projects / thirdparty / glibc.git / blame
| Commit | Line | Data |
|---|---|---|
| f7eac6eb | 1 | /* |
| e4d82761 | 2 | * IBM Accurate Mathematical Library |
| aeb25823 | 3 | * written by International Business Machines Corp. |
| 0c59a196 | 4 | * Copyright (C) 2001, 2009 Free Software Foundation |
| f7eac6eb | 5 | * |
| e4d82761 UD |
6 | * This program is free software; you can redistribute it and/or modify |
| 7 | * it under the terms of the GNU Lesser General Public License as published by | |
| cc7375ce | 8 | * the Free Software Foundation; either version 2.1 of the License, or |
| e4d82761 | 9 | * (at your option) any later version. |
| f7eac6eb | 10 | * |
| e4d82761 UD |
11 | * This program is distributed in the hope that it will be useful, |
| 12 | * but WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 13 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
| c6c6dd48 | 14 | * GNU Lesser General Public License for more details. |
| f7eac6eb | 15 | * |
| e4d82761 UD |
16 | * You should have received a copy of the GNU Lesser General Public License |
| 17 | * along with this program; if not, write to the Free Software | |
| 18 | * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. | |
| f7eac6eb | 19 | */ |
| e4d82761 UD |
20 | /****************************************************************************/ |
| 21 | /* */ | |
| 22 | /* MODULE_NAME:usncs.c */ | |
| 23 | /* */ | |
| 24 | /* FUNCTIONS: usin */ | |
| 25 | /* ucos */ | |
| 26 | /* slow */ | |
| 27 | /* slow1 */ | |
| 28 | /* slow2 */ | |
| 29 | /* sloww */ | |
| 30 | /* sloww1 */ | |
| 31 | /* sloww2 */ | |
| 32 | /* bsloww */ | |
| 33 | /* bsloww1 */ | |
| 34 | /* bsloww2 */ | |
| 35 | /* cslow2 */ | |
| 36 | /* csloww */ | |
| 37 | /* csloww1 */ | |
| 38 | /* csloww2 */ | |
| 39 | /* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */ | |
| 40 | /* branred.c sincos32.c dosincos.c mpa.c */ | |
| 41 | /* sincos.tbl */ | |
| 42 | /* */ | |
| 43 | /* An ultimate sin and routine. Given an IEEE double machine number x */ | |
| 44 | /* it computes the correctly rounded (to nearest) value of sin(x) or cos(x) */ | |
| 45 | /* Assumption: Machine arithmetic operations are performed in */ | |
| 46 | /* round to nearest mode of IEEE 754 standard. */ | |
| 47 | /* */ | |
| 48 | /****************************************************************************/ | |
| f7eac6eb | 49 | |
| f7eac6eb | 50 | |
| 0c59a196 | 51 | #include <errno.h> |
| e4d82761 UD |
52 | #include "endian.h" |
| 53 | #include "mydefs.h" | |
| 54 | #include "usncs.h" | |
| 55 | #include "MathLib.h" | |
| 56 | #include "sincos.tbl" | |
| 15b3c029 | 57 | #include "math_private.h" |
| e4d82761 UD |
58 | |
| 59 | static const double | |
| 60 | sn3 = -1.66666666666664880952546298448555E-01, | |
| 61 | sn5 = 8.33333214285722277379541354343671E-03, | |
| 62 | cs2 = 4.99999999999999999999950396842453E-01, | |
| 63 | cs4 = -4.16666666666664434524222570944589E-02, | |
| 64 | cs6 = 1.38888874007937613028114285595617E-03; | |
| 65 | ||
| ca58f1db UD |
66 | void __dubsin(double x, double dx, double w[]); |
| 67 | void __docos(double x, double dx, double w[]); | |
| 50944bca UD |
68 | double __mpsin(double x, double dx); |
| 69 | double __mpcos(double x, double dx); | |
| 70 | double __mpsin1(double x); | |
| 71 | double __mpcos1(double x); | |
| e4d82761 UD |
72 | static double slow(double x); |
| 73 | static double slow1(double x); | |
| 74 | static double slow2(double x); | |
| 75 | static double sloww(double x, double dx, double orig); | |
| 76 | static double sloww1(double x, double dx, double orig); | |
| 77 | static double sloww2(double x, double dx, double orig, int n); | |
| 78 | static double bsloww(double x, double dx, double orig, int n); | |
| 79 | static double bsloww1(double x, double dx, double orig, int n); | |
| 80 | static double bsloww2(double x, double dx, double orig, int n); | |
| ca58f1db | 81 | int __branred(double x, double *a, double *aa); |
| e4d82761 UD |
82 | static double cslow2(double x); |
| 83 | static double csloww(double x, double dx, double orig); | |
| 84 | static double csloww1(double x, double dx, double orig); | |
| 85 | static double csloww2(double x, double dx, double orig, int n); | |
| 86 | /*******************************************************************/ | |
| 87 | /* An ultimate sin routine. Given an IEEE double machine number x */ | |
| 88 | /* it computes the correctly rounded (to nearest) value of sin(x) */ | |
| 89 | /*******************************************************************/ | |
| ca58f1db | 90 | double __sin(double x){ |
| 50944bca UD |
91 | double xx,res,t,cor,y,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2; |
| 92 | #if 0 | |
| 93 | double w[2]; | |
| 94 | #endif | |
| e4d82761 | 95 | mynumber u,v; |
| 50944bca UD |
96 | int4 k,m,n; |
| 97 | #if 0 | |
| 98 | int4 nn; | |
| 99 | #endif | |
| e4d82761 UD |
100 | |
| 101 | u.x = x; | |
| 102 | m = u.i[HIGH_HALF]; | |
| 103 | k = 0x7fffffff&m; /* no sign */ | |
| 104 | if (k < 0x3e500000) /* if x->0 =>sin(x)=x */ | |
| 105 | return x; | |
| 106 | /*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/ | |
| 107 | else if (k < 0x3fd00000){ | |
| 108 | xx = x*x; | |
| 109 | /*Taylor series */ | |
| 110 | t = ((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*(xx*x); | |
| 111 | res = x+t; | |
| 112 | cor = (x-res)+t; | |
| 113 | return (res == res + 1.07*cor)? res : slow(x); | |
| 114 | } /* else if (k < 0x3fd00000) */ | |
| 115 | /*---------------------------- 0.25<|x|< 0.855469---------------------- */ | |
| 116 | else if (k < 0x3feb6000) { | |
| 117 | u.x=(m>0)?big.x+x:big.x-x; | |
| 118 | y=(m>0)?x-(u.x-big.x):x+(u.x-big.x); | |
| 119 | xx=y*y; | |
| 120 | s = y + y*xx*(sn3 +xx*sn5); | |
| 121 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 122 | k=u.i[LOW_HALF]<<2; | |
| 123 | sn=(m>0)?sincos.x[k]:-sincos.x[k]; | |
| 124 | ssn=(m>0)?sincos.x[k+1]:-sincos.x[k+1]; | |
| 125 | cs=sincos.x[k+2]; | |
| 126 | ccs=sincos.x[k+3]; | |
| 127 | cor=(ssn+s*ccs-sn*c)+cs*s; | |
| 128 | res=sn+cor; | |
| 129 | cor=(sn-res)+cor; | |
| 130 | return (res==res+1.025*cor)? res : slow1(x); | |
| 131 | } /* else if (k < 0x3feb6000) */ | |
| 132 | ||
| 133 | /*----------------------- 0.855469 <|x|<2.426265 ----------------------*/ | |
| 134 | else if (k < 0x400368fd ) { | |
| 135 | ||
| 136 | y = (m>0)? hp0.x-x:hp0.x+x; | |
| 137 | if (y>=0) { | |
| 138 | u.x = big.x+y; | |
| 139 | y = (y-(u.x-big.x))+hp1.x; | |
| 140 | } | |
| 141 | else { | |
| 142 | u.x = big.x-y; | |
| 143 | y = (-hp1.x) - (y+(u.x-big.x)); | |
| 144 | } | |
| 145 | xx=y*y; | |
| 146 | s = y + y*xx*(sn3 +xx*sn5); | |
| 147 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 148 | k=u.i[LOW_HALF]<<2; | |
| 149 | sn=sincos.x[k]; | |
| 150 | ssn=sincos.x[k+1]; | |
| 151 | cs=sincos.x[k+2]; | |
| 152 | ccs=sincos.x[k+3]; | |
| 153 | cor=(ccs-s*ssn-cs*c)-sn*s; | |
| 154 | res=cs+cor; | |
| 155 | cor=(cs-res)+cor; | |
| 156 | return (res==res+1.020*cor)? ((m>0)?res:-res) : slow2(x); | |
| 157 | } /* else if (k < 0x400368fd) */ | |
| 158 | ||
| 159 | /*-------------------------- 2.426265<|x|< 105414350 ----------------------*/ | |
| 160 | else if (k < 0x419921FB ) { | |
| 161 | t = (x*hpinv.x + toint.x); | |
| 162 | xn = t - toint.x; | |
| 163 | v.x = t; | |
| 164 | y = (x - xn*mp1.x) - xn*mp2.x; | |
| 165 | n =v.i[LOW_HALF]&3; | |
| 166 | da = xn*mp3.x; | |
| 167 | a=y-da; | |
| 168 | da = (y-a)-da; | |
| 169 | eps = ABS(x)*1.2e-30; | |
| 170 | ||
| 171 | switch (n) { /* quarter of unit circle */ | |
| 172 | case 0: | |
| 173 | case 2: | |
| 174 | xx = a*a; | |
| 175 | if (n) {a=-a;da=-da;} | |
| 176 | if (xx < 0.01588) { | |
| 177 | /*Taylor series */ | |
| 178 | t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da; | |
| 179 | res = a+t; | |
| 180 | cor = (a-res)+t; | |
| 181 | cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps; | |
| 182 | return (res == res + cor)? res : sloww(a,da,x); | |
| f7eac6eb | 183 | } |
| e4d82761 UD |
184 | else { |
| 185 | if (a>0) | |
| 186 | {m=1;t=a;db=da;} | |
| 187 | else | |
| 188 | {m=0;t=-a;db=-da;} | |
| 189 | u.x=big.x+t; | |
| 190 | y=t-(u.x-big.x); | |
| 191 | xx=y*y; | |
| 192 | s = y + (db+y*xx*(sn3 +xx*sn5)); | |
| 193 | c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 194 | k=u.i[LOW_HALF]<<2; | |
| 195 | sn=sincos.x[k]; | |
| 196 | ssn=sincos.x[k+1]; | |
| 197 | cs=sincos.x[k+2]; | |
| 198 | ccs=sincos.x[k+3]; | |
| 199 | cor=(ssn+s*ccs-sn*c)+cs*s; | |
| 200 | res=sn+cor; | |
| 201 | cor=(sn-res)+cor; | |
| 202 | cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps; | |
| 203 | return (res==res+cor)? ((m)?res:-res) : sloww1(a,da,x); | |
| 204 | } | |
| 205 | break; | |
| 206 | ||
| 207 | case 1: | |
| 208 | case 3: | |
| 209 | if (a<0) | |
| 210 | {a=-a;da=-da;} | |
| 211 | u.x=big.x+a; | |
| 212 | y=a-(u.x-big.x)+da; | |
| 213 | xx=y*y; | |
| 214 | k=u.i[LOW_HALF]<<2; | |
| 215 | sn=sincos.x[k]; | |
| 216 | ssn=sincos.x[k+1]; | |
| 217 | cs=sincos.x[k+2]; | |
| 218 | ccs=sincos.x[k+3]; | |
| 219 | s = y + y*xx*(sn3 +xx*sn5); | |
| 220 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 221 | cor=(ccs-s*ssn-cs*c)-sn*s; | |
| 222 | res=cs+cor; | |
| 223 | cor=(cs-res)+cor; | |
| 224 | cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps; | |
| 225 | return (res==res+cor)? ((n&2)?-res:res) : sloww2(a,da,x,n); | |
| 226 | ||
| 227 | break; | |
| 228 | ||
| 229 | } | |
| 230 | ||
| 231 | } /* else if (k < 0x419921FB ) */ | |
| 232 | ||
| 233 | /*---------------------105414350 <|x|< 281474976710656 --------------------*/ | |
| 234 | else if (k < 0x42F00000 ) { | |
| 235 | t = (x*hpinv.x + toint.x); | |
| 236 | xn = t - toint.x; | |
| 237 | v.x = t; | |
| 238 | xn1 = (xn+8.0e22)-8.0e22; | |
| 239 | xn2 = xn - xn1; | |
| 240 | y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x); | |
| 241 | n =v.i[LOW_HALF]&3; | |
| 242 | da = xn1*pp3.x; | |
| 243 | t=y-da; | |
| 244 | da = (y-t)-da; | |
| 245 | da = (da - xn2*pp3.x) -xn*pp4.x; | |
| 246 | a = t+da; | |
| 247 | da = (t-a)+da; | |
| 248 | eps = 1.0e-24; | |
| 249 | ||
| 250 | switch (n) { | |
| 251 | case 0: | |
| 252 | case 2: | |
| 253 | xx = a*a; | |
| 254 | if (n) {a=-a;da=-da;} | |
| 255 | if (xx < 0.01588) { | |
| 256 | /* Taylor series */ | |
| 257 | t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da; | |
| 258 | res = a+t; | |
| 259 | cor = (a-res)+t; | |
| 260 | cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps; | |
| 261 | return (res == res + cor)? res : bsloww(a,da,x,n); | |
| 262 | } | |
| 263 | else { | |
| 264 | if (a>0) {m=1;t=a;db=da;} | |
| 265 | else {m=0;t=-a;db=-da;} | |
| 266 | u.x=big.x+t; | |
| 267 | y=t-(u.x-big.x); | |
| 268 | xx=y*y; | |
| 269 | s = y + (db+y*xx*(sn3 +xx*sn5)); | |
| 270 | c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 271 | k=u.i[LOW_HALF]<<2; | |
| 272 | sn=sincos.x[k]; | |
| 273 | ssn=sincos.x[k+1]; | |
| 274 | cs=sincos.x[k+2]; | |
| 275 | ccs=sincos.x[k+3]; | |
| 276 | cor=(ssn+s*ccs-sn*c)+cs*s; | |
| 277 | res=sn+cor; | |
| 278 | cor=(sn-res)+cor; | |
| 279 | cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps; | |
| 280 | return (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n); | |
| 281 | } | |
| 282 | break; | |
| 283 | ||
| 284 | case 1: | |
| 285 | case 3: | |
| 286 | if (a<0) | |
| 287 | {a=-a;da=-da;} | |
| 288 | u.x=big.x+a; | |
| 289 | y=a-(u.x-big.x)+da; | |
| 290 | xx=y*y; | |
| 291 | k=u.i[LOW_HALF]<<2; | |
| 292 | sn=sincos.x[k]; | |
| 293 | ssn=sincos.x[k+1]; | |
| 294 | cs=sincos.x[k+2]; | |
| 295 | ccs=sincos.x[k+3]; | |
| 296 | s = y + y*xx*(sn3 +xx*sn5); | |
| 297 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 298 | cor=(ccs-s*ssn-cs*c)-sn*s; | |
| 299 | res=cs+cor; | |
| 300 | cor=(cs-res)+cor; | |
| 301 | cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps; | |
| 302 | return (res==res+cor)? ((n&2)?-res:res) : bsloww2(a,da,x,n); | |
| 303 | ||
| 304 | break; | |
| 305 | ||
| 306 | } | |
| 307 | ||
| 308 | } /* else if (k < 0x42F00000 ) */ | |
| 309 | ||
| 310 | /* -----------------281474976710656 <|x| <2^1024----------------------------*/ | |
| 311 | else if (k < 0x7ff00000) { | |
| 312 | ||
| ca58f1db | 313 | n = __branred(x,&a,&da); |
| e4d82761 UD |
314 | switch (n) { |
| 315 | case 0: | |
| 316 | if (a*a < 0.01588) return bsloww(a,da,x,n); | |
| 317 | else return bsloww1(a,da,x,n); | |
| 318 | break; | |
| 319 | case 2: | |
| 320 | if (a*a < 0.01588) return bsloww(-a,-da,x,n); | |
| 321 | else return bsloww1(-a,-da,x,n); | |
| 322 | break; | |
| 323 | ||
| 324 | case 1: | |
| 325 | case 3: | |
| 326 | return bsloww2(a,da,x,n); | |
| 327 | break; | |
| 328 | } | |
| 329 | ||
| 330 | } /* else if (k < 0x7ff00000 ) */ | |
| 331 | ||
| 332 | /*--------------------- |x| > 2^1024 ----------------------------------*/ | |
| 0c59a196 UD |
333 | else { |
| 334 | if (k == 0x7ff00000 && u.i[LOW_HALF] == 0) | |
| 335 | __set_errno (EDOM); | |
| 336 | return x / x; | |
| 337 | } | |
| e4d82761 UD |
338 | return 0; /* unreachable */ |
| 339 | } | |
| 340 | ||
| 341 | ||
| 342 | /*******************************************************************/ | |
| 343 | /* An ultimate cos routine. Given an IEEE double machine number x */ | |
| 344 | /* it computes the correctly rounded (to nearest) value of cos(x) */ | |
| 345 | /*******************************************************************/ | |
| 346 | ||
| ca58f1db | 347 | double __cos(double x) |
| e4d82761 UD |
348 | { |
| 349 | double y,xx,res,t,cor,s,c,sn,ssn,cs,ccs,xn,a,da,db,eps,xn1,xn2; | |
| 350 | mynumber u,v; | |
| 351 | int4 k,m,n; | |
| 352 | ||
| 353 | u.x = x; | |
| 354 | m = u.i[HIGH_HALF]; | |
| 355 | k = 0x7fffffff&m; | |
| 356 | ||
| 357 | if (k < 0x3e400000 ) return 1.0; /* |x|<2^-27 => cos(x)=1 */ | |
| 358 | ||
| 359 | else if (k < 0x3feb6000 ) {/* 2^-27 < |x| < 0.855469 */ | |
| 360 | y=ABS(x); | |
| 361 | u.x = big.x+y; | |
| 362 | y = y-(u.x-big.x); | |
| 363 | xx=y*y; | |
| 364 | s = y + y*xx*(sn3 +xx*sn5); | |
| 365 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 366 | k=u.i[LOW_HALF]<<2; | |
| 367 | sn=sincos.x[k]; | |
| 368 | ssn=sincos.x[k+1]; | |
| 369 | cs=sincos.x[k+2]; | |
| 370 | ccs=sincos.x[k+3]; | |
| 371 | cor=(ccs-s*ssn-cs*c)-sn*s; | |
| 372 | res=cs+cor; | |
| 373 | cor=(cs-res)+cor; | |
| 374 | return (res==res+1.020*cor)? res : cslow2(x); | |
| 375 | ||
| 376 | } /* else if (k < 0x3feb6000) */ | |
| 377 | ||
| 378 | else if (k < 0x400368fd ) {/* 0.855469 <|x|<2.426265 */; | |
| 379 | y=hp0.x-ABS(x); | |
| 380 | a=y+hp1.x; | |
| 381 | da=(y-a)+hp1.x; | |
| 382 | xx=a*a; | |
| 383 | if (xx < 0.01588) { | |
| 384 | t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da; | |
| 385 | res = a+t; | |
| 386 | cor = (a-res)+t; | |
| 387 | cor = (cor>0)? 1.02*cor+1.0e-31 : 1.02*cor -1.0e-31; | |
| 388 | return (res == res + cor)? res : csloww(a,da,x); | |
| 389 | } | |
| 390 | else { | |
| 391 | if (a>0) {m=1;t=a;db=da;} | |
| 392 | else {m=0;t=-a;db=-da;} | |
| 393 | u.x=big.x+t; | |
| 394 | y=t-(u.x-big.x); | |
| 395 | xx=y*y; | |
| 396 | s = y + (db+y*xx*(sn3 +xx*sn5)); | |
| 397 | c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 398 | k=u.i[LOW_HALF]<<2; | |
| 399 | sn=sincos.x[k]; | |
| 400 | ssn=sincos.x[k+1]; | |
| 401 | cs=sincos.x[k+2]; | |
| 402 | ccs=sincos.x[k+3]; | |
| 403 | cor=(ssn+s*ccs-sn*c)+cs*s; | |
| 404 | res=sn+cor; | |
| 405 | cor=(sn-res)+cor; | |
| 406 | cor = (cor>0)? 1.035*cor+1.0e-31 : 1.035*cor-1.0e-31; | |
| 407 | return (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x); | |
| f7eac6eb | 408 | } |
| e4d82761 UD |
409 | |
| 410 | } /* else if (k < 0x400368fd) */ | |
| 411 | ||
| 412 | ||
| 413 | else if (k < 0x419921FB ) {/* 2.426265<|x|< 105414350 */ | |
| 414 | t = (x*hpinv.x + toint.x); | |
| 415 | xn = t - toint.x; | |
| 416 | v.x = t; | |
| 417 | y = (x - xn*mp1.x) - xn*mp2.x; | |
| 418 | n =v.i[LOW_HALF]&3; | |
| 419 | da = xn*mp3.x; | |
| 420 | a=y-da; | |
| 421 | da = (y-a)-da; | |
| 422 | eps = ABS(x)*1.2e-30; | |
| 423 | ||
| 424 | switch (n) { | |
| 425 | case 1: | |
| 426 | case 3: | |
| 427 | xx = a*a; | |
| 428 | if (n == 1) {a=-a;da=-da;} | |
| 429 | if (xx < 0.01588) { | |
| 430 | t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da; | |
| 431 | res = a+t; | |
| 432 | cor = (a-res)+t; | |
| 433 | cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps; | |
| 434 | return (res == res + cor)? res : csloww(a,da,x); | |
| 435 | } | |
| 436 | else { | |
| 437 | if (a>0) {m=1;t=a;db=da;} | |
| 438 | else {m=0;t=-a;db=-da;} | |
| 439 | u.x=big.x+t; | |
| 440 | y=t-(u.x-big.x); | |
| 441 | xx=y*y; | |
| 442 | s = y + (db+y*xx*(sn3 +xx*sn5)); | |
| 443 | c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 444 | k=u.i[LOW_HALF]<<2; | |
| 445 | sn=sincos.x[k]; | |
| 446 | ssn=sincos.x[k+1]; | |
| 447 | cs=sincos.x[k+2]; | |
| 448 | ccs=sincos.x[k+3]; | |
| 449 | cor=(ssn+s*ccs-sn*c)+cs*s; | |
| 450 | res=sn+cor; | |
| 451 | cor=(sn-res)+cor; | |
| 452 | cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps; | |
| 453 | return (res==res+cor)? ((m)?res:-res) : csloww1(a,da,x); | |
| 454 | } | |
| 455 | break; | |
| 456 | ||
| 457 | case 0: | |
| 458 | case 2: | |
| 459 | if (a<0) {a=-a;da=-da;} | |
| 460 | u.x=big.x+a; | |
| 461 | y=a-(u.x-big.x)+da; | |
| 462 | xx=y*y; | |
| 463 | k=u.i[LOW_HALF]<<2; | |
| 464 | sn=sincos.x[k]; | |
| 465 | ssn=sincos.x[k+1]; | |
| 466 | cs=sincos.x[k+2]; | |
| 467 | ccs=sincos.x[k+3]; | |
| 468 | s = y + y*xx*(sn3 +xx*sn5); | |
| 469 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 470 | cor=(ccs-s*ssn-cs*c)-sn*s; | |
| 471 | res=cs+cor; | |
| 472 | cor=(cs-res)+cor; | |
| 473 | cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps; | |
| 474 | return (res==res+cor)? ((n)?-res:res) : csloww2(a,da,x,n); | |
| 475 | ||
| 476 | break; | |
| 477 | ||
| 478 | } | |
| 479 | ||
| 480 | } /* else if (k < 0x419921FB ) */ | |
| 481 | ||
| 482 | ||
| 483 | else if (k < 0x42F00000 ) { | |
| 484 | t = (x*hpinv.x + toint.x); | |
| 485 | xn = t - toint.x; | |
| 486 | v.x = t; | |
| 487 | xn1 = (xn+8.0e22)-8.0e22; | |
| 488 | xn2 = xn - xn1; | |
| 489 | y = ((((x - xn1*mp1.x) - xn1*mp2.x)-xn2*mp1.x)-xn2*mp2.x); | |
| 490 | n =v.i[LOW_HALF]&3; | |
| 491 | da = xn1*pp3.x; | |
| 492 | t=y-da; | |
| 493 | da = (y-t)-da; | |
| 494 | da = (da - xn2*pp3.x) -xn*pp4.x; | |
| 495 | a = t+da; | |
| 496 | da = (t-a)+da; | |
| 497 | eps = 1.0e-24; | |
| 498 | ||
| 499 | switch (n) { | |
| 500 | case 1: | |
| 501 | case 3: | |
| 502 | xx = a*a; | |
| 503 | if (n==1) {a=-a;da=-da;} | |
| 504 | if (xx < 0.01588) { | |
| 505 | t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + s1.x)*a - 0.5*da)*xx+da; | |
| 506 | res = a+t; | |
| 507 | cor = (a-res)+t; | |
| 508 | cor = (cor>0)? 1.02*cor+eps : 1.02*cor -eps; | |
| 509 | return (res == res + cor)? res : bsloww(a,da,x,n); | |
| 510 | } | |
| 511 | else { | |
| 512 | if (a>0) {m=1;t=a;db=da;} | |
| 513 | else {m=0;t=-a;db=-da;} | |
| 514 | u.x=big.x+t; | |
| 515 | y=t-(u.x-big.x); | |
| 516 | xx=y*y; | |
| 517 | s = y + (db+y*xx*(sn3 +xx*sn5)); | |
| 518 | c = y*db+xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 519 | k=u.i[LOW_HALF]<<2; | |
| 520 | sn=sincos.x[k]; | |
| 521 | ssn=sincos.x[k+1]; | |
| 522 | cs=sincos.x[k+2]; | |
| 523 | ccs=sincos.x[k+3]; | |
| 524 | cor=(ssn+s*ccs-sn*c)+cs*s; | |
| 525 | res=sn+cor; | |
| 526 | cor=(sn-res)+cor; | |
| 527 | cor = (cor>0)? 1.035*cor+eps : 1.035*cor-eps; | |
| 528 | return (res==res+cor)? ((m)?res:-res) : bsloww1(a,da,x,n); | |
| 529 | } | |
| 530 | break; | |
| 531 | ||
| 532 | case 0: | |
| 533 | case 2: | |
| 534 | if (a<0) {a=-a;da=-da;} | |
| 535 | u.x=big.x+a; | |
| 536 | y=a-(u.x-big.x)+da; | |
| 537 | xx=y*y; | |
| 538 | k=u.i[LOW_HALF]<<2; | |
| 539 | sn=sincos.x[k]; | |
| 540 | ssn=sincos.x[k+1]; | |
| 541 | cs=sincos.x[k+2]; | |
| 542 | ccs=sincos.x[k+3]; | |
| 543 | s = y + y*xx*(sn3 +xx*sn5); | |
| 544 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 545 | cor=(ccs-s*ssn-cs*c)-sn*s; | |
| 546 | res=cs+cor; | |
| 547 | cor=(cs-res)+cor; | |
| 548 | cor = (cor>0)? 1.025*cor+eps : 1.025*cor-eps; | |
| 549 | return (res==res+cor)? ((n)?-res:res) : bsloww2(a,da,x,n); | |
| 550 | break; | |
| 551 | ||
| 552 | } | |
| 553 | ||
| 554 | } /* else if (k < 0x42F00000 ) */ | |
| 555 | ||
| 556 | else if (k < 0x7ff00000) {/* 281474976710656 <|x| <2^1024 */ | |
| 557 | ||
| ca58f1db | 558 | n = __branred(x,&a,&da); |
| e4d82761 UD |
559 | switch (n) { |
| 560 | case 1: | |
| 561 | if (a*a < 0.01588) return bsloww(-a,-da,x,n); | |
| 562 | else return bsloww1(-a,-da,x,n); | |
| 563 | break; | |
| 564 | case 3: | |
| 565 | if (a*a < 0.01588) return bsloww(a,da,x,n); | |
| 566 | else return bsloww1(a,da,x,n); | |
| 567 | break; | |
| 568 | ||
| 569 | case 0: | |
| 570 | case 2: | |
| 571 | return bsloww2(a,da,x,n); | |
| 572 | break; | |
| 573 | } | |
| 574 | ||
| 575 | } /* else if (k < 0x7ff00000 ) */ | |
| 576 | ||
| 577 | ||
| 578 | ||
| 579 | ||
| 0c59a196 UD |
580 | else { |
| 581 | if (k == 0x7ff00000 && u.i[LOW_HALF] == 0) | |
| 582 | __set_errno (EDOM); | |
| 583 | return x / x; /* |x| > 2^1024 */ | |
| 584 | } | |
| e4d82761 UD |
585 | return 0; |
| 586 | ||
| 587 | } | |
| 588 | ||
| 589 | /************************************************************************/ | |
| 590 | /* Routine compute sin(x) for 2^-26 < |x|< 0.25 by Taylor with more */ | |
| 591 | /* precision and if still doesn't accurate enough by mpsin or dubsin */ | |
| 592 | /************************************************************************/ | |
| 593 | ||
| 594 | static double slow(double x) { | |
| 595 | static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ | |
| 596 | double y,x1,x2,xx,r,t,res,cor,w[2]; | |
| 597 | x1=(x+th2_36)-th2_36; | |
| 598 | y = aa.x*x1*x1*x1; | |
| 599 | r=x+y; | |
| 600 | x2=x-x1; | |
| 601 | xx=x*x; | |
| 602 | t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2; | |
| 603 | t=((x-r)+y)+t; | |
| 604 | res=r+t; | |
| 605 | cor = (r-res)+t; | |
| 606 | if (res == res + 1.0007*cor) return res; | |
| 607 | else { | |
| ca58f1db | 608 | __dubsin(ABS(x),0,w); |
| e4d82761 | 609 | if (w[0] == w[0]+1.000000001*w[1]) return (x>0)?w[0]:-w[0]; |
| 50944bca | 610 | else return (x>0)?__mpsin(x,0):-__mpsin(-x,0); |
| e4d82761 UD |
611 | } |
| 612 | } | |
| 613 | /*******************************************************************************/ | |
| 614 | /* Routine compute sin(x) for 0.25<|x|< 0.855469 by sincos.tbl and Taylor */ | |
| 615 | /* and if result still doesn't accurate enough by mpsin or dubsin */ | |
| 616 | /*******************************************************************************/ | |
| 617 | ||
| 618 | static double slow1(double x) { | |
| 619 | mynumber u; | |
| 620 | double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res; | |
| 621 | static const double t22 = 6291456.0; | |
| 622 | int4 k; | |
| 623 | y=ABS(x); | |
| 624 | u.x=big.x+y; | |
| 625 | y=y-(u.x-big.x); | |
| 626 | xx=y*y; | |
| 627 | s = y*xx*(sn3 +xx*sn5); | |
| 628 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 629 | k=u.i[LOW_HALF]<<2; | |
| 630 | sn=sincos.x[k]; /* Data */ | |
| 631 | ssn=sincos.x[k+1]; /* from */ | |
| 632 | cs=sincos.x[k+2]; /* tables */ | |
| 633 | ccs=sincos.x[k+3]; /* sincos.tbl */ | |
| 634 | y1 = (y+t22)-t22; | |
| 635 | y2 = y - y1; | |
| 636 | c1 = (cs+t22)-t22; | |
| 637 | c2=(cs-c1)+ccs; | |
| 638 | cor=(ssn+s*ccs+cs*s+c2*y+c1*y2)-sn*c; | |
| 639 | y=sn+c1*y1; | |
| 640 | cor = cor+((sn-y)+c1*y1); | |
| 641 | res=y+cor; | |
| 642 | cor=(y-res)+cor; | |
| 643 | if (res == res+1.0005*cor) return (x>0)?res:-res; | |
| 644 | else { | |
| ca58f1db | 645 | __dubsin(ABS(x),0,w); |
| e4d82761 | 646 | if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0]; |
| 50944bca | 647 | else return (x>0)?__mpsin(x,0):-__mpsin(-x,0); |
| e4d82761 UD |
648 | } |
| 649 | } | |
| 650 | /**************************************************************************/ | |
| 651 | /* Routine compute sin(x) for 0.855469 <|x|<2.426265 by sincos.tbl */ | |
| 652 | /* and if result still doesn't accurate enough by mpsin or dubsin */ | |
| 653 | /**************************************************************************/ | |
| 654 | static double slow2(double x) { | |
| 655 | mynumber u; | |
| 656 | double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res,del; | |
| 657 | static const double t22 = 6291456.0; | |
| 658 | int4 k; | |
| 659 | y=ABS(x); | |
| 660 | y = hp0.x-y; | |
| 661 | if (y>=0) { | |
| 662 | u.x = big.x+y; | |
| 663 | y = y-(u.x-big.x); | |
| 664 | del = hp1.x; | |
| 665 | } | |
| 666 | else { | |
| 667 | u.x = big.x-y; | |
| 668 | y = -(y+(u.x-big.x)); | |
| 669 | del = -hp1.x; | |
| 670 | } | |
| 671 | xx=y*y; | |
| 672 | s = y*xx*(sn3 +xx*sn5); | |
| 673 | c = y*del+xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 674 | k=u.i[LOW_HALF]<<2; | |
| 675 | sn=sincos.x[k]; | |
| 676 | ssn=sincos.x[k+1]; | |
| 677 | cs=sincos.x[k+2]; | |
| 678 | ccs=sincos.x[k+3]; | |
| 679 | y1 = (y+t22)-t22; | |
| 680 | y2 = (y - y1)+del; | |
| 681 | e1 = (sn+t22)-t22; | |
| 682 | e2=(sn-e1)+ssn; | |
| 683 | cor=(ccs-cs*c-e1*y2-e2*y)-sn*s; | |
| 684 | y=cs-e1*y1; | |
| 685 | cor = cor+((cs-y)-e1*y1); | |
| 686 | res=y+cor; | |
| 687 | cor=(y-res)+cor; | |
| 688 | if (res == res+1.0005*cor) return (x>0)?res:-res; | |
| 689 | else { | |
| 690 | y=ABS(x)-hp0.x; | |
| 691 | y1=y-hp1.x; | |
| 692 | y2=(y-y1)-hp1.x; | |
| ca58f1db | 693 | __docos(y1,y2,w); |
| e4d82761 | 694 | if (w[0] == w[0]+1.000000005*w[1]) return (x>0)?w[0]:-w[0]; |
| 50944bca | 695 | else return (x>0)?__mpsin(x,0):-__mpsin(-x,0); |
| e4d82761 UD |
696 | } |
| 697 | } | |
| 698 | /***************************************************************************/ | |
| 699 | /* Routine compute sin(x+dx) (Double-Length number) where x is small enough*/ | |
| 700 | /* to use Taylor series around zero and (x+dx) */ | |
| 701 | /* in first or third quarter of unit circle.Routine receive also */ | |
| 702 | /* (right argument) the original value of x for computing error of */ | |
| 703 | /* result.And if result not accurate enough routine calls mpsin1 or dubsin */ | |
| 704 | /***************************************************************************/ | |
| 705 | ||
| 706 | static double sloww(double x,double dx, double orig) { | |
| 707 | static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ | |
| 708 | double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn; | |
| 709 | union {int4 i[2]; double x;} v; | |
| 710 | int4 n; | |
| 711 | x1=(x+th2_36)-th2_36; | |
| 712 | y = aa.x*x1*x1*x1; | |
| 713 | r=x+y; | |
| 714 | x2=(x-x1)+dx; | |
| 715 | xx=x*x; | |
| 716 | t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx; | |
| 717 | t=((x-r)+y)+t; | |
| 718 | res=r+t; | |
| 719 | cor = (r-res)+t; | |
| 720 | cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30; | |
| 721 | if (res == res + cor) return res; | |
| 722 | else { | |
| ca58f1db | 723 | (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w); |
| e4d82761 UD |
724 | cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30; |
| 725 | if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; | |
| 726 | else { | |
| 727 | t = (orig*hpinv.x + toint.x); | |
| 728 | xn = t - toint.x; | |
| 729 | v.x = t; | |
| 730 | y = (orig - xn*mp1.x) - xn*mp2.x; | |
| 731 | n =v.i[LOW_HALF]&3; | |
| 732 | da = xn*pp3.x; | |
| 733 | t=y-da; | |
| 734 | da = (y-t)-da; | |
| 735 | y = xn*pp4.x; | |
| 736 | a = t - y; | |
| 737 | da = ((t-a)-y)+da; | |
| 738 | if (n&2) {a=-a; da=-da;} | |
| ca58f1db | 739 | (a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w); |
| e4d82761 UD |
740 | cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40; |
| 741 | if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0]; | |
| 50944bca | 742 | else return __mpsin1(orig); |
| e4d82761 UD |
743 | } |
| 744 | } | |
| 745 | } | |
| 746 | /***************************************************************************/ | |
| 747 | /* Routine compute sin(x+dx) (Double-Length number) where x in first or */ | |
| 748 | /* third quarter of unit circle.Routine receive also (right argument) the */ | |
| 749 | /* original value of x for computing error of result.And if result not */ | |
| 750 | /* accurate enough routine calls mpsin1 or dubsin */ | |
| 751 | /***************************************************************************/ | |
| 752 | ||
| 753 | static double sloww1(double x, double dx, double orig) { | |
| 754 | mynumber u; | |
| 755 | double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res; | |
| 756 | static const double t22 = 6291456.0; | |
| 757 | int4 k; | |
| 758 | y=ABS(x); | |
| 759 | u.x=big.x+y; | |
| 760 | y=y-(u.x-big.x); | |
| 761 | dx=(x>0)?dx:-dx; | |
| 762 | xx=y*y; | |
| 763 | s = y*xx*(sn3 +xx*sn5); | |
| 764 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 765 | k=u.i[LOW_HALF]<<2; | |
| 766 | sn=sincos.x[k]; | |
| 767 | ssn=sincos.x[k+1]; | |
| 768 | cs=sincos.x[k+2]; | |
| 769 | ccs=sincos.x[k+3]; | |
| 770 | y1 = (y+t22)-t22; | |
| 771 | y2 = (y - y1)+dx; | |
| 772 | c1 = (cs+t22)-t22; | |
| 773 | c2=(cs-c1)+ccs; | |
| 774 | cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c; | |
| 775 | y=sn+c1*y1; | |
| 776 | cor = cor+((sn-y)+c1*y1); | |
| 777 | res=y+cor; | |
| 778 | cor=(y-res)+cor; | |
| 779 | cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig); | |
| 780 | if (res == res + cor) return (x>0)?res:-res; | |
| 781 | else { | |
| ca58f1db | 782 | __dubsin(ABS(x),dx,w); |
| e4d82761 UD |
783 | cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig); |
| 784 | if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; | |
| 50944bca | 785 | else return __mpsin1(orig); |
| e4d82761 UD |
786 | } |
| 787 | } | |
| 788 | /***************************************************************************/ | |
| 789 | /* Routine compute sin(x+dx) (Double-Length number) where x in second or */ | |
| 790 | /* fourth quarter of unit circle.Routine receive also the original value */ | |
| 791 | /* and quarter(n= 1or 3)of x for computing error of result.And if result not*/ | |
| 792 | /* accurate enough routine calls mpsin1 or dubsin */ | |
| 793 | /***************************************************************************/ | |
| 794 | ||
| 795 | static double sloww2(double x, double dx, double orig, int n) { | |
| 796 | mynumber u; | |
| 797 | double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res; | |
| 798 | static const double t22 = 6291456.0; | |
| 799 | int4 k; | |
| 800 | y=ABS(x); | |
| 801 | u.x=big.x+y; | |
| 802 | y=y-(u.x-big.x); | |
| 803 | dx=(x>0)?dx:-dx; | |
| 804 | xx=y*y; | |
| 805 | s = y*xx*(sn3 +xx*sn5); | |
| 806 | c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 807 | k=u.i[LOW_HALF]<<2; | |
| 808 | sn=sincos.x[k]; | |
| 809 | ssn=sincos.x[k+1]; | |
| 810 | cs=sincos.x[k+2]; | |
| 811 | ccs=sincos.x[k+3]; | |
| 812 | ||
| 813 | y1 = (y+t22)-t22; | |
| 814 | y2 = (y - y1)+dx; | |
| 815 | e1 = (sn+t22)-t22; | |
| 816 | e2=(sn-e1)+ssn; | |
| 817 | cor=(ccs-cs*c-e1*y2-e2*y)-sn*s; | |
| 818 | y=cs-e1*y1; | |
| 819 | cor = cor+((cs-y)-e1*y1); | |
| 820 | res=y+cor; | |
| 821 | cor=(y-res)+cor; | |
| 822 | cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig); | |
| 823 | if (res == res + cor) return (n&2)?-res:res; | |
| 824 | else { | |
| ca58f1db | 825 | __docos(ABS(x),dx,w); |
| e4d82761 UD |
826 | cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig); |
| 827 | if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0]; | |
| 50944bca | 828 | else return __mpsin1(orig); |
| e4d82761 UD |
829 | } |
| 830 | } | |
| 831 | /***************************************************************************/ | |
| 832 | /* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ | |
| 833 | /* is small enough to use Taylor series around zero and (x+dx) */ | |
| 834 | /* in first or third quarter of unit circle.Routine receive also */ | |
| 835 | /* (right argument) the original value of x for computing error of */ | |
| 836 | /* result.And if result not accurate enough routine calls other routines */ | |
| 837 | /***************************************************************************/ | |
| 838 | ||
| 839 | static double bsloww(double x,double dx, double orig,int n) { | |
| 840 | static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ | |
| 50944bca UD |
841 | double y,x1,x2,xx,r,t,res,cor,w[2]; |
| 842 | #if 0 | |
| 843 | double a,da,xn; | |
| e4d82761 | 844 | union {int4 i[2]; double x;} v; |
| 50944bca | 845 | #endif |
| e4d82761 UD |
846 | x1=(x+th2_36)-th2_36; |
| 847 | y = aa.x*x1*x1*x1; | |
| 848 | r=x+y; | |
| 849 | x2=(x-x1)+dx; | |
| 850 | xx=x*x; | |
| 851 | t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx; | |
| 852 | t=((x-r)+y)+t; | |
| 853 | res=r+t; | |
| 854 | cor = (r-res)+t; | |
| 855 | cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24; | |
| 856 | if (res == res + cor) return res; | |
| 857 | else { | |
| ca58f1db | 858 | (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w); |
| e4d82761 UD |
859 | cor = (w[1]>0)? 1.000000001*w[1] + 1.1e-24 : 1.000000001*w[1] - 1.1e-24; |
| 860 | if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; | |
| 50944bca | 861 | else return (n&1)?__mpcos1(orig):__mpsin1(orig); |
| e4d82761 UD |
862 | } |
| 863 | } | |
| 864 | ||
| 865 | /***************************************************************************/ | |
| 866 | /* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ | |
| 867 | /* in first or third quarter of unit circle.Routine receive also */ | |
| 868 | /* (right argument) the original value of x for computing error of result.*/ | |
| 869 | /* And if result not accurate enough routine calls other routines */ | |
| 870 | /***************************************************************************/ | |
| 871 | ||
| 872 | static double bsloww1(double x, double dx, double orig,int n) { | |
| 873 | mynumber u; | |
| 874 | double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res; | |
| 875 | static const double t22 = 6291456.0; | |
| 876 | int4 k; | |
| 877 | y=ABS(x); | |
| 878 | u.x=big.x+y; | |
| 879 | y=y-(u.x-big.x); | |
| 880 | dx=(x>0)?dx:-dx; | |
| 881 | xx=y*y; | |
| 882 | s = y*xx*(sn3 +xx*sn5); | |
| 883 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 884 | k=u.i[LOW_HALF]<<2; | |
| 885 | sn=sincos.x[k]; | |
| 886 | ssn=sincos.x[k+1]; | |
| 887 | cs=sincos.x[k+2]; | |
| 888 | ccs=sincos.x[k+3]; | |
| 889 | y1 = (y+t22)-t22; | |
| 890 | y2 = (y - y1)+dx; | |
| 891 | c1 = (cs+t22)-t22; | |
| 892 | c2=(cs-c1)+ccs; | |
| 893 | cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c; | |
| 894 | y=sn+c1*y1; | |
| 895 | cor = cor+((sn-y)+c1*y1); | |
| 896 | res=y+cor; | |
| 897 | cor=(y-res)+cor; | |
| 898 | cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24; | |
| 899 | if (res == res + cor) return (x>0)?res:-res; | |
| 900 | else { | |
| ca58f1db | 901 | __dubsin(ABS(x),dx,w); |
| e4d82761 UD |
902 | cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24: 1.000000005*w[1]-1.1e-24; |
| 903 | if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; | |
| 50944bca | 904 | else return (n&1)?__mpcos1(orig):__mpsin1(orig); |
| e4d82761 UD |
905 | } |
| 906 | } | |
| 907 | ||
| 908 | /***************************************************************************/ | |
| 909 | /* Routine compute sin(x+dx) or cos(x+dx) (Double-Length number) where x */ | |
| 910 | /* in second or fourth quarter of unit circle.Routine receive also the */ | |
| 911 | /* original value and quarter(n= 1or 3)of x for computing error of result. */ | |
| 912 | /* And if result not accurate enough routine calls other routines */ | |
| 913 | /***************************************************************************/ | |
| 914 | ||
| 915 | static double bsloww2(double x, double dx, double orig, int n) { | |
| 916 | mynumber u; | |
| 917 | double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res; | |
| 918 | static const double t22 = 6291456.0; | |
| 919 | int4 k; | |
| 920 | y=ABS(x); | |
| 921 | u.x=big.x+y; | |
| 922 | y=y-(u.x-big.x); | |
| 923 | dx=(x>0)?dx:-dx; | |
| 924 | xx=y*y; | |
| 925 | s = y*xx*(sn3 +xx*sn5); | |
| 926 | c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 927 | k=u.i[LOW_HALF]<<2; | |
| 928 | sn=sincos.x[k]; | |
| 929 | ssn=sincos.x[k+1]; | |
| 930 | cs=sincos.x[k+2]; | |
| 931 | ccs=sincos.x[k+3]; | |
| 932 | ||
| 933 | y1 = (y+t22)-t22; | |
| 934 | y2 = (y - y1)+dx; | |
| 935 | e1 = (sn+t22)-t22; | |
| 936 | e2=(sn-e1)+ssn; | |
| 937 | cor=(ccs-cs*c-e1*y2-e2*y)-sn*s; | |
| 938 | y=cs-e1*y1; | |
| 939 | cor = cor+((cs-y)-e1*y1); | |
| 940 | res=y+cor; | |
| 941 | cor=(y-res)+cor; | |
| 942 | cor = (cor>0)? 1.0005*cor+1.1e-24 : 1.0005*cor-1.1e-24; | |
| 943 | if (res == res + cor) return (n&2)?-res:res; | |
| 944 | else { | |
| ca58f1db | 945 | __docos(ABS(x),dx,w); |
| e4d82761 UD |
946 | cor = (w[1]>0)? 1.000000005*w[1]+1.1e-24 : 1.000000005*w[1]-1.1e-24; |
| 947 | if (w[0] == w[0]+cor) return (n&2)?-w[0]:w[0]; | |
| 50944bca | 948 | else return (n&1)?__mpsin1(orig):__mpcos1(orig); |
| e4d82761 UD |
949 | } |
| 950 | } | |
| 951 | ||
| 952 | /************************************************************************/ | |
| 953 | /* Routine compute cos(x) for 2^-27 < |x|< 0.25 by Taylor with more */ | |
| 954 | /* precision and if still doesn't accurate enough by mpcos or docos */ | |
| 955 | /************************************************************************/ | |
| 956 | ||
| 957 | static double cslow2(double x) { | |
| 958 | mynumber u; | |
| 959 | double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res; | |
| 960 | static const double t22 = 6291456.0; | |
| 961 | int4 k; | |
| 962 | y=ABS(x); | |
| 963 | u.x = big.x+y; | |
| 964 | y = y-(u.x-big.x); | |
| 965 | xx=y*y; | |
| 966 | s = y*xx*(sn3 +xx*sn5); | |
| 967 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 968 | k=u.i[LOW_HALF]<<2; | |
| 969 | sn=sincos.x[k]; | |
| 970 | ssn=sincos.x[k+1]; | |
| 971 | cs=sincos.x[k+2]; | |
| 972 | ccs=sincos.x[k+3]; | |
| 973 | y1 = (y+t22)-t22; | |
| 974 | y2 = y - y1; | |
| 975 | e1 = (sn+t22)-t22; | |
| 976 | e2=(sn-e1)+ssn; | |
| 977 | cor=(ccs-cs*c-e1*y2-e2*y)-sn*s; | |
| 978 | y=cs-e1*y1; | |
| 979 | cor = cor+((cs-y)-e1*y1); | |
| 980 | res=y+cor; | |
| 981 | cor=(y-res)+cor; | |
| 982 | if (res == res+1.0005*cor) | |
| 983 | return res; | |
| 984 | else { | |
| 985 | y=ABS(x); | |
| ca58f1db | 986 | __docos(y,0,w); |
| e4d82761 | 987 | if (w[0] == w[0]+1.000000005*w[1]) return w[0]; |
| 50944bca | 988 | else return __mpcos(x,0); |
| e4d82761 UD |
989 | } |
| 990 | } | |
| 991 | ||
| 992 | /***************************************************************************/ | |
| 993 | /* Routine compute cos(x+dx) (Double-Length number) where x is small enough*/ | |
| 994 | /* to use Taylor series around zero and (x+dx) .Routine receive also */ | |
| 995 | /* (right argument) the original value of x for computing error of */ | |
| 996 | /* result.And if result not accurate enough routine calls other routines */ | |
| 997 | /***************************************************************************/ | |
| 998 | ||
| 999 | ||
| 1000 | static double csloww(double x,double dx, double orig) { | |
| 1001 | static const double th2_36 = 206158430208.0; /* 1.5*2**37 */ | |
| 1002 | double y,x1,x2,xx,r,t,res,cor,w[2],a,da,xn; | |
| 1003 | union {int4 i[2]; double x;} v; | |
| 1004 | int4 n; | |
| 1005 | x1=(x+th2_36)-th2_36; | |
| 1006 | y = aa.x*x1*x1*x1; | |
| 1007 | r=x+y; | |
| 1008 | x2=(x-x1)+dx; | |
| 1009 | xx=x*x; | |
| 1010 | /* Taylor series */ | |
| 1011 | t = (((((s5.x*xx + s4.x)*xx + s3.x)*xx + s2.x)*xx + bb.x)*xx + 3.0*aa.x*x1*x2)*x +aa.x*x2*x2*x2+dx; | |
| 1012 | t=((x-r)+y)+t; | |
| 1013 | res=r+t; | |
| 1014 | cor = (r-res)+t; | |
| 1015 | cor = (cor>0)? 1.0005*cor+ABS(orig)*3.1e-30 : 1.0005*cor-ABS(orig)*3.1e-30; | |
| 1016 | if (res == res + cor) return res; | |
| 1017 | else { | |
| ca58f1db | 1018 | (x>0)? __dubsin(x,dx,w) : __dubsin(-x,-dx,w); |
| e4d82761 UD |
1019 | cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-30 : 1.000000001*w[1] - ABS(orig)*1.1e-30; |
| 1020 | if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; | |
| 1021 | else { | |
| 1022 | t = (orig*hpinv.x + toint.x); | |
| 1023 | xn = t - toint.x; | |
| 1024 | v.x = t; | |
| 1025 | y = (orig - xn*mp1.x) - xn*mp2.x; | |
| 1026 | n =v.i[LOW_HALF]&3; | |
| 1027 | da = xn*pp3.x; | |
| 1028 | t=y-da; | |
| 1029 | da = (y-t)-da; | |
| 1030 | y = xn*pp4.x; | |
| 1031 | a = t - y; | |
| 1032 | da = ((t-a)-y)+da; | |
| 1033 | if (n==1) {a=-a; da=-da;} | |
| ca58f1db | 1034 | (a>0)? __dubsin(a,da,w) : __dubsin(-a,-da,w); |
| e4d82761 UD |
1035 | cor = (w[1]>0)? 1.000000001*w[1] + ABS(orig)*1.1e-40 : 1.000000001*w[1] - ABS(orig)*1.1e-40; |
| 1036 | if (w[0] == w[0]+cor) return (a>0)?w[0]:-w[0]; | |
| 50944bca | 1037 | else return __mpcos1(orig); |
| e4d82761 UD |
1038 | } |
| 1039 | } | |
| 1040 | } | |
| 1041 | ||
| 1042 | /***************************************************************************/ | |
| 1043 | /* Routine compute sin(x+dx) (Double-Length number) where x in first or */ | |
| 1044 | /* third quarter of unit circle.Routine receive also (right argument) the */ | |
| 1045 | /* original value of x for computing error of result.And if result not */ | |
| 1046 | /* accurate enough routine calls other routines */ | |
| 1047 | /***************************************************************************/ | |
| 1048 | ||
| 1049 | static double csloww1(double x, double dx, double orig) { | |
| 1050 | mynumber u; | |
| 1051 | double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,c1,c2,xx,cor,res; | |
| 1052 | static const double t22 = 6291456.0; | |
| 1053 | int4 k; | |
| 1054 | y=ABS(x); | |
| 1055 | u.x=big.x+y; | |
| 1056 | y=y-(u.x-big.x); | |
| 1057 | dx=(x>0)?dx:-dx; | |
| 1058 | xx=y*y; | |
| 1059 | s = y*xx*(sn3 +xx*sn5); | |
| 1060 | c = xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 1061 | k=u.i[LOW_HALF]<<2; | |
| 1062 | sn=sincos.x[k]; | |
| 1063 | ssn=sincos.x[k+1]; | |
| 1064 | cs=sincos.x[k+2]; | |
| 1065 | ccs=sincos.x[k+3]; | |
| 1066 | y1 = (y+t22)-t22; | |
| 1067 | y2 = (y - y1)+dx; | |
| 1068 | c1 = (cs+t22)-t22; | |
| 1069 | c2=(cs-c1)+ccs; | |
| 1070 | cor=(ssn+s*ccs+cs*s+c2*y+c1*y2-sn*y*dx)-sn*c; | |
| 1071 | y=sn+c1*y1; | |
| 1072 | cor = cor+((sn-y)+c1*y1); | |
| 1073 | res=y+cor; | |
| 1074 | cor=(y-res)+cor; | |
| 1075 | cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig); | |
| 1076 | if (res == res + cor) return (x>0)?res:-res; | |
| 1077 | else { | |
| ca58f1db | 1078 | __dubsin(ABS(x),dx,w); |
| e4d82761 UD |
1079 | cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig); |
| 1080 | if (w[0] == w[0]+cor) return (x>0)?w[0]:-w[0]; | |
| 50944bca | 1081 | else return __mpcos1(orig); |
| e4d82761 UD |
1082 | } |
| 1083 | } | |
| 1084 | ||
| 1085 | ||
| 1086 | /***************************************************************************/ | |
| 1087 | /* Routine compute sin(x+dx) (Double-Length number) where x in second or */ | |
| 1088 | /* fourth quarter of unit circle.Routine receive also the original value */ | |
| 1089 | /* and quarter(n= 1or 3)of x for computing error of result.And if result not*/ | |
| 1090 | /* accurate enough routine calls other routines */ | |
| 1091 | /***************************************************************************/ | |
| 1092 | ||
| 1093 | static double csloww2(double x, double dx, double orig, int n) { | |
| 1094 | mynumber u; | |
| 1095 | double sn,ssn,cs,ccs,s,c,w[2],y,y1,y2,e1,e2,xx,cor,res; | |
| 1096 | static const double t22 = 6291456.0; | |
| 1097 | int4 k; | |
| 1098 | y=ABS(x); | |
| 1099 | u.x=big.x+y; | |
| 1100 | y=y-(u.x-big.x); | |
| 1101 | dx=(x>0)?dx:-dx; | |
| 1102 | xx=y*y; | |
| 1103 | s = y*xx*(sn3 +xx*sn5); | |
| 1104 | c = y*dx+xx*(cs2 +xx*(cs4 + xx*cs6)); | |
| 1105 | k=u.i[LOW_HALF]<<2; | |
| 1106 | sn=sincos.x[k]; | |
| 1107 | ssn=sincos.x[k+1]; | |
| 1108 | cs=sincos.x[k+2]; | |
| 1109 | ccs=sincos.x[k+3]; | |
| 1110 | ||
| 1111 | y1 = (y+t22)-t22; | |
| 1112 | y2 = (y - y1)+dx; | |
| 1113 | e1 = (sn+t22)-t22; | |
| 1114 | e2=(sn-e1)+ssn; | |
| 1115 | cor=(ccs-cs*c-e1*y2-e2*y)-sn*s; | |
| 1116 | y=cs-e1*y1; | |
| 1117 | cor = cor+((cs-y)-e1*y1); | |
| 1118 | res=y+cor; | |
| 1119 | cor=(y-res)+cor; | |
| 1120 | cor = (cor>0)? 1.0005*cor+3.1e-30*ABS(orig) : 1.0005*cor-3.1e-30*ABS(orig); | |
| 1121 | if (res == res + cor) return (n)?-res:res; | |
| 1122 | else { | |
| ca58f1db | 1123 | __docos(ABS(x),dx,w); |
| e4d82761 UD |
1124 | cor = (w[1]>0)? 1.000000005*w[1]+1.1e-30*ABS(orig) : 1.000000005*w[1]-1.1e-30*ABS(orig); |
| 1125 | if (w[0] == w[0]+cor) return (n)?-w[0]:w[0]; | |
| 50944bca | 1126 | else return __mpcos1(orig); |
| e4d82761 UD |
1127 | } |
| 1128 | } | |
| 1129 | ||
| ca58f1db UD |
1130 | weak_alias (__cos, cos) |
| 1131 | weak_alias (__sin, sin) | |
| 1132 | ||
| cccda09f | 1133 | #ifdef NO_LONG_DOUBLE |
| ca58f1db UD |
1134 | strong_alias (__sin, __sinl) |
| 1135 | weak_alias (__sin, sinl) | |
| 1136 | strong_alias (__cos, __cosl) | |
| 1137 | weak_alias (__cos, cosl) | |
| cccda09f | 1138 | #endif |