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[/] [openrisc/] [trunk/] [gnu-stable/] [newlib-1.18.0/] [newlib/] [libm/] [math/] [ef_pow.c] - Blame information for rev 862

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Line No. Rev Author Line
1 207 jeremybenn
/* 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
/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
15
 
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#include "fdlibm.h"
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#ifdef __v810__
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#define const 
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#endif
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#ifdef __STDC__
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static const float
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#else
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static float
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#endif
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bp[] = {1.0, 1.5,},
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dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
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dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
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zero    =  0.0,
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one     =  1.0,
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two     =  2.0,
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two24   =  16777216.0,  /* 0x4b800000 */
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huge    =  1.0e30,
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tiny    =  1.0e-30,
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        /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
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L1  =  6.0000002384e-01, /* 0x3f19999a */
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L2  =  4.2857143283e-01, /* 0x3edb6db7 */
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L3  =  3.3333334327e-01, /* 0x3eaaaaab */
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L4  =  2.7272811532e-01, /* 0x3e8ba305 */
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L5  =  2.3066075146e-01, /* 0x3e6c3255 */
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L6  =  2.0697501302e-01, /* 0x3e53f142 */
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P1   =  1.6666667163e-01, /* 0x3e2aaaab */
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P2   = -2.7777778450e-03, /* 0xbb360b61 */
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P3   =  6.6137559770e-05, /* 0x388ab355 */
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P4   = -1.6533901999e-06, /* 0xb5ddea0e */
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P5   =  4.1381369442e-08, /* 0x3331bb4c */
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lg2  =  6.9314718246e-01, /* 0x3f317218 */
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lg2_h  =  6.93145752e-01, /* 0x3f317200 */
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lg2_l  =  1.42860654e-06, /* 0x35bfbe8c */
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ovt =  4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
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cp    =  9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
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cp_h  =  9.6179199219e-01, /* 0x3f763800 =head of cp */
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cp_l  =  4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
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ivln2    =  1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
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ivln2_h  =  1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
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ivln2_l  =  7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
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#ifdef __STDC__
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        float __ieee754_powf(float x, float y)
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#else
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        float __ieee754_powf(x,y)
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        float x, y;
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#endif
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{
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        float z,ax,z_h,z_l,p_h,p_l;
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        float y1,t1,t2,r,s,t,u,v,w;
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        __int32_t i,j,k,yisint,n;
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        __int32_t hx,hy,ix,iy,is;
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        GET_FLOAT_WORD(hx,x);
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        GET_FLOAT_WORD(hy,y);
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        ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
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    /* y==zero: x**0 = 1 */
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        if(FLT_UWORD_IS_ZERO(iy)) return one;
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    /* x|y==NaN return NaN unless x==1 then return 1 */
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        if(FLT_UWORD_IS_NAN(ix) ||
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           FLT_UWORD_IS_NAN(iy))
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            if(ix==0x3f800000) return one;
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            else return nanf("");
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    /* determine if y is an odd int when x < 0
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     * yisint = 0       ... y is not an integer
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     * yisint = 1       ... y is an odd int
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     * yisint = 2       ... y is an even int
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     */
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        yisint  = 0;
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        if(hx<0) {
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            if(iy>=0x4b800000) yisint = 2; /* even integer y */
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            else if(iy>=0x3f800000) {
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                k = (iy>>23)-0x7f;         /* exponent */
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                j = iy>>(23-k);
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                if((j<<(23-k))==iy) yisint = 2-(j&1);
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            }
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        }
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    /* special value of y */
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        if (FLT_UWORD_IS_INFINITE(iy)) {        /* y is +-inf */
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            if (ix==0x3f800000)
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                return one;             /* +-1**+-inf = 1 */
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            else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
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                return (hy>=0)? y: zero;
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            else                        /* (|x|<1)**-,+inf = inf,0 */
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                return (hy<0)?-y: zero;
107
        }
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        if(iy==0x3f800000) {    /* y is  +-1 */
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            if(hy<0) return one/x; else return x;
110
        }
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        if(hy==0x40000000) return x*x; /* y is  2 */
112
        if(hy==0x3f000000) {    /* y is  0.5 */
113
            if(hx>=0)    /* x >= +0 */
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            return __ieee754_sqrtf(x);
115
        }
116
 
117
        ax   = fabsf(x);
118
    /* special value of x */
119
        if(FLT_UWORD_IS_INFINITE(ix)||FLT_UWORD_IS_ZERO(ix)||ix==0x3f800000){
120
            z = ax;                     /*x is +-0,+-inf,+-1*/
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            if(hy<0) z = one/z;  /* z = (1/|x|) */
122
            if(hx<0) {
123
                if(((ix-0x3f800000)|yisint)==0) {
124
                    z = (z-z)/(z-z); /* (-1)**non-int is NaN */
125
                } else if(yisint==1)
126
                    z = -z;             /* (x<0)**odd = -(|x|**odd) */
127
            }
128
            return z;
129
        }
130
 
131
    /* (x<0)**(non-int) is NaN */
132
        if(((((__uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
133
 
134
    /* |y| is huge */
135
        if(iy>0x4d000000) { /* if |y| > 2**27 */
136
        /* over/underflow if x is not close to one */
137
            if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
138
            if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
139
        /* now |1-x| is tiny <= 2**-20, suffice to compute
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           log(x) by x-x^2/2+x^3/3-x^4/4 */
141
            t = ax-1;           /* t has 20 trailing zeros */
142
            w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
143
            u = ivln2_h*t;      /* ivln2_h has 16 sig. bits */
144
            v = t*ivln2_l-w*ivln2;
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            t1 = u+v;
146
            GET_FLOAT_WORD(is,t1);
147
            SET_FLOAT_WORD(t1,is&0xfffff000);
148
            t2 = v-(t1-u);
149
        } else {
150
            float s2,s_h,s_l,t_h,t_l;
151
            n = 0;
152
        /* take care subnormal number */
153
            if(FLT_UWORD_IS_SUBNORMAL(ix))
154
                {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
155
            n  += ((ix)>>23)-0x7f;
156
            j  = ix&0x007fffff;
157
        /* determine interval */
158
            ix = j|0x3f800000;          /* normalize ix */
159
            if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
160
            else if(j<0x5db3d7) k=1;    /* |x|<sqrt(3)   */
161
            else {k=0;n+=1;ix -= 0x00800000;}
162
            SET_FLOAT_WORD(ax,ix);
163
 
164
        /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
165
            u = ax-bp[k];               /* bp[0]=1.0, bp[1]=1.5 */
166
            v = one/(ax+bp[k]);
167
            s = u*v;
168
            s_h = s;
169
            GET_FLOAT_WORD(is,s_h);
170
            SET_FLOAT_WORD(s_h,is&0xfffff000);
171
        /* t_h=ax+bp[k] High */
172
            SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
173
            t_l = ax - (t_h-bp[k]);
174
            s_l = v*((u-s_h*t_h)-s_h*t_l);
175
        /* compute log(ax) */
176
            s2 = s*s;
177
            r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
178
            r += s_l*(s_h+s);
179
            s2  = s_h*s_h;
180
            t_h = (float)3.0+s2+r;
181
            GET_FLOAT_WORD(is,t_h);
182
            SET_FLOAT_WORD(t_h,is&0xfffff000);
183
            t_l = r-((t_h-(float)3.0)-s2);
184
        /* u+v = s*(1+...) */
185
            u = s_h*t_h;
186
            v = s_l*t_h+t_l*s;
187
        /* 2/(3log2)*(s+...) */
188
            p_h = u+v;
189
            GET_FLOAT_WORD(is,p_h);
190
            SET_FLOAT_WORD(p_h,is&0xfffff000);
191
            p_l = v-(p_h-u);
192
            z_h = cp_h*p_h;             /* cp_h+cp_l = 2/(3*log2) */
193
            z_l = cp_l*p_h+p_l*cp+dp_l[k];
194
        /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
195
            t = (float)n;
196
            t1 = (((z_h+z_l)+dp_h[k])+t);
197
            GET_FLOAT_WORD(is,t1);
198
            SET_FLOAT_WORD(t1,is&0xfffff000);
199
            t2 = z_l-(((t1-t)-dp_h[k])-z_h);
200
        }
201
 
202
        s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
203
        if(((((__uint32_t)hx>>31)-1)|(yisint-1))==0)
204
            s = -one;   /* (-ve)**(odd int) */
205
 
206
    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
207
        GET_FLOAT_WORD(is,y);
208
        SET_FLOAT_WORD(y1,is&0xfffff000);
209
        p_l = (y-y1)*t1+y*t2;
210
        p_h = y1*t1;
211
        z = p_l+p_h;
212
        GET_FLOAT_WORD(j,z);
213
        i = j&0x7fffffff;
214
        if (j>0) {
215
            if (i>FLT_UWORD_EXP_MAX)
216
                return s*huge*huge;                     /* overflow */
217
            else if (i==FLT_UWORD_EXP_MAX)
218
                if(p_l+ovt>z-p_h) return s*huge*huge;   /* overflow */
219
        } else {
220
            if (i>FLT_UWORD_EXP_MIN)
221
                return s*tiny*tiny;                     /* underflow */
222
            else if (i==FLT_UWORD_EXP_MIN)
223
                if(p_l<=z-p_h) return s*tiny*tiny;      /* underflow */
224
        }
225
    /*
226
     * compute 2**(p_h+p_l)
227
     */
228
        k = (i>>23)-0x7f;
229
        n = 0;
230
        if(i>0x3f000000) {              /* if |z| > 0.5, set n = [z+0.5] */
231
            n = j+(0x00800000>>(k+1));
232
            k = ((n&0x7fffffff)>>23)-0x7f;      /* new k for n */
233
            SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
234
            n = ((n&0x007fffff)|0x00800000)>>(23-k);
235
            if(j<0) n = -n;
236
            p_h -= t;
237
        }
238
        t = p_l+p_h;
239
        GET_FLOAT_WORD(is,t);
240
        SET_FLOAT_WORD(t,is&0xfffff000);
241
        u = t*lg2_h;
242
        v = (p_l-(t-p_h))*lg2+t*lg2_l;
243
        z = u+v;
244
        w = v-(z-u);
245
        t  = z*z;
246
        t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
247
        r  = (z*t1)/(t1-two)-(w+z*w);
248
        z  = one-(r-z);
249
        GET_FLOAT_WORD(j,z);
250
        j += (n<<23);
251
        if((j>>23)<=0) z = scalbnf(z,(int)n);    /* subnormal output */
252
        else SET_FLOAT_WORD(z,j);
253
        return s*z;
254
}

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