円周率の計算 (15) -- BBP 公式による計算 (4)
ATtiny10 版のプログラムができました。
全てアセンブラ記述で、プログラム・サイズは 860 バイト (430 ワード) です。 思ったより小さくなりました。
SRAM の使用量はデータ 22 バイト、スタック 6 バイトの計 28 バイトで、まだ 4 バイト余っています。
内蔵 8 MHz クロックを使い、PB2 (4 番ピン) から 38.4 kbps のシリアル信号を出力します。
実行時間は 1000 桁の出力で約 2 分、8191 桁の出力で約 3 時間 27 分です。
プログラム・サイズに余裕があったので、出力フォーマットを
- 10 桁ごとに空白を入れ、1 行に 50 桁を出力、
- 20 行ごと、つまり 1000 桁ごとに空行を入れる
ように変更しました。
出力をキャプチャした結果を下に示します。 (途中省略)
ATtiny10 Pi by BBP algorithm (8191 hex digits) pi = 3. 243F6A8885 A308D31319 8A2E037073 44A4093822 299F31D008 2EFA98EC4E 6C89452821 E638D01377 BE5466CF34 E90C6CC0AC 29B7C97C50 DD3F84D5B5 B547091792 16D5D98979 FB1BD1310B A698DFB5AC 2FFD72DBD0 1ADFB7B8E1 AFED6A267E 96BA7C9045 F12C7F9924 A19947B391 6CF70801F2 E2858EFC16 636920D871 574E69A458 FEA3F4933D 7E0D95748F 728EB65871 8BCD588215 4AEE7B54A4 1DC25A59B5 9C30D5392A F26013C5D1 B023286085 F0CA417918 B8DB38EF8E 79DCB0603A 180E6C9E0E 8BB01E8A3E D71577C1BD 314B2778AF 2FDA55605C 60E65525F3 AA55AB9457 48986263E8 144055CA39 6A2AAB10B6 B4CC5C3411 41E8CEA154 86AF7C72E9 93B3EE1411 636FBC2A2B A9C55D7418 31F6CE5C3E 169B87931E AFD6BA336C 24CF5C7A32 5381289586 773B8F4898 6B4BB9AFC4 BFE81B6628 219361D809 CCFB21A991 487CAC605D EC8032EF84 5D5DE98575 B1DC262302 EB651B8823 893E81D396 ACC50F6D6F F383F44239 2E0B4482A4 84200469C8 F04A9E1F9B 5E21C66842 F6E96C9A67 0C9C61ABD3 88F06A51A0 D2D8542F68 960FA728AB 5133A36EEF 0B6C137A3B E4BA3BF050 7EFB2A98A1 F1651D39AF 017666CA59 3E82430E88 8CEE861945 6F9FB47D84 A5C33B8B5E BEE06F75D8 85C1207340 1A449F56C1 6AA64ED3AA 62363F7706 1BFEDF7242 9B023D37D0 D724D00A12 48DB0FEAD3 . . . . < 1001 桁目から 8000 桁目まで省略 > . . . . 6E16369788 D273CCDE96 629281B949 D04C50901B 71C65614E6 C6C7BD327A 140A45E1D0 06C3F27B9A C9AA53FD62 A80F00BB25 BFE235BDD2 F671126905 B2040222B6 CBCF7CCD76 9C2B53113E C01640E3D3 38ABBD6025 47ADF0BA38 209CF746CE 75
出力桁数は 8192 桁ですが、最後の「75」が正しくは「76」なので、正しい桁数としては 8191 桁になります。
オブジェクトの HEX ファイルを下に示します。
:020000020000FC :1000000020C000000D0A415474696E7931300D0A28 :1000100050692062792042425020616C676F72699A :1000200074686D202838313931206865782064691A :1000300067697473290D0A7069203D20332E0D0AFB :10004000000008ED0CBF00E006BF0FE50DBF00E0AB :100050000EBF0FE002B9129A0A9AE2E0F0E4608162 :1000600089B7860F89BF10E080E084AB80E085AB64 :10007000E2E0F0E04FD158D180E090E088A999A962 :10008000E0E4F0E008E011930A95E9F781E064E02C :10009000BDD084E062E8BAD085E061E8B7D086E000 :1000A00061E8B4D0E8E4F0E024E0829141D184A397 :1000B00082958F7083AB84A38F7080AB839580AB68 :1000C000855089F480AB80E23CD183A3839583ABD8 :1000D000855049F483AB28D185A3839585AB8451A2 :1000E00011F485AB21D180A363A36295607F8F70EB :1000F000862B84AB2A95C9F688A199A1885F9F4F6A :1001000088A999A960E070E28617970708F4B8CF2C :100110000BD1FFCFE0E4F0E0CAE4D0E032A33595A4 :10012000330F2FEF10F4622772278081861F81938F :100130008081871F819306E0699137FD6227808166 :10014000861F81930A95C1F7089502C0841B950B01 :1001500084179507D8F720E030E014C060FF08C08E :10016000280F391F18F02417350710F0241B350B02 :10017000880F991F18F08417950710F0841B950BB2 :10018000769567956117710749F7822F932F232B77 :10019000089501E18417950718F0841B950B889446 :1001A000661F771F0A9521F0881F991FB0F3F2CFC1 :1001B000609570950895CC27DD274130510711F1E6 :1001C000E82FF92FC1E0A0E1B0E002C0A41BB50BFD :1001D000A417B507D8F713C0E0FF08C08C2F9D2FD8 :1001E0006A2F7B2FB2DFC82FD92F61F08A2F9B2F68 :1001F0006A2F7B2FAADFA82FB92FF695E795E11775 :10020000F10751F78C2F9D2FCD2B089583AB62AB57 :1002100040E050E040AB51AB2AC040A351A388A1BD :1002200099A1841B950B440F551F440F551F440F74 :10023000551F03A3400F511FBEDF99F062A36770E3 :1002400070E083DF71F060E070E0C0E5D0E023E0B3 :10025000A0DF7A936A9360E070E02A95C9F799DF8E :1002600059DF40A351A34F5F5F4F40AB51AB88A113 :1002700099A14817590788F248A159A140C040A345 :1002800051A3440F551F440F551F440F551F03A37F :10029000400F511F4130510771F1EAE4F0E006E0F0 :1002A00011930A95E9F7F0A3E8A1FE1BE3E0EF2321 :1002B000EE0FEE0F90E070E060E082A38770E03018 :1002C00031F09695879577956795EA95D1F7FC700B :1002D000F695C0E5D0E0CF1BD10B23E0F6952F1BA0 :1002E00050F039F056DF7A936A9360E070E02A9517 :1002F000C9F74FDF0FDF40A351A34F5F5F4F40AB04 :1003000051AB88A199A1805F9F4F4817590708F406 :10031000B6CF0895EE0FFF1FE050F04C8191803072 :1003200009F408950ED0FACF8DE00BD08AE009C011 :10033000682F829501D0862F8F708A3008F0895FF0 :10034000805D80959AE073E47A95F1F708F0129A4F :0C03500008F4129886959A95B1F708956C :00000001FF
プログラム・サイズに余裕があったので、シリアルのボーレート調節は、内蔵クロック自体を OSCCAL の値を調整して、本来の 8 MHz に近づけるようにしました。
上のオブジェクトのアドレス 0x0002 にデフォルトの OSCCAL 値に対して加算するオフセット値を (チェックサムも変更した上で) 書き込めば、ソースをいじらなくても調整できます。
アセンブラ・ソースを下に示します。
AVRStudio の AVR アセンブラ・プロジェクトを作成し、下のファイルをプロジェクトに登録してアセンブルします。
使用したのは AVRStudio 4.19 (Build 730) で、他の環境では試していません。
シリアル出力端子は、ソース・リストの「outport」定義部分を変更すれば変えることができます。
; ; piBBP10.asm : Pi calculation by BBP algorithm ; (8191 hexadecimal digits) ; for Atmel AVR ATtiny10 ; (Flash ROM 1KB, SRAM 32B) ; using integer arithmetics only ; ; based on "piqpr8.c" (2006-9-8) ; by David H. Bailey ; ; 2012/10/24 created by pcm1723 ; ; .include "tn10def.inc" .nolist .include "tn10def.inc" .list ; ; select output port for software serial TxD ; ; .set outport = PORTB0 ; PB0 (pin 1) ; .set outport = PORTB1 ; PB1 (pin 3) .set outport = PORTB2 ; PB2 (pin 4) ; .set outport = PORTB3 ; PB3 (pin 6) .dseg ; ; global variables ; .equ N_digits = 8192 .equ N_step = 8 .equ N_frac = 4 ; sum: .byte (2*N_frac) ; uint16_t sum[N_frac] id: .byte 2 ; uint16_t id fract: .byte (2*N_frac-2) ; uint16_t fract[N_frac-1] k: .byte 2 ; uint16_t k coef: .byte 1 ; uint8_t coef m: .byte 1 ; uint8_t m h_cnt1: .byte 1 ; output column counter 1 h_cnt2: .byte 1 ; output column counter 2 ; .cseg rjmp reset_entry ; OSCCAL_adj: .dw 0x00 ; banner_str: .db 0x0d,0x0a .db 'A','T','t','i','n','y','1','0' .db 0x0d,0x0a .db 'P','i',' ','b','y',' ','B','B','P',' ' .db 'a','l','g','o','r','i','t','h','m', ' ' .db '(','8','1','9','1',' ','h','e','x',' ' .db 'd','i','g','i','t','s',')',0x0d .db 0x0a,'p','i',' ','=',' ','3','.' .db 0x0d,0x0a,0,0 ; reset_entry: ; ; setup clock prescaler to 1/1 (8 MHz) ; ldi r16,0xD8 ; protect signature out CCP,r16 ; CCP <-- 0xD8 ldi r16,0x00 ; 0x00 = 1/1 out CLKPSR,r16 ; set CLocK PreScaleR ; ; setup SP ; ldi r16,low(RAMEND) ; RAMEND out SPL,r16 ; set low byte of SP ldi r16,high(RAMEND) ; RAMEND out SPH,r16 ; set high byte of SP ; ; setup GPIO ; ldi r16,0x0F out PORTB,r16 ; enable pull up sbi PORTB,outport ; PBx = "H" sbi DDRB,outport ; PBx = OUTPUT ; ; adjust OSCCAL value ; ldi r30,low(2*OSCCAL_adj+MAPPED_FLASH_START) ldi r31,high(2*OSCCAL_adj+MAPPED_FLASH_START) ld r22,Z ; get adjust value for OSCCAL in r24,OSCCAL add r24,r22 out OSCCAL,r24 ; adjust OSCCAL main: ldi r17,0 ; zero register ldi r24,0x00 sts h_cnt1,r24 ; initialize column counter 1, 0 ldi r24,0x00 sts h_cnt2,r24 ; inutialize column counter 2 ldi r30,low(banner_str) ldi r31,high(banner_str) rcall xmit_str ; transmit banner stirng rcall xmit_nl ; CR/LF ; for (id = 0; id < N_digits; id += N_step) ldi r24,0 ldi r25,0 sts id,r24 sts id+1,r25 ; id = 0 id_loop1: ; ; clear sum[] ; ldi r30,low(sum) ldi r31,high(sum) ldi r16,(N_frac*2) clr_sum1: st Z+,r17 dec r16 brne clr_sum1 ; ldi r24,1 ; m = 1 ldi r22,0x04 ; coef = 4, sub_flag = 0 rcall series ; series(id, m, coef) ; ldi r24,4 ; m = 4 ldi r22,0x82 ; coef = 2, sub_flag = 1 rcall series ; series(id, m, coef) ; ldi r24,5 ; m = 5 ldi r22,0x81 ; coef = 1, sub_flag = 1 rcall series ; series(id, m, coef) ; ldi r24,6 ; m = 6 ldi r22,0x81 ; coef = 1, sub_flag = 1 rcall series ; series(id, m, coef) ; ; now, result in sum[0]..sum[N_frac-1] ; ldi r30,low(sum+2*N_frac) ldi r31,high(sum+2*N_frac) ; Z = (R31:R30) = &(sum[N_frac]) ldi r18,4 ; set loop counter to 4, (4 * 2 = 8 hex digits) hex_out1: ld r24,--Z ; get data byte rcall xmit_hex2 ; transmit 2 hex digits ; ; output formatting ; lds r24,h_cnt1 swap r24 andi r24,0x0F sts m,r24 ; unpack column counter1 ; lds r24,h_cnt1 andi r24,0x0F sts k,r24 ; unpack column counter0 ; inc r24 ; (cnt0 + 1) sts k,r24 ; update cnt0 subi r24,5 ; modulo 5 brne hex_out3 sts k,r24 ; clear cnt0 ldi r24,0x20 rcall xmit ; output a space ; lds r24,m ; R24 = cnt1 inc r24 ; (cnt1 + 1) sts m,r24 ; update cnt1 subi r24,5 ; modulo 5 brne hex_out3 sts m,r24 ; clear cnt1 rcall xmit_nl ; output CR/LF ; lds r24,h_cnt2 ; R24 = h_cnt2 inc r24 ; (h_cnt2 + 1) sts h_cnt2,r24 ; update h_cnt2 subi r24,20 ; modulo 20 brne hex_out3 sts h_cnt2,r24 ; clear h_cnt2 rcall xmit_nl ; output CR/LF hex_out3: ; ; pack column counters ; lds r24,k ; R24 = cnt0 lds r22,m ; R22 = cnt1 swap r22 ; lower nibble to upper nibble andi r22,0xF0 ; upper nibble andi r24,0x0F ; lower nibble or r24,r22 ; combine sts h_cnt1,r24 ; update h_cnt1 dec r18 ; decrement loop counter brne hex_out1 ; more to do? ; ; loop condition check ; lds r24,id lds r25,id+1 ; (R25:R24) = id subi r24,low(-N_step) sbci r25,high(-N_step) ; (R25:R24) + N_step sts id,r24 sts id+1,r25 ; id += N_step ldi r22,low(N_digits) ldi r23,high(N_digits) cp r24,r22 cpc r25,r23 ; (id - N_digits) brsh id_loop_end ; loop finished rjmp id_loop1 ; for (id = ...) loop ; id_loop_end: rcall xmit_nl ; transmit a newline rjmp pc ; ; ; ; .include "testprog.inc" ; ; ; ;---------------------------------------------------------------------------; ; ; Prototype : ; ; void add_sub_frac( void ); ; ; Least significant 16-bit word of fract left in R23:R22 ; ; local variable: ; (uint8_t *) s_p = R31:R30 (Z, sum[] pointer ) ; (uint8_t *) f_p = R29:R28 (Y, fract[] pointer) ; ; uint8_t ff = R22 ; R19 : sub_flag ; R18 : const. 0xFF for 1's complement ; R16 : loop counter ; add_sub_frac: ldi r30,low(sum) ldi r31,high(sum) ; (R31:R30) = &(sum[0]) ldi r28,low(fract) ldi r29,high(fract) ; (R29:R28) = &(fract[0]) ; lds r19,coef ; b7 of coef is sub_flag asr r19 ; copy b7 lsl r19 ; C = sub_flag, b7 = sub_flag ser r18 ; R18 = 0xff brcc asf_1 ; branch if not subtract eor r22,r18 ; 1's complement for subtract eor r23,r18 ; 1's complement for subtract asf_1: ld r24,Z ; R24 = s_p[0] adc r24,r22 ; add/sub fract st Z+,r24 ; store result ld r24,Z ; R24 = s_p[1] adc r24,r23 ; add/sub fract st Z+,r24 ; store result ; ldi r16,(2*N_frac-2) ; set loop counter ; asf_2: ld r22,Y+ ; ff (R22) = *(f_p++) sbrc r19,7 ; test sub_flag, skip if not subtract eor r22,r18 ; 1's complement for subtract asf_3: ld r24,Z ; R24 = *s_p adc r24,r22 ; (*f_p) + ff st Z+,r24 ; (*f_p++) = result of add/sub dec r16 ; decrement loop counter brne asf_2 ; more to do? ret ; ;---------------------------------------------------------------------------; ; ; Prototype : ; ; uint16_t mulmod(uint16_t a, uint16_t b, uint16_t ak); ; argument: R25:R24, R23:R22, R21:R20 ; ; function result: R25:R24 ; ; local variable : R19:R18 ; mulmod: mm_1: rjmp mm_3 ; mm_2: sub r24, r20 sbc r25, r21 ; a = a - ak mm_3: cp r24, r20 cpc r25, r21 ; a - ak brsh mm_2 ; branch if SAME or HIGHER ldi r18, 0x00 ; ldi r19, 0x00 ; r = 0 rjmp mm_7 ; mm_4: sbrs r22, 0 ; skip if (1 == b0) rjmp mm_5 ; jump if (0 == b0) add r18, r24 adc r19, r25 ; r = r + a brcs mm_45 ; branch if carry occurred cp r18, r20 ; cpc r19, r21 ; r - ak brlo mm_5 ; branch if LOWER mm_45: sub r18, r20 sbc r19, r21 ; r = r - ak mm_5: lsl r24 rol r25 brcs mm_55 ; branch if carry occurred cp r24, r20 cpc r25, r21 ; a - ak brlo mm_6 ; branch if LOWER mm_55: sub r24, r20 sbc r25, r21 ; a = a - ak mm_6: lsr r23 ror r22 ; b = b / 2 mm_7: cp r22, r17 cpc r23, r17 ; b - 0 brne mm_4 ; branch if (0 != b) mov r24, r18 mov r25, r19 or r18,r19 ; for zero test ret ; ;---------------------------------------------------------------------------; ; ; Prototype : ; ; uint32_t divmod( uint32_t dividend, uint16_t divisor); ; argument: R25:R24:R23:R22, R21:R20 ; dend3:dend2:dend1:dend0, visor1:visor0 ; ; function result: R25:R24 = 16 bit remainder ; dend3:dend2 ; ; R23:R22 = 16 bit quotient ; dend1:dend0 ; ; work register: R16 = loop counter ; lcnt ; ; ; register symbol name defines ; .def dend3 = r25 .def dend2 = r24 .def dend1 = r23 .def dend0 = r22 .def visor1 = r21 .def visor0 = r20 .def lcnt = r16 ; divmod: ldi lcnt,17 ; set loop count to (16+1) dm_1: cp dend2,visor0 cpc dend3,visor1 ; (dend3:dend2) - (visor1:visor0) brcs dm_2 ; branch if not subtractable dm_15: sub dend2,visor0 sbc dend3,visor1 ; (dend3:dend2) -= (visor1:visor0) clc ; force Carry cleared dm_2: rol dend0 ; shift-in quotient (inverted) rol dend1 ; shift-out lower part of dividend dec lcnt ; decrement loop count breq dm_3 ; more to do? rol dend2 ; rol dend3 ; left shift partial remainder brcs dm_15 ; force subtraction if Carry rjmp dm_1 ; division loop ; dm_3: com dend0 com dend1 ; adjust quotient ret ; ;---------------------------------------------------------------------------; ; ; Prototype : ; ; uint16_t expm ( uint16_t p, dummy, uint16_t ak ) ; argument: R25:R24, R23:R22, R21:R20 ; move to: R31:R30 ; ; function result: R25:R24 ; ; work register: R29:R28 = uint16_t r ; ; R27:R26 = uint16_t b ; expm: clr r28 clr r29 ; assume result = 0 cpi r20,1 cpc r21,r17 ; (ak1:ak0) - 1 breq ex_ret ; (1 == ak) early return mov r30,r24 mov r31,r25 ; argument "p" move to R31:R30 ldi r28,1 ; (r1:r0) = 1; ldi r26,16 ; ldi r27,0 ; (b1:b0) = 16; rjmp ex_2 ; while loop ex_1: sub r26,r20 sbc r27,r21 ; (b1:b0) -= (ak1:ak0); ex_2: ; ; while (b >= ak) ... cp r26,r20 cpc r27,r21 ; (b1:b0) - (ak1:ak0) brsh ex_1 ; branch if SAME or HIGHER rjmp ex_5 ; while loop condition check ex_3: sbrs r30,0 ; if (0x01 & p) rjmp ex_4 ; branch if not ; ; (1 == (0x01 & p)) ; ; r = (r * b) mod ak mov r24,r28 mov r25,r29 ; (r25:r24) = (r) mov r22,r26 mov r23,r27 ; (r23:r22) = (b) ; ; (r21:r20) is already (ak) rcall mulmod ; mulmod(r, b, ak) mov r28,r24 mov r29,r25 ; (r) = function result breq ex_ret ; return if result = 0 ; ex_4: ; b = (b * b) mod ak mov r24,r26 mov r25,r27 ; (r25:r24) = (b) mov r22,r26 mov r23,r27 ; (r23:r22) = (b) ; ; (r21:r20) is already (ak) rcall mulmod ; mulmod(b, b, ak) mov r26,r24 mov r27,r25 ; (b) = function result ; lsr r31 ror r30 ; p >>= 1; ex_5: ; while (p) cp r30,r17 cpc r31,r17 ; (p1:p0) - 0 brne ex_3 ; go to top of while loop ex_ret: mov r24,r28 mov r25,r29 ; return(r) or r28,r29 ; for zero test ret ;---------------------------------------------------------------------------; ; ; Prototype : ; ; void series ( uint8_t m, uint8_t coef ) ; argument: R24, R22 ; ; parameter in global variable: ; ; uint16_t id ; uint8_t m <-- R24 on entry ; uint8_t coef <-- R22 on entry ; ; grobal variable for local use ; ; uint16_t k = R21:R20 ; ; local variable: ; uint16_t ak = R21:R20 ; (uint8_t *) f_p = R29:R28 (Y, fract[] pointer) ; loop counter, misc = R16 ; series: sts m,r24 ; m = 1 sts coef,r22 ; coef = 4 ; ; first term of the series ; ; for (k = 0; k < id; k++) { ldi r20,0 ldi r21,0 sts k,r20 sts k+1,r21 ; k = 0 ser_1: rjmp ser_5 ; for() condition check ser_2: lds r20,k lds r21,k+1 ; (R21:R20) = k lds r24,id lds r25,id+1 ; (R25:R24) = id sub r24,r20 sbc r25,r21 ; (R25:R24) = (id - k) ; lsl r20 rol r21 lsl r20 rol r21 lsl r20 rol r21 ; 8 * k lds r16,m ; R16 = m add r20,r16 adc r21,r17 ; (R21:R20) = (8 * k + m) = ak rcall expm ; t = (R25:R24) = expm((id - k), ak) breq ser_45 ; skip calc if expm() result = 0 lds r22,coef andi r22,0x07 ; extract coef (3 bits) ldi r23,0 ; zero extend to uint16_t rcall mulmod ; (R25:R24) = mulmod(t, coef, ak) breq ser_45 ; skip calc if mulmod() result = 0 ldi r22,0 ldi r23,0 ; low word of prem = (R23:R22) = 0 ; ; prem = (R25:R24:R23:R22) ldi r28,low(fract+(2*N_frac-2)) ldi r29,high(fract+(2*N_frac-2)) ; f_p = &(fract[N_frac-1] ldi r18,(N_frac-1) ; set loop counter to (N_frac-1) times ser_3: rcall divmod ; (rem:quo) = (R25:R24:R23:R22) = divmod(prem, ak) st -Y,r23 st -Y,r22 ; *(--f_p) = quotient = (R23:R22) ldi r22,0 ldi r23,0 ; low word of prem = (R23:R22) = 0 dec r18 ; decrement loop count brne ser_3 ; branch if not end of loop rcall divmod ; (rem:quo) = (R25:R24:R23:R22) = divmod(prem, ak) ; ; don't store the last 16-bit word (left in R23:R22) ser_4: rcall add_sub_frac ; add_sub_frac() ; ; for-loop end condition test ; ser_45: lds r20,k lds r21,k+1 ; (R21:R20) = k subi r20,low(-1) sbci r21,high(-1) ; increment sts k,r20 sts k+1,r21 ; k += 1 ser_5: lds r24,id lds r25,id+1 cp r20,r24 cpc r21,r25 ; (k - id) brlo ser_2 ; branch if LOWER ; ; second term of the series ; ; for (k = id; k < id + (N_frac * 4); k++){ lds r20,id lds r21,id+1 rjmp ser_19 ; for() condition check ser_7: lds r20,k lds r21,k+1 ; (R21:R20) = k ; lsl r20 rol r21 lsl r20 rol r21 lsl r20 rol r21 ; 8 * k lds r16,m ; R16 = m add r20,r16 adc r21,r17 ; (R21:R20) = (8 * k + m) = ak cpi r20,1 cpc r21,r17 breq ser_13 ; skip calc if (1 == ak) ; ; clear fract[] buffer ; ldi r30,low(fract) ldi r31,high(fract) ; Z = (R31:R30) = f_p = &(fract[0]) ldi r16,(2*N_frac-2) ; set loop count ser_8: st Z+,r17 ; clear dec r16 ; decrement loop counter brne ser_8 ; more to do? ; lds r31,k ; R31 = (uint8_t) k lds r30,id ; R30 = (uint8_t) id sub r31,r30 ; R31 = (uint8_t)(k - id) ldi r30,0x03 ; bit mask for b1,b0 and r30,r31 ; sft = R30 = (0x03 & (uint8_t)(k - id)) lsl r30 lsl r30 ; sft <<= 2 ; ldi r25,0 ldi r23,0 ldi r22,0 ; (R25:R24:R23:R22) = 000:coef:0000 lds r24,coef andi r24,0x07 ; R24 = coef (sub_flag bit removed) cpi r30,0 breq ser_10 ; branch if (0 == sft) ser_9: lsr r25 ror r24 ror r23 ror r22 ; (R25:R24:R23:R22) >>= 1 dec r30 ; decrement loop count brne ser_9 ; more to do? ser_10: andi r31,0x0c ; bit mask for b3,b2 lsr r31 ; adjust for byte offset ; ldi r28,low(fract+(2*N_frac-2)) ldi r29,high(fract+(2*N_frac-2)) ; f_p = &(fract[N_frac-1] sub r28,r31 ; sbc r29,r17 ; X = (R29:R28) -= (byte offset) ldi r18,(N_frac-1) ; set loop counter to (N_frac-1) times lsr r31 ; adjust for word count sub r18,r31 ; adjust loop count brlo ser_13 ; if LOWER, skip calc at all breq ser_12 ; Least Significant word calc only ser_11: rcall divmod ; (rem:quo) = (R25:R24:R23:R22) = divmod(prem, ak) st -Y,r23 st -Y,r22 ; *(--f_p) = quotient = (R23:R22) ldi r22,0 ldi r23,0 ; low word of prem = (R23:R22) = 0 dec r18 ; decrement loop count brne ser_11 ; branch if not end of loop ser_12: rcall divmod ; (rem:quo) = (R25:R24:R23:R22) = divmod(prem, ak) rcall add_sub_frac ; add_sub_frac() ser_13: ; ; for-loop end condition test ; ; for (k = id; k < (id + (N_frac * 4)); k++){ lds r20,k lds r21,k+1 ; (R21:R20) = k subi r20,low(-1) sbci r21,high(-1) ; increment ser_19: sts k,r20 sts k+1,r21 ; k = (R21:R20) lds r24,id lds r25,id+1 ; (R25:R24) = id subi r24,low(-4*N_frac) sbci r25,high(-4*N_frac) ; (R25:R24) + (4*N_frac) cp r20,r24 cpc r21,r25 ; (k - (id + 4 * N_frac)) brsh ser_99 ; return if SAME or HIGHER rjmp ser_7 ; branch if LOWER ; ser_99: ret ;---------------------------------------------------------------------------; ; ; omit rcvr() func ; and add xmit_nl(), xmit_hex1(), xmit_hex2(), xmit_str() func ; ; 2012/10/16 pcm1723 ; ;---------------------------------------------------------------------------; ; Software implemented UART module ; ; (C)ChaN, 2005 (http://elm-chan.org/) ; ;---------------------------------------------------------------------------; ; Bit rate settings: ; ; 1MHz 2MHz 4MHz 6MHz 8MHz 10MHz 12MHz 16MHz 20MHz ; 2.4kbps 138 - - - - - - - - ; 4.8kbps 68 138 - - - - - - - ; 9.6kbps 33 68 138 208 - - - - - ; 19.2kbps - 33 68 102 138 173 208 - - ; 38.4kbps - - 33 50 68 85 102 138 172 ; 57.6kbps - - 21 33 44 56 68 91 114 ; 115.2kbps - - - - 21 27 33 44 56 #define BPS 68 ; Bit delay. (see above table) #define BIDIR 0 ; 0:Separated Tx/Rx, 1:Shared Tx/Rx #define OUT_1 sbi PORTB,outport ; Output 1 #define OUT_0 cbi PORTB,outport ; Output 0 ;---------------------------------------------------------------------------; ; Transmit null terminated string pointed by Z (R31:R30) ; ; Prototype: void xmit_nl( void ); ; xmit_str: lsl r30 rol r31 ; convert word offset to byte offset subi r30,low(-MAPPED_FLASH_START) sbci r31,high(-MAPPED_FLASH_START) ; adjust for PROGMEM in data space xmit_str1: ld r24,Z+ ; get a char cpi r24,0 ; compare against 0 brne xmit_str2 ret ; return if null found xmit_str2: rcall xmit ; transmit a char rjmp xmit_str1 ; loop ; ;---------------------------------------------------------------------------; ; Transmit a newline (CR/LF sequence) ; ; Prototype: void xmit_nl( void ); ; xmit_nl: ldi r24,0x0D ; CR rcall xmit ; transmit ldi r24,0x0A ; LF rjmp xmit ; transmit ; ;---------------------------------------------------------------------------; ; Transmit 2 hex digit in R24 ; ; Prototype : ; ; void xmit_hex2(uint8_t d); ; xmit_hex2: mov r22,r24 ; save copy of R24 swap r24 ; upper nibble to lower rcall xmit_hex1 ; transmit hex 1 digit mov r24,r22 ; restore R24 ; ; fall into xmit_hex1() ; ;---------------------------------------------------------------------------; ; Transmit a hex digit in lower nibble of R24 ; ; Prototype : ; ; void xmit_hex1(uint8_t d) { ; d &= 0x0F; ; xmit( (9 < d) ? ('A' + d - 10) : ('0' + d)); ; } ; xmit_hex1: andi r24, 0x0F ; extract lower nibble cpi r24, 10 ; 10 brcs xh1_1 ; branch if (10 > r24) subi r24, -('A' - '0' - 10) xh1_1: subi r24, -('0') ; ; fall into xmit() ; ;---------------------------------------------------------------------------; ; Transmit a byte in serial format of N81 ; ;Prototype: void xmit (uint8_t data); ;Size: 16 words xmit: ; ret #if BIDIR ldi r23, BPS-1 ;Pre-idle time for bidirectional data line xm_5: dec r23 ; brne xm_5 ;/ #endif ; in r16, SREG ;Save flags com r24 ;C = start bit ldi r25, 10 ;Bit counter ; cli ;Start critical section xm_1: ldi r23, BPS-1 ;----- Bit transferring loop xm_2: dec r23 ;Wait for a bit time brne xm_2 ;/ brcs xm_3 ;MISO = bit to be sent OUT_1 ; xm_3: brcc xm_4 ; OUT_0 ;/ xm_4: lsr r24 ;Get next bit into C dec r25 ;All bits sent? brne xm_1 ; no, coutinue ; out SREG, r16 ;End of critical section ret
