Subversion Repositories or1k

|
|       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