1 /*
2 * Copyright (c) 2005, 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 */
24
25 #include "incls/_precompiled.incl"
26 #include "incls/_sharedRuntimeTrans.cpp.incl"
27
28 // This file contains copies of the fdlibm routines used by
29 // StrictMath. It turns out that it is almost always required to use
30 // these runtime routines; the Intel CPU doesn't meet the Java
31 // specification for sin/cos outside a certain limited argument range,
32 // and the SPARC CPU doesn't appear to have sin/cos instructions. It
33 // also turns out that avoiding the indirect call through function
34 // pointer out to libjava.so in SharedRuntime speeds these routines up
35 // by roughly 15% on both Win32/x86 and Solaris/SPARC.
36
37 // Enabling optimizations in this file causes incorrect code to be
38 // generated; can not figure out how to turn down optimization for one
39 // file in the IDE on Windows
40 #ifdef WIN32
41 # pragma optimize ( "", off )
42 #endif
43
44 #include <math.h>
45
46 // VM_LITTLE_ENDIAN is #defined appropriately in the Makefiles
47 // [jk] this is not 100% correct because the float word order may different
48 // from the byte order (e.g. on ARM)
49 #ifdef VM_LITTLE_ENDIAN
50 # define __HI(x) *(1+(int*)&x)
51 # define __LO(x) *(int*)&x
52 #else
53 # define __HI(x) *(int*)&x
54 # define __LO(x) *(1+(int*)&x)
55 #endif
56
57 double copysign(double x, double y) {
58 __HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000);
59 return x;
60 }
61
62 /*
63 * ====================================================
64 * Copyright (c) 1998 Oracle and/or its affiliates. All rights reserved.
65 *
66 * Developed at SunSoft, a Sun Microsystems, Inc. business.
67 * Permission to use, copy, modify, and distribute this
68 * software is freely granted, provided that this notice
69 * is preserved.
70 * ====================================================
71 */
72
73 /*
74 * scalbn (double x, int n)
75 * scalbn(x,n) returns x* 2**n computed by exponent
76 * manipulation rather than by actually performing an
77 * exponentiation or a multiplication.
78 */
79
80 static const double
81 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
82 twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
83 hugeX = 1.0e+300,
84 tiny = 1.0e-300;
85
86 double scalbn (double x, int n) {
87 int k,hx,lx;
88 hx = __HI(x);
89 lx = __LO(x);
90 k = (hx&0x7ff00000)>>20; /* extract exponent */
91 if (k==0) { /* 0 or subnormal x */
92 if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
93 x *= two54;
94 hx = __HI(x);
95 k = ((hx&0x7ff00000)>>20) - 54;
96 if (n< -50000) return tiny*x; /*underflow*/
97 }
98 if (k==0x7ff) return x+x; /* NaN or Inf */
99 k = k+n;
100 if (k > 0x7fe) return hugeX*copysign(hugeX,x); /* overflow */
101 if (k > 0) /* normal result */
102 {__HI(x) = (hx&0x800fffff)|(k<<20); return x;}
103 if (k <= -54) {
104 if (n > 50000) /* in case integer overflow in n+k */
105 return hugeX*copysign(hugeX,x); /*overflow*/
106 else return tiny*copysign(tiny,x); /*underflow*/
107 }
108 k += 54; /* subnormal result */
109 __HI(x) = (hx&0x800fffff)|(k<<20);
110 return x*twom54;
111 }
112
113 /* __ieee754_log(x)
114 * Return the logrithm of x
115 *
116 * Method :
117 * 1. Argument Reduction: find k and f such that
118 * x = 2^k * (1+f),
119 * where sqrt(2)/2 < 1+f < sqrt(2) .
120 *
121 * 2. Approximation of log(1+f).
122 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
123 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
124 * = 2s + s*R
125 * We use a special Reme algorithm on [0,0.1716] to generate
126 * a polynomial of degree 14 to approximate R The maximum error
127 * of this polynomial approximation is bounded by 2**-58.45. In
128 * other words,
129 * 2 4 6 8 10 12 14
130 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
131 * (the values of Lg1 to Lg7 are listed in the program)
132 * and
133 * | 2 14 | -58.45
134 * | Lg1*s +...+Lg7*s - R(z) | <= 2
135 * | |
136 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
137 * In order to guarantee error in log below 1ulp, we compute log
138 * by
139 * log(1+f) = f - s*(f - R) (if f is not too large)
140 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
141 *
142 * 3. Finally, log(x) = k*ln2 + log(1+f).
143 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
144 * Here ln2 is split into two floating point number:
145 * ln2_hi + ln2_lo,
146 * where n*ln2_hi is always exact for |n| < 2000.
147 *
148 * Special cases:
149 * log(x) is NaN with signal if x < 0 (including -INF) ;
150 * log(+INF) is +INF; log(0) is -INF with signal;
151 * log(NaN) is that NaN with no signal.
152 *
153 * Accuracy:
154 * according to an error analysis, the error is always less than
155 * 1 ulp (unit in the last place).
156 *
157 * Constants:
158 * The hexadecimal values are the intended ones for the following
159 * constants. The decimal values may be used, provided that the
160 * compiler will convert from decimal to binary accurately enough
161 * to produce the hexadecimal values shown.
162 */
163
164 static const double
165 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
166 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
167 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
168 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
169 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
170 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
171 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
172 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
173 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
174
175 static double zero = 0.0;
176
177 static double __ieee754_log(double x) {
178 double hfsq,f,s,z,R,w,t1,t2,dk;
179 int k,hx,i,j;
180 unsigned lx;
181
182 hx = __HI(x); /* high word of x */
183 lx = __LO(x); /* low word of x */
184
185 k=0;
186 if (hx < 0x00100000) { /* x < 2**-1022 */
187 if (((hx&0x7fffffff)|lx)==0)
188 return -two54/zero; /* log(+-0)=-inf */
189 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
190 k -= 54; x *= two54; /* subnormal number, scale up x */
191 hx = __HI(x); /* high word of x */
192 }
193 if (hx >= 0x7ff00000) return x+x;
194 k += (hx>>20)-1023;
195 hx &= 0x000fffff;
196 i = (hx+0x95f64)&0x100000;
197 __HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
198 k += (i>>20);
199 f = x-1.0;
200 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
201 if(f==zero) {
202 if (k==0) return zero;
203 else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;}
204 }
205 R = f*f*(0.5-0.33333333333333333*f);
206 if(k==0) return f-R; else {dk=(double)k;
207 return dk*ln2_hi-((R-dk*ln2_lo)-f);}
208 }
209 s = f/(2.0+f);
210 dk = (double)k;
211 z = s*s;
212 i = hx-0x6147a;
213 w = z*z;
214 j = 0x6b851-hx;
215 t1= w*(Lg2+w*(Lg4+w*Lg6));
216 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
217 i |= j;
218 R = t2+t1;
219 if(i>0) {
220 hfsq=0.5*f*f;
221 if(k==0) return f-(hfsq-s*(hfsq+R)); else
222 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
223 } else {
224 if(k==0) return f-s*(f-R); else
225 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
226 }
227 }
228
229 JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x))
230 return __ieee754_log(x);
231 JRT_END
232
233 /* __ieee754_log10(x)
234 * Return the base 10 logarithm of x
235 *
236 * Method :
237 * Let log10_2hi = leading 40 bits of log10(2) and
238 * log10_2lo = log10(2) - log10_2hi,
239 * ivln10 = 1/log(10) rounded.
240 * Then
241 * n = ilogb(x),
242 * if(n<0) n = n+1;
243 * x = scalbn(x,-n);
244 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
245 *
246 * Note 1:
247 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
248 * mode must set to Round-to-Nearest.
249 * Note 2:
250 * [1/log(10)] rounded to 53 bits has error .198 ulps;
251 * log10 is monotonic at all binary break points.
252 *
253 * Special cases:
254 * log10(x) is NaN with signal if x < 0;
255 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
256 * log10(NaN) is that NaN with no signal;
257 * log10(10**N) = N for N=0,1,...,22.
258 *
259 * Constants:
260 * The hexadecimal values are the intended ones for the following constants.
261 * The decimal values may be used, provided that the compiler will convert
262 * from decimal to binary accurately enough to produce the hexadecimal values
263 * shown.
264 */
265
266 static const double
267 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
268 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
269 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
270
271 static double __ieee754_log10(double x) {
272 double y,z;
273 int i,k,hx;
274 unsigned lx;
275
276 hx = __HI(x); /* high word of x */
277 lx = __LO(x); /* low word of x */
278
279 k=0;
280 if (hx < 0x00100000) { /* x < 2**-1022 */
281 if (((hx&0x7fffffff)|lx)==0)
282 return -two54/zero; /* log(+-0)=-inf */
283 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
284 k -= 54; x *= two54; /* subnormal number, scale up x */
285 hx = __HI(x); /* high word of x */
286 }
287 if (hx >= 0x7ff00000) return x+x;
288 k += (hx>>20)-1023;
289 i = ((unsigned)k&0x80000000)>>31;
290 hx = (hx&0x000fffff)|((0x3ff-i)<<20);
291 y = (double)(k+i);
292 __HI(x) = hx;
293 z = y*log10_2lo + ivln10*__ieee754_log(x);
294 return z+y*log10_2hi;
295 }
296
297 JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x))
298 return __ieee754_log10(x);
299 JRT_END
300
301
302 /* __ieee754_exp(x)
303 * Returns the exponential of x.
304 *
305 * Method
306 * 1. Argument reduction:
307 * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
308 * Given x, find r and integer k such that
309 *
310 * x = k*ln2 + r, |r| <= 0.5*ln2.
311 *
312 * Here r will be represented as r = hi-lo for better
313 * accuracy.
314 *
315 * 2. Approximation of exp(r) by a special rational function on
316 * the interval [0,0.34658]:
317 * Write
318 * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
319 * We use a special Reme algorithm on [0,0.34658] to generate
320 * a polynomial of degree 5 to approximate R. The maximum error
321 * of this polynomial approximation is bounded by 2**-59. In
322 * other words,
323 * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
324 * (where z=r*r, and the values of P1 to P5 are listed below)
325 * and
326 * | 5 | -59
327 * | 2.0+P1*z+...+P5*z - R(z) | <= 2
328 * | |
329 * The computation of exp(r) thus becomes
330 * 2*r
331 * exp(r) = 1 + -------
332 * R - r
333 * r*R1(r)
334 * = 1 + r + ----------- (for better accuracy)
335 * 2 - R1(r)
336 * where
337 * 2 4 10
338 * R1(r) = r - (P1*r + P2*r + ... + P5*r ).
339 *
340 * 3. Scale back to obtain exp(x):
341 * From step 1, we have
342 * exp(x) = 2^k * exp(r)
343 *
344 * Special cases:
345 * exp(INF) is INF, exp(NaN) is NaN;
346 * exp(-INF) is 0, and
347 * for finite argument, only exp(0)=1 is exact.
348 *
349 * Accuracy:
350 * according to an error analysis, the error is always less than
351 * 1 ulp (unit in the last place).
352 *
353 * Misc. info.
354 * For IEEE double
355 * if x > 7.09782712893383973096e+02 then exp(x) overflow
356 * if x < -7.45133219101941108420e+02 then exp(x) underflow
357 *
358 * Constants:
359 * The hexadecimal values are the intended ones for the following
360 * constants. The decimal values may be used, provided that the
361 * compiler will convert from decimal to binary accurately enough
362 * to produce the hexadecimal values shown.
363 */
364
365 static const double
366 one = 1.0,
367 halF[2] = {0.5,-0.5,},
368 twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
369 o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
370 u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
371 ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
372 -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
373 ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
374 -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
375 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
376 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
377 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
378 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
379 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
380 P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
381
382 static double __ieee754_exp(double x) {
383 double y,hi=0,lo=0,c,t;
384 int k=0,xsb;
385 unsigned hx;
386
387 hx = __HI(x); /* high word of x */
388 xsb = (hx>>31)&1; /* sign bit of x */
389 hx &= 0x7fffffff; /* high word of |x| */
390
391 /* filter out non-finite argument */
392 if(hx >= 0x40862E42) { /* if |x|>=709.78... */
393 if(hx>=0x7ff00000) {
394 if(((hx&0xfffff)|__LO(x))!=0)
395 return x+x; /* NaN */
396 else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
397 }
398 if(x > o_threshold) return hugeX*hugeX; /* overflow */
399 if(x < u_threshold) return twom1000*twom1000; /* underflow */
400 }
401
402 /* argument reduction */
403 if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
404 if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
405 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
406 } else {
407 k = (int)(invln2*x+halF[xsb]);
408 t = k;
409 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
410 lo = t*ln2LO[0];
411 }
412 x = hi - lo;
413 }
414 else if(hx < 0x3e300000) { /* when |x|<2**-28 */
415 if(hugeX+x>one) return one+x;/* trigger inexact */
416 }
417 else k = 0;
418
419 /* x is now in primary range */
420 t = x*x;
421 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
422 if(k==0) return one-((x*c)/(c-2.0)-x);
423 else y = one-((lo-(x*c)/(2.0-c))-hi);
424 if(k >= -1021) {
425 __HI(y) += (k<<20); /* add k to y's exponent */
426 return y;
427 } else {
428 __HI(y) += ((k+1000)<<20);/* add k to y's exponent */
429 return y*twom1000;
430 }
431 }
432
433 JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x))
434 return __ieee754_exp(x);
435 JRT_END
436
437 /* __ieee754_pow(x,y) return x**y
438 *
439 * n
440 * Method: Let x = 2 * (1+f)
441 * 1. Compute and return log2(x) in two pieces:
442 * log2(x) = w1 + w2,
443 * where w1 has 53-24 = 29 bit trailing zeros.
444 * 2. Perform y*log2(x) = n+y' by simulating muti-precision
445 * arithmetic, where |y'|<=0.5.
446 * 3. Return x**y = 2**n*exp(y'*log2)
447 *
448 * Special cases:
449 * 1. (anything) ** 0 is 1
450 * 2. (anything) ** 1 is itself
451 * 3. (anything) ** NAN is NAN
452 * 4. NAN ** (anything except 0) is NAN
453 * 5. +-(|x| > 1) ** +INF is +INF
454 * 6. +-(|x| > 1) ** -INF is +0
455 * 7. +-(|x| < 1) ** +INF is +0
456 * 8. +-(|x| < 1) ** -INF is +INF
457 * 9. +-1 ** +-INF is NAN
458 * 10. +0 ** (+anything except 0, NAN) is +0
459 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
460 * 12. +0 ** (-anything except 0, NAN) is +INF
461 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
462 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
463 * 15. +INF ** (+anything except 0,NAN) is +INF
464 * 16. +INF ** (-anything except 0,NAN) is +0
465 * 17. -INF ** (anything) = -0 ** (-anything)
466 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
467 * 19. (-anything except 0 and inf) ** (non-integer) is NAN
468 *
469 * Accuracy:
470 * pow(x,y) returns x**y nearly rounded. In particular
471 * pow(integer,integer)
472 * always returns the correct integer provided it is
473 * representable.
474 *
475 * Constants :
476 * The hexadecimal values are the intended ones for the following
477 * constants. The decimal values may be used, provided that the
478 * compiler will convert from decimal to binary accurately enough
479 * to produce the hexadecimal values shown.
480 */
481
482 static const double
483 bp[] = {1.0, 1.5,},
484 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
485 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
486 zeroX = 0.0,
487 two = 2.0,
488 two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
489 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
490 L1X = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
491 L2X = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
492 L3X = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
493 L4X = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
494 L5X = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
495 L6X = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
496 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
497 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
498 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
499 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
500 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
501 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
502 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
503 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
504 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
505 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
506
507 double __ieee754_pow(double x, double y) {
508 double z,ax,z_h,z_l,p_h,p_l;
509 double y1,t1,t2,r,s,t,u,v,w;
510 int i0,i1,i,j,k,yisint,n;
511 int hx,hy,ix,iy;
512 unsigned lx,ly;
513
514 i0 = ((*(int*)&one)>>29)^1; i1=1-i0;
515 hx = __HI(x); lx = __LO(x);
516 hy = __HI(y); ly = __LO(y);
517 ix = hx&0x7fffffff; iy = hy&0x7fffffff;
518
519 /* y==zero: x**0 = 1 */
520 if((iy|ly)==0) return one;
521
522 /* +-NaN return x+y */
523 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
524 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
525 return x+y;
526
527 /* determine if y is an odd int when x < 0
528 * yisint = 0 ... y is not an integer
529 * yisint = 1 ... y is an odd int
530 * yisint = 2 ... y is an even int
531 */
532 yisint = 0;
533 if(hx<0) {
534 if(iy>=0x43400000) yisint = 2; /* even integer y */
535 else if(iy>=0x3ff00000) {
536 k = (iy>>20)-0x3ff; /* exponent */
537 if(k>20) {
538 j = ly>>(52-k);
539 if((unsigned)(j<<(52-k))==ly) yisint = 2-(j&1);
540 } else if(ly==0) {
541 j = iy>>(20-k);
542 if((j<<(20-k))==iy) yisint = 2-(j&1);
543 }
544 }
545 }
546
547 /* special value of y */
548 if(ly==0) {
549 if (iy==0x7ff00000) { /* y is +-inf */
550 if(((ix-0x3ff00000)|lx)==0)
551 return y - y; /* inf**+-1 is NaN */
552 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
553 return (hy>=0)? y: zeroX;
554 else /* (|x|<1)**-,+inf = inf,0 */
555 return (hy<0)?-y: zeroX;
556 }
557 if(iy==0x3ff00000) { /* y is +-1 */
558 if(hy<0) return one/x; else return x;
559 }
560 if(hy==0x40000000) return x*x; /* y is 2 */
561 if(hy==0x3fe00000) { /* y is 0.5 */
562 if(hx>=0) /* x >= +0 */
563 return sqrt(x);
564 }
565 }
566
567 ax = fabsd(x);
568 /* special value of x */
569 if(lx==0) {
570 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
571 z = ax; /*x is +-0,+-inf,+-1*/
572 if(hy<0) z = one/z; /* z = (1/|x|) */
573 if(hx<0) {
574 if(((ix-0x3ff00000)|yisint)==0) {
575 #ifdef CAN_USE_NAN_DEFINE
576 z = NAN;
577 #else
578 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
579 #endif
580 } else if(yisint==1)
581 z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */
582 }
583 return z;
584 }
585 }
586
587 n = (hx>>31)+1;
588
589 /* (x<0)**(non-int) is NaN */
590 if((n|yisint)==0)
591 #ifdef CAN_USE_NAN_DEFINE
592 return NAN;
593 #else
594 return (x-x)/(x-x);
595 #endif
596
597 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
598 if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
599
600 /* |y| is huge */
601 if(iy>0x41e00000) { /* if |y| > 2**31 */
602 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
603 if(ix<=0x3fefffff) return (hy<0)? hugeX*hugeX:tiny*tiny;
604 if(ix>=0x3ff00000) return (hy>0)? hugeX*hugeX:tiny*tiny;
605 }
606 /* over/underflow if x is not close to one */
607 if(ix<0x3fefffff) return (hy<0)? s*hugeX*hugeX:s*tiny*tiny;
608 if(ix>0x3ff00000) return (hy>0)? s*hugeX*hugeX:s*tiny*tiny;
609 /* now |1-x| is tiny <= 2**-20, suffice to compute
610 log(x) by x-x^2/2+x^3/3-x^4/4 */
611 t = ax-one; /* t has 20 trailing zeros */
612 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
613 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
614 v = t*ivln2_l-w*ivln2;
615 t1 = u+v;
616 __LO(t1) = 0;
617 t2 = v-(t1-u);
618 } else {
619 double ss,s2,s_h,s_l,t_h,t_l;
620 n = 0;
621 /* take care subnormal number */
622 if(ix<0x00100000)
623 {ax *= two53; n -= 53; ix = __HI(ax); }
624 n += ((ix)>>20)-0x3ff;
625 j = ix&0x000fffff;
626 /* determine interval */
627 ix = j|0x3ff00000; /* normalize ix */
628 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
629 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
630 else {k=0;n+=1;ix -= 0x00100000;}
631 __HI(ax) = ix;
632
633 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
634 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
635 v = one/(ax+bp[k]);
636 ss = u*v;
637 s_h = ss;
638 __LO(s_h) = 0;
639 /* t_h=ax+bp[k] High */
640 t_h = zeroX;
641 __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
642 t_l = ax - (t_h-bp[k]);
643 s_l = v*((u-s_h*t_h)-s_h*t_l);
644 /* compute log(ax) */
645 s2 = ss*ss;
646 r = s2*s2*(L1X+s2*(L2X+s2*(L3X+s2*(L4X+s2*(L5X+s2*L6X)))));
647 r += s_l*(s_h+ss);
648 s2 = s_h*s_h;
649 t_h = 3.0+s2+r;
650 __LO(t_h) = 0;
651 t_l = r-((t_h-3.0)-s2);
652 /* u+v = ss*(1+...) */
653 u = s_h*t_h;
654 v = s_l*t_h+t_l*ss;
655 /* 2/(3log2)*(ss+...) */
656 p_h = u+v;
657 __LO(p_h) = 0;
658 p_l = v-(p_h-u);
659 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
660 z_l = cp_l*p_h+p_l*cp+dp_l[k];
661 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
662 t = (double)n;
663 t1 = (((z_h+z_l)+dp_h[k])+t);
664 __LO(t1) = 0;
665 t2 = z_l-(((t1-t)-dp_h[k])-z_h);
666 }
667
668 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
669 y1 = y;
670 __LO(y1) = 0;
671 p_l = (y-y1)*t1+y*t2;
672 p_h = y1*t1;
673 z = p_l+p_h;
674 j = __HI(z);
675 i = __LO(z);
676 if (j>=0x40900000) { /* z >= 1024 */
677 if(((j-0x40900000)|i)!=0) /* if z > 1024 */
678 return s*hugeX*hugeX; /* overflow */
679 else {
680 if(p_l+ovt>z-p_h) return s*hugeX*hugeX; /* overflow */
681 }
682 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
683 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
684 return s*tiny*tiny; /* underflow */
685 else {
686 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
687 }
688 }
689 /*
690 * compute 2**(p_h+p_l)
691 */
692 i = j&0x7fffffff;
693 k = (i>>20)-0x3ff;
694 n = 0;
695 if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
696 n = j+(0x00100000>>(k+1));
697 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
698 t = zeroX;
699 __HI(t) = (n&~(0x000fffff>>k));
700 n = ((n&0x000fffff)|0x00100000)>>(20-k);
701 if(j<0) n = -n;
702 p_h -= t;
703 }
704 t = p_l+p_h;
705 __LO(t) = 0;
706 u = t*lg2_h;
707 v = (p_l-(t-p_h))*lg2+t*lg2_l;
708 z = u+v;
709 w = v-(z-u);
710 t = z*z;
711 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
712 r = (z*t1)/(t1-two)-(w+z*w);
713 z = one-(r-z);
714 j = __HI(z);
715 j += (n<<20);
716 if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
717 else __HI(z) += (n<<20);
718 return s*z;
719 }
720
721
722 JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y))
723 return __ieee754_pow(x, y);
724 JRT_END
725
726 #ifdef WIN32
727 # pragma optimize ( "", on )
728 #endif