arch/m68k/fpsp040/ssin.S

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 |       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA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