1 /* ef_pow.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 "fdlibm.h"
17 
18 #ifdef __v810__
19 #define const
20 #endif
21 
22 #ifdef __STDC__
23 static const float
24 #else
25 static float
26 #endif
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 huge	=  1.0e30,
35 tiny    =  1.0e-30,
36 	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
37 L1  =  6.0000002384e-01, /* 0x3f19999a */
38 L2  =  4.2857143283e-01, /* 0x3edb6db7 */
39 L3  =  3.3333334327e-01, /* 0x3eaaaaab */
40 L4  =  2.7272811532e-01, /* 0x3e8ba305 */
41 L5  =  2.3066075146e-01, /* 0x3e6c3255 */
42 L6  =  2.0697501302e-01, /* 0x3e53f142 */
43 P1   =  1.6666667163e-01, /* 0x3e2aaaab */
44 P2   = -2.7777778450e-03, /* 0xbb360b61 */
45 P3   =  6.6137559770e-05, /* 0x388ab355 */
46 P4   = -1.6533901999e-06, /* 0xb5ddea0e */
47 P5   =  4.1381369442e-08, /* 0x3331bb4c */
48 lg2  =  6.9314718246e-01, /* 0x3f317218 */
49 lg2_h  =  6.93145752e-01, /* 0x3f317200 */
50 lg2_l  =  1.42860654e-06, /* 0x35bfbe8c */
51 ovt =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
52 cp    =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
53 cp_h  =  9.6179199219e-01, /* 0x3f763800 =head of cp */
54 cp_l  =  4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
55 ivln2    =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
56 ivln2_h  =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
57 ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
58 
59 #ifdef __STDC__
__ieee754_powf(float x,float y)60 	float __ieee754_powf(float x, float y)
61 #else
62 	float __ieee754_powf(x,y)
63 	float x, y;
64 #endif
65 {
66 	float z,ax,z_h,z_l,p_h,p_l;
67 	float y1,t1,t2,r,s,t,u,v,w;
68 	__int32_t i,j,k,yisint,n;
69 	__int32_t hx,hy,ix,iy,is;
70 
71 	GET_FLOAT_WORD(hx,x);
72 	GET_FLOAT_WORD(hy,y);
73 	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
74 
75     /* y==zero: x**0 = 1 */
76 	if(FLT_UWORD_IS_ZERO(iy)) return one;
77 
78     /* x|y==NaN return NaN unless x==1 then return 1 */
79 	if(FLT_UWORD_IS_NAN(ix) ||
80 	   FLT_UWORD_IS_NAN(iy)) {
81 	    if(ix==0x3f800000) return one;
82 	    else return nanf("");
83 	}
84 
85     /* determine if y is an odd int when x < 0
86      * yisint = 0	... y is not an integer
87      * yisint = 1	... y is an odd int
88      * yisint = 2	... y is an even int
89      */
90 	yisint  = 0;
91 	if(hx<0) {
92 	    if(iy>=0x4b800000) yisint = 2; /* even integer y */
93 	    else if(iy>=0x3f800000) {
94 		k = (iy>>23)-0x7f;	   /* exponent */
95 		j = iy>>(23-k);
96 		if((j<<(23-k))==iy) yisint = 2-(j&1);
97 	    }
98 	}
99 
100     /* special value of y */
101 	if (FLT_UWORD_IS_INFINITE(iy)) {	/* y is +-inf */
102 	    if (ix==0x3f800000)
103 		return one;		/* +-1**+-inf = 1 */
104 	    else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
105 	        return (hy>=0)? y: zero;
106 	    else			/* (|x|<1)**-,+inf = inf,0 */
107 	        return (hy<0)?-y: zero;
108 	}
109 	if(iy==0x3f800000) {	/* y is  +-1 */
110 	    if(hy<0) return one/x; else return x;
111 	}
112 	if(hy==0x40000000) return x*x; /* y is  2 */
113 	if(hy==0x3f000000) {	/* y is  0.5 */
114 	    if(hx>=0)	/* x >= +0 */
115 	    return __ieee754_sqrtf(x);
116 	}
117 
118 	ax   = fabsf(x);
119     /* special value of x */
120 	if(FLT_UWORD_IS_INFINITE(ix)||FLT_UWORD_IS_ZERO(ix)||ix==0x3f800000){
121 	    z = ax;			/*x is +-0,+-inf,+-1*/
122 	    if(hy<0) z = one/z;	/* z = (1/|x|) */
123 	    if(hx<0) {
124 		if(((ix-0x3f800000)|yisint)==0) {
125 		    z = (z-z)/(z-z); /* (-1)**non-int is NaN */
126 		} else if(yisint==1)
127 		    z = -z;		/* (x<0)**odd = -(|x|**odd) */
128 	    }
129 	    return z;
130 	}
131 
132     /* (x<0)**(non-int) is NaN */
133 	if(((((__uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
134 
135     /* |y| is huge */
136 	if(iy>0x4d000000) { /* if |y| > 2**27 */
137 	/* over/underflow if x is not close to one */
138 	    if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
139 	    if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
140 	/* now |1-x| is tiny <= 2**-20, suffice to compute
141 	   log(x) by x-x^2/2+x^3/3-x^4/4 */
142 	    t = ax-1;		/* t has 20 trailing zeros */
143 	    w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
144 	    u = ivln2_h*t;	/* ivln2_h has 16 sig. bits */
145 	    v = t*ivln2_l-w*ivln2;
146 	    t1 = u+v;
147 	    GET_FLOAT_WORD(is,t1);
148 	    SET_FLOAT_WORD(t1,is&0xfffff000);
149 	    t2 = v-(t1-u);
150 	} else {
151 	    float s2,s_h,s_l,t_h,t_l;
152 	    n = 0;
153 	/* take care subnormal number */
154 	    if(FLT_UWORD_IS_SUBNORMAL(ix))
155 		{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
156 	    n  += ((ix)>>23)-0x7f;
157 	    j  = ix&0x007fffff;
158 	/* determine interval */
159 	    ix = j|0x3f800000;		/* normalize ix */
160 	    if(j<=0x1cc471) k=0;	/* |x|<sqrt(3/2) */
161 	    else if(j<0x5db3d7) k=1;	/* |x|<sqrt(3)   */
162 	    else {k=0;n+=1;ix -= 0x00800000;}
163 	    SET_FLOAT_WORD(ax,ix);
164 
165 	/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
166 	    u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
167 	    v = one/(ax+bp[k]);
168 	    s = u*v;
169 	    s_h = s;
170 	    GET_FLOAT_WORD(is,s_h);
171 	    SET_FLOAT_WORD(s_h,is&0xfffff000);
172 	/* t_h=ax+bp[k] High */
173 	    SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
174 	    t_l = ax - (t_h-bp[k]);
175 	    s_l = v*((u-s_h*t_h)-s_h*t_l);
176 	/* compute log(ax) */
177 	    s2 = s*s;
178 	    r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
179 	    r += s_l*(s_h+s);
180 	    s2  = s_h*s_h;
181 	    t_h = (float)3.0+s2+r;
182 	    GET_FLOAT_WORD(is,t_h);
183 	    SET_FLOAT_WORD(t_h,is&0xfffff000);
184 	    t_l = r-((t_h-(float)3.0)-s2);
185 	/* u+v = s*(1+...) */
186 	    u = s_h*t_h;
187 	    v = s_l*t_h+t_l*s;
188 	/* 2/(3log2)*(s+...) */
189 	    p_h = u+v;
190 	    GET_FLOAT_WORD(is,p_h);
191 	    SET_FLOAT_WORD(p_h,is&0xfffff000);
192 	    p_l = v-(p_h-u);
193 	    z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
194 	    z_l = cp_l*p_h+p_l*cp+dp_l[k];
195 	/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
196 	    t = (float)n;
197 	    t1 = (((z_h+z_l)+dp_h[k])+t);
198 	    GET_FLOAT_WORD(is,t1);
199 	    SET_FLOAT_WORD(t1,is&0xfffff000);
200 	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
201 	}
202 
203 	s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
204 	if(((((__uint32_t)hx>>31)-1)|(yisint-1))==0)
205 	    s = -one;	/* (-ve)**(odd int) */
206 
207     /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
208 	GET_FLOAT_WORD(is,y);
209 	SET_FLOAT_WORD(y1,is&0xfffff000);
210 	p_l = (y-y1)*t1+y*t2;
211 	p_h = y1*t1;
212 	z = p_l+p_h;
213 	GET_FLOAT_WORD(j,z);
214 	i = j&0x7fffffff;
215 	if (j>0) {
216 	    if (i>FLT_UWORD_EXP_MAX)
217 	        return s*huge*huge;			/* overflow */
218 	    else if (i==FLT_UWORD_EXP_MAX)
219 	        if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
220         } else {
221 	    if (i>FLT_UWORD_EXP_MIN)
222 	        return s*tiny*tiny;			/* underflow */
223 	    else if (i==FLT_UWORD_EXP_MIN)
224 	        if(p_l<=z-p_h) return s*tiny*tiny;	/* underflow */
225 	}
226     /*
227      * compute 2**(p_h+p_l)
228      */
229 	k = (i>>23)-0x7f;
230 	n = 0;
231 	if(i>0x3f000000) {		/* if |z| > 0.5, set n = [z+0.5] */
232 	    n = j+(0x00800000>>(k+1));
233 	    k = ((n&0x7fffffff)>>23)-0x7f;	/* new k for n */
234 	    SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
235 	    n = ((n&0x007fffff)|0x00800000)>>(23-k);
236 	    if(j<0) n = -n;
237 	    p_h -= t;
238 	}
239 	t = p_l+p_h;
240 	GET_FLOAT_WORD(is,t);
241 	SET_FLOAT_WORD(t,is&0xfffff000);
242 	u = t*lg2_h;
243 	v = (p_l-(t-p_h))*lg2+t*lg2_l;
244 	z = u+v;
245 	w = v-(z-u);
246 	t  = z*z;
247 	t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
248 	r  = (z*t1)/(t1-two)-(w+z*w);
249 	z  = one-(r-z);
250 	GET_FLOAT_WORD(j,z);
251 	j += (n<<23);
252 	if((j>>23)<=0) z = scalbnf(z,(int)n);	/* subnormal output */
253 	else SET_FLOAT_WORD(z,j);
254 	return s*z;
255 }
256