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 |       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
  95 BOUNDS1:        .long 0x3FD78000,0x4004BC7E
  96 TWOBYPI:        .long 0x3FE45F30,0x6DC9C883
  97
  98 SINA7:  .long 0xBD6AAA77,0xCCC994F5
  99 SINA6:  .long 0x3DE61209,0x7AAE8DA1
 100
 101 SINA5:  .long 0xBE5AE645,0x2A118AE4
 102 SINA4:  .long 0x3EC71DE3,0xA5341531
 103
 104 SINA3:  .long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000
 105
 106 SINA2:  .long 0x3FF80000,0x88888888,0x888859AF,0x00000000
 107
 108 SINA1:  .long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000
 109
 110 COSB8:  .long 0x3D2AC4D0,0xD6011EE3
 111 COSB7:  .long 0xBDA9396F,0x9F45AC19
 112
 113 COSB6:  .long 0x3E21EED9,0x0612C972
 114 COSB5:  .long 0xBE927E4F,0xB79D9FCF
 115
 116 COSB4:  .long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000
 117
 118 COSB3:  .long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000
 119
 120 COSB2:  .long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E
 121 COSB1:  .long 0xBF000000
 122
 123 INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A
 124
 125 TWOPI1: .long 0x40010000,0xC90FDAA2,0x00000000,0x00000000
 126 TWOPI2: .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
 152 ssind:
 153 |--SIN(X) = X FOR DENORMALIZED X
 154         bra             t_extdnrm
 155
 156         .global scosd
 157 scosd:
 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
 169 ssin:
 170 |--SET ADJN TO 0
 171         movel           #0,ADJN(%a6)
 172         bras            SINBGN
 173
 174         .global scos
 175 scos:
 176 |--SET ADJN TO 1
 177         movel           #1,ADJN(%a6)
 178
 179 SINBGN:
 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
 193 SOK1:
 194         cmpil           #0x4004BC7E,%d0         | ...|X| < 15 PI?
 195         blts            SINMAIN
 196         bra             REDUCEX
 197
 198 SINMAIN:
 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
 220 SINCONT:
 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
 230 SINPOLY:
 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
 285 COSPOLY:
 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
 349 SINBORS:
 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
 356 SINSM:
 357         movel           ADJN(%a6),%d0
 358         cmpil           #0,%d0
 359         bgts            COSTINY
 360
 361 SINTINY:
 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
 368 COSTINY:
 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
 376 REDUCEX:
 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)
 402 red_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
 413 LOOP:
 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
 421 CONTLOOP:
 422         subil           #27,%d0  | ...D0 IS L := K-27
 423         movel           #0,ENDFLAG(%a6)
 424         bras            WORK
 425 LASTLOOP:
 426         clrl            %d0             | ...D0 IS L := 0
 427         movel           #1,ENDFLAG(%a6)
 428
 429 WORK:
 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
 511 RESTORE:
 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
 524 ssincosd:
 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
 532 ssincos:
 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
 547 SCOK1:
 548         cmpil           #0x4004BC7E,%d0         | ...|X| < 15 PI?
 549         blts            SCMAIN
 550         bra             REDUCEX
 551
 552
 553 SCMAIN:
 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
 573 SCCONT:
 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
 583 NODD:
 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
 660 NEVEN:
 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
 727 SCBORS:
 728         cmpil           #0x3FFF8000,%d0
 729         bgt             REDUCEX
 730
 731
 732 SCSM:
 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