1| 2| ssin.sa 3.3 7/29/91 3| 4| The entry point sSIN computes the sine of an input argument 5| sCOS computes the cosine, and sSINCOS computes both. The 6| corresponding entry points with a "d" computes the same 7| corresponding function values for denormalized inputs. 8| 9| Input: Double-extended number X in location pointed to 10| by address register a0. 11| 12| Output: The function value sin(X) or cos(X) returned in Fp0 if SIN or 13| COS is requested. Otherwise, for SINCOS, sin(X) is returned 14| in Fp0, and cos(X) is returned in Fp1. 15| 16| Modifies: Fp0 for SIN or COS; both Fp0 and Fp1 for SINCOS. 17| 18| Accuracy and Monotonicity: The returned result is within 1 ulp in 19| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the 20| result is subsequently rounded to double precision. The 21| result is provably monotonic in double precision. 22| 23| Speed: The programs sSIN and sCOS take approximately 150 cycles for 24| input argument X such that |X| < 15Pi, which is the usual 25| situation. The speed for sSINCOS is approximately 190 cycles. 26| 27| Algorithm: 28| 29| SIN and COS: 30| 1. If SIN is invoked, set AdjN := 0; otherwise, set AdjN := 1. 31| 32| 2. If |X| >= 15Pi or |X| < 2**(-40), go to 7. 33| 34| 3. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let 35| k = N mod 4, so in particular, k = 0,1,2,or 3. Overwrite 36| k by k := k + AdjN. 37| 38| 4. If k is even, go to 6. 39| 40| 5. (k is odd) Set j := (k-1)/2, sgn := (-1)**j. Return sgn*cos(r) 41| where cos(r) is approximated by an even polynomial in r, 42| 1 + r*r*(B1+s*(B2+ ... + s*B8)), s = r*r. 43| Exit. 44| 45| 6. (k is even) Set j := k/2, sgn := (-1)**j. Return sgn*sin(r) 46| where sin(r) is approximated by an odd polynomial in r 47| r + r*s*(A1+s*(A2+ ... + s*A7)), s = r*r. 48| Exit. 49| 50| 7. If |X| > 1, go to 9. 51| 52| 8. (|X|<2**(-40)) If SIN is invoked, return X; otherwise return 1. 53| 54| 9. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 3. 55| 56| SINCOS: 57| 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6. 58| 59| 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let 60| k = N mod 4, so in particular, k = 0,1,2,or 3. 61| 62| 3. If k is even, go to 5. 63| 64| 4. (k is odd) Set j1 := (k-1)/2, j2 := j1 (EOR) (k mod 2), i.e. 65| j1 exclusive or with the l.s.b. of k. 66| sgn1 := (-1)**j1, sgn2 := (-1)**j2. 67| SIN(X) = sgn1 * cos(r) and COS(X) = sgn2*sin(r) where 68| sin(r) and cos(r) are computed as odd and even polynomials 69| in r, respectively. Exit 70| 71| 5. (k is even) Set j1 := k/2, sgn1 := (-1)**j1. 72| SIN(X) = sgn1 * sin(r) and COS(X) = sgn1*cos(r) where 73| sin(r) and cos(r) are computed as odd and even polynomials 74| in r, respectively. Exit 75| 76| 6. If |X| > 1, go to 8. 77| 78| 7. (|X|<2**(-40)) SIN(X) = X and COS(X) = 1. Exit. 79| 80| 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2. 81| 82 83| Copyright (C) Motorola, Inc. 1990 84| All Rights Reserved 85| 86| For details on the license for this file, please see the 87| file, README, in this same directory. 88 89|SSIN idnt 2,1 | Motorola 040 Floating Point Software Package 90 91 |section 8 92 93#include "fpsp.h" 94 95BOUNDS1: .long 0x3FD78000,0x4004BC7E 96TWOBYPI: .long 0x3FE45F30,0x6DC9C883 97 98SINA7: .long 0xBD6AAA77,0xCCC994F5 99SINA6: .long 0x3DE61209,0x7AAE8DA1 100 101SINA5: .long 0xBE5AE645,0x2A118AE4 102SINA4: .long 0x3EC71DE3,0xA5341531 103 104SINA3: .long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000 105 106SINA2: .long 0x3FF80000,0x88888888,0x888859AF,0x00000000 107 108SINA1: .long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000 109 110COSB8: .long 0x3D2AC4D0,0xD6011EE3 111COSB7: .long 0xBDA9396F,0x9F45AC19 112 113COSB6: .long 0x3E21EED9,0x0612C972 114COSB5: .long 0xBE927E4F,0xB79D9FCF 115 116COSB4: .long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000 117 118COSB3: .long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000 119 120COSB2: .long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E 121COSB1: .long 0xBF000000 122 123INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A 124 125TWOPI1: .long 0x40010000,0xC90FDAA2,0x00000000,0x00000000 126TWOPI2: .long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000 127 128 |xref PITBL 129 130 .set INARG,FP_SCR4 131 132 .set X,FP_SCR5 133 .set XDCARE,X+2 134 .set XFRAC,X+4 135 136 .set RPRIME,FP_SCR1 137 .set SPRIME,FP_SCR2 138 139 .set POSNEG1,L_SCR1 140 .set TWOTO63,L_SCR1 141 142 .set ENDFLAG,L_SCR2 143 .set N,L_SCR2 144 145 .set ADJN,L_SCR3 146 147 | xref t_frcinx 148 |xref t_extdnrm 149 |xref sto_cos 150 151 .global ssind 152ssind: 153|--SIN(X) = X FOR DENORMALIZED X 154 bra t_extdnrm 155 156 .global scosd 157scosd: 158|--COS(X) = 1 FOR DENORMALIZED X 159 160 fmoves #0x3F800000,%fp0 161| 162| 9D25B Fix: Sometimes the previous fmove.s sets fpsr bits 163| 164 fmovel #0,%fpsr 165| 166 bra t_frcinx 167 168 .global ssin 169ssin: 170|--SET ADJN TO 0 171 movel #0,ADJN(%a6) 172 bras SINBGN 173 174 .global scos 175scos: 176|--SET ADJN TO 1 177 movel #1,ADJN(%a6) 178 179SINBGN: 180|--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE 181 182 fmovex (%a0),%fp0 | ...LOAD INPUT 183 184 movel (%a0),%d0 185 movew 4(%a0),%d0 186 fmovex %fp0,X(%a6) 187 andil #0x7FFFFFFF,%d0 | ...COMPACTIFY X 188 189 cmpil #0x3FD78000,%d0 | ...|X| >= 2**(-40)? 190 bges SOK1 191 bra SINSM 192 193SOK1: 194 cmpil #0x4004BC7E,%d0 | ...|X| < 15 PI? 195 blts SINMAIN 196 bra REDUCEX 197 198SINMAIN: 199|--THIS IS THE USUAL CASE, |X| <= 15 PI. 200|--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP. 201 fmovex %fp0,%fp1 202 fmuld TWOBYPI,%fp1 | ...X*2/PI 203 204|--HIDE THE NEXT THREE INSTRUCTIONS 205 lea PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32 206 207 208|--FP1 IS NOW READY 209 fmovel %fp1,N(%a6) | ...CONVERT TO INTEGER 210 211 movel N(%a6),%d0 212 asll #4,%d0 213 addal %d0,%a1 | ...A1 IS THE ADDRESS OF N*PIBY2 214| ...WHICH IS IN TWO PIECES Y1 & Y2 215 216 fsubx (%a1)+,%fp0 | ...X-Y1 217|--HIDE THE NEXT ONE 218 fsubs (%a1),%fp0 | ...FP0 IS R = (X-Y1)-Y2 219 220SINCONT: 221|--continuation from REDUCEX 222 223|--GET N+ADJN AND SEE IF SIN(R) OR COS(R) IS NEEDED 224 movel N(%a6),%d0 225 addl ADJN(%a6),%d0 | ...SEE IF D0 IS ODD OR EVEN 226 rorl #1,%d0 | ...D0 WAS ODD IFF D0 IS NEGATIVE 227 cmpil #0,%d0 228 blt COSPOLY 229 230SINPOLY: 231|--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J. 232|--THEN WE RETURN SGN*SIN(R). SGN*SIN(R) IS COMPUTED BY 233|--R' + R'*S*(A1 + S(A2 + S(A3 + S(A4 + ... + SA7)))), WHERE 234|--R' = SGN*R, S=R*R. THIS CAN BE REWRITTEN AS 235|--R' + R'*S*( [A1+T(A3+T(A5+TA7))] + [S(A2+T(A4+TA6))]) 236|--WHERE T=S*S. 237|--NOTE THAT A3 THROUGH A7 ARE STORED IN DOUBLE PRECISION 238|--WHILE A1 AND A2 ARE IN DOUBLE-EXTENDED FORMAT. 239 fmovex %fp0,X(%a6) | ...X IS R 240 fmulx %fp0,%fp0 | ...FP0 IS S 241|---HIDE THE NEXT TWO WHILE WAITING FOR FP0 242 fmoved SINA7,%fp3 243 fmoved SINA6,%fp2 244|--FP0 IS NOW READY 245 fmovex %fp0,%fp1 246 fmulx %fp1,%fp1 | ...FP1 IS T 247|--HIDE THE NEXT TWO WHILE WAITING FOR FP1 248 249 rorl #1,%d0 250 andil #0x80000000,%d0 251| ...LEAST SIG. BIT OF D0 IN SIGN POSITION 252 eorl %d0,X(%a6) | ...X IS NOW R'= SGN*R 253 254 fmulx %fp1,%fp3 | ...TA7 255 fmulx %fp1,%fp2 | ...TA6 256 257 faddd SINA5,%fp3 | ...A5+TA7 258 faddd SINA4,%fp2 | ...A4+TA6 259 260 fmulx %fp1,%fp3 | ...T(A5+TA7) 261 fmulx %fp1,%fp2 | ...T(A4+TA6) 262 263 faddd SINA3,%fp3 | ...A3+T(A5+TA7) 264 faddx SINA2,%fp2 | ...A2+T(A4+TA6) 265 266 fmulx %fp3,%fp1 | ...T(A3+T(A5+TA7)) 267 268 fmulx %fp0,%fp2 | ...S(A2+T(A4+TA6)) 269 faddx SINA1,%fp1 | ...A1+T(A3+T(A5+TA7)) 270 fmulx X(%a6),%fp0 | ...R'*S 271 272 faddx %fp2,%fp1 | ...[A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))] 273|--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING 274|--FP2 RELEASED, RESTORE NOW AND TAKE FULL ADVANTAGE OF HIDING 275 276 277 fmulx %fp1,%fp0 | ...SIN(R')-R' 278|--FP1 RELEASED. 279 280 fmovel %d1,%FPCR |restore users exceptions 281 faddx X(%a6),%fp0 |last inst - possible exception set 282 bra t_frcinx 283 284 285COSPOLY: 286|--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J. 287|--THEN WE RETURN SGN*COS(R). SGN*COS(R) IS COMPUTED BY 288|--SGN + S'*(B1 + S(B2 + S(B3 + S(B4 + ... + SB8)))), WHERE 289|--S=R*R AND S'=SGN*S. THIS CAN BE REWRITTEN AS 290|--SGN + S'*([B1+T(B3+T(B5+TB7))] + [S(B2+T(B4+T(B6+TB8)))]) 291|--WHERE T=S*S. 292|--NOTE THAT B4 THROUGH B8 ARE STORED IN DOUBLE PRECISION 293|--WHILE B2 AND B3 ARE IN DOUBLE-EXTENDED FORMAT, B1 IS -1/2 294|--AND IS THEREFORE STORED AS SINGLE PRECISION. 295 296 fmulx %fp0,%fp0 | ...FP0 IS S 297|---HIDE THE NEXT TWO WHILE WAITING FOR FP0 298 fmoved COSB8,%fp2 299 fmoved COSB7,%fp3 300|--FP0 IS NOW READY 301 fmovex %fp0,%fp1 302 fmulx %fp1,%fp1 | ...FP1 IS T 303|--HIDE THE NEXT TWO WHILE WAITING FOR FP1 304 fmovex %fp0,X(%a6) | ...X IS S 305 rorl #1,%d0 306 andil #0x80000000,%d0 307| ...LEAST SIG. BIT OF D0 IN SIGN POSITION 308 309 fmulx %fp1,%fp2 | ...TB8 310|--HIDE THE NEXT TWO WHILE WAITING FOR THE XU 311 eorl %d0,X(%a6) | ...X IS NOW S'= SGN*S 312 andil #0x80000000,%d0 313 314 fmulx %fp1,%fp3 | ...TB7 315|--HIDE THE NEXT TWO WHILE WAITING FOR THE XU 316 oril #0x3F800000,%d0 | ...D0 IS SGN IN SINGLE 317 movel %d0,POSNEG1(%a6) 318 319 faddd COSB6,%fp2 | ...B6+TB8 320 faddd COSB5,%fp3 | ...B5+TB7 321 322 fmulx %fp1,%fp2 | ...T(B6+TB8) 323 fmulx %fp1,%fp3 | ...T(B5+TB7) 324 325 faddd COSB4,%fp2 | ...B4+T(B6+TB8) 326 faddx COSB3,%fp3 | ...B3+T(B5+TB7) 327 328 fmulx %fp1,%fp2 | ...T(B4+T(B6+TB8)) 329 fmulx %fp3,%fp1 | ...T(B3+T(B5+TB7)) 330 331 faddx COSB2,%fp2 | ...B2+T(B4+T(B6+TB8)) 332 fadds COSB1,%fp1 | ...B1+T(B3+T(B5+TB7)) 333 334 fmulx %fp2,%fp0 | ...S(B2+T(B4+T(B6+TB8))) 335|--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING 336|--FP2 RELEASED. 337 338 339 faddx %fp1,%fp0 340|--FP1 RELEASED 341 342 fmulx X(%a6),%fp0 343 344 fmovel %d1,%FPCR |restore users exceptions 345 fadds POSNEG1(%a6),%fp0 |last inst - possible exception set 346 bra t_frcinx 347 348 349SINBORS: 350|--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION. 351|--IF |X| < 2**(-40), RETURN X OR 1. 352 cmpil #0x3FFF8000,%d0 353 bgts REDUCEX 354 355 356SINSM: 357 movel ADJN(%a6),%d0 358 cmpil #0,%d0 359 bgts COSTINY 360 361SINTINY: 362 movew #0x0000,XDCARE(%a6) | ...JUST IN CASE 363 fmovel %d1,%FPCR |restore users exceptions 364 fmovex X(%a6),%fp0 |last inst - possible exception set 365 bra t_frcinx 366 367 368COSTINY: 369 fmoves #0x3F800000,%fp0 370 371 fmovel %d1,%FPCR |restore users exceptions 372 fsubs #0x00800000,%fp0 |last inst - possible exception set 373 bra t_frcinx 374 375 376REDUCEX: 377|--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW. 378|--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING 379|--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE. 380 381 fmovemx %fp2-%fp5,-(%a7) | ...save FP2 through FP5 382 movel %d2,-(%a7) 383 fmoves #0x00000000,%fp1 384|--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that 385|--there is a danger of unwanted overflow in first LOOP iteration. In this 386|--case, reduce argument by one remainder step to make subsequent reduction 387|--safe. 388 cmpil #0x7ffeffff,%d0 |is argument dangerously large? 389 bnes LOOP 390 movel #0x7ffe0000,FP_SCR2(%a6) |yes 391| ;create 2**16383*PI/2 392 movel #0xc90fdaa2,FP_SCR2+4(%a6) 393 clrl FP_SCR2+8(%a6) 394 ftstx %fp0 |test sign of argument 395 movel #0x7fdc0000,FP_SCR3(%a6) |create low half of 2**16383* 396| ;PI/2 at FP_SCR3 397 movel #0x85a308d3,FP_SCR3+4(%a6) 398 clrl FP_SCR3+8(%a6) 399 fblt red_neg 400 orw #0x8000,FP_SCR2(%a6) |positive arg 401 orw #0x8000,FP_SCR3(%a6) 402red_neg: 403 faddx FP_SCR2(%a6),%fp0 |high part of reduction is exact 404 fmovex %fp0,%fp1 |save high result in fp1 405 faddx FP_SCR3(%a6),%fp0 |low part of reduction 406 fsubx %fp0,%fp1 |determine low component of result 407 faddx FP_SCR3(%a6),%fp1 |fp0/fp1 are reduced argument. 408 409|--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4. 410|--integer quotient will be stored in N 411|--Intermediate remainder is 66-bit long; (R,r) in (FP0,FP1) 412 413LOOP: 414 fmovex %fp0,INARG(%a6) | ...+-2**K * F, 1 <= F < 2 415 movew INARG(%a6),%d0 416 movel %d0,%a1 | ...save a copy of D0 417 andil #0x00007FFF,%d0 418 subil #0x00003FFF,%d0 | ...D0 IS K 419 cmpil #28,%d0 420 bles LASTLOOP 421CONTLOOP: 422 subil #27,%d0 | ...D0 IS L := K-27 423 movel #0,ENDFLAG(%a6) 424 bras WORK 425LASTLOOP: 426 clrl %d0 | ...D0 IS L := 0 427 movel #1,ENDFLAG(%a6) 428 429WORK: 430|--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN 431|--THAT INT( X * (2/PI) / 2**(L) ) < 2**29. 432 433|--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63), 434|--2**L * (PIby2_1), 2**L * (PIby2_2) 435 436 movel #0x00003FFE,%d2 | ...BIASED EXPO OF 2/PI 437 subl %d0,%d2 | ...BIASED EXPO OF 2**(-L)*(2/PI) 438 439 movel #0xA2F9836E,FP_SCR1+4(%a6) 440 movel #0x4E44152A,FP_SCR1+8(%a6) 441 movew %d2,FP_SCR1(%a6) | ...FP_SCR1 is 2**(-L)*(2/PI) 442 443 fmovex %fp0,%fp2 444 fmulx FP_SCR1(%a6),%fp2 445|--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN 446|--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N 447|--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT 448|--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE 449|--US THE DESIRED VALUE IN FLOATING POINT. 450 451|--HIDE SIX CYCLES OF INSTRUCTION 452 movel %a1,%d2 453 swap %d2 454 andil #0x80000000,%d2 455 oril #0x5F000000,%d2 | ...D2 IS SIGN(INARG)*2**63 IN SGL 456 movel %d2,TWOTO63(%a6) 457 458 movel %d0,%d2 459 addil #0x00003FFF,%d2 | ...BIASED EXPO OF 2**L * (PI/2) 460 461|--FP2 IS READY 462 fadds TWOTO63(%a6),%fp2 | ...THE FRACTIONAL PART OF FP1 IS ROUNDED 463 464|--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1 and 2**(L)*Piby2_2 465 movew %d2,FP_SCR2(%a6) 466 clrw FP_SCR2+2(%a6) 467 movel #0xC90FDAA2,FP_SCR2+4(%a6) 468 clrl FP_SCR2+8(%a6) | ...FP_SCR2 is 2**(L) * Piby2_1 469 470|--FP2 IS READY 471 fsubs TWOTO63(%a6),%fp2 | ...FP2 is N 472 473 addil #0x00003FDD,%d0 474 movew %d0,FP_SCR3(%a6) 475 clrw FP_SCR3+2(%a6) 476 movel #0x85A308D3,FP_SCR3+4(%a6) 477 clrl FP_SCR3+8(%a6) | ...FP_SCR3 is 2**(L) * Piby2_2 478 479 movel ENDFLAG(%a6),%d0 480 481|--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and 482|--P2 = 2**(L) * Piby2_2 483 fmovex %fp2,%fp4 484 fmulx FP_SCR2(%a6),%fp4 | ...W = N*P1 485 fmovex %fp2,%fp5 486 fmulx FP_SCR3(%a6),%fp5 | ...w = N*P2 487 fmovex %fp4,%fp3 488|--we want P+p = W+w but |p| <= half ulp of P 489|--Then, we need to compute A := R-P and a := r-p 490 faddx %fp5,%fp3 | ...FP3 is P 491 fsubx %fp3,%fp4 | ...W-P 492 493 fsubx %fp3,%fp0 | ...FP0 is A := R - P 494 faddx %fp5,%fp4 | ...FP4 is p = (W-P)+w 495 496 fmovex %fp0,%fp3 | ...FP3 A 497 fsubx %fp4,%fp1 | ...FP1 is a := r - p 498 499|--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but 500|--|r| <= half ulp of R. 501 faddx %fp1,%fp0 | ...FP0 is R := A+a 502|--No need to calculate r if this is the last loop 503 cmpil #0,%d0 504 bgt RESTORE 505 506|--Need to calculate r 507 fsubx %fp0,%fp3 | ...A-R 508 faddx %fp3,%fp1 | ...FP1 is r := (A-R)+a 509 bra LOOP 510 511RESTORE: 512 fmovel %fp2,N(%a6) 513 movel (%a7)+,%d2 514 fmovemx (%a7)+,%fp2-%fp5 515 516 517 movel ADJN(%a6),%d0 518 cmpil #4,%d0 519 520 blt SINCONT 521 bras SCCONT 522 523 .global ssincosd 524ssincosd: 525|--SIN AND COS OF X FOR DENORMALIZED X 526 527 fmoves #0x3F800000,%fp1 528 bsr sto_cos |store cosine result 529 bra t_extdnrm 530 531 .global ssincos 532ssincos: 533|--SET ADJN TO 4 534 movel #4,ADJN(%a6) 535 536 fmovex (%a0),%fp0 | ...LOAD INPUT 537 538 movel (%a0),%d0 539 movew 4(%a0),%d0 540 fmovex %fp0,X(%a6) 541 andil #0x7FFFFFFF,%d0 | ...COMPACTIFY X 542 543 cmpil #0x3FD78000,%d0 | ...|X| >= 2**(-40)? 544 bges SCOK1 545 bra SCSM 546 547SCOK1: 548 cmpil #0x4004BC7E,%d0 | ...|X| < 15 PI? 549 blts SCMAIN 550 bra REDUCEX 551 552 553SCMAIN: 554|--THIS IS THE USUAL CASE, |X| <= 15 PI. 555|--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP. 556 fmovex %fp0,%fp1 557 fmuld TWOBYPI,%fp1 | ...X*2/PI 558 559|--HIDE THE NEXT THREE INSTRUCTIONS 560 lea PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32 561 562 563|--FP1 IS NOW READY 564 fmovel %fp1,N(%a6) | ...CONVERT TO INTEGER 565 566 movel N(%a6),%d0 567 asll #4,%d0 568 addal %d0,%a1 | ...ADDRESS OF N*PIBY2, IN Y1, Y2 569 570 fsubx (%a1)+,%fp0 | ...X-Y1 571 fsubs (%a1),%fp0 | ...FP0 IS R = (X-Y1)-Y2 572 573SCCONT: 574|--continuation point from REDUCEX 575 576|--HIDE THE NEXT TWO 577 movel N(%a6),%d0 578 rorl #1,%d0 579 580 cmpil #0,%d0 | ...D0 < 0 IFF N IS ODD 581 bge NEVEN 582 583NODD: 584|--REGISTERS SAVED SO FAR: D0, A0, FP2. 585 586 fmovex %fp0,RPRIME(%a6) 587 fmulx %fp0,%fp0 | ...FP0 IS S = R*R 588 fmoved SINA7,%fp1 | ...A7 589 fmoved COSB8,%fp2 | ...B8 590 fmulx %fp0,%fp1 | ...SA7 591 movel %d2,-(%a7) 592 movel %d0,%d2 593 fmulx %fp0,%fp2 | ...SB8 594 rorl #1,%d2 595 andil #0x80000000,%d2 596 597 faddd SINA6,%fp1 | ...A6+SA7 598 eorl %d0,%d2 599 andil #0x80000000,%d2 600 faddd COSB7,%fp2 | ...B7+SB8 601 602 fmulx %fp0,%fp1 | ...S(A6+SA7) 603 eorl %d2,RPRIME(%a6) 604 movel (%a7)+,%d2 605 fmulx %fp0,%fp2 | ...S(B7+SB8) 606 rorl #1,%d0 607 andil #0x80000000,%d0 608 609 faddd SINA5,%fp1 | ...A5+S(A6+SA7) 610 movel #0x3F800000,POSNEG1(%a6) 611 eorl %d0,POSNEG1(%a6) 612 faddd COSB6,%fp2 | ...B6+S(B7+SB8) 613 614 fmulx %fp0,%fp1 | ...S(A5+S(A6+SA7)) 615 fmulx %fp0,%fp2 | ...S(B6+S(B7+SB8)) 616 fmovex %fp0,SPRIME(%a6) 617 618 faddd SINA4,%fp1 | ...A4+S(A5+S(A6+SA7)) 619 eorl %d0,SPRIME(%a6) 620 faddd COSB5,%fp2 | ...B5+S(B6+S(B7+SB8)) 621 622 fmulx %fp0,%fp1 | ...S(A4+...) 623 fmulx %fp0,%fp2 | ...S(B5+...) 624 625 faddd SINA3,%fp1 | ...A3+S(A4+...) 626 faddd COSB4,%fp2 | ...B4+S(B5+...) 627 628 fmulx %fp0,%fp1 | ...S(A3+...) 629 fmulx %fp0,%fp2 | ...S(B4+...) 630 631 faddx SINA2,%fp1 | ...A2+S(A3+...) 632 faddx COSB3,%fp2 | ...B3+S(B4+...) 633 634 fmulx %fp0,%fp1 | ...S(A2+...) 635 fmulx %fp0,%fp2 | ...S(B3+...) 636 637 faddx SINA1,%fp1 | ...A1+S(A2+...) 638 faddx COSB2,%fp2 | ...B2+S(B3+...) 639 640 fmulx %fp0,%fp1 | ...S(A1+...) 641 fmulx %fp2,%fp0 | ...S(B2+...) 642 643 644 645 fmulx RPRIME(%a6),%fp1 | ...R'S(A1+...) 646 fadds COSB1,%fp0 | ...B1+S(B2...) 647 fmulx SPRIME(%a6),%fp0 | ...S'(B1+S(B2+...)) 648 649 movel %d1,-(%sp) |restore users mode & precision 650 andil #0xff,%d1 |mask off all exceptions 651 fmovel %d1,%FPCR 652 faddx RPRIME(%a6),%fp1 | ...COS(X) 653 bsr sto_cos |store cosine result 654 fmovel (%sp)+,%FPCR |restore users exceptions 655 fadds POSNEG1(%a6),%fp0 | ...SIN(X) 656 657 bra t_frcinx 658 659 660NEVEN: 661|--REGISTERS SAVED SO FAR: FP2. 662 663 fmovex %fp0,RPRIME(%a6) 664 fmulx %fp0,%fp0 | ...FP0 IS S = R*R 665 fmoved COSB8,%fp1 | ...B8 666 fmoved SINA7,%fp2 | ...A7 667 fmulx %fp0,%fp1 | ...SB8 668 fmovex %fp0,SPRIME(%a6) 669 fmulx %fp0,%fp2 | ...SA7 670 rorl #1,%d0 671 andil #0x80000000,%d0 672 faddd COSB7,%fp1 | ...B7+SB8 673 faddd SINA6,%fp2 | ...A6+SA7 674 eorl %d0,RPRIME(%a6) 675 eorl %d0,SPRIME(%a6) 676 fmulx %fp0,%fp1 | ...S(B7+SB8) 677 oril #0x3F800000,%d0 678 movel %d0,POSNEG1(%a6) 679 fmulx %fp0,%fp2 | ...S(A6+SA7) 680 681 faddd COSB6,%fp1 | ...B6+S(B7+SB8) 682 faddd SINA5,%fp2 | ...A5+S(A6+SA7) 683 684 fmulx %fp0,%fp1 | ...S(B6+S(B7+SB8)) 685 fmulx %fp0,%fp2 | ...S(A5+S(A6+SA7)) 686 687 faddd COSB5,%fp1 | ...B5+S(B6+S(B7+SB8)) 688 faddd SINA4,%fp2 | ...A4+S(A5+S(A6+SA7)) 689 690 fmulx %fp0,%fp1 | ...S(B5+...) 691 fmulx %fp0,%fp2 | ...S(A4+...) 692 693 faddd COSB4,%fp1 | ...B4+S(B5+...) 694 faddd SINA3,%fp2 | ...A3+S(A4+...) 695 696 fmulx %fp0,%fp1 | ...S(B4+...) 697 fmulx %fp0,%fp2 | ...S(A3+...) 698 699 faddx COSB3,%fp1 | ...B3+S(B4+...) 700 faddx SINA2,%fp2 | ...A2+S(A3+...) 701 702 fmulx %fp0,%fp1 | ...S(B3+...) 703 fmulx %fp0,%fp2 | ...S(A2+...) 704 705 faddx COSB2,%fp1 | ...B2+S(B3+...) 706 faddx SINA1,%fp2 | ...A1+S(A2+...) 707 708 fmulx %fp0,%fp1 | ...S(B2+...) 709 fmulx %fp2,%fp0 | ...s(a1+...) 710 711 712 713 fadds COSB1,%fp1 | ...B1+S(B2...) 714 fmulx RPRIME(%a6),%fp0 | ...R'S(A1+...) 715 fmulx SPRIME(%a6),%fp1 | ...S'(B1+S(B2+...)) 716 717 movel %d1,-(%sp) |save users mode & precision 718 andil #0xff,%d1 |mask off all exceptions 719 fmovel %d1,%FPCR 720 fadds POSNEG1(%a6),%fp1 | ...COS(X) 721 bsr sto_cos |store cosine result 722 fmovel (%sp)+,%FPCR |restore users exceptions 723 faddx RPRIME(%a6),%fp0 | ...SIN(X) 724 725 bra t_frcinx 726 727SCBORS: 728 cmpil #0x3FFF8000,%d0 729 bgt REDUCEX 730 731 732SCSM: 733 movew #0x0000,XDCARE(%a6) 734 fmoves #0x3F800000,%fp1 735 736 movel %d1,-(%sp) |save users mode & precision 737 andil #0xff,%d1 |mask off all exceptions 738 fmovel %d1,%FPCR 739 fsubs #0x00800000,%fp1 740 bsr sto_cos |store cosine result 741 fmovel (%sp)+,%FPCR |restore users exceptions 742 fmovex X(%a6),%fp0 743 bra t_frcinx 744 745 |end 746