1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 #include "bsd_privatef.h"
13
bsd__ieee754_powf(float x,float y)14 float bsd__ieee754_powf(float x, float y)
15 {
16 float z,ax,z_h,z_l,p_h,p_l;
17 float y1,t1,t2,r,s,sn,t,u,v,w;
18 int32_t i,j,k,yisint,n;
19 int32_t hx,hy,ix,iy,is;
20
21 GET_FLOAT_WORD(hx,x);
22 GET_FLOAT_WORD(hy,y);
23 ix = hx&0x7fffffff; iy = hy&0x7fffffff;
24
25 /* y==zero: x**0 = 1 */
26 if(iy==0) return one;
27
28 /* x==1: 1**y = 1, even if y is NaN */
29 if (hx==0x3f800000) return one;
30
31 /* y!=zero: result is NaN if either arg is NaN */
32 if(ix > 0x7f800000 ||
33 iy > 0x7f800000)
34 return (x+0.0F)+(y+0.0F);
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>=0x4b800000) yisint = 2; /* even integer y */
44 else if(iy>=0x3f800000) {
45 k = (iy>>23)-0x7f; /* exponent */
46 j = iy>>(23-k);
47 if((j<<(23-k))==iy) yisint = 2-(j&1);
48 }
49 }
50
51 /* special value of y */
52 if (iy==0x7f800000) { /* y is +-inf */
53 if (ix==0x3f800000)
54 return one; /* (-1)**+-inf is NaN */
55 else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
56 return (hy>=0)? y: zero;
57 else /* (|x|<1)**-,+inf = inf,0 */
58 return (hy<0)?-y: zero;
59 }
60 if(iy==0x3f800000) { /* y is +-1 */
61 if(hy<0) return one/x; else return x;
62 }
63 if(hy==0x40000000) return x*x; /* y is 2 */
64 if(hy==0x3f000000) { /* y is 0.5 */
65 if(hx>=0) /* x >= +0 */
66 return sqrtf(x);
67 }
68
69 ax = fabsf(x);
70 /* special value of x */
71 if(ix==0x7f800000||ix==0||ix==0x3f800000){
72 z = ax; /*x is +-0,+-inf,+-1*/
73 if(hy<0) z = one/z; /* z = (1/|x|) */
74 if(hx<0) {
75 if(((ix-0x3f800000)|yisint)==0) {
76 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
77 } else if(yisint==1)
78 z = -z; /* (x<0)**odd = -(|x|**odd) */
79 }
80 return z;
81 }
82
83 n = ((u_int32_t)hx>>31)-1;
84
85 /* (x<0)**(non-int) is NaN */
86 if((n|yisint)==0) return (x-x)/(x-x);
87
88 sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
89 if((n|(yisint-1))==0) sn = -one; /* (-ve)**(odd int) */
90
91 /* |y| is huge */
92 if(iy>0x4d000000) { /* if |y| > 2**27 */
93 /* over/underflow if x is not close to one */
94 if(ix<0x3f7ffff8) return (hy<0)? sn*huge*huge:sn*tiny*tiny;
95 if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*tiny*tiny;
96 /* now |1-x| is tiny <= 2**-20, suffice to compute
97 log(x) by x-x^2/2+x^3/3-x^4/4 */
98 t = ax-1; /* t has 20 trailing zeros */
99 w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
100 u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
101 v = t*ivln2_l-w*ivln2;
102 t1 = u+v;
103 GET_FLOAT_WORD(is,t1);
104 SET_FLOAT_WORD(t1,is&0xfffff000);
105 t2 = v-(t1-u);
106 } else {
107 float s2,s_h,s_l,t_h,t_l;
108 n = 0;
109 /* take care subnormal number */
110 if(ix<0x00800000)
111 {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
112 n += ((ix)>>23)-0x7f;
113 j = ix&0x007fffff;
114 /* determine interval */
115 ix = j|0x3f800000; /* normalize ix */
116 if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
117 else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
118 else {k=0;n+=1;ix -= 0x00800000;}
119 SET_FLOAT_WORD(ax,ix);
120
121 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
122 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
123 v = one/(ax+bp[k]);
124 s = u*v;
125 s_h = s;
126 GET_FLOAT_WORD(is,s_h);
127 SET_FLOAT_WORD(s_h,is&0xfffff000);
128 /* t_h=ax+bp[k] High */
129 is = ((ix>>1)&0xfffff000)|0x20000000;
130 SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21));
131 t_l = ax - (t_h-bp[k]);
132 s_l = v*((u-s_h*t_h)-s_h*t_l);
133 /* compute log(ax) */
134 s2 = s*s;
135 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
136 r += s_l*(s_h+s);
137 s2 = s_h*s_h;
138 t_h = (float)3.0+s2+r;
139 GET_FLOAT_WORD(is,t_h);
140 SET_FLOAT_WORD(t_h,is&0xfffff000);
141 t_l = r-((t_h-(float)3.0)-s2);
142 /* u+v = s*(1+...) */
143 u = s_h*t_h;
144 v = s_l*t_h+t_l*s;
145 /* 2/(3log2)*(s+...) */
146 p_h = u+v;
147 GET_FLOAT_WORD(is,p_h);
148 SET_FLOAT_WORD(p_h,is&0xfffff000);
149 p_l = v-(p_h-u);
150 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
151 z_l = cp_l*p_h+p_l*cp+dp_l[k];
152 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
153 t = (float)n;
154 t1 = (((z_h+z_l)+dp_h[k])+t);
155 GET_FLOAT_WORD(is,t1);
156 SET_FLOAT_WORD(t1,is&0xfffff000);
157 t2 = z_l-(((t1-t)-dp_h[k])-z_h);
158 }
159
160 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
161 GET_FLOAT_WORD(is,y);
162 SET_FLOAT_WORD(y1,is&0xfffff000);
163 p_l = (y-y1)*t1+y*t2;
164 p_h = y1*t1;
165 z = p_l+p_h;
166 GET_FLOAT_WORD(j,z);
167 if (j>0x43000000) /* if z > 128 */
168 return sn*huge*huge; /* overflow */
169 else if (j==0x43000000) { /* if z == 128 */
170 if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
171 }
172 else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
173 return sn*tiny*tiny; /* underflow */
174 else if ((j&0xffffffff)==0xc3160000){ /* z == -150 */
175 if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
176 }
177 /*
178 * compute 2**(p_h+p_l)
179 */
180 i = j&0x7fffffff;
181 k = (i>>23)-0x7f;
182 n = 0;
183 if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
184 n = j+(0x00800000>>(k+1));
185 k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
186 SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
187 n = ((n&0x007fffff)|0x00800000)>>(23-k);
188 if(j<0) n = -n;
189 p_h -= t;
190 }
191 t = p_l+p_h;
192 GET_FLOAT_WORD(is,t);
193 SET_FLOAT_WORD(t,is&0xffff8000);
194 u = t*lg2_h;
195 v = (p_l-(t-p_h))*lg2+t*lg2_l;
196 z = u+v;
197 w = v-(z-u);
198 t = z*z;
199 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
200 r = (z*t1)/(t1-two)-(w+z*w);
201 z = one-(r-z);
202 GET_FLOAT_WORD(j,z);
203 j += (n<<23);
204 if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */
205 else SET_FLOAT_WORD(z,j);
206 return sn*z;
207 }
208