1 /* origin: FreeBSD /usr/src/lib/msun/src/e_powf.c */
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
13 * ====================================================
20 dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
21 dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
25 two24 = 16777216.0, /* 0x4b800000 */
28 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
29 L1 = 6.0000002384e-01, /* 0x3f19999a */
30 L2 = 4.2857143283e-01, /* 0x3edb6db7 */
31 L3 = 3.3333334327e-01, /* 0x3eaaaaab */
32 L4 = 2.7272811532e-01, /* 0x3e8ba305 */
33 L5 = 2.3066075146e-01, /* 0x3e6c3255 */
34 L6 = 2.0697501302e-01, /* 0x3e53f142 */
35 P1 = 1.6666667163e-01, /* 0x3e2aaaab */
36 P2 = -2.7777778450e-03, /* 0xbb360b61 */
37 P3 = 6.6137559770e-05, /* 0x388ab355 */
38 P4 = -1.6533901999e-06, /* 0xb5ddea0e */
39 P5 = 4.1381369442e-08, /* 0x3331bb4c */
40 lg2 = 6.9314718246e-01, /* 0x3f317218 */
41 lg2_h = 6.93145752e-01, /* 0x3f317200 */
42 lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
43 ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
44 cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
45 cp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */
46 cp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */
47 ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
48 ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
49 ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
51 float powf(float x, float y)
53 float z,ax,z_h,z_l,p_h,p_l;
54 float y1,t1,t2,r,s,sn,t,u,v,w;
55 int32_t i,j,k,yisint,n;
56 int32_t hx,hy,ix,iy,is;
58 GET_FLOAT_WORD(hx, x);
59 GET_FLOAT_WORD(hy, y);
63 /* y == zero: x**0 = 1 */
67 /* x == 1: 1**y = 1, even if y is NaN */
71 /* y != zero: result is NaN if either arg is NaN */
72 if (ix > 0x7f800000 || iy > 0x7f800000)
73 return (x+0.0f) + (y+0.0f);
75 /* determine if y is an odd int when x < 0
76 * yisint = 0 ... y is not an integer
77 * yisint = 1 ... y is an odd int
78 * yisint = 2 ... y is an even int
83 yisint = 2; /* even integer y */
84 else if (iy >= 0x3f800000) {
85 k = (iy>>23) - 0x7f; /* exponent */
87 if ((j<<(23-k)) == iy)
92 /* special value of y */
93 if (iy == 0x7f800000) { /* y is +-inf */
94 if (ix == 0x3f800000) /* (-1)**+-inf is 1 */
96 else if (ix > 0x3f800000) /* (|x|>1)**+-inf = inf,0 */
97 return hy >= 0 ? y : zero;
98 else /* (|x|<1)**+-inf = 0,inf */
99 return hy < 0 ? -y : zero;
101 if (iy == 0x3f800000) { /* y is +-1 */
106 if (hy == 0x40000000) /* y is 2 */
108 if (hy == 0x3f000000) { /* y is 0.5 */
109 if (hx >= 0) /* x >= +0 */
114 /* special value of x */
115 if (ix == 0x7f800000 || ix == 0 || ix == 0x3f800000) { /* x is +-0,+-inf,+-1 */
117 if (hy < 0) /* z = (1/|x|) */
120 if (((ix-0x3f800000)|yisint) == 0) {
121 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
122 } else if (yisint == 1)
123 z = -z; /* (x<0)**odd = -(|x|**odd) */
128 n = ((uint32_t)hx>>31) - 1;
130 /* (x<0)**(non-int) is NaN */
134 sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
135 if ((n|(yisint-1)) == 0) /* (-ve)**(odd int) */
139 if (iy > 0x4d000000) { /* if |y| > 2**27 */
140 /* over/underflow if x is not close to one */
142 return hy < 0 ? sn*huge*huge : sn*tiny*tiny;
144 return hy > 0 ? sn*huge*huge : sn*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 - 1; /* t has 20 trailing zeros */
148 w = (t*t)*(0.5f - t*(0.333333333333f - t*0.25f));
149 u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
150 v = t*ivln2_l - w*ivln2;
152 GET_FLOAT_WORD(is, t1);
153 SET_FLOAT_WORD(t1, is & 0xfffff000);
156 float s2,s_h,s_l,t_h,t_l;
158 /* take care subnormal number */
159 if (ix < 0x00800000) {
162 GET_FLOAT_WORD(ix, ax);
164 n += ((ix)>>23) - 0x7f;
166 /* determine interval */
167 ix = j | 0x3f800000; /* normalize ix */
168 if (j <= 0x1cc471) /* |x|<sqrt(3/2) */
170 else if (j < 0x5db3d7) /* |x|<sqrt(3) */
177 SET_FLOAT_WORD(ax, ix);
179 /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
180 u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
184 GET_FLOAT_WORD(is, s_h);
185 SET_FLOAT_WORD(s_h, is & 0xfffff000);
186 /* t_h=ax+bp[k] High */
187 is = ((ix>>1) & 0xfffff000) | 0x20000000;
188 SET_FLOAT_WORD(t_h, is + 0x00400000 + (k<<21));
189 t_l = ax - (t_h - bp[k]);
190 s_l = v*((u - s_h*t_h) - s_h*t_l);
191 /* compute log(ax) */
193 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
197 GET_FLOAT_WORD(is, t_h);
198 SET_FLOAT_WORD(t_h, is & 0xfffff000);
199 t_l = r - ((t_h - 3.0f) - s2);
200 /* u+v = s*(1+...) */
203 /* 2/(3log2)*(s+...) */
205 GET_FLOAT_WORD(is, p_h);
206 SET_FLOAT_WORD(p_h, is & 0xfffff000);
208 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
209 z_l = cp_l*p_h + p_l*cp+dp_l[k];
210 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
212 t1 = (((z_h + z_l) + dp_h[k]) + t);
213 GET_FLOAT_WORD(is, t1);
214 SET_FLOAT_WORD(t1, is & 0xfffff000);
215 t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
218 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
219 GET_FLOAT_WORD(is, y);
220 SET_FLOAT_WORD(y1, is & 0xfffff000);
221 p_l = (y-y1)*t1 + y*t2;
224 GET_FLOAT_WORD(j, z);
225 if (j > 0x43000000) /* if z > 128 */
226 return sn*huge*huge; /* overflow */
227 else if (j == 0x43000000) { /* if z == 128 */
228 if (p_l + ovt > z - p_h)
229 return sn*huge*huge; /* overflow */
230 } else if ((j&0x7fffffff) > 0x43160000) /* z < -150 */ // FIXME: check should be (uint32_t)j > 0xc3160000
231 return sn*tiny*tiny; /* underflow */
232 else if (j == 0xc3160000) { /* z == -150 */
234 return sn*tiny*tiny; /* underflow */
237 * compute 2**(p_h+p_l)
242 if (i > 0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
243 n = j + (0x00800000>>(k+1));
244 k = ((n&0x7fffffff)>>23) - 0x7f; /* new k for n */
245 SET_FLOAT_WORD(t, n & ~(0x007fffff>>k));
246 n = ((n&0x007fffff)|0x00800000)>>(23-k);
252 GET_FLOAT_WORD(is, t);
253 SET_FLOAT_WORD(t, is & 0xffff8000);
255 v = (p_l-(t-p_h))*lg2 + t*lg2_l;
259 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
260 r = (z*t1)/(t1-two) - (w+z*w);
262 GET_FLOAT_WORD(j, z);
264 if ((j>>23) <= 0) /* subnormal output */
267 SET_FLOAT_WORD(z, j);