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1623 |
jcastillo |
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| ssin.sa 3.3 7/29/91
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| The entry point sSIN computes the sine of an input argument
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| sCOS computes the cosine, and sSINCOS computes both. The
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| corresponding entry points with a "d" computes the same
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| corresponding function values for denormalized inputs.
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| Input: Double-extended number X in location pointed to
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| by address register a0.
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| Output: The function value sin(X) or cos(X) returned in Fp0 if SIN or
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| COS is requested. Otherwise, for SINCOS, sin(X) is returned
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| in Fp0, and cos(X) is returned in Fp1.
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| Modifies: Fp0 for SIN or COS; both Fp0 and Fp1 for SINCOS.
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| Accuracy and Monotonicity: The returned result is within 1 ulp in
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| 64 significant bit, i.e. within 0.5001 ulp to 53 bits if the
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| result is subsequently rounded to double precision. The
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| result is provably monotonic in double precision.
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| Speed: The programs sSIN and sCOS take approximately 150 cycles for
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| input argument X such that |X| < 15Pi, which is the usual
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| situation. The speed for sSINCOS is approximately 190 cycles.
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| Algorithm:
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| SIN and COS:
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| 1. If SIN is invoked, set AdjN := 0; otherwise, set AdjN := 1.
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| 2. If |X| >= 15Pi or |X| < 2**(-40), go to 7.
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| 3. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
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| k = N mod 4, so in particular, k = 0,1,2,or 3. Overwrite
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| k by k := k + AdjN.
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| 4. If k is even, go to 6.
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| 5. (k is odd) Set j := (k-1)/2, sgn := (-1)**j. Return sgn*cos(r)
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| where cos(r) is approximated by an even polynomial in r,
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| 1 + r*r*(B1+s*(B2+ ... + s*B8)), s = r*r.
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| Exit.
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| 6. (k is even) Set j := k/2, sgn := (-1)**j. Return sgn*sin(r)
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| where sin(r) is approximated by an odd polynomial in r
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| r + r*s*(A1+s*(A2+ ... + s*A7)), s = r*r.
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| Exit.
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| 7. If |X| > 1, go to 9.
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| 8. (|X|<2**(-40)) If SIN is invoked, return X; otherwise return 1.
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| 9. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 3.
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| SINCOS:
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| 1. If |X| >= 15Pi or |X| < 2**(-40), go to 6.
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| 2. Decompose X as X = N(Pi/2) + r where |r| <= Pi/4. Let
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| k = N mod 4, so in particular, k = 0,1,2,or 3.
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| 3. If k is even, go to 5.
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| 4. (k is odd) Set j1 := (k-1)/2, j2 := j1 (EOR) (k mod 2), i.e.
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| j1 exclusive or with the l.s.b. of k.
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| sgn1 := (-1)**j1, sgn2 := (-1)**j2.
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| SIN(X) = sgn1 * cos(r) and COS(X) = sgn2*sin(r) where
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| sin(r) and cos(r) are computed as odd and even polynomials
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| in r, respectively. Exit
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| 5. (k is even) Set j1 := k/2, sgn1 := (-1)**j1.
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| SIN(X) = sgn1 * sin(r) and COS(X) = sgn1*cos(r) where
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| sin(r) and cos(r) are computed as odd and even polynomials
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| in r, respectively. Exit
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| 6. If |X| > 1, go to 8.
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| 7. (|X|<2**(-40)) SIN(X) = X and COS(X) = 1. Exit.
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| 8. Overwrite X by X := X rem 2Pi. Now that |X| <= Pi, go back to 2.
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| Copyright (C) Motorola, Inc. 1990
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| All Rights Reserved
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| THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
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| The copyright notice above does not evidence any
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| actual or intended publication of such source code.
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|SSIN idnt 2,1 | Motorola 040 Floating Point Software Package
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|section 8
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.include "fpsp.h"
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BOUNDS1: .long 0x3FD78000,0x4004BC7E
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TWOBYPI: .long 0x3FE45F30,0x6DC9C883
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SINA7: .long 0xBD6AAA77,0xCCC994F5
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SINA6: .long 0x3DE61209,0x7AAE8DA1
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SINA5: .long 0xBE5AE645,0x2A118AE4
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SINA4: .long 0x3EC71DE3,0xA5341531
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SINA3: .long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000
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SINA2: .long 0x3FF80000,0x88888888,0x888859AF,0x00000000
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SINA1: .long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000
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COSB8: .long 0x3D2AC4D0,0xD6011EE3
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COSB7: .long 0xBDA9396F,0x9F45AC19
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COSB6: .long 0x3E21EED9,0x0612C972
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COSB5: .long 0xBE927E4F,0xB79D9FCF
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COSB4: .long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000
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COSB3: .long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000
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COSB2: .long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E
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COSB1: .long 0xBF000000
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INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A
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TWOPI1: .long 0x40010000,0xC90FDAA2,0x00000000,0x00000000
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TWOPI2: .long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000
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|xref PITBL
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.set INARG,FP_SCR4
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.set X,FP_SCR5
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.set XDCARE,X+2
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.set XFRAC,X+4
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.set RPRIME,FP_SCR1
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.set SPRIME,FP_SCR2
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.set POSNEG1,L_SCR1
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.set TWOTO63,L_SCR1
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.set ENDFLAG,L_SCR2
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.set N,L_SCR2
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.set ADJN,L_SCR3
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| xref t_frcinx
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|xref t_extdnrm
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|xref sto_cos
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.global ssind
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ssind:
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|--SIN(X) = X FOR DENORMALIZED X
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bra t_extdnrm
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.global scosd
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scosd:
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|--COS(X) = 1 FOR DENORMALIZED X
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fmoves #0x3F800000,%fp0
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| 9D25B Fix: Sometimes the previous fmove.s sets fpsr bits
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fmovel #0,%fpsr
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bra t_frcinx
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.global ssin
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ssin:
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|--SET ADJN TO 0
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movel #0,ADJN(%a6)
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bras SINBGN
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.global scos
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scos:
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|--SET ADJN TO 1
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movel #1,ADJN(%a6)
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SINBGN:
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|--SAVE FPCR, FP1. CHECK IF |X| IS TOO SMALL OR LARGE
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fmovex (%a0),%fp0 | ...LOAD INPUT
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movel (%a0),%d0
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movew 4(%a0),%d0
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fmovex %fp0,X(%a6)
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andil #0x7FFFFFFF,%d0 | ...COMPACTIFY X
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cmpil #0x3FD78000,%d0 | ...|X| >= 2**(-40)?
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bges SOK1
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bra SINSM
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SOK1:
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cmpil #0x4004BC7E,%d0 | ...|X| < 15 PI?
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blts SINMAIN
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bra REDUCEX
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SINMAIN:
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|--THIS IS THE USUAL CASE, |X| <= 15 PI.
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|--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
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fmovex %fp0,%fp1
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fmuld TWOBYPI,%fp1 | ...X*2/PI
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|--HIDE THE NEXT THREE INSTRUCTIONS
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lea PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32
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|--FP1 IS NOW READY
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fmovel %fp1,N(%a6) | ...CONVERT TO INTEGER
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movel N(%a6),%d0
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asll #4,%d0
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addal %d0,%a1 | ...A1 IS THE ADDRESS OF N*PIBY2
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| ...WHICH IS IN TWO PIECES Y1 & Y2
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fsubx (%a1)+,%fp0 | ...X-Y1
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|--HIDE THE NEXT ONE
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fsubs (%a1),%fp0 | ...FP0 IS R = (X-Y1)-Y2
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SINCONT:
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|--continuation from REDUCEX
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|--GET N+ADJN AND SEE IF SIN(R) OR COS(R) IS NEEDED
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movel N(%a6),%d0
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addl ADJN(%a6),%d0 | ...SEE IF D0 IS ODD OR EVEN
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rorl #1,%d0 | ...D0 WAS ODD IFF D0 IS NEGATIVE
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cmpil #0,%d0
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blt COSPOLY
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SINPOLY:
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|--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
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|--THEN WE RETURN SGN*SIN(R). SGN*SIN(R) IS COMPUTED BY
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|--R' + R'*S*(A1 + S(A2 + S(A3 + S(A4 + ... + SA7)))), WHERE
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|--R' = SGN*R, S=R*R. THIS CAN BE REWRITTEN AS
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|--R' + R'*S*( [A1+T(A3+T(A5+TA7))] + [S(A2+T(A4+TA6))])
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|--WHERE T=S*S.
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|--NOTE THAT A3 THROUGH A7 ARE STORED IN DOUBLE PRECISION
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|--WHILE A1 AND A2 ARE IN DOUBLE-EXTENDED FORMAT.
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fmovex %fp0,X(%a6) | ...X IS R
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fmulx %fp0,%fp0 | ...FP0 IS S
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|---HIDE THE NEXT TWO WHILE WAITING FOR FP0
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fmoved SINA7,%fp3
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fmoved SINA6,%fp2
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|--FP0 IS NOW READY
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fmovex %fp0,%fp1
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fmulx %fp1,%fp1 | ...FP1 IS T
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|--HIDE THE NEXT TWO WHILE WAITING FOR FP1
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rorl #1,%d0
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andil #0x80000000,%d0
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| ...LEAST SIG. BIT OF D0 IN SIGN POSITION
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eorl %d0,X(%a6) | ...X IS NOW R'= SGN*R
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fmulx %fp1,%fp3 | ...TA7
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fmulx %fp1,%fp2 | ...TA6
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faddd SINA5,%fp3 | ...A5+TA7
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faddd SINA4,%fp2 | ...A4+TA6
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fmulx %fp1,%fp3 | ...T(A5+TA7)
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fmulx %fp1,%fp2 | ...T(A4+TA6)
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faddd SINA3,%fp3 | ...A3+T(A5+TA7)
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faddx SINA2,%fp2 | ...A2+T(A4+TA6)
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fmulx %fp3,%fp1 | ...T(A3+T(A5+TA7))
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fmulx %fp0,%fp2 | ...S(A2+T(A4+TA6))
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faddx SINA1,%fp1 | ...A1+T(A3+T(A5+TA7))
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fmulx X(%a6),%fp0 | ...R'*S
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faddx %fp2,%fp1 | ...[A1+T(A3+T(A5+TA7))]+[S(A2+T(A4+TA6))]
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|--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING
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|--FP2 RELEASED, RESTORE NOW AND TAKE FULL ADVANTAGE OF HIDING
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fmulx %fp1,%fp0 | ...SIN(R')-R'
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|--FP1 RELEASED.
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fmovel %d1,%FPCR |restore users exceptions
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faddx X(%a6),%fp0 |last inst - possible exception set
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bra t_frcinx
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COSPOLY:
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|--LET J BE THE LEAST SIG. BIT OF D0, LET SGN := (-1)**J.
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|--THEN WE RETURN SGN*COS(R). SGN*COS(R) IS COMPUTED BY
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|--SGN + S'*(B1 + S(B2 + S(B3 + S(B4 + ... + SB8)))), WHERE
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|--S=R*R AND S'=SGN*S. THIS CAN BE REWRITTEN AS
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|--SGN + S'*([B1+T(B3+T(B5+TB7))] + [S(B2+T(B4+T(B6+TB8)))])
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|--WHERE T=S*S.
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|--NOTE THAT B4 THROUGH B8 ARE STORED IN DOUBLE PRECISION
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|--WHILE B2 AND B3 ARE IN DOUBLE-EXTENDED FORMAT, B1 IS -1/2
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|--AND IS THEREFORE STORED AS SINGLE PRECISION.
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fmulx %fp0,%fp0 | ...FP0 IS S
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|---HIDE THE NEXT TWO WHILE WAITING FOR FP0
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fmoved COSB8,%fp2
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fmoved COSB7,%fp3
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|--FP0 IS NOW READY
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fmovex %fp0,%fp1
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|
|
fmulx %fp1,%fp1 | ...FP1 IS T
|
| 304 |
|
|
|--HIDE THE NEXT TWO WHILE WAITING FOR FP1
|
| 305 |
|
|
fmovex %fp0,X(%a6) | ...X IS S
|
| 306 |
|
|
rorl #1,%d0
|
| 307 |
|
|
andil #0x80000000,%d0
|
| 308 |
|
|
| ...LEAST SIG. BIT OF D0 IN SIGN POSITION
|
| 309 |
|
|
|
| 310 |
|
|
fmulx %fp1,%fp2 | ...TB8
|
| 311 |
|
|
|--HIDE THE NEXT TWO WHILE WAITING FOR THE XU
|
| 312 |
|
|
eorl %d0,X(%a6) | ...X IS NOW S'= SGN*S
|
| 313 |
|
|
andil #0x80000000,%d0
|
| 314 |
|
|
|
| 315 |
|
|
fmulx %fp1,%fp3 | ...TB7
|
| 316 |
|
|
|--HIDE THE NEXT TWO WHILE WAITING FOR THE XU
|
| 317 |
|
|
oril #0x3F800000,%d0 | ...D0 IS SGN IN SINGLE
|
| 318 |
|
|
movel %d0,POSNEG1(%a6)
|
| 319 |
|
|
|
| 320 |
|
|
faddd COSB6,%fp2 | ...B6+TB8
|
| 321 |
|
|
faddd COSB5,%fp3 | ...B5+TB7
|
| 322 |
|
|
|
| 323 |
|
|
fmulx %fp1,%fp2 | ...T(B6+TB8)
|
| 324 |
|
|
fmulx %fp1,%fp3 | ...T(B5+TB7)
|
| 325 |
|
|
|
| 326 |
|
|
faddd COSB4,%fp2 | ...B4+T(B6+TB8)
|
| 327 |
|
|
faddx COSB3,%fp3 | ...B3+T(B5+TB7)
|
| 328 |
|
|
|
| 329 |
|
|
fmulx %fp1,%fp2 | ...T(B4+T(B6+TB8))
|
| 330 |
|
|
fmulx %fp3,%fp1 | ...T(B3+T(B5+TB7))
|
| 331 |
|
|
|
| 332 |
|
|
faddx COSB2,%fp2 | ...B2+T(B4+T(B6+TB8))
|
| 333 |
|
|
fadds COSB1,%fp1 | ...B1+T(B3+T(B5+TB7))
|
| 334 |
|
|
|
| 335 |
|
|
fmulx %fp2,%fp0 | ...S(B2+T(B4+T(B6+TB8)))
|
| 336 |
|
|
|--FP3 RELEASED, RESTORE NOW AND TAKE SOME ADVANTAGE OF HIDING
|
| 337 |
|
|
|--FP2 RELEASED.
|
| 338 |
|
|
|
| 339 |
|
|
|
| 340 |
|
|
faddx %fp1,%fp0
|
| 341 |
|
|
|--FP1 RELEASED
|
| 342 |
|
|
|
| 343 |
|
|
fmulx X(%a6),%fp0
|
| 344 |
|
|
|
| 345 |
|
|
fmovel %d1,%FPCR |restore users exceptions
|
| 346 |
|
|
fadds POSNEG1(%a6),%fp0 |last inst - possible exception set
|
| 347 |
|
|
bra t_frcinx
|
| 348 |
|
|
|
| 349 |
|
|
|
| 350 |
|
|
SINBORS:
|
| 351 |
|
|
|--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION.
|
| 352 |
|
|
|--IF |X| < 2**(-40), RETURN X OR 1.
|
| 353 |
|
|
cmpil #0x3FFF8000,%d0
|
| 354 |
|
|
bgts REDUCEX
|
| 355 |
|
|
|
| 356 |
|
|
|
| 357 |
|
|
SINSM:
|
| 358 |
|
|
movel ADJN(%a6),%d0
|
| 359 |
|
|
cmpil #0,%d0
|
| 360 |
|
|
bgts COSTINY
|
| 361 |
|
|
|
| 362 |
|
|
SINTINY:
|
| 363 |
|
|
movew #0x0000,XDCARE(%a6) | ...JUST IN CASE
|
| 364 |
|
|
fmovel %d1,%FPCR |restore users exceptions
|
| 365 |
|
|
fmovex X(%a6),%fp0 |last inst - possible exception set
|
| 366 |
|
|
bra t_frcinx
|
| 367 |
|
|
|
| 368 |
|
|
|
| 369 |
|
|
COSTINY:
|
| 370 |
|
|
fmoves #0x3F800000,%fp0
|
| 371 |
|
|
|
| 372 |
|
|
fmovel %d1,%FPCR |restore users exceptions
|
| 373 |
|
|
fsubs #0x00800000,%fp0 |last inst - possible exception set
|
| 374 |
|
|
bra t_frcinx
|
| 375 |
|
|
|
| 376 |
|
|
|
| 377 |
|
|
REDUCEX:
|
| 378 |
|
|
|--WHEN REDUCEX IS USED, THE CODE WILL INEVITABLY BE SLOW.
|
| 379 |
|
|
|--THIS REDUCTION METHOD, HOWEVER, IS MUCH FASTER THAN USING
|
| 380 |
|
|
|--THE REMAINDER INSTRUCTION WHICH IS NOW IN SOFTWARE.
|
| 381 |
|
|
|
| 382 |
|
|
fmovemx %fp2-%fp5,-(%a7) | ...save FP2 through FP5
|
| 383 |
|
|
movel %d2,-(%a7)
|
| 384 |
|
|
fmoves #0x00000000,%fp1
|
| 385 |
|
|
|--If compact form of abs(arg) in d0=$7ffeffff, argument is so large that
|
| 386 |
|
|
|--there is a danger of unwanted overflow in first LOOP iteration. In this
|
| 387 |
|
|
|--case, reduce argument by one remainder step to make subsequent reduction
|
| 388 |
|
|
|--safe.
|
| 389 |
|
|
cmpil #0x7ffeffff,%d0 |is argument dangerously large?
|
| 390 |
|
|
bnes LOOP
|
| 391 |
|
|
movel #0x7ffe0000,FP_SCR2(%a6) |yes
|
| 392 |
|
|
| ;create 2**16383*PI/2
|
| 393 |
|
|
movel #0xc90fdaa2,FP_SCR2+4(%a6)
|
| 394 |
|
|
clrl FP_SCR2+8(%a6)
|
| 395 |
|
|
ftstx %fp0 |test sign of argument
|
| 396 |
|
|
movel #0x7fdc0000,FP_SCR3(%a6) |create low half of 2**16383*
|
| 397 |
|
|
| ;PI/2 at FP_SCR3
|
| 398 |
|
|
movel #0x85a308d3,FP_SCR3+4(%a6)
|
| 399 |
|
|
clrl FP_SCR3+8(%a6)
|
| 400 |
|
|
fblt red_neg
|
| 401 |
|
|
orw #0x8000,FP_SCR2(%a6) |positive arg
|
| 402 |
|
|
orw #0x8000,FP_SCR3(%a6)
|
| 403 |
|
|
red_neg:
|
| 404 |
|
|
faddx FP_SCR2(%a6),%fp0 |high part of reduction is exact
|
| 405 |
|
|
fmovex %fp0,%fp1 |save high result in fp1
|
| 406 |
|
|
faddx FP_SCR3(%a6),%fp0 |low part of reduction
|
| 407 |
|
|
fsubx %fp0,%fp1 |determine low component of result
|
| 408 |
|
|
faddx FP_SCR3(%a6),%fp1 |fp0/fp1 are reduced argument.
|
| 409 |
|
|
|
| 410 |
|
|
|--ON ENTRY, FP0 IS X, ON RETURN, FP0 IS X REM PI/2, |X| <= PI/4.
|
| 411 |
|
|
|--integer quotient will be stored in N
|
| 412 |
|
|
|--Intermediate remainder is 66-bit long; (R,r) in (FP0,FP1)
|
| 413 |
|
|
|
| 414 |
|
|
LOOP:
|
| 415 |
|
|
fmovex %fp0,INARG(%a6) | ...+-2**K * F, 1 <= F < 2
|
| 416 |
|
|
movew INARG(%a6),%d0
|
| 417 |
|
|
movel %d0,%a1 | ...save a copy of D0
|
| 418 |
|
|
andil #0x00007FFF,%d0
|
| 419 |
|
|
subil #0x00003FFF,%d0 | ...D0 IS K
|
| 420 |
|
|
cmpil #28,%d0
|
| 421 |
|
|
bles LASTLOOP
|
| 422 |
|
|
CONTLOOP:
|
| 423 |
|
|
subil #27,%d0 | ...D0 IS L := K-27
|
| 424 |
|
|
movel #0,ENDFLAG(%a6)
|
| 425 |
|
|
bras WORK
|
| 426 |
|
|
LASTLOOP:
|
| 427 |
|
|
clrl %d0 | ...D0 IS L := 0
|
| 428 |
|
|
movel #1,ENDFLAG(%a6)
|
| 429 |
|
|
|
| 430 |
|
|
WORK:
|
| 431 |
|
|
|--FIND THE REMAINDER OF (R,r) W.R.T. 2**L * (PI/2). L IS SO CHOSEN
|
| 432 |
|
|
|--THAT INT( X * (2/PI) / 2**(L) ) < 2**29.
|
| 433 |
|
|
|
| 434 |
|
|
|--CREATE 2**(-L) * (2/PI), SIGN(INARG)*2**(63),
|
| 435 |
|
|
|--2**L * (PIby2_1), 2**L * (PIby2_2)
|
| 436 |
|
|
|
| 437 |
|
|
movel #0x00003FFE,%d2 | ...BIASED EXPO OF 2/PI
|
| 438 |
|
|
subl %d0,%d2 | ...BIASED EXPO OF 2**(-L)*(2/PI)
|
| 439 |
|
|
|
| 440 |
|
|
movel #0xA2F9836E,FP_SCR1+4(%a6)
|
| 441 |
|
|
movel #0x4E44152A,FP_SCR1+8(%a6)
|
| 442 |
|
|
movew %d2,FP_SCR1(%a6) | ...FP_SCR1 is 2**(-L)*(2/PI)
|
| 443 |
|
|
|
| 444 |
|
|
fmovex %fp0,%fp2
|
| 445 |
|
|
fmulx FP_SCR1(%a6),%fp2
|
| 446 |
|
|
|--WE MUST NOW FIND INT(FP2). SINCE WE NEED THIS VALUE IN
|
| 447 |
|
|
|--FLOATING POINT FORMAT, THE TWO FMOVE'S FMOVE.L FP <--> N
|
| 448 |
|
|
|--WILL BE TOO INEFFICIENT. THE WAY AROUND IT IS THAT
|
| 449 |
|
|
|--(SIGN(INARG)*2**63 + FP2) - SIGN(INARG)*2**63 WILL GIVE
|
| 450 |
|
|
|--US THE DESIRED VALUE IN FLOATING POINT.
|
| 451 |
|
|
|
| 452 |
|
|
|--HIDE SIX CYCLES OF INSTRUCTION
|
| 453 |
|
|
movel %a1,%d2
|
| 454 |
|
|
swap %d2
|
| 455 |
|
|
andil #0x80000000,%d2
|
| 456 |
|
|
oril #0x5F000000,%d2 | ...D2 IS SIGN(INARG)*2**63 IN SGL
|
| 457 |
|
|
movel %d2,TWOTO63(%a6)
|
| 458 |
|
|
|
| 459 |
|
|
movel %d0,%d2
|
| 460 |
|
|
addil #0x00003FFF,%d2 | ...BIASED EXPO OF 2**L * (PI/2)
|
| 461 |
|
|
|
| 462 |
|
|
|--FP2 IS READY
|
| 463 |
|
|
fadds TWOTO63(%a6),%fp2 | ...THE FRACTIONAL PART OF FP1 IS ROUNDED
|
| 464 |
|
|
|
| 465 |
|
|
|--HIDE 4 CYCLES OF INSTRUCTION; creating 2**(L)*Piby2_1 and 2**(L)*Piby2_2
|
| 466 |
|
|
movew %d2,FP_SCR2(%a6)
|
| 467 |
|
|
clrw FP_SCR2+2(%a6)
|
| 468 |
|
|
movel #0xC90FDAA2,FP_SCR2+4(%a6)
|
| 469 |
|
|
clrl FP_SCR2+8(%a6) | ...FP_SCR2 is 2**(L) * Piby2_1
|
| 470 |
|
|
|
| 471 |
|
|
|--FP2 IS READY
|
| 472 |
|
|
fsubs TWOTO63(%a6),%fp2 | ...FP2 is N
|
| 473 |
|
|
|
| 474 |
|
|
addil #0x00003FDD,%d0
|
| 475 |
|
|
movew %d0,FP_SCR3(%a6)
|
| 476 |
|
|
clrw FP_SCR3+2(%a6)
|
| 477 |
|
|
movel #0x85A308D3,FP_SCR3+4(%a6)
|
| 478 |
|
|
clrl FP_SCR3+8(%a6) | ...FP_SCR3 is 2**(L) * Piby2_2
|
| 479 |
|
|
|
| 480 |
|
|
movel ENDFLAG(%a6),%d0
|
| 481 |
|
|
|
| 482 |
|
|
|--We are now ready to perform (R+r) - N*P1 - N*P2, P1 = 2**(L) * Piby2_1 and
|
| 483 |
|
|
|--P2 = 2**(L) * Piby2_2
|
| 484 |
|
|
fmovex %fp2,%fp4
|
| 485 |
|
|
fmulx FP_SCR2(%a6),%fp4 | ...W = N*P1
|
| 486 |
|
|
fmovex %fp2,%fp5
|
| 487 |
|
|
fmulx FP_SCR3(%a6),%fp5 | ...w = N*P2
|
| 488 |
|
|
fmovex %fp4,%fp3
|
| 489 |
|
|
|--we want P+p = W+w but |p| <= half ulp of P
|
| 490 |
|
|
|--Then, we need to compute A := R-P and a := r-p
|
| 491 |
|
|
faddx %fp5,%fp3 | ...FP3 is P
|
| 492 |
|
|
fsubx %fp3,%fp4 | ...W-P
|
| 493 |
|
|
|
| 494 |
|
|
fsubx %fp3,%fp0 | ...FP0 is A := R - P
|
| 495 |
|
|
faddx %fp5,%fp4 | ...FP4 is p = (W-P)+w
|
| 496 |
|
|
|
| 497 |
|
|
fmovex %fp0,%fp3 | ...FP3 A
|
| 498 |
|
|
fsubx %fp4,%fp1 | ...FP1 is a := r - p
|
| 499 |
|
|
|
| 500 |
|
|
|--Now we need to normalize (A,a) to "new (R,r)" where R+r = A+a but
|
| 501 |
|
|
|--|r| <= half ulp of R.
|
| 502 |
|
|
faddx %fp1,%fp0 | ...FP0 is R := A+a
|
| 503 |
|
|
|--No need to calculate r if this is the last loop
|
| 504 |
|
|
cmpil #0,%d0
|
| 505 |
|
|
bgt RESTORE
|
| 506 |
|
|
|
| 507 |
|
|
|--Need to calculate r
|
| 508 |
|
|
fsubx %fp0,%fp3 | ...A-R
|
| 509 |
|
|
faddx %fp3,%fp1 | ...FP1 is r := (A-R)+a
|
| 510 |
|
|
bra LOOP
|
| 511 |
|
|
|
| 512 |
|
|
RESTORE:
|
| 513 |
|
|
fmovel %fp2,N(%a6)
|
| 514 |
|
|
movel (%a7)+,%d2
|
| 515 |
|
|
fmovemx (%a7)+,%fp2-%fp5
|
| 516 |
|
|
|
| 517 |
|
|
|
| 518 |
|
|
movel ADJN(%a6),%d0
|
| 519 |
|
|
cmpil #4,%d0
|
| 520 |
|
|
|
| 521 |
|
|
blt SINCONT
|
| 522 |
|
|
bras SCCONT
|
| 523 |
|
|
|
| 524 |
|
|
.global ssincosd
|
| 525 |
|
|
ssincosd:
|
| 526 |
|
|
|--SIN AND COS OF X FOR DENORMALIZED X
|
| 527 |
|
|
|
| 528 |
|
|
fmoves #0x3F800000,%fp1
|
| 529 |
|
|
bsr sto_cos |store cosine result
|
| 530 |
|
|
bra t_extdnrm
|
| 531 |
|
|
|
| 532 |
|
|
.global ssincos
|
| 533 |
|
|
ssincos:
|
| 534 |
|
|
|--SET ADJN TO 4
|
| 535 |
|
|
movel #4,ADJN(%a6)
|
| 536 |
|
|
|
| 537 |
|
|
fmovex (%a0),%fp0 | ...LOAD INPUT
|
| 538 |
|
|
|
| 539 |
|
|
movel (%a0),%d0
|
| 540 |
|
|
movew 4(%a0),%d0
|
| 541 |
|
|
fmovex %fp0,X(%a6)
|
| 542 |
|
|
andil #0x7FFFFFFF,%d0 | ...COMPACTIFY X
|
| 543 |
|
|
|
| 544 |
|
|
cmpil #0x3FD78000,%d0 | ...|X| >= 2**(-40)?
|
| 545 |
|
|
bges SCOK1
|
| 546 |
|
|
bra SCSM
|
| 547 |
|
|
|
| 548 |
|
|
SCOK1:
|
| 549 |
|
|
cmpil #0x4004BC7E,%d0 | ...|X| < 15 PI?
|
| 550 |
|
|
blts SCMAIN
|
| 551 |
|
|
bra REDUCEX
|
| 552 |
|
|
|
| 553 |
|
|
|
| 554 |
|
|
SCMAIN:
|
| 555 |
|
|
|--THIS IS THE USUAL CASE, |X| <= 15 PI.
|
| 556 |
|
|
|--THE ARGUMENT REDUCTION IS DONE BY TABLE LOOK UP.
|
| 557 |
|
|
fmovex %fp0,%fp1
|
| 558 |
|
|
fmuld TWOBYPI,%fp1 | ...X*2/PI
|
| 559 |
|
|
|
| 560 |
|
|
|--HIDE THE NEXT THREE INSTRUCTIONS
|
| 561 |
|
|
lea PITBL+0x200,%a1 | ...TABLE OF N*PI/2, N = -32,...,32
|
| 562 |
|
|
|
| 563 |
|
|
|
| 564 |
|
|
|--FP1 IS NOW READY
|
| 565 |
|
|
fmovel %fp1,N(%a6) | ...CONVERT TO INTEGER
|
| 566 |
|
|
|
| 567 |
|
|
movel N(%a6),%d0
|
| 568 |
|
|
asll #4,%d0
|
| 569 |
|
|
addal %d0,%a1 | ...ADDRESS OF N*PIBY2, IN Y1, Y2
|
| 570 |
|
|
|
| 571 |
|
|
fsubx (%a1)+,%fp0 | ...X-Y1
|
| 572 |
|
|
fsubs (%a1),%fp0 | ...FP0 IS R = (X-Y1)-Y2
|
| 573 |
|
|
|
| 574 |
|
|
SCCONT:
|
| 575 |
|
|
|--continuation point from REDUCEX
|
| 576 |
|
|
|
| 577 |
|
|
|--HIDE THE NEXT TWO
|
| 578 |
|
|
movel N(%a6),%d0
|
| 579 |
|
|
rorl #1,%d0
|
| 580 |
|
|
|
| 581 |
|
|
cmpil #0,%d0 | ...D0 < 0 IFF N IS ODD
|
| 582 |
|
|
bge NEVEN
|
| 583 |
|
|
|
| 584 |
|
|
NODD:
|
| 585 |
|
|
|--REGISTERS SAVED SO FAR: D0, A0, FP2.
|
| 586 |
|
|
|
| 587 |
|
|
fmovex %fp0,RPRIME(%a6)
|
| 588 |
|
|
fmulx %fp0,%fp0 | ...FP0 IS S = R*R
|
| 589 |
|
|
fmoved SINA7,%fp1 | ...A7
|
| 590 |
|
|
fmoved COSB8,%fp2 | ...B8
|
| 591 |
|
|
fmulx %fp0,%fp1 | ...SA7
|
| 592 |
|
|
movel %d2,-(%a7)
|
| 593 |
|
|
movel %d0,%d2
|
| 594 |
|
|
fmulx %fp0,%fp2 | ...SB8
|
| 595 |
|
|
rorl #1,%d2
|
| 596 |
|
|
andil #0x80000000,%d2
|
| 597 |
|
|
|
| 598 |
|
|
faddd SINA6,%fp1 | ...A6+SA7
|
| 599 |
|
|
eorl %d0,%d2
|
| 600 |
|
|
andil #0x80000000,%d2
|
| 601 |
|
|
faddd COSB7,%fp2 | ...B7+SB8
|
| 602 |
|
|
|
| 603 |
|
|
fmulx %fp0,%fp1 | ...S(A6+SA7)
|
| 604 |
|
|
eorl %d2,RPRIME(%a6)
|
| 605 |
|
|
movel (%a7)+,%d2
|
| 606 |
|
|
fmulx %fp0,%fp2 | ...S(B7+SB8)
|
| 607 |
|
|
rorl #1,%d0
|
| 608 |
|
|
andil #0x80000000,%d0
|
| 609 |
|
|
|
| 610 |
|
|
faddd SINA5,%fp1 | ...A5+S(A6+SA7)
|
| 611 |
|
|
movel #0x3F800000,POSNEG1(%a6)
|
| 612 |
|
|
eorl %d0,POSNEG1(%a6)
|
| 613 |
|
|
faddd COSB6,%fp2 | ...B6+S(B7+SB8)
|
| 614 |
|
|
|
| 615 |
|
|
fmulx %fp0,%fp1 | ...S(A5+S(A6+SA7))
|
| 616 |
|
|
fmulx %fp0,%fp2 | ...S(B6+S(B7+SB8))
|
| 617 |
|
|
fmovex %fp0,SPRIME(%a6)
|
| 618 |
|
|
|
| 619 |
|
|
faddd SINA4,%fp1 | ...A4+S(A5+S(A6+SA7))
|
| 620 |
|
|
eorl %d0,SPRIME(%a6)
|
| 621 |
|
|
faddd COSB5,%fp2 | ...B5+S(B6+S(B7+SB8))
|
| 622 |
|
|
|
| 623 |
|
|
fmulx %fp0,%fp1 | ...S(A4+...)
|
| 624 |
|
|
fmulx %fp0,%fp2 | ...S(B5+...)
|
| 625 |
|
|
|
| 626 |
|
|
faddd SINA3,%fp1 | ...A3+S(A4+...)
|
| 627 |
|
|
faddd COSB4,%fp2 | ...B4+S(B5+...)
|
| 628 |
|
|
|
| 629 |
|
|
fmulx %fp0,%fp1 | ...S(A3+...)
|
| 630 |
|
|
fmulx %fp0,%fp2 | ...S(B4+...)
|
| 631 |
|
|
|
| 632 |
|
|
faddx SINA2,%fp1 | ...A2+S(A3+...)
|
| 633 |
|
|
faddx COSB3,%fp2 | ...B3+S(B4+...)
|
| 634 |
|
|
|
| 635 |
|
|
fmulx %fp0,%fp1 | ...S(A2+...)
|
| 636 |
|
|
fmulx %fp0,%fp2 | ...S(B3+...)
|
| 637 |
|
|
|
| 638 |
|
|
faddx SINA1,%fp1 | ...A1+S(A2+...)
|
| 639 |
|
|
faddx COSB2,%fp2 | ...B2+S(B3+...)
|
| 640 |
|
|
|
| 641 |
|
|
fmulx %fp0,%fp1 | ...S(A1+...)
|
| 642 |
|
|
fmulx %fp2,%fp0 | ...S(B2+...)
|
| 643 |
|
|
|
| 644 |
|
|
|
| 645 |
|
|
|
| 646 |
|
|
fmulx RPRIME(%a6),%fp1 | ...R'S(A1+...)
|
| 647 |
|
|
fadds COSB1,%fp0 | ...B1+S(B2...)
|
| 648 |
|
|
fmulx SPRIME(%a6),%fp0 | ...S'(B1+S(B2+...))
|
| 649 |
|
|
|
| 650 |
|
|
movel %d1,-(%sp) |restore users mode & precision
|
| 651 |
|
|
andil #0xff,%d1 |mask off all exceptions
|
| 652 |
|
|
fmovel %d1,%FPCR
|
| 653 |
|
|
faddx RPRIME(%a6),%fp1 | ...COS(X)
|
| 654 |
|
|
bsr sto_cos |store cosine result
|
| 655 |
|
|
fmovel (%sp)+,%FPCR |restore users exceptions
|
| 656 |
|
|
fadds POSNEG1(%a6),%fp0 | ...SIN(X)
|
| 657 |
|
|
|
| 658 |
|
|
bra t_frcinx
|
| 659 |
|
|
|
| 660 |
|
|
|
| 661 |
|
|
NEVEN:
|
| 662 |
|
|
|--REGISTERS SAVED SO FAR: FP2.
|
| 663 |
|
|
|
| 664 |
|
|
fmovex %fp0,RPRIME(%a6)
|
| 665 |
|
|
fmulx %fp0,%fp0 | ...FP0 IS S = R*R
|
| 666 |
|
|
fmoved COSB8,%fp1 | ...B8
|
| 667 |
|
|
fmoved SINA7,%fp2 | ...A7
|
| 668 |
|
|
fmulx %fp0,%fp1 | ...SB8
|
| 669 |
|
|
fmovex %fp0,SPRIME(%a6)
|
| 670 |
|
|
fmulx %fp0,%fp2 | ...SA7
|
| 671 |
|
|
rorl #1,%d0
|
| 672 |
|
|
andil #0x80000000,%d0
|
| 673 |
|
|
faddd COSB7,%fp1 | ...B7+SB8
|
| 674 |
|
|
faddd SINA6,%fp2 | ...A6+SA7
|
| 675 |
|
|
eorl %d0,RPRIME(%a6)
|
| 676 |
|
|
eorl %d0,SPRIME(%a6)
|
| 677 |
|
|
fmulx %fp0,%fp1 | ...S(B7+SB8)
|
| 678 |
|
|
oril #0x3F800000,%d0
|
| 679 |
|
|
movel %d0,POSNEG1(%a6)
|
| 680 |
|
|
fmulx %fp0,%fp2 | ...S(A6+SA7)
|
| 681 |
|
|
|
| 682 |
|
|
faddd COSB6,%fp1 | ...B6+S(B7+SB8)
|
| 683 |
|
|
faddd SINA5,%fp2 | ...A5+S(A6+SA7)
|
| 684 |
|
|
|
| 685 |
|
|
fmulx %fp0,%fp1 | ...S(B6+S(B7+SB8))
|
| 686 |
|
|
fmulx %fp0,%fp2 | ...S(A5+S(A6+SA7))
|
| 687 |
|
|
|
| 688 |
|
|
faddd COSB5,%fp1 | ...B5+S(B6+S(B7+SB8))
|
| 689 |
|
|
faddd SINA4,%fp2 | ...A4+S(A5+S(A6+SA7))
|
| 690 |
|
|
|
| 691 |
|
|
fmulx %fp0,%fp1 | ...S(B5+...)
|
| 692 |
|
|
fmulx %fp0,%fp2 | ...S(A4+...)
|
| 693 |
|
|
|
| 694 |
|
|
faddd COSB4,%fp1 | ...B4+S(B5+...)
|
| 695 |
|
|
faddd SINA3,%fp2 | ...A3+S(A4+...)
|
| 696 |
|
|
|
| 697 |
|
|
fmulx %fp0,%fp1 | ...S(B4+...)
|
| 698 |
|
|
fmulx %fp0,%fp2 | ...S(A3+...)
|
| 699 |
|
|
|
| 700 |
|
|
faddx COSB3,%fp1 | ...B3+S(B4+...)
|
| 701 |
|
|
faddx SINA2,%fp2 | ...A2+S(A3+...)
|
| 702 |
|
|
|
| 703 |
|
|
fmulx %fp0,%fp1 | ...S(B3+...)
|
| 704 |
|
|
fmulx %fp0,%fp2 | ...S(A2+...)
|
| 705 |
|
|
|
| 706 |
|
|
faddx COSB2,%fp1 | ...B2+S(B3+...)
|
| 707 |
|
|
faddx SINA1,%fp2 | ...A1+S(A2+...)
|
| 708 |
|
|
|
| 709 |
|
|
fmulx %fp0,%fp1 | ...S(B2+...)
|
| 710 |
|
|
fmulx %fp2,%fp0 | ...s(a1+...)
|
| 711 |
|
|
|
| 712 |
|
|
|
| 713 |
|
|
|
| 714 |
|
|
fadds COSB1,%fp1 | ...B1+S(B2...)
|
| 715 |
|
|
fmulx RPRIME(%a6),%fp0 | ...R'S(A1+...)
|
| 716 |
|
|
fmulx SPRIME(%a6),%fp1 | ...S'(B1+S(B2+...))
|
| 717 |
|
|
|
| 718 |
|
|
movel %d1,-(%sp) |save users mode & precision
|
| 719 |
|
|
andil #0xff,%d1 |mask off all exceptions
|
| 720 |
|
|
fmovel %d1,%FPCR
|
| 721 |
|
|
fadds POSNEG1(%a6),%fp1 | ...COS(X)
|
| 722 |
|
|
bsr sto_cos |store cosine result
|
| 723 |
|
|
fmovel (%sp)+,%FPCR |restore users exceptions
|
| 724 |
|
|
faddx RPRIME(%a6),%fp0 | ...SIN(X)
|
| 725 |
|
|
|
| 726 |
|
|
bra t_frcinx
|
| 727 |
|
|
|
| 728 |
|
|
SCBORS:
|
| 729 |
|
|
cmpil #0x3FFF8000,%d0
|
| 730 |
|
|
bgt REDUCEX
|
| 731 |
|
|
|
| 732 |
|
|
|
| 733 |
|
|
SCSM:
|
| 734 |
|
|
movew #0x0000,XDCARE(%a6)
|
| 735 |
|
|
fmoves #0x3F800000,%fp1
|
| 736 |
|
|
|
| 737 |
|
|
movel %d1,-(%sp) |save users mode & precision
|
| 738 |
|
|
andil #0xff,%d1 |mask off all exceptions
|
| 739 |
|
|
fmovel %d1,%FPCR
|
| 740 |
|
|
fsubs #0x00800000,%fp1
|
| 741 |
|
|
bsr sto_cos |store cosine result
|
| 742 |
|
|
fmovel (%sp)+,%FPCR |restore users exceptions
|
| 743 |
|
|
fmovex X(%a6),%fp0
|
| 744 |
|
|
bra t_frcinx
|
| 745 |
|
|
|
| 746 |
|
|
|end
|
