POK
e_powf.c
1 /*
2  * POK header
3  *
4  * The following file is a part of the POK project. Any modification should
5  * made according to the POK licence. You CANNOT use this file or a part of
6  * this file is this part of a file for your own project
7  *
8  * For more information on the POK licence, please see our LICENCE FILE
9  *
10  * Please follow the coding guidelines described in doc/CODING_GUIDELINES
11  *
12  * Copyright (c) 2007-2009 POK team
13  *
14  * Created by julien on Fri Jan 30 14:41:34 2009
15  */
16 
17 /* e_powf.c -- float version of e_pow.c.
18  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
19  */
20 
21 /*
22  * ====================================================
23  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
24  *
25  * Developed at SunPro, a Sun Microsystems, Inc. business.
26  * Permission to use, copy, modify, and distribute this
27  * software is freely granted, provided that this notice
28  * is preserved.
29  * ====================================================
30  */
31 
32 #ifdef POK_NEEDS_LIBMATH
33 
34 #include <libm.h>
35 #include "math_private.h"
36 
37 static const float huge = 1.0e+30, tiny = 1.0e-30;
38 
39 static const float
40 bp[] = {1.0, 1.5,},
41 dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
42 dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
43 zero = 0.0,
44 one = 1.0,
45 two = 2.0,
46 two24 = 16777216.0, /* 0x4b800000 */
47  /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
48 L1 = 6.0000002384e-01, /* 0x3f19999a */
49 L2 = 4.2857143283e-01, /* 0x3edb6db7 */
50 L3 = 3.3333334327e-01, /* 0x3eaaaaab */
51 L4 = 2.7272811532e-01, /* 0x3e8ba305 */
52 L5 = 2.3066075146e-01, /* 0x3e6c3255 */
53 L6 = 2.0697501302e-01, /* 0x3e53f142 */
54 P1 = 1.6666667163e-01, /* 0x3e2aaaab */
55 P2 = -2.7777778450e-03, /* 0xbb360b61 */
56 P3 = 6.6137559770e-05, /* 0x388ab355 */
57 P4 = -1.6533901999e-06, /* 0xb5ddea0e */
58 P5 = 4.1381369442e-08, /* 0x3331bb4c */
59 lg2 = 6.9314718246e-01, /* 0x3f317218 */
60 lg2_h = 6.93145752e-01, /* 0x3f317200 */
61 lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
62 ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
63 cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
64 cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
65 cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
66 ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
67 ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
68 ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
69 
70 float
71 __ieee754_powf(float x, float y)
72 {
73  float z,ax,z_h,z_l,p_h,p_l;
74  float yy1,t1,t2,r,s,t,u,v,w;
75  int32_t i,j,k,yisint,n;
76  int32_t hx,hy,ix,iy,is;
77 
78  GET_FLOAT_WORD(hx,x);
79  GET_FLOAT_WORD(hy,y);
80  ix = hx&0x7fffffff; iy = hy&0x7fffffff;
81 
82  /* y==zero: x**0 = 1 */
83  if(iy==0) return one;
84 
85  /* +-NaN return x+y */
86  if(ix > 0x7f800000 ||
87  iy > 0x7f800000)
88  return x+y;
89 
90  /* determine if y is an odd int when x < 0
91  * yisint = 0 ... y is not an integer
92  * yisint = 1 ... y is an odd int
93  * yisint = 2 ... y is an even int
94  */
95  yisint = 0;
96  if(hx<0) {
97  if(iy>=0x4b800000) yisint = 2; /* even integer y */
98  else if(iy>=0x3f800000) {
99  k = (iy>>23)-0x7f; /* exponent */
100  j = iy>>(23-k);
101  if((j<<(23-k))==iy) yisint = 2-(j&1);
102  }
103  }
104 
105  /* special value of y */
106  if (iy==0x7f800000) { /* y is +-inf */
107  if (ix==0x3f800000)
108  return y - y; /* inf**+-1 is NaN */
109  else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
110  return (hy>=0)? y: zero;
111  else /* (|x|<1)**-,+inf = inf,0 */
112  return (hy<0)?-y: zero;
113  }
114  if(iy==0x3f800000) { /* y is +-1 */
115  if(hy<0) return one/x; else return x;
116  }
117  if(hy==0x40000000) return x*x; /* y is 2 */
118  if(hy==0x3f000000) { /* y is 0.5 */
119  if(hx>=0) /* x >= +0 */
120  return __ieee754_sqrtf(x);
121  }
122 
123  ax = fabsf(x);
124  /* special value of x */
125  if(ix==0x7f800000||ix==0||ix==0x3f800000){
126  z = ax; /*x is +-0,+-inf,+-1*/
127  if(hy<0) z = one/z; /* z = (1/|x|) */
128  if(hx<0) {
129  if(((ix-0x3f800000)|yisint)==0) {
130  z = (z-z)/(z-z); /* (-1)**non-int is NaN */
131  } else if(yisint==1)
132  z = -z; /* (x<0)**odd = -(|x|**odd) */
133  }
134  return z;
135  }
136 
137  /* (x<0)**(non-int) is NaN */
138  if(((((uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
139 
140  /* |y| is huge */
141  if(iy>0x4d000000) { /* if |y| > 2**27 */
142  /* over/underflow if x is not close to one */
143  if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
144  if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
145  /* now |1-x| is tiny <= 2**-20, suffice to compute
146  log(x) by x-x^2/2+x^3/3-x^4/4 */
147  t = ax-one; /* t has 20 trailing zeros */
148  w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
149  u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
150  v = t*ivln2_l-w*ivln2;
151  t1 = u+v;
152  GET_FLOAT_WORD(is,t1);
153  SET_FLOAT_WORD(t1,is&0xfffff000);
154  t2 = v-(t1-u);
155  } else {
156  float s2,s_h,s_l,t_h,t_l;
157  n = 0;
158  /* take care subnormal number */
159  if(ix<0x00800000)
160  {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
161  n += ((ix)>>23)-0x7f;
162  j = ix&0x007fffff;
163  /* determine interval */
164  ix = j|0x3f800000; /* normalize ix */
165  if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
166  else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
167  else {k=0;n+=1;ix -= 0x00800000;}
168  SET_FLOAT_WORD(ax,ix);
169 
170  /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
171  u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
172  v = one/(ax+bp[k]);
173  s = u*v;
174  s_h = s;
175  GET_FLOAT_WORD(is,s_h);
176  SET_FLOAT_WORD(s_h,is&0xfffff000);
177  /* t_h=ax+bp[k] High */
178  SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
179  t_l = ax - (t_h-bp[k]);
180  s_l = v*((u-s_h*t_h)-s_h*t_l);
181  /* compute log(ax) */
182  s2 = s*s;
183  r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
184  r += s_l*(s_h+s);
185  s2 = s_h*s_h;
186  t_h = (float)3.0+s2+r;
187  GET_FLOAT_WORD(is,t_h);
188  SET_FLOAT_WORD(t_h,is&0xfffff000);
189  t_l = r-((t_h-(float)3.0)-s2);
190  /* u+v = s*(1+...) */
191  u = s_h*t_h;
192  v = s_l*t_h+t_l*s;
193  /* 2/(3log2)*(s+...) */
194  p_h = u+v;
195  GET_FLOAT_WORD(is,p_h);
196  SET_FLOAT_WORD(p_h,is&0xfffff000);
197  p_l = v-(p_h-u);
198  z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
199  z_l = cp_l*p_h+p_l*cp+dp_l[k];
200  /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
201  t = (float)n;
202  t1 = (((z_h+z_l)+dp_h[k])+t);
203  GET_FLOAT_WORD(is,t1);
204  SET_FLOAT_WORD(t1,is&0xfffff000);
205  t2 = z_l-(((t1-t)-dp_h[k])-z_h);
206  }
207 
208  s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
209  if(((((uint32_t)hx>>31)-1)|(yisint-1))==0)
210  s = -one; /* (-ve)**(odd int) */
211 
212  /* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */
213  GET_FLOAT_WORD(is,y);
214  SET_FLOAT_WORD(yy1,is&0xfffff000);
215  p_l = (y-yy1)*t1+y*t2;
216  p_h = yy1*t1;
217  z = p_l+p_h;
218  GET_FLOAT_WORD(j,z);
219  if (j>0x43000000) /* if z > 128 */
220  return s*huge*huge; /* overflow */
221  else if (j==0x43000000) { /* if z == 128 */
222  if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
223  }
224  else if ((uint32_t)j==0xc3160000){ /* z == -150 */
225  if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
226  }
227  else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
228  return s*tiny*tiny; /* underflow */
229  /*
230  * compute 2**(p_h+p_l)
231  */
232  i = j&0x7fffffff;
233  k = (i>>23)-0x7f;
234  n = 0;
235  if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
236  n = j+(0x00800000>>(k+1));
237  k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
238  SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
239  n = ((n&0x007fffff)|0x00800000)>>(23-k);
240  if(j<0) n = -n;
241  p_h -= t;
242  }
243  t = p_l+p_h;
244  GET_FLOAT_WORD(is,t);
245  SET_FLOAT_WORD(t,is&0xfffff000);
246  u = t*lg2_h;
247  v = (p_l-(t-p_h))*lg2+t*lg2_l;
248  z = u+v;
249  w = v-(z-u);
250  t = z*z;
251  t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
252  r = (z*t1)/(t1-two)-(w+z*w);
253  z = one-(r-z);
254  GET_FLOAT_WORD(j,z);
255  j += (n<<23);
256  if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */
257  else SET_FLOAT_WORD(z,j);
258  return s*z;
259 }
260 
261 #endif