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#if defined(LIBM_SCCS) && !defined(lint)
17static char rcsid[] = "$NetBSD: e_powf.c,v 1.7 1996/04/08 15:43:44 phil Exp $";
18#endif
19
20#include "math.h"
21#include "math_private.h"
22
23static const float huge = 1.0e+30, tiny = 1.0e-30;
24
25#ifdef __STDC__
26static const float
27#else
28static float
29#endif
30bp[] = {1.0, 1.5,},
31dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
32dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
33zero    =  0.0,
34one	=  1.0,
35two	=  2.0,
36two24	=  16777216.0,	/* 0x4b800000 */
37	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
38L1  =  6.0000002384e-01, /* 0x3f19999a */
39L2  =  4.2857143283e-01, /* 0x3edb6db7 */
40L3  =  3.3333334327e-01, /* 0x3eaaaaab */
41L4  =  2.7272811532e-01, /* 0x3e8ba305 */
42L5  =  2.3066075146e-01, /* 0x3e6c3255 */
43L6  =  2.0697501302e-01, /* 0x3e53f142 */
44P1   =  1.6666667163e-01, /* 0x3e2aaaab */
45P2   = -2.7777778450e-03, /* 0xbb360b61 */
46P3   =  6.6137559770e-05, /* 0x388ab355 */
47P4   = -1.6533901999e-06, /* 0xb5ddea0e */
48P5   =  4.1381369442e-08, /* 0x3331bb4c */
49lg2  =  6.9314718246e-01, /* 0x3f317218 */
50lg2_h  =  6.93145752e-01, /* 0x3f317200 */
51lg2_l  =  1.42860654e-06, /* 0x35bfbe8c */
52ovt =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
53cp    =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
54cp_h  =  9.6179199219e-01, /* 0x3f763800 =head of cp */
55cp_l  =  4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
56ivln2    =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
57ivln2_h  =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
58ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
59
60#ifdef __STDC__
61	float __ieee754_powf(float x, float y)
62#else
63	float __ieee754_powf(x,y)
64	float x, y;
65#endif
66{
67	float z,ax,z_h,z_l,p_h,p_l;
68	float y1,t1,t2,r,s,t,u,v,w;
69	int32_t i,j,k,yisint,n;
70	int32_t hx,hy,ix,iy,is;
71
72	GET_FLOAT_WORD(hx,x);
73	GET_FLOAT_WORD(hy,y);
74	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
75
76    /* y==zero: x**0 = 1 */
77	if(iy==0) return one;
78
79    /* x==+-1 */
80	if(x == 1.0) return one;
81	if(x == -1.0 && isinf(y)) return one;
82
83    /* +-NaN return x+y */
84	if(ix > 0x7f800000 ||
85	   iy > 0x7f800000)
86		return x+y;
87
88    /* determine if y is an odd int when x < 0
89     * yisint = 0	... y is not an integer
90     * yisint = 1	... y is an odd int
91     * yisint = 2	... y is an even int
92     */
93	yisint  = 0;
94	if(hx<0) {
95	    if(iy>=0x4b800000) yisint = 2; /* even integer y */
96	    else if(iy>=0x3f800000) {
97		k = (iy>>23)-0x7f;	   /* exponent */
98		j = iy>>(23-k);
99		if((j<<(23-k))==iy) yisint = 2-(j&1);
100	    }
101	}
102
103    /* special value of y */
104	if (iy==0x7f800000) {	/* y is +-inf */
105	    if (ix==0x3f800000)
106	        return  y - y;	/* inf**+-1 is NaN */
107	    else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
108	        return (hy>=0)? y: zero;
109	    else			/* (|x|<1)**-,+inf = inf,0 */
110	        return (hy<0)?-y: zero;
111	}
112	if(iy==0x3f800000) {	/* y is  +-1 */
113	    if(hy<0) return one/x; else return x;
114	}
115	if(hy==0x40000000) return x*x; /* y is  2 */
116	if(hy==0x3f000000) {	/* y is  0.5 */
117	    if(hx>=0)	/* x >= +0 */
118	    return __ieee754_sqrtf(x);
119	}
120
121	ax   = fabsf(x);
122    /* special value of x */
123	if(ix==0x7f800000||ix==0||ix==0x3f800000){
124	    z = ax;			/*x is +-0,+-inf,+-1*/
125	    if(hy<0) z = one/z;	/* z = (1/|x|) */
126	    if(hx<0) {
127		if(((ix-0x3f800000)|yisint)==0) {
128		    z = (z-z)/(z-z); /* (-1)**non-int is NaN */
129		} else if(yisint==1)
130		    z = -z;		/* (x<0)**odd = -(|x|**odd) */
131	    }
132	    return z;
133	}
134
135    /* (x<0)**(non-int) is NaN */
136	if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
137
138    /* |y| is huge */
139	if(iy>0x4d000000) { /* if |y| > 2**27 */
140	/* over/underflow if x is not close to one */
141	    if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
142	    if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
143	/* now |1-x| is tiny <= 2**-20, suffice to compute
144	   log(x) by x-x^2/2+x^3/3-x^4/4 */
145	    t = x-1;		/* t has 20 trailing zeros */
146	    w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
147	    u = ivln2_h*t;	/* ivln2_h has 16 sig. bits */
148	    v = t*ivln2_l-w*ivln2;
149	    t1 = u+v;
150	    GET_FLOAT_WORD(is,t1);
151	    SET_FLOAT_WORD(t1,is&0xfffff000);
152	    t2 = v-(t1-u);
153	} else {
154	    float s2,s_h,s_l,t_h,t_l;
155	    n = 0;
156	/* take care subnormal number */
157	    if(ix<0x00800000)
158		{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
159	    n  += ((ix)>>23)-0x7f;
160	    j  = ix&0x007fffff;
161	/* determine interval */
162	    ix = j|0x3f800000;		/* normalize ix */
163	    if(j<=0x1cc471) k=0;	/* |x|<sqrt(3/2) */
164	    else if(j<0x5db3d7) k=1;	/* |x|<sqrt(3)   */
165	    else {k=0;n+=1;ix -= 0x00800000;}
166	    SET_FLOAT_WORD(ax,ix);
167
168	/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
169	    u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
170	    v = one/(ax+bp[k]);
171	    s = u*v;
172	    s_h = s;
173	    GET_FLOAT_WORD(is,s_h);
174	    SET_FLOAT_WORD(s_h,is&0xfffff000);
175	/* t_h=ax+bp[k] High */
176	    SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
177	    t_l = ax - (t_h-bp[k]);
178	    s_l = v*((u-s_h*t_h)-s_h*t_l);
179	/* compute log(ax) */
180	    s2 = s*s;
181	    r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
182	    r += s_l*(s_h+s);
183	    s2  = s_h*s_h;
184	    t_h = (float)3.0+s2+r;
185	    GET_FLOAT_WORD(is,t_h);
186	    SET_FLOAT_WORD(t_h,is&0xfffff000);
187	    t_l = r-((t_h-(float)3.0)-s2);
188	/* u+v = s*(1+...) */
189	    u = s_h*t_h;
190	    v = s_l*t_h+t_l*s;
191	/* 2/(3log2)*(s+...) */
192	    p_h = u+v;
193	    GET_FLOAT_WORD(is,p_h);
194	    SET_FLOAT_WORD(p_h,is&0xfffff000);
195	    p_l = v-(p_h-u);
196	    z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
197	    z_l = cp_l*p_h+p_l*cp+dp_l[k];
198	/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
199	    t = (float)n;
200	    t1 = (((z_h+z_l)+dp_h[k])+t);
201	    GET_FLOAT_WORD(is,t1);
202	    SET_FLOAT_WORD(t1,is&0xfffff000);
203	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
204	}
205
206	s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
207	if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
208	    s = -one;	/* (-ve)**(odd int) */
209
210    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
211	GET_FLOAT_WORD(is,y);
212	SET_FLOAT_WORD(y1,is&0xfffff000);
213	p_l = (y-y1)*t1+y*t2;
214	p_h = y1*t1;
215	z = p_l+p_h;
216	GET_FLOAT_WORD(j,z);
217	if (j>0x43000000)				/* if z > 128 */
218	    return s*huge*huge;				/* overflow */
219	else if (j==0x43000000) {			/* if z == 128 */
220	    if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
221	}
222	else if ((j&0x7fffffff)>0x43160000)		/* z <= -150 */
223	    return s*tiny*tiny;				/* underflow */
224	else if ((u_int32_t) j==0xc3160000){		/* z == -150 */
225	    if(p_l<=z-p_h) return s*tiny*tiny;		/* underflow */
226	}
227    /*
228     * compute 2**(p_h+p_l)
229     */
230	i = j&0x7fffffff;
231	k = (i>>23)-0x7f;
232	n = 0;
233	if(i>0x3f000000) {		/* if |z| > 0.5, set n = [z+0.5] */
234	    n = j+(0x00800000>>(k+1));
235	    k = ((n&0x7fffffff)>>23)-0x7f;	/* new k for n */
236	    SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
237	    n = ((n&0x007fffff)|0x00800000)>>(23-k);
238	    if(j<0) n = -n;
239	    p_h -= t;
240	}
241	t = p_l+p_h;
242	GET_FLOAT_WORD(is,t);
243	SET_FLOAT_WORD(t,is&0xfffff000);
244	u = t*lg2_h;
245	v = (p_l-(t-p_h))*lg2+t*lg2_l;
246	z = u+v;
247	w = v-(z-u);
248	t  = z*z;
249	t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
250	r  = (z*t1)/(t1-two)-(w+z*w);
251	z  = one-(r-z);
252	GET_FLOAT_WORD(j,z);
253	j += (n<<23);
254	if((j>>23)<=0) z = __scalbnf(z,n);	/* subnormal output */
255	else SET_FLOAT_WORD(z,j);
256	return s*z;
257}
258