Mercurial > hg > graal-compiler
annotate src/share/vm/runtime/sharedRuntimeTrig.cpp @ 18096:ca6d25be853b jdk8u25-b13
8044269: Analysis of archive files.
Summary: Add checksum verification.
Reviewed-by: iklam, dholmes, mschoene
| author | jiangli |
|---|---|
| date | Tue, 12 Aug 2014 17:46:16 -0400 |
| parents | bdd155477289 |
| children | 8a9bb7821e28 631c3a4ea10c |
| rev | line source |
|---|---|
| 0 | 1 /* |
| 1972 | 2 * Copyright (c) 2001, 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 | |
| 1485 | 46 /* The above workaround now causes more problems with the latest MS compiler. |
| 47 * Visual Studio 2010's /GS option tries to guard against buffer overruns. | |
| 48 * /GS is on by default if you specify optimizations, which we do globally | |
| 49 * via /W3 /O2. However the above selective turning off of optimizations means | |
| 50 * that /GS issues a warning "4748". And since we treat warnings as errors (/WX) | |
| 51 * then the compilation fails. There are several possible solutions | |
| 52 * (1) Remove that pragma above as obsolete with VS2010 - requires testing. | |
| 53 * (2) Stop treating warnings as errors - would be a backward step | |
| 54 * (3) Disable /GS - may help performance but you lose the security checks | |
| 55 * (4) Disable the warning with "#pragma warning( disable : 4748 )" | |
| 56 * (5) Disable planting the code with __declspec(safebuffers) | |
| 57 * I've opted for (5) although we should investigate the local performance | |
| 58 * benefits of (1) and global performance benefit of (3). | |
| 59 */ | |
| 60 #if defined(WIN32) && (defined(_MSC_VER) && (_MSC_VER >= 1600)) | |
| 61 #define SAFEBUF __declspec(safebuffers) | |
| 62 #else | |
| 63 #define SAFEBUF | |
| 64 #endif | |
| 65 | |
| 0 | 66 #include <math.h> |
| 67 | |
| 68 // VM_LITTLE_ENDIAN is #defined appropriately in the Makefiles | |
| 69 // [jk] this is not 100% correct because the float word order may different | |
| 70 // from the byte order (e.g. on ARM) | |
| 71 #ifdef VM_LITTLE_ENDIAN | |
| 72 # define __HI(x) *(1+(int*)&x) | |
| 73 # define __LO(x) *(int*)&x | |
| 74 #else | |
| 75 # define __HI(x) *(int*)&x | |
| 76 # define __LO(x) *(1+(int*)&x) | |
| 77 #endif | |
| 78 | |
| 79 static double copysignA(double x, double y) { | |
| 80 __HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000); | |
| 81 return x; | |
| 82 } | |
| 83 | |
| 84 /* | |
| 85 * scalbn (double x, int n) | |
| 86 * scalbn(x,n) returns x* 2**n computed by exponent | |
| 87 * manipulation rather than by actually performing an | |
| 88 * exponentiation or a multiplication. | |
| 89 */ | |
| 90 | |
| 91 static const double | |
| 92 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ | |
| 93 twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ | |
| 94 hugeX = 1.0e+300, | |
| 95 tiny = 1.0e-300; | |
| 96 | |
| 97 static double scalbnA (double x, int n) { | |
| 98 int k,hx,lx; | |
| 99 hx = __HI(x); | |
| 100 lx = __LO(x); | |
| 101 k = (hx&0x7ff00000)>>20; /* extract exponent */ | |
| 102 if (k==0) { /* 0 or subnormal x */ | |
| 103 if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ | |
| 104 x *= two54; | |
| 105 hx = __HI(x); | |
| 106 k = ((hx&0x7ff00000)>>20) - 54; | |
| 107 if (n< -50000) return tiny*x; /*underflow*/ | |
| 108 } | |
| 109 if (k==0x7ff) return x+x; /* NaN or Inf */ | |
| 110 k = k+n; | |
| 111 if (k > 0x7fe) return hugeX*copysignA(hugeX,x); /* overflow */ | |
| 112 if (k > 0) /* normal result */ | |
| 113 {__HI(x) = (hx&0x800fffff)|(k<<20); return x;} | |
| 114 if (k <= -54) { | |
| 115 if (n > 50000) /* in case integer overflow in n+k */ | |
| 116 return hugeX*copysignA(hugeX,x); /*overflow*/ | |
| 117 else return tiny*copysignA(tiny,x); /*underflow*/ | |
| 118 } | |
| 119 k += 54; /* subnormal result */ | |
| 120 __HI(x) = (hx&0x800fffff)|(k<<20); | |
| 121 return x*twom54; | |
| 122 } | |
| 123 | |
| 124 /* | |
| 125 * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) | |
| 126 * double x[],y[]; int e0,nx,prec; int ipio2[]; | |
| 127 * | |
| 128 * __kernel_rem_pio2 return the last three digits of N with | |
| 129 * y = x - N*pi/2 | |
| 130 * so that |y| < pi/2. | |
| 131 * | |
| 132 * The method is to compute the integer (mod 8) and fraction parts of | |
| 133 * (2/pi)*x without doing the full multiplication. In general we | |
| 134 * skip the part of the product that are known to be a huge integer ( | |
| 135 * more accurately, = 0 mod 8 ). Thus the number of operations are | |
| 136 * independent of the exponent of the input. | |
| 137 * | |
| 138 * (2/pi) is represented by an array of 24-bit integers in ipio2[]. | |
| 139 * | |
| 140 * Input parameters: | |
| 141 * x[] The input value (must be positive) is broken into nx | |
| 142 * pieces of 24-bit integers in double precision format. | |
| 143 * x[i] will be the i-th 24 bit of x. The scaled exponent | |
| 144 * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 | |
| 145 * match x's up to 24 bits. | |
| 146 * | |
| 147 * Example of breaking a double positive z into x[0]+x[1]+x[2]: | |
| 148 * e0 = ilogb(z)-23 | |
| 149 * z = scalbn(z,-e0) | |
| 150 * for i = 0,1,2 | |
| 151 * x[i] = floor(z) | |
| 152 * z = (z-x[i])*2**24 | |
| 153 * | |
| 154 * | |
| 155 * y[] ouput result in an array of double precision numbers. | |
| 156 * The dimension of y[] is: | |
| 157 * 24-bit precision 1 | |
| 158 * 53-bit precision 2 | |
| 159 * 64-bit precision 2 | |
| 160 * 113-bit precision 3 | |
| 161 * The actual value is the sum of them. Thus for 113-bit | |
| 162 * precsion, one may have to do something like: | |
| 163 * | |
| 164 * long double t,w,r_head, r_tail; | |
| 165 * t = (long double)y[2] + (long double)y[1]; | |
| 166 * w = (long double)y[0]; | |
| 167 * r_head = t+w; | |
| 168 * r_tail = w - (r_head - t); | |
| 169 * | |
| 170 * e0 The exponent of x[0] | |
| 171 * | |
| 172 * nx dimension of x[] | |
| 173 * | |
| 174 * prec an interger indicating the precision: | |
| 175 * 0 24 bits (single) | |
| 176 * 1 53 bits (double) | |
| 177 * 2 64 bits (extended) | |
| 178 * 3 113 bits (quad) | |
| 179 * | |
| 180 * ipio2[] | |
| 181 * integer array, contains the (24*i)-th to (24*i+23)-th | |
| 182 * bit of 2/pi after binary point. The corresponding | |
| 183 * floating value is | |
| 184 * | |
| 185 * ipio2[i] * 2^(-24(i+1)). | |
| 186 * | |
| 187 * External function: | |
| 188 * double scalbn(), floor(); | |
| 189 * | |
| 190 * | |
| 191 * Here is the description of some local variables: | |
| 192 * | |
| 193 * jk jk+1 is the initial number of terms of ipio2[] needed | |
| 194 * in the computation. The recommended value is 2,3,4, | |
| 195 * 6 for single, double, extended,and quad. | |
| 196 * | |
| 197 * jz local integer variable indicating the number of | |
| 198 * terms of ipio2[] used. | |
| 199 * | |
| 200 * jx nx - 1 | |
| 201 * | |
| 202 * jv index for pointing to the suitable ipio2[] for the | |
| 203 * computation. In general, we want | |
| 204 * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 | |
| 205 * is an integer. Thus | |
| 206 * e0-3-24*jv >= 0 or (e0-3)/24 >= jv | |
| 207 * Hence jv = max(0,(e0-3)/24). | |
| 208 * | |
| 209 * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. | |
| 210 * | |
| 211 * q[] double array with integral value, representing the | |
| 212 * 24-bits chunk of the product of x and 2/pi. | |
| 213 * | |
| 214 * q0 the corresponding exponent of q[0]. Note that the | |
| 215 * exponent for q[i] would be q0-24*i. | |
| 216 * | |
| 217 * PIo2[] double precision array, obtained by cutting pi/2 | |
| 218 * into 24 bits chunks. | |
| 219 * | |
| 220 * f[] ipio2[] in floating point | |
| 221 * | |
| 222 * iq[] integer array by breaking up q[] in 24-bits chunk. | |
| 223 * | |
| 224 * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] | |
| 225 * | |
| 226 * ih integer. If >0 it indicats q[] is >= 0.5, hence | |
| 227 * it also indicates the *sign* of the result. | |
| 228 * | |
| 229 */ | |
| 230 | |
| 231 | |
| 232 /* | |
| 233 * Constants: | |
| 234 * The hexadecimal values are the intended ones for the following | |
| 235 * constants. The decimal values may be used, provided that the | |
| 236 * compiler will convert from decimal to binary accurately enough | |
| 237 * to produce the hexadecimal values shown. | |
| 238 */ | |
| 239 | |
| 240 | |
| 241 static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ | |
| 242 | |
| 243 static const double PIo2[] = { | |
| 244 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ | |
| 245 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ | |
| 246 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ | |
| 247 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ | |
| 248 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ | |
| 249 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ | |
| 250 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ | |
| 251 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ | |
| 252 }; | |
| 253 | |
| 254 static const double | |
| 255 zeroB = 0.0, | |
| 256 one = 1.0, | |
| 257 two24B = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ | |
| 258 twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ | |
| 259 | |
| 1485 | 260 static SAFEBUF int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2) { |
| 0 | 261 int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; |
| 262 double z,fw,f[20],fq[20],q[20]; | |
| 263 | |
| 264 /* initialize jk*/ | |
| 265 jk = init_jk[prec]; | |
| 266 jp = jk; | |
| 267 | |
| 268 /* determine jx,jv,q0, note that 3>q0 */ | |
| 269 jx = nx-1; | |
| 270 jv = (e0-3)/24; if(jv<0) jv=0; | |
| 271 q0 = e0-24*(jv+1); | |
| 272 | |
| 273 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ | |
| 274 j = jv-jx; m = jx+jk; | |
| 275 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zeroB : (double) ipio2[j]; | |
| 276 | |
| 277 /* compute q[0],q[1],...q[jk] */ | |
| 278 for (i=0;i<=jk;i++) { | |
| 279 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; | |
| 280 } | |
| 281 | |
| 282 jz = jk; | |
| 283 recompute: | |
| 284 /* distill q[] into iq[] reversingly */ | |
| 285 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { | |
| 286 fw = (double)((int)(twon24* z)); | |
| 287 iq[i] = (int)(z-two24B*fw); | |
| 288 z = q[j-1]+fw; | |
| 289 } | |
| 290 | |
| 291 /* compute n */ | |
| 292 z = scalbnA(z,q0); /* actual value of z */ | |
| 293 z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ | |
| 294 n = (int) z; | |
| 295 z -= (double)n; | |
| 296 ih = 0; | |
| 297 if(q0>0) { /* need iq[jz-1] to determine n */ | |
| 298 i = (iq[jz-1]>>(24-q0)); n += i; | |
| 299 iq[jz-1] -= i<<(24-q0); | |
| 300 ih = iq[jz-1]>>(23-q0); | |
| 301 } | |
| 302 else if(q0==0) ih = iq[jz-1]>>23; | |
| 303 else if(z>=0.5) ih=2; | |
| 304 | |
| 305 if(ih>0) { /* q > 0.5 */ | |
| 306 n += 1; carry = 0; | |
| 307 for(i=0;i<jz ;i++) { /* compute 1-q */ | |
| 308 j = iq[i]; | |
| 309 if(carry==0) { | |
| 310 if(j!=0) { | |
| 311 carry = 1; iq[i] = 0x1000000- j; | |
| 312 } | |
| 313 } else iq[i] = 0xffffff - j; | |
| 314 } | |
| 315 if(q0>0) { /* rare case: chance is 1 in 12 */ | |
| 316 switch(q0) { | |
| 317 case 1: | |
| 318 iq[jz-1] &= 0x7fffff; break; | |
| 319 case 2: | |
| 320 iq[jz-1] &= 0x3fffff; break; | |
| 321 } | |
| 322 } | |
| 323 if(ih==2) { | |
| 324 z = one - z; | |
| 325 if(carry!=0) z -= scalbnA(one,q0); | |
| 326 } | |
| 327 } | |
| 328 | |
| 329 /* check if recomputation is needed */ | |
| 330 if(z==zeroB) { | |
| 331 j = 0; | |
| 332 for (i=jz-1;i>=jk;i--) j |= iq[i]; | |
| 333 if(j==0) { /* need recomputation */ | |
| 334 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ | |
| 335 | |
| 336 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ | |
| 337 f[jx+i] = (double) ipio2[jv+i]; | |
| 338 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; | |
| 339 q[i] = fw; | |
| 340 } | |
| 341 jz += k; | |
| 342 goto recompute; | |
| 343 } | |
| 344 } | |
| 345 | |
| 346 /* chop off zero terms */ | |
| 347 if(z==0.0) { | |
| 348 jz -= 1; q0 -= 24; | |
| 349 while(iq[jz]==0) { jz--; q0-=24;} | |
| 350 } else { /* break z into 24-bit if neccessary */ | |
| 351 z = scalbnA(z,-q0); | |
| 352 if(z>=two24B) { | |
| 353 fw = (double)((int)(twon24*z)); | |
| 354 iq[jz] = (int)(z-two24B*fw); | |
| 355 jz += 1; q0 += 24; | |
| 356 iq[jz] = (int) fw; | |
| 357 } else iq[jz] = (int) z ; | |
| 358 } | |
| 359 | |
| 360 /* convert integer "bit" chunk to floating-point value */ | |
| 361 fw = scalbnA(one,q0); | |
| 362 for(i=jz;i>=0;i--) { | |
| 363 q[i] = fw*(double)iq[i]; fw*=twon24; | |
| 364 } | |
| 365 | |
| 366 /* compute PIo2[0,...,jp]*q[jz,...,0] */ | |
| 367 for(i=jz;i>=0;i--) { | |
| 368 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; | |
| 369 fq[jz-i] = fw; | |
| 370 } | |
| 371 | |
| 372 /* compress fq[] into y[] */ | |
| 373 switch(prec) { | |
| 374 case 0: | |
| 375 fw = 0.0; | |
| 376 for (i=jz;i>=0;i--) fw += fq[i]; | |
| 377 y[0] = (ih==0)? fw: -fw; | |
| 378 break; | |
| 379 case 1: | |
| 380 case 2: | |
| 381 fw = 0.0; | |
| 382 for (i=jz;i>=0;i--) fw += fq[i]; | |
| 383 y[0] = (ih==0)? fw: -fw; | |
| 384 fw = fq[0]-fw; | |
| 385 for (i=1;i<=jz;i++) fw += fq[i]; | |
| 386 y[1] = (ih==0)? fw: -fw; | |
| 387 break; | |
| 388 case 3: /* painful */ | |
| 389 for (i=jz;i>0;i--) { | |
| 390 fw = fq[i-1]+fq[i]; | |
| 391 fq[i] += fq[i-1]-fw; | |
| 392 fq[i-1] = fw; | |
| 393 } | |
| 394 for (i=jz;i>1;i--) { | |
| 395 fw = fq[i-1]+fq[i]; | |
| 396 fq[i] += fq[i-1]-fw; | |
| 397 fq[i-1] = fw; | |
| 398 } | |
| 399 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; | |
| 400 if(ih==0) { | |
| 401 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; | |
| 402 } else { | |
| 403 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; | |
| 404 } | |
| 405 } | |
| 406 return n&7; | |
| 407 } | |
| 408 | |
| 409 | |
| 410 /* | |
| 411 * ==================================================== | |
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412 * Copyright (c) 1993 Oracle and/or its affilates. All rights reserved. |
| 0 | 413 * |
| 414 * Developed at SunPro, a Sun Microsystems, Inc. business. | |
| 415 * Permission to use, copy, modify, and distribute this | |
| 416 * software is freely granted, provided that this notice | |
| 417 * is preserved. | |
| 418 * ==================================================== | |
| 419 * | |
| 420 */ | |
| 421 | |
| 422 /* __ieee754_rem_pio2(x,y) | |
| 423 * | |
| 424 * return the remainder of x rem pi/2 in y[0]+y[1] | |
| 425 * use __kernel_rem_pio2() | |
| 426 */ | |
| 427 | |
| 428 /* | |
| 429 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi | |
| 430 */ | |
| 431 static const int two_over_pi[] = { | |
| 432 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, | |
| 433 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, | |
| 434 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, | |
| 435 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, | |
| 436 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, | |
| 437 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, | |
| 438 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, | |
| 439 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, | |
| 440 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, | |
| 441 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, | |
| 442 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, | |
| 443 }; | |
| 444 | |
| 445 static const int npio2_hw[] = { | |
| 446 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, | |
| 447 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, | |
| 448 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, | |
| 449 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, | |
| 450 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, | |
| 451 0x404858EB, 0x404921FB, | |
| 452 }; | |
| 453 | |
| 454 /* | |
| 455 * invpio2: 53 bits of 2/pi | |
| 456 * pio2_1: first 33 bit of pi/2 | |
| 457 * pio2_1t: pi/2 - pio2_1 | |
| 458 * pio2_2: second 33 bit of pi/2 | |
| 459 * pio2_2t: pi/2 - (pio2_1+pio2_2) | |
| 460 * pio2_3: third 33 bit of pi/2 | |
| 461 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) | |
| 462 */ | |
| 463 | |
| 464 static const double | |
| 465 zeroA = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ | |
| 466 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ | |
| 467 two24A = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ | |
| 468 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ | |
| 469 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ | |
| 470 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ | |
| 471 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ | |
| 472 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ | |
| 473 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ | |
| 474 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ | |
| 475 | |
| 1485 | 476 static SAFEBUF int __ieee754_rem_pio2(double x, double *y) { |
| 0 | 477 double z,w,t,r,fn; |
| 478 double tx[3]; | |
| 479 int e0,i,j,nx,n,ix,hx,i0; | |
| 480 | |
| 481 i0 = ((*(int*)&two24A)>>30)^1; /* high word index */ | |
| 482 hx = *(i0+(int*)&x); /* high word of x */ | |
| 483 ix = hx&0x7fffffff; | |
| 484 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ | |
| 485 {y[0] = x; y[1] = 0; return 0;} | |
| 486 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ | |
| 487 if(hx>0) { | |
| 488 z = x - pio2_1; | |
| 489 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ | |
| 490 y[0] = z - pio2_1t; | |
| 491 y[1] = (z-y[0])-pio2_1t; | |
| 492 } else { /* near pi/2, use 33+33+53 bit pi */ | |
| 493 z -= pio2_2; | |
| 494 y[0] = z - pio2_2t; | |
| 495 y[1] = (z-y[0])-pio2_2t; | |
| 496 } | |
| 497 return 1; | |
| 498 } else { /* negative x */ | |
| 499 z = x + pio2_1; | |
| 500 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ | |
| 501 y[0] = z + pio2_1t; | |
| 502 y[1] = (z-y[0])+pio2_1t; | |
| 503 } else { /* near pi/2, use 33+33+53 bit pi */ | |
| 504 z += pio2_2; | |
| 505 y[0] = z + pio2_2t; | |
| 506 y[1] = (z-y[0])+pio2_2t; | |
| 507 } | |
| 508 return -1; | |
| 509 } | |
| 510 } | |
| 511 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ | |
| 512 t = fabsd(x); | |
| 513 n = (int) (t*invpio2+half); | |
| 514 fn = (double)n; | |
| 515 r = t-fn*pio2_1; | |
| 516 w = fn*pio2_1t; /* 1st round good to 85 bit */ | |
| 517 if(n<32&&ix!=npio2_hw[n-1]) { | |
| 518 y[0] = r-w; /* quick check no cancellation */ | |
| 519 } else { | |
| 520 j = ix>>20; | |
| 521 y[0] = r-w; | |
| 522 i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff); | |
| 523 if(i>16) { /* 2nd iteration needed, good to 118 */ | |
| 524 t = r; | |
| 525 w = fn*pio2_2; | |
| 526 r = t-w; | |
| 527 w = fn*pio2_2t-((t-r)-w); | |
| 528 y[0] = r-w; | |
| 529 i = j-(((*(i0+(int*)&y[0]))>>20)&0x7ff); | |
| 530 if(i>49) { /* 3rd iteration need, 151 bits acc */ | |
| 531 t = r; /* will cover all possible cases */ | |
| 532 w = fn*pio2_3; | |
| 533 r = t-w; | |
| 534 w = fn*pio2_3t-((t-r)-w); | |
| 535 y[0] = r-w; | |
| 536 } | |
| 537 } | |
| 538 } | |
| 539 y[1] = (r-y[0])-w; | |
| 540 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} | |
| 541 else return n; | |
| 542 } | |
| 543 /* | |
| 544 * all other (large) arguments | |
| 545 */ | |
| 546 if(ix>=0x7ff00000) { /* x is inf or NaN */ | |
| 547 y[0]=y[1]=x-x; return 0; | |
| 548 } | |
| 549 /* set z = scalbn(|x|,ilogb(x)-23) */ | |
| 550 *(1-i0+(int*)&z) = *(1-i0+(int*)&x); | |
| 551 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ | |
| 552 *(i0+(int*)&z) = ix - (e0<<20); | |
| 553 for(i=0;i<2;i++) { | |
| 554 tx[i] = (double)((int)(z)); | |
| 555 z = (z-tx[i])*two24A; | |
| 556 } | |
| 557 tx[2] = z; | |
| 558 nx = 3; | |
| 559 while(tx[nx-1]==zeroA) nx--; /* skip zero term */ | |
| 560 n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); | |
| 561 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} | |
| 562 return n; | |
| 563 } | |
| 564 | |
| 565 | |
| 566 /* __kernel_sin( x, y, iy) | |
| 567 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 | |
| 568 * Input x is assumed to be bounded by ~pi/4 in magnitude. | |
| 569 * Input y is the tail of x. | |
| 570 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). | |
| 571 * | |
| 572 * Algorithm | |
| 573 * 1. Since sin(-x) = -sin(x), we need only to consider positive x. | |
| 574 * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. | |
| 575 * 3. sin(x) is approximated by a polynomial of degree 13 on | |
| 576 * [0,pi/4] | |
| 577 * 3 13 | |
| 578 * sin(x) ~ x + S1*x + ... + S6*x | |
| 579 * where | |
| 580 * | |
| 581 * |sin(x) 2 4 6 8 10 12 | -58 | |
| 582 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 | |
| 583 * | x | | |
| 584 * | |
| 585 * 4. sin(x+y) = sin(x) + sin'(x')*y | |
| 586 * ~ sin(x) + (1-x*x/2)*y | |
| 587 * For better accuracy, let | |
| 588 * 3 2 2 2 2 | |
| 589 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) | |
| 590 * then 3 2 | |
| 591 * sin(x) = x + (S1*x + (x *(r-y/2)+y)) | |
| 592 */ | |
| 593 | |
| 594 static const double | |
| 595 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ | |
| 596 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ | |
| 597 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ | |
| 598 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ | |
| 599 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ | |
| 600 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ | |
| 601 | |
| 602 static double __kernel_sin(double x, double y, int iy) | |
| 603 { | |
| 604 double z,r,v; | |
| 605 int ix; | |
| 606 ix = __HI(x)&0x7fffffff; /* high word of x */ | |
| 607 if(ix<0x3e400000) /* |x| < 2**-27 */ | |
| 608 {if((int)x==0) return x;} /* generate inexact */ | |
| 609 z = x*x; | |
| 610 v = z*x; | |
| 611 r = S2+z*(S3+z*(S4+z*(S5+z*S6))); | |
| 612 if(iy==0) return x+v*(S1+z*r); | |
| 613 else return x-((z*(half*y-v*r)-y)-v*S1); | |
| 614 } | |
| 615 | |
| 616 /* | |
| 617 * __kernel_cos( x, y ) | |
| 618 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 | |
| 619 * Input x is assumed to be bounded by ~pi/4 in magnitude. | |
| 620 * Input y is the tail of x. | |
| 621 * | |
| 622 * Algorithm | |
| 623 * 1. Since cos(-x) = cos(x), we need only to consider positive x. | |
| 624 * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. | |
| 625 * 3. cos(x) is approximated by a polynomial of degree 14 on | |
| 626 * [0,pi/4] | |
| 627 * 4 14 | |
| 628 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x | |
| 629 * where the remez error is | |
| 630 * | |
| 631 * | 2 4 6 8 10 12 14 | -58 | |
| 632 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 | |
| 633 * | | | |
| 634 * | |
| 635 * 4 6 8 10 12 14 | |
| 636 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then | |
| 637 * cos(x) = 1 - x*x/2 + r | |
| 638 * since cos(x+y) ~ cos(x) - sin(x)*y | |
| 639 * ~ cos(x) - x*y, | |
| 640 * a correction term is necessary in cos(x) and hence | |
| 641 * cos(x+y) = 1 - (x*x/2 - (r - x*y)) | |
| 642 * For better accuracy when x > 0.3, let qx = |x|/4 with | |
| 643 * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. | |
| 644 * Then | |
| 645 * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). | |
| 646 * Note that 1-qx and (x*x/2-qx) is EXACT here, and the | |
| 647 * magnitude of the latter is at least a quarter of x*x/2, | |
| 648 * thus, reducing the rounding error in the subtraction. | |
| 649 */ | |
| 650 | |
| 651 static const double | |
| 652 C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ | |
| 653 C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ | |
| 654 C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ | |
| 655 C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ | |
| 656 C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ | |
| 657 C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ | |
| 658 | |
| 659 static double __kernel_cos(double x, double y) | |
| 660 { | |
| 14411 | 661 double a,h,z,r,qx; |
| 0 | 662 int ix; |
| 663 ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/ | |
| 664 if(ix<0x3e400000) { /* if x < 2**27 */ | |
| 665 if(((int)x)==0) return one; /* generate inexact */ | |
| 666 } | |
| 667 z = x*x; | |
| 668 r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); | |
| 669 if(ix < 0x3FD33333) /* if |x| < 0.3 */ | |
| 670 return one - (0.5*z - (z*r - x*y)); | |
| 671 else { | |
| 672 if(ix > 0x3fe90000) { /* x > 0.78125 */ | |
| 673 qx = 0.28125; | |
| 674 } else { | |
| 675 __HI(qx) = ix-0x00200000; /* x/4 */ | |
| 676 __LO(qx) = 0; | |
| 677 } | |
| 14411 | 678 h = 0.5*z-qx; |
| 679 a = one-qx; | |
| 680 return a - (h - (z*r-x*y)); | |
| 0 | 681 } |
| 682 } | |
| 683 | |
| 684 /* __kernel_tan( x, y, k ) | |
| 685 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 | |
| 686 * Input x is assumed to be bounded by ~pi/4 in magnitude. | |
| 687 * Input y is the tail of x. | |
| 688 * Input k indicates whether tan (if k=1) or | |
| 689 * -1/tan (if k= -1) is returned. | |
| 690 * | |
| 691 * Algorithm | |
| 692 * 1. Since tan(-x) = -tan(x), we need only to consider positive x. | |
| 693 * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. | |
| 694 * 3. tan(x) is approximated by a odd polynomial of degree 27 on | |
| 695 * [0,0.67434] | |
| 696 * 3 27 | |
| 697 * tan(x) ~ x + T1*x + ... + T13*x | |
| 698 * where | |
| 699 * | |
| 700 * |tan(x) 2 4 26 | -59.2 | |
| 701 * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 | |
| 702 * | x | | |
| 703 * | |
| 704 * Note: tan(x+y) = tan(x) + tan'(x)*y | |
| 705 * ~ tan(x) + (1+x*x)*y | |
| 706 * Therefore, for better accuracy in computing tan(x+y), let | |
| 707 * 3 2 2 2 2 | |
| 708 * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) | |
| 709 * then | |
| 710 * 3 2 | |
| 711 * tan(x+y) = x + (T1*x + (x *(r+y)+y)) | |
| 712 * | |
| 713 * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then | |
| 714 * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) | |
| 715 * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) | |
| 716 */ | |
| 717 | |
| 718 static const double | |
| 719 pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ | |
| 720 pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */ | |
| 721 T[] = { | |
| 722 3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */ | |
| 723 1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */ | |
| 724 5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */ | |
| 725 2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */ | |
| 726 8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */ | |
| 727 3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */ | |
| 728 1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */ | |
| 729 5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */ | |
| 730 2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */ | |
| 731 7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */ | |
| 732 7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */ | |
| 733 -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */ | |
| 734 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */ | |
| 735 }; | |
| 736 | |
| 737 static double __kernel_tan(double x, double y, int iy) | |
| 738 { | |
| 739 double z,r,v,w,s; | |
| 740 int ix,hx; | |
| 741 hx = __HI(x); /* high word of x */ | |
| 742 ix = hx&0x7fffffff; /* high word of |x| */ | |
| 743 if(ix<0x3e300000) { /* x < 2**-28 */ | |
| 744 if((int)x==0) { /* generate inexact */ | |
| 745 if (((ix | __LO(x)) | (iy + 1)) == 0) | |
| 746 return one / fabsd(x); | |
| 747 else { | |
| 748 if (iy == 1) | |
| 749 return x; | |
| 750 else { /* compute -1 / (x+y) carefully */ | |
| 751 double a, t; | |
| 752 | |
| 753 z = w = x + y; | |
| 754 __LO(z) = 0; | |
| 755 v = y - (z - x); | |
| 756 t = a = -one / w; | |
| 757 __LO(t) = 0; | |
| 758 s = one + t * z; | |
| 759 return t + a * (s + t * v); | |
| 760 } | |
| 761 } | |
| 762 } | |
| 763 } | |
| 764 if(ix>=0x3FE59428) { /* |x|>=0.6744 */ | |
| 765 if(hx<0) {x = -x; y = -y;} | |
| 766 z = pio4-x; | |
| 767 w = pio4lo-y; | |
| 768 x = z+w; y = 0.0; | |
| 769 } | |
| 770 z = x*x; | |
| 771 w = z*z; | |
| 772 /* Break x^5*(T[1]+x^2*T[2]+...) into | |
| 773 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + | |
| 774 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) | |
| 775 */ | |
| 776 r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); | |
| 777 v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); | |
| 778 s = z*x; | |
| 779 r = y + z*(s*(r+v)+y); | |
| 780 r += T[0]*s; | |
| 781 w = x+r; | |
| 782 if(ix>=0x3FE59428) { | |
| 783 v = (double)iy; | |
| 784 return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); | |
| 785 } | |
| 786 if(iy==1) return w; | |
| 787 else { /* if allow error up to 2 ulp, | |
| 788 simply return -1.0/(x+r) here */ | |
| 789 /* compute -1.0/(x+r) accurately */ | |
| 790 double a,t; | |
| 791 z = w; | |
| 792 __LO(z) = 0; | |
| 793 v = r-(z - x); /* z+v = r+x */ | |
| 794 t = a = -1.0/w; /* a = -1.0/w */ | |
| 795 __LO(t) = 0; | |
| 796 s = 1.0+t*z; | |
| 797 return t+a*(s+t*v); | |
| 798 } | |
| 799 } | |
| 800 | |
| 801 | |
| 802 //---------------------------------------------------------------------- | |
| 803 // | |
| 804 // Routines for new sin/cos implementation | |
| 805 // | |
| 806 //---------------------------------------------------------------------- | |
| 807 | |
| 808 /* sin(x) | |
| 809 * Return sine function of x. | |
| 810 * | |
| 811 * kernel function: | |
| 812 * __kernel_sin ... sine function on [-pi/4,pi/4] | |
| 813 * __kernel_cos ... cose function on [-pi/4,pi/4] | |
| 814 * __ieee754_rem_pio2 ... argument reduction routine | |
| 815 * | |
| 816 * Method. | |
| 817 * Let S,C and T denote the sin, cos and tan respectively on | |
| 818 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 | |
| 819 * in [-pi/4 , +pi/4], and let n = k mod 4. | |
| 820 * We have | |
| 821 * | |
| 822 * n sin(x) cos(x) tan(x) | |
| 823 * ---------------------------------------------------------- | |
| 824 * 0 S C T | |
| 825 * 1 C -S -1/T | |
| 826 * 2 -S -C T | |
| 827 * 3 -C S -1/T | |
| 828 * ---------------------------------------------------------- | |
| 829 * | |
| 830 * Special cases: | |
| 831 * Let trig be any of sin, cos, or tan. | |
| 832 * trig(+-INF) is NaN, with signals; | |
| 833 * trig(NaN) is that NaN; | |
| 834 * | |
| 835 * Accuracy: | |
| 836 * TRIG(x) returns trig(x) nearly rounded | |
| 837 */ | |
| 838 | |
| 839 JRT_LEAF(jdouble, SharedRuntime::dsin(jdouble x)) | |
| 840 double y[2],z=0.0; | |
| 841 int n, ix; | |
| 842 | |
| 843 /* High word of x. */ | |
| 844 ix = __HI(x); | |
| 845 | |
| 846 /* |x| ~< pi/4 */ | |
| 847 ix &= 0x7fffffff; | |
| 848 if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); | |
| 849 | |
| 850 /* sin(Inf or NaN) is NaN */ | |
| 851 else if (ix>=0x7ff00000) return x-x; | |
| 852 | |
| 853 /* argument reduction needed */ | |
| 854 else { | |
| 855 n = __ieee754_rem_pio2(x,y); | |
| 856 switch(n&3) { | |
| 857 case 0: return __kernel_sin(y[0],y[1],1); | |
| 858 case 1: return __kernel_cos(y[0],y[1]); | |
| 859 case 2: return -__kernel_sin(y[0],y[1],1); | |
| 860 default: | |
| 861 return -__kernel_cos(y[0],y[1]); | |
| 862 } | |
| 863 } | |
| 864 JRT_END | |
| 865 | |
| 866 /* cos(x) | |
| 867 * Return cosine function of x. | |
| 868 * | |
| 869 * kernel function: | |
| 870 * __kernel_sin ... sine function on [-pi/4,pi/4] | |
| 871 * __kernel_cos ... cosine function on [-pi/4,pi/4] | |
| 872 * __ieee754_rem_pio2 ... argument reduction routine | |
| 873 * | |
| 874 * Method. | |
| 875 * Let S,C and T denote the sin, cos and tan respectively on | |
| 876 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 | |
| 877 * in [-pi/4 , +pi/4], and let n = k mod 4. | |
| 878 * We have | |
| 879 * | |
| 880 * n sin(x) cos(x) tan(x) | |
| 881 * ---------------------------------------------------------- | |
| 882 * 0 S C T | |
| 883 * 1 C -S -1/T | |
| 884 * 2 -S -C T | |
| 885 * 3 -C S -1/T | |
| 886 * ---------------------------------------------------------- | |
| 887 * | |
| 888 * Special cases: | |
| 889 * Let trig be any of sin, cos, or tan. | |
| 890 * trig(+-INF) is NaN, with signals; | |
| 891 * trig(NaN) is that NaN; | |
| 892 * | |
| 893 * Accuracy: | |
| 894 * TRIG(x) returns trig(x) nearly rounded | |
| 895 */ | |
| 896 | |
| 897 JRT_LEAF(jdouble, SharedRuntime::dcos(jdouble x)) | |
| 898 double y[2],z=0.0; | |
| 899 int n, ix; | |
| 900 | |
| 901 /* High word of x. */ | |
| 902 ix = __HI(x); | |
| 903 | |
| 904 /* |x| ~< pi/4 */ | |
| 905 ix &= 0x7fffffff; | |
| 906 if(ix <= 0x3fe921fb) return __kernel_cos(x,z); | |
| 907 | |
| 908 /* cos(Inf or NaN) is NaN */ | |
| 909 else if (ix>=0x7ff00000) return x-x; | |
| 910 | |
| 911 /* argument reduction needed */ | |
| 912 else { | |
| 913 n = __ieee754_rem_pio2(x,y); | |
| 914 switch(n&3) { | |
| 915 case 0: return __kernel_cos(y[0],y[1]); | |
| 916 case 1: return -__kernel_sin(y[0],y[1],1); | |
| 917 case 2: return -__kernel_cos(y[0],y[1]); | |
| 918 default: | |
| 919 return __kernel_sin(y[0],y[1],1); | |
| 920 } | |
| 921 } | |
| 922 JRT_END | |
| 923 | |
| 924 /* tan(x) | |
| 925 * Return tangent function of x. | |
| 926 * | |
| 927 * kernel function: | |
| 928 * __kernel_tan ... tangent function on [-pi/4,pi/4] | |
| 929 * __ieee754_rem_pio2 ... argument reduction routine | |
| 930 * | |
| 931 * Method. | |
| 932 * Let S,C and T denote the sin, cos and tan respectively on | |
| 933 * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 | |
| 934 * in [-pi/4 , +pi/4], and let n = k mod 4. | |
| 935 * We have | |
| 936 * | |
| 937 * n sin(x) cos(x) tan(x) | |
| 938 * ---------------------------------------------------------- | |
| 939 * 0 S C T | |
| 940 * 1 C -S -1/T | |
| 941 * 2 -S -C T | |
| 942 * 3 -C S -1/T | |
| 943 * ---------------------------------------------------------- | |
| 944 * | |
| 945 * Special cases: | |
| 946 * Let trig be any of sin, cos, or tan. | |
| 947 * trig(+-INF) is NaN, with signals; | |
| 948 * trig(NaN) is that NaN; | |
| 949 * | |
| 950 * Accuracy: | |
| 951 * TRIG(x) returns trig(x) nearly rounded | |
| 952 */ | |
| 953 | |
| 954 JRT_LEAF(jdouble, SharedRuntime::dtan(jdouble x)) | |
| 955 double y[2],z=0.0; | |
| 956 int n, ix; | |
| 957 | |
| 958 /* High word of x. */ | |
| 959 ix = __HI(x); | |
| 960 | |
| 961 /* |x| ~< pi/4 */ | |
| 962 ix &= 0x7fffffff; | |
| 963 if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); | |
| 964 | |
| 965 /* tan(Inf or NaN) is NaN */ | |
| 966 else if (ix>=0x7ff00000) return x-x; /* NaN */ | |
| 967 | |
| 968 /* argument reduction needed */ | |
| 969 else { | |
| 970 n = __ieee754_rem_pio2(x,y); | |
| 971 return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even | |
| 972 -1 -- n odd */ | |
| 973 } | |
| 974 JRT_END | |
| 975 | |
| 976 | |
| 977 #ifdef WIN32 | |
| 978 # pragma optimize ( "", on ) | |
| 979 #endif |