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Java SE 11 Virtual Machine for .NET
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e_pow.cs
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1/*
2 * Copyright (c) 1998, 2004, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26/* __ieee754_pow(x,y) return x**y
27 *
28 * n
29 * Method: Let x = 2 * (1+f)
30 * 1. Compute and return log2(x) in two pieces:
31 * log2(x) = w1 + w2,
32 * where w1 has 53-24 = 29 bit trailing zeros.
33 * 2. Perform y*log2(x) = n+y' by simulating muti-precision
34 * arithmetic, where |y'|<=0.5.
35 * 3. Return x**y = 2**n*exp(y'*log2)
36 *
37 * Special cases:
38 * 1. (anything) ** 0 is 1
39 * 2. (anything) ** 1 is itself
40 * 3. (anything) ** NAN is NAN
41 * 4. NAN ** (anything except 0) is NAN
42 * 5. +-(|x| > 1) ** +INF is +INF
43 * 6. +-(|x| > 1) ** -INF is +0
44 * 7. +-(|x| < 1) ** +INF is +0
45 * 8. +-(|x| < 1) ** -INF is +INF
46 * 9. +-1 ** +-INF is NAN
47 * 10. +0 ** (+anything except 0, NAN) is +0
48 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
49 * 12. +0 ** (-anything except 0, NAN) is +INF
50 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
51 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
52 * 15. +INF ** (+anything except 0,NAN) is +INF
53 * 16. +INF ** (-anything except 0,NAN) is +0
54 * 17. -INF ** (anything) = -0 ** (-anything)
55 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
56 * 19. (-anything except 0 and inf) ** (non-integer) is NAN
57 *
58 * Accuracy:
59 * pow(x,y) returns x**y nearly rounded. In particular
60 * pow(integer,integer)
61 * always returns the correct integer provided it is
62 * representable.
63 *
64 * Constants :
65 * The hexadecimal values are the intended ones for the following
66 * constants. The decimal values may be used, provided that the
67 * compiler will convert from decimal to binary accurately enough
68 * to produce the hexadecimal values shown.
69 */
70using unsigned = System.UInt32;
71#pragma warning disable 168
72
73namespace IKVM.Runtime.Util.Java.Lang
74{
75 static partial class fdlibm
76 {
77 static readonly double[] bp = { 1.0, 1.5, };
78 static readonly double[] dp_h = { 0.0, 5.84962487220764160156e-01, }; /* 0x3FE2B803, 0x40000000 */
79 static readonly double[] dp_l = { 0.0, 1.35003920212974897128e-08, }; /* 0x3E4CFDEB, 0x43CFD006 */
80
81 internal static double __ieee754_pow(double x, double y)
82 {
83 const double zero = 0.0,
84 one = 1.0,
85 two = 2.0,
86 two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
87 huge = 1.0e300,
88 tiny = 1.0e-300,
89 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
90 L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
91 L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
92 L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
93 L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
94 L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
95 L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
96 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
97 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
98 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
99 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
100 P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
101 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
102 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
103 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
104 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
105 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
106 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
107 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
108 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
109 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
110 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
111
112 double z, ax, z_h, z_l, p_h, p_l;
113 double y1, t1, t2, r, s, t, u, v, w;
114 int i0, i1, i, j, k, yisint, n;
115 int hx, hy, ix, iy;
116 unsigned lx, ly;
117
118 hx = __HI(x); lx = (uint)__LO(x);
119 hy = __HI(y); ly = (uint)__LO(y);
120 ix = hx & 0x7fffffff; iy = hy & 0x7fffffff;
121
122 /* y==zero: x**0 = 1 */
123 if ((iy | (int)ly) == 0) return one;
124
125 /* +-NaN return x+y */
126 if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) ||
127 iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0)))
128 return x + y;
129
130 /* determine if y is an odd int when x < 0
131 * yisint = 0 ... y is not an integer
132 * yisint = 1 ... y is an odd int
133 * yisint = 2 ... y is an even int
134 */
135 yisint = 0;
136 if (hx < 0)
137 {
138 if (iy >= 0x43400000) yisint = 2; /* even integer y */
139 else if (iy >= 0x3ff00000)
140 {
141 k = (iy >> 20) - 0x3ff; /* exponent */
142 if (k > 20)
143 {
144 j = (int)(ly >> (52 - k));
145 if ((j << (52 - k)) == (int)ly) yisint = 2 - (j & 1);
146 }
147 else if (ly == 0)
148 {
149 j = iy >> (20 - k);
150 if ((j << (20 - k)) == iy) yisint = 2 - (j & 1);
151 }
152 }
153 }
154
155 /* special value of y */
156 if (ly == 0)
157 {
158 if (iy == 0x7ff00000)
159 { /* y is +-inf */
160 if (((ix - 0x3ff00000) | (int)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)
168 { /* y is +-1 */
169 if (hy < 0) return one / x; else return x;
170 }
171 if (hy == 0x40000000) return x * x; /* y is 2 */
172 if (hy == 0x3fe00000)
173 { /* y is 0.5 */
174 if (hx >= 0) /* x >= +0 */
175 return sqrt(x);
176 }
177 }
178
179 ax = fabs(x);
180 /* special value of x */
181 if (lx == 0)
182 {
183 if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000)
184 {
185 z = ax; /*x is +-0,+-inf,+-1*/
186 if (hy < 0) z = one / z; /* z = (1/|x|) */
187 if (hx < 0)
188 {
189 if (((ix - 0x3ff00000) | yisint) == 0)
190 {
191 z = (z - z) / (z - z); /* (-1)**non-int is NaN */
192 }
193 else if (yisint == 1)
194 z = -1.0 * z; /* (x<0)**odd = -(|x|**odd) */
195 }
196 return z;
197 }
198 }
199
200 n = (hx >> 31) + 1;
201
202 /* (x<0)**(non-int) is NaN */
203 if ((n | yisint) == 0) return (x - x) / (x - x);
204
205 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
206 if ((n | (yisint - 1)) == 0) s = -one;/* (-ve)**(odd int) */
207
208 /* |y| is huge */
209 if (iy > 0x41e00000)
210 { /* if |y| > 2**31 */
211 if (iy > 0x43f00000)
212 { /* if |y| > 2**64, must o/uflow */
213 if (ix <= 0x3fefffff) return (hy < 0) ? huge * huge : tiny * tiny;
214 if (ix >= 0x3ff00000) return (hy > 0) ? huge * huge : tiny * tiny;
215 }
216 /* over/underflow if x is not close to one */
217 if (ix < 0x3fefffff) return (hy < 0) ? s * huge * huge : s * tiny * tiny;
218 if (ix > 0x3ff00000) return (hy > 0) ? s * huge * huge : s * tiny * tiny;
219 /* now |1-x| is tiny <= 2**-20, suffice to compute
220 log(x) by x-x^2/2+x^3/3-x^4/4 */
221 t = ax - one; /* t has 20 trailing zeros */
222 w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
223 u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
224 v = t * ivln2_l - w * ivln2;
225 t1 = u + v;
226 t1 = __LO(t1, 0);
227 t2 = v - (t1 - u);
228 }
229 else
230 {
231 double ss, s2, s_h, s_l, t_h, t_l;
232 n = 0;
233 /* take care subnormal number */
234 if (ix < 0x00100000)
235 { ax *= two53; n -= 53; ix = __HI(ax); }
236 n += ((ix) >> 20) - 0x3ff;
237 j = ix & 0x000fffff;
238 /* determine interval */
239 ix = j | 0x3ff00000; /* normalize ix */
240 if (j <= 0x3988E) k = 0; /* |x|<sqrt(3/2) */
241 else if (j < 0xBB67A) k = 1; /* |x|<sqrt(3) */
242 else { k = 0; n += 1; ix -= 0x00100000; }
243 ax = __HI(ax, ix);
244
245 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
246 u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
247 v = one / (ax + bp[k]);
248 ss = u * v;
249 s_h = ss;
250 s_h = __LO(s_h, 0);
251 /* t_h=ax+bp[k] High */
252 t_h = zero;
253 t_h = __HI(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
254 t_l = ax - (t_h - bp[k]);
255 s_l = v * ((u - s_h * t_h) - s_h * t_l);
256 /* compute log(ax) */
257 s2 = ss * ss;
258 r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
259 r += s_l * (s_h + ss);
260 s2 = s_h * s_h;
261 t_h = 3.0 + s2 + r;
262 t_h = __LO(t_h, 0);
263 t_l = r - ((t_h - 3.0) - s2);
264 /* u+v = ss*(1+...) */
265 u = s_h * t_h;
266 v = s_l * t_h + t_l * ss;
267 /* 2/(3log2)*(ss+...) */
268 p_h = u + v;
269 p_h = __LO(p_h, 0);
270 p_l = v - (p_h - u);
271 z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
272 z_l = cp_l * p_h + p_l * cp + dp_l[k];
273 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
274 t = (double)n;
275 t1 = (((z_h + z_l) + dp_h[k]) + t);
276 t1 = __LO(t1, 0);
277 t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
278 }
279
280 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
281 y1 = y;
282 y1 = __LO(y1, 0);
283 p_l = (y - y1) * t1 + y * t2;
284 p_h = y1 * t1;
285 z = p_l + p_h;
286 j = __HI(z);
287 i = __LO(z);
288 if (j >= 0x40900000)
289 { /* z >= 1024 */
290 if (((j - 0x40900000) | i) != 0) /* if z > 1024 */
291 return s * huge * huge; /* overflow */
292 else
293 {
294 if (p_l + ovt > z - p_h) return s * huge * huge; /* overflow */
295 }
296 }
297 else if ((j & 0x7fffffff) >= 0x4090cc00)
298 { /* z <= -1075 */
299 if (((int)(j - 0xc090cc00) | i) != 0) /* z < -1075 */
300 return s * tiny * tiny; /* underflow */
301 else
302 {
303 if (p_l <= z - p_h) return s * tiny * tiny; /* underflow */
304 }
305 }
306 /*
307 * compute 2**(p_h+p_l)
308 */
309 i = j & 0x7fffffff;
310 k = (i >> 20) - 0x3ff;
311 n = 0;
312 if (i > 0x3fe00000)
313 { /* if |z| > 0.5, set n = [z+0.5] */
314 n = j + (0x00100000 >> (k + 1));
315 k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
316 t = zero;
317 t = __HI(t, (n & ~(0x000fffff >> k)));
318 n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
319 if (j < 0) n = -n;
320 p_h -= t;
321 }
322 t = p_l + p_h;
323 t = __LO(t, 0);
324 u = t * lg2_h;
325 v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
326 z = u + v;
327 w = v - (z - u);
328 t = z * z;
329 t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
330 r = (z * t1) / (t1 - two) - (w + z * w);
331 z = one - (r - z);
332 j = __HI(z);
333 j += (n << 20);
334 if ((j >> 20) <= 0) z = scalbn(z, n); /* subnormal output */
335 else z = __HI(z, __HI(z) + (n << 20));
336 return s * z;
337 }
338 }
339}
unsigned
System.UInt32 unsigned
Definition e_pow.cs:70