1 /* e_powf.c -- float version of e_pow.c.
2 * 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 * ====================================================
17 #include "math_private.h"
21 dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
22 dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
26 two24 = 16777216.0, /* 0x4b800000 */
29 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
30 L1 = 6.0000002384e-01, /* 0x3f19999a */
31 L2 = 4.2857143283e-01, /* 0x3edb6db7 */
32 L3 = 3.3333334327e-01, /* 0x3eaaaaab */
33 L4 = 2.7272811532e-01, /* 0x3e8ba305 */
34 L5 = 2.3066075146e-01, /* 0x3e6c3255 */
35 L6 = 2.0697501302e-01, /* 0x3e53f142 */
36 P1 = 1.6666667163e-01, /* 0x3e2aaaab */
37 P2 = -2.7777778450e-03, /* 0xbb360b61 */
38 P3 = 6.6137559770e-05, /* 0x388ab355 */
39 P4 = -1.6533901999e-06, /* 0xb5ddea0e */
40 P5 = 4.1381369442e-08, /* 0x3331bb4c */
41 lg2 = 6.9314718246e-01, /* 0x3f317218 */
42 lg2_h = 6.93145752e-01, /* 0x3f317200 */
43 lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
44 ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
45 cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
46 cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
47 cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
48 ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
49 ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
50 ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
53 powf(float x, float y)
55 float z,ax,z_h,z_l,p_h,p_l;
56 float y1,t1,t2,r,s,sn,t,u,v,w;
57 int32_t i,j,k,yisint,n;
58 int32_t hx,hy,ix,iy,is;
62 ix = hx&0x7fffffff; iy = hy&0x7fffffff;
64 /* y==zero: x**0 = 1 */
67 /* +-NaN return x+y */
72 /* determine if y is an odd int when x < 0
73 * yisint = 0 ... y is not an integer
74 * yisint = 1 ... y is an odd int
75 * yisint = 2 ... y is an even int
79 if(iy>=0x4b800000) yisint = 2; /* even integer y */
80 else if(iy>=0x3f800000) {
81 k = (iy>>23)-0x7f; /* exponent */
83 if((j<<(23-k))==iy) yisint = 2-(j&1);
87 /* special value of y */
88 if (iy==0x7f800000) { /* y is +-inf */
90 return y - y; /* inf**+-1 is NaN */
91 else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
92 return (hy>=0)? y: zero;
93 else /* (|x|<1)**-,+inf = inf,0 */
94 return (hy<0)?-y: zero;
96 if(iy==0x3f800000) { /* y is +-1 */
97 if(hy<0) return one/x; else return x;
99 if(hy==0x40000000) return x*x; /* y is 2 */
100 if(hy==0x3f000000) { /* y is 0.5 */
101 if(hx>=0) /* x >= +0 */
106 /* special value of x */
107 if(ix==0x7f800000||ix==0||ix==0x3f800000){
108 z = ax; /*x is +-0,+-inf,+-1*/
109 if(hy<0) z = one/z; /* z = (1/|x|) */
111 if(((ix-0x3f800000)|yisint)==0) {
112 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
114 z = -z; /* (x<0)**odd = -(|x|**odd) */
119 n = ((uint32_t)hx>>31)-1;
121 /* (x<0)**(non-int) is NaN */
122 if((n|yisint)==0) return (x-x)/(x-x);
124 sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
125 if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */
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)? sn*huge*huge:sn*tiny*tiny;
131 if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*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;
139 GET_FLOAT_WORD(is,t1);
140 SET_FLOAT_WORD(t1,is&0xfffff000);
143 float s2,s_h,s_l,t_h,t_l;
145 /* take care subnormal number */
147 {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
148 n += ((ix)>>23)-0x7f;
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);
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 */
162 GET_FLOAT_WORD(is,s_h);
163 SET_FLOAT_WORD(s_h,is&0xfffff000);
164 /* t_h=ax+bp[k] High */
165 is = ((ix>>1)&0xfffff000)|0x20000000;
166 SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21));
167 t_l = ax - (t_h-bp[k]);
168 s_l = v*((u-s_h*t_h)-s_h*t_l);
169 /* compute log(ax) */
171 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
174 t_h = (float)3.0+s2+r;
175 GET_FLOAT_WORD(is,t_h);
176 SET_FLOAT_WORD(t_h,is&0xfffff000);
177 t_l = r-((t_h-(float)3.0)-s2);
178 /* u+v = s*(1+...) */
181 /* 2/(3log2)*(s+...) */
183 GET_FLOAT_WORD(is,p_h);
184 SET_FLOAT_WORD(p_h,is&0xfffff000);
186 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
187 z_l = cp_l*p_h+p_l*cp+dp_l[k];
188 /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
190 t1 = (((z_h+z_l)+dp_h[k])+t);
191 GET_FLOAT_WORD(is,t1);
192 SET_FLOAT_WORD(t1,is&0xfffff000);
193 t2 = z_l-(((t1-t)-dp_h[k])-z_h);
196 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
197 GET_FLOAT_WORD(is,y);
198 SET_FLOAT_WORD(y1,is&0xfffff000);
199 p_l = (y-y1)*t1+y*t2;
203 if (j>0x43000000) /* if z > 128 */
204 return sn*huge*huge; /* overflow */
205 else if (j==0x43000000) { /* if z == 128 */
206 if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
208 else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
209 return sn*tiny*tiny; /* underflow */
210 else if (j==0xc3160000){ /* z == -150 */
211 if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */
214 * compute 2**(p_h+p_l)
219 if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
220 n = j+(0x00800000>>(k+1));
221 k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
222 SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
223 n = ((n&0x007fffff)|0x00800000)>>(23-k);
228 GET_FLOAT_WORD(is,t);
229 SET_FLOAT_WORD(t,is&0xffff8000);
231 v = (p_l-(t-p_h))*lg2+t*lg2_l;
235 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
236 r = (z*t1)/(t1-two)-(w+z*w);
240 if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */
241 else SET_FLOAT_WORD(z,j);