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//

//      $Id: ssin.S,v 1.2 2001-09-27 12:01:22 chris Exp $

//

//      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 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.defs"

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