Mercurial > hg > graal-compiler
annotate src/share/vm/runtime/sharedRuntimeTrans.cpp @ 17936:968a17f18337
8042786: Proper fix for 8032566
Summary: Check for overflow cases in range checks and collapse it if we can.
Reviewed-by: jrose, iveresov
author | kvn |
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date | Fri, 16 May 2014 12:05:14 -0700 |
parents | bdd155477289 |
children | 8a9bb7821e28 631c3a4ea10c |
rev | line source |
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0 | 1 /* |
1972 | 2 * Copyright (c) 2005, 2010, 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 | |
43 # pragma optimize ( "", off ) | |
44 #endif | |
45 | |
46 #include <math.h> | |
47 | |
48 // VM_LITTLE_ENDIAN is #defined appropriately in the Makefiles | |
49 // [jk] this is not 100% correct because the float word order may different | |
50 // from the byte order (e.g. on ARM) | |
51 #ifdef VM_LITTLE_ENDIAN | |
52 # define __HI(x) *(1+(int*)&x) | |
53 # define __LO(x) *(int*)&x | |
54 #else | |
55 # define __HI(x) *(int*)&x | |
56 # define __LO(x) *(1+(int*)&x) | |
57 #endif | |
58 | |
14411 | 59 #if !defined(AIX) |
0 | 60 double copysign(double x, double y) { |
61 __HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000); | |
62 return x; | |
63 } | |
14411 | 64 #endif |
0 | 65 |
66 /* | |
67 * ==================================================== | |
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68 * Copyright (c) 1998 Oracle and/or its affiliates. All rights reserved. |
0 | 69 * |
70 * Developed at SunSoft, a Sun Microsystems, Inc. business. | |
71 * Permission to use, copy, modify, and distribute this | |
72 * software is freely granted, provided that this notice | |
73 * is preserved. | |
74 * ==================================================== | |
75 */ | |
76 | |
77 /* | |
78 * scalbn (double x, int n) | |
79 * scalbn(x,n) returns x* 2**n computed by exponent | |
80 * manipulation rather than by actually performing an | |
81 * exponentiation or a multiplication. | |
82 */ | |
83 | |
84 static const double | |
85 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ | |
86 twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ | |
87 hugeX = 1.0e+300, | |
88 tiny = 1.0e-300; | |
89 | |
14411 | 90 #if !defined(AIX) |
0 | 91 double scalbn (double x, int n) { |
92 int k,hx,lx; | |
93 hx = __HI(x); | |
94 lx = __LO(x); | |
95 k = (hx&0x7ff00000)>>20; /* extract exponent */ | |
96 if (k==0) { /* 0 or subnormal x */ | |
97 if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ | |
98 x *= two54; | |
99 hx = __HI(x); | |
100 k = ((hx&0x7ff00000)>>20) - 54; | |
101 if (n< -50000) return tiny*x; /*underflow*/ | |
102 } | |
103 if (k==0x7ff) return x+x; /* NaN or Inf */ | |
104 k = k+n; | |
105 if (k > 0x7fe) return hugeX*copysign(hugeX,x); /* overflow */ | |
106 if (k > 0) /* normal result */ | |
107 {__HI(x) = (hx&0x800fffff)|(k<<20); return x;} | |
108 if (k <= -54) { | |
109 if (n > 50000) /* in case integer overflow in n+k */ | |
110 return hugeX*copysign(hugeX,x); /*overflow*/ | |
111 else return tiny*copysign(tiny,x); /*underflow*/ | |
112 } | |
113 k += 54; /* subnormal result */ | |
114 __HI(x) = (hx&0x800fffff)|(k<<20); | |
115 return x*twom54; | |
116 } | |
14411 | 117 #endif |
0 | 118 |
119 /* __ieee754_log(x) | |
120 * Return the logrithm of x | |
121 * | |
122 * Method : | |
123 * 1. Argument Reduction: find k and f such that | |
124 * x = 2^k * (1+f), | |
125 * where sqrt(2)/2 < 1+f < sqrt(2) . | |
126 * | |
127 * 2. Approximation of log(1+f). | |
128 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) | |
129 * = 2s + 2/3 s**3 + 2/5 s**5 + ....., | |
130 * = 2s + s*R | |
131 * We use a special Reme algorithm on [0,0.1716] to generate | |
132 * a polynomial of degree 14 to approximate R The maximum error | |
133 * of this polynomial approximation is bounded by 2**-58.45. In | |
134 * other words, | |
135 * 2 4 6 8 10 12 14 | |
136 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s | |
137 * (the values of Lg1 to Lg7 are listed in the program) | |
138 * and | |
139 * | 2 14 | -58.45 | |
140 * | Lg1*s +...+Lg7*s - R(z) | <= 2 | |
141 * | | | |
142 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. | |
143 * In order to guarantee error in log below 1ulp, we compute log | |
144 * by | |
145 * log(1+f) = f - s*(f - R) (if f is not too large) | |
146 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) | |
147 * | |
148 * 3. Finally, log(x) = k*ln2 + log(1+f). | |
149 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) | |
150 * Here ln2 is split into two floating point number: | |
151 * ln2_hi + ln2_lo, | |
152 * where n*ln2_hi is always exact for |n| < 2000. | |
153 * | |
154 * Special cases: | |
155 * log(x) is NaN with signal if x < 0 (including -INF) ; | |
156 * log(+INF) is +INF; log(0) is -INF with signal; | |
157 * log(NaN) is that NaN with no signal. | |
158 * | |
159 * Accuracy: | |
160 * according to an error analysis, the error is always less than | |
161 * 1 ulp (unit in the last place). | |
162 * | |
163 * Constants: | |
164 * The hexadecimal values are the intended ones for the following | |
165 * constants. The decimal values may be used, provided that the | |
166 * compiler will convert from decimal to binary accurately enough | |
167 * to produce the hexadecimal values shown. | |
168 */ | |
169 | |
170 static const double | |
171 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ | |
172 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ | |
173 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ | |
174 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ | |
175 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ | |
176 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ | |
177 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ | |
178 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ | |
179 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ | |
180 | |
181 static double zero = 0.0; | |
182 | |
183 static double __ieee754_log(double x) { | |
184 double hfsq,f,s,z,R,w,t1,t2,dk; | |
185 int k,hx,i,j; | |
186 unsigned lx; | |
187 | |
188 hx = __HI(x); /* high word of x */ | |
189 lx = __LO(x); /* low word of x */ | |
190 | |
191 k=0; | |
192 if (hx < 0x00100000) { /* x < 2**-1022 */ | |
193 if (((hx&0x7fffffff)|lx)==0) | |
194 return -two54/zero; /* log(+-0)=-inf */ | |
195 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ | |
196 k -= 54; x *= two54; /* subnormal number, scale up x */ | |
197 hx = __HI(x); /* high word of x */ | |
198 } | |
199 if (hx >= 0x7ff00000) return x+x; | |
200 k += (hx>>20)-1023; | |
201 hx &= 0x000fffff; | |
202 i = (hx+0x95f64)&0x100000; | |
203 __HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */ | |
204 k += (i>>20); | |
205 f = x-1.0; | |
206 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ | |
207 if(f==zero) { | |
208 if (k==0) return zero; | |
209 else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;} | |
210 } | |
211 R = f*f*(0.5-0.33333333333333333*f); | |
212 if(k==0) return f-R; else {dk=(double)k; | |
213 return dk*ln2_hi-((R-dk*ln2_lo)-f);} | |
214 } | |
215 s = f/(2.0+f); | |
216 dk = (double)k; | |
217 z = s*s; | |
218 i = hx-0x6147a; | |
219 w = z*z; | |
220 j = 0x6b851-hx; | |
221 t1= w*(Lg2+w*(Lg4+w*Lg6)); | |
222 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); | |
223 i |= j; | |
224 R = t2+t1; | |
225 if(i>0) { | |
226 hfsq=0.5*f*f; | |
227 if(k==0) return f-(hfsq-s*(hfsq+R)); else | |
228 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); | |
229 } else { | |
230 if(k==0) return f-s*(f-R); else | |
231 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); | |
232 } | |
233 } | |
234 | |
235 JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x)) | |
236 return __ieee754_log(x); | |
237 JRT_END | |
238 | |
239 /* __ieee754_log10(x) | |
240 * Return the base 10 logarithm of x | |
241 * | |
242 * Method : | |
243 * Let log10_2hi = leading 40 bits of log10(2) and | |
244 * log10_2lo = log10(2) - log10_2hi, | |
245 * ivln10 = 1/log(10) rounded. | |
246 * Then | |
247 * n = ilogb(x), | |
248 * if(n<0) n = n+1; | |
249 * x = scalbn(x,-n); | |
250 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) | |
251 * | |
252 * Note 1: | |
253 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding | |
254 * mode must set to Round-to-Nearest. | |
255 * Note 2: | |
256 * [1/log(10)] rounded to 53 bits has error .198 ulps; | |
257 * log10 is monotonic at all binary break points. | |
258 * | |
259 * Special cases: | |
260 * log10(x) is NaN with signal if x < 0; | |
261 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; | |
262 * log10(NaN) is that NaN with no signal; | |
263 * log10(10**N) = N for N=0,1,...,22. | |
264 * | |
265 * Constants: | |
266 * The hexadecimal values are the intended ones for the following constants. | |
267 * The decimal values may be used, provided that the compiler will convert | |
268 * from decimal to binary accurately enough to produce the hexadecimal values | |
269 * shown. | |
270 */ | |
271 | |
272 static const double | |
273 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ | |
274 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ | |
275 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ | |
276 | |
277 static double __ieee754_log10(double x) { | |
278 double y,z; | |
279 int i,k,hx; | |
280 unsigned lx; | |
281 | |
282 hx = __HI(x); /* high word of x */ | |
283 lx = __LO(x); /* low word of x */ | |
284 | |
285 k=0; | |
286 if (hx < 0x00100000) { /* x < 2**-1022 */ | |
287 if (((hx&0x7fffffff)|lx)==0) | |
288 return -two54/zero; /* log(+-0)=-inf */ | |
289 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ | |
290 k -= 54; x *= two54; /* subnormal number, scale up x */ | |
291 hx = __HI(x); /* high word of x */ | |
292 } | |
293 if (hx >= 0x7ff00000) return x+x; | |
294 k += (hx>>20)-1023; | |
295 i = ((unsigned)k&0x80000000)>>31; | |
296 hx = (hx&0x000fffff)|((0x3ff-i)<<20); | |
297 y = (double)(k+i); | |
298 __HI(x) = hx; | |
299 z = y*log10_2lo + ivln10*__ieee754_log(x); | |
300 return z+y*log10_2hi; | |
301 } | |
302 | |
303 JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x)) | |
304 return __ieee754_log10(x); | |
305 JRT_END | |
306 | |
307 | |
308 /* __ieee754_exp(x) | |
309 * Returns the exponential of x. | |
310 * | |
311 * Method | |
312 * 1. Argument reduction: | |
313 * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. | |
314 * Given x, find r and integer k such that | |
315 * | |
316 * x = k*ln2 + r, |r| <= 0.5*ln2. | |
317 * | |
318 * Here r will be represented as r = hi-lo for better | |
319 * accuracy. | |
320 * | |
321 * 2. Approximation of exp(r) by a special rational function on | |
322 * the interval [0,0.34658]: | |
323 * Write | |
324 * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... | |
325 * We use a special Reme algorithm on [0,0.34658] to generate | |
326 * a polynomial of degree 5 to approximate R. The maximum error | |
327 * of this polynomial approximation is bounded by 2**-59. In | |
328 * other words, | |
329 * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 | |
330 * (where z=r*r, and the values of P1 to P5 are listed below) | |
331 * and | |
332 * | 5 | -59 | |
333 * | 2.0+P1*z+...+P5*z - R(z) | <= 2 | |
334 * | | | |
335 * The computation of exp(r) thus becomes | |
336 * 2*r | |
337 * exp(r) = 1 + ------- | |
338 * R - r | |
339 * r*R1(r) | |
340 * = 1 + r + ----------- (for better accuracy) | |
341 * 2 - R1(r) | |
342 * where | |
343 * 2 4 10 | |
344 * R1(r) = r - (P1*r + P2*r + ... + P5*r ). | |
345 * | |
346 * 3. Scale back to obtain exp(x): | |
347 * From step 1, we have | |
348 * exp(x) = 2^k * exp(r) | |
349 * | |
350 * Special cases: | |
351 * exp(INF) is INF, exp(NaN) is NaN; | |
352 * exp(-INF) is 0, and | |
353 * for finite argument, only exp(0)=1 is exact. | |
354 * | |
355 * Accuracy: | |
356 * according to an error analysis, the error is always less than | |
357 * 1 ulp (unit in the last place). | |
358 * | |
359 * Misc. info. | |
360 * For IEEE double | |
361 * if x > 7.09782712893383973096e+02 then exp(x) overflow | |
362 * if x < -7.45133219101941108420e+02 then exp(x) underflow | |
363 * | |
364 * Constants: | |
365 * The hexadecimal values are the intended ones for the following | |
366 * constants. The decimal values may be used, provided that the | |
367 * compiler will convert from decimal to binary accurately enough | |
368 * to produce the hexadecimal values shown. | |
369 */ | |
370 | |
371 static const double | |
372 one = 1.0, | |
373 halF[2] = {0.5,-0.5,}, | |
374 twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ | |
375 o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ | |
376 u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ | |
377 ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ | |
378 -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ | |
379 ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ | |
380 -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ | |
381 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ | |
382 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ | |
383 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ | |
384 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ | |
385 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ | |
386 P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ | |
387 | |
388 static double __ieee754_exp(double x) { | |
389 double y,hi=0,lo=0,c,t; | |
390 int k=0,xsb; | |
391 unsigned hx; | |
392 | |
393 hx = __HI(x); /* high word of x */ | |
394 xsb = (hx>>31)&1; /* sign bit of x */ | |
395 hx &= 0x7fffffff; /* high word of |x| */ | |
396 | |
397 /* filter out non-finite argument */ | |
398 if(hx >= 0x40862E42) { /* if |x|>=709.78... */ | |
399 if(hx>=0x7ff00000) { | |
400 if(((hx&0xfffff)|__LO(x))!=0) | |
401 return x+x; /* NaN */ | |
402 else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ | |
403 } | |
404 if(x > o_threshold) return hugeX*hugeX; /* overflow */ | |
405 if(x < u_threshold) return twom1000*twom1000; /* underflow */ | |
406 } | |
407 | |
408 /* argument reduction */ | |
409 if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ | |
410 if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ | |
411 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; | |
412 } else { | |
413 k = (int)(invln2*x+halF[xsb]); | |
414 t = k; | |
415 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ | |
416 lo = t*ln2LO[0]; | |
417 } | |
418 x = hi - lo; | |
419 } | |
420 else if(hx < 0x3e300000) { /* when |x|<2**-28 */ | |
421 if(hugeX+x>one) return one+x;/* trigger inexact */ | |
422 } | |
423 else k = 0; | |
424 | |
425 /* x is now in primary range */ | |
426 t = x*x; | |
427 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); | |
428 if(k==0) return one-((x*c)/(c-2.0)-x); | |
429 else y = one-((lo-(x*c)/(2.0-c))-hi); | |
430 if(k >= -1021) { | |
431 __HI(y) += (k<<20); /* add k to y's exponent */ | |
432 return y; | |
433 } else { | |
434 __HI(y) += ((k+1000)<<20);/* add k to y's exponent */ | |
435 return y*twom1000; | |
436 } | |
437 } | |
438 | |
439 JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x)) | |
440 return __ieee754_exp(x); | |
441 JRT_END | |
442 | |
443 /* __ieee754_pow(x,y) return x**y | |
444 * | |
445 * n | |
446 * Method: Let x = 2 * (1+f) | |
447 * 1. Compute and return log2(x) in two pieces: | |
448 * log2(x) = w1 + w2, | |
449 * where w1 has 53-24 = 29 bit trailing zeros. | |
450 * 2. Perform y*log2(x) = n+y' by simulating muti-precision | |
451 * arithmetic, where |y'|<=0.5. | |
452 * 3. Return x**y = 2**n*exp(y'*log2) | |
453 * | |
454 * Special cases: | |
455 * 1. (anything) ** 0 is 1 | |
456 * 2. (anything) ** 1 is itself | |
457 * 3. (anything) ** NAN is NAN | |
458 * 4. NAN ** (anything except 0) is NAN | |
459 * 5. +-(|x| > 1) ** +INF is +INF | |
460 * 6. +-(|x| > 1) ** -INF is +0 | |
461 * 7. +-(|x| < 1) ** +INF is +0 | |
462 * 8. +-(|x| < 1) ** -INF is +INF | |
463 * 9. +-1 ** +-INF is NAN | |
464 * 10. +0 ** (+anything except 0, NAN) is +0 | |
465 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 | |
466 * 12. +0 ** (-anything except 0, NAN) is +INF | |
467 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF | |
468 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) | |
469 * 15. +INF ** (+anything except 0,NAN) is +INF | |
470 * 16. +INF ** (-anything except 0,NAN) is +0 | |
471 * 17. -INF ** (anything) = -0 ** (-anything) | |
472 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) | |
473 * 19. (-anything except 0 and inf) ** (non-integer) is NAN | |
474 * | |
475 * Accuracy: | |
476 * pow(x,y) returns x**y nearly rounded. In particular | |
477 * pow(integer,integer) | |
478 * always returns the correct integer provided it is | |
479 * representable. | |
480 * | |
481 * Constants : | |
482 * The hexadecimal values are the intended ones for the following | |
483 * constants. The decimal values may be used, provided that the | |
484 * compiler will convert from decimal to binary accurately enough | |
485 * to produce the hexadecimal values shown. | |
486 */ | |
487 | |
488 static const double | |
489 bp[] = {1.0, 1.5,}, | |
490 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ | |
491 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ | |
492 zeroX = 0.0, | |
493 two = 2.0, | |
494 two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ | |
495 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ | |
496 L1X = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ | |
497 L2X = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ | |
498 L3X = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ | |
499 L4X = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ | |
500 L5X = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ | |
501 L6X = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ | |
502 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ | |
503 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ | |
504 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ | |
505 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ | |
506 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ | |
507 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ | |
508 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ | |
509 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ | |
510 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ | |
511 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ | |
512 | |
513 double __ieee754_pow(double x, double y) { | |
514 double z,ax,z_h,z_l,p_h,p_l; | |
515 double y1,t1,t2,r,s,t,u,v,w; | |
516 int i0,i1,i,j,k,yisint,n; | |
517 int hx,hy,ix,iy; | |
518 unsigned lx,ly; | |
519 | |
520 i0 = ((*(int*)&one)>>29)^1; i1=1-i0; | |
521 hx = __HI(x); lx = __LO(x); | |
522 hy = __HI(y); ly = __LO(y); | |
523 ix = hx&0x7fffffff; iy = hy&0x7fffffff; | |
524 | |
525 /* y==zero: x**0 = 1 */ | |
526 if((iy|ly)==0) return one; | |
527 | |
528 /* +-NaN return x+y */ | |
529 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || | |
530 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) | |
531 return x+y; | |
532 | |
533 /* determine if y is an odd int when x < 0 | |
534 * yisint = 0 ... y is not an integer | |
535 * yisint = 1 ... y is an odd int | |
536 * yisint = 2 ... y is an even int | |
537 */ | |
538 yisint = 0; | |
539 if(hx<0) { | |
540 if(iy>=0x43400000) yisint = 2; /* even integer y */ | |
541 else if(iy>=0x3ff00000) { | |
542 k = (iy>>20)-0x3ff; /* exponent */ | |
543 if(k>20) { | |
544 j = ly>>(52-k); | |
545 if((unsigned)(j<<(52-k))==ly) yisint = 2-(j&1); | |
546 } else if(ly==0) { | |
547 j = iy>>(20-k); | |
548 if((j<<(20-k))==iy) yisint = 2-(j&1); | |
549 } | |
550 } | |
551 } | |
552 | |
553 /* special value of y */ | |
554 if(ly==0) { | |
555 if (iy==0x7ff00000) { /* y is +-inf */ | |
556 if(((ix-0x3ff00000)|lx)==0) | |
557 return y - y; /* inf**+-1 is NaN */ | |
558 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ | |
559 return (hy>=0)? y: zeroX; | |
560 else /* (|x|<1)**-,+inf = inf,0 */ | |
561 return (hy<0)?-y: zeroX; | |
562 } | |
563 if(iy==0x3ff00000) { /* y is +-1 */ | |
564 if(hy<0) return one/x; else return x; | |
565 } | |
566 if(hy==0x40000000) return x*x; /* y is 2 */ | |
567 if(hy==0x3fe00000) { /* y is 0.5 */ | |
568 if(hx>=0) /* x >= +0 */ | |
569 return sqrt(x); | |
570 } | |
571 } | |
572 | |
573 ax = fabsd(x); | |
574 /* special value of x */ | |
575 if(lx==0) { | |
576 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ | |
577 z = ax; /*x is +-0,+-inf,+-1*/ | |
578 if(hy<0) z = one/z; /* z = (1/|x|) */ | |
579 if(hx<0) { | |
580 if(((ix-0x3ff00000)|yisint)==0) { | |
1681
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581 #ifdef CAN_USE_NAN_DEFINE |
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582 z = NAN; |
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583 #else |
0 | 584 z = (z-z)/(z-z); /* (-1)**non-int is NaN */ |
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585 #endif |
0 | 586 } else if(yisint==1) |
587 z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */ | |
588 } | |
589 return z; | |
590 } | |
591 } | |
592 | |
593 n = (hx>>31)+1; | |
594 | |
595 /* (x<0)**(non-int) is NaN */ | |
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596 if((n|yisint)==0) |
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597 #ifdef CAN_USE_NAN_DEFINE |
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598 return NAN; |
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599 #else |
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600 return (x-x)/(x-x); |
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601 #endif |
0 | 602 |
603 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ | |
604 if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ | |
605 | |
606 /* |y| is huge */ | |
607 if(iy>0x41e00000) { /* if |y| > 2**31 */ | |
608 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ | |
609 if(ix<=0x3fefffff) return (hy<0)? hugeX*hugeX:tiny*tiny; | |
610 if(ix>=0x3ff00000) return (hy>0)? hugeX*hugeX:tiny*tiny; | |
611 } | |
612 /* over/underflow if x is not close to one */ | |
613 if(ix<0x3fefffff) return (hy<0)? s*hugeX*hugeX:s*tiny*tiny; | |
614 if(ix>0x3ff00000) return (hy>0)? s*hugeX*hugeX:s*tiny*tiny; | |
615 /* now |1-x| is tiny <= 2**-20, suffice to compute | |
616 log(x) by x-x^2/2+x^3/3-x^4/4 */ | |
617 t = ax-one; /* t has 20 trailing zeros */ | |
618 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); | |
619 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ | |
620 v = t*ivln2_l-w*ivln2; | |
621 t1 = u+v; | |
622 __LO(t1) = 0; | |
623 t2 = v-(t1-u); | |
624 } else { | |
625 double ss,s2,s_h,s_l,t_h,t_l; | |
626 n = 0; | |
627 /* take care subnormal number */ | |
628 if(ix<0x00100000) | |
629 {ax *= two53; n -= 53; ix = __HI(ax); } | |
630 n += ((ix)>>20)-0x3ff; | |
631 j = ix&0x000fffff; | |
632 /* determine interval */ | |
633 ix = j|0x3ff00000; /* normalize ix */ | |
634 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ | |
635 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ | |
636 else {k=0;n+=1;ix -= 0x00100000;} | |
637 __HI(ax) = ix; | |
638 | |
639 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ | |
640 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ | |
641 v = one/(ax+bp[k]); | |
642 ss = u*v; | |
643 s_h = ss; | |
644 __LO(s_h) = 0; | |
645 /* t_h=ax+bp[k] High */ | |
646 t_h = zeroX; | |
647 __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18); | |
648 t_l = ax - (t_h-bp[k]); | |
649 s_l = v*((u-s_h*t_h)-s_h*t_l); | |
650 /* compute log(ax) */ | |
651 s2 = ss*ss; | |
652 r = s2*s2*(L1X+s2*(L2X+s2*(L3X+s2*(L4X+s2*(L5X+s2*L6X))))); | |
653 r += s_l*(s_h+ss); | |
654 s2 = s_h*s_h; | |
655 t_h = 3.0+s2+r; | |
656 __LO(t_h) = 0; | |
657 t_l = r-((t_h-3.0)-s2); | |
658 /* u+v = ss*(1+...) */ | |
659 u = s_h*t_h; | |
660 v = s_l*t_h+t_l*ss; | |
661 /* 2/(3log2)*(ss+...) */ | |
662 p_h = u+v; | |
663 __LO(p_h) = 0; | |
664 p_l = v-(p_h-u); | |
665 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ | |
666 z_l = cp_l*p_h+p_l*cp+dp_l[k]; | |
667 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ | |
668 t = (double)n; | |
669 t1 = (((z_h+z_l)+dp_h[k])+t); | |
670 __LO(t1) = 0; | |
671 t2 = z_l-(((t1-t)-dp_h[k])-z_h); | |
672 } | |
673 | |
674 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ | |
675 y1 = y; | |
676 __LO(y1) = 0; | |
677 p_l = (y-y1)*t1+y*t2; | |
678 p_h = y1*t1; | |
679 z = p_l+p_h; | |
680 j = __HI(z); | |
681 i = __LO(z); | |
682 if (j>=0x40900000) { /* z >= 1024 */ | |
683 if(((j-0x40900000)|i)!=0) /* if z > 1024 */ | |
684 return s*hugeX*hugeX; /* overflow */ | |
685 else { | |
686 if(p_l+ovt>z-p_h) return s*hugeX*hugeX; /* overflow */ | |
687 } | |
688 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ | |
689 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ | |
690 return s*tiny*tiny; /* underflow */ | |
691 else { | |
692 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ | |
693 } | |
694 } | |
695 /* | |
696 * compute 2**(p_h+p_l) | |
697 */ | |
698 i = j&0x7fffffff; | |
699 k = (i>>20)-0x3ff; | |
700 n = 0; | |
701 if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ | |
702 n = j+(0x00100000>>(k+1)); | |
703 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ | |
704 t = zeroX; | |
705 __HI(t) = (n&~(0x000fffff>>k)); | |
706 n = ((n&0x000fffff)|0x00100000)>>(20-k); | |
707 if(j<0) n = -n; | |
708 p_h -= t; | |
709 } | |
710 t = p_l+p_h; | |
711 __LO(t) = 0; | |
712 u = t*lg2_h; | |
713 v = (p_l-(t-p_h))*lg2+t*lg2_l; | |
714 z = u+v; | |
715 w = v-(z-u); | |
716 t = z*z; | |
717 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); | |
718 r = (z*t1)/(t1-two)-(w+z*w); | |
719 z = one-(r-z); | |
720 j = __HI(z); | |
721 j += (n<<20); | |
722 if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ | |
723 else __HI(z) += (n<<20); | |
724 return s*z; | |
725 } | |
726 | |
727 | |
728 JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y)) | |
729 return __ieee754_pow(x, y); | |
730 JRT_END | |
731 | |
732 #ifdef WIN32 | |
733 # pragma optimize ( "", on ) | |
734 #endif |