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Diffstat (limited to 'c/src/lib/libcpu/m68k/m68040/fpsp/ssin.S')
| -rw-r--r-- | c/src/lib/libcpu/m68k/m68040/fpsp/ssin.S | 748 |
1 files changed, 748 insertions, 0 deletions
diff --git a/c/src/lib/libcpu/m68k/m68040/fpsp/ssin.S b/c/src/lib/libcpu/m68k/m68040/fpsp/ssin.S new file mode 100644 index 0000000000..9c93c95940 --- /dev/null +++ b/c/src/lib/libcpu/m68k/m68040/fpsp/ssin.S @@ -0,0 +1,748 @@ +// +// $Id$ +// +// 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 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 +// +// THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA +// The copyright notice above does not evidence any +// actual or intended publication of such source code. + +//SSIN idnt 2,1 | Motorola 040 Floating Point Software Package + + |section 8 + +#include "fpsp.defs" + +BOUNDS1: .long 0x3FD78000,0x4004BC7E +TWOBYPI: .long 0x3FE45F30,0x6DC9C883 + +SINA7: .long 0xBD6AAA77,0xCCC994F5 +SINA6: .long 0x3DE61209,0x7AAE8DA1 + +SINA5: .long 0xBE5AE645,0x2A118AE4 +SINA4: .long 0x3EC71DE3,0xA5341531 + +SINA3: .long 0xBF2A01A0,0x1A018B59,0x00000000,0x00000000 + +SINA2: .long 0x3FF80000,0x88888888,0x888859AF,0x00000000 + +SINA1: .long 0xBFFC0000,0xAAAAAAAA,0xAAAAAA99,0x00000000 + +COSB8: .long 0x3D2AC4D0,0xD6011EE3 +COSB7: .long 0xBDA9396F,0x9F45AC19 + +COSB6: .long 0x3E21EED9,0x0612C972 +COSB5: .long 0xBE927E4F,0xB79D9FCF + +COSB4: .long 0x3EFA01A0,0x1A01D423,0x00000000,0x00000000 + +COSB3: .long 0xBFF50000,0xB60B60B6,0x0B61D438,0x00000000 + +COSB2: .long 0x3FFA0000,0xAAAAAAAA,0xAAAAAB5E +COSB1: .long 0xBF000000 + +INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A + +TWOPI1: .long 0x40010000,0xC90FDAA2,0x00000000,0x00000000 +TWOPI2: .long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000 + + |xref PITBL + + .set INARG,FP_SCR4 + + .set X,FP_SCR5 + .set XDCARE,X+2 + .set XFRAC,X+4 + + .set RPRIME,FP_SCR1 + .set SPRIME,FP_SCR2 + + .set POSNEG1,L_SCR1 + .set TWOTO63,L_SCR1 + + .set ENDFLAG,L_SCR2 + .set N,L_SCR2 + + .set ADJN,L_SCR3 + + | xref t_frcinx + |xref t_extdnrm + |xref sto_cos + + .global ssind +ssind: +//--SIN(X) = X FOR DENORMALIZED X + bra t_extdnrm + + .global scosd +scosd: +//--COS(X) = 1 FOR DENORMALIZED X + + fmoves #0x3F800000,%fp0 +// +// 9D25B Fix: Sometimes the previous fmove.s sets fpsr bits +// + fmovel #0,%fpsr +// + bra t_frcinx + + .global ssin +ssin: +//--SET ADJN TO 0 + 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 |