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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