| MOTOROLA MICROPROCESSOR & MEMORY TECHNOLOGY GROUP | M68000 Hi-Performance Microprocessor Division | M68040 Software Package | | M68040 Software Package Copyright (c) 1993, 1994 Motorola Inc. | All rights reserved. | | THE SOFTWARE is provided on an "AS IS" basis and without warranty. | To the maximum extent permitted by applicable law, | MOTOROLA DISCLAIMS ALL WARRANTIES WHETHER EXPRESS OR IMPLIED, | INCLUDING IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A | PARTICULAR PURPOSE and any warranty against infringement with | regard to the SOFTWARE (INCLUDING ANY MODIFIED VERSIONS THEREOF) | and any accompanying written materials. | | To the maximum extent permitted by applicable law, | IN NO EVENT SHALL MOTOROLA BE LIABLE FOR ANY DAMAGES WHATSOEVER | (INCLUDING WITHOUT LIMITATION, DAMAGES FOR LOSS OF BUSINESS | PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, OR | OTHER PECUNIARY LOSS) ARISING OF THE USE OR INABILITY TO USE THE | SOFTWARE. Motorola assumes no responsibility for the maintenance | and support of the SOFTWARE. | | You are hereby granted a copyright license to use, modify, and | distribute the SOFTWARE so long as this entire notice is retained | without alteration in any modified and/or redistributed versions, | and that such modified versions are clearly identified as such. | No licenses are granted by implication, estoppel or otherwise | under any patents or trademarks of Motorola, Inc. | | 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 funtion 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. Overwirte | 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. | |SSIN IDNT 2,1 Motorola 040 Floating Point Software Package .text .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 clrl a6@(ADJN) bras SINBGN .global scos scos: |--SET ADJN TO 1 movel #1,a6@(ADJN) SINBGN: |--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE fmovex a0@,FP0 |...LOAD INPUT movel A0@,D0 movew A0@(4),D0 fmovex FP0,a6@(X) 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,a6@(N) |...CONVERT TO INTEGER movel a6@(N),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 a6@(N),D0 addl a6@(ADJN),D0 |...SEE IF D0 IS ODD OR EVEN rorl #1,D0 |...D0 WAS ODD IFF D0 IS NEGATIVE tstl 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,a6@(X) |...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,a6@(X) |...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 a6@(X),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 a6@(X),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,a6@(X) |...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,a6@(X) |...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,a6@(POSNEG1) 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 a6@(X),FP0 fmovel d1,FPCR |restore users exceptions fadds a6@(POSNEG1),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 a6@(ADJN),D0 tstl D0 bgts COSTINY SINTINY: clrw a6@(XDCARE) |...JUST IN CASE fmovel d1,FPCR |restore users exceptions fmovex a6@(X),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=0x7ffeffff, 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,a6@(FP_SCR2) |yes | ;create 2**16383*PI/2 movel #0xc90fdaa2,a6@(FP_SCR2+4) clrl a6@(FP_SCR2+8) ftstx fp0 |test sign of argument movel #0x7fdc0000,a6@(FP_SCR3) |create low half of 2**16383* | ;PI/2 at FP_SCR3 movel #0x85a308d3,a6@(FP_SCR3+4) clrl a6@(FP_SCR3+8) fblt red_neg orw #0x8000,a6@(FP_SCR2) |positive arg orw #0x8000,a6@(FP_SCR3) red_neg: faddx a6@(FP_SCR2),fp0 |high part of reduction is exact fmovex fp0,fp1 |save high result in fp1 faddx a6@(FP_SCR3),fp0 |low part of reduction fsubx fp0,fp1 |determine low component of result faddx a6@(FP_SCR3),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 |--Intermeditate remainder is 66-bit long; (R,r) in (FP0,FP1) LOOP: fmovex FP0,a6@(INARG) |...+-2**K * F, 1 <= F < 2 movew a6@(INARG),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 clrl a6@(ENDFLAG) bras WORK LASTLOOP: clrl D0 |...D0 IS L := 0 movel #1,a6@(ENDFLAG) 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,a6@(FP_SCR1+4) movel #0x4E44152A,a6@(FP_SCR1+8) movew D2,a6@(FP_SCR1) |...FP_SCR1 is 2**(-L)*(2/PI) fmovex FP0,FP2 fmulx a6@(FP_SCR1),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,a6@(TWOTO63) movel D0,D2 addil #0x00003FFF,D2 |...BIASED EXPO OF 2**L * (PI/2) |--FP2 IS READY fadds a6@(TWOTO63),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,a6@(FP_SCR2) clrw a6@(FP_SCR2+2) movel #0xC90FDAA2,a6@(FP_SCR2+4) clrl a6@(FP_SCR2+8) |...FP_SCR2 is 2**(L) * Piby2_1 |--FP2 IS READY fsubs a6@(TWOTO63),FP2 |...FP2 is N addil #0x00003FDD,D0 movew D0,a6@(FP_SCR3) clrw a6@(FP_SCR3+2) movel #0x85A308D3,a6@(FP_SCR3+4) clrl a6@(FP_SCR3+8) |...FP_SCR3 is 2**(L) * Piby2_2 movel a6@(ENDFLAG),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 a6@(FP_SCR2),FP4 |...W = N*P1 fmovex FP2,FP5 fmulx a6@(FP_SCR3),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 tstl 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,a6@(N) movel A7@+,D2 fmovemx A7@+,FP2-FP5 movel a6@(ADJN),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,a6@(ADJN) fmovex a0@,FP0 |...LOAD INPUT movel A0@,D0 movew A0@(4),D0 fmovex FP0,a6@(X) 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,a6@(N) |...CONVERT TO INTEGER movel a6@(N),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 a6@(N),D0 rorl #1,D0 tstl D0 |...D0 < 0 IFF N IS ODD bge NEVEN NODD: |--REGISTERS SAVED SO FAR: D0, A0, FP2. fmovex FP0,a6@(RPRIME) 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,a6@(RPRIME) movel A7@+,d2 fmulx FP0,FP2 |...S(B7+SB8) rorl #1,D0 andil #0x80000000,D0 faddd SINA5,FP1 |...A5+S(A6+SA7) movel #0x3F800000,a6@(POSNEG1) eorl D0,a6@(POSNEG1) 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,a6@(SPRIME) faddd SINA4,FP1 |...A4+S(A5+S(A6+SA7)) eorl D0,a6@(SPRIME) 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 a6@(RPRIME),FP1 |...R'S(A1+...) fadds COSB1,FP0 |...B1+S(B2...) fmulx a6@(SPRIME),FP0 |...S'(B1+S(B2+...)) movel d1,sp@- |restore users mode & precision andil #0xff,d1 |mask off all exceptions fmovel d1,FPCR faddx a6@(RPRIME),FP1 |...COS(X) bsr sto_cos |store cosine result fmovel sp@+,FPCR |restore users exceptions fadds a6@(POSNEG1),FP0 |...SIN(X) bra t_frcinx NEVEN: |--REGISTERS SAVED SO FAR: FP2. fmovex FP0,a6@(RPRIME) fmulx FP0,FP0 |...FP0 IS S = R*R fmoved COSB8,FP1 |...B8 fmoved SINA7,FP2 |...A7 fmulx FP0,FP1 |...SB8 fmovex FP0,a6@(SPRIME) fmulx FP0,FP2 |...SA7 rorl #1,D0 andil #0x80000000,D0 faddd COSB7,FP1 |...B7+SB8 faddd SINA6,FP2 |...A6+SA7 eorl D0,a6@(RPRIME) eorl D0,a6@(SPRIME) fmulx FP0,FP1 |...S(B7+SB8) oril #0x3F800000,D0 movel D0,a6@(POSNEG1) 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 a6@(RPRIME),FP0 |...R'S(A1+...) fmulx a6@(SPRIME),FP1 |...S'(B1+S(B2+...)) movel d1,sp@- |save users mode & precision andil #0xff,d1 |mask off all exceptions fmovel d1,FPCR fadds a6@(POSNEG1),FP1 |...COS(X) bsr sto_cos |store cosine result fmovel sp@+,FPCR |restore users exceptions faddx a6@(RPRIME),FP0 |...SIN(X) bra t_frcinx SCBORS: cmpil #0x3FFF8000,D0 bgt REDUCEX SCSM: clrw a6@(XDCARE) 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 a6@(X),FP0 bra t_frcinx | end