blob: 043c91cdd6574d4840d0566eefeb349389c8b17b [file] [log] [blame]
 | | 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