Subversion Repositories openrisc_2011-10-31

//
//      $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