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annotate src/share/vm/runtime/sharedRuntimeTrans.cpp @ 23007:3c8b53552a43
4505697: nsk/jdi/ExceptionEvent/_itself_/exevent006 and exevent008 tests fail with InvocationTargetException
Reviewed-by: dcubed, dholmes, sspitsyn
author | jbachorik |
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date | Mon, 24 Feb 2014 10:28:22 +0100 |
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0 | 1 /* |
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2 * Copyright (c) 2005, 2014, Oracle and/or its affiliates. All rights reserved. |
0 | 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. | |
8 * | |
9 * This code is distributed in the hope that it will be useful, but WITHOUT | |
10 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
11 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
12 * version 2 for more details (a copy is included in the LICENSE file that | |
13 * accompanied this code). | |
14 * | |
15 * You should have received a copy of the GNU General Public License version | |
16 * 2 along with this work; if not, write to the Free Software Foundation, | |
17 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. | |
18 * | |
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19 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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20 * or visit www.oracle.com if you need additional information or have any |
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21 * questions. |
0 | 22 * |
23 */ | |
24 | |
1972 | 25 #include "precompiled.hpp" |
26 #include "prims/jni.h" | |
27 #include "runtime/interfaceSupport.hpp" | |
28 #include "runtime/sharedRuntime.hpp" | |
0 | 29 |
30 // This file contains copies of the fdlibm routines used by | |
31 // StrictMath. It turns out that it is almost always required to use | |
32 // these runtime routines; the Intel CPU doesn't meet the Java | |
33 // specification for sin/cos outside a certain limited argument range, | |
34 // and the SPARC CPU doesn't appear to have sin/cos instructions. It | |
35 // also turns out that avoiding the indirect call through function | |
36 // pointer out to libjava.so in SharedRuntime speeds these routines up | |
37 // by roughly 15% on both Win32/x86 and Solaris/SPARC. | |
38 | |
39 // Enabling optimizations in this file causes incorrect code to be | |
40 // generated; can not figure out how to turn down optimization for one | |
41 // file in the IDE on Windows | |
42 #ifdef WIN32 | |
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43 # pragma warning( disable: 4748 ) // /GS can not protect parameters and local variables from local buffer overrun because optimizations are disabled in function |
0 | 44 # pragma optimize ( "", off ) |
45 #endif | |
46 | |
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47 #include "runtime/sharedRuntimeMath.hpp" |
0 | 48 |
49 /* __ieee754_log(x) | |
50 * Return the logrithm of x | |
51 * | |
52 * Method : | |
53 * 1. Argument Reduction: find k and f such that | |
54 * x = 2^k * (1+f), | |
55 * where sqrt(2)/2 < 1+f < sqrt(2) . | |
56 * | |
57 * 2. Approximation of log(1+f). | |
58 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) | |
59 * = 2s + 2/3 s**3 + 2/5 s**5 + ....., | |
60 * = 2s + s*R | |
61 * We use a special Reme algorithm on [0,0.1716] to generate | |
62 * a polynomial of degree 14 to approximate R The maximum error | |
63 * of this polynomial approximation is bounded by 2**-58.45. In | |
64 * other words, | |
65 * 2 4 6 8 10 12 14 | |
66 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s | |
67 * (the values of Lg1 to Lg7 are listed in the program) | |
68 * and | |
69 * | 2 14 | -58.45 | |
70 * | Lg1*s +...+Lg7*s - R(z) | <= 2 | |
71 * | | | |
72 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. | |
73 * In order to guarantee error in log below 1ulp, we compute log | |
74 * by | |
75 * log(1+f) = f - s*(f - R) (if f is not too large) | |
76 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) | |
77 * | |
78 * 3. Finally, log(x) = k*ln2 + log(1+f). | |
79 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) | |
80 * Here ln2 is split into two floating point number: | |
81 * ln2_hi + ln2_lo, | |
82 * where n*ln2_hi is always exact for |n| < 2000. | |
83 * | |
84 * Special cases: | |
85 * log(x) is NaN with signal if x < 0 (including -INF) ; | |
86 * log(+INF) is +INF; log(0) is -INF with signal; | |
87 * log(NaN) is that NaN with no signal. | |
88 * | |
89 * Accuracy: | |
90 * according to an error analysis, the error is always less than | |
91 * 1 ulp (unit in the last place). | |
92 * | |
93 * Constants: | |
94 * The hexadecimal values are the intended ones for the following | |
95 * constants. The decimal values may be used, provided that the | |
96 * compiler will convert from decimal to binary accurately enough | |
97 * to produce the hexadecimal values shown. | |
98 */ | |
99 | |
100 static const double | |
101 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ | |
102 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ | |
103 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ | |
104 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ | |
105 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ | |
106 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ | |
107 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ | |
108 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ | |
109 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ | |
110 | |
111 static double zero = 0.0; | |
112 | |
113 static double __ieee754_log(double x) { | |
114 double hfsq,f,s,z,R,w,t1,t2,dk; | |
115 int k,hx,i,j; | |
116 unsigned lx; | |
117 | |
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118 hx = high(x); /* high word of x */ |
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119 lx = low(x); /* low word of x */ |
0 | 120 |
121 k=0; | |
122 if (hx < 0x00100000) { /* x < 2**-1022 */ | |
123 if (((hx&0x7fffffff)|lx)==0) | |
124 return -two54/zero; /* log(+-0)=-inf */ | |
125 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ | |
126 k -= 54; x *= two54; /* subnormal number, scale up x */ | |
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127 hx = high(x); /* high word of x */ |
0 | 128 } |
129 if (hx >= 0x7ff00000) return x+x; | |
130 k += (hx>>20)-1023; | |
131 hx &= 0x000fffff; | |
132 i = (hx+0x95f64)&0x100000; | |
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133 set_high(&x, hx|(i^0x3ff00000)); /* normalize x or x/2 */ |
0 | 134 k += (i>>20); |
135 f = x-1.0; | |
136 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ | |
137 if(f==zero) { | |
138 if (k==0) return zero; | |
139 else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;} | |
140 } | |
141 R = f*f*(0.5-0.33333333333333333*f); | |
142 if(k==0) return f-R; else {dk=(double)k; | |
143 return dk*ln2_hi-((R-dk*ln2_lo)-f);} | |
144 } | |
145 s = f/(2.0+f); | |
146 dk = (double)k; | |
147 z = s*s; | |
148 i = hx-0x6147a; | |
149 w = z*z; | |
150 j = 0x6b851-hx; | |
151 t1= w*(Lg2+w*(Lg4+w*Lg6)); | |
152 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); | |
153 i |= j; | |
154 R = t2+t1; | |
155 if(i>0) { | |
156 hfsq=0.5*f*f; | |
157 if(k==0) return f-(hfsq-s*(hfsq+R)); else | |
158 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); | |
159 } else { | |
160 if(k==0) return f-s*(f-R); else | |
161 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); | |
162 } | |
163 } | |
164 | |
165 JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x)) | |
166 return __ieee754_log(x); | |
167 JRT_END | |
168 | |
169 /* __ieee754_log10(x) | |
170 * Return the base 10 logarithm of x | |
171 * | |
172 * Method : | |
173 * Let log10_2hi = leading 40 bits of log10(2) and | |
174 * log10_2lo = log10(2) - log10_2hi, | |
175 * ivln10 = 1/log(10) rounded. | |
176 * Then | |
177 * n = ilogb(x), | |
178 * if(n<0) n = n+1; | |
179 * x = scalbn(x,-n); | |
180 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) | |
181 * | |
182 * Note 1: | |
183 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding | |
184 * mode must set to Round-to-Nearest. | |
185 * Note 2: | |
186 * [1/log(10)] rounded to 53 bits has error .198 ulps; | |
187 * log10 is monotonic at all binary break points. | |
188 * | |
189 * Special cases: | |
190 * log10(x) is NaN with signal if x < 0; | |
191 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; | |
192 * log10(NaN) is that NaN with no signal; | |
193 * log10(10**N) = N for N=0,1,...,22. | |
194 * | |
195 * Constants: | |
196 * The hexadecimal values are the intended ones for the following constants. | |
197 * The decimal values may be used, provided that the compiler will convert | |
198 * from decimal to binary accurately enough to produce the hexadecimal values | |
199 * shown. | |
200 */ | |
201 | |
202 static const double | |
203 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ | |
204 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ | |
205 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ | |
206 | |
207 static double __ieee754_log10(double x) { | |
208 double y,z; | |
209 int i,k,hx; | |
210 unsigned lx; | |
211 | |
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212 hx = high(x); /* high word of x */ |
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213 lx = low(x); /* low word of x */ |
0 | 214 |
215 k=0; | |
216 if (hx < 0x00100000) { /* x < 2**-1022 */ | |
217 if (((hx&0x7fffffff)|lx)==0) | |
218 return -two54/zero; /* log(+-0)=-inf */ | |
219 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ | |
220 k -= 54; x *= two54; /* subnormal number, scale up x */ | |
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221 hx = high(x); /* high word of x */ |
0 | 222 } |
223 if (hx >= 0x7ff00000) return x+x; | |
224 k += (hx>>20)-1023; | |
225 i = ((unsigned)k&0x80000000)>>31; | |
226 hx = (hx&0x000fffff)|((0x3ff-i)<<20); | |
227 y = (double)(k+i); | |
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228 set_high(&x, hx); |
0 | 229 z = y*log10_2lo + ivln10*__ieee754_log(x); |
230 return z+y*log10_2hi; | |
231 } | |
232 | |
233 JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x)) | |
234 return __ieee754_log10(x); | |
235 JRT_END | |
236 | |
237 | |
238 /* __ieee754_exp(x) | |
239 * Returns the exponential of x. | |
240 * | |
241 * Method | |
242 * 1. Argument reduction: | |
243 * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. | |
244 * Given x, find r and integer k such that | |
245 * | |
246 * x = k*ln2 + r, |r| <= 0.5*ln2. | |
247 * | |
248 * Here r will be represented as r = hi-lo for better | |
249 * accuracy. | |
250 * | |
251 * 2. Approximation of exp(r) by a special rational function on | |
252 * the interval [0,0.34658]: | |
253 * Write | |
254 * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... | |
255 * We use a special Reme algorithm on [0,0.34658] to generate | |
256 * a polynomial of degree 5 to approximate R. The maximum error | |
257 * of this polynomial approximation is bounded by 2**-59. In | |
258 * other words, | |
259 * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 | |
260 * (where z=r*r, and the values of P1 to P5 are listed below) | |
261 * and | |
262 * | 5 | -59 | |
263 * | 2.0+P1*z+...+P5*z - R(z) | <= 2 | |
264 * | | | |
265 * The computation of exp(r) thus becomes | |
266 * 2*r | |
267 * exp(r) = 1 + ------- | |
268 * R - r | |
269 * r*R1(r) | |
270 * = 1 + r + ----------- (for better accuracy) | |
271 * 2 - R1(r) | |
272 * where | |
273 * 2 4 10 | |
274 * R1(r) = r - (P1*r + P2*r + ... + P5*r ). | |
275 * | |
276 * 3. Scale back to obtain exp(x): | |
277 * From step 1, we have | |
278 * exp(x) = 2^k * exp(r) | |
279 * | |
280 * Special cases: | |
281 * exp(INF) is INF, exp(NaN) is NaN; | |
282 * exp(-INF) is 0, and | |
283 * for finite argument, only exp(0)=1 is exact. | |
284 * | |
285 * Accuracy: | |
286 * according to an error analysis, the error is always less than | |
287 * 1 ulp (unit in the last place). | |
288 * | |
289 * Misc. info. | |
290 * For IEEE double | |
291 * if x > 7.09782712893383973096e+02 then exp(x) overflow | |
292 * if x < -7.45133219101941108420e+02 then exp(x) underflow | |
293 * | |
294 * Constants: | |
295 * The hexadecimal values are the intended ones for the following | |
296 * constants. The decimal values may be used, provided that the | |
297 * compiler will convert from decimal to binary accurately enough | |
298 * to produce the hexadecimal values shown. | |
299 */ | |
300 | |
301 static const double | |
302 one = 1.0, | |
303 halF[2] = {0.5,-0.5,}, | |
304 twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ | |
305 o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ | |
306 u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ | |
307 ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ | |
308 -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ | |
309 ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ | |
310 -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ | |
311 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ | |
312 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ | |
313 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ | |
314 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ | |
315 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ | |
316 P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ | |
317 | |
318 static double __ieee754_exp(double x) { | |
319 double y,hi=0,lo=0,c,t; | |
320 int k=0,xsb; | |
321 unsigned hx; | |
322 | |
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323 hx = high(x); /* high word of x */ |
0 | 324 xsb = (hx>>31)&1; /* sign bit of x */ |
325 hx &= 0x7fffffff; /* high word of |x| */ | |
326 | |
327 /* filter out non-finite argument */ | |
328 if(hx >= 0x40862E42) { /* if |x|>=709.78... */ | |
329 if(hx>=0x7ff00000) { | |
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330 if(((hx&0xfffff)|low(x))!=0) |
0 | 331 return x+x; /* NaN */ |
332 else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ | |
333 } | |
334 if(x > o_threshold) return hugeX*hugeX; /* overflow */ | |
335 if(x < u_threshold) return twom1000*twom1000; /* underflow */ | |
336 } | |
337 | |
338 /* argument reduction */ | |
339 if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ | |
340 if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ | |
341 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; | |
342 } else { | |
343 k = (int)(invln2*x+halF[xsb]); | |
344 t = k; | |
345 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ | |
346 lo = t*ln2LO[0]; | |
347 } | |
348 x = hi - lo; | |
349 } | |
350 else if(hx < 0x3e300000) { /* when |x|<2**-28 */ | |
351 if(hugeX+x>one) return one+x;/* trigger inexact */ | |
352 } | |
353 else k = 0; | |
354 | |
355 /* x is now in primary range */ | |
356 t = x*x; | |
357 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); | |
358 if(k==0) return one-((x*c)/(c-2.0)-x); | |
359 else y = one-((lo-(x*c)/(2.0-c))-hi); | |
360 if(k >= -1021) { | |
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361 set_high(&y, high(y) + (k<<20)); /* add k to y's exponent */ |
0 | 362 return y; |
363 } else { | |
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364 set_high(&y, high(y) + ((k+1000)<<20)); /* add k to y's exponent */ |
0 | 365 return y*twom1000; |
366 } | |
367 } | |
368 | |
369 JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x)) | |
370 return __ieee754_exp(x); | |
371 JRT_END | |
372 | |
373 /* __ieee754_pow(x,y) return x**y | |
374 * | |
375 * n | |
376 * Method: Let x = 2 * (1+f) | |
377 * 1. Compute and return log2(x) in two pieces: | |
378 * log2(x) = w1 + w2, | |
379 * where w1 has 53-24 = 29 bit trailing zeros. | |
380 * 2. Perform y*log2(x) = n+y' by simulating muti-precision | |
381 * arithmetic, where |y'|<=0.5. | |
382 * 3. Return x**y = 2**n*exp(y'*log2) | |
383 * | |
384 * Special cases: | |
385 * 1. (anything) ** 0 is 1 | |
386 * 2. (anything) ** 1 is itself | |
387 * 3. (anything) ** NAN is NAN | |
388 * 4. NAN ** (anything except 0) is NAN | |
389 * 5. +-(|x| > 1) ** +INF is +INF | |
390 * 6. +-(|x| > 1) ** -INF is +0 | |
391 * 7. +-(|x| < 1) ** +INF is +0 | |
392 * 8. +-(|x| < 1) ** -INF is +INF | |
393 * 9. +-1 ** +-INF is NAN | |
394 * 10. +0 ** (+anything except 0, NAN) is +0 | |
395 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 | |
396 * 12. +0 ** (-anything except 0, NAN) is +INF | |
397 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF | |
398 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) | |
399 * 15. +INF ** (+anything except 0,NAN) is +INF | |
400 * 16. +INF ** (-anything except 0,NAN) is +0 | |
401 * 17. -INF ** (anything) = -0 ** (-anything) | |
402 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) | |
403 * 19. (-anything except 0 and inf) ** (non-integer) is NAN | |
404 * | |
405 * Accuracy: | |
406 * pow(x,y) returns x**y nearly rounded. In particular | |
407 * pow(integer,integer) | |
408 * always returns the correct integer provided it is | |
409 * representable. | |
410 * | |
411 * Constants : | |
412 * The hexadecimal values are the intended ones for the following | |
413 * constants. The decimal values may be used, provided that the | |
414 * compiler will convert from decimal to binary accurately enough | |
415 * to produce the hexadecimal values shown. | |
416 */ | |
417 | |
418 static const double | |
419 bp[] = {1.0, 1.5,}, | |
420 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ | |
421 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ | |
422 zeroX = 0.0, | |
423 two = 2.0, | |
424 two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ | |
425 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ | |
426 L1X = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ | |
427 L2X = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ | |
428 L3X = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ | |
429 L4X = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ | |
430 L5X = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ | |
431 L6X = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ | |
432 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ | |
433 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ | |
434 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ | |
435 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ | |
436 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ | |
437 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ | |
438 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ | |
439 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ | |
440 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ | |
441 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ | |
442 | |
443 double __ieee754_pow(double x, double y) { | |
444 double z,ax,z_h,z_l,p_h,p_l; | |
445 double y1,t1,t2,r,s,t,u,v,w; | |
446 int i0,i1,i,j,k,yisint,n; | |
447 int hx,hy,ix,iy; | |
448 unsigned lx,ly; | |
449 | |
450 i0 = ((*(int*)&one)>>29)^1; i1=1-i0; | |
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451 hx = high(x); lx = low(x); |
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452 hy = high(y); ly = low(y); |
0 | 453 ix = hx&0x7fffffff; iy = hy&0x7fffffff; |
454 | |
455 /* y==zero: x**0 = 1 */ | |
456 if((iy|ly)==0) return one; | |
457 | |
458 /* +-NaN return x+y */ | |
459 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || | |
460 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) | |
461 return x+y; | |
462 | |
463 /* determine if y is an odd int when x < 0 | |
464 * yisint = 0 ... y is not an integer | |
465 * yisint = 1 ... y is an odd int | |
466 * yisint = 2 ... y is an even int | |
467 */ | |
468 yisint = 0; | |
469 if(hx<0) { | |
470 if(iy>=0x43400000) yisint = 2; /* even integer y */ | |
471 else if(iy>=0x3ff00000) { | |
472 k = (iy>>20)-0x3ff; /* exponent */ | |
473 if(k>20) { | |
474 j = ly>>(52-k); | |
475 if((unsigned)(j<<(52-k))==ly) yisint = 2-(j&1); | |
476 } else if(ly==0) { | |
477 j = iy>>(20-k); | |
478 if((j<<(20-k))==iy) yisint = 2-(j&1); | |
479 } | |
480 } | |
481 } | |
482 | |
483 /* special value of y */ | |
484 if(ly==0) { | |
485 if (iy==0x7ff00000) { /* y is +-inf */ | |
486 if(((ix-0x3ff00000)|lx)==0) | |
487 return y - y; /* inf**+-1 is NaN */ | |
488 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ | |
489 return (hy>=0)? y: zeroX; | |
490 else /* (|x|<1)**-,+inf = inf,0 */ | |
491 return (hy<0)?-y: zeroX; | |
492 } | |
493 if(iy==0x3ff00000) { /* y is +-1 */ | |
494 if(hy<0) return one/x; else return x; | |
495 } | |
496 if(hy==0x40000000) return x*x; /* y is 2 */ | |
497 if(hy==0x3fe00000) { /* y is 0.5 */ | |
498 if(hx>=0) /* x >= +0 */ | |
499 return sqrt(x); | |
500 } | |
501 } | |
502 | |
503 ax = fabsd(x); | |
504 /* special value of x */ | |
505 if(lx==0) { | |
506 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ | |
507 z = ax; /*x is +-0,+-inf,+-1*/ | |
508 if(hy<0) z = one/z; /* z = (1/|x|) */ | |
509 if(hx<0) { | |
510 if(((ix-0x3ff00000)|yisint)==0) { | |
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511 #ifdef CAN_USE_NAN_DEFINE |
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512 z = NAN; |
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513 #else |
0 | 514 z = (z-z)/(z-z); /* (-1)**non-int is NaN */ |
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515 #endif |
0 | 516 } else if(yisint==1) |
517 z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */ | |
518 } | |
519 return z; | |
520 } | |
521 } | |
522 | |
523 n = (hx>>31)+1; | |
524 | |
525 /* (x<0)**(non-int) is NaN */ | |
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526 if((n|yisint)==0) |
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527 #ifdef CAN_USE_NAN_DEFINE |
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528 return NAN; |
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529 #else |
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530 return (x-x)/(x-x); |
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531 #endif |
0 | 532 |
533 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ | |
534 if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ | |
535 | |
536 /* |y| is huge */ | |
537 if(iy>0x41e00000) { /* if |y| > 2**31 */ | |
538 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ | |
539 if(ix<=0x3fefffff) return (hy<0)? hugeX*hugeX:tiny*tiny; | |
540 if(ix>=0x3ff00000) return (hy>0)? hugeX*hugeX:tiny*tiny; | |
541 } | |
542 /* over/underflow if x is not close to one */ | |
543 if(ix<0x3fefffff) return (hy<0)? s*hugeX*hugeX:s*tiny*tiny; | |
544 if(ix>0x3ff00000) return (hy>0)? s*hugeX*hugeX:s*tiny*tiny; | |
545 /* now |1-x| is tiny <= 2**-20, suffice to compute | |
546 log(x) by x-x^2/2+x^3/3-x^4/4 */ | |
547 t = ax-one; /* t has 20 trailing zeros */ | |
548 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); | |
549 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ | |
550 v = t*ivln2_l-w*ivln2; | |
551 t1 = u+v; | |
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552 set_low(&t1, 0); |
0 | 553 t2 = v-(t1-u); |
554 } else { | |
555 double ss,s2,s_h,s_l,t_h,t_l; | |
556 n = 0; | |
557 /* take care subnormal number */ | |
558 if(ix<0x00100000) | |
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559 {ax *= two53; n -= 53; ix = high(ax); } |
0 | 560 n += ((ix)>>20)-0x3ff; |
561 j = ix&0x000fffff; | |
562 /* determine interval */ | |
563 ix = j|0x3ff00000; /* normalize ix */ | |
564 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ | |
565 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ | |
566 else {k=0;n+=1;ix -= 0x00100000;} | |
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567 set_high(&ax, ix); |
0 | 568 |
569 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ | |
570 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ | |
571 v = one/(ax+bp[k]); | |
572 ss = u*v; | |
573 s_h = ss; | |
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574 set_low(&s_h, 0); |
0 | 575 /* t_h=ax+bp[k] High */ |
576 t_h = zeroX; | |
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577 set_high(&t_h, ((ix>>1)|0x20000000)+0x00080000+(k<<18)); |
0 | 578 t_l = ax - (t_h-bp[k]); |
579 s_l = v*((u-s_h*t_h)-s_h*t_l); | |
580 /* compute log(ax) */ | |
581 s2 = ss*ss; | |
582 r = s2*s2*(L1X+s2*(L2X+s2*(L3X+s2*(L4X+s2*(L5X+s2*L6X))))); | |
583 r += s_l*(s_h+ss); | |
584 s2 = s_h*s_h; | |
585 t_h = 3.0+s2+r; | |
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586 set_low(&t_h, 0); |
0 | 587 t_l = r-((t_h-3.0)-s2); |
588 /* u+v = ss*(1+...) */ | |
589 u = s_h*t_h; | |
590 v = s_l*t_h+t_l*ss; | |
591 /* 2/(3log2)*(ss+...) */ | |
592 p_h = u+v; | |
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593 set_low(&p_h, 0); |
0 | 594 p_l = v-(p_h-u); |
595 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ | |
596 z_l = cp_l*p_h+p_l*cp+dp_l[k]; | |
597 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ | |
598 t = (double)n; | |
599 t1 = (((z_h+z_l)+dp_h[k])+t); | |
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600 set_low(&t1, 0); |
0 | 601 t2 = z_l-(((t1-t)-dp_h[k])-z_h); |
602 } | |
603 | |
604 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ | |
605 y1 = y; | |
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606 set_low(&y1, 0); |
0 | 607 p_l = (y-y1)*t1+y*t2; |
608 p_h = y1*t1; | |
609 z = p_l+p_h; | |
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610 j = high(z); |
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611 i = low(z); |
0 | 612 if (j>=0x40900000) { /* z >= 1024 */ |
613 if(((j-0x40900000)|i)!=0) /* if z > 1024 */ | |
614 return s*hugeX*hugeX; /* overflow */ | |
615 else { | |
616 if(p_l+ovt>z-p_h) return s*hugeX*hugeX; /* overflow */ | |
617 } | |
618 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ | |
619 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ | |
620 return s*tiny*tiny; /* underflow */ | |
621 else { | |
622 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ | |
623 } | |
624 } | |
625 /* | |
626 * compute 2**(p_h+p_l) | |
627 */ | |
628 i = j&0x7fffffff; | |
629 k = (i>>20)-0x3ff; | |
630 n = 0; | |
631 if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ | |
632 n = j+(0x00100000>>(k+1)); | |
633 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ | |
634 t = zeroX; | |
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635 set_high(&t, (n&~(0x000fffff>>k))); |
0 | 636 n = ((n&0x000fffff)|0x00100000)>>(20-k); |
637 if(j<0) n = -n; | |
638 p_h -= t; | |
639 } | |
640 t = p_l+p_h; | |
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641 set_low(&t, 0); |
0 | 642 u = t*lg2_h; |
643 v = (p_l-(t-p_h))*lg2+t*lg2_l; | |
644 z = u+v; | |
645 w = v-(z-u); | |
646 t = z*z; | |
647 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); | |
648 r = (z*t1)/(t1-two)-(w+z*w); | |
649 z = one-(r-z); | |
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650 j = high(z); |
0 | 651 j += (n<<20); |
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652 if((j>>20)<=0) z = scalbnA(z,n); /* subnormal output */ |
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653 else set_high(&z, high(z) + (n<<20)); |
0 | 654 return s*z; |
655 } | |
656 | |
657 | |
658 JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y)) | |
659 return __ieee754_pow(x, y); | |
660 JRT_END | |
661 | |
662 #ifdef WIN32 | |
663 # pragma optimize ( "", on ) | |
664 #endif |