| /* Copyright (c) 2005, Dmitry Xmelkov |
| All rights reserved. |
| |
| Redistribution and use in source and binary forms, with or without |
| modification, are permitted provided that the following conditions are met: |
| |
| * Redistributions of source code must retain the above copyright |
| notice, this list of conditions and the following disclaimer. |
| * Redistributions in binary form must reproduce the above copyright |
| notice, this list of conditions and the following disclaimer in |
| the documentation and/or other materials provided with the |
| distribution. |
| * Neither the name of the copyright holders nor the names of |
| contributors may be used to endorse or promote products derived |
| from this software without specific prior written permission. |
| |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE |
| LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| POSSIBILITY OF SUCH DAMAGE. */ |
| |
| /* $Id: ftoa_engine.S 2191 2010-11-05 13:45:57Z arcanum $ */ |
| |
| #if !defined(__AVR_TINY__) |
| |
| #ifndef __DOXYGEN__ |
| |
| #include "macros.inc" |
| #include "ftoa_engine.h" |
| |
| #if defined(__AVR_HAVE_LPMX__) && __AVR_HAVE_LPMX__ |
| # define AVR_ENH_LPM 1 |
| #else |
| # define AVR_ENH_LPM 0 |
| #endif |
| |
| /* |
| int __ftoa_engine (double val, char *buf, |
| unsigned char prec, unsigned char maxdgs) |
| Input: |
| val - value to convert |
| buf - output buffer address |
| prec - precision: number of decimal digits is 'prec + 1' |
| maxdgs - (0 if unused) precision restriction for "%f" specification |
| |
| Output: |
| return - decimal exponent of first digit |
| buf[0] - flags (FTOA_***) |
| buf[1],... - decimal digits |
| Number of digits: |
| maxdgs == 0 ? prec+1 : |
| (buf[0] & FTOA_CARRY) == 0 || buf[1] != '1' ? |
| aver(1, maxdgs+exp, prec+1) : |
| aver(1, masdgs+exp-1, prec+1) |
| |
| Notes: |
| * Output string is not 0-terminated. For possibility of user's buffer |
| usage in any case. |
| * If used, 'maxdgs' is a number of digits for value with zero exponent. |
| */ |
| |
| /* Input */ |
| #define maxdgs r16 |
| #define prec r18 |
| #define buf_lo r20 |
| #define buf_hi r21 |
| #define val_lo r22 |
| #define val_hi r23 |
| #define val_hlo r24 |
| #define val_hhi r25 |
| |
| /* Float value parse */ |
| #define flag r19 |
| |
| /* Multiplication of mantisses */ |
| #define exp_sv r17 |
| #define mlt_1 r19 /* lowest result byte */ |
| #define mlt_2 r14 |
| #define mlt_3 r15 |
| #define mlt_4 r20 |
| #define mlt_5 r21 |
| #define mlt_6 r28 |
| #define mlt_7 r29 |
| |
| /* Conversion to string */ |
| #define pwr_2 r1 /* lowest byte of 'powr10' element */ |
| #define pwr_3 r17 |
| #define pwr_4 r19 |
| #define pwr_5 r22 |
| #define pwr_6 r25 |
| #define pwr_7 r0 |
| #define digit r23 |
| #define exp10 r24 |
| |
| /* Fixed */ |
| #define zero r1 |
| |
| ASSEMBLY_CLIB_SECTION |
| |
| .global __ftoa_engine |
| .type __ftoa_engine, "function" |
| __ftoa_engine: |
| |
| /* -------------------------------------------------------------------- |
| Float value parse. |
| */ |
| ; limit 'prec' |
| cpi prec, 8 |
| brlo 1f |
| ldi prec, 7 |
| 1: |
| ; init. |
| clr flag |
| X_movw XL, buf_lo |
| ; val_hhi := exponent, sign test and remove |
| #if FTOA_MINUS != 1 |
| # error FTOA_MINUS must be 1: add with carry used |
| #endif |
| lsl val_hhi |
| adc flag, zero ; FTOA_MINUS |
| sbrc val_hlo, 7 |
| ori val_hhi, 1 |
| ; zero test |
| adiw val_hlo, 0 |
| cpc val_lo, zero |
| cpc val_hi, zero |
| brne 3f |
| ; return 0 |
| ori flag, FTOA_ZERO |
| subi prec, -2 |
| 2: st X+, flag |
| ldi flag, '0' |
| dec prec |
| brne 2b |
| ret ; r24,r25 == 0 |
| 3: |
| ; infinity, NaN ? |
| #if FTOA_NAN != 2 * FTOA_INF |
| # error Must: FTOA_NAN == 2*FTOA_INF: 'rjmp' is absent |
| #endif |
| cpi val_hhi, 0xff |
| brlo 6f |
| cpi val_hlo, 0x80 |
| cpc val_hi, zero |
| cpc val_lo, zero |
| breq 5f |
| subi flag, -FTOA_INF ; FTOA_NAN |
| 5: subi flag, -FTOA_INF |
| 6: |
| ; write flags byte |
| st X+, flag |
| ; hidden bit |
| cpi val_hhi, 1 |
| brlo 7f ; if subnormal value |
| ori val_hlo, 0x80 |
| 7: adc val_hhi, zero |
| ; pushes |
| push r29 |
| push r28 |
| push r17 |
| push r16 |
| push r15 |
| push r14 |
| |
| /* -------------------------------------------------------------------- |
| Multiplication of mantisses (val and table). |
| At the begin: |
| val_hlo .. val_lo - input value mantisse |
| val_hhi - input value exponent |
| X - second byte address (string begin) |
| At the end: |
| mlt_7 .. mlt_2 - multiplication result |
| exp10 - decimal exponent |
| */ |
| |
| ; save |
| mov exp_sv, val_hhi |
| ; Z := & base10[exp / 8] (sizeof(base10[0]) == 5) |
| andi val_hhi, ~7 |
| lsr val_hhi ; (exp/8) * 4 |
| mov ZL, val_hhi |
| lsr val_hhi |
| lsr val_hhi ; exp/8 |
| add ZL, val_hhi ; (exp/8) * 5 |
| clr ZH |
| subi ZL, lo8(-(.L_base10)) |
| sbci ZH, hi8(-(.L_base10)) |
| ; highest mantissa byte (mult. shifting prepare) |
| clr val_hhi |
| ; result initializ. |
| clr mlt_1 |
| clr mlt_2 |
| clr mlt_3 |
| X_movw mlt_4, mlt_2 |
| X_movw mlt_6, mlt_2 |
| |
| ; multiply to 1-st table byte |
| #if AVR_ENH_LPM |
| lpm r0, Z+ |
| #else |
| lpm |
| adiw ZL, 1 |
| #endif |
| sec ; for loop end control |
| ror r0 |
| ; addition |
| 10: brcc 11f |
| add mlt_1, val_lo |
| adc mlt_2, val_hi |
| adc mlt_3, val_hlo |
| adc mlt_4, val_hhi |
| adc mlt_5, zero |
| ; arg shift |
| 11: lsl val_lo |
| rol val_hi |
| rol val_hlo |
| rol val_hhi |
| ; next bit |
| lsr r0 |
| brne 10b |
| |
| ; second table byte |
| #if AVR_ENH_LPM |
| lpm r0, Z+ ; C flag is stay 1 |
| #else |
| lpm |
| adiw ZL, 1 |
| sec |
| #endif |
| ror r0 |
| ; addition |
| 12: brcc 13f |
| add mlt_2, val_hi ; val_hi is the least byte now |
| adc mlt_3, val_hlo |
| adc mlt_4, val_hhi |
| adc mlt_5, val_lo |
| adc mlt_6, zero |
| ; arg shift |
| 13: lsl val_hi |
| rol val_hlo |
| rol val_hhi |
| rol val_lo |
| ; next bit |
| lsr r0 |
| brne 12b |
| |
| ; 3-t table byte |
| #if AVR_ENH_LPM |
| lpm r0, Z+ ; C flag is stay 1 |
| #else |
| lpm |
| adiw ZL, 1 |
| sec |
| #endif |
| ror r0 |
| ; addition |
| 14: brcc 15f |
| add mlt_3, val_hlo ; val_hlo is the least byte now |
| adc mlt_4, val_hhi |
| adc mlt_5, val_lo |
| adc mlt_6, val_hi |
| adc mlt_7, zero |
| ; arg shift |
| 15: lsl val_hlo |
| rol val_hhi |
| rol val_lo |
| rol val_hi |
| ; next bit |
| lsr r0 |
| brne 14b |
| |
| ; 4-t table byte |
| #if AVR_ENH_LPM |
| lpm r0, Z+ ; C flag is stay 1 |
| #else |
| lpm |
| #endif |
| ror r0 |
| ; addition |
| 16: brcc 17f |
| add mlt_4, val_hhi ; val_hhi is the least byte now |
| adc mlt_5, val_lo |
| adc mlt_6, val_hi |
| adc mlt_7, val_hlo |
| ; arg shift |
| 17: lsl val_hhi |
| rol val_lo |
| rol val_hi |
| rol val_hlo |
| ; next bit |
| lsr r0 |
| brne 16b |
| |
| ; decimal exponent |
| #if AVR_ENH_LPM |
| lpm exp10, Z |
| #else |
| adiw ZL, 1 |
| lpm |
| mov exp10, r0 |
| #endif |
| |
| ; result shift: mlt_7..2 >>= (~exp & 7) |
| com exp_sv |
| andi exp_sv, 7 |
| breq 19f |
| 18: lsr mlt_7 |
| ror mlt_6 |
| ror mlt_5 |
| ror mlt_4 |
| ror mlt_3 |
| ror mlt_2 |
| dec exp_sv |
| brne 18b |
| 19: |
| |
| /* -------------------------------------------------------------------- |
| Conversion to string. |
| |
| Registers usage: |
| mlt_7 .. mlt_2 - new mantissa (multiplication result) |
| pwr_7 .. pwr_2 - 'powr10' table element |
| Z - 'powr10' table pointer |
| X - output string pointer |
| maxdgs - number of digits |
| prec - number of digits stays to output |
| exp10 - decimal exponent |
| digit - conversion process |
| |
| At the end: |
| X - end of buffer (nonfilled byte) |
| exp10 - corrected dec. exponent |
| mlt_7 .. mlt_2 - remainder |
| pwr_7 .. pwr_2 - last powr10[] element |
| |
| Notes: |
| * It is possible to leave out powr10'x table with subnormal value. |
| Result: accuracy degrease on the rounding phase. No matter: high |
| precision with subnormals is not needed. (Now 0x00000001 is converted |
| exactly on prec = 5, i.e. 6 digits.) |
| */ |
| |
| ; to find first digit |
| ldi ZL, lo8(.L_powr10) |
| ldi ZH, hi8(.L_powr10) |
| set |
| ; 'pwr10' element reading |
| .L_digit: |
| X_lpm pwr_2, Z+ |
| X_lpm pwr_3, Z+ |
| X_lpm pwr_4, Z+ |
| X_lpm pwr_5, Z+ |
| X_lpm pwr_6, Z+ |
| X_lpm pwr_7, Z+ |
| ; 'digit' init. |
| ldi digit, '0' - 1 |
| ; subtraction loop |
| 20: inc digit |
| sub mlt_2, pwr_2 |
| sbc mlt_3, pwr_3 |
| sbc mlt_4, pwr_4 |
| sbc mlt_5, pwr_5 |
| sbc mlt_6, pwr_6 |
| sbc mlt_7, pwr_7 |
| brsh 20b |
| ; restore mult |
| add mlt_2, pwr_2 |
| adc mlt_3, pwr_3 |
| adc mlt_4, pwr_4 |
| adc mlt_5, pwr_5 |
| adc mlt_6, pwr_6 |
| adc mlt_7, pwr_7 |
| ; analisys |
| brtc 25f |
| cpi digit, '0' |
| brne 21f ; this is the first digit finded |
| dec exp10 |
| rjmp .L_digit |
| ; now is the first digit |
| 21: clt |
| ; number of digits |
| subi maxdgs, 1 |
| brlo 23f ; maxdgs was 0 |
| add maxdgs, exp10 |
| brpl 22f |
| clr maxdgs |
| 22: cp maxdgs, prec |
| brsh 23f |
| mov prec, maxdgs |
| 23: inc prec |
| mov maxdgs, prec |
| ; operate digit |
| 25: cpi digit, '0' + 10 |
| brlo 27f |
| ; overflow, digit > '9' |
| ldi digit, '9' |
| 26: st X+, digit |
| dec prec |
| brne 26b |
| rjmp .L_up |
| ; write digit |
| 27: st X+, digit |
| dec prec |
| brne .L_digit |
| |
| /* -------------------------------------------------------------------- |
| Rounding. |
| */ |
| .L_round: |
| ; pwr10 /= 2 |
| lsr pwr_7 |
| ror pwr_6 |
| ror pwr_5 |
| ror pwr_4 |
| ror pwr_3 |
| ror pwr_2 |
| ; mult -= pwr10 (half of last 'pwr10' value) |
| sub mlt_2, pwr_2 |
| sbc mlt_3, pwr_3 |
| sbc mlt_4, pwr_4 |
| sbc mlt_5, pwr_5 |
| sbc mlt_6, pwr_6 |
| sbc mlt_7, pwr_7 |
| ; rounding direction? |
| brlo .L_rest |
| ; round to up |
| .L_up: |
| inc prec |
| ld digit, -X |
| inc digit |
| cpi digit, '9' + 1 |
| brlo 31f |
| ldi digit, '0' |
| 31: st X, digit |
| cpse prec, maxdgs |
| brsh .L_up |
| ; it was a carry to master digit |
| ld digit, -X ; flags |
| ori digit, FTOA_CARRY ; 'C' is not changed |
| st X+, digit |
| brlo .L_rest ; above comparison |
| ; overflow |
| inc exp10 |
| ldi digit, '1' |
| 32: st X+, digit |
| ldi digit, '0' |
| dec prec |
| brne 32b |
| ; restore |
| .L_rest: |
| clr zero |
| pop r14 |
| pop r15 |
| pop r16 |
| pop r17 |
| pop r28 |
| pop r29 |
| ; return |
| clr r25 |
| sbrc exp10, 7 ; high byte |
| com r25 |
| ret |
| |
| .size __ftoa_engine, . - __ftoa_engine |
| |
| /* -------------------------------------------------------------------- |
| Tables. '.L_powr10' is placed first -- for subnormals stability. |
| */ |
| .section .progmem.data,"a",@progbits |
| |
| .type .L_powr10, "object" |
| .L_powr10: |
| .byte 0, 64, 122, 16, 243, 90 ; 100000000000000 |
| .byte 0, 160, 114, 78, 24, 9 ; 10000000000000 |
| .byte 0, 16, 165, 212, 232, 0 ; 1000000000000 |
| .byte 0, 232, 118, 72, 23, 0 ; 100000000000 |
| .byte 0, 228, 11, 84, 2, 0 ; 10000000000 |
| .byte 0, 202, 154, 59, 0, 0 ; 1000000000 |
| .byte 0, 225, 245, 5, 0, 0 ; 100000000 |
| .byte 128, 150, 152, 0, 0, 0 ; 10000000 |
| .byte 64, 66, 15, 0, 0, 0 ; 1000000 |
| .byte 160, 134, 1, 0, 0, 0 ; 100000 |
| .byte 16, 39, 0, 0, 0, 0 ; 10000 |
| .byte 232, 3, 0, 0, 0, 0 ; 1000 |
| .byte 100, 0, 0, 0, 0, 0 ; 100 |
| .byte 10, 0, 0, 0, 0, 0 ; 10 |
| .byte 1, 0, 0, 0, 0, 0 ; 1 |
| .size .L_powr10, . - .L_powr10 |
| |
| .type .L_base10, "object" |
| .L_base10: |
| .byte 44, 118, 216, 136, -36 ; 2295887404 |
| .byte 103, 79, 8, 35, -33 ; 587747175 |
| .byte 193, 223, 174, 89, -31 ; 1504632769 |
| .byte 177, 183, 150, 229, -29 ; 3851859889 |
| .byte 228, 83, 198, 58, -26 ; 986076132 |
| .byte 81, 153, 118, 150, -24 ; 2524354897 |
| .byte 230, 194, 132, 38, -21 ; 646234854 |
| .byte 137, 140, 155, 98, -19 ; 1654361225 |
| .byte 64, 124, 111, 252, -17 ; 4235164736 |
| .byte 188, 156, 159, 64, -14 ; 1084202172 |
| .byte 186, 165, 111, 165, -12 ; 2775557562 |
| .byte 144, 5, 90, 42, -9 ; 710542736 |
| .byte 92, 147, 107, 108, -7 ; 1818989404 |
| .byte 103, 109, 193, 27, -4 ; 465661287 |
| .byte 224, 228, 13, 71, -2 ; 1192092896 |
| .byte 245, 32, 230, 181, 0 ; 3051757813 |
| .byte 208, 237, 144, 46, 3 ; 781250000 |
| .byte 0, 148, 53, 119, 5 ; 2000000000 |
| .byte 0, 128, 132, 30, 8 ; 512000000 |
| .byte 0, 0, 32, 78, 10 ; 1310720000 |
| .byte 0, 0, 0, 200, 12 ; 3355443200 |
| .byte 51, 51, 51, 51, 15 ; 858993459 |
| .byte 152, 110, 18, 131, 17 ; 2199023256 |
| .byte 65, 239, 141, 33, 20 ; 562949953 |
| .byte 137, 59, 230, 85, 22 ; 1441151881 |
| .byte 207, 254, 230, 219, 24 ; 3689348815 |
| .byte 209, 132, 75, 56, 27 ; 944473297 |
| .byte 247, 124, 29, 144, 29 ; 2417851639 |
| .byte 164, 187, 228, 36, 32 ; 618970020 |
| .byte 50, 132, 114, 94, 34 ; 1584563250 |
| .byte 129, 0, 201, 241, 36 ; 4056481921 |
| .byte 236, 161, 229, 61, 39 ; 1038459372 |
| .size .L_base10, . - .L_base10 |
| |
| .end |
| #endif /* !__DOXYGEN__ */ |
| |
| #endif /* !defined(__AVR_TINY__) */ |
