1 2 /* 3 * Copyright (c) 1998, 2004, Oracle and/or its affiliates. All rights reserved. 4 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. 5 * 6 * This code is free software; you can redistribute it and/or modify it 7 * under the terms of the GNU General Public License version 2 only, as 8 * published by the Free Software Foundation. Oracle designates this 9 * particular file as subject to the "Classpath" exception as provided 10 * by Oracle in the LICENSE file that accompanied this code. 11 * 12 * This code is distributed in the hope that it will be useful, but WITHOUT 13 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 14 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 15 * version 2 for more details (a copy is included in the LICENSE file that 16 * accompanied this code). 17 * 18 * You should have received a copy of the GNU General Public License version 19 * 2 along with this work; if not, write to the Free Software Foundation, 20 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. 21 * 22 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA 23 * or visit www.oracle.com if you need additional information or have any 24 * questions. 25 */ 26 27 /* __ieee754_pow(x,y) return x**y 28 * 29 * n 30 * Method: Let x = 2 * (1+f) 31 * 1. Compute and return log2(x) in two pieces: 32 * log2(x) = w1 + w2, 33 * where w1 has 53-24 = 29 bit trailing zeros. 34 * 2. Perform y*log2(x) = n+y' by simulating muti-precision 35 * arithmetic, where |y'|<=0.5. 36 * 3. Return x**y = 2**n*exp(y'*log2) 37 * 38 * Special cases: 39 * 1. (anything) ** 0 is 1 40 * 2. (anything) ** 1 is itself 41 * 3. (anything) ** NAN is NAN 42 * 4. NAN ** (anything except 0) is NAN 43 * 5. +-(|x| > 1) ** +INF is +INF 44 * 6. +-(|x| > 1) ** -INF is +0 45 * 7. +-(|x| < 1) ** +INF is +0 46 * 8. +-(|x| < 1) ** -INF is +INF 47 * 9. +-1 ** +-INF is NAN 51 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF 52 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) 53 * 15. +INF ** (+anything except 0,NAN) is +INF 54 * 16. +INF ** (-anything except 0,NAN) is +0 55 * 17. -INF ** (anything) = -0 ** (-anything) 56 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) 57 * 19. (-anything except 0 and inf) ** (non-integer) is NAN 58 * 59 * Accuracy: 60 * pow(x,y) returns x**y nearly rounded. In particular 61 * pow(integer,integer) 62 * always returns the correct integer provided it is 63 * representable. 64 * 65 * Constants : 66 * The hexadecimal values are the intended ones for the following 67 * constants. The decimal values may be used, provided that the 68 * compiler will convert from decimal to binary accurately enough 69 * to produce the hexadecimal values shown. 70 */ 71 72 #include "fdlibm.h" 73 74 #ifdef __STDC__ 75 static const double 76 #else 77 static double 78 #endif 79 bp[] = {1.0, 1.5,}, 80 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ 81 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ 82 zero = 0.0, 83 one = 1.0, 84 two = 2.0, 85 two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ 86 huge = 1.0e300, 87 tiny = 1.0e-300, 88 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ 89 L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ 90 L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ 91 L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ 92 L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ 93 L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ 94 L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ 95 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ 96 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ 97 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ 98 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ 99 P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ 100 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 101 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ 102 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ 103 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ 104 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ 105 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ 106 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ 107 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ 108 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ 109 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ 110 111 #ifdef __STDC__ 112 double __ieee754_pow(double x, double y) 113 #else 114 double __ieee754_pow(x,y) 115 double x, y; 116 #endif 117 { 118 double z,ax,z_h,z_l,p_h,p_l; 119 double y1,t1,t2,r,s,t,u,v,w; 120 int i0,i1,i,j,k,yisint,n; 121 int hx,hy,ix,iy; 122 unsigned lx,ly; 123 124 i0 = ((*(int*)&one)>>29)^1; i1=1-i0; 125 hx = __HI(x); lx = __LO(x); 126 hy = __HI(y); ly = __LO(y); 127 ix = hx&0x7fffffff; iy = hy&0x7fffffff; 128 129 /* y==zero: x**0 = 1 */ 130 if((iy|ly)==0) return one; 131 132 /* +-NaN return x+y */ 133 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || 134 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) 135 return x+y; 136 137 /* determine if y is an odd int when x < 0 138 * yisint = 0 ... y is not an integer 139 * yisint = 1 ... y is an odd int 140 * yisint = 2 ... y is an even int 141 */ 142 yisint = 0; 143 if(hx<0) { 144 if(iy>=0x43400000) yisint = 2; /* even integer y */ 145 else if(iy>=0x3ff00000) { 146 k = (iy>>20)-0x3ff; /* exponent */ 147 if(k>20) { 148 j = ly>>(52-k); 149 if((j<<(52-k))==ly) yisint = 2-(j&1); 150 } else if(ly==0) { 151 j = iy>>(20-k); 152 if((j<<(20-k))==iy) yisint = 2-(j&1); 153 } 154 } 155 } 156 157 /* special value of y */ 158 if(ly==0) { 159 if (iy==0x7ff00000) { /* y is +-inf */ 160 if(((ix-0x3ff00000)|lx)==0) 161 return y - y; /* inf**+-1 is NaN */ 162 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ 163 return (hy>=0)? y: zero; 164 else /* (|x|<1)**-,+inf = inf,0 */ 165 return (hy<0)?-y: zero; 166 } 167 if(iy==0x3ff00000) { /* y is +-1 */ 168 if(hy<0) return one/x; else return x; 169 } 170 if(hy==0x40000000) return x*x; /* y is 2 */ 171 if(hy==0x3fe00000) { /* y is 0.5 */ 172 if(hx>=0) /* x >= +0 */ 173 return sqrt(x); 174 } 175 } 176 177 ax = fabs(x); 178 /* special value of x */ 179 if(lx==0) { 180 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ 181 z = ax; /*x is +-0,+-inf,+-1*/ 182 if(hy<0) z = one/z; /* z = (1/|x|) */ 183 if(hx<0) { 184 if(((ix-0x3ff00000)|yisint)==0) { 185 z = (z-z)/(z-z); /* (-1)**non-int is NaN */ 186 } else if(yisint==1) 187 z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */ 188 } 189 return z; 190 } 191 } 192 193 n = (hx>>31)+1; 194 195 /* (x<0)**(non-int) is NaN */ 196 if((n|yisint)==0) return (x-x)/(x-x); 197 198 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ 199 if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ 200 201 /* |y| is huge */ 202 if(iy>0x41e00000) { /* if |y| > 2**31 */ 203 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ 204 if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; 205 if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; 206 } 207 /* over/underflow if x is not close to one */ 208 if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny; 209 if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny; 210 /* now |1-x| is tiny <= 2**-20, suffice to compute 211 log(x) by x-x^2/2+x^3/3-x^4/4 */ 212 t = ax-one; /* t has 20 trailing zeros */ 213 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); 214 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ 215 v = t*ivln2_l-w*ivln2; 216 t1 = u+v; 217 __LO(t1) = 0; 218 t2 = v-(t1-u); 219 } else { 220 double ss,s2,s_h,s_l,t_h,t_l; 221 n = 0; 222 /* take care subnormal number */ 223 if(ix<0x00100000) 224 {ax *= two53; n -= 53; ix = __HI(ax); } 225 n += ((ix)>>20)-0x3ff; 226 j = ix&0x000fffff; 227 /* determine interval */ 228 ix = j|0x3ff00000; /* normalize ix */ 229 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ 230 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ 231 else {k=0;n+=1;ix -= 0x00100000;} 232 __HI(ax) = ix; 233 234 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ 235 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ 236 v = one/(ax+bp[k]); 237 ss = u*v; 238 s_h = ss; 239 __LO(s_h) = 0; 240 /* t_h=ax+bp[k] High */ 241 t_h = zero; 242 __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18); 243 t_l = ax - (t_h-bp[k]); 244 s_l = v*((u-s_h*t_h)-s_h*t_l); 245 /* compute log(ax) */ 246 s2 = ss*ss; 247 r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); 248 r += s_l*(s_h+ss); 249 s2 = s_h*s_h; 250 t_h = 3.0+s2+r; 251 __LO(t_h) = 0; 252 t_l = r-((t_h-3.0)-s2); 253 /* u+v = ss*(1+...) */ 254 u = s_h*t_h; 255 v = s_l*t_h+t_l*ss; 256 /* 2/(3log2)*(ss+...) */ 257 p_h = u+v; 258 __LO(p_h) = 0; 259 p_l = v-(p_h-u); 260 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ 261 z_l = cp_l*p_h+p_l*cp+dp_l[k]; 262 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ 263 t = (double)n; 264 t1 = (((z_h+z_l)+dp_h[k])+t); 265 __LO(t1) = 0; 266 t2 = z_l-(((t1-t)-dp_h[k])-z_h); 267 } 268 269 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ 270 y1 = y; 271 __LO(y1) = 0; 272 p_l = (y-y1)*t1+y*t2; 273 p_h = y1*t1; 274 z = p_l+p_h; 275 j = __HI(z); 276 i = __LO(z); 277 if (j>=0x40900000) { /* z >= 1024 */ 278 if(((j-0x40900000)|i)!=0) /* if z > 1024 */ 279 return s*huge*huge; /* overflow */ 280 else { 281 if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ 282 } 283 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ 284 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ 285 return s*tiny*tiny; /* underflow */ 286 else { 287 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ 288 } 289 } 290 /* 291 * compute 2**(p_h+p_l) 292 */ 293 i = j&0x7fffffff; 294 k = (i>>20)-0x3ff; 295 n = 0; 296 if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ 297 n = j+(0x00100000>>(k+1)); 298 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ 299 t = zero; 300 __HI(t) = (n&~(0x000fffff>>k)); 301 n = ((n&0x000fffff)|0x00100000)>>(20-k); 302 if(j<0) n = -n; 303 p_h -= t; 304 } 305 t = p_l+p_h; 306 __LO(t) = 0; 307 u = t*lg2_h; 308 v = (p_l-(t-p_h))*lg2+t*lg2_l; 309 z = u+v; 310 w = v-(z-u); 311 t = z*z; 312 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); 313 r = (z*t1)/(t1-two)-(w+z*w); 314 z = one-(r-z); 315 j = __HI(z); 316 j += (n<<20); 317 if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ 318 else __HI(z) += (n<<20); 319 return s*z; 320 } | 1 package java.lang; 2 3 /** 4 * Port of the "Freely Distributable Math Library", version 4.3, from C to Java. 5 */ 6 class FdLibm { 7 /** 8 * Return the low-order 32 bits of the double argument as an int. 9 */ 10 private static int __LO(double x) { 11 long transducer = Double.doubleToLongBits(x); 12 return (int)transducer; 13 } 14 15 /** 16 * Return the a double with its low-order bits reset. 17 */ 18 private static double __LO(double x, int low) { 19 long transX = Double.doubleToLongBits(x); 20 return Double.longBitsToDouble((transX & 0xFFFF_FFFF_0000_0000L)|low ); 21 } 22 23 /** 24 * Return the high-order 32 bits of the double argument as an int. 25 */ 26 private static int __HI(double x) { 27 long transducer = Double.doubleToLongBits(x); 28 return (int)(transducer >> 32); 29 } 30 /** 31 * Return the a double with its high-order bits reset. 32 */ 33 private static double __HI(double x, int high) { 34 long transX = Double.doubleToLongBits(x); 35 return Double.longBitsToDouble((transX & 0x0000_0000_FFFF_FFFFL)|( ((long)high)) << 32 ); 36 } 37 38 /** 39 * Return x**y 40 * 41 * n 42 * Method: Let x = 2 * (1+f) 43 * 1. Compute and return log2(x) in two pieces: 44 * log2(x) = w1 + w2, 45 * where w1 has 53-24 = 29 bit trailing zeros. 46 * 2. Perform y*log2(x) = n+y' by simulating muti-precision 47 * arithmetic, where |y'|<=0.5. 48 * 3. Return x**y = 2**n*exp(y'*log2) 49 * 50 * Special cases: 51 * 1. (anything) ** 0 is 1 52 * 2. (anything) ** 1 is itself 53 * 3. (anything) ** NAN is NAN 54 * 4. NAN ** (anything except 0) is NAN 55 * 5. +-(|x| > 1) ** +INF is +INF 56 * 6. +-(|x| > 1) ** -INF is +0 57 * 7. +-(|x| < 1) ** +INF is +0 58 * 8. +-(|x| < 1) ** -INF is +INF 59 * 9. +-1 ** +-INF is NAN 63 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF 64 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) 65 * 15. +INF ** (+anything except 0,NAN) is +INF 66 * 16. +INF ** (-anything except 0,NAN) is +0 67 * 17. -INF ** (anything) = -0 ** (-anything) 68 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) 69 * 19. (-anything except 0 and inf) ** (non-integer) is NAN 70 * 71 * Accuracy: 72 * pow(x,y) returns x**y nearly rounded. In particular 73 * pow(integer,integer) 74 * always returns the correct integer provided it is 75 * representable. 76 * 77 * Constants : 78 * The hexadecimal values are the intended ones for the following 79 * constants. The decimal values may be used, provided that the 80 * compiler will convert from decimal to binary accurately enough 81 * to produce the hexadecimal values shown. 82 */ 83 public static class Pow { 84 static final double bp[] = {1.0, 1.5,}; 85 static final double dp_h[] = { 0.0, 0x1.2b8034p-1,}; // 5.84962487220764160156e-01 86 static final double dp_l[] = { 0.0, 0x1.cfdeb43cfd006p-27,}; // 1.35003920212974897128e-08 87 static final double zero = 0.0; 88 static final double one = 1.0; 89 static final double two = 2.0; 90 static final double two53 = 0x1.0p53; // 9007199254740992.0 91 static final double huge = 1.0e300; 92 static final double tiny = 1.0e-300; 93 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ 94 static final double L1 = 0x1.3333333333303p-1; // 5.99999999999994648725e-01 95 static final double L2 = 0x1.b6db6db6fabffp-2; // 4.28571428578550184252e-01 96 static final double L3 = 0x1.55555518f264dp-2; // 3.33333329818377432918e-01 97 static final double L4 = 0x1.17460a91d4101p-2; // 2.72728123808534006489e-01 98 static final double L5 = 0x1.d864a93c9db65p-3; // 2.30660745775561754067e-01 99 static final double L6 = 0x1.a7e284a454eefp-3; // 2.06975017800338417784e-01 100 static final double P1 = 0x1.555555555553ep-3; // 1.66666666666666019037e-01 101 static final double P2 = -0x1.6c16c16bebd93p-9; // -2.77777777770155933842e-03 102 static final double P3 = 0x1.1566aaf25de2cp-14; // 6.61375632143793436117e-05 103 static final double P4 = -0x1.bbd41c5d26bf1p-20; // -1.65339022054652515390e-06 104 static final double P5 = 0x1.6376972bea4d0p-25; // 4.13813679705723846039e-08 105 static final double lg2 = 0x1.62e42fefa39efp-1; // 6.93147180559945286227e-01 106 static final double lg2_h = 0x1.62e43p-1; // 6.93147182464599609375e-01 107 static final double lg2_l = -0x1.05c610ca86c39p-29; // -1.90465429995776804525e-09 108 static final double ovt = 8.0085662595372944372e-0017; // -(1024-log2(ovfl+.5ulp)) 109 static final double cp = 0x1.ec709dc3a03fdp-1; // 9.61796693925975554329e-01 = 2/(3ln2) 110 static final double cp_h = 0x1.ec709ep-1; // 9.61796700954437255859e-01 = (float)cp 111 static final double cp_l = -0x1.e2fe0145b01f5p-28; // -7.02846165095275826516e-09 = tail of cp_h 112 static final double ivln2 = 0x1.71547652b82fep0; // 1.44269504088896338700e+00 = 1/ln2 113 static final double ivln2_h = 0x1.715476p0; // 1.44269502162933349609e+00 = 24 bits of 1/ln2 114 static final double ivln2_l = 0x1.4ae0bf85ddf44p-26; // 1.92596299112661746887e-08 = 1/ln2 tail 115 116 public static double pow(double x, double y) { 117 double z, ax, z_h, z_l, p_h, p_l; 118 double y1, t1, t2, r, s, t, u, v, w; 119 int i, j, k, yisint, n; 120 int hx, hy, ix, iy; 121 /*unsigned*/ int lx, ly; 122 123 hx = __HI(x); 124 lx = __LO(x); 125 hy = __HI(y); 126 ly = __LO(y); 127 ix = hx & 0x7fffffff; 128 iy = hy & 0x7fffffff; 129 130 /* y==zero: x**0 = 1 */ 131 if (y == 0.0) 132 return 1.0; 133 134 /* +-NaN return x+y */ 135 if (Double.isNaN(x) || Double.isNaN(y)) 136 return x + y; 137 138 /* determine if y is an odd int when x < 0 139 * yisint = 0 ... y is not an integer 140 * yisint = 1 ... y is an odd int 141 * yisint = 2 ... y is an even int 142 */ 143 yisint = 0; 144 if (hx < 0) { 145 if (iy >= 0x43400000) 146 yisint = 2; /* even integer y */ 147 else if (iy >= 0x3ff00000) { 148 k = (iy >> 20) - 0x3ff; /* exponent */ 149 if (k > 20) { 150 j = ly >> (52-k); 151 if ((j << (52-k) )==ly) 152 yisint = 2 - (j&1); 153 } else if (ly == 0) { 154 j = iy >> (20-k); 155 if ((j << (20-k))==iy) { 156 yisint = 2-(j & 1); 157 } 158 } 159 } 160 } 161 162 /* special value of y */ 163 if ( ly == 0 ) { 164 if (iy == 0x7ff00000) { /* y is +-inf */ 165 if (((ix - 0x3ff00000) | lx) == 0) 166 return y - y; /* inf**+-1 is NaN */ 167 else if (ix >= 0x3ff00000) /* (|x| > 1)**+-inf = inf,0 */ 168 return (hy >= 0) ? y: zero; 169 else /* (|x| < 1)**-,+inf = inf,0 */ 170 return (hy < 0) ? -y: zero; 171 } 172 if (iy == 0x3ff00000) { /* y is +-1 */ 173 if (hy < 0) 174 return one/x; 175 else 176 return x; 177 } 178 if (hy == 0x40000000) 179 return x*x; /* y is 2 */ 180 if (hy == 0x3fe00000) { /* y is 0.5 */ 181 if (hx >= 0) /* x >= +0 */ 182 return Math.sqrt(x); 183 } 184 } 185 186 ax = Math.abs(x); 187 /* special value of x */ 188 if (lx == 0) { 189 if (ix == 0x7ff00000 || ix==0 || ix == 0x3ff00000){ 190 z = ax; /*x is +-0,+-inf,+-1*/ 191 if (hy < 0) 192 z = one/z; /* z = (1/|x|) */ 193 if (hx < 0) { 194 if (((ix - 0x3ff00000) | yisint)==0) { 195 z = (z-z)/(z-z); /* (-1)**non-int is NaN */ 196 } else if (yisint == 1) 197 z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */ 198 } 199 return z; 200 } 201 } 202 203 n = (hx >> 31)+1; 204 205 /* (x<0)**(non-int) is NaN */ 206 if ((n | yisint) == 0) 207 return (x-x)/(x-x); 208 209 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ 210 if ( (n | (yisint-1)) == 0) 211 s = -one;/* (-ve)**(odd int) */ 212 213 /* |y| is huge */ 214 if(iy > 0x41e00000) { /* if |y| > 2**31 */ 215 if(iy > 0x43f00000){ /* if |y| > 2**64, must o/uflow */ 216 if (ix <= 0x3fefffff) 217 return (hy < 0) ? huge*huge : tiny*tiny; 218 if (ix >= 0x3ff00000) 219 return (hy > 0) ? huge*huge : tiny*tiny; 220 } 221 /* over/underflow if x is not close to one */ 222 if (ix < 0x3fefffff) 223 return (hy < 0) ? s*huge*huge : s*tiny*tiny; 224 if (ix > 0x3ff00000) 225 return (hy > 0) ? s*huge*huge : s*tiny*tiny; 226 /* now |1-x| is tiny <= 2**-20, suffice to compute 227 log(x) by x-x^2/2+x^3/3-x^4/4 */ 228 t = ax-one; /* t has 20 trailing zeros */ 229 w = (t*t) * (0.5-t*(0.3333333333333333333333-t*0.25)); 230 u = ivln2_h * t; /* ivln2_h has 21 sig. bits */ 231 v = t*ivln2_l-w*ivln2; 232 t1 = u + v; 233 t1 =__LO(t1, 0); 234 t2 = v-(t1-u); 235 } else { 236 double ss, s2, s_h, s_l, t_h, t_l; 237 n = 0; 238 /* take care subnormal number */ 239 if (ix < 0x00100000) { 240 ax *= two53; 241 n -= 53; 242 ix = __HI(ax); 243 } 244 n += ((ix) >> 20) - 0x3ff; 245 j = ix & 0x000fffff; 246 /* determine interval */ 247 ix = j | 0x3ff00000; /* normalize ix */ 248 if(j <= 0x3988E) 249 k=0; /* |x| <sqrt(3/2) */ 250 else if (j < 0xBB67A) 251 k=1; /* |x| <sqrt(3) */ 252 else { 253 k = 0; 254 n += 1; 255 ix -= 0x00100000; 256 } 257 ax = __HI(ax, ix); 258 259 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ 260 u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ 261 v = one / (ax + bp[k]); 262 ss = u * v; 263 s_h = ss; 264 s_h = __LO(s_h, 0); 265 /* t_h=ax+bp[k] High */ 266 t_h = zero; 267 t_h = __HI(t_h, ((ix >> 1)|0x20000000)+0x00080000+(k << 18) ); 268 t_l = ax - (t_h - bp[k]); 269 s_l = v * ((u- s_h * t_h) - s_h * t_l); 270 /* compute log(ax) */ 271 s2 = ss * ss; 272 r = s2 * s2* (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6))))); 273 r += s_l * (s_h + ss); 274 s2 = s_h * s_h; 275 t_h = 3.0 + s2 + r; 276 t_h = __LO(t_h, 0); 277 t_l = r-((t_h - 3.0)-s2); 278 /* u+v = ss*(1+...) */ 279 u = s_h * t_h; 280 v = s_l * t_h + t_l * ss; 281 /* 2/(3log2)*(ss+...) */ 282 p_h = u + v; 283 p_h = __LO(p_h, 0); 284 p_l = v-(p_h-u); 285 z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ 286 z_l = cp_l * p_h + p_l * cp + dp_l[k]; 287 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ 288 t = (double)n; 289 t1 = (((z_h + z_l) + dp_h[k]) + t); 290 t1 = __LO(t1, 0); 291 t2 = z_l - (((t1-t)-dp_h[k])-z_h); 292 } 293 294 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ 295 y1 = y; 296 y1 = __LO(y1, 0); 297 p_l = (y-y1) * t1 + y *t2; 298 p_h = y1 * t1; 299 z = p_l + p_h; 300 j = __HI(z); 301 i = __LO(z); 302 if (j >= 0x40900000) { /* z >= 1024 */ 303 if (((j - 0x40900000) | i)!=0) /* if z > 1024 */ 304 return s*huge*huge; /* overflow */ 305 else { 306 if (p_l+ovt>z-p_h) 307 return s*huge*huge; /* overflow */ 308 } 309 } else if ((j & 0x7fffffff) >= 0x4090cc00 ) { /* z <= -1075 */ 310 if (((j-0xc090cc00)|i)!=0) /* z < -1075 */ 311 return s*tiny*tiny; /* underflow */ 312 else { 313 if(p_l<=z-p_h) 314 return s*tiny*tiny; /* underflow */ 315 } 316 } 317 /* 318 * compute 2**(p_h+p_l) 319 */ 320 i = j & 0x7fffffff; 321 k = (i >> 20)-0x3ff; 322 n = 0; 323 if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ 324 n = j + (0x00100000 >> (k+1)); 325 k = ((n & 0x7fffffff) >> 20)-0x3ff; /* new k for n */ 326 t = zero; 327 t = __HI(t, (n & ~(0x000fffff >> k)) ); 328 n = ((n & 0x000fffff)|0x00100000) >> (20-k); 329 if (j < 0) 330 n = -n; 331 p_h -= t; 332 } 333 t = p_l+p_h; 334 t = __LO(t, 0); 335 u = t * lg2_h; 336 v = (p_l-(t-p_h))* lg2 + t * lg2_l; 337 z = u + v; 338 w = v-(z-u); 339 t = z * z; 340 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); 341 r = (z*t1)/(t1-two)-(w+z*w); 342 z = one - (r-z); 343 j = __HI(z); 344 j += (n << 20); 345 if ((j >> 20) <= 0) 346 z = Math.scalb(z, n); /* subnormal output */ 347 else { 348 int z_hi = __HI(z); 349 z_hi += (n << 20); 350 z = __HI(z, z_hi); 351 } 352 return s * z; 353 } 354 } 355 } |