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Furs 23 Nov 2018, 18:59
Decimals are "different", you need to think of them differently. 0.5 is half of 1, so in binary it is 0.1 (with one fractional digit, you have 0.0, 0.1, 1.0, etc, basically 0.5 step increments in decimal). So it's a different "5" than the 5 from 5.0 (left of decimal).
A simple way, but not very good (because of overflow), is to convert it from integer as before (e.g. via cvtsi2ss as you mentioned), and then divide by 10^digits. For example, say you have 5 decimal digits: Code: 42.12345 It's simple but has problems with overflow, only good if you have limited number of fractional digits. |
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23 Nov 2018, 18:59 |
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redsock 23 Nov 2018, 19:20
This is a hard (IMO) problem space... Some very good reading (and how I chose to implement it in my own library) that also explains the binary format and helped me grok it: https://www.cs.indiana.edu/~dyb/pubs/FP-Printing-PLDI96.pdf ... as well as searching for string$to_double and string$from_double in my implementation: https://2ton.com.au/library_as_html/string32.inc.html ...
The 3/10 problem (as explained in the above paper) in my implementation goes <-> 0.3 (from_double and to_double again produces the same binary format). Using naive/faster implementations, 0.3 becomes 0.29999... etc. There is no simple way that I am aware of to deal with all of that hahah, messy  |
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23 Nov 2018, 19:20 |
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Mikl___ 23 Nov 2018, 19:28
Hi, Ali.A! Did you want to find an algorithm?
Your sample +1.25=(-1)^{Sign}x 2^{exponent} x 1,mantissa +1.25 > 0 --> Sign=0 log2(1.25)=0.321928095 --> exponent=0 exponent in "offset code" = 0 + 127 = 127 = 0x7F = 0111.1111 23 (bits in the mantissa) - 0 (exponent) = 23 mantissa = 2^{23} x (1.25 - 2^{0})=2^{23} x 0.25= 2097152= 0x200000= 010.0000.0000.0000.0000.0000b 1 bit(Sign)+8 bits(exponent)+23 bits(mantissa)=32 bits in single precision floating point value Code: Sign| exponent |mantissa 0|011 1.111 1|010.0000.0000.0000.0000.0000 3 F A 0 0 0 0 0 Sample of Furs -42.12345 -42.12345 < 0 Sign=1 log2(42.12345)=5.396551696 exponent in "offset code" = 5 + 127 =132=0x84=1000.0100 23 (bits in the mantissa) - 5 (exponent) = 18 mantissa = 2^{18} x (42.12345 - 2^{5})=2^{18} x 10.12345=2653801.6768~2653802=0x287E6A=010.1000.0111.1110.0110.1010 Code: Sign| exponent |mantissa 1|100 0.010 0|010.1000.0111.1110.0110.1010 C 2 2 8 7 E 6 A IEEE-754 Floating Point Converter Last edited by Mikl___ on 25 Nov 2018, 02:37; edited 7 times in total |
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23 Nov 2018, 19:28 |
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fasmnewbie 24 Nov 2018, 04:07
redsock wrote: This is a hard (IMO) problem space... Some very good reading (and how I chose to implement it in my own library) that also explains the binary format and helped me grok it: https://www.cs.indiana.edu/~dyb/pubs/FP-Printing-PLDI96.pdf ... as well as searching for string$to_double and string$from_double in my implementation: https://2ton.com.au/library_as_html/string32.inc.html ... |
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24 Nov 2018, 04:07 |
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Mikl___ 25 Nov 2018, 05:02
Ali.A it's MASM
Code: ; FpuAtoFL ; ----------------------------------------------------------------------- ; This procedure was written by Raymond Filiatreault, December 2002 ; Modified January, 2004, to eliminate .data section and remove some ; redundant code. ; Modified March 2004 to avoid any potential data loss from the FPU ; Revised January 2005 to free the FPU st7 register if necessary. ; Revised December 2006 to avoid a minuscule error when processing strings ; which do not have any decimal digit. ; ; This FpuAtoFL function converts a decimal number from a zero terminated ; alphanumeric string format (Src) to an 80-bit REAL number and returns ; the result as an 80-bit REAL number at the specified destination (the ; FPU itself or a memory location), unless an invalid operation is ; reported by the FPU or the definition of the parameters (with uID) is ; invalid. ; ; The source can be a string in regular numeric format or in scientific ; notation. The number of digits (excluding all leading 0's and trailing ; decimal 0's) must not exceed 18. If in scientific format, the exponent ; must be within +/-4931 ; ; The source is checked for validity. The procedure returns an error if ; a character other than those acceptable is detected prior to the ; terminating zero or the above limits are exceeded. ; ; This procedure is based on converting the digits into a specific packed ; decimal format which can be used by the FPU and then adjusted for an ; exponent of 10. ; ; Only EAX is used to return error or success. All other CPU registers ; are preserved. ; ; IF the FPU is specified as the destination for the result, ; the st7 data register will become the st0 data register where the ; result will be returned (any valid data in that register would ; have been trashed). ; ; ----------------------------------------------------------------------- .386 .model flat, stdcall ; 32 bit memory model option casemap :none ; case sensitive include Fpu.inc .code FpuAtoFL proc public lpSrc:DWORD, lpDest:DWORD, uID:DWORD LOCAL content[108] :BYTE LOCAL tempst :TBYTE LOCAL bcdstrf :TBYTE LOCAL bcdstri :TBYTE fsave content push ebx push ecx push edx push esi push edi xor eax,eax xor ebx,ebx xor edx,edx lea edi,bcdstri stosd stosd stosd stosd stosd lea edi,bcdstri+8 mov esi,lpSrc mov ecx,18 @@: lodsb cmp al," " jz @B ;eliminate leading spaces or al,al ;is string empty? jnz @F atoflerr: frstor content atoflerr1: xor eax,eax pop edi pop esi pop edx pop ecx pop ebx ret ;check for leading sign @@: cmp al,"+" jz @F cmp al,"-" jnz integer mov ah,80h @@: mov [edi+1],ah ;put sign byte in bcd strings mov [edi+11],ah xor eax,eax lodsb ;-------------------------------------------- ;convert the integer digits to packed decimal ;-------------------------------------------- integer: cmp al,"." jnz @F lea edi,bcdstri call load_integer lodsb lea edi,bcdstrf+8 mov cl,18 and bh,4 jmp decimals @@: cmp al,"e" jnz @F .if cl == 18 jmp atoflerr ;error if no digit other than 0 before e .endif lea edi,bcdstri call load_integer jmp scient @@: cmp al,"E" jnz @F .if cl == 18 jmp atoflerr ;error if no digit other than 0 before E .endif lea edi,bcdstri call load_integer jmp scient @@: or al,al jnz @F test bh,4 jz atoflerr ;error if no numerical digit before terminating 0 lea edi,bcdstri call load_integer jmp laststep @@: sub al,"0" jc atoflerr ;unacceptable character jnz @F test bh,2 jnz @F or bh,4 ;at least 1 numerical character lodsb jmp integer @@: cmp al,9 ja atoflerr ;unacceptable character or bh,6 ;at least 1 non-zero numerical character sub ecx,1 jc atoflerr ;more than 18 integer digits mov ah,al lodsb cmp al,"." jnz @F mov al,0 ror ax,4 mov [edi],al lea edi,bcdstri call load_integer lea edi,bcdstrf+8 mov cl,18 and bh,4 lodsb jmp decimals @@: cmp al,"e" jnz @F mov al,0 ror ax,4 mov [edi],al lea edi,bcdstri call load_integer jmp scient @@: cmp al,"E" jnz @F mov al,0 ror ax,4 mov [edi],al lea edi,bcdstri call load_integer jmp scient @@: or al,al jnz @F ror ax,4 mov [edi],al lea edi,bcdstri call load_integer jmp laststep @@: sub al,"0" jc atoflerr ;unacceptable character cmp al,9 ja atoflerr ;unacceptable character dec ecx rol al,4 ror ax,4 mov [edi],al dec edi lodsb jmp integer ;-------------------------------------------- ;convert the decimal digits to packed decimal ;-------------------------------------------- decimals: cmp al,"e" jnz @F lea edi,bcdstrf call load_decimal jmp scient @@: cmp al,"E" jnz @F lea edi,bcdstrf call load_decimal jmp scient @@: or al,al jnz @F test bh,4 jz atoflerr ;error if no numerical digit before terminating 0 lea edi,bcdstrf call load_decimal jmp laststep @@: sub al,"0" jc atoflerr ;unacceptable character cmp al,9 ja atoflerr ;unacceptable character or bh,4 ;at least 1 numerical character .if al != 0 or bh,2 .endif sub ecx,1 jnc @F .if al == 0 ;if trailing decimal 0 inc ecx lodsb jmp decimals .endif jmp atoflerr @@: mov ah,al decimal1: lodsb cmp al,"e" jnz @F mov al,0 ror ax,4 mov [edi],al lea edi,bcdstrf call load_decimal jmp scient @@: cmp al,"E" jnz @F mov al,0 ror ax,4 mov [edi],al lea edi,bcdstrf call load_decimal jmp scient @@: or al,al jnz @F test bh,4 jz atoflerr ;error if no numerical digit before terminating 0 mov al,0 ror ax,4 mov [edi],al lea edi,bcdstrf call load_decimal jmp laststep @@: sub al,"0" jc atoflerr ;unacceptable character cmp al,9 ja atoflerr ;unacceptable character .if al != 0 or bh,2 ;at least one non-zero decimal digit .endif dec ecx rol al,4 ror ax,4 mov [edi],al dec edi lodsb jmp decimals laststep: fstsw ax ;retrieve exception flags from FPU fwait shr al,1 ;test for invalid operation jc atoflerr ;clean-up and return error laststep2: test uID,DEST_FPU ;check where result should be stored jnz @F ;destination is the FPU mov eax,lpDest fstp tbyte ptr[eax] ;store result at specified address jmp restore @@: fstp tempst ;store result temporarily restore: frstor content ;restore all previous FPU registers jz @F ffree st(7) ;free it if not already empty fld tempst @@: or al,1 ;to insure EAX!=0 @@: pop edi pop esi pop edx pop ecx pop ebx ret scient: xor eax,eax xor edx,edx lodsb cmp al,"+" jz @F cmp al,"-" jnz scient1 stc rcr eax,1 ;keep sign of exponent in most significant bit of EAX @@: lodsb ;get next digit after sign scient1: push eax and eax,0ffh jnz @F ;continue if 1st byte of exponent is not terminating 0 scienterr: pop eax jmp atoflerr ;no exponent @@: sub al,30h jc scienterr ;unacceptable character cmp al,9 ja scienterr ;unacceptable character add edx,edx ;x2 lea edx,[edx+edx*4] ;x2x5=x10 add edx,eax cmp edx,4931 ja scienterr ;exponent too large lodsb or al,al jnz @B pop eax ;retrieve exponent sign flag rcl eax,1 ;is most significant bit set? jnc @F neg edx @@: call XexpY fmul jmp laststep FpuAtoFL endp ; ;put 10 to the proper exponent (value in EDX) on the FPU XexpY: push edx fild dword ptr[esp] ;load the exponent fldl2t ;load log2(10) fmul ;->log2(10)*exponent pop edx ;at this point, only the log base 2 of the 10^exponent is on the FPU ;the FPU can compute the antilog only with the mantissa ;the characteristic of the logarithm must thus be removed fld st(0) ;copy the logarithm frndint ;keep only the characteristic fsub st(1),st ;keeps only the mantissa fxch ;get the mantissa on top f2xm1 ;->2^(mantissa)-1 fld1 fadd ;add 1 back ;the number must now be readjusted for the characteristic of the logarithm fscale ;scale it with the characteristic ;the characteristic is still on the FPU and must be removed fstp st(1) ;clean-up the register ret ;shifts the packed BCD string of the integers to the integer position ;EDI points to the BCD string ;ECX = count of positions for shifting the BCD string load_integer: push esi .if cl == 18 fldz .else mov esi,edi sub ecx,18 neg ecx shr ecx,1 push edi .if !CARRY? ;even number of integer digits mov edx,9 sub edx,ecx add esi,edx rep movsb .else ;odd number of integer digits mov edx,8 sub edx,ecx add esi,edx xor eax,eax lodsb rol ax,4 test ecx,ecx .if !ZERO? @@: rol ah,4 lodsb rol ax,4 stosb dec ecx jnz @B .endif mov [edi],ah inc edi .endif mov ecx,edx xor eax,eax rep stosb pop edi fbld tbyte ptr[edi] .endif pop esi ret ;converts the decimal portion in the packed BCD string to binary ;EDI points to the BCD string load_decimal: test bh,2 jnz @F ret @@: .if cl == 18 fldz .else fbld tbyte ptr[edi] mov edx,-18 call XexpY fmul .endif fadd ret end |
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25 Nov 2018, 05:02 |
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Ali.Z 27 Nov 2018, 17:55
Mikl___ wrote: algorithm im bad in math, math names and symbols ... but thank you for spending such time. (much appreciated) _________________ Asm For Wise Humans |
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27 Nov 2018, 17:55 |
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donn 27 Nov 2018, 19:38
Conceptually, it's like binary scientific notation.
https://en.wikipedia.org/wiki/Single-precision_floating-point_format There are only 3 parts as the others have mentioned: sign, exponent, and the fraction. If you want an exact view of the format: - There may also be an implicit leading bit which provides some extra precision. - The exponent does not start at 0. You have to subtract 127 from it in the case of single precision. Just to recap: With scientific notation, you multiply a representation of a number with only a single digit and a fraction by 10 or 2 to an exponent. This use of an exponent leads to the name floating point and allows really big and small numbers to compress into only a few bits at the cost of imprecision. So, with binary floating point numbers, the fraction uses a non-decimal base, base 2, and as was already mentioned, the fractional part is not tenths, hundredths, but the equivalent with base 2. Historically, I think Konrad Zuse came up with the first binary floating point implementation. I find the format intriguing also and tried parsing it a while ago in 32-bit. It can be frustrating not having any indication if the parsing is correct or not until the end. If you still have any interest, I'll post my 32-bit and 64-bit versions this evening. They were only for learning purposes, so I might try improving them with some of redsock's methods. |
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27 Nov 2018, 19:38 |
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