|
| 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