?? l_setox.s
字號:
.long 0x3FFF0000,0xDE60F482,0x5E0E9124,0x9E8BE175 .long 0x3FFF0000,0xE0CCDEEC,0x2A94E110,0x20032C4B .long 0x3FFF0000,0xE33F8972,0xBE8A5A50,0x2004DFF5 .long 0x3FFF0000,0xE5B906E7,0x7C8348A8,0x1E72F47A .long 0x3FFF0000,0xE8396A50,0x3C4BDC68,0x1F722F22 .long 0x3FFF0000,0xEAC0C6E7,0xDD243930,0xA017E945 .long 0x3FFF0000,0xED4F301E,0xD9942B84,0x1F401A5B .long 0x3FFF0000,0xEFE4B99B,0xDCDAF5CC,0x9FB9A9E3 .long 0x3FFF0000,0xF281773C,0x59FFB138,0x20744C05 .long 0x3FFF0000,0xF5257D15,0x2486CC2C,0x1F773A19 .long 0x3FFF0000,0xF7D0DF73,0x0AD13BB8,0x1FFE90D5 .long 0x3FFF0000,0xFA83B2DB,0x722A033C,0xA041ED22 .long 0x3FFF0000,0xFD3E0C0C,0xF486C174,0x1F853F3A#define ADJFLAG L_SCR2#define SCALE FP_SCR1#define ADJSCALE FP_SCR2#define SC FP_SCR3#define ONEBYSC FP_SCR4| xref __l_t_frcinx| xref __l_t_extdnrm| xref __l_t_unfl| xref __l_t_ovfl .text .globl __l_setoxd__l_setoxd:|--entry point for EXP(X), X is denormalized movel a0@,d0 andil #0x80000000,d0 oril #0x00800000,d0 |...sign(X)*2^(-126) movel d0,a7@-/* fmoves &0x3F800000,fp0 */ .long 0xf23c4400,0x3f800000 fmovel d1,fpcr fadds a7@+,fp0 jra __l_t_frcinx .globl __l_setox__l_setox:/* |--entry point for EXP(X), here X is finite, non-zero, and not NaN's */|--Step 1. movel a0@,d0 |...load part of input X andil #0x7FFF0000,d0 |...biased expo. of X cmpil #0x3FBE0000,d0 |...2^(-65) jge EXPC1 |...normal case jra EXPSMEXPC1:|--The case |X| >= 2^(-65) movew a0@(4),d0 |...expo. and partial sig. of |X| cmpil #0x400CB167,d0 |...16380 log2 trunc. 16 bits jlt EXPMAIN |...normal case jra EXPBIGEXPMAIN:|--Step 2.|--This is the normal branch: 2^(-65) <= |X| < 16380 log2. fmovex a0@,fp0 |...load input from a0@ fmovex fp0,fp1/* fmuls &0x42B8AA3B,fp0 */ .long 0xf23c4423,0x42b8aa3b fmovemx fp2/fp3,a7@- |...save fp2 movel #0,a6@(ADJFLAG) fmovel fp0,d0 |...N = int( X * 64/log2 ) lea EXPTBL,a1 fmovel d0,fp0 |...convert to floating-format movel d0,a6@(L_SCR1) |...save N temporarily andil #0x3F,d0 |...D0 is J = N mod 64 lsll #4,d0 addal d0,a1 |...address of 2^(J/64) movel a6@(L_SCR1),d0 asrl #6,d0 |...D0 is M addiw #0x3FFF,d0 |...biased expo. of 2^(M) movew L2,a6@(L_SCR1) |...prefetch L2, no need in CBEXPCONT1:|--Step 3.|--fp1,fp2 saved on the stack. fp0 is N, fp1 is X,|--a0 points to 2^(J/64), D0 is biased expo. of 2^(M) fmovex fp0,fp2/* fmuls &0xBC317218,fp0 */ .long 0xf23c4423,0xbc317218 fmulx L2,fp2 |...N * L2, L1+L2 = -log2/64 faddx fp1,fp0 |...X + N*L1 faddx fp2,fp0 |...fp0 is R, reduced arg.| MOVE.w #0x3FA5,EXPA3 |...load EXPA3 in cache|--Step 4.|--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL|-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5))))|--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R|--[R+R*S*(A2+S*A4)] + [S*(A1+S*(A3+S*A5))] fmovex fp0,fp1 fmulx fp1,fp1 |...fp1 IS S = R*R/* fmoves &0x3AB60B70,fp2 */ .long 0xf23c4500,0x3ab60b70| MOVE.w #0,a1@(2) |...load 2^(J/64) in cache fmulx fp1,fp2 |...fp2 IS S*A5 fmovex fp1,fp3/* fmuls &0x3C088895,fp3 */ .long 0xf23c45a3,0x3c088895 faddd EXPA3,fp2 |...fp2 IS a3+S*A5 faddd EXPA2,fp3 |...fp3 IS a2+S*A4 fmulx fp1,fp2 |...fp2 IS S*(A3+S*A5) movew d0,a6@(SCALE) |...SCALE is 2^(M) in extended clrw a6@(SCALE+2) movel #0x80000000,a6@(SCALE+4) clrl a6@(SCALE+8) fmulx fp1,fp3 |...fp3 IS S*(A2+S*A4)/* fadds &0x3F000000,fp2 */ .long 0xf23c4522,0x3f000000 fmulx fp0,fp3 |...fp3 IS R*S*(A2+S*A4) fmulx fp1,fp2 |...fp2 IS S*(A1+S*(A3+S*A5)) faddx fp3,fp0 |...fp0 IS R+R*S*(A2+S*A4),| |...fp3 released fmovex a1@+,fp1 |...fp1 is lead. pt. of 2^(J/64) faddx fp2,fp0 |...fp0 is EXP(R) - 1| |...fp2 released|--Step 5|--final reconstruction process|--EXP(X) = 2^M * ( 2^(J/64) + 2^(J/64)*(EXP(R)-1) ) fmulx fp1,fp0 |...2^(J/64)*(Exp(R)-1) fmovemx a7@+,fp2/fp3 |...fp2 restored fadds a1@,fp0 |...accurate 2^(J/64) faddx fp1,fp0 |...2^(J/64) + 2^(J/64)*... movel a6@(ADJFLAG),d0|--Step 6 tstl d0 jeq NORMALADJUST: fmulx a6@(ADJSCALE),fp0NORMAL: fmovel d1,fpcr |...restore user fpcr fmulx a6@(SCALE),fp0 |...multiply 2^(M) jra __l_t_frcinxEXPSM:|--Step 7 fmovemx a0@,fp0-fp0 |...in case X is denormalized fmovel d1,fpcr/* fadds &0x3F800000,fp0 */ .long 0xf23c4422,0x3f800000 jra __l_t_frcinxEXPBIG:|--Step 8 cmpil #0x400CB27C,d0 |...16480 log2 jgt EXP2BIG|--Steps 8.2 -- 8.6 fmovex a0@,fp0 |...load input from a0@ fmovex fp0,fp1/* fmuls &0x42B8AA3B,fp0 */ .long 0xf23c4423,0x42b8aa3b fmovemx fp2/fp3,a7@- |...save fp2 movel #1,a6@(ADJFLAG) fmovel fp0,d0 |...N = int( X * 64/log2 ) lea EXPTBL,a1 fmovel d0,fp0 |...convert to floating-format movel d0,a6@(L_SCR1) |...save N temporarily andil #0x3F,d0 |...D0 is J = N mod 64 lsll #4,d0 addal d0,a1 |...address of 2^(J/64) movel a6@(L_SCR1),d0 asrl #6,d0 |...D0 is K movel d0,a6@(L_SCR1) |...save K temporarily asrl #1,d0 |...D0 is M1 subl d0,a6@(L_SCR1) |...a1 is M addiw #0x3FFF,d0 |...biased expo. of 2^(M1) movew d0,a6@(ADJSCALE) |...ADJSCALE := 2^(M1) clrw a6@(ADJSCALE+2) movel #0x80000000,a6@(ADJSCALE+4) clrl a6@(ADJSCALE+8) movel a6@(L_SCR1),d0 |...D0 is M addiw #0x3FFF,d0 |...biased expo. of 2^(M) jra EXPCONT1 |...go back to Step 3EXP2BIG:|--Step 9 fmovel d1,fpcr movel a0@,d0 bclr #sign_bit,a0@ |...setox always returns positive cmpil #0,d0 jlt __l_t_unfl jra __l_t_ovfl .globl __l_setoxm1d__l_setoxm1d:|--entry point for EXPM1(X), here X is denormalized|--Step 0. jra __l_t_extdnrm .globl __l_setoxm1__l_setoxm1:|--entry point for EXPM1(X), here X is finite, non-zero, non-NaN|--Step 1.|--Step 1.1 movel a0@,d0 |...load part of input X andil #0x7FFF0000,d0 |...biased expo. of X cmpil #0x3FFD0000,d0 |...1/4 jge EM1CON1 |...|X| >= 1/4 jra EM1SMEM1CON1:|--Step 1.3|--The case |X| >= 1/4 movew a0@(4),d0 |...expo. and partial sig. of |X| cmpil #0x4004C215,d0 |...70log2 rounded up to 16 bits jle EM1MAIN |...1/4 <= |X| <= 70log2 jra EM1BIGEM1MAIN:|--Step 2.|--This is the case: 1/4 <= |X| <= 70 log2. fmovex a0@,fp0 |...load input from a0@ fmovex fp0,fp1/* fmuls &0x42B8AA3B,fp0 */ .long 0xf23c4423,0x42b8aa3b fmovemx fp2/fp3,a7@- |...save fp2| MOVE.w #0x3F81,EM1A4 |...prefetch in CB mode fmovel fp0,d0 |...N = int( X * 64/log2 ) lea EXPTBL,a1 fmovel d0,fp0 |...convert to floating-format movel d0,a6@(L_SCR1) |...save N temporarily andil #0x3F,d0 |...D0 is J = N mod 64 lsll #4,d0 addal d0,a1 |...address of 2^(J/64) movel a6@(L_SCR1),d0 asrl #6,d0 |...D0 is M movel d0,a6@(L_SCR1) |...save a copy of M| MOVE.w #0x3FDC,L2 |...prefetch L2 in CB mode|--Step 3.|--fp1,fp2 saved on the stack. fp0 is N, fp1 is X,|--a0 points to 2^(J/64), D0 and a1 both contain M fmovex fp0,fp2/* fmuls &0xBC317218,fp0 */ .long 0xf23c4423,0xbc317218 fmulx L2,fp2 |...N * L2, L1+L2 = -log2/64 faddx fp1,fp0 |...X + N*L1 faddx fp2,fp0 |...fp0 is R, reduced arg.| MOVE.w #0x3FC5,EM1A2 |...load EM1A2 in cache addiw #0x3FFF,d0 |...D0 is biased expo. of 2^M|--Step 4.|--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL|-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*(A5 + R*A6)))))|--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R|--[R*S*(A2+S*(A4+S*A6))] + [R+S*(A1+S*(A3+S*A5))] fmovex fp0,fp1 fmulx fp1,fp1 |...fp1 IS S = R*R/* fmoves &0x3950097B,fp2 */ .long 0xf23c4500,0x3950097b| MOVE.w #0,a1@(2) |...load 2^(J/64) in cache fmulx fp1,fp2 |...fp2 IS S*A6 fmovex fp1,fp3/* fmuls &0x3AB60B6A,fp3 */ .long 0xf23c45a3,0x3ab60b6a faddd EM1A4,fp2 |...fp2 IS a4+S*A6 faddd EM1A3,fp3 |...fp3 IS a3+S*A5 movew d0,a6@(SC) |...SC is 2^(M) in extended clrw a6@(SC+2) movel #0x80000000,a6@(SC+4) clrl a6@(SC+8) fmulx fp1,fp2 |...fp2 IS S*(A4+S*A6) movel a6@(L_SCR1),d0 |...D0 is M negw d0 |...D0 is -M fmulx fp1,fp3 |...fp3 IS S*(A3+S*A5) addiw #0x3FFF,d0 |...biased expo. of 2^(-M) faddd EM1A2,fp2 |...fp2 IS a2+S*(A4+S*A6)/* fadds &0x3F000000,fp3 */ .long 0xf23c45a2,0x3f000000 fmulx fp1,fp2 |...fp2 IS S*(A2+S*(A4+S*A6)) oriw #0x8000,d0 |...signed/expo. of -2^(-M) movew d0,a6@(ONEBYSC) |...OnebySc is -2^(-M) clrw a6@(ONEBYSC+2) movel #0x80000000,a6@(ONEBYSC+4) clrl a6@(ONEBYSC+8) fmulx fp3,fp1 |...fp1 IS S*(A1+S*(A3+S*A5))| |...fp3 released fmulx fp0,fp2 |...fp2 IS R*S*(A2+S*(A4+S*A6)) faddx fp1,fp0 |...fp0 IS R+S*(A1+S*(A3+S*A5))| |...fp1 released faddx fp2,fp0 |...fp0 IS EXP(R)-1| |...fp2 released fmovemx a7@+,fp2/fp3 |...fp2 restored|--Step 5|--Compute 2^(J/64)*p fmulx a1@,fp0 |...2^(J/64)*(Exp(R)-1)|--Step 6|--Step 6.1 movel a6@(L_SCR1),d0 |...retrieve M cmpil #63,d0 jle MLE63|--Step 6.2 M >= 64 fmoves a1@(12),fp1 |...fp1 is t faddx a6@(ONEBYSC),fp1 |...fp1 is t+OnebySc faddx fp1,fp0 |...p+(t+OnebySc), fp1 released faddx a1@,fp0 |...T+(p+(t+OnebySc)) jra EM1SCALEMLE63:|--Step 6.3 M <= 63 cmpil #-3,d0 jge MGEN3MLTN3:|--Step 6.4 M <= -4 fadds a1@(12),fp0 |...p+t faddx a1@,fp0 |...T+(p+t) faddx a6@(ONEBYSC),fp0 |...OnebySc + (T+(p+t)) jra EM1SCALEMGEN3:|--Step 6.5 -3 <= M <= 63 fmovex a1@+,fp1 |...fp1 is T fadds a1@,fp0 |...fp0 is p+t faddx a6@(ONEBYSC),fp1 |...fp1 is T+OnebySc faddx fp1,fp0 |...(T+OnebySc)+(p+t)EM1SCALE:|--Step 6.6 fmovel d1,fpcr fmulx a6@(SC),fp0 jra __l_t_frcinxEM1SM:|--Step 7 |X| < 1/4. cmpil #0x3FBE0000,d0 |...2^(-65) jge EM1POLYEM1TINY:|--Step 8 |X| < 2^(-65) cmpil #0x00330000,d0 |...2^(-16312) jlt EM12TINY|--Step 8.2 movel #0x80010000,a6@(SC) |...SC is -2^(-16382) movel #0x80000000,a6@(SC+4) clrl a6@(SC+8) fmovex a0@,fp0 fmovel d1,fpcr faddx a6@(SC),fp0 jra __l_t_frcinxEM12TINY:|--Step 8.3 fmovex a0@,fp0 fmuld TWO140,fp0 movel #0x80010000,a6@(SC) movel #0x80000000,a6@(SC+4) clrl a6@(SC+8) faddx a6@(SC),fp0 fmovel d1,fpcr fmuld TWON140,fp0 jra __l_t_frcinxEM1POLY:|--Step 9 exp(X)-1 by a simple polynomial fmovex a0@,fp0 |...fp0 is X fmulx fp0,fp0 |...fp0 is S := X*X fmovemx fp2/fp3,a7@- |...save fp2/* fmoves &0x2F30CAA8,fp1 */ .long 0xf23c4480,0x2f30caa8 fmulx fp0,fp1 |...fp1 is S*B12/* fmoves &0x310F8290,fp2 */ .long 0xf23c4500,0x310f8290/* fadds &0x32D73220,fp1 */ .long 0xf23c44a2,0x32d73220 fmulx fp0,fp2 |...fp2 is S*B11 fmulx fp0,fp1 |...fp1 is S*(B10 + .../* fadds &0x3493F281,fp2 */ .long 0xf23c4522,0x3493f281 faddd EM1B8,fp1 |...fp1 is B8+S*... fmulx fp0,fp2 |...fp2 is S*(B9+... fmulx fp0,fp1 |...fp1 is S*(B8+... faddd EM1B7,fp2 |...fp2 is B7+S*... faddd EM1B6,fp1 |...fp1 is B6+S*... fmulx fp0,fp2 |...fp2 is S*(B7+... fmulx fp0,fp1 |...fp1 is S*(B6+... faddd EM1B5,fp2 |...fp2 is B5+S*... faddd EM1B4,fp1 |...fp1 is B4+S*... fmulx fp0,fp2 |...fp2 is S*(B5+... fmulx fp0,fp1 |...fp1 is S*(B4+... faddd EM1B3,fp2 |...fp2 is B3+S*... faddx EM1B2,fp1 |...fp1 is B2+S*... fmulx fp0,fp2 |...fp2 is S*(B3+... fmulx fp0,fp1 |...fp1 is S*(B2+... fmulx fp0,fp2 |...fp2 is S*S*(B3+...) fmulx a0@,fp1 |...fp1 is X*S*(B2.../* fmuls &0x3F000000,fp0 */ .long 0xf23c4423,0x3f000000 faddx fp2,fp1 |...fp1 is Q| |...fp2 released fmovemx a7@+,fp2/fp3 |...fp2 restored faddx fp1,fp0 |...fp0 is S*B1+Q| |...fp1 released fmovel d1,fpcr faddx a0@,fp0 jra __l_t_frcinxEM1BIG:|--Step 10 |X| > 70 log2 movel a0@,d0 cmpil #0,d0 jgt EXPC1|--Step 10.2/* fmoves &0xBF800000,fp0 */ .long 0xf23c4400,0xbf800000 fmovel d1,fpcr/* fadds &0x00800000,fp0 */ .long 0xf23c4422,0x00800000 jra __l_t_frcinx| end
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