Thu, 22 May 2014 11:36:23 -0400
8043301: Duplicate definitions in vm/runtime/sharedRuntimeTrans.cpp versus math.h in VS2013
Summary: Factor out definitions of copysignA and scalbnA into new file sharedRuntimeMath.hpp
Reviewed-by: kvn
1 /*
2 * Copyright (c) 2005, 2014, 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 "runtime/sharedRuntimeMath.hpp"
48 /* __ieee754_log(x)
49 * Return the logrithm of x
50 *
51 * Method :
52 * 1. Argument Reduction: find k and f such that
53 * x = 2^k * (1+f),
54 * where sqrt(2)/2 < 1+f < sqrt(2) .
55 *
56 * 2. Approximation of log(1+f).
57 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
58 * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
59 * = 2s + s*R
60 * We use a special Reme algorithm on [0,0.1716] to generate
61 * a polynomial of degree 14 to approximate R The maximum error
62 * of this polynomial approximation is bounded by 2**-58.45. In
63 * other words,
64 * 2 4 6 8 10 12 14
65 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
66 * (the values of Lg1 to Lg7 are listed in the program)
67 * and
68 * | 2 14 | -58.45
69 * | Lg1*s +...+Lg7*s - R(z) | <= 2
70 * | |
71 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
72 * In order to guarantee error in log below 1ulp, we compute log
73 * by
74 * log(1+f) = f - s*(f - R) (if f is not too large)
75 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
76 *
77 * 3. Finally, log(x) = k*ln2 + log(1+f).
78 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
79 * Here ln2 is split into two floating point number:
80 * ln2_hi + ln2_lo,
81 * where n*ln2_hi is always exact for |n| < 2000.
82 *
83 * Special cases:
84 * log(x) is NaN with signal if x < 0 (including -INF) ;
85 * log(+INF) is +INF; log(0) is -INF with signal;
86 * log(NaN) is that NaN with no signal.
87 *
88 * Accuracy:
89 * according to an error analysis, the error is always less than
90 * 1 ulp (unit in the last place).
91 *
92 * Constants:
93 * The hexadecimal values are the intended ones for the following
94 * constants. The decimal values may be used, provided that the
95 * compiler will convert from decimal to binary accurately enough
96 * to produce the hexadecimal values shown.
97 */
99 static const double
100 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
101 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
102 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
103 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
104 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
105 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
106 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
107 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
108 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
110 static double zero = 0.0;
112 static double __ieee754_log(double x) {
113 double hfsq,f,s,z,R,w,t1,t2,dk;
114 int k,hx,i,j;
115 unsigned lx;
117 hx = __HI(x); /* high word of x */
118 lx = __LO(x); /* low word of x */
120 k=0;
121 if (hx < 0x00100000) { /* x < 2**-1022 */
122 if (((hx&0x7fffffff)|lx)==0)
123 return -two54/zero; /* log(+-0)=-inf */
124 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
125 k -= 54; x *= two54; /* subnormal number, scale up x */
126 hx = __HI(x); /* high word of x */
127 }
128 if (hx >= 0x7ff00000) return x+x;
129 k += (hx>>20)-1023;
130 hx &= 0x000fffff;
131 i = (hx+0x95f64)&0x100000;
132 __HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */
133 k += (i>>20);
134 f = x-1.0;
135 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
136 if(f==zero) {
137 if (k==0) return zero;
138 else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;}
139 }
140 R = f*f*(0.5-0.33333333333333333*f);
141 if(k==0) return f-R; else {dk=(double)k;
142 return dk*ln2_hi-((R-dk*ln2_lo)-f);}
143 }
144 s = f/(2.0+f);
145 dk = (double)k;
146 z = s*s;
147 i = hx-0x6147a;
148 w = z*z;
149 j = 0x6b851-hx;
150 t1= w*(Lg2+w*(Lg4+w*Lg6));
151 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
152 i |= j;
153 R = t2+t1;
154 if(i>0) {
155 hfsq=0.5*f*f;
156 if(k==0) return f-(hfsq-s*(hfsq+R)); else
157 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
158 } else {
159 if(k==0) return f-s*(f-R); else
160 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
161 }
162 }
164 JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x))
165 return __ieee754_log(x);
166 JRT_END
168 /* __ieee754_log10(x)
169 * Return the base 10 logarithm of x
170 *
171 * Method :
172 * Let log10_2hi = leading 40 bits of log10(2) and
173 * log10_2lo = log10(2) - log10_2hi,
174 * ivln10 = 1/log(10) rounded.
175 * Then
176 * n = ilogb(x),
177 * if(n<0) n = n+1;
178 * x = scalbn(x,-n);
179 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
180 *
181 * Note 1:
182 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
183 * mode must set to Round-to-Nearest.
184 * Note 2:
185 * [1/log(10)] rounded to 53 bits has error .198 ulps;
186 * log10 is monotonic at all binary break points.
187 *
188 * Special cases:
189 * log10(x) is NaN with signal if x < 0;
190 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
191 * log10(NaN) is that NaN with no signal;
192 * log10(10**N) = N for N=0,1,...,22.
193 *
194 * Constants:
195 * The hexadecimal values are the intended ones for the following constants.
196 * The decimal values may be used, provided that the compiler will convert
197 * from decimal to binary accurately enough to produce the hexadecimal values
198 * shown.
199 */
201 static const double
202 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
203 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
204 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
206 static double __ieee754_log10(double x) {
207 double y,z;
208 int i,k,hx;
209 unsigned lx;
211 hx = __HI(x); /* high word of x */
212 lx = __LO(x); /* low word of x */
214 k=0;
215 if (hx < 0x00100000) { /* x < 2**-1022 */
216 if (((hx&0x7fffffff)|lx)==0)
217 return -two54/zero; /* log(+-0)=-inf */
218 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
219 k -= 54; x *= two54; /* subnormal number, scale up x */
220 hx = __HI(x); /* high word of x */
221 }
222 if (hx >= 0x7ff00000) return x+x;
223 k += (hx>>20)-1023;
224 i = ((unsigned)k&0x80000000)>>31;
225 hx = (hx&0x000fffff)|((0x3ff-i)<<20);
226 y = (double)(k+i);
227 __HI(x) = hx;
228 z = y*log10_2lo + ivln10*__ieee754_log(x);
229 return z+y*log10_2hi;
230 }
232 JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x))
233 return __ieee754_log10(x);
234 JRT_END
237 /* __ieee754_exp(x)
238 * Returns the exponential of x.
239 *
240 * Method
241 * 1. Argument reduction:
242 * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
243 * Given x, find r and integer k such that
244 *
245 * x = k*ln2 + r, |r| <= 0.5*ln2.
246 *
247 * Here r will be represented as r = hi-lo for better
248 * accuracy.
249 *
250 * 2. Approximation of exp(r) by a special rational function on
251 * the interval [0,0.34658]:
252 * Write
253 * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
254 * We use a special Reme algorithm on [0,0.34658] to generate
255 * a polynomial of degree 5 to approximate R. The maximum error
256 * of this polynomial approximation is bounded by 2**-59. In
257 * other words,
258 * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
259 * (where z=r*r, and the values of P1 to P5 are listed below)
260 * and
261 * | 5 | -59
262 * | 2.0+P1*z+...+P5*z - R(z) | <= 2
263 * | |
264 * The computation of exp(r) thus becomes
265 * 2*r
266 * exp(r) = 1 + -------
267 * R - r
268 * r*R1(r)
269 * = 1 + r + ----------- (for better accuracy)
270 * 2 - R1(r)
271 * where
272 * 2 4 10
273 * R1(r) = r - (P1*r + P2*r + ... + P5*r ).
274 *
275 * 3. Scale back to obtain exp(x):
276 * From step 1, we have
277 * exp(x) = 2^k * exp(r)
278 *
279 * Special cases:
280 * exp(INF) is INF, exp(NaN) is NaN;
281 * exp(-INF) is 0, and
282 * for finite argument, only exp(0)=1 is exact.
283 *
284 * Accuracy:
285 * according to an error analysis, the error is always less than
286 * 1 ulp (unit in the last place).
287 *
288 * Misc. info.
289 * For IEEE double
290 * if x > 7.09782712893383973096e+02 then exp(x) overflow
291 * if x < -7.45133219101941108420e+02 then exp(x) underflow
292 *
293 * Constants:
294 * The hexadecimal values are the intended ones for the following
295 * constants. The decimal values may be used, provided that the
296 * compiler will convert from decimal to binary accurately enough
297 * to produce the hexadecimal values shown.
298 */
300 static const double
301 one = 1.0,
302 halF[2] = {0.5,-0.5,},
303 twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
304 o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
305 u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
306 ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
307 -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
308 ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
309 -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
310 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
311 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
312 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
313 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
314 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
315 P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
317 static double __ieee754_exp(double x) {
318 double y,hi=0,lo=0,c,t;
319 int k=0,xsb;
320 unsigned hx;
322 hx = __HI(x); /* high word of x */
323 xsb = (hx>>31)&1; /* sign bit of x */
324 hx &= 0x7fffffff; /* high word of |x| */
326 /* filter out non-finite argument */
327 if(hx >= 0x40862E42) { /* if |x|>=709.78... */
328 if(hx>=0x7ff00000) {
329 if(((hx&0xfffff)|__LO(x))!=0)
330 return x+x; /* NaN */
331 else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
332 }
333 if(x > o_threshold) return hugeX*hugeX; /* overflow */
334 if(x < u_threshold) return twom1000*twom1000; /* underflow */
335 }
337 /* argument reduction */
338 if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
339 if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
340 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
341 } else {
342 k = (int)(invln2*x+halF[xsb]);
343 t = k;
344 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
345 lo = t*ln2LO[0];
346 }
347 x = hi - lo;
348 }
349 else if(hx < 0x3e300000) { /* when |x|<2**-28 */
350 if(hugeX+x>one) return one+x;/* trigger inexact */
351 }
352 else k = 0;
354 /* x is now in primary range */
355 t = x*x;
356 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
357 if(k==0) return one-((x*c)/(c-2.0)-x);
358 else y = one-((lo-(x*c)/(2.0-c))-hi);
359 if(k >= -1021) {
360 __HI(y) += (k<<20); /* add k to y's exponent */
361 return y;
362 } else {
363 __HI(y) += ((k+1000)<<20);/* add k to y's exponent */
364 return y*twom1000;
365 }
366 }
368 JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x))
369 return __ieee754_exp(x);
370 JRT_END
372 /* __ieee754_pow(x,y) return x**y
373 *
374 * n
375 * Method: Let x = 2 * (1+f)
376 * 1. Compute and return log2(x) in two pieces:
377 * log2(x) = w1 + w2,
378 * where w1 has 53-24 = 29 bit trailing zeros.
379 * 2. Perform y*log2(x) = n+y' by simulating muti-precision
380 * arithmetic, where |y'|<=0.5.
381 * 3. Return x**y = 2**n*exp(y'*log2)
382 *
383 * Special cases:
384 * 1. (anything) ** 0 is 1
385 * 2. (anything) ** 1 is itself
386 * 3. (anything) ** NAN is NAN
387 * 4. NAN ** (anything except 0) is NAN
388 * 5. +-(|x| > 1) ** +INF is +INF
389 * 6. +-(|x| > 1) ** -INF is +0
390 * 7. +-(|x| < 1) ** +INF is +0
391 * 8. +-(|x| < 1) ** -INF is +INF
392 * 9. +-1 ** +-INF is NAN
393 * 10. +0 ** (+anything except 0, NAN) is +0
394 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
395 * 12. +0 ** (-anything except 0, NAN) is +INF
396 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
397 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
398 * 15. +INF ** (+anything except 0,NAN) is +INF
399 * 16. +INF ** (-anything except 0,NAN) is +0
400 * 17. -INF ** (anything) = -0 ** (-anything)
401 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
402 * 19. (-anything except 0 and inf) ** (non-integer) is NAN
403 *
404 * Accuracy:
405 * pow(x,y) returns x**y nearly rounded. In particular
406 * pow(integer,integer)
407 * always returns the correct integer provided it is
408 * representable.
409 *
410 * Constants :
411 * The hexadecimal values are the intended ones for the following
412 * constants. The decimal values may be used, provided that the
413 * compiler will convert from decimal to binary accurately enough
414 * to produce the hexadecimal values shown.
415 */
417 static const double
418 bp[] = {1.0, 1.5,},
419 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
420 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
421 zeroX = 0.0,
422 two = 2.0,
423 two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
424 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
425 L1X = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
426 L2X = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
427 L3X = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
428 L4X = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
429 L5X = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
430 L6X = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
431 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
432 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
433 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
434 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
435 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
436 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
437 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
438 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
439 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
440 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
442 double __ieee754_pow(double x, double y) {
443 double z,ax,z_h,z_l,p_h,p_l;
444 double y1,t1,t2,r,s,t,u,v,w;
445 int i0,i1,i,j,k,yisint,n;
446 int hx,hy,ix,iy;
447 unsigned lx,ly;
449 i0 = ((*(int*)&one)>>29)^1; i1=1-i0;
450 hx = __HI(x); lx = __LO(x);
451 hy = __HI(y); ly = __LO(y);
452 ix = hx&0x7fffffff; iy = hy&0x7fffffff;
454 /* y==zero: x**0 = 1 */
455 if((iy|ly)==0) return one;
457 /* +-NaN return x+y */
458 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
459 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
460 return x+y;
462 /* determine if y is an odd int when x < 0
463 * yisint = 0 ... y is not an integer
464 * yisint = 1 ... y is an odd int
465 * yisint = 2 ... y is an even int
466 */
467 yisint = 0;
468 if(hx<0) {
469 if(iy>=0x43400000) yisint = 2; /* even integer y */
470 else if(iy>=0x3ff00000) {
471 k = (iy>>20)-0x3ff; /* exponent */
472 if(k>20) {
473 j = ly>>(52-k);
474 if((unsigned)(j<<(52-k))==ly) yisint = 2-(j&1);
475 } else if(ly==0) {
476 j = iy>>(20-k);
477 if((j<<(20-k))==iy) yisint = 2-(j&1);
478 }
479 }
480 }
482 /* special value of y */
483 if(ly==0) {
484 if (iy==0x7ff00000) { /* y is +-inf */
485 if(((ix-0x3ff00000)|lx)==0)
486 return y - y; /* inf**+-1 is NaN */
487 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
488 return (hy>=0)? y: zeroX;
489 else /* (|x|<1)**-,+inf = inf,0 */
490 return (hy<0)?-y: zeroX;
491 }
492 if(iy==0x3ff00000) { /* y is +-1 */
493 if(hy<0) return one/x; else return x;
494 }
495 if(hy==0x40000000) return x*x; /* y is 2 */
496 if(hy==0x3fe00000) { /* y is 0.5 */
497 if(hx>=0) /* x >= +0 */
498 return sqrt(x);
499 }
500 }
502 ax = fabsd(x);
503 /* special value of x */
504 if(lx==0) {
505 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
506 z = ax; /*x is +-0,+-inf,+-1*/
507 if(hy<0) z = one/z; /* z = (1/|x|) */
508 if(hx<0) {
509 if(((ix-0x3ff00000)|yisint)==0) {
510 #ifdef CAN_USE_NAN_DEFINE
511 z = NAN;
512 #else
513 z = (z-z)/(z-z); /* (-1)**non-int is NaN */
514 #endif
515 } else if(yisint==1)
516 z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */
517 }
518 return z;
519 }
520 }
522 n = (hx>>31)+1;
524 /* (x<0)**(non-int) is NaN */
525 if((n|yisint)==0)
526 #ifdef CAN_USE_NAN_DEFINE
527 return NAN;
528 #else
529 return (x-x)/(x-x);
530 #endif
532 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
533 if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
535 /* |y| is huge */
536 if(iy>0x41e00000) { /* if |y| > 2**31 */
537 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
538 if(ix<=0x3fefffff) return (hy<0)? hugeX*hugeX:tiny*tiny;
539 if(ix>=0x3ff00000) return (hy>0)? hugeX*hugeX:tiny*tiny;
540 }
541 /* over/underflow if x is not close to one */
542 if(ix<0x3fefffff) return (hy<0)? s*hugeX*hugeX:s*tiny*tiny;
543 if(ix>0x3ff00000) return (hy>0)? s*hugeX*hugeX:s*tiny*tiny;
544 /* now |1-x| is tiny <= 2**-20, suffice to compute
545 log(x) by x-x^2/2+x^3/3-x^4/4 */
546 t = ax-one; /* t has 20 trailing zeros */
547 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
548 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
549 v = t*ivln2_l-w*ivln2;
550 t1 = u+v;
551 __LO(t1) = 0;
552 t2 = v-(t1-u);
553 } else {
554 double ss,s2,s_h,s_l,t_h,t_l;
555 n = 0;
556 /* take care subnormal number */
557 if(ix<0x00100000)
558 {ax *= two53; n -= 53; ix = __HI(ax); }
559 n += ((ix)>>20)-0x3ff;
560 j = ix&0x000fffff;
561 /* determine interval */
562 ix = j|0x3ff00000; /* normalize ix */
563 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
564 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
565 else {k=0;n+=1;ix -= 0x00100000;}
566 __HI(ax) = ix;
568 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
569 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
570 v = one/(ax+bp[k]);
571 ss = u*v;
572 s_h = ss;
573 __LO(s_h) = 0;
574 /* t_h=ax+bp[k] High */
575 t_h = zeroX;
576 __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
577 t_l = ax - (t_h-bp[k]);
578 s_l = v*((u-s_h*t_h)-s_h*t_l);
579 /* compute log(ax) */
580 s2 = ss*ss;
581 r = s2*s2*(L1X+s2*(L2X+s2*(L3X+s2*(L4X+s2*(L5X+s2*L6X)))));
582 r += s_l*(s_h+ss);
583 s2 = s_h*s_h;
584 t_h = 3.0+s2+r;
585 __LO(t_h) = 0;
586 t_l = r-((t_h-3.0)-s2);
587 /* u+v = ss*(1+...) */
588 u = s_h*t_h;
589 v = s_l*t_h+t_l*ss;
590 /* 2/(3log2)*(ss+...) */
591 p_h = u+v;
592 __LO(p_h) = 0;
593 p_l = v-(p_h-u);
594 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
595 z_l = cp_l*p_h+p_l*cp+dp_l[k];
596 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
597 t = (double)n;
598 t1 = (((z_h+z_l)+dp_h[k])+t);
599 __LO(t1) = 0;
600 t2 = z_l-(((t1-t)-dp_h[k])-z_h);
601 }
603 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
604 y1 = y;
605 __LO(y1) = 0;
606 p_l = (y-y1)*t1+y*t2;
607 p_h = y1*t1;
608 z = p_l+p_h;
609 j = __HI(z);
610 i = __LO(z);
611 if (j>=0x40900000) { /* z >= 1024 */
612 if(((j-0x40900000)|i)!=0) /* if z > 1024 */
613 return s*hugeX*hugeX; /* overflow */
614 else {
615 if(p_l+ovt>z-p_h) return s*hugeX*hugeX; /* overflow */
616 }
617 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
618 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
619 return s*tiny*tiny; /* underflow */
620 else {
621 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
622 }
623 }
624 /*
625 * compute 2**(p_h+p_l)
626 */
627 i = j&0x7fffffff;
628 k = (i>>20)-0x3ff;
629 n = 0;
630 if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
631 n = j+(0x00100000>>(k+1));
632 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
633 t = zeroX;
634 __HI(t) = (n&~(0x000fffff>>k));
635 n = ((n&0x000fffff)|0x00100000)>>(20-k);
636 if(j<0) n = -n;
637 p_h -= t;
638 }
639 t = p_l+p_h;
640 __LO(t) = 0;
641 u = t*lg2_h;
642 v = (p_l-(t-p_h))*lg2+t*lg2_l;
643 z = u+v;
644 w = v-(z-u);
645 t = z*z;
646 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
647 r = (z*t1)/(t1-two)-(w+z*w);
648 z = one-(r-z);
649 j = __HI(z);
650 j += (n<<20);
651 if((j>>20)<=0) z = scalbnA(z,n); /* subnormal output */
652 else __HI(z) += (n<<20);
653 return s*z;
654 }
657 JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y))
658 return __ieee754_pow(x, y);
659 JRT_END
661 #ifdef WIN32
662 # pragma optimize ( "", on )
663 #endif