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Diffstat (limited to 'c/src/lib/libcpu/m68k/m68040/fpsp/stan.S')
| -rw-r--r-- | c/src/lib/libcpu/m68k/m68040/fpsp/stan.S | 457 |
1 files changed, 0 insertions, 457 deletions
diff --git a/c/src/lib/libcpu/m68k/m68040/fpsp/stan.S b/c/src/lib/libcpu/m68k/m68040/fpsp/stan.S deleted file mode 100644 index 33cad35f48..0000000000 --- a/c/src/lib/libcpu/m68k/m68040/fpsp/stan.S +++ /dev/null @@ -1,457 +0,0 @@ -#include "fpsp-namespace.h" -// -// -// stan.sa 3.3 7/29/91 -// -// The entry point stan computes the tangent of -// an input argument; -// stand does the same except for denormalized input. -// -// Input: Double-extended number X in location pointed to -// by address register a0. -// -// Output: The value tan(X) returned in floating-point register Fp0. -// -// Accuracy and Monotonicity: The returned result is within 3 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 program sTAN takes approximately 170 cycles for -// input argument X such that |X| < 15Pi, which is the the usual -// situation. -// -// Algorithm: -// -// 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 2, so in particular, k = 0 or 1. -// -// 3. If k is odd, go to 5. -// -// 4. (k is even) Tan(X) = tan(r) and tan(r) is approximated by a -// rational function U/V where -// U = r + r*s*(P1 + s*(P2 + s*P3)), and -// V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r. -// Exit. -// -// 4. (k is odd) Tan(X) = -cot(r). Since tan(r) is approximated by a -// rational function U/V where -// U = r + r*s*(P1 + s*(P2 + s*P3)), and -// V = 1 + s*(Q1 + s*(Q2 + s*(Q3 + s*Q4))), s = r*r, -// -Cot(r) = -V/U. Exit. -// -// 6. If |X| > 1, go to 8. -// -// 7. (|X|<2**(-40)) Tan(X) = X. 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 -// - -// Copyright (C) Motorola, Inc. 1990 -// All Rights Reserved -// -// THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA -// The copyright notice above does not evidence any -// actual or intended publication of such source code. - -//STAN idnt 2,1 | Motorola 040 Floating Point Software Package - - |section 8 - -#include "fpsp.defs" - -BOUNDS1: .long 0x3FD78000,0x4004BC7E -TWOBYPI: .long 0x3FE45F30,0x6DC9C883 - -TANQ4: .long 0x3EA0B759,0xF50F8688 -TANP3: .long 0xBEF2BAA5,0xA8924F04 - -TANQ3: .long 0xBF346F59,0xB39BA65F,0x00000000,0x00000000 - -TANP2: .long 0x3FF60000,0xE073D3FC,0x199C4A00,0x00000000 - -TANQ2: .long 0x3FF90000,0xD23CD684,0x15D95FA1,0x00000000 - -TANP1: .long 0xBFFC0000,0x8895A6C5,0xFB423BCA,0x00000000 - -TANQ1: .long 0xBFFD0000,0xEEF57E0D,0xA84BC8CE,0x00000000 - -INVTWOPI: .long 0x3FFC0000,0xA2F9836E,0x4E44152A,0x00000000 - -TWOPI1: .long 0x40010000,0xC90FDAA2,0x00000000,0x00000000 -TWOPI2: .long 0x3FDF0000,0x85A308D4,0x00000000,0x00000000 - -//--N*PI/2, -32 <= N <= 32, IN A LEADING TERM IN EXT. AND TRAILING -//--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT -//--MOST 69 BITS LONG. - .global PITBL -PITBL: - .long 0xC0040000,0xC90FDAA2,0x2168C235,0x21800000 - .long 0xC0040000,0xC2C75BCD,0x105D7C23,0xA0D00000 - .long 0xC0040000,0xBC7EDCF7,0xFF523611,0xA1E80000 - .long 0xC0040000,0xB6365E22,0xEE46F000,0x21480000 - .long 0xC0040000,0xAFEDDF4D,0xDD3BA9EE,0xA1200000 - .long 0xC0040000,0xA9A56078,0xCC3063DD,0x21FC0000 - .long 0xC0040000,0xA35CE1A3,0xBB251DCB,0x21100000 - .long 0xC0040000,0x9D1462CE,0xAA19D7B9,0xA1580000 - .long 0xC0040000,0x96CBE3F9,0x990E91A8,0x21E00000 - .long 0xC0040000,0x90836524,0x88034B96,0x20B00000 - .long 0xC0040000,0x8A3AE64F,0x76F80584,0xA1880000 - .long 0xC0040000,0x83F2677A,0x65ECBF73,0x21C40000 - .long 0xC0030000,0xFB53D14A,0xA9C2F2C2,0x20000000 - .long 0xC0030000,0xEEC2D3A0,0x87AC669F,0x21380000 - .long 0xC0030000,0xE231D5F6,0x6595DA7B,0xA1300000 - .long 0xC0030000,0xD5A0D84C,0x437F4E58,0x9FC00000 - .long 0xC0030000,0xC90FDAA2,0x2168C235,0x21000000 - .long 0xC0030000,0xBC7EDCF7,0xFF523611,0xA1680000 - .long 0xC0030000,0xAFEDDF4D,0xDD3BA9EE,0xA0A00000 - .long 0xC0030000,0xA35CE1A3,0xBB251DCB,0x20900000 - .long 0xC0030000,0x96CBE3F9,0x990E91A8,0x21600000 - .long 0xC0030000,0x8A3AE64F,0x76F80584,0xA1080000 - .long 0xC0020000,0xFB53D14A,0xA9C2F2C2,0x1F800000 - .long 0xC0020000,0xE231D5F6,0x6595DA7B,0xA0B00000 - .long 0xC0020000,0xC90FDAA2,0x2168C235,0x20800000 - .long 0xC0020000,0xAFEDDF4D,0xDD3BA9EE,0xA0200000 - .long 0xC0020000,0x96CBE3F9,0x990E91A8,0x20E00000 - .long 0xC0010000,0xFB53D14A,0xA9C2F2C2,0x1F000000 - .long 0xC0010000,0xC90FDAA2,0x2168C235,0x20000000 - .long 0xC0010000,0x96CBE3F9,0x990E91A8,0x20600000 - .long 0xC0000000,0xC90FDAA2,0x2168C235,0x1F800000 - .long 0xBFFF0000,0xC90FDAA2,0x2168C235,0x1F000000 - .long 0x00000000,0x00000000,0x00000000,0x00000000 - .long 0x3FFF0000,0xC90FDAA2,0x2168C235,0x9F000000 - .long 0x40000000,0xC90FDAA2,0x2168C235,0x9F800000 - .long 0x40010000,0x96CBE3F9,0x990E91A8,0xA0600000 - .long 0x40010000,0xC90FDAA2,0x2168C235,0xA0000000 - .long 0x40010000,0xFB53D14A,0xA9C2F2C2,0x9F000000 - .long 0x40020000,0x96CBE3F9,0x990E91A8,0xA0E00000 - .long 0x40020000,0xAFEDDF4D,0xDD3BA9EE,0x20200000 - .long 0x40020000,0xC90FDAA2,0x2168C235,0xA0800000 - .long 0x40020000,0xE231D5F6,0x6595DA7B,0x20B00000 - .long 0x40020000,0xFB53D14A,0xA9C2F2C2,0x9F800000 - .long 0x40030000,0x8A3AE64F,0x76F80584,0x21080000 - .long 0x40030000,0x96CBE3F9,0x990E91A8,0xA1600000 - .long 0x40030000,0xA35CE1A3,0xBB251DCB,0xA0900000 - .long 0x40030000,0xAFEDDF4D,0xDD3BA9EE,0x20A00000 - .long 0x40030000,0xBC7EDCF7,0xFF523611,0x21680000 - .long 0x40030000,0xC90FDAA2,0x2168C235,0xA1000000 - .long 0x40030000,0xD5A0D84C,0x437F4E58,0x1FC00000 - .long 0x40030000,0xE231D5F6,0x6595DA7B,0x21300000 - .long 0x40030000,0xEEC2D3A0,0x87AC669F,0xA1380000 - .long 0x40030000,0xFB53D14A,0xA9C2F2C2,0xA0000000 - .long 0x40040000,0x83F2677A,0x65ECBF73,0xA1C40000 - .long 0x40040000,0x8A3AE64F,0x76F80584,0x21880000 - .long 0x40040000,0x90836524,0x88034B96,0xA0B00000 - .long 0x40040000,0x96CBE3F9,0x990E91A8,0xA1E00000 - .long 0x40040000,0x9D1462CE,0xAA19D7B9,0x21580000 - .long 0x40040000,0xA35CE1A3,0xBB251DCB,0xA1100000 - .long 0x40040000,0xA9A56078,0xCC3063DD,0xA1FC0000 - .long 0x40040000,0xAFEDDF4D,0xDD3BA9EE,0x21200000 - .long 0x40040000,0xB6365E22,0xEE46F000,0xA1480000 - .long 0x40040000,0xBC7EDCF7,0xFF523611,0x21E80000 - .long 0x40040000,0xC2C75BCD,0x105D7C23,0x20D00000 - .long 0x40040000,0xC90FDAA2,0x2168C235,0xA1800000 - - .set INARG,FP_SCR4 - - .set TWOTO63,L_SCR1 - .set ENDFLAG,L_SCR2 - .set N,L_SCR3 - - | xref t_frcinx - |xref t_extdnrm - - .global stand -stand: -//--TAN(X) = X FOR DENORMALIZED X - - bra t_extdnrm - - .global stan -stan: - fmovex (%a0),%fp0 // ...LOAD INPUT - - movel (%a0),%d0 - movew 4(%a0),%d0 - andil #0x7FFFFFFF,%d0 - - cmpil #0x3FD78000,%d0 // ...|X| >= 2**(-40)? - bges TANOK1 - bra TANSM -TANOK1: - cmpil #0x4004BC7E,%d0 // ...|X| < 15 PI? - blts TANMAIN - bra REDUCEX - - -TANMAIN: -//--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 TWO INSTRUCTIONS - leal PITBL+0x200,%a1 // ...TABLE OF N*PI/2, N = -32,...,32 - -//--FP1 IS NOW READY - fmovel %fp1,%d0 // ...CONVERT TO INTEGER - - asll #4,%d0 - addal %d0,%a1 // ...ADDRESS N*PIBY2 IN Y1, Y2 - - fsubx (%a1)+,%fp0 // ...X-Y1 -//--HIDE THE NEXT ONE - - fsubs (%a1),%fp0 // ...FP0 IS R = (X-Y1)-Y2 - - rorl #5,%d0 - andil #0x80000000,%d0 // ...D0 WAS ODD IFF D0 < 0 - -TANCONT: - - cmpil #0,%d0 - blt NODD - - fmovex %fp0,%fp1 - fmulx %fp1,%fp1 // ...S = R*R - - fmoved TANQ4,%fp3 - fmoved TANP3,%fp2 - - fmulx %fp1,%fp3 // ...SQ4 - fmulx %fp1,%fp2 // ...SP3 - - faddd TANQ3,%fp3 // ...Q3+SQ4 - faddx TANP2,%fp2 // ...P2+SP3 - - fmulx %fp1,%fp3 // ...S(Q3+SQ4) - fmulx %fp1,%fp2 // ...S(P2+SP3) - - faddx TANQ2,%fp3 // ...Q2+S(Q3+SQ4) - faddx TANP1,%fp2 // ...P1+S(P2+SP3) - - fmulx %fp1,%fp3 // ...S(Q2+S(Q3+SQ4)) - fmulx %fp1,%fp2 // ...S(P1+S(P2+SP3)) - - faddx TANQ1,%fp3 // ...Q1+S(Q2+S(Q3+SQ4)) - fmulx %fp0,%fp2 // ...RS(P1+S(P2+SP3)) - - fmulx %fp3,%fp1 // ...S(Q1+S(Q2+S(Q3+SQ4))) - - - faddx %fp2,%fp0 // ...R+RS(P1+S(P2+SP3)) - - - fadds #0x3F800000,%fp1 // ...1+S(Q1+...) - - fmovel %d1,%fpcr //restore users exceptions - fdivx %fp1,%fp0 //last inst - possible exception set - - bra t_frcinx - -NODD: - fmovex %fp0,%fp1 - fmulx %fp0,%fp0 // ...S = R*R - - fmoved TANQ4,%fp3 - fmoved TANP3,%fp2 - - fmulx %fp0,%fp3 // ...SQ4 - fmulx %fp0,%fp2 // ...SP3 - - faddd TANQ3,%fp3 // ...Q3+SQ4 - faddx TANP2,%fp2 // ...P2+SP3 - - fmulx %fp0,%fp3 // ...S(Q3+SQ4) - fmulx %fp0,%fp2 // ...S(P2+SP3) - - faddx TANQ2,%fp3 // ...Q2+S(Q3+SQ4) - faddx TANP1,%fp2 // ...P1+S(P2+SP3) - - fmulx %fp0,%fp3 // ...S(Q2+S(Q3+SQ4)) - fmulx %fp0,%fp2 // ...S(P1+S(P2+SP3)) - - faddx TANQ1,%fp3 // ...Q1+S(Q2+S(Q3+SQ4)) - fmulx %fp1,%fp2 // ...RS(P1+S(P2+SP3)) - - fmulx %fp3,%fp0 // ...S(Q1+S(Q2+S(Q3+SQ4))) - - - faddx %fp2,%fp1 // ...R+RS(P1+S(P2+SP3)) - fadds #0x3F800000,%fp0 // ...1+S(Q1+...) - - - fmovex %fp1,-(%sp) - eoril #0x80000000,(%sp) - - fmovel %d1,%fpcr //restore users exceptions - fdivx (%sp)+,%fp0 //last inst - possible exception set - - bra t_frcinx - -TANBORS: -//--IF |X| > 15PI, WE USE THE GENERAL ARGUMENT REDUCTION. -//--IF |X| < 2**(-40), RETURN X OR 1. - cmpil #0x3FFF8000,%d0 - bgts REDUCEX - -TANSM: - - fmovex %fp0,-(%sp) - fmovel %d1,%fpcr //restore users exceptions - fmovex (%sp)+,%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 N(%a6),%d0 - rorl #1,%d0 - - - bra TANCONT - - |end |