Converting string to real4

RuiLoureiro · April 15, 2013, 04:35:25 AM

Hi all,

. Sometimes some friends here ask me where is the
ASM file. (Hi Dave ! Hi qWord !)

. Well, in this post i give ConvertString4D.inc
which contains the ASM ConvertString4D procedure,
constants and macros, and a text file Converter4.txt
where i explain something about that. (See Converter4.zip below)

. ConvertString4D procedure is a proc that converts
a null terminated string into a real4 dword variable.
The string may be written like this one:

"-123.4567E-1" or the same as " - 000 1 2 3 . 45 67 E - 0001"

It takes 119 cycles more or less in my P4.
(qWord, in your i7 119 may give 40, no ?)

. TestCnvDD9.exe shows conversions of 10 strings
by all converters

. Please, could you run TestCnvDD10.exe
and show the results here ?
Thanks
Rui

NOTE: ConvertString4Y0 doesnt convert a string like this:
"- 123" or "-001236789" or "-1.234 E5" (spaces and more than 8 integers)

About each converter
--------------------

Code Select


                    load   stack   intermediate    save    conversion
                           access    buffer     FPU & CPU    method       obs.
------------------------------------------------------------------------------
1  ConvertString4BZ 1 byte   ebp        yes          no         BCD       (1,3)        

2  ConvertString4BX 1 byte   ebp        yes          yes        BCD       (1,3)

3  ConvertString4BY 1 byte   esp        yes          no         BCD       (1,3)

4  ConvertString4B  1 byte   esp        yes          yes        BCD       (1,3)

5  ConvertString4BW 1 byte   ebp         no          no         BCD       (1,3)

6  ConvertString4BF 1 byte   esp         no          no         BCD       (1,3)
-------------------------------------------------------------------------------
7  ConvertString4Y0 1 byte   ebp         no          no        direct     (1)

8  ConvertString4Y  1 byte   ebp         no          no        direct     (2)

9  ConvertString4YM 1 byte   ebp         no          no        direct     (2)

10 ConvertString4YF 1 byte   esp         no          no        direct     (2)
--------------------------------------------------------------------------------
11 ConvertString4T  1 byte   ebp         yes         no        xlatb      (2)

12 ConvertString4TX 1  "     esp         yes         no        xlatb      (2)

13 ConvertString4TY 1 byte   esp         yes         no       code table  (2)

14 ConvertString4TW 1  "     esp         yes         no           "       (2)  

15 ConvertString4T4 4  "     esp         yes         no           "       (2)
--------------------------------------------------------------------------------
16 ConvertString4D  1  "     ebp          no         no        direct     (2) 

17 ConvertString4DS 1  "     ebp          no         yes       direct     (2)   
---------------------------------------------------------------------------------
obs. (1) no spaces/no zeroes
     (2) remove spaces/zeroes
     (3) rcl strings sampled from right to left
     (4) all use tables of qwords to get the power of 10: 10^n or 10^-n

file: TestCnvDD9.exe

It is to show the results in P4 XP sp3
converting 10 different strings
--------------------------------------

Code Select


ConvertString4TW
 1234.567

ConvertString4T4
 1234.567

ConvertString4D
 1234.567

ConvertString4DS
 1234.567

 *** STOP RclStr04 +1234.567 ***
converting _RclStr05 +1234E+12

ConvertString4B
 1.2339999E+15

ConvertString4BX
 1.2339999E+15

ConvertString4BZ
 1.2339999E+15

ConvertString4BY
 1.2339999E+15

ConvertString4BW
 1.2339999E+15

ConvertString4BF
 1.2339999E+15

ConvertString4Y0
 1.2339999E+15

ConvertString4Y
 1.2339999E+15

ConvertString4YM
 1.2339999E+15

ConvertString4YF
 1.2339999E+15

ConvertString4T
 1.2339999E+15

ConvertString4TX
 1.2339999E+15

ConvertString4TY
 1.2339999E+15

ConvertString4TW
 1.2339999E+15

ConvertString4T4
 1.2339999E+15

ConvertString4D
 1.2339999E+15

ConvertString4DS
 1.2339999E+15

 *** STOP RclStr05 +1234E+12 ***
converting _RclStr06 .567E+12

ConvertString4B
1 ERROR eax
ConvertString4BX
1 ERROR eax
ConvertString4BZ
1 ERROR eax
ConvertString4BY
1 ERROR eax
ConvertString4BW
1 ERROR eax
ConvertString4BF
1 ERROR eax
ConvertString4Y0
 5.6699997E+11

ConvertString4Y
 5.6699997E+11

ConvertString4YM
 5.6699997E+11

ConvertString4YF
 5.6699997E+11

ConvertString4T
 5.6699997E+11

ConvertString4TX
 5.6699997E+11

ConvertString4TY
 5.6699997E+11

ConvertString4TW
 5.6699997E+11

ConvertString4T4
 5.6699997E+11

ConvertString4D
 5.6699997E+11

ConvertString4DS
 5.6699997E+11

 *** STOP RclStr06 .567E+12 ***
converting _RclStr07 +1234.567E+12

ConvertString4B
 1.234567E+15

ConvertString4BX
 1.234567E+15

ConvertString4BZ
 1.234567E+15

ConvertString4BY
 1.234567E+15

ConvertString4BW
 1.234567E+15

ConvertString4BF
 1.234567E+15

ConvertString4Y0
 1.234567E+15

ConvertString4Y
 1.234567E+15

ConvertString4YM
 1.234567E+15

ConvertString4YF
 1.234567E+15

ConvertString4T
 1.234567E+15

ConvertString4TX
 1.234567E+15

ConvertString4TY
 1.234567E+15

ConvertString4TW
 1.234567E+15

ConvertString4T4
 1.234567E+15

ConvertString4D
 1.234567E+15

ConvertString4DS
 1.234567E+15

 *** STOP RclStr07 +1234.567E+12 ***
converting _RclStr08 +000000 012 34.56 7 E + 000012

ConvertString4B
3 ERROR eax
ConvertString4BX
3 ERROR eax
ConvertString4BZ
3 ERROR eax
ConvertString4BY
3 ERROR eax
ConvertString4BW
3 ERROR eax
ConvertString4BF
1 ERROR eax
ConvertString4Y0
1 ERROR eax
ConvertString4Y
 1.234567E+15

ConvertString4YM
 1.234567E+15

ConvertString4YF
 1.234567E+15

ConvertString4T
 1.234567E+15

ConvertString4TX
 1.234567E+15

ConvertString4TY
 1.234567E+15

ConvertString4TW
 1.234567E+15

ConvertString4T4
 1.234567E+15

ConvertString4D
 1.234567E+15

ConvertString4DS
 1.234567E+15

 *** STOP RclStr08 +000000 012 34.56 7 E + 000012 ***
converting _RclStr09 +1.234E+45

ConvertString4B
8 ERROR eax
ConvertString4BX
8 ERROR eax
ConvertString4BZ
8 ERROR eax
ConvertString4BY
8 ERROR eax
ConvertString4BW
8 ERROR eax
ConvertString4BF
8 ERROR eax
ConvertString4Y0
8 ERROR eax
ConvertString4Y
8 ERROR eax
ConvertString4YM
8 ERROR eax
ConvertString4YF
8 ERROR eax
ConvertString4T
8 ERROR eax
ConvertString4TX
8 ERROR eax
ConvertString4TY
8 ERROR eax
ConvertString4TW
8 ERROR eax
ConvertString4T4
8 ERROR eax
ConvertString4D
8 ERROR eax
ConvertString4DS
8 ERROR eax
 *** STOP RclStr09 +1.234E+45 ***
converting _RclStr10 +1.234E-45

ConvertString4B
8 ERROR eax
ConvertString4BX
8 ERROR eax
ConvertString4BZ
8 ERROR eax
ConvertString4BY
8 ERROR eax
ConvertString4BW
8 ERROR eax
ConvertString4BF
8 ERROR eax
ConvertString4Y0
7 ERROR eax
ConvertString4Y
 1.4012985E-45

ConvertString4YM
 1.4012985E-45

ConvertString4YF
 1.4012985E-45

ConvertString4T
 1.4012985E-45

ConvertString4TX
 1.4012985E-45

ConvertString4TY
 1.4012985E-45

ConvertString4TW
 1.4012985E-45

ConvertString4T4
 1.4012985E-45

ConvertString4D
 1.4012985E-45

ConvertString4DS
 1.4012985E-45

 *** STOP RclStr10 +1.234E-45 and END ***

file: TestCnvDD10.exe

My results in P4 XP sp3
-----------------------

Quote
converting _RclStr04 +1234.567

2665 cycles, ConvertString4, _RclStr04

2642 cycles, ConvertString4BX, _RclStr04

566 cycles, ConvertString4BZ, _RclStr04

528 cycles, ConvertString4BY, _RclStr04

452 cycles, ConvertString4BW, _RclStr04

455 cycles, ConvertString4BF, _RclStr04

107 cycles, ConvertString4Y0, _RclStr04

127 cycles, ConvertString4Y, _RclStr04

138 cycles, ConvertString4YM, _RclStr04

122 cycles, ConvertString4YF, _RclStr04

231 cycles, ConvertString4T, _RclStr04

177 cycles, ConvertString4TX, _RclStr04

169 cycles, ConvertString4TY, _RclStr04

151 cycles, ConvertString4TW, _RclStr04

211 cycles, ConvertString4T4, _RclStr04

119 cycles, ConvertString4D, _RclStr04

2218 cycles, ConvertString4DS, _RclStr04

*** STOP and END ***

***** Time table *****

107 cycles, ConvertString4Y0, direct - no spaces, no zeroes
119 cycles, ConvertString4D, direct
122 cycles, ConvertString4YF, direct
127 cycles, ConvertString4Y, direct
138 cycles, ConvertString4YM, direct
151 cycles, ConvertString4TW, code table
169 cycles, ConvertString4TY, code table
177 cycles, ConvertString4TX, xlatb
211 cycles, ConvertString4T4, code table
231 cycles, ConvertString4T, xlatb
452 cycles, ConvertString4BW, BCD
455 cycles, ConvertString4BF, BCD
528 cycles, ConvertString4BY, BCD
566 cycles, ConvertString4BZ, BCD
2218 cycles, ConvertString4DS, direct, save FPU
2642 cycles, ConvertString4BX, BCD, save FPU
2665 cycles, ConvertString4B, BCD, save FPU
********** END **********

Gunther · April 15, 2013, 05:05:59 AM

Hi RuiLoureiro

here are my results with an i7 (Windows 64 bit):

Quote
converting _RclStr04 +1234.567

677 cycles, ConvertString4, _RclStr04

636 cycles, ConvertString4BX, _RclStr04

208 cycles, ConvertString4BZ, _RclStr04

198 cycles, ConvertString4BY, _RclStr04

195 cycles, ConvertString4BW, _RclStr04

182 cycles, ConvertString4BF, _RclStr04

44 cycles, ConvertString4Y0, _RclStr04

50 cycles, ConvertString4Y, _RclStr04

46 cycles, ConvertString4YM, _RclStr04

51 cycles, ConvertString4YF, _RclStr04

84 cycles, ConvertString4T, _RclStr04

66 cycles, ConvertString4TX, _RclStr04

57 cycles, ConvertString4TY, _RclStr04

62 cycles, ConvertString4TW, _RclStr04

67 cycles, ConvertString4T4, _RclStr04

49 cycles, ConvertString4D, _RclStr04

483 cycles, ConvertString4DS, _RclStr04

*** STOP and END ***

***** Time table *****

44 cycles, ConvertString4Y0, direct - no spaces, no zeroes
46 cycles, ConvertString4YM, direct
49 cycles, ConvertString4D, direct
50 cycles, ConvertString4Y, direct
51 cycles, ConvertString4YF, direct
57 cycles, ConvertString4TY, code table
62 cycles, ConvertString4TW, code table
66 cycles, ConvertString4TX, xlatb
67 cycles, ConvertString4T4, code table
84 cycles, ConvertString4T, xlatb
182 cycles, ConvertString4BF, BCD
195 cycles, ConvertString4BW, BCD
198 cycles, ConvertString4BY, BCD
208 cycles, ConvertString4BZ, BCD
483 cycles, ConvertString4D, direct, save FPU
636 cycles, ConvertString4BX, BCD, save FPU
677 cycles, ConvertString4B, BCD, save FPU
********** END **********

Gunther

RuiLoureiro · April 15, 2013, 05:27:34 AM

Hi Gunther
Thanks ! :icon14:

----------------------------------------------------
Converting from string to real4 using FPU
----------------------------------------------------

We know it is an old story that many of us know well.
Nevertheless, there are people that want to try to write
his own converter or they are trying to learn.
For this reason, i will try to remember some basic concepts
based on a general example, to be simple. This is just to
answer some questions like «why you do this ?»,
«why you do that ?» ...

Quote
----------------
A. introduction
----------------

If our string is defined as _string db "-1234.567E+12",0
or _string db "-1234.567e+12",0

In general, we have only the symbols: '0' to '9', '+', '-', '.', 'E' and 'e'

In general, we have 3 parts:

1. integer part: -1234 ( from starting point to '.' )
2. decimal part: 567 ( after '.' to 'E' )
3. exponent part: +12 ( after 'E' to 0 )

This -1234.567E+12 means this: -1234.567 * 10^+12

But -1234.567 = -(1234 + 0.567)

or = -1234 - 0.567 = -1234 - 567 * 10^-3

= (-1234) + (-567) * (10^-3) (to use + instead of -)

( 0.567 = 567 * 10^-3 where 3 is the number of decimal places = ndd ).

note: if we have an expression 10^-n, then -n means «go backward n digits»
if we have an expression 10^+n, then +n means «go forward n digits»

Finally, we have the complete expression

-1234.567E+12= -1234.567 * 10^+12 = [(-1234) + (-567 * 10^-4)] * 10^+12

= (ecx + edi * 10^-ebx) * 10^edx
where:
ecx = integer part
edi = decimal part (has the same sign as the integer part)
ebx = number of decimal places (is allways a positive value)
edx = exponent

-------------------------------------------------------
B. floating point notation or scientific notation
-------------------------------------------------------

siiiiii.dddddddEsxxxx where s = sign +/- e or E = 10^ factor
i = integer digit
d = decimal digit
x = exponent digit

means or stands for: siiiiii.ddddddd * 10^sxxxx (well, 's' is one 's' not the same!)

we have 3 things:
1. integer part = siiiiii
2. decimal part = sddddddd (the sign is implied)
3 exponent part = sxxxx => power part = 10^sxxxx

all different cases
----------------------

case 1: 1234 -> start with integer

case 2: .567 -> start with decimal (point)

case 3: E+12 -> start with power. this case should be error
because e+10 may be 2.718281828459045+10=12.718281828459045
and not scientific notation

case 4: 1234.567 -> integer plus decimal

case 5: 1234E+12 -> integer plus power

case 6: .567E+12 -> decimal plus power

case 7: 1234.567E+12 -> integer plus decimal plus power

other cases: 1.234E+45 or 1.234E-45 (overflow/underflow)

------------------------------
C. spaces or not spaces
------------------------------

Is there another meaning for -123.45 6782 than the same as -123.456782 ?
or
Is there another meaning for -1 23.45 67 82 than the same as -123.456782 ?

I like to write with spaces and i dont like to get error from a converter
if i use spaces. The converter should remove it.

--------------------------------------
D. one idea to parse the string
--------------------------------------

note: if we want to use FPU, we should define 3 local variables
For instance, integerDD, decimalDD, exponentDD (all dwords)
because we cannot pass values in registers to FPU

1. find the sign (and save it if it is negative)

2. a) IntegerPart
-----------------

a1) get the character to AL and subtract 30h

. If carry set, we have 3/4 cases:
. -2 is '.' -> go to DecimalPart
. -16 is space (if we want)
. -48 is 0 => endinteger
. unacceptable character
. cmp al, 9
jbe isdigit -> save it or do what you want

. now, it must be:
. 21 is 'E' -> go to ExponentPart
. 53 is 'e'
. unacceptable character

b) DecimalPart
----------------

b1) get the character to AL and subtract 30h

. If carry set, we have 2/3 cases:
. -16 is space (if we want)
. -48 is 0 => enddecimal
. unacceptable character
. cmp al, 9
jbe isdigit -> save it or do what you want

. now, it must be:
. 21 is 'E' -> go to ExponentPart
. 53 is 'e'
. unacceptable character

c) ExponentPart
------------------

c1) find the sign (and save it if it is negative)

c2) get the character to AL and subtract 30h

. If carry set, we have 2/3 cases:
. -16 is space (if we want)
. -48 is 0 => endexponent
. unacceptable character
. cmp al, 9
jbe isdigit -> save it or do what you want

. now it must be:
. unacceptable character

endinteger: we must have at least 1 integer or integer = 0 or error
----------

enddecimal: we must have at least 1 integer or integer = 0 or error
----------

endexponent: we must have at least 1 integer or 1 decimal or error
----------- (.E should be error)
neg the value if negative

3. now, we have the values of each part in integerDD, decimalDD, exponentDD

3.1 change the sign of integerDD and decimalDD if there is sign

3.2 load the values into FPU and compute the expression

fild integerDD
fild decimalDD

multiply by 10^-ndd (ndd=number of decimal digits)

multiply by 10^exponentDD

4. store the result
(and test if there is an error if you want. The result may be infinity!)

-----------------------------------------
D1. one solution to remove spaces
------------------------------------------

When we start, we test if space (al=20h) and then the sign.

Whenever we start IntegerPart or DecimalPart or ExponentPart
we test if space (al=20h.)

If we are in IntegerPart or ExponentPart, then we test sign
and then we test space or zeros (may be -000555).

---------------------------
D2. removing zeroes
---------------------------

In cases like 000000123.25E00032 the integer part has not 9 digits but 3
So, while it is '0', get another and dont go to the next step.

---------------------------
D3. errors
---------------------------

We have 3 types of erros:

1. user erros

a) expression error

b) unacceptable character

c) more than 8 integer digits

d) more than 7 decimal digits

e) more than 2 exponet digits

2. programming errors

a) undefined pointers

3. FPU errors

a) invalid operation

b) overflow/underflow

c) Indefinite or NAN number

-------------------------------------------
D.4 To multiply by 10 and add eax
-------------------------------------------

solution 1: lea edx, [edx+edx*4]
lea edx, [eax+edx*2]

solution 2: imul edx, 10
add edx, eax
...

---------------------------
E. Real4 format
---------------------------

offset: +0 +16 +22 +31
---------------------------------------------
|f23 | f1|e0 e7|S|
---------------------------------------------

a) S bit 31 = sign -> 0 = positive, 1= negative

to test sign bit: «test eax, 80000000H» or «and eax, 80000000H»

b) 8 exponent bits: bits e0-e7 , from offset 23 to 30

to extract exponent bits: «and eax, 7F800000H»

or «shl eax, 23»
«and eax, 0FFh»

exponent bits
-------------
exponent < 0 -> < 7Fh
if exponent = 0 -> = 7Fh=127 (real expoent=0 => exponent bits=7Fh)
exponent > 0 -> > 7Fh

if expoent bits = FFh => NAN

if NAN and fraction bits= 0 => INFINITY (S=0 => +infinity S=1 => -infinity)

if NAN and fraction bits= 1 => INDEFINITE

c) 23 fraction bits: bits f1 - f23, from offset 0 to 22

to extract fraction bits: «and eax, 07FFFFFH»

-------------------------------
F. test real4 format in EAX
-------------------------------
move a dword from memory to eax.
If it is in st(0), move it to memory

output:

stc: is Indefinite or NAN

clc: is a number (not infinity)

TestReal4 proc

or eax, eax
jz short @F

shr eax, 23 ; exponent and sign in AX; AH=sign AL=exponent
cmp al, 0FFh
je short _isNan

; ---------------
; is real4 number
; ---------------
@@: clc
ret
; --------------------------------
; is INFINITY or INDEFINITY or NAN
; --------------------------------
_isNan: stc
ret
TestReal4 endp

--------------------------------------
examine 1 real4 format in EAX
--------------------------------------
move a dword from memory to eax
If it is in st(0), move it to memory

output:

stc: is Indefinite or NAN

clc: EAX = 0 is 0
= 1 is +INFINITY
= 2 is -INFINITY
= 3 is POSITIVE
= 4 is NEGATIVE

Examine1Real4 proc

or eax, eax
jnz short @F

; -------------
; is 0 -> EAX=0
; -------------
clc
ret

@@: mov edx, eax
shr edx, 23 ;exponent and sign in DX; DH=sign DL=exponent
and eax, 07FFFFFH ; fraction in EAX
;
cmp dl, 0FFh
je short _isNan

; ---------------
; is real4 number
; ---------------
mov eax, 3
shr dh, 1
jnc short _isRealP
; -----------
; is negative
; -----------
add eax, 1
; -----------
; is positive
; -----------
_isRealP: clc
ret

_isNan: or eax, eax
jz short _isInfinity

; --------------------
; is indefinite or NAN
; --------------------
stc
ret

_isInfinity: mov eax, 3
shr dh, 1
jnc short _isInfinityP

; ------------
; is -infinity
; ------------
add eax, 1

; ------------
; is +infinity
; ------------
_isInfinityP: stc
ret
Examine1Real4 endp

-------------------------------------
examine 2 real4 format in EAX
--------------------------------------
move a dword from memory to eax
If it is in st(0), move it to memory

output:

stc: is Indefinite or NAN

clc: EAX = 0 is a number
= 1 is INFINITY

Examine2Real4 proc

or eax, eax
jnz short @F

; -------------
; is 0 -> EAX=0
; -------------
_isNumber: xor eax, eax
clc
ret

@@: mov edx, eax
shr edx, 23 ; exponent and sign in DX; DH=sign DL=exponent
and eax, 07FFFFFH ; fraction in EAX
;
cmp dl, 0FFh
jne short _isNumber

or eax, eax
jz short _isInfinity

; --------------------
; is indefinite or NAN
; --------------------
stc
ret

_isInfinity: mov eax, 1
clc
ret
Examine2Real4 endp

Gunther · April 15, 2013, 05:47:11 AM

Hi RuiLoureiro,

good explanation and a good refresher. :t

Gunther

GoneFishing · April 15, 2013, 07:59:41 PM

Hi RuiLoureiro!
Here are tests for Celeron D:
TestCnvDD9:

Code Select

ConvertString4YF
 1234.0

ConvertString4T
 1234.0

ConvertString4TX
 1234.0

ConvertString4TY
 1234.0

ConvertString4TW
 1234.0

ConvertString4T4
 1234.0

ConvertString4D
 1234.0

ConvertString4DS
 1234.0

 *** STOP RclStr01 +1234 ***
converting _RclStr02 .567

ConvertString4B
1 ERROR eax
ConvertString4BX
1 ERROR eax
ConvertString4BZ
1 ERROR eax
ConvertString4BY
1 ERROR eax
ConvertString4BW
1 ERROR eax
ConvertString4BF
1 ERROR eax
ConvertString4Y0
 0.567

ConvertString4Y
 0.567

ConvertString4YM
 0.567

ConvertString4YF
 0.567

ConvertString4T
 0.567

ConvertString4TX
 0.567

ConvertString4TY
 0.567

ConvertString4TW
 0.567

ConvertString4T4
 0.567

ConvertString4D
 0.567

ConvertString4DS
 0.567

 *** STOP RclStr02 .567 ***
converting _RclStr03 E+12

ConvertString4B
1 ERROR eax
ConvertString4BX
1 ERROR eax
ConvertString4BZ
1 ERROR eax
ConvertString4BY
1 ERROR eax
ConvertString4BW
1 ERROR eax
ConvertString4BF
1 ERROR eax
ConvertString4Y0
1 ERROR eax
ConvertString4Y
1 ERROR eax
ConvertString4YM
1 ERROR eax
ConvertString4YF
1 ERROR eax
ConvertString4T
1 ERROR eax
ConvertString4TX
1 ERROR eax
ConvertString4TY
1 ERROR eax
ConvertString4TW
1 ERROR eax
ConvertString4T4
1 ERROR eax
ConvertString4D
1 ERROR eax
ConvertString4DS
1 ERROR eax
 *** STOP RclStr03 E+12 ***
converting _RclStr04 +1234.567

ConvertString4B
 1234.567

ConvertString4BX
 1234.567

ConvertString4BZ
 1234.567

ConvertString4BY
 1234.567

ConvertString4BW
 1234.567

ConvertString4BF
 1234.567

ConvertString4Y0
 1234.567

ConvertString4Y
 1234.567

ConvertString4YM
 1234.567

ConvertString4YF
 1234.567

ConvertString4T
 1234.567

ConvertString4TX
 1234.567

ConvertString4TY
 1234.567

ConvertString4TW
 1234.567

ConvertString4T4
 1234.567

ConvertString4D
 1234.567

ConvertString4DS
 1234.567

 *** STOP RclStr04 +1234.567 ***
converting _RclStr05 +1234E+12

ConvertString4B
 1.2339999E+15

ConvertString4BX
 1.2339999E+15

ConvertString4BZ
 1.2339999E+15

ConvertString4BY
 1.2339999E+15

ConvertString4BW
 1.2339999E+15

ConvertString4BF
 1.2339999E+15

ConvertString4Y0
 1.2339999E+15

ConvertString4Y
 1.2339999E+15

ConvertString4YM
 1.2339999E+15

ConvertString4YF
 1.2339999E+15

ConvertString4T
 1.2339999E+15

ConvertString4TX
 1.2339999E+15

ConvertString4TY
 1.2339999E+15

ConvertString4TW
 1.2339999E+15

ConvertString4T4
 1.2339999E+15

ConvertString4D
 1.2339999E+15

ConvertString4DS
 1.2339999E+15

 *** STOP RclStr05 +1234E+12 ***
converting _RclStr06 .567E+12

ConvertString4B
1 ERROR eax
ConvertString4BX
1 ERROR eax
ConvertString4BZ
1 ERROR eax
ConvertString4BY
1 ERROR eax
ConvertString4BW
1 ERROR eax
ConvertString4BF
1 ERROR eax
ConvertString4Y0
 5.6699997E+11

ConvertString4Y
 5.6699997E+11

ConvertString4YM
 5.6699997E+11

ConvertString4YF
 5.6699997E+11

ConvertString4T
 5.6699997E+11

ConvertString4TX
 5.6699997E+11

ConvertString4TY
 5.6699997E+11

ConvertString4TW
 5.6699997E+11

ConvertString4T4
 5.6699997E+11

ConvertString4D
 5.6699997E+11

ConvertString4DS
 5.6699997E+11

 *** STOP RclStr06 .567E+12 ***
converting _RclStr07 +1234.567E+12

ConvertString4B
 1.234567E+15

ConvertString4BX
 1.234567E+15

ConvertString4BZ
 1.234567E+15

ConvertString4BY
 1.234567E+15

ConvertString4BW
 1.234567E+15

ConvertString4BF
 1.234567E+15

ConvertString4Y0
 1.234567E+15

ConvertString4Y
 1.234567E+15

ConvertString4YM
 1.234567E+15

ConvertString4YF
 1.234567E+15

ConvertString4T
 1.234567E+15

ConvertString4TX
 1.234567E+15

ConvertString4TY
 1.234567E+15

ConvertString4TW
 1.234567E+15

ConvertString4T4
 1.234567E+15

ConvertString4D
 1.234567E+15

ConvertString4DS
 1.234567E+15

 *** STOP RclStr07 +1234.567E+12 ***
converting _RclStr08 +000000 012 34.56 7 E + 000012

ConvertString4B
3 ERROR eax
ConvertString4BX
3 ERROR eax
ConvertString4BZ
3 ERROR eax
ConvertString4BY
3 ERROR eax
ConvertString4BW
3 ERROR eax
ConvertString4BF
1 ERROR eax
ConvertString4Y0
1 ERROR eax
ConvertString4Y
 1.234567E+15

ConvertString4YM
 1.234567E+15

ConvertString4YF
 1.234567E+15

ConvertString4T
 1.234567E+15

ConvertString4TX
 1.234567E+15

ConvertString4TY
 1.234567E+15

ConvertString4TW
 1.234567E+15

ConvertString4T4
 1.234567E+15

ConvertString4D
 1.234567E+15

ConvertString4DS
 1.234567E+15

 *** STOP RclStr08 +000000 012 34.56 7 E + 000012 ***
converting _RclStr09 +1.234E+45

ConvertString4B
8 ERROR eax
ConvertString4BX
8 ERROR eax
ConvertString4BZ
8 ERROR eax
ConvertString4BY
8 ERROR eax
ConvertString4BW
8 ERROR eax
ConvertString4BF
8 ERROR eax
ConvertString4Y0
8 ERROR eax
ConvertString4Y
8 ERROR eax
ConvertString4YM
8 ERROR eax
ConvertString4YF
8 ERROR eax
ConvertString4T
8 ERROR eax
ConvertString4TX
8 ERROR eax
ConvertString4TY
8 ERROR eax
ConvertString4TW
8 ERROR eax
ConvertString4T4
8 ERROR eax
ConvertString4D
8 ERROR eax
ConvertString4DS
8 ERROR eax
 *** STOP RclStr09 +1.234E+45 ***
converting _RclStr10 +1.234E-45

ConvertString4B
8 ERROR eax
ConvertString4BX
8 ERROR eax
ConvertString4BZ
8 ERROR eax
ConvertString4BY
8 ERROR eax
ConvertString4BW
8 ERROR eax
ConvertString4BF
8 ERROR eax
ConvertString4Y0
7 ERROR eax
ConvertString4Y
 1.4012985E-45

ConvertString4YM
 1.4012985E-45

ConvertString4YF
 1.4012985E-45

ConvertString4T
 1.4012985E-45

ConvertString4TX
 1.4012985E-45

ConvertString4TY
 1.4012985E-45

ConvertString4TW
 1.4012985E-45

ConvertString4T4
 1.4012985E-45

ConvertString4D
 1.4012985E-45

ConvertString4DS
 1.4012985E-45

 *** STOP RclStr10 +1.234E-45 and END ***

TestCncDD10:

Quoteconverting _RclStr04 +1234.567

2566 cycles, ConvertString4, _RclStr04

2662 cycles, ConvertString4BX, _RclStr04

603 cycles, ConvertString4BZ, _RclStr04

561 cycles, ConvertString4BY, _RclStr04

446 cycles, ConvertString4BW, _RclStr04

465 cycles, ConvertString4BF, _RclStr04

113 cycles, ConvertString4Y0, _RclStr04

128 cycles, ConvertString4Y, _RclStr04

135 cycles, ConvertString4YM, _RclStr04

125 cycles, ConvertString4YF, _RclStr04

239 cycles, ConvertString4T, _RclStr04

181 cycles, ConvertString4TX, _RclStr04

174 cycles, ConvertString4TY, _RclStr04

157 cycles, ConvertString4TW, _RclStr04

218 cycles, ConvertString4T4, _RclStr04

115 cycles, ConvertString4D, _RclStr04

2221 cycles, ConvertString4DS, _RclStr04

*** STOP and END ***

***** Time table *****

113 cycles, ConvertString4Y0, direct - no spaces, no zeroes
115 cycles, ConvertString4D, direct
125 cycles, ConvertString4YF, direct
128 cycles, ConvertString4Y, direct
135 cycles, ConvertString4YM, direct
157 cycles, ConvertString4TW, code table
174 cycles, ConvertString4TY, code table
181 cycles, ConvertString4TX, xlatb
218 cycles, ConvertString4T4, code table
239 cycles, ConvertString4T, xlatb
446 cycles, ConvertString4BW, BCD
465 cycles, ConvertString4BF, BCD
561 cycles, ConvertString4BY, BCD
603 cycles, ConvertString4BZ, BCD
2221 cycles, ConvertString4D, direct, save FPU
2566 cycles, ConvertString4B, BCD, save FPU
2662 cycles, ConvertString4BX, BCD, save FPU
********** END **********

Thanks for your explanations on floating point basics . That's just what I want to understand (I'm among those trying to learn)
:t

dedndave · April 16, 2013, 12:47:51 AM

going from a real to a string is fun
going from a string to a real is hard work :t

i was wondering - without me reading 15 more miles of documentation
do the fraction bits have any meaning for NaN's ?

EDIT - i see they can carry a "payload"
not much in the way of a description, though - lol
other than it may be some sort of ordinal indicating where the problem originated

RuiLoureiro · April 20, 2013, 05:05:00 AM

Quote from: Gunther on April 15, 2013, 05:47:11 AM
Hi RuiLoureiro,

good explanation and a good refresher. :t

Gunther

Thanks Gunther :t

RuiLoureiro · April 20, 2013, 05:10:51 AM

Quote from: vertograd on April 15, 2013, 07:59:41 PM
Hi RuiLoureiro!
...
Thanks for your explanations on floating point basics . That's just what I want to understand (I'm among those trying to learn)
:t

Hi vertograd :t
I dont like to do things without some explanations
i was a teacher so...
And i try to be clear, but sometimes ... we dont know
Thanks
more: this converter was the best i did

RuiLoureiro · April 20, 2013, 06:22:19 AM

Quote from: dedndave on April 16, 2013, 12:47:51 AM
going from a real to a string is fun
going from a string to a real is hard work :t

i was wondering - without me reading 15 more miles of documentation
do the fraction bits have any meaning for NaN's ?

Dave,
i dont know. I think that FPU set it to NAN when it fails to
do some operation and set fraction to 0 if beyond the limit.
We need to know the details about the hardware, thing
that i have no time now to follow.

dedndave · April 20, 2013, 07:19:12 AM

the special case values for REAL4 and REAL8 are pretty simple

a few more caveats when you do REAL10

RuiLoureiro · April 20, 2013, 11:54:24 PM

Quote from: dedndave on April 20, 2013, 07:19:12 AM
the special case values for REAL4 and REAL8 are pretty simple
a few more caveats when you do REAL10

What ? the calculator works with real10, i dont know any problems

dedndave · April 21, 2013, 01:23:04 AM

my mistake, Rui :redface:

i guess going from Ascii Decimal to REAL, you don't encounter all the caveats
it either fits or it doesn't - lol
and if it doesn't fit, you can assign the largest or smalllest value that does fit

i was thinking about going from REAL to Ascii Decimal
the REAL4 and REAL8 formats are a little simpler than REAL10

Code Select

REAL4/REAL8
Exponent   Fraction   Meaning

   0          0       Signed Zero
   0        <> 0      Signed Denormal
 Other       Any      Signed Normal
All 1's       0       Signed Infinity
All 1's     <> 0      NaN

Code Select

REAL10
  Exponent                     Significand                  Meaning

    0000       0000_0000_0000_0000                          Signed Zero
               0000_0000_0000_0001 to 7FFF_FFFF_FFFF_FFFF   Signed Denormal
               8000_0000_0000_0000 to FFFF_FFFF_FFFF_FFFF   Signed Pseudo-Denormal

0001 to 7FFE   0000_0000_0000_0000 to 7FFF_FFFF_FFFF_FFFF   Invalid
               8000_0000_0000_0000 to FFFF_FFFF_FFFF_FFFF   Signed Normal

    7FFF       0000_0000_0000_0000 to 7FFF_FFFF_FFFF_FFFF   Invalid
               8000_0000_0000_0000                          Signed Infinity
               8000_0000_0000_0001 to BFFF_FFFF_FFFF_FFFF   Signaling NaN
               C000_0000_0000_0000                          Indefinite Quiet NaN
               C000_0000_0000_0001 to FFFF_FFFF_FFFF_FFFF   Quiet NaN

RuiLoureiro · April 21, 2013, 05:13:46 AM

Good to know, Dave ! :t
One of these days i will use that info

RuiLoureiro · April 24, 2013, 04:27:58 AM

Quote
REAL10
Exponent Significand Meaning

0000 0000_0000_0000_0000 Signed Zero
0000_0000_0000_0001 to 7FFF_FFFF_FFFF_FFFF Signed Denormal
8000_0000_0000_0000 to FFFF_FFFF_FFFF_FFFF Signed Pseudo-Denormal

0001 to 7FFE 0000_0000_0000_0000 to 7FFF_FFFF_FFFF_FFFF Invalid
8000_0000_0000_0000 to FFFF_FFFF_FFFF_FFFF Signed Normal

7FFF 0000_0000_0000_0000 to 7FFF_FFFF_FFFF_FFFF Invalid
8000_0000_0000_0000 Signed Infinity
8000_0000_0000_0001 to BFFF_FFFF_FFFF_FFFF Signaling NaN
C000_0000_0000_0000 Indefinite Quiet NaN
C000_0000_0000_0001 to FFFF_FFFF_FFFF_FFFF Quiet NaN

Dave,
when exponent is 7FFF

is this -Infinity ?
8000_0000_0000_0000 Signed Infinity
so this is +Infinity, no ?
0000_0000_0000_0000 Signed Infinity

So, where is the bit 79 = sign bit ?
If the S+exponent = 7FFFh -> sign = +
= FFFFh -> sign = -
Where is the problem ?

dedndave · April 24, 2013, 04:35:00 AM

the problem is, you are looking at info for the REAL10 format
there are 10 bytes, or 5 words - you are looking at 4 words :P
the first column shows the exponent, bits 78 to 64
the second column shows the significand, bits 63 to 0

+infinity = 7FFF_8000_0000_0000_0000
-infinity = FFFF_8000_0000_0000_0000

The MASM Forum

News: