Electronics - Number Systems and Codes

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No attempt is made to represent a history of changes in this file. It documents only the current state of affairs. If you are using XLINK in the Embedded Workbench integrated development environment, you may need a newer version of the Embedded Workbench for the relevant target in order to take full advantage of recently added features.

Simple-code is a simple binary format that is primarily meant as a format for flash loading. It is available for all processors. See simple-code for more information about this format. Raw-binary is a binary image format. It contains no header, no starting point, no address information of any kind, nothing but pure binary data.

The first byte of the file is the first byte in the program. The file contains all bytes between the first and the last byte in the program, including any and all gaps.

Note that there is no way to discern the entry address of the program from the contents of the file, no such information is available in the file and it must thus be kept tracked of in some other way, perhaps in the file's name. Uses the S1 and 0x95 binary options 10 s complement of binary number systems record types, which use bit addresses.

Uses the S2 and 0x95 binary options 10 s complement of binary number systems record types, which use bit addresses. Uses the S3 and S7 record types, which use bit addresses. The motorola output format uses a mixture of the record types, depending on the range of addresses output. See the COFF section of this document for more information about this format. See the ELF section of this document for more information about this format.

If there is a need to supply format variant options for the second format, these can be added to the "-y" option after a comma. The new version of the output format can, in addition to a number of other smaller improvements, result in a very significant reduction in the size of the output file. Also be sure to check the compiler release notes for any pertinent information on this issue. Source code for a SIMPLE reader is provided to make it easy to handle particular output requirements at a customer site.

See the xcoff78k section of this document for more information about this format. XLINK supports a 0x95 binary options 10 s complement of binary number systems of format variant modifiers that govern particular subtleties in the IEEE output format through the use of the -y command line option.

Combinations of format variant modifiers can be used by specifying more than one flag character in a single -y command line option. The available format variant modifiers for IEEE are: Note that you will need to use the 'l' and 'b' modifiers as well -ylbm.

One way these can occur is if an enum is declared in a block. This can sometimes drastically reduce the size of the output file. The available format variant modifiers for xcoff78k are: Irrespective of the setting of this modifier, section names are always truncated to 7 characters if longer and module names are truncated to 31 characters. Turn on this modifier to get them included. Some debuggers prefer to have the debug information in ascending line number order instead. Turn on this modifier to make XLINK produce debug information that is sorted in ascending line number order.

Checksums and fillers -H -J -h 5. The new 'x' flag to the -J option reverses the endianess of the computed checksum. Checksum 16 bits with reversed bit order in each iteration and generate a 4-byte 2's complement checksum with reversed endianess.

Examples of reversed endianess: If the 1-byte checksum was 0x73 the reversed checksum will be 0x If the 2-byte checksum was 0xC2 the reversed checksum will be 0xC If the 4-byte checksum was 0x3AC25 the reversed checksum will be 0x25AC XLINK now supports the use of a checksum unit length larger than then 8 bits.

This is primarily used to make the linker generated checksum match the one computed by special CRC hardware that checksums more than 8 bits in every iteration.

Three different sizes are currently supported, 8 bits this is the default16 bits W flag and 32 bits L flag. Checksum 32 bits in each iteration and generate a 2-byte checksum.

Checksum 16 bits with reversed bit order in each iteration and generate a 4-byte 2's complement checksum. The fill string must have an even length and every specified character must be a hexadecimal digit 0-F. Specifying several fill commands for the same address generates error In the normal case the bytes are specified and XLINK is free to pick any suitable order that includes the specified bytes and a byte is only checksummed once, regardless of how many times the address of the byte is specified.

A byte will be checksummed as many times as it is specified. This will add the start and end address of the segment to the range that is checksummed. An explicit range of hexadecimal addresses, like FF. An address is only used once, regardless of how many time it is specified in the ranges of checksum command. The checksumming will start on address 40 and end on addressthe byte on each address will be used exactly once even though some addresses were specified in more then one range.

By default, initial values are non-mirrored. Specifying bytewise and mirrored initial values is simply 0x95 binary options 10 s complement of binary number systems convenient way of specifying the same initial value both in XLINK and in the verification step, in cases where best binary options strategies brentwood tn verification step uses bytewise or mirrored initial values.

Mirroring is the process of reversing all the bits in a binary number,see mirroring below. If nothing else is 0x95 binary options 10 s complement of binary number systems this is a bitwise initial value. This specifies that initial is a bytewise initial value. Bitwise initial values If a bitwise initial value is specified on the checksum command line, that value is used as the initial value of sum in the classic bit-by-bit crc calculation below.

For an N-byte checksum you need to feed N x 8 zero bits through the bit-by-bit algorithm after the last bit has been entered. This allows the last N x 8 bits of the checksum to 0x95 binary options 10 s complement of binary number systems out. Command line example -J2,crc16,,,0x The above command line option specifies a 2-byte crc16 checksum where the initial value of sum in the bit-by-bit C-function above would be 0x Additional information See technical note for more details about bit-by-bit crc: The bit-by-bit algorithm is called slow crc in IAR technical support documentation.

Bitwise initial values are sometimes called indirect initial values in texts about crc. Bytewise initial values If a bytewise initial value is specified on the 0x95 binary options 10 s complement of binary number systems line, that value is used as the initial value of sum in the byte-by-byte crc calculation below.

Byte-by-byte crc algorithms are faster than bit-by-bit crc algorithms. The byte-by-byte algorithm below executes faster but uses more space than the bit-by-bit algorithm above. It uses a table of precomputed crc values. See technical note for more information about crc tables. The byte-by-byte algorithm does not need any final zero bits. Command line example -J2,crc16,,, 0x1D0F The above command line option specifies a 2-byte crc16 checksum where the initial value of sum in the byte-by-byte C-function above would be 0x1D0F.

The byte-by-byte algorithm computes exactly the same checksum as the bit-by-bit algorithm once the final zeroes have been fed through the bit-by-bit algorithm. They cannot use the same initial value due to differences in how the initial value is handled. Additional information See technical note for more details about byte-by-byte crc.

The byte-by-byte algorithm is called fast crc in IAR technical support documentation. Bytewise initial values are sometimes called direct initial values in texts about crc: Mirrored initial values If an initial value is specified on the checksum command line with the m prefix, that value is mirrored before it is used. Mirroring is the process of reversing all the bits in a binary number. If the number has N bits, bit 0 and bit N-1 are swapped, as is bit 1 and bit N-2 and so on. Additional information Mirroring is sometimes called reflection in texts about crc.

The value of the checksum value symbol will be the calculated checksum of the checksum command, not the address of the checksum bytes that is the value of the checksum symbol. Note that this symbol cannot be accessed from the program as it is added after the link phase.

The checksum value symbol is generated to help a debugger make a quick check to see if the code in target ROM is the same as that in a debug file. Note also that there are circumstances in which the code will be different even though the checksums are the same. One such circumstance is for position-independent code that is located at different addresses in different images, since the checksum only depends on the contents of bytes, and not their addresses.

The crc16 checksum for a program is 0x and resides on the address 0x7FFE. This initial value is listed in the linker listfile. Each command line option specifies one checksum, which will be 0x95 binary options 10 s complement of binary number systems from any bytes that occur in the given ranges. No bytes from the checksum itself, or from any checksums specified after it are incl uded in the calculation. The bytes are processed in order of increasing addresses.

In this case the symbol is also included in the final program. If a symbol name is explicitly specified, that particular checksum is only included in the final program if it is referenced by any included parts of the program, or if the -g require global entries command line option is used for the symbol.

If no alignment is specified, an alignment of 1 is used. If no ranges are specified, all bytes in the final program are included in the calculation. The value of each checksum, and which bytes in what order were included in the calculation, is listed in the linker list file. All available bytes in the program are included in the calculation.

The linker can introduce gaps because of alignment restrictions, or to fill ranges given in segment placement options. The normal behavior, when no -H option is given, is that these gaps are not given a value in the output file.

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All functions which return a result of type float are implemented as macros, although many of them exist as TIOS entries. This is done because the GCC convention for returning floating point values as function results differs from the convention expected by the TIOS.

This note is mainly unimportant from the user's point of view. The result is always in radians. If the argument is not in range from -1 to 1, acos will return NAN.

If the argument is not in range from -1 to 1, asin will return NAN. So, the result is in the range - pi to pi. If both x and y are zeros, atan2 returns NAN. It recognizes the character representation of a floating point number, made up of the following:.

This limitation is caused by using some TIOS calls which needs such number format. Anyway, it is very easy to "preprocess" any string to satisfy this convention before calling to atof by routine like the following assuming that c is a char variable, and i is an integer variable:. It returns NAN if the input string cannot be converted i. In fact, this function returns the same value as the argument, but with different interpretation. This function, in a way, performs typecasting from a bcd type to an ordinary float type.

At the fundamental level, bcdadd and fadd are the same routine. At the fundamental level, bcdbcd and flt are the same routine. At the fundamental level, bcdcmp and fcmp are the same routine. At the fundamental level, bcddiv and fdiv are the same routine. At the fundamental level, bcdlong and trunc are the same routine. At the fundamental level, bcdmul and fmul are the same routine. At the fundamental level, bcdneg and fneg are the same routine.

At the fundamental level, bcdsub and fsub are the same routine. See also sqrt and atan2. See sqrt , atan2 , sin and cos. At the fundamental level, fadd is exactly the same routine as bcdadd. This function may be useful as a comparison function for qsort function from stdlib. All relation operators applied to floating point types are implemented through implicite calls of this function. At the fundamental level, fcmp is exactly the same routine as bcdcmp.

All kind of zeros are equal from the aspect of comparation. Transfinite values are incomparable, and the result of fcmp is unpredictable usually 1, but this is not guarantee if any argument is transfinite.

At the fundamental level, fdiv is exactly the same routine as bcddiv. Also, it returns NAN if both arguments are zeros or infinities. Yet one deprecated macro. FEXP ,5 represents number 2. Anyway, you don't need to use FEXP any more: The first part is true; the second is not. More precise, FEXP shifts m to the left enough number of times to produce correct normalized mantissa see bcd for more info. For more description about internal format of floating point numbers, see bcd.

This function, in a way, performs typecasting from an ordinary float type to a bcd type. Beware that returned value is not an lvalue ordinary C functions never return lvalues, by the way , so you can not do something like.

This routine performs the same operation as casting a long integer value to float type using the ' float ' typecast operator, but it is kept here to allow compatibility with older programs created before TIGCC introduced floating point operators i. This function is automatically called when any floating point function is called with a long integer argument, to force a promotion of an integer to a floating point type.

In other words, integer values will be automatically promoted to the floating point type when necessary. Also, you can calculate sin a where a is an integer. In both cases, flt will be called automatically to perform the promotion. At the fundamental level, flt is exactly the same routine as bcdbcd. FLT is a now deprecated macro which is kept here only to retain compatibility with programs which are written with older releases of TIGCC before 0.

Now, FLT x,y will simply be translated to x. FLT ,15 will be translated to Anyway, you don't need to use the FLT macro any more. At the fundamental level, fmul is exactly the same routine as bcdmul. This routine performs the same operation as the C '-' unary minus operator applied to a floating point operand, but it is kept here to allow compatibility with older programs created before TIGCC introduced floating point operators i. At the fundamental level, fneg is exactly the same routine as bcdneg.

It checks whether the floating point with the exponent exponent and the mantissa pointed to by mantissa is reducable to an integer. It checks whether the integer part of the floating point with the exponent exponent and the mantissa pointed to by mantissa is an odd number. Also returns TRUE if the integer part is zero, although zero is not an odd number.

This routine is analogous to frexp in ANSI C math library, except using base ten rather than base two. This routine performs the same operation as the C '-' operator applied to floating point operands, but it is kept here to allow compatibility with older programs created before TIGCC introduced floating point operators i.

At the fundamental level, fsub is exactly the same routine as bcdsub. This is equivalent to the length of the hypotenuse of a right triangle, if the lengths of the two sides are x and y. However, as far as I know, you need not to call this function explicitely anywhere in your program, because TIOS does it in the boot code.

As this function is removed from AMS 2. This routine performs a set of arithmetic operations on binary coded decimal floating point values.

Operands may be in MC registers, in the memory, or in "floating point registers" they are, in fact, memory locations on the stack frame from the aspect of the emulator. It may give additional flexibility for ASM programmers sometimes the argument may be in the register, sometimes in the memory, etc.

But in C, the arguments are always on the stack, so this flexibility is not necessary. Infinite values are produced when the result is unbounded for example dividing by zero , or in case of overflow. These two special numbers are treated very similarly in TIOS.

It calculates the arc sine, the arc cosine or the arc tangent of the floating point value pointed to by xptr , and stores the result in the floating point destination pointed to by result. Parameter option determines which inverse trigonometric function will be calculated: I don't know whether these values are the only legal values for option , but I believe so.

The parameter xptr is not a pointer to const value. This means that the value pointed to by it may be changed. In normal cases this would not appear, but this need not to be true if the structure pointed to by xptr contains wrong values for example, arguments out of the function domain, unnormalized values, etc.

Strictly speaking, ldexp10 is a macro, not a function. This routine is analogous to ldexp in ANSI C math library, except using base ten rather than base two. It stores the integer in a floating point destination pointed to by ipart and returns the fractional part of x. If both x and y are zeros, pow will return 1. If x is negative, the correct result will be produced only if y can be represented as a whole number, or as a fraction with odd denominator; otherwise, pow will return a garbage not NAN which sometimes even not satisfy the floating point BCD format digits greater than 9 etc.

Rounds the floating point number to 12 significant digits, throwing an error if unsuccessful. TIOS always does such rounding before storing a floating point value to a variable.

See also notes related to sin and cos. If the argument is negative, there will be no error, but the result will be invalid. Also, it will return NAN if the argument is so big that reducing to the main period can't be performed without complete losing of significant digits i. It calculates simultaneously the sine, the cosine and the tangent of the floating point value pointed to by xptr , and stores the results in floating point destinations pointed to by sine , cosine and tangent.

Parameter option is not very clear to me: I only noticed that the tangent will not be calculated if option is not equal to 4.

I included the description of this routine here only due to completeness: Returns zero in a case of overflow. This routine performs the same operation as casting a floating point value to an int type using ' int ' , ' unsigned int ' and ' long ' typecast operators, but it is kept here to allow compatibility with older programs created before TIGCC introduced floating point operators i.

This function is automatically called when any function which needs an integer is called with a floating point arguments, to force a truncation of a floating point value to an integer. In both cases, trunc will be called automatically to perform the truncation. At the fundamental level, trunc is exactly the same routine as bcdlong. FIVE is a predefined floating point constant with value 5.

FOUR is a predefined floating point constant with value 4. HALF is a predefined floating point constant with value 0. NAN is an acronyme of "Not a Number". TIOS generates NAN when nothing can be deduced about the magnitude of the result for example, when dividing zero by zero, or when substracting two infinities of the same sign.

Also, TIOS generates NAN when the argument of a function is out of legal range, excluding values of the argument which produces infinity results.