+bp[k] High */
144 t_h = zero;
145 SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
146 t_l = ax - (t_h-bp[k]);
147 s_l = v*((u-s_h*t_h)-s_h*t_l);
148 /* compute log(ax) */
149 s2 = ss*ss;
150 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
151 r += s_l*(s_h+ss);
152 s2 = s_h*s_h;
153 t_h = 3.0+s2+r;
154 SET_LOW_WORD(t_h,0);
155 t_l = r-((t_h-3.0)-s2);
156 /* u+v = ss*(1+...) */
157 u = s_h*t_h;
158 v = s_l*t_h+t_l*ss;
159 /* 2/(3log2)*(ss+...) */
160 p_h = u+v;
161 SET_LOW_WORD(p_h,0);
162 p_l = v-(p_h-u);
163 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
164 z_l = cp_l*p_h+p_l*cp+dp_l[k];
165 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
166 t = (double)n;
167 t1 = (((z_h+z_l)+dp_h[k])+t);
168 SET_LOW_WORD(t1,0);
169 t2 = z_l-(((t1-t)-dp_h[k])-z_h);
170 }
171
172 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
173 y1 = y;
174 SET_LOW_WORD(y1,0);
175 p_l = (y-y1)*t1+y*t2;
176 p_h = y1*t1;
177 z = p_l+p_h;
178 EXTRACT_WORDS(j,i,z);
179 if (j>=0x40900000) { /* z >= 1024 */
180 if(((j-0x40900000)|i)!=0) /* if z > 1024 */
181 return s*huge*huge; /* overflow */
182 else {
183 if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
184 }
185 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
186 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
187 return s*tiny*tiny; /* underflow */
188 else {
189 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
190 }
191 }
192 /*
193 * compute 2**(p_h+p_l)
194 */
195 i = j&0x7fffffff;
196 k = (i>>20)-0x3ff;
197 n = 0;
198 if (i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
199 n = j+(0x00100000>>(k+1));
200 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
201 t = zero;
202 SET_HIGH_WORD(t,n&~(0x000fffff>>k));
203 n = ((n&0x000fffff)|0x00100000)>>(20-k);
204 if(j<0) n = -n;
205 p_h -= t;
206 }
207 t = p_l+p_h;
208 SET_LOW_WORD(t,0);
209 u = t*lg2_h;
210 v = (p_l-(t-p_h))*lg2+t*lg2_l;
211 z = u+v;
212 w = v-(z-u);
213 t = z*z;
214 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
215 r = (z*t1)/(t1-two)-(w+z*w);
216 z = one-(r-z);
217 GET_HIGH_WORD(j,z);
218 j += (n<<20);
219 if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
220 else SET_HIGH_WORD(z,j);
221 return s*z;
222 }
223