Thu, 22 Aug 2013 09:39:54 -0700
8023033: PPC64 (part 13): basic changes for AIX
Summary: Added AIX includes alpha-sorted before BSD. Fix compilation issues with xlC in shared code. Basic shared platform dependend adaption (vm_version etc.).
Reviewed-by: kvn, dholmes, stefank
1 /*
2 * Copyright (c) 2005, 2010, 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.
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 *
19 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
20 * or visit www.oracle.com if you need additional information or have any
21 * questions.
22 *
23 */
25 #include "precompiled.hpp"
26 #include "prims/jni.h"
27 #include "runtime/interfaceSupport.hpp"
28 #include "runtime/sharedRuntime.hpp"
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.
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
46 #include <math.h>
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
59 #if !defined(AIX)
60 double copysign(double x, double y) {
61 __HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000);
62 return x;
63 }
64 #endif
66 /*
67 * ====================================================
68 * Copyright (c) 1998 Oracle and/or its affiliates. All rights reserved.
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 */
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 */
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;
90 #if !defined(AIX)
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 }
117 #endif
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 */
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 */
181 static double zero = 0.0;
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;
188 hx = __HI(x); /* high word of x */
189 lx = __LO(x); /* low word of x */
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 }
235 JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x))
236 return __ieee754_log(x);
237 JRT_END
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 */
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 */
277 static double __ieee754_log10(double x) {
278 double y,z;
279 int i,k,hx;
280 unsigned lx;
282 hx = __HI(x); /* high word of x */
283 lx = __LO(x); /* low word of x */
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 }
303 JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x))
304 return __ieee754_log10(x);
305 JRT_END
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 */
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 */
388 static double __ieee754_exp(double x) {
389 double y,hi=0,lo=0,c,t;
390 int k=0,xsb;
391 unsigned hx;
393 hx = __HI(x); /* high word of x */
394 xsb = (hx>>31)&1; /* sign bit of x */
395 hx &= 0x7fffffff; /* high word of |x| */
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 }
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;
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 }
439 JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x))
440 return __ieee754_exp(x);
441 JRT_END
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 */
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*/
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;
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;
525 /* y==zero: x**0 = 1 */
526 if((iy|ly)==0) return one;
528 /* +-NaN return x+y */
529 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
530 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
531 return x+y;
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 }
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 }
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) {
581 #ifdef CAN_USE_NAN_DEFINE
582 z = NAN;
583 #else
584 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
585 #endif
586 } else if(yisint==1)
587 z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */
588 }
589 return z;
590 }
591 }
593 n = (hx>>31)+1;
595 /* (x<0)**(non-int) is NaN */
596 if((n|yisint)==0)
597 #ifdef CAN_USE_NAN_DEFINE
598 return NAN;
599 #else
600 return (x-x)/(x-x);
601 #endif
603 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
604 if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
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;
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 }
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 }
728 JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y))
729 return __ieee754_pow(x, y);
730 JRT_END
732 #ifdef WIN32
733 # pragma optimize ( "", on )
734 #endif