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|

|       ssin.sa 3.3 7/29/91

|

|       The entry point sSIN computes the sine of an input argument

|       sCOS computes the cosine, and sSINCOS computes both. The

|       corresponding entry points with a "d" computes the same

|       corresponding function values for denormalized inputs.

|

|       Input: Double-extended number X in location pointed to

|               by address register a0.

|

|       Output: The function value sin(X) or cos(X) returned in Fp0 if SIN or

|               COS is requested. Otherwise, for SINCOS, sin(X) is returned

|               in Fp0, and cos(X) is returned in Fp1.

|

|       Modifies: Fp0 for SIN or COS; both Fp0 and Fp1 for SINCOS.

|

|       Accuracy and Monotonicity: The returned result is within 1 ulp in

|               64 significant bit, i.e. within 0.5001 ulp to 53 bits if the

|               result is subsequently rounded to double precision. The

|               result is provably monotonic in double precision.

|

|       Speed: The programs sSIN and sCOS take approximately 150 cycles for

|               input argument X such that |X| < 15Pi, which is the usual

|               situation. The speed for sSINCOS is approximately 190 cycles.

|

|       Algorithm:

|

|       SIN and COS:

|       1. If SIN is invoked, set AdjN := 0; otherwise, set AdjN := 1.

|

|       2. If |X| >= 15Pi or |X| < 2**(-40), go to 7.

|

|       3. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let

|               k = N mod 4, so in particular, k = 0,1,2,or 3. Overwrite

|               k by k := k + AdjN.

|

|       4. If k is even, go to 6.

|

|       5. (k is odd) Set j := (k-1)/2, sgn := (-1)**j. Return sgn*cos(r)

|               where cos(r) is approximated by an even polynomial in r,

|               1 + r*r*(B1+s*(B2+ ... + s*B8)),        s = r*r.

|               Exit.

|

|       6. (k is even) Set j := k/2, sgn := (-1)**j. Return sgn*sin(r)

|               where sin(r) is approximated by an odd polynomial in r

|               r + r*s*(A1+s*(A2+ ... + s*A7)),        s = r*r.

|               Exit.

|

|       7. If |X| > 1, go to 9.

|

|       8. (|X|<2**(-40)) If SIN is invoked, return X; otherwise return 1.

|

|       9. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 3.

|

|       SINCOS:

|       1. If |X| >= 15Pi or |X| < 2**(-40), go to 6.

|

|       2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let

|               k = N mod 4, so in particular, k = 0,1,2,or 3.

|

|       3. If k is even, go to 5.

|

|       4. (k is odd) Set j1 := (k-1)/2, j2 := j1 (EOR) (k mod 2), i.e.

|               j1 exclusive or with the l.s.b. of k.

|               sgn1 := (-1)**j1, sgn2 := (-1)**j2.

|               SIN(X) = sgn1 * cos(r) and COS(X) = sgn2*sin(r) where

|               sin(r) and cos(r) are computed as odd and even polynomials

|               in r, respectively. Exit

|

|       5. (k is even) Set j1 := k/2, sgn1 := (-1)**j1.

|               SIN(X) = sgn1 * sin(r) and COS(X) = sgn1*cos(r) where

|               sin(r) and cos(r) are computed as odd and even polynomials

|               in r, respectively. Exit

|

|       6. If |X| > 1, go to 8.

|

|       7. (|X|<2**(-40)) SIN(X) = X and COS(X) = 1. Exit.

|

|       8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2.

|

|               Copyright (C) Motorola, Inc. 1990

|                       All Rights Reserved

|

|       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA

|       The copyright notice above does not evidence any

|       actual or intended publication of such source code.

|SSIN   idnt    2,1 | Motorola 040 Floating Point Software Package

        |section        8

        .include "fpsp.h"

BOUNDS1:        .long 0x3FD78000,0x4004BC7E

TWOBYPI:        .long 0x3FE45F30,0x6DC9C883

SINA7:  .long 0xBD6AAA77,0xCCC994F5

SINA6:  .long 0x3DE61209,0x7AAE8DA1

SINA5:  .long 0xBE5AE645,0x2A118AE4

SINA4:  .long 0x3EC71DE3,0xA5341531

SINA3:  .long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000

SINA2:  .long 0x3FF80000,0x88888888,0x888859AF,0x00000000

SINA1:  .long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000

COSB8:  .long 0x3D2AC4D0,0xD6011EE3

COSB7:  .long 0xBDA9396F,0x9F45AC19

COSB6:  .long 0x3E21EED9,0x0612C972

COSB5:  .long 0xBE927E4F,0xB79D9FCF

COSB4:  .long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000

COSB3:  .long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000

COSB2:  .long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E

COSB1:  .long 0xBF000000

INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A

TWOPI1: .long 0x40010000,0xC90FDAA2,0x00000000,0x00000000

TWOPI2: .long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000

        |xref   PITBL

        .set    INARG,FP_SCR4

        .set    X,FP_SCR5

        .set    XDCARE,X+2

        .set    XFRAC,X+4

        .set    RPRIME,FP_SCR1

        .set    SPRIME,FP_SCR2

        .set    POSNEG1,L_SCR1

        .set    TWOTO63,L_SCR1

        .set    ENDFLAG,L_SCR2

        .set    N,L_SCR2

        .set    ADJN,L_SCR3

        | xref  t_frcinx

        |xref   t_extdnrm

        |xref   sto_cos

        .global ssind

ssind:

|--SIN(X) = X FOR DENORMALIZED X

        bra             t_extdnrm

        .global scosd

scosd:

|--COS(X) = 1 FOR DENORMALIZED X

        fmoves          #0x3F800000,%fp0

|

|       9D25B Fix: Sometimes the previous fmove.s sets fpsr bits

|

        fmovel          #0,%fpsr

|

        bra             t_frcinx

        .global ssin

ssin:

|--SET ADJN TO 0

        movel           #0,ADJN(%a6)

        bras            SINBGN

        .global scos

scos:

|--SET ADJN TO 1

        movel           #1,ADJN(%a6)

SINBGN:

|--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE

        fmovex          (%a0),%fp0      | ...LOAD INPUT

        movel           (%a0),%d0

        movew           4(%a0),%d0

        fmovex          %fp0,X(%a6)

        andil           #0x7FFFFFFF,%d0         | ...COMPACTIFY X

        cmpil           #0x3FD78000,%d0         | ...|X| >= 2**(-40)?

        bges            SOK1

        bra             SINSM

SOK1:

        cmpil           #0x4004BC7E,%d0         | ...|X| < 15 PI?

        blts            SINMAIN

        bra             REDUCEX

SINMAIN:

|--THIS IS THE USUAL CASE, |X| <= 15 PI.

|--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.

        fmovex          %fp0,%fp1

        fmuld           TWOBYPI,%fp1    | ...X*2/PI

|--HIDE THE NEXT THREE INSTRUCTIONS

        lea             PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32

|--FP1 IS NOW READY

        fmovel          %fp1,N(%a6)             | ...CONVERT TO INTEGER

        movel           N(%a6),%d0

        asll            #4,%d0

        addal           %d0,%a1 | ...A1 IS THE ADDRESS OF N*PIBY2

|                               ...WHICH IS IN TWO PIECES Y1 & Y2

        fsubx           (%a1)+,%fp0     | ...X-Y1

|--HIDE THE NEXT ONE

        fsubs           (%a1),%fp0      | ...FP0 IS R = (X-Y1)-Y2

SINCONT:

|--continuation from REDUCEX

|--GET N+ADJN AND SEE IF SIN(R) OR COS(R) IS NEEDED

        movel           N(%a6),%d0

        addl            ADJN(%a6),%d0   | ...SEE IF D0 IS ODD OR EVEN

        rorl            #1,%d0  | ...D0 WAS ODD IFF D0 IS NEGATIVE

        cmpil           #0,%d0

        blt             COSPOLY

SINPOLY:

|--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.

|--THEN WE RETURN       SGN*SIN(R). SGN*SIN(R) IS COMPUTED BY

|--R' + R'*S*(A1 + S(A2 + S(A3 + S(A4 + ... + SA7)))), WHERE

|--R' = SGN*R, S=R*R. THIS CAN BE REWRITTEN AS

|--R' + R'*S*( [A1+T(A3+T(A5+TA7))] + [S(A2+T(A4+TA6))])

|--WHERE T=S*S.

|--NOTE THAT A3 THROUGH A7 ARE STORED IN DOUBLE PRECISION

|--WHILE A1 AND A2 ARE IN DOUBLE-EXTENDED FORMAT.

        fmovex          %fp0,X(%a6)     | ...X IS R

        fmulx           %fp0,%fp0       | ...FP0 IS S

|---HIDE THE NEXT TWO WHILE WAITING FOR FP0

        fmoved          SINA7,%fp3

        fmoved          SINA6,%fp2

|--FP0 IS NOW READY

        fmovex          %fp0,%fp1

        fmulx           %fp1,%fp1       | ...FP1 IS T

|--HIDE THE NEXT TWO WHILE WAITING FOR FP1

        rorl            #1,%d0

        andil           #0x80000000,%d0

|                               ...LEAST SIG. BIT OF D0 IN SIGN POSITION

        eorl            %d0,X(%a6)      | ...X IS NOW R'= SGN*R

        fmulx           %fp1,%fp3       | ...TA7

        fmulx           %fp1,%fp2       | ...TA6

        faddd           SINA5,%fp3 | ...A5+TA7

        faddd           SINA4,%fp2 | ...A4+TA6

        fmulx           %fp1,%fp3       | ...T(A5+TA7)

        fmulx           %fp1,%fp2       | ...T(A4+TA6)

        faddd           SINA3,%fp3 | ...A3+T(A5+TA7)

        faddx           SINA2,%fp2 | ...A2+T(A4+TA6)

        fmulx           %fp3,%fp1       | ...T(A3+T(A5+TA7))

        fmulx           %fp0,%fp2       | ...S(A2+T(A4+TA6))

        faddx           SINA1,%fp1 | ...A1+T(A3+T(A5+TA7))

        fmulx           X(%a6),%fp0     | ...R'*S

        faddx           %fp2,%fp1       | ...[A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))]

|--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING

|--FP2 RELEASED, RESTORE NOW AND TAKE FULL ADVANTAGE OF HIDING

        fmulx           %fp1,%fp0               | ...SIN(R')-R'

|--FP1 RELEASED.

        fmovel          %d1,%FPCR               |restore users exceptions

        faddx           X(%a6),%fp0             |last inst - possible exception set

        bra             t_frcinx

COSPOLY:

|--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.

|--THEN WE RETURN       SGN*COS(R). SGN*COS(R) IS COMPUTED BY

|--SGN + S'*(B1 + S(B2 + S(B3 + S(B4 + ... + SB8)))), WHERE

|--S=R*R AND S'=SGN*S. THIS CAN BE REWRITTEN AS

|--SGN + S'*([B1+T(B3+T(B5+TB7))] + [S(B2+T(B4+T(B6+TB8)))])

|--WHERE T=S*S.

|--NOTE THAT B4 THROUGH B8 ARE STORED IN DOUBLE PRECISION

|--WHILE B2 AND B3 ARE IN DOUBLE-EXTENDED FORMAT, B1 IS -1/2

|--AND IS THEREFORE STORED AS SINGLE PRECISION.

        fmulx           %fp0,%fp0       | ...FP0 IS S

|---HIDE THE NEXT TWO WHILE WAITING FOR FP0

        fmoved          COSB8,%fp2

        fmoved          COSB7,%fp3

|--FP0 IS NOW READY

        fmovex          %fp0,%fp1

        fmulx           %fp1,%fp1       | ...FP1 IS T

|--HIDE THE NEXT TWO WHILE WAITING FOR FP1

        fmovex          %fp0,X(%a6)     | ...X IS S

        rorl            #1,%d0

        andil           #0x80000000,%d0

|                       ...LEAST SIG. BIT OF D0 IN SIGN POSITION

        fmulx           %fp1,%fp2       | ...TB8

|--HIDE THE NEXT TWO WHILE WAITING FOR THE XU

        eorl            %d0,X(%a6)      | ...X IS NOW S'= SGN*S

        andil           #0x80000000,%d0

        fmulx           %fp1,%fp3       | ...TB7

|--HIDE THE NEXT TWO WHILE WAITING FOR THE XU

        oril            #0x3F800000,%d0 | ...D0 IS SGN IN SINGLE

        movel           %d0,POSNEG1(%a6)

        faddd           COSB6,%fp2 | ...B6+TB8

        faddd           COSB5,%fp3 | ...B5+TB7

        fmulx           %fp1,%fp2       | ...T(B6+TB8)

        fmulx           %fp1,%fp3       | ...T(B5+TB7)

        faddd           COSB4,%fp2 | ...B4+T(B6+TB8)

        faddx           COSB3,%fp3 | ...B3+T(B5+TB7)

        fmulx           %fp1,%fp2       | ...T(B4+T(B6+TB8))

        fmulx           %fp3,%fp1       | ...T(B3+T(B5+TB7))

        faddx           COSB2,%fp2 | ...B2+T(B4+T(B6+TB8))

        fadds           COSB1,%fp1 | ...B1+T(B3+T(B5+TB7))

        fmulx           %fp2,%fp0       | ...S(B2+T(B4+T(B6+TB8)))

|--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING

|--FP2 RELEASED.

        faddx           %fp1,%fp0

|--FP1 RELEASED

        fmulx           X(%a6),%fp0

        fmovel          %d1,%FPCR               |restore users exceptions

        fadds           POSNEG1(%a6),%fp0       |last inst - possible exception set

        bra             t_frcinx

SINBORS:

|--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.

|--IF |X| < 2**(-40), RETURN X OR 1.

        cmpil           #0x3FFF8000,%d0

        bgts            REDUCEX

SINSM:

        movel           ADJN(%a6),%d0

        cmpil           #0,%d0

        bgts            COSTINY

SINTINY:

        movew           #0x0000,XDCARE(%a6)     | ...JUST IN CASE

        fmovel          %d1,%FPCR               |restore users exceptions

        fmovex          X(%a6),%fp0             |last inst - possible exception set

        bra             t_frcinx

COSTINY:

        fmoves          #0x3F800000,%fp0

        fmovel          %d1,%FPCR               |restore users exceptions

        fsubs           #0x00800000,%fp0        |last inst - possible exception set

        bra             t_frcinx

REDUCEX:

|--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.

|--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING

|--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.

        fmovemx %fp2-%fp5,-(%a7)        | ...save FP2 through FP5

        movel           %d2,-(%a7)

        fmoves         #0x00000000,%fp1

|--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that

|--there is a danger of unwanted overflow in first LOOP iteration.  In this

|--case, reduce argument by one remainder step to make subsequent reduction

|--safe.

        cmpil   #0x7ffeffff,%d0         |is argument dangerously large?

        bnes    LOOP

        movel   #0x7ffe0000,FP_SCR2(%a6)        |yes

|                                       ;create 2**16383*PI/2

        movel   #0xc90fdaa2,FP_SCR2+4(%a6)

        clrl    FP_SCR2+8(%a6)

        ftstx   %fp0                    |test sign of argument

        movel   #0x7fdc0000,FP_SCR3(%a6)        |create low half of 2**16383*

|                                       ;PI/2 at FP_SCR3

        movel   #0x85a308d3,FP_SCR3+4(%a6)

        clrl   FP_SCR3+8(%a6)

        fblt    red_neg

        orw     #0x8000,FP_SCR2(%a6)    |positive arg

        orw     #0x8000,FP_SCR3(%a6)

red_neg:

        faddx  FP_SCR2(%a6),%fp0                |high part of reduction is exact

        fmovex  %fp0,%fp1               |save high result in fp1

        faddx  FP_SCR3(%a6),%fp0                |low part of reduction

        fsubx  %fp0,%fp1                        |determine low component of result

        faddx  FP_SCR3(%a6),%fp1                |fp0/fp1 are reduced argument.

|--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.

|--integer quotient will be stored in N

|--Intermediate remainder is 66-bit long; (R,r) in (FP0,FP1)

LOOP:

        fmovex          %fp0,INARG(%a6) | ...+-2**K * F, 1 <= F < 2

        movew           INARG(%a6),%d0

        movel          %d0,%a1          | ...save a copy of D0

        andil           #0x00007FFF,%d0

        subil           #0x00003FFF,%d0 | ...D0 IS K

        cmpil           #28,%d0

        bles            LASTLOOP

CONTLOOP:

        subil           #27,%d0  | ...D0 IS L := K-27

        movel           #0,ENDFLAG(%a6)

        bras            WORK

LASTLOOP:

        clrl            %d0             | ...D0 IS L := 0

        movel           #1,ENDFLAG(%a6)

WORK:

|--FIND THE REMAINDER OF (R,r) W.R.T.   2**L * (PI/2). L IS SO CHOSEN

|--THAT INT( X * (2/PI) / 2**(L) ) < 2**29.

|--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63),

|--2**L * (PIby2_1), 2**L * (PIby2_2)

        movel           #0x00003FFE,%d2 | ...BIASED EXPO OF 2/PI

        subl            %d0,%d2         | ...BIASED EXPO OF 2**(-L)*(2/PI)

        movel           #0xA2F9836E,FP_SCR1+4(%a6)

        movel           #0x4E44152A,FP_SCR1+8(%a6)

        movew           %d2,FP_SCR1(%a6)        | ...FP_SCR1 is 2**(-L)*(2/PI)

        fmovex          %fp0,%fp2

        fmulx           FP_SCR1(%a6),%fp2

|--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN

|--FLOATING POINT FORMAT, THE TWO FMOVE'S       FMOVE.L FP <--> N

|--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT

|--(SIGN(INARG)*2**63   +       FP2) - SIGN(INARG)*2**63 WILL GIVE

|--US THE DESIRED VALUE IN FLOATING POINT.

|--HIDE SIX CYCLES OF INSTRUCTION

        movel           %a1,%d2

        swap            %d2

        andil           #0x80000000,%d2

        oril            #0x5F000000,%d2 | ...D2 IS SIGN(INARG)*2**63 IN SGL

        movel           %d2,TWOTO63(%a6)

        movel           %d0,%d2

        addil           #0x00003FFF,%d2 | ...BIASED EXPO OF 2**L * (PI/2)

|--FP2 IS READY

        fadds           TWOTO63(%a6),%fp2       | ...THE FRACTIONAL PART OF FP1 IS ROUNDED

|--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1  and  2**(L)*Piby2_2

        movew           %d2,FP_SCR2(%a6)

        clrw           FP_SCR2+2(%a6)

        movel           #0xC90FDAA2,FP_SCR2+4(%a6)

        clrl            FP_SCR2+8(%a6)          | ...FP_SCR2 is  2**(L) * Piby2_1

|--FP2 IS READY

        fsubs           TWOTO63(%a6),%fp2               | ...FP2 is N

        addil           #0x00003FDD,%d0

        movew           %d0,FP_SCR3(%a6)

        clrw           FP_SCR3+2(%a6)

        movel           #0x85A308D3,FP_SCR3+4(%a6)

        clrl            FP_SCR3+8(%a6)          | ...FP_SCR3 is 2**(L) * Piby2_2

        movel           ENDFLAG(%a6),%d0

|--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and

|--P2 = 2**(L) * Piby2_2

        fmovex          %fp2,%fp4

        fmulx           FP_SCR2(%a6),%fp4               | ...W = N*P1

        fmovex          %fp2,%fp5

        fmulx           FP_SCR3(%a6),%fp5               | ...w = N*P2

        fmovex          %fp4,%fp3

|--we want P+p = W+w  but  |p| <= half ulp of P

|--Then, we need to compute  A := R-P   and  a := r-p

        faddx           %fp5,%fp3                       | ...FP3 is P

        fsubx           %fp3,%fp4                       | ...W-P

        fsubx           %fp3,%fp0                       | ...FP0 is A := R - P

        faddx           %fp5,%fp4                       | ...FP4 is p = (W-P)+w

        fmovex          %fp0,%fp3                       | ...FP3 A

        fsubx           %fp4,%fp1                       | ...FP1 is a := r - p

|--Now we need to normalize (A,a) to  "new (R,r)" where R+r = A+a but

|--|r| <= half ulp of R.

        faddx           %fp1,%fp0                       | ...FP0 is R := A+a

|--No need to calculate r if this is the last loop

        cmpil           #0,%d0

        bgt             RESTORE

|--Need to calculate r

        fsubx           %fp0,%fp3                       | ...A-R

        faddx           %fp3,%fp1                       | ...FP1 is r := (A-R)+a

        bra             LOOP

RESTORE:

        fmovel          %fp2,N(%a6)

        movel           (%a7)+,%d2

        fmovemx (%a7)+,%fp2-%fp5

        movel           ADJN(%a6),%d0

        cmpil           #4,%d0

        blt             SINCONT

        bras            SCCONT

        .global ssincosd

ssincosd:

|--SIN AND COS OF X FOR DENORMALIZED X

        fmoves          #0x3F800000,%fp1

        bsr             sto_cos         |store cosine result

        bra             t_extdnrm

        .global ssincos

ssincos:

|--SET ADJN TO 4

        movel           #4,ADJN(%a6)

        fmovex          (%a0),%fp0      | ...LOAD INPUT

        movel           (%a0),%d0

        movew           4(%a0),%d0

        fmovex          %fp0,X(%a6)

        andil           #0x7FFFFFFF,%d0         | ...COMPACTIFY X

        cmpil           #0x3FD78000,%d0         | ...|X| >= 2**(-40)?

        bges            SCOK1

        bra             SCSM

SCOK1:

        cmpil           #0x4004BC7E,%d0         | ...|X| < 15 PI?

        blts            SCMAIN

        bra             REDUCEX

SCMAIN:

|--THIS IS THE USUAL CASE, |X| <= 15 PI.

|--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.

        fmovex          %fp0,%fp1

        fmuld           TWOBYPI,%fp1    | ...X*2/PI

|--HIDE THE NEXT THREE INSTRUCTIONS

        lea             PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32

|--FP1 IS NOW READY

        fmovel          %fp1,N(%a6)             | ...CONVERT TO INTEGER

        movel           N(%a6),%d0

        asll            #4,%d0

        addal           %d0,%a1         | ...ADDRESS OF N*PIBY2, IN Y1, Y2

        fsubx           (%a1)+,%fp0     | ...X-Y1

        fsubs           (%a1),%fp0      | ...FP0 IS R = (X-Y1)-Y2

SCCONT:

|--continuation point from REDUCEX

|--HIDE THE NEXT TWO

        movel           N(%a6),%d0

        rorl            #1,%d0

        cmpil           #0,%d0          | ...D0 < 0 IFF N IS ODD

        bge             NEVEN

NODD:

|--REGISTERS SAVED SO FAR: D0, A0, FP2.

        fmovex          %fp0,RPRIME(%a6)

        fmulx           %fp0,%fp0        | ...FP0 IS S = R*R

        fmoved          SINA7,%fp1      | ...A7

        fmoved          COSB8,%fp2      | ...B8

        fmulx           %fp0,%fp1        | ...SA7

        movel           %d2,-(%a7)

        movel           %d0,%d2

        fmulx           %fp0,%fp2        | ...SB8

        rorl            #1,%d2

        andil           #0x80000000,%d2

        faddd           SINA6,%fp1      | ...A6+SA7

        eorl            %d0,%d2

        andil           #0x80000000,%d2

        faddd           COSB7,%fp2      | ...B7+SB8

        fmulx           %fp0,%fp1        | ...S(A6+SA7)

        eorl            %d2,RPRIME(%a6)

        movel           (%a7)+,%d2

        fmulx           %fp0,%fp2        | ...S(B7+SB8)

        rorl            #1,%d0

        andil           #0x80000000,%d0

        faddd           SINA5,%fp1      | ...A5+S(A6+SA7)

        movel           #0x3F800000,POSNEG1(%a6)

        eorl            %d0,POSNEG1(%a6)

        faddd           COSB6,%fp2      | ...B6+S(B7+SB8)

        fmulx           %fp0,%fp1        | ...S(A5+S(A6+SA7))

        fmulx           %fp0,%fp2        | ...S(B6+S(B7+SB8))

        fmovex          %fp0,SPRIME(%a6)

        faddd           SINA4,%fp1      | ...A4+S(A5+S(A6+SA7))

        eorl            %d0,SPRIME(%a6)

        faddd           COSB5,%fp2      | ...B5+S(B6+S(B7+SB8))

        fmulx           %fp0,%fp1        | ...S(A4+...)

        fmulx           %fp0,%fp2        | ...S(B5+...)

        faddd           SINA3,%fp1      | ...A3+S(A4+...)

        faddd           COSB4,%fp2      | ...B4+S(B5+...)

        fmulx           %fp0,%fp1        | ...S(A3+...)

        fmulx           %fp0,%fp2        | ...S(B4+...)

        faddx           SINA2,%fp1      | ...A2+S(A3+...)

        faddx           COSB3,%fp2      | ...B3+S(B4+...)

        fmulx           %fp0,%fp1        | ...S(A2+...)

        fmulx           %fp0,%fp2        | ...S(B3+...)

        faddx           SINA1,%fp1      | ...A1+S(A2+...)

        faddx           COSB2,%fp2      | ...B2+S(B3+...)

        fmulx           %fp0,%fp1        | ...S(A1+...)

        fmulx           %fp2,%fp0        | ...S(B2+...)

        fmulx           RPRIME(%a6),%fp1        | ...R'S(A1+...)

        fadds           COSB1,%fp0      | ...B1+S(B2...)

        fmulx           SPRIME(%a6),%fp0        | ...S'(B1+S(B2+...))

        movel           %d1,-(%sp)      |restore users mode & precision

        andil           #0xff,%d1               |mask off all exceptions

        fmovel          %d1,%FPCR

        faddx           RPRIME(%a6),%fp1        | ...COS(X)

        bsr             sto_cos         |store cosine result

        fmovel          (%sp)+,%FPCR    |restore users exceptions

        fadds           POSNEG1(%a6),%fp0       | ...SIN(X)

        bra             t_frcinx

NEVEN:

|--REGISTERS SAVED SO FAR: FP2.

        fmovex          %fp0,RPRIME(%a6)

        fmulx           %fp0,%fp0        | ...FP0 IS S = R*R

        fmoved          COSB8,%fp1                      | ...B8

        fmoved          SINA7,%fp2                      | ...A7

        fmulx           %fp0,%fp1        | ...SB8

        fmovex          %fp0,SPRIME(%a6)

        fmulx           %fp0,%fp2        | ...SA7

        rorl            #1,%d0

        andil           #0x80000000,%d0

        faddd           COSB7,%fp1      | ...B7+SB8

        faddd           SINA6,%fp2      | ...A6+SA7

        eorl            %d0,RPRIME(%a6)

        eorl            %d0,SPRIME(%a6)

        fmulx           %fp0,%fp1        | ...S(B7+SB8)

        oril            #0x3F800000,%d0

        movel           %d0,POSNEG1(%a6)

        fmulx           %fp0,%fp2        | ...S(A6+SA7)

        faddd           COSB6,%fp1      | ...B6+S(B7+SB8)

        faddd           SINA5,%fp2      | ...A5+S(A6+SA7)

        fmulx           %fp0,%fp1        | ...S(B6+S(B7+SB8))

        fmulx           %fp0,%fp2        | ...S(A5+S(A6+SA7))

        faddd           COSB5,%fp1      | ...B5+S(B6+S(B7+SB8))

        faddd           SINA4,%fp2      | ...A4+S(A5+S(A6+SA7))

        fmulx           %fp0,%fp1        | ...S(B5+...)

        fmulx           %fp0,%fp2        | ...S(A4+...)

        faddd           COSB4,%fp1      | ...B4+S(B5+...)

        faddd           SINA3,%fp2      | ...A3+S(A4+...)

        fmulx           %fp0,%fp1        | ...S(B4+...)

        fmulx           %fp0,%fp2        | ...S(A3+...)

        faddx           COSB3,%fp1      | ...B3+S(B4+...)

        faddx           SINA2,%fp2      | ...A2+S(A3+...)

        fmulx           %fp0,%fp1        | ...S(B3+...)

        fmulx           %fp0,%fp2        | ...S(A2+...)

        faddx           COSB2,%fp1      | ...B2+S(B3+...)

        faddx           SINA1,%fp2      | ...A1+S(A2+...)

        fmulx           %fp0,%fp1        | ...S(B2+...)

        fmulx           %fp2,%fp0        | ...s(a1+...)

        fadds           COSB1,%fp1      | ...B1+S(B2...)

        fmulx           RPRIME(%a6),%fp0        | ...R'S(A1+...)

        fmulx           SPRIME(%a6),%fp1        | ...S'(B1+S(B2+...))

        movel           %d1,-(%sp)      |save users mode & precision

        andil           #0xff,%d1               |mask off all exceptions

        fmovel          %d1,%FPCR

        fadds           POSNEG1(%a6),%fp1       | ...COS(X)

        bsr             sto_cos         |store cosine result

        fmovel          (%sp)+,%FPCR    |restore users exceptions

        faddx           RPRIME(%a6),%fp0        | ...SIN(X)

        bra             t_frcinx

SCBORS:

        cmpil           #0x3FFF8000,%d0

        bgt             REDUCEX

SCSM:

        movew           #0x0000,XDCARE(%a6)

        fmoves          #0x3F800000,%fp1

        movel           %d1,-(%sp)      |save users mode & precision

        andil           #0xff,%d1               |mask off all exceptions

        fmovel          %d1,%FPCR

        fsubs           #0x00800000,%fp1

        bsr             sto_cos         |store cosine result

        fmovel          (%sp)+,%FPCR    |restore users exceptions

        fmovex          X(%a6),%fp0

        bra             t_frcinx

        |end