| | |
| | 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 |
| | |
| | For details on the license for this file, please see the |
| | file, README, in this same directory. |
| |
| |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 |
