1/* e_powf.c -- float version of e_pow.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16#include <math.h>
17#include <math_private.h>
18
19static const float huge = 1.0e+30, tiny = 1.0e-30;
20
21static const float
22bp[] = {1.0, 1.5,},
23dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
24dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
25zero = 0.0,
26one = 1.0,
27two = 2.0,
28two24 = 16777216.0, /* 0x4b800000 */
29 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
30L1 = 6.0000002384e-01, /* 0x3f19999a */
31L2 = 4.2857143283e-01, /* 0x3edb6db7 */
32L3 = 3.3333334327e-01, /* 0x3eaaaaab */
33L4 = 2.7272811532e-01, /* 0x3e8ba305 */
34L5 = 2.3066075146e-01, /* 0x3e6c3255 */
35L6 = 2.0697501302e-01, /* 0x3e53f142 */
36P1 = 1.6666667163e-01, /* 0x3e2aaaab */
37P2 = -2.7777778450e-03, /* 0xbb360b61 */
38P3 = 6.6137559770e-05, /* 0x388ab355 */
39P4 = -1.6533901999e-06, /* 0xb5ddea0e */
40P5 = 4.1381369442e-08, /* 0x3331bb4c */
41lg2 = 6.9314718246e-01, /* 0x3f317218 */
42lg2_h = 6.93145752e-01, /* 0x3f317200 */
43lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
44ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
45cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
46cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
47cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
48ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
49ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
50ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
51
52float
53__ieee754_powf(float x, float y)
54{
55 float z,ax,z_h,z_l,p_h,p_l;
56 float y1,t1,t2,r,s,t,u,v,w;
57 int32_t i,j,k,yisint,n;
58 int32_t hx,hy,ix,iy,is;
59
60 GET_FLOAT_WORD(hx,x);
61 GET_FLOAT_WORD(hy,y);
62 ix = hx&0x7fffffff; iy = hy&0x7fffffff;
63
64 /* y==zero: x**0 = 1 */
65 if(iy==0) return one;
66
67 /* x==+-1 */
68 if(x == 1.0) return one;
69 if(x == -1.0 && isinf(y)) return one;
70
71 /* +-NaN return x+y */
72 if(__builtin_expect(ix > 0x7f800000 ||
73 iy > 0x7f800000, 0))
74 return x+y;
75
76 /* determine if y is an odd int when x < 0
77 * yisint = 0 ... y is not an integer
78 * yisint = 1 ... y is an odd int
79 * yisint = 2 ... y is an even int
80 */
81 yisint = 0;
82 if(hx<0) {
83 if(iy>=0x4b800000) yisint = 2; /* even integer y */
84 else if(iy>=0x3f800000) {
85 k = (iy>>23)-0x7f; /* exponent */
86 j = iy>>(23-k);
87 if((j<<(23-k))==iy) yisint = 2-(j&1);
88 }
89 }
90
91 /* special value of y */
92 if (__builtin_expect(iy==0x7f800000, 0)) { /* y is +-inf */
93 if (ix==0x3f800000)
94 return y - y; /* inf**+-1 is NaN */
95 else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
96 return (hy>=0)? y: zero;
97 else /* (|x|<1)**-,+inf = inf,0 */
98 return (hy<0)?-y: zero;
99 }
100 if(iy==0x3f800000) { /* y is +-1 */
101 if(hy<0) return one/x; else return x;
102 }
103 if(hy==0x40000000) return x*x; /* y is 2 */
104 if(hy==0x3f000000) { /* y is 0.5 */
105 if(__builtin_expect(hx>=0, 1)) /* x >= +0 */
106 return __ieee754_sqrtf(x);
107 }
108
109 ax = fabsf(x);
110 /* special value of x */
111 if(__builtin_expect(ix==0x7f800000||ix==0||ix==0x3f800000, 0)){
112 z = ax; /*x is +-0,+-inf,+-1*/
113 if(hy<0) z = one/z; /* z = (1/|x|) */
114 if(hx<0) {
115 if(((ix-0x3f800000)|yisint)==0) {
116 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
117 } else if(yisint==1)
118 z = -z; /* (x<0)**odd = -(|x|**odd) */
119 }
120 return z;
121 }
122
123 /* (x<0)**(non-int) is NaN */
124 if(__builtin_expect(((((u_int32_t)hx>>31)-1)|yisint)==0, 0))
125 return (x-x)/(x-x);
126
127 /* |y| is huge */
128 if(__builtin_expect(iy>0x4d000000, 0)) { /* if |y| > 2**27 */
129 /* over/underflow if x is not close to one */
130 if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
131 if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
132 /* now |1-x| is tiny <= 2**-20, suffice to compute
133 log(x) by x-x^2/2+x^3/3-x^4/4 */
134 t = ax-1; /* t has 20 trailing zeros */
135 w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
136 u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
137 v = t*ivln2_l-w*ivln2;
138 t1 = u+v;
139 GET_FLOAT_WORD(is,t1);
140 SET_FLOAT_WORD(t1,is&0xfffff000);
141 t2 = v-(t1-u);
142 } else {
143 float s2,s_h,s_l,t_h,t_l;
144 /* Avoid internal underflow for tiny y. The exact value
145 of y does not matter if |y| <= 2**-32. */
146 if (iy < 0x2f800000)
147 SET_FLOAT_WORD (y, (hy & 0x80000000) | 0x2f800000);
148 n = 0;
149 /* take care subnormal number */
150 if(ix<0x00800000)
151 {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
152 n += ((ix)>>23)-0x7f;
153 j = ix&0x007fffff;
154 /* determine interval */
155 ix = j|0x3f800000; /* normalize ix */
156 if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
157 else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
158 else {k=0;n+=1;ix -= 0x00800000;}
159 SET_FLOAT_WORD(ax,ix);
160
161 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
162 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
163 v = one/(ax+bp[k]);
164 s = u*v;
165 s_h = s;
166 GET_FLOAT_WORD(is,s_h);
167 SET_FLOAT_WORD(s_h,is&0xfffff000);
168 /* t_h=ax+bp[k] High */
169 SET_FLOAT_WORD (t_h,
170 ((((ix>>1)|0x20000000)+0x00400000+(k<<21))
171 & 0xfffff000));
172 t_l = ax - (t_h-bp[k]);
173 s_l = v*((u-s_h*t_h)-s_h*t_l);
174 /* compute log(ax) */
175 s2 = s*s;
176 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
177 r += s_l*(s_h+s);
178 s2 = s_h*s_h;
179 t_h = (float)3.0+s2+r;
180 GET_FLOAT_WORD(is,t_h);
181 SET_FLOAT_WORD(t_h,is&0xfffff000);
182 t_l = r-((t_h-(float)3.0)-s2);
183 /* u+v = s*(1+...) */
184 u = s_h*t_h;
185 v = s_l*t_h+t_l*s;
186 /* 2/(3log2)*(s+...) */
187 p_h = u+v;
188 GET_FLOAT_WORD(is,p_h);
189 SET_FLOAT_WORD(p_h,is&0xfffff000);
190 p_l = v-(p_h-u);
191 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
192 z_l = cp_l*p_h+p_l*cp+dp_l[k];
193 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
194 t = (float)n;
195 t1 = (((z_h+z_l)+dp_h[k])+t);
196 GET_FLOAT_WORD(is,t1);
197 SET_FLOAT_WORD(t1,is&0xfffff000);
198 t2 = z_l-(((t1-t)-dp_h[k])-z_h);
199 }
200
201 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
202 if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
203 s = -one; /* (-ve)**(odd int) */
204
205 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
206 GET_FLOAT_WORD(is,y);
207 SET_FLOAT_WORD(y1,is&0xfffff000);
208 p_l = (y-y1)*t1+y*t2;
209 p_h = y1*t1;
210 z = p_l+p_h;
211 GET_FLOAT_WORD(j,z);
212 if (__builtin_expect(j>0x43000000, 0)) /* if z > 128 */
213 return s*huge*huge; /* overflow */
214 else if (__builtin_expect(j==0x43000000, 0)) { /* if z == 128 */
215 if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
216 }
217 else if (__builtin_expect((j&0x7fffffff)>0x43160000, 0))/* z <= -150 */
218 return s*tiny*tiny; /* underflow */
219 else if (__builtin_expect((u_int32_t) j==0xc3160000, 0)){/* z == -150*/
220 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
221 }
222 /*
223 * compute 2**(p_h+p_l)
224 */
225 i = j&0x7fffffff;
226 k = (i>>23)-0x7f;
227 n = 0;
228 if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
229 n = j+(0x00800000>>(k+1));
230 k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
231 SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
232 n = ((n&0x007fffff)|0x00800000)>>(23-k);
233 if(j<0) n = -n;
234 p_h -= t;
235 }
236 t = p_l+p_h;
237 GET_FLOAT_WORD(is,t);
238 SET_FLOAT_WORD(t,is&0xfffff000);
239 u = t*lg2_h;
240 v = (p_l-(t-p_h))*lg2+t*lg2_l;
241 z = u+v;
242 w = v-(z-u);
243 t = z*z;
244 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
245 r = (z*t1)/(t1-two)-(w+z*w);
246 z = one-(r-z);
247 GET_FLOAT_WORD(j,z);
248 j += (n<<23);
249 if((j>>23)<=0) /* subnormal output */
250 {
251 z = __scalbnf (z, n);
252 float force_underflow = z * z;
253 math_force_eval (force_underflow);
254 }
255 else SET_FLOAT_WORD(z,j);
256 return s*z;
257}
258strong_alias (__ieee754_powf, __powf_finite)
259