|
|
| 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
|
