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Expand PMF_FN_* macros.
[netbsd-mini2440.git] / lib / libm / src / e_powf.c
blobb702f111efd6737b7024b3ef292a78e40ebcdf7c
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 <sys/cdefs.h>
17 #if defined(LIBM_SCCS) && !defined(lint)
18 __RCSID("$NetBSD: e_powf.c,v 1.13 2008/04/25 22:21:53 christos Exp $");
19 #endif
20
21 #include "math.h"
22 #include "math_private.h"
23
24 static const float huge = 1.0e+30, tiny = 1.0e-30;
25
26 static const float
27 bp[] = {1.0, 1.5,},
28 dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
29 dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
30 zero = 0.0,
31 one = 1.0,
32 two = 2.0,
33 two24 = 16777216.0, /* 0x4b800000 */
34 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
35 L1 = 6.0000002384e-01, /* 0x3f19999a */
36 L2 = 4.2857143283e-01, /* 0x3edb6db7 */
37 L3 = 3.3333334327e-01, /* 0x3eaaaaab */
38 L4 = 2.7272811532e-01, /* 0x3e8ba305 */
39 L5 = 2.3066075146e-01, /* 0x3e6c3255 */
40 L6 = 2.0697501302e-01, /* 0x3e53f142 */
41 P1 = 1.6666667163e-01, /* 0x3e2aaaab */
42 P2 = -2.7777778450e-03, /* 0xbb360b61 */
43 P3 = 6.6137559770e-05, /* 0x388ab355 */
44 P4 = -1.6533901999e-06, /* 0xb5ddea0e */
45 P5 = 4.1381369442e-08, /* 0x3331bb4c */
46 lg2 = 6.9314718246e-01, /* 0x3f317218 */
47 lg2_h = 6.93145752e-01, /* 0x3f317200 */
48 lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
49 ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
50 cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
51 cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
52 cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
53 ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
54 ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
55 ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
56
57 float
58 __ieee754_powf(float x, float y)
59 {
60 float z,ax,z_h,z_l,p_h,p_l;
61 float yy1,t1,t2,r,s,t,u,v,w;
62 int32_t i,j,k,yisint,n;
63 int32_t hx,hy,ix,iy,is;
64
65 GET_FLOAT_WORD(hx,x);
66 GET_FLOAT_WORD(hy,y);
67 ix = hx&0x7fffffff; iy = hy&0x7fffffff;
68
69 /* y==zero: x**0 = 1 */
70 if(iy==0) return one;
71
72 /* +-NaN return x+y */
73 if(ix > 0x7f800000 ||
74 iy > 0x7f800000)
75 return x+y;
76
77 /* determine if y is an odd int when x < 0
78 * yisint = 0 ... y is not an integer
79 * yisint = 1 ... y is an odd int
80 * yisint = 2 ... y is an even int
81 */
82 yisint = 0;
83 if(hx<0) {
84 if(iy>=0x4b800000) yisint = 2; /* even integer y */
85 else if(iy>=0x3f800000) {
86 k = (iy>>23)-0x7f; /* exponent */
87 j = iy>>(23-k);
88 if((j<<(23-k))==iy) yisint = 2-(j&1);
89 }
90 }
91
92 /* special value of y */
93 if (iy==0x7f800000) { /* y is +-inf */
94 if (ix==0x3f800000)
95 return y - y; /* inf**+-1 is NaN */
96 else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
97 return (hy>=0)? y: zero;
98 else /* (|x|<1)**-,+inf = inf,0 */
99 return (hy<0)?-y: zero;
100 }
101 if(iy==0x3f800000) { /* y is +-1 */
102 if(hy<0) return one/x; else return x;
103 }
104 if(hy==0x40000000) return x*x; /* y is 2 */
105 if(hy==0x3f000000) { /* y is 0.5 */
106 if(hx>=0) /* x >= +0 */
107 return __ieee754_sqrtf(x);
108 }
109
110 ax = fabsf(x);
111 /* special value of x */
112 if(ix==0x7f800000||ix==0||ix==0x3f800000){
113 z = ax; /*x is +-0,+-inf,+-1*/
114 if(hy<0) z = one/z; /* z = (1/|x|) */
115 if(hx<0) {
116 if(((ix-0x3f800000)|yisint)==0) {
117 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
118 } else if(yisint==1)
119 z = -z; /* (x<0)**odd = -(|x|**odd) */
120 }
121 return z;
122 }
123
124 /* (x<0)**(non-int) is NaN */
125 if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
126
127 /* |y| is huge */
128 if(iy>0x4d000000) { /* 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-one; /* 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 n = 0;
145 /* take care subnormal number */
146 if(ix<0x00800000)
147 {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
148 n += ((ix)>>23)-0x7f;
149 j = ix&0x007fffff;
150 /* determine interval */
151 ix = j|0x3f800000; /* normalize ix */
152 if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
153 else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
154 else {k=0;n+=1;ix -= 0x00800000;}
155 SET_FLOAT_WORD(ax,ix);
156
157 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
158 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
159 v = one/(ax+bp[k]);
160 s = u*v;
161 s_h = s;
162 GET_FLOAT_WORD(is,s_h);
163 SET_FLOAT_WORD(s_h,is&0xfffff000);
164 /* t_h=ax+bp[k] High */
165 SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
166 t_l = ax - (t_h-bp[k]);
167 s_l = v*((u-s_h*t_h)-s_h*t_l);
168 /* compute log(ax) */
169 s2 = s*s;
170 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
171 r += s_l*(s_h+s);
172 s2 = s_h*s_h;
173 t_h = (float)3.0+s2+r;
174 GET_FLOAT_WORD(is,t_h);
175 SET_FLOAT_WORD(t_h,is&0xfffff000);
176 t_l = r-((t_h-(float)3.0)-s2);
177 /* u+v = s*(1+...) */
178 u = s_h*t_h;
179 v = s_l*t_h+t_l*s;
180 /* 2/(3log2)*(s+...) */
181 p_h = u+v;
182 GET_FLOAT_WORD(is,p_h);
183 SET_FLOAT_WORD(p_h,is&0xfffff000);
184 p_l = v-(p_h-u);
185 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
186 z_l = cp_l*p_h+p_l*cp+dp_l[k];
187 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
188 t = (float)n;
189 t1 = (((z_h+z_l)+dp_h[k])+t);
190 GET_FLOAT_WORD(is,t1);
191 SET_FLOAT_WORD(t1,is&0xfffff000);
192 t2 = z_l-(((t1-t)-dp_h[k])-z_h);
193 }
194
195 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
196 if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
197 s = -one; /* (-ve)**(odd int) */
198
199 /* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */
200 GET_FLOAT_WORD(is,y);
201 SET_FLOAT_WORD(yy1,is&0xfffff000);
202 p_l = (y-yy1)*t1+y*t2;
203 p_h = yy1*t1;
204 z = p_l+p_h;
205 GET_FLOAT_WORD(j,z);
206 if (j>0x43000000) /* if z > 128 */
207 return s*huge*huge; /* overflow */
208 else if (j==0x43000000) { /* if z == 128 */
209 if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
210 }
211 else if ((uint32_t)j==0xc3160000){ /* z == -150 */
212 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
213 }
214 else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
215 return s*tiny*tiny; /* underflow */
216 /*
217 * compute 2**(p_h+p_l)
218 */
219 i = j&0x7fffffff;
220 k = (i>>23)-0x7f;
221 n = 0;
222 if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
223 n = j+(0x00800000>>(k+1));
224 k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
225 SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
226 n = ((n&0x007fffff)|0x00800000)>>(23-k);
227 if(j<0) n = -n;
228 p_h -= t;
229 }
230 t = p_l+p_h;
231 GET_FLOAT_WORD(is,t);
232 SET_FLOAT_WORD(t,is&0xfffff000);
233 u = t*lg2_h;
234 v = (p_l-(t-p_h))*lg2+t*lg2_l;
235 z = u+v;
236 w = v-(z-u);
237 t = z*z;
238 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
239 r = (z*t1)/(t1-two)-(w+z*w);
240 z = one-(r-z);
241 GET_FLOAT_WORD(j,z);
242 j += (n<<23);
243 if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */
244 else SET_FLOAT_WORD(z,j);
245 return s*z;
246 }
NetBSD on the FriendlyARM MINI2440