Data::SecsPack - pack and unpack numbers in accordance with SEMI E5-94

Data-SecsPack documentation Contained in the Data-SecsPack distribution.

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NAME

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Data::SecsPack - pack and unpack numbers in accordance with SEMI E5-94

SYNOPSIS

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 #####
 # Subroutine interface
 #  
 use Data::SecsPack qw(bytes2int config float2binary 
                    ifloat2binary int2bytes   
                    pack_float pack_int pack_num  
                    str2float str2int 
                    unpack_float unpack_int unpack_num);

 $big_integer = bytes2int( @bytes );

 $old_value = config( $option );
 $old_value = config( $option => $new_value);

 ($binary_magnitude, $binary_exponent) = float2binary($magnitude, $exponent, @options); 

 ($binary_magnitude, $binary_exponent) = ifloat2binary($imagnitude, $iexponent, @options);

 @bytes = int2bytes( $big_integer );

 ($format, $floats) = pack_float($format, @string_floats, [@options]);

 ($format, $integers) = pack_int($format, @string_integers, [@options]);

 ($format, $numbers, @string) = pack_num($format, @strings, [@options]);

 $float = str2float($string, [@options]);
 (\@strings, @floats) = str2float(@strings, [@options]);

 $integer = str2int($string, [@options]);
 (\@strings, @integers) = str2int(@strings, [@options]);

 \@ingegers = unpack_int($format, $integer_string, @options);

 \@floats   = unpack_float($format, $float_string, @options); 

 \@numbers  = unpack_num($format, $number_string), @options; 

 #####
 # Class, Object interface
 #
 # For class interface, use Data::SecsPack instead of $self
 #
 use Data::SecsPack;

 $secspack = 'Data::SecsPack';  # uses built-in config object

 $secspack = new Data::SecsPack(@options);

 $big_integer = bytes2int( @bytes );

 ($binary_magnitude, $binary_exponent) = $secspack->float2binary($magnitude, $exponent, @options); 

 ($binary_magnitude, $binary_exponent) = $secspack->ifloat2binary($imagnitude, $iexponent, @options);

 @bytes = $secspack->int2bytes( $big_integer );

 ($format, $floats) = $secspack->pack_float($format, @string_integers, [@options]);

 ($format, $integers) = $secspack->pack_int($format, @string_integers, [@options]);

 ($format, $numbers, @strings) = $secspack->pack_num($format, @strings, [@options]);

 $integer = $secspack->str2int($string, [@options])
 (\@strings, @integers) = $secspack->str2int(@strings, [@options]);

 $float = $secspack->str2float($string, [@options]);
 (\@strings, @floats) = $secspack->str2float(@strings, [@options]);

 \@ingegers = $secspack->unpack_int($format, $integer_string, @options); 

 \@floats   = $secspack->unpack_float($format, $float_string, @options); 

 \@numbers  = $secspack->unpack_num($format, $number_string, @options);

Generally, if a subroutine will process a list of options, @options, that subroutine will also process an array reference, \@options, [@options], or hash reference, \%options, {@options}. If a subroutine will process an array reference, \@options, [@options], that subroutine will also process a hash reference, \%options, {@options}. See the description for a subroutine for details and exceptions.

DESCRIPTION

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The subroutines in the Data::SecsPack module packs and unpacks numbers in accordance with SEMI E5-94. The E5-94 establishes the standard for communication between the equipment used to fabricate semiconductors and the host computer that controls the fabrication. The equipment in a semiconductor factory (fab) or any other fab contains every conceivable known microprocessor and operating system known to man. And there are a lot of specialize real-time embedded processors and speciallize real-time embedded operating systems in addition to the those in the PC world.

The communcication between host and equipment used packed nested list data structures that include arrays of characters, integers and floats. The standard has been in place and widely used in China, Germany, Korea, Japan, France, Italy and the most remote corners on this planent for decades. The basic data structure and packed data formats have not changed for decades.

This stands in direct contradiction to the common conceptions of many in the Perl community and most other communities. The following quote is taken from page 761, Programming Perl third edition, discussing the pack subroutine:

"Floating-point numbers are in the native machine format only. Because of the variety of floating format and lack of a standard "network" represenation, no facility for interchange has been made. This means that packed floating-point data written on one machine may not be readable on another. That is a problem even when both machines use IEEE floating-point arithmetic, because the endian-ness of memory representation is not part of the IEEE spec."

There are a lot of things that go over the net that have industry or military standards but no RFCs. So unless you dig them out, you will never know they exist. While RFC and military standards may be freely copyied, industry standards are usually copyrighted. This means if you want to read the standard, you have to pay whatever the market bears. ISO standards, SEMI stardards, American National Standards, IEEE standards beside being boring are expensive. In other words, you do not see them flying out the door at the local Barnes and Nobles. In fact, you will not even find them inside the door.

It very easy to run these non RFC standard protocols over the net. Out of 64,000 ports, pick a port of opportunity (hopefully not one of those low RFC preassigned ports) and configure the equipment and host to the same IP and port. Many times the software will allow a remote console that is watch only. The watch console may even be a web server on port 80. If there is a remote soft console, you can call up or e-mail the equipment manufacturer's engineer in say Glouster, MA, USA and tell him the IP and port so he can watch his manchine mangle a cassette of wafers with a potential retail value of half million dollars.

SEMI E5-94 and their precessors do standardize the endian-ness of floating point, the packing of nested data, used in many programming languages, and much, much more. The endian-ness of SEMI E5-94 is the first MSB byte, floats sign bit first. Maybe this is because it makes it easy to spot numbers in a packed data structure.

The nested data has many performance advantages over the common SQL culture of viewing and representing data as tables. The automated fabs of the world make use of SEMI E5-94 nested data not only for real-time communication (TCP/IP RS-2332 etc) between machines but also for snail-time processing as such things as logs and performance data.

Does this standard communications protocol ensure that everything goes smoothly without any glitches with this wild mixture of hardware and software talking to each other in real time? Of course not. Bytes get reverse. Data gets jumbled from point A to point B. Machine time to test software is non-existance. Big ticket, multi-million dollar fab equipment has to work to earn its keep. And, then there is the everyday business of suiting up, with humblizing hair nets, going through air and other showers with your favorite or not so favorite co-worker just to get into the clean room. And make sure not to do anything that will scatch a wafer with a lot of Intel Pentiums on them. It is totally amazing that the product does get out the door.

SECSII Format

The Data::SecsPack suroutines packs and unpacks numbers in accordance with SEMI, http://www.semi.org, E5-94, Semiconductor Equipment Communications Standard 2 (SECS-II), avaiable from

 Semiconductor Equipment and Materials International
 805 East Middlefield Road,
 Mountain View, CA 94043-4080 USA
 (415) 964-5111
 Easylink: 62819945
 http://www.semi.org

The format of SEMI E5-94 numbers are established by below Table 1. 

               Table 1 Item Format Codes

 unpacked   binary  octal  hex   description
 ---------------------------------------------------------
 T          001001   11    0x24  Boolean
 S8         011000   30    0x60  8-byte integer (signed)
 S1         011001   31    0x62  1-byte integer (signed)
 S2         011010   32    0x64  2-byte integer (signed)
 S4         011100   34    0x70  4-byte integer (signed)
 F8         100000   40    0x80  8-byte floating
 F4         100100   44    0x90  4-byte floating
 U8         101000   50    0xA0  8-byte integer (unsigned)
 U1         101001   51    0xA4  1-byte integer (unsigned)
 U2         101010   52    0xA8  2-byte integer (unsigned)
 U4         101100   54    0xB0  4-byte integer (unsigned)

Table 1 complies to SEMI E5-94 Table 1, p.94, with an unpack text symbol and hex columns added. The hex column is the upper Most Significant Bits (MSB) 6 bits of the format code in the SEMI E5-94 item header (IH)

In accordance with SEMI E5-94 6.2.2,

1

the Most Significat Byte (MSB) of numbers for formats S2, S4, S8, U2, U4, U8 is sent first

2

the signed bit for formats F4 and F8 are sent first.

3

Signed integer formats S1, S2, S4, S8 are two's complement

The memory layout for Data::SecsPack is the SEMI E5-94 "byte sent first" has the lowest memory address.

IEEE 754-1985 Standard

The SEMI E5-94 F4 format complies to IEEE 754-1985 float and the F8 format complies to IEEE 754-1985 double. The IEEE 754-1985 standard is available from:

 IEEE Service Center
 445 Hoe Lane,
 Piscataway, NJ 08854

The SEMI E5-94 F4, IEEE 754-1985 float, is 32 bits with the bits assigned follows: 

 S EEE EEEE EMMM MMMM MMMM MMMM MMMM MMMM

where S = sign bit, E = 8 exponent bits M = 23 mantissa bits

The format of the float S, E, and M are as follows:

Sign of the number

The sign is one bit, 0 for positive and 1 for negative.

exponent

The exponent is 8 bits and may be positive or negative. The IEEE 754 exponent uses excess-127 format. The excess-127 format adds 127 to the exponent. The exponent is re-created by subtracting 127 from the exponent.

Magnitude of the number

The magnitude or mantissa is a 23 bit unsigned binary number where the radix is adjusted to make the magnitude fall between 1 and 2. The magnitude is stored ignoring the 1 and filling in the trailing bits until there are 23 of them.

The SEMI E5-94 F4, IEEE 754-1985 double, is 64 bits with S,E,M as follows: S = sign bit, E = 11 exponent bits M = 52 mantissa bits

The format of the float S, E, and M are as follows:

Sign of the number

The sign is one bit, 0 for positive and 1 for negative.

exponent

The exponent is 8 bits and may be positive or negative. The IEEE 754 exponent uses excess-1027 format. The excess-1027 format adds 1027 to the exponent. The exponent is re-created by subtracting 1027 from the exponent.

Magnitude of the number

The magnitude or mantissa is a 52 bit unsigned binary number where the radix is adjusted to make the magnitude fall between 1 and 2. The magnitude is stored ignoring the 1 and filling in the trailing bits until there are 52 of them.

For example, to find the IEEE 754-1985 float of -10.5

SUBROUTINES

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bytes2int

 $big_integer = bytes2int( @bytes );

The bytes2int subroutine counvers a @bytes binary number with the Most Significant Byte (MSB) $byte[0] to a decimal string number $big_integer using the Data::BigInt program module. As such, the only limitations on the number of binary bytes and decimal digits is the resources of the computer.

config

 $old_value = config( $option );
 $old_value = config( $option => $new_value);
 (@all_options) = config( );

When Perl loads the Data::SecsPack program module, Perl creates the Data::SecsPack subroutine Data::SecsPack object $Data::SecsPack::subroutine_secs using the new method. Using the config subroutine writes and reads the $Data::SecsPack::subroutine_secs object.

Using the config as a class method,

 Data::SecsPack->config( @_ )

also writes and reads the $Data::SecsPack::subroutine_secs object.

Using the config as an object method writes and reads that object.

The Data:SecsPack subroutines used as methods for that object will use the object underlying data for their startup (default options) instead of the $Data::SecsPack::subroutine_secs object. It goes without saying that that object should have been created using one of the following:

 $object = $class->Data::SecsPack::new(@_)
 $object = Data::SecsPack::new(@_)
 $object = new Data::SecsPack(@_)

The underlying object data for the Data::SecsPack options defaults is the class Data::Startup object $Data::SecsPack::default_options. For object oriented conservative purist, the config subroutine is the accessor function for the underlying object hash.

Since the data are all options whose names and usage is frozen as part of the Data::SecsPack interface, the more liberal minded, may avoid the config accessor function layer, and access the object data directly by a statement such as

 $Data::SecsPack::default_options->{version};

The options are as follows:

 used by                                     values default  
 subroutine    option                        value 1st
 ----------------------------------------------------------
               big_float_version              \d+\.\d+
               big_int_version                \d+\.\d+
               version                        \d+\.\d+

               warnings                        0 1
               die                             0 1

 bytes2int 

 float2binary  decimal_integer_digits          20 \d+
               extra_decimal_fraction_digits    5 \d+
               decimal_fraction_digits       
               binary_fraction_bytes

 ifloat2binary decimal_fraction_digits         25 \d+
               binary_fraction_bytes           10 \d+

 int2bytes

 pack_float    decimal_integer_digits          
               extra_decimal_fraction_digits   
               decimal_fraction_digits       
               binary_fraction_bytes

 pack_int 

 pack_num      nomix                            0 1
               decimal_integer_digits          
               extra_decimal_fraction_digits   
               decimal_fraction_digits       
               binary_fraction_bytes

 unpack_float
 unpack_int
 unpack_num

For options with a default value and subroutine, see the subroutine for a description of the option. Each subroutine that uses an option or uses a subroutine that uses an option has an option input. The option input overrides the startup option from the <Data::SecsPack> object.

The description of the options without a subroutine are as follows:

 option              description
 --------------------------------------------------------------
 big_float_version   Math::BigFloat version
 big_int_version     Math::BigInt version
 version             Data::SecsPack version

 warnings            issue a warning on subroutine events
 die                 die on subroutine events

They really versions should not be changed unless the intend is to provided fraudulent versions.

float2binary

 ($binary_magnitude, $binary_exponent) = float2binary($magnitude, $exponent); 
 ($binary_magnitude, $binary_exponent) = float2binary($magnitude, $exponent, @options); 
 ($binary_magnitude, $binary_exponent) = float2binary($magnitude, $exponent, [@options]); 
 ($binary_magnitude, $binary_exponent) = float2binary($magnitude, $exponent, {@options});

The ifloat2binary subroutine converts a decimal float with a base ten $magnitude and $exponent to a binary float with a base two $binary_magnitude and $binary_exponent.

The ifloat2binary assumes that the decimal point is set by iexponent so that there is one decimal integer digit in imagnitude The ifloat2binary produces a $binary_exponent so that the first byte of $binary_magnitude is 1 and the rest of the bytes are a base 2 fraction.

The float2binary subroutine uses the ifloat2binary for the small $exponent part and the Math::BigFloat subroutines to correct the ifloat2binary for the remaing exponent factor outside the range of the ifloat2binary subroutine.

The float2binary subroutine uses the options decimal_integer_digits, $decial_fraction_digits, extra_decimal_fraction_digits in determining the $iexponent passed to the ifloat2binary subroutine. The option decimal_integer_digits is the largest positive base ten $iexponent while smallest $ixponent is the half $decial_fraction_digits + extra_decimal_fraction_digits. The float2binary subroutine extra_decimal_fraction_digits only for negative $iexponent. The float2binary subroutine uses any base ten $exponent from $iexponent breakout to adjust the ifloat2binary subroutine results using native float arith.

If the float2binary subroutine encounters an event where it cannot continue, it halts processing, and returns the event as

  (undef,$event)

The events are as follows:

 "No inputs\n\tData::SecsPack::float2binary-1\n"

The float2binary also passes on any ifloat2binary events. Check the $binary_magnitude for an undef, to see if the subroutine cannot process the decimal exponent.

ifloat2binary

 ($binary_magnitude, $binary_exponent) = ifloat2binary($imagnitude, $iexponent);
 ($binary_magnitude, $binary_exponent) = ifloat2binary($imagnitude, $iexponent, @options);
 ($binary_magnitude, $binary_exponent) = ifloat2binary($imagnitude, $iexponent, [@options]);
 ($binary_magnitude, $binary_exponent) = ifloat2binary($imagnitude, $iexponent, {@options});

The $ifloat2binary subroutine converts a decimal float with a base ten $imagnitude and $iexponent using the Math::BigInt program module to a binary float with a base two $binary_magnitude and a base two $binary_exponent. The $ifloat2binary assumes that the decimal point is set by iexponent so that there is one decimal integer digit in imagnitude The ifloat2binary produces a $binary_exponent so that the first byte of $binary_magnitude is 1 and the rest of the bytes are a base 2 fraction.

Since all the calculations use basic integer arith, there are practical limits on the computer resources. Basically the limit is that with a zero exponent, the decimal point is within the significant imagnitude digits. Within these limitations, the accuracy, by chosen large enough limits for the binary fraction, is perfect.

If the ifloat2binary subroutine encounters an event where it cannot continue, it halts processing, and returns the event as

  (undef,$event)

The events are as follows:

 "No inputs\n\tData::SecsPack::ifloat2binary-1\n"
 "The exponent, $exponent, is out of range for $magnitude.\n\tData::SecsPack::ifloat2binary-2\n"

Check the $binary_magnitude for an undef, to see if the subroutine cannot process the decimal exponent.

The first step of the ifloat2binary subroutine is zero out iexponent by breaking up the imagnitude into an integer part integer and fractional part fraction consist with the iexponent. The c<ifloat2binary> will add as many significant decimal zeros to the right of integer in order to zero out iexponent; likewise it will add as many decimal zeros to the left of integer to zero out exponent within the limit set by the option decimal_fraction_digits. If ifloat2binary cannot zero out iexponent without violating the decimal_fraction_digits, ifloat2binary will discontinue processing and return an undef $binary_magnitude with and error message in $binary_exponent.

This design is based on the fact that the conversion of integer decimal to binary decimal is one to one, while the conversion of fractional decimal to binary decimal is not. When converting from decimal fractions with finite digits to binary fractions repeating binary fractions of infinity size are possible, and do happen quite frequently. An unlimited repeating binary fraction will quickly use all computer resources. The binary_fraction_bytes option provides this ungraceful event by limiting the number of fractional binary bytes. The default limits of 20 decimal_fraction_digits and binary_fraction_bytes 10 bytes provides a full range of 0 - 255 for each binary byte. The ten bytes are three more bytes then are ever used in the largest F8 SEMI float format.

The the following example illustrates the method used by ifloat2binary to convert decimal fracional digits to binary fractional bytes. Convert a 6 digit decimal fraction string into a binary fraction as follows:

 N[0-999999]      
 -----------  =  
   10^6          

 byte0    byte1   byte2    256         R2
 ----- +  ----- + ----- + ----- * ------------
 256^1    256^2   256^3   256^4     10 ^ 6

Six digits was chosen so that the integer arith, using a 256 base, does not over flow 32 bit signed integer arith

 256 *   99999     =   25599744
 256 *  999999     =  255999744
 signed 32 bit max = 2147483648 / 256 = 8377608
 256 * 9999999     = 2559999744

Note with quad arith this technique would yield 16 decimal fractional digits as follows:

 256 * 9999999999999999  =  2559999999999999744
 signed 64 bit max       =  9223372036854775808 / 256 = 36028797018963868
 256 * 99999999999999999 = 25599999999999999744

 Thus, need to get quad arith running.

 Basic step

  1      256 * N[0-999999]     1                     R0[0-999744]
 --- *   ----------------  =  ---- ( byte0[0-255] + ------------ ) 
 256         10 ^ 6           256                     10^6

The results will have a range of 

  1
 ---- ( 0.000000 to 255.999744)
 256

The fractional part, R0 is a six-digit decimal. Repeating the basic step three types gives the desired results. QED.

 2nd Iteration

  1      256 * R0[0-999744]       1                   R1[0-934464]
 --- *   --------------      =  ---- ( byte1[0-255] + ------------) 
 256         10 ^ 6              256                    10^6

 3rd Iteration

  1      256 * R1[0-934464]       1                   R2[0-222784]
 --- *   --------------      =  ---- ( byte2[0-239] + ------------) 
 256         10 ^ 6              256                    10^6

Taking this out to ten bytes the first six decimal digits N[0-999999] yields bytes in the following ranges:

 byte    power      range    10^6 remainder
 ------------------------------------------ 
   0     256^-1     0-255    [0-999744]
   1     256^-2     0-255    [0-934464]
   2     256^-3     0-239    [0-222784]
   3     256^-4     0-57     [0-032704]
   4     256^-5     0-8      [0-372224]
   5     256^-6     0-95     [0-293440]
   6     256^-7     0-75     [0-120640]
   7     256^-8     0-30     [0-883840]
   8     256^-9     0-226    [0-263040]
   9     256^-10    0-67     [0-338249]

The first two binary fractional bytes have full range. The rest except for byte 9 are not very close. This makes one wonder about the accuracy loss in translating from binary fractions to decimal fractions. One wonders just why have all theses problems with not just binary and decimal factions but fractions in general. Isn't mathematics wonderful.

For example in convert from decimal to binary fractions there is no clean one to one conversion as for integers. For example, look at the below table of conversions: 

 -1    -2     -3     -4     -5     binary power as a decimal   
 0.5   0.25  0.125 0.0625 0.03125  decimal power 
                                   decimal 
  0     0      0      0      0     0.00000
  0     0      0      0      1     0.03125
  0     0      0      1      1     0.0625
  0     0      1      0      0     0.125
  0     0      1      0      1     0.15625
  0     0      1      1      0     0.1875
  0     0      1      1      1     0.21875
  1     0      0      0      0     0.50000

int2bytes

 @bytes = int2bytes( $big_integer );

The int2bytes subroutine uses the Data:BigInt program module to convert an integer text string $bit_integer into a byte array, @bytes, the Most Significant Byte (MSB) being $bytes[0]. There is no limits on the size of $big_integer or @bytes except for the resources of the computer.

new

 $secspack = new Data::Secs2( @options );
 $secspack = new Data::Secs2( [@options] );
 $secspack = new Data::Secs2( {options} );

The new subroutine provides a method to set local options once for any of the other subroutines. The options may be modified at any time by $secspack-config($option => $new_value)>. Calling any of the subroutines as a $secspack method will perform that subroutine with the options saved in secspack.

pack_float

 ($format, $floats) = pack_float($format, @string_integers);
 ($format, $floats) = pack_float($format, @string_integers, [@options]);
 ($format, $floats) = pack_float($format, @string_integersm {@options});

The pack_float subroutine takes an array of strings, <@string_integers>, and a float format code, as specifed in the above Item Format Code Table, and packs all the integers, decimals and floats as a float the $format in accordance with SEMI E5-94. The pack_int subroutine also accepts the format code F and format codes with out the bytes-per-element number and packs the numbers in the format using the less space. In any case, the pack_int subroutine returns the correct $format of the packed $integers.

If the pack_float subroutine encounters an event where it cannot continue, it halts processing, and returns the event as

  (undef,$event)

The events are as follows:

 "No inputs.\n\tData::SecsPack::pack_float-1\n"
 "Format $format is not a floating point format.\n\tData::SecsPack::pack_float-2\n"
 "F4 exponent overflow.\n\tData::SecsPack::pack_float-3\n"
 "F4 xponent underflow.\n\tData::SecsPack::pack_float-4\n"
 "F8 exponent overflow.\n\tData::SecsPack::pack_float-5\n"
 "F8 xponent underflow.\n\tData::SecsPack::pack_float-6\n"

The float2binary also passes on any float2binary and ifloat2binary events. Check the $format for an undef, to see if the subroutine cannot continue processing.

pack_int

 ($format, $integers) = pack_int($format, @string_integers);
 ($format, $integers) = pack_int($format, @string_integers, [@options]);
 ($format, $integers) = pack_int($format, @string_integers, {options});

The pack_int subroutine takes an array of strings, <@string_integers>, and a format code, as specifed in the above Item Format Code Table and packs the integers, $integers in the $format in accordance with SEMI E5-94. The pack_int subroutine also accepts the format code I I1 I2 I8 and format codes with out the bytes-per-element number and packs the numbers in the format using the less space, with unsigned preferred over signed. In any case, the pack_int subroutine returns the correct $format of the packed $integers.

If the pack_int subroutine encounters an event where it cannot continue, it halts processing, and returns the event as

  (undef,$event)

The events are as follows:

 "No inputs.\n\tData::SecsPack::pack_int-1\n"
 "Format $format is not an integer format.\ntData::SecsPack::pack_int-2\n"
 "No integers in the input.\ntData::SecsPack::pack_int-3\n"
 "Signed number encountered when unsigned specified.\ntData::SecsPack::pack_int-4\n"
 "Integer bigger than format length of $max_bytes bytes.\ntData::SecsPack::pack_int-5\n"

Check the $format for an undef, to see if the subroutine cannot continue processing.

pack_num

 ($format, $numbers, @strings) = pack_num($format, @strings);
 ($format, $numbers, @strings) = pack_num($format, @strings, [@options]);
 ($format, $numbers, @strings) = pack_num($format, @strings, {@options});

The pack_num subroutine takes leading numbers in @strings and packs them in the $format in accordance with SEMI E5-94. The pack_num subroutine returns the stripped @strings data naked of all leading numbers in $format.

The pack_num subroutine also accepts $format of I I1 I2 I4 F For these format codes, pack_num is extremely liberal and accepts processes all numbers consistence with the $format and packs one or more numbers in the SEMI E5-94 format that takes the least space. In this case, the return $format is changed to the SEMI E5-94 from the Item FOrmat Code Table of the packed numbers.

For the I $format, if the nomix option is set, the pack_num subroutine will pack all leading, integers, decimals and floats as multicell float with the smallest space; otherwise, it will stop at the first decimal or float encountered and just pack the integers.

The pack_num subroutine processes @strings in two steps. In the first step, the pack_num subroutine uses str2int and/or str2float subroutines to parse the leading numbers from the @strings as follows:

 ([@strings], @integers) = str2int(@strings); 
 ([@strings], @floats) = str2float(@strings);

In the second step, the pack_num subroutine uses pack_int and/or pacK_float to pack the parsed numbers.

If the pack_nym subroutine encounters an event where it cannot continue, it halts processing, and returns the event as

  (undef,$event)

The events are as follows:

 "No inputs.\n\tData::SecsPack::pack_num-1\n"
 "Format $format is not an integer or floating point format.\ntData::SecsPack::pack_num-2\n"
 "No numbers in the input.\ntData::SecsPack::pack_num-3\n"

The float2binary also passes on any float2binary ifloat2binary pack_int pack_float events. Check the $format for an undef, to see if the subroutine cannot continue processing.

str2float

 $float = str2float($string);
 $float = str2float($string, [@options]);
 $float = str2float($string, {@options});

 (\@strings, @floats) = str2float(@strings);
 (\@strings, @floats) = str2float(@strings, [@options]);
 (\@strings, @floats) = str2float(@strings, {@options});

Obsoleted and superceded by the Data::Str2Num-str2float> subroutine in the Data::Str2Num package.

str2int

 $integer = str2int($string);
 $integer = str2int($string, [@options]);
 $integer = str2int($string, {@options});

 (\@strings, @integers) = str2int(@strings); 
 (\@strings, @integers) = str2int(@strings, [@options]); 
 (\@strings, @integers) = str2int(@strings, {@options});

Obsoleted and superceded by the Data::Str2Num-str2integer> subroutine in the Data::Str2Num package.

unpack_float

 \@floats   = unpack_float($format, $float_string);
 \@floats   = unpack_float($format, $float_string, @options);
 \@floats   = unpack_float($format, $float_string, [@options]);
 \@floats   = unpack_float($format, $float_string, {@options});

The unpack_num subroutine unpacks an array of floats $float_string packed in accordance with SEMI-E5 $format. A valid $format, in accordance with the above Item Format Code Table, is F4 F8.

If the unpack_float subroutine encounters an event where it cannot continue, it halts processing, and returns the event as

 $event

The events are as follows:

 "No inputs\ntData::SecsPack::unpack_float-1\n"
 "Format $format_in not supported.\n"tData::SecsPack::unpack_float-2\n"

The unpack_num subroutine, thus, returns a reference, \@floats, to the unpacked float array or scalar error message $event. To determine a valid return or an error, check that ref of the return exists or is 'ARRAY'.

unpack_int

 \@integers = unpack_int($format, $integer_string); 
 \@integers = unpack_int($format, $integer_string, @options); 
 \@integers = unpack_int($format, $integer_string, [@options]); 
 \@integers = unpack_int($format, $integer_string, {@options});

The unpack_num subroutine unpacks an array of numbers $string_numbers packed in accordance with SEMI-E5 $format. A valid $format, in accordance with the above Item Format Code Table, is S1 S2 S4 U1 U2 U4 T.

The unpack_num returns a reference, \@integers, to the unpacked integer array or scalar error message $error. To determine a valid return or an error, check that ref of the return exists or is 'ARRAY'.

If the unpack_float subroutine encounters an event where it cannot continue, it halts processing, and returns the event as

  $event

The events are as follows:

 "No inputs\ntData::SecsPack::unpack_int-1\n"
 "Format $format_in not supported.\n"tData::SecsPack::unpack_int-2\n"

The unpack_num subroutine, thus, returns a reference, \@floats, to the unpacked float array or scalar error message $event. To determine a valid return or an error, check that ref of the return exists or is 'ARRAY'.

unpack_num

 \@numbers  = unpack_num($format, $number_string); 
 \@numbers  = unpack_num($format, $number_string, @options); 
 \@numbers  = unpack_num($format, $number_string, [@options]); 
 \@numbers  = unpack_num($format, $number_string, {@options});

The unpack_num subroutine unpacks an array of numbers $number_string packed in accordance with SEMI E5-94 $format. A valid $format, in accordance with the above Item Format Code Table, is S1 S2 S4 U1 U2 U4 F4 F8 T. The unpack_num subroutine uses either unpack_float or unpack_int depending upon $format.

The pack_num subroutine does not generate any events but the subroutine does pass on any pack_int and pack_float events, returning them as a string. The unpack_num subroutine, thus, returns a reference, \@numbers, to the unpacked number array or scalar error message $event. To determine a valid return or an error, check that ref of the return exists or is 'ARRAY'.

REQUIREMENTS

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Coming.

DEMONSTRATION

Top

 #########
 # perl SecsPack.d
 ###

~~~~~~ Demonstration overview ~~~~~

The results from executing the Perl Code follow on the next lines as comments. For example,

 2 + 2
 # 4

~~~~~~ The demonstration follows ~~~~~

     use File::Package;
     my $fp = 'File::Package';

     my $uut = 'Data::SecsPack';
     my $loaded;

     #####
     # Provide a scalar or array context.
     #
     my ($result,@result);

 ##################
 # UUT Loaded
 # 

    my $errors = $fp->load_package($uut, 
        qw(bytes2int float2binary 
           ifloat2binary int2bytes   
           pack_float pack_int pack_num  
           str2float str2int 
           unpack_float unpack_int unpack_num) );
 $errors

 # ''
 #

 ##################
 # str2int('0xFF')
 # 

 $result = $uut->str2int('0xFF')

 # '255'
 #

 ##################
 # str2int('255')
 # 

 $result = $uut->str2int('255')

 # '255'
 #

 ##################
 # str2int('hello')
 # 

 $result = $uut->str2int('hello')

 # undef
 #

 ##################
 # str2int(1E20)
 # 

 $result = $uut->str2int(1E20)

 # undef
 #

 ##################
 # str2int(' 78 45 25', ' 512E4 1024 hello world') @numbers
 # 

 my ($strings, @numbers) = str2int(' 78 45 25', ' 512E4 1024 hello world')
 [@numbers]

 # [
 #          '78',
 #          '45',
 #          '25'
 #        ]
 #

 ##################
 # str2int(' 78 45 25', ' 512E4 1024 hello world') @strings
 # 

 join( ' ', @$strings)

 # '512E4 1024 hello world'
 #

 ##################
 # str2float(' 78 -2.4E-6 0.0025 0', ' 512E4 hello world') numbers
 # 

 ($strings, @numbers) = str2float(' 78 -2.4E-6 0.0025  0', ' 512E4 hello world')
 [@numbers]

 # [
 #          [
 #            '78',
 #            '1'
 #          ],
 #          [
 #            '-24',
 #            '-6'
 #          ],
 #          [
 #            '25',
 #            -3
 #          ],
 #          [
 #            '0',
 #            -1
 #          ],
 #          [
 #            '512',
 #            '6'
 #          ]
 #        ]
 #

 ##################
 # str2float(' 78 -2.4E-6 0.0025 0', ' 512E4 hello world') @strings
 # 

 join( ' ', @$strings)

 # 'hello world'
 #

 ##################
 # str2float(' 78 -2.4E-6 0.0025 0xFF 077 0', ' 512E4 hello world', {ascii_float => 1}) numbers
 # 

 ($strings, @numbers) = str2float(' 78 -2.4E-6 0.0025 0xFF 077 0', ' 512E4 hello world', {ascii_float => 1})
 [@numbers]

 # [
 #          '78',
 #          '-2.4E-6',
 #          '0.0025',
 #          '255',
 #          '63',
 #          '0',
 #          '512E4'
 #        ]
 #

 ##################
 # str2float(' 78 -2.4E-6 0.0025 0xFF 077 0', ' 512E4 hello world', {ascii_float => 1}) @strings
 # 

 join( ' ', @$strings)

 # 'hello world'
 #
      my @test_strings = ('78 45 25', '512 1024 100000 hello world');
      my $test_string_text = join ' ',@test_strings;
      my $test_format = 'I';
      my $expected_format = 'U4';
      my $expected_numbers = '0000004e0000002d000000190000020000000400000186a0';
      my $expected_strings = ['hello world'];
      my $expected_unpack = [78, 45, 25, 512, 1024, 100000];

      my ($format, $numbers, @strings) = pack_num('I',@test_strings);

 ##################
 # pack_num(I, 78 45 25 512 1024 100000 hello world) format
 # 

 $format

 # 'U4'
 #

 ##################
 # pack_num(I, 78 45 25 512 1024 100000 hello world) numbers
 # 

 unpack('H*',$numbers)

 # '0000004e0000002d000000190000020000000400000186a0'
 #

 ##################
 # pack_num(I, 78 45 25 512 1024 100000 hello world) @strings
 # 

 [@strings]

 # [
 #          'hello world'
 #        ]
 #

 ##################
 # unpack_num(U4, 78 45 25 512 1024 100000 hello world) error check
 # 

 ref(my $unpack_numbers = unpack_num($expected_format,$numbers))

 # 'ARRAY'
 #

 ##################
 # unpack_num(U4, 78 45 25 512 1024 100000 hello world) numbers
 # 

 $unpack_numbers

 # [
 #          '78',
 #          '45',
 #          '25',
 #          '512',
 #          '1024',
 #          '100000'
 #        ]
 #

      @test_strings = ('78 4.5 .25', '6.45E10 hello world');
      $test_string_text = join ' ',@test_strings;
      $test_format = 'I';
      $expected_format = 'F8';
      $expected_numbers = '405380000000000040120000000000003fd0000000000000422e08ffca000000';
      $expected_strings = ['hello world'];
      my @expected_unpack = (
           '7.800000000000017486E1', 
           '4.500000000000006245E0',
           '2.5E-1',
           '6.4500000000000376452E10'
      );

      ($format, $numbers, @strings) = pack_num('I',@test_strings);

 ##################
 # pack_num(I, 78 4.5 .25 6.45E10 hello world) format
 # 

 $format

 # 'F8'
 #

 ##################
 # pack_num(I, 78 4.5 .25 6.45E10 hello world) numbers
 # 

 unpack('H*',$numbers)

 # '405380000000000040120000000000003fd0000000000000422e08ffca000000'
 #

 ##################
 # pack_num(I, 78 4.5 .25 6.45E10 hello world) @strings
 # 

 [@strings]

 # [
 #          'hello world'
 #        ]
 #

 ##################
 # unpack_num(F8, 78 4.5 .25 6.45E10 hello world) error check
 # 

 ref($unpack_numbers = unpack_num($expected_format,$numbers))

 # 'ARRAY'
 #

 ##################
 # unpack_num(F8, 78 4.5 .25 6.45E10 hello world) numbers
 # 

 $unpack_numbers

 # [
 #          '7.800000000000017486E1',
 #          '4.500000000000006245E0',
 #          '2.5E-1',
 #          '6.4500000000000376452E10'
 #        ]
 #

QUALITY ASSURANCE

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Running the test script SecsPack.t and SecsPackStress.t verifies the requirements for this module. The tmake.pl cover script for Test::STDmaker|Test::STDmaker automatically generated the SecsPack.t and SecsPackStress.t test scripts, the SecsPack.d and SecsPackStress.d demo scripts, and the t::Data::SecsPack and t::Data::SecsPackStress STD program module PODs, from the t::Data::SecsPack and t::Data::SecsPackStress program module's content. The t::Data::SecsPack and t::Data::SecsPackStress program modules are in the distribution file Data-SecsPack-$VERSION.tar.gz.

NOTES

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AUTHOR

The holder of the copyright and maintainer is

<support@SoftwareDiamonds.com>

Copyrighted (c) 2002 Software Diamonds

All Rights Reserved

BINDING REQUIREMENTS NOTICE

Binding requirements are indexed with the pharse 'shall[dd]' where dd is an unique number for each header section. This conforms to standard federal government practices, STD490A 3.2.3.6 (3.2.3.6 in Docs::US_DOD::STD490A). In accordance with the License, Software Diamonds is not liable for any requirement, binding or otherwise.

LICENSE

Software Diamonds permits the redistribution and use in source and binary forms, with or without modification, provided that the following conditions are met:

1

Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

2

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.

3

Commercial installation of the binary or source must visually present to the installer the above copyright notice, this list of conditions intact, that the original source is available at http://softwarediamonds.com and provide means for the installer to actively accept the list of conditions; otherwise, a license fee must be paid to Softwareware Diamonds.

SOFTWARE DIAMONDS, http://www.softwarediamonds.com, PROVIDES THIS SOFTWARE '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 SOFTWARE DIAMONDS 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 USE OF THIS SOFTWARE, EVEN IF ADVISED OF NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE POSSIBILITY OF SUCH DAMAGE.

SEE_ALSO:

Top

SEMI, http://www.semi.org
Math::BigInt
Math::BigFloat
Data::Secs2
Docs::Site_SVD::Data_SecsPack
Test::STDmaker
Data::Str2Num
Data-SecsPack documentation Contained in the Data-SecsPack distribution. 
#!perl
#
# The copyright notice and plain old documentation (POD)
# are at the end of this file.
#
package  Data::SecsPack;

use strict;
use 5.001;
use warnings;
use warnings::register;

use Math::BigInt 1.50 lib => 'GMP';
use Math::BigFloat 1.39;
use Data::Startup;
use Data::Str2Num 0.05;

use vars qw( $VERSION $DATE $FILE);
$VERSION = '0.08';
$DATE = '2004/05/21';
$FILE = __FILE__;

use vars qw(@ISA @EXPORT_OK);
require Exporter;
@ISA=('Exporter');
@EXPORT_OK = qw(bytes2int config float2binary 
                ifloat2binary int2bytes 
                pack_float pack_int pack_num  
                str2float  str2int
                unpack_float unpack_int unpack_num);

use vars qw($default_options);
$default_options = new Data::SecsPack;

#######
# Object used to set default, startup, options values.
#
sub new
{
   Data::Startup->new(
 
      ######
      # Make Test variables visible to tech_config
      #  
      big_int_version => Math::BigInt->config()->{'version'},
      big_float_version => $Math::BigFloat::VERSION,
      binary_fraction_bytes => 10,
      decimal_fraction_digits => 25,
      decimal_integer_digits => 20,
      die => 0,
      extra_decimal_fraction_digits => 5,
      version => $VERSION,
      warnings => 0,
   );

}

########
#
# use SelfLoader;
# 1
# __DATA__


###########
# Transform integer to bytes
#
sub bytes2int
{
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     my @integer_bytes = @_; # copy @_ so do not mangle @_
     return () unless @integer_bytes;
   
     my $integer = Math::BigInt->new('0');
     foreach (@integer_bytes) {   
         $integer->blsft(8); 
         $integer->bior($_); 
     }
     $integer->bstr();
}


######
# Provide a way to module wide configure
#
sub config
{
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     $default_options = Data::SecsPack->new() unless $default_options;
     $default_options->config(@_);
}


#####
#
#
sub float2binary
{ 
     my $event;
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     $default_options = Data::SecsPack->new() unless ref($default_options);
     unless(defined($_[0])) {
         $event = "No inputs\ntData::SecsPack::float2binary-1\n";
         goto EVENT;
     }

     my ($magnitude,$exponent,@options) = @_;
     my $options = $default_options->override(@options);

     (my $sign,$magnitude) = ($1,$2) if $magnitude =~ /^\s*([+-]?)\s*(\d+)/;
     $exponent = $1 if $exponent =~ /^\s*(\d+)/;
     unless(defined($magnitude) && defined($exponent)) {
         $event = "No inputs\ntData::SecsPack::float2binary-1\n";
         goto EVENT;
     }
     $sign = '' unless defined $sign;

     ########
     # Choose the exponent for the ifloat to minimize the float exponent.
     # For some floats, the entire conversion is done with straingth forward
     # integer arith multiplies, divides and shifts. There is a practical
     # resource limitation for large positive exponents. Limit the resources
     # to exponents under 20. 
     #
     my $ifloat_exponent = 0;
     if(0 < $exponent) {
         my $int_digits = $options->{decimal_integer_digits};
         $ifloat_exponent = ($exponent <= $int_digits) ? $exponent : $int_digits;
         $exponent -= $ifloat_exponent;
     }
     elsif( $exponent < 0) {
         my $frac_digits = $options->{extra_decimal_fraction_digits};
         $ifloat_exponent = ($exponent >= -$frac_digits) ? $exponent : -$frac_digits;
         $options->{decimal_fraction_digits} -= $ifloat_exponent * 2; # - - is a plus
         $exponent -= $ifloat_exponent;
     }

     ########
     # The decimal $integer and $fraction to binary simple float with the first byte
     # of the $binary_magnitude equal to 1 and the binary decimal point between the
     # first and second byte.
     #
     my ($binary_magnitude, $binary_exponent) = ifloat2binary($magnitude, $ifloat_exponent,$options);

     ############
     # Process big decimal exponents. Convert them into integer $exponent_binary_power
     # $exponent_binary_magnitude
     # 
     #
     # 10^$exp = 2^$bin_exp = $bin_exp = $exp * ln(10) / ln(2);
     #
     # ln(10) / ln(2) = 3.32192809488736
     #
     my $exponent_conversion_error;
     if($exponent) {

          ######
          # $exponent is integer while ln(10)/ln(2) has a 25 place fraction. These the resulting
          # integer also has 25 place fraction
          #
          my $exponent_binary_power = Math::BigInt->new($exponent)->bmul(33219280948873623478703194)->bstr();
          my $exponent_factor_magnitude = '0.' . substr($exponent_binary_power, -25, 25);
          $exponent_binary_power = substr($exponent_binary_power, 0,length($exponent_binary_power) - 25);
          $exponent_factor_magnitude = '-' . $exponent_factor_magnitude if ($exponent < 0);

          #################
          # Add the integer part to the exponent 
          # 
          $binary_exponent += $exponent_binary_power;

          #############
          # Determine the decimal float for the fractional base 2 exponent from converting
          # the base 10 exponent to a base 2 exponent. Adjust the signicant digits so
          # that they will not cause an overflow when converting to a binary exponent
          # using the ifloat2binary subroutine.
          # 
          $exponent_factor_magnitude = Math::BigFloat->new(2,$options->{decimal_fraction_digits})
                      ->bpow($exponent_factor_magnitude)->bstr();

          ########
          # Multiply the conversion from power of base 10 to base 2
          # fractional base2 exponent factor with the magnitude.
          # Both are binary floats.
          #
          my $exponent_factor_exponent = index($exponent_factor_magnitude,'.')-1;
          $exponent_factor_magnitude =~ s/\.//;

          ($exponent_factor_magnitude, $exponent_factor_exponent) = 
                 ifloat2binary($exponent_factor_magnitude, $exponent_factor_exponent,$options);

          #############
          # Float multipy the conversion correction and the magnitude
          # 
          ($binary_magnitude,$binary_exponent) = float_multiply( 
                      $binary_magnitude,$binary_exponent,
                      $exponent_factor_magnitude,$exponent_factor_exponent);

     }
     $binary_magnitude =~ s/^\+//;
     return ($sign . $binary_magnitude, $binary_exponent);

EVENT:
    if($options->{warnings} ) {
        warn($event);
    }
    elsif($options->{die}) {
        die($event);
    }
    return (undef,$event);
}


######
#
#
sub float_multiply
{
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);

     my ($magnitude1, $exponent1, $magnitude2, $exponent2) = @_;
     return (0,0) unless defined($magnitude1) && defined($exponent1) &&
                            defined($magnitude2) && defined($exponent2);

     $exponent1 += $exponent2;
     $magnitude1 = Math::BigInt->new($magnitude1)->bmul($magnitude2);

     #########
     # 1.[0-98888+] * 1.[0-99999+]   = [1.0-4.0]
     #
     # Test to see if the multiplication produce integer bits other than 1 and if
     # so move the binary decimal point so that the integer part is 1
     # 
     my @bytes = int2bytes($magnitude1);
     my $shift;
     if( $bytes[0] > 4 ) {
         $shift = 2;  # should not occure unless have terrible accuracy problem
     }
     elsif( $bytes[0] > 2) {
         $shift = 1;
     }
     if($shift) {
         $magnitude1 = Math::BigInt->new($magnitude1)->brsft($shift);
         $exponent1 += $shift;
     }

     ($magnitude1,$exponent1);
}



#####
#
#
sub ifloat2binary
{   
     my $event;
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     $default_options = Data::SecsPack->new() unless ref($default_options);
     unless(defined($_[0])) {
         $event = "No inputs\ntData::SecsPack::ifloat2binary-1\n";
         goto EVENT;
     }

     my ($magnitude,$exponent,@options) = @_;
     my $options = $default_options->override( @options);

     my $sign = $magnitude =~ s/^([+-])// ? $1 : '';
     unless(defined($magnitude) && defined($exponent)) {
         $event = "No inputs\ntData::SecsPack::ifloat2binary-1\n";
         goto EVENT;
     }
     $sign = '' unless defined $sign;

     ######
     # Break up the magnitude into integer and decimal parts
     #
     # Decimal point placed so one significant decimal digit
     # Move the decimal point to comply to the exponent;
     #
     $magnitude = $1 if $magnitude =~ /^\s*(\S+)/; # comments, leading, trailing white space
     $exponent = $1 if $exponent =~ /^\s*(\S+)/;
     my $decimal_fraction_digits =  $options->{decimal_fraction_digits}; 
     $decimal_fraction_digits = 30 unless $decimal_fraction_digits;  # Beyond quad accuracy
  
     $exponent++;
     my ($integer,$fraction) = (0,$magnitude);
     if(0 < $exponent) {
         if($exponent <= length($magnitude)) {
             $integer = substr($magnitude,0,$exponent);
             $fraction = substr($magnitude,$exponent);
         }
         else {
             $integer .= $magnitude . '0'x ($exponent-length($magnitude));
             $fraction = 0;
         }
     }
     elsif($exponent < 0) {
         $exponent = -$exponent;

         unless( $exponent <= ($decimal_fraction_digits/2) ) {
             $event = "The exponent, $exponent, is out of range for $magnitude.\n" .
                          "\tData::SecsPack::ifloat2binary-2\n";
             goto EVENT;
         }
                 ;
         $integer = 0;
         $fraction = ('0' x $exponent) . $fraction;
     }
     $fraction .= '0' x ($decimal_fraction_digits - length($fraction)) if $fraction;
        
     ########
     # Get the bytes of the integer.
     #
     my @integer_bytes = int2bytes($integer); # MSB first

     #######
     # Determine the bytes for the fraction
     #
     my @fraction_bytes = ();
     if($fraction) {
         my $max_bytes = $options->{binary_fraction_bytes};
         my $base_divider = '1' . '0' x $decimal_fraction_digits;
         $fraction =~ s/^\s*\.?//;  # strip any leadhing dots spaces
         $max_bytes = 8 unless $max_bytes;

         my ($i,$quo,$rem);
         $fraction = Math::BigInt->new($fraction);
         for($i=0; $i < $max_bytes; $i++) {
             $fraction->blsft(8);
             ($quo,$fraction) = $fraction->bdiv($base_divider);
             push @fraction_bytes,$quo->bstr();
             last if ($fraction->is_zero());
         } 
     }

     #######
     # Shift the binary decimal point so that the magnitude, $integer most
     # significant bit is 1
     # 
     while(@integer_bytes && $integer_bytes[0] == 0) {
         shift @integer_bytes;
     }
     while(@fraction_bytes && $fraction_bytes[-1] == 0) {
          pop @fraction_bytes;
     }

     #######
     # Move the binary decimal point so that the decimal point is just after
     # the first byte and the first byte has bits.
     #
     my $binary_exponent = 0;
     if(@integer_bytes) {
         $binary_exponent = (scalar @integer_bytes - 1) << 3;   
     }

     ########
     # Left Shift
     # 
     elsif(@fraction_bytes) {
         while( $fraction_bytes[0] == 0 ) {
             shift @fraction_bytes;
             $binary_exponent -= 8;
         }
     }

     #######
     # Shift right until the last bit of the first byte is 1
     # and all the leading bits are 0. The decimal point is
     # between the first and 2nd bytes.
     #
     my $shift = 0;
     if(@integer_bytes) {
         my $test_byte = $integer_bytes[0];
         while($test_byte && $test_byte ne 1) {
             $test_byte = $test_byte >> 1;
             $test_byte &= 0x7F; # case the shift is arith
             $shift++;
         }
         $binary_exponent += $shift;
          
     }
     else {
         my $test_byte = $fraction_bytes[0];
         while($test_byte && $test_byte ne 1) {
             $test_byte = $test_byte >> 1;
             $test_byte &= 0x7F; # case the shift is arith
             $shift++;
         }
         $binary_exponent += ($shift - 8);
          
     }

     #######
     # Add enough 0 to ensure do not drop bits into the bit bucket and enough
     # space for a extra or two right shifts.
     #
     my $binary_magnitude = bytes2int(@integer_bytes,@fraction_bytes,'0','0');
     $binary_magnitude = Math::BigInt->new($binary_magnitude)->brsft($shift) if $shift;
     $binary_magnitude =~ s/^\+//; # drop BigInt + sign
     return ($sign . $binary_magnitude, $binary_exponent);


EVENT:
    if($options->{warnings} ) {
        warn($event);
    }
    elsif($options->{die}) {
        die($event);
    }
    return (undef,$event);
}



###########
# Transform integer to bytes
#
sub int2bytes
{
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     my $integer = shift;
     return () unless $integer;
   
     #######
     # Break the integer up into byes
     # 
     my @integer_bytes = ();
    
     if ($integer == 0) {
         push @integer_bytes, 0;
     }
     elsif ($integer == -1) {
         push @integer_bytes, -1;
     }
     else { 
         my $byte;
         $integer = Math::BigInt->new($integer);
         while($integer->is_zero()  == 0  && $integer->bcmp(-1) != 0) {
             $byte = $integer->copy();   
             push @integer_bytes,$byte->band(0xFF)->bstr();
             $integer->brsft(8); 
         }
     }
     reverse @integer_bytes; # MSB first
}


#####
#
#
sub pack_float
{
     my $event;
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     $default_options = Data::SecsPack->new() unless ref($default_options);
     unless(defined($_[0])) {
         $event = "No inputs\ntData::SecsPack::pack_float-1\n";
         goto EVENT;
     }

     my $format = shift;
     my $options = ref($_[-1]) && ref($_[-1]) ne 'ARRAY' ? $default_options->override(pop @_) : $default_options;

     unless($format eq 'F4' || $format eq 'F8' || $format eq 'F') {
         $event = "Format $format is not a floating point format.\n\tData::SecsPack::pack_float-2\n";
         goto EVENT;
     }

     ######
     # Do not use $_ off a @_ array. If do, then modify
     # the input symbol in the calling subroutine name 
     # space. Very hard to predict the outcome.
     #
     my @string_float = @_;
     my @floats = ();
     my $bytes_per_cell = '4';
     my ($sign,$magnitude,$exponent_sign,$exponent);
     foreach (@string_float) {

         ($magnitude, $exponent) = float2binary( @$_, $options );
         return ($magnitude, $exponent) unless defined $magnitude; # error trap      

         if($format eq 'F') {

             #####
             # magnitude is decimal digits
             #
             if($exponent < -128 || $exponent > 128 || length($magnitude) > 10) {
                 $bytes_per_cell = 8;
             }

         }

         push @floats,[$magnitude,$exponent];

    }

    ######
    # Pack the floating points.
    #
    $format = $format . $bytes_per_cell if ($format eq 'F');
    my (@float_bytes);
    my $floats = '';
    my $exponent_excess;
    foreach  (@floats) {

         ($magnitude,$exponent) = @$_;
         $exponent = 0 unless $exponent;
         $exponent =~ s/^\+//;
         $sign = $magnitude =~ s/^([+-])// ? $1 : '';

         ########
         # Pack the sign, magitude(integer) and exponent
         # (Actually the machine dependent part. So here what can
         # do is something like File::Spec to support the different
         # platforms.)
         # 
         # Will be replacing the leading 1 of the magnitude with the sign
         # bit. Thus shift right one to get the magnitude to line up properly
         # for the F4, F8 IEEE format.
         #

         #########
         # Pack the exponent
         #
         if($format eq 'F4') {
             
             #######
             # There are sign bit and eight exp bits in front of
             # of the $magnitude. The first byte contains only a
             # 1 that need to be drop. Shifting one to the right
             # lines up the magitude, not counting the leading one
             # correctly
             #
             $magnitude = Math::BigInt->new($magnitude)->brsft(1)->bstr();
             @float_bytes = int2bytes($magnitude);
             unshift @float_bytes,0;

             #######
             # Using only four bytes
             # 
             while( @float_bytes < 4) {
                 push @float_bytes,0;
             }             

             ######
             # Zero out the leading sign and exponent fields.
             #  
             $float_bytes[0] &= 0x0;
             $float_bytes[1] &= 0x7F;

             ######
             # Or in the sign bit
             #                  
             $float_bytes[0] |= 0x80 if ($sign eq '-');

             ######
             # Or in the exponent
             # 
             $exponent_excess = 127 + $exponent;
             if(255 < $exponent_excess) {  # overflow
                 $event = "F4 exponent overflow\n\tData::SecsPack::pack_float-3\n";
                 goto EVENT;
             }
             if($exponent_excess < 0) {  # underflow
                 $event = "F4 exponent underflow\n\tData::SecsPack::pack_float-4\n";
                 goto EVENT;
             }
             if($magnitude == 0) {
                 $float_bytes[1] = 0;
                 $float_bytes[2] = 0;
                 $float_bytes[3] = 0;
             }
             else {
                 $float_bytes[1] |= ($exponent_excess & 0x01) << 7;
                 $float_bytes[0] |= ($exponent_excess >>1) & 0x7F;
             }
             $floats .= pack 'C4',@float_bytes;
         }             

         #######
         # F8 exponent is 11 bits 2^11 = 2048
         #
         else {

             $magnitude = Math::BigInt->new($magnitude)->brsft(4)->bstr();
             @float_bytes = int2bytes($magnitude);
             unshift @float_bytes,0;

             while( @float_bytes < 8) {
                 push @float_bytes,0;
             }             

             ######
             # Zero out the leading sign and exponent fields.
             #  
             $float_bytes[0] &= 0x00;
             $float_bytes[1] &= 0x0F;

             ######
             # Or in the sign bit
             #                  
             $float_bytes[0] |= 0x80 if ($sign eq '-');

             $exponent_excess = 1023 + $exponent;
             if(2048 < $exponent_excess) {  # overflow
                 $event = "F8 exponent overflow\n\tData::SecsPack::pack_float-5\n";
                 goto EVENT;
             }
             if($exponent_excess < 0) {  # underflow
                 $event = "F8 exponent underflow\n\tData::SecsPack::pack_float-6\n";
                 goto EVENT;
             }
             if($magnitude == 0) {
                 $float_bytes[1] = 0;
                 $float_bytes[2] = 0;
                 $float_bytes[3] = 0;
                 $float_bytes[4] = 0;
                 $float_bytes[5] = 0;
                 $float_bytes[6] = 0;
                 $float_bytes[7] = 0;
             }
             else {
                 $float_bytes[1] |= ($exponent_excess & 0x0F) << 4;
                 $float_bytes[0] |= ($exponent_excess >> 4) & 0x7F;
             }
             $floats .= pack 'C8',@float_bytes;
         }
     }
 
     return ($format, $floats);

EVENT:
    if($options->{warnings} ) {
        warn($event);
    }
    elsif($options->{die}) {
        die($event);
    }
    (undef,$event);
}




#####
# Pack a list of integers, twos complement, MSB first order.
# Assumming the native computer does two's arith.
#
sub pack_int
{
     my $event;
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     $default_options = Data::SecsPack->new() unless ref($default_options);
     unless(defined($_[0])) {
         $event = "No inputs\ntData::SecsPack::pack_int-1\n";
     }
     my $options = ref($_[-1]) ? $default_options->override(pop @_ ) : $default_options ;

     my $format = shift;
     my $format_length;
     ($format,$format_length) = $format =~ /([SUIT])(\d+)?/;
     unless($format && !($format eq 'T' && $format_length)) {
         $event = "Format $format is not an integer format.\ntData::SecsPack::pack_int-2\n";
     }

     ######
     # Do not use $_ off a @_ array. If do, then modify
     # the input symbol in the calling subroutine name 
     # space. Very hard to predict the outcome.
     #
     my @string_integer = @_;

     my @integers=();
     my ($max_bytes, $pos_range) = (0,0);
     my @bytes;
     my ($integer,$num_bytes);
     my $str_format = 'U';
     use integer;
     foreach (@string_integer) {
         $str_format = 'S' if Math::BigInt->new($_)->bcmp(0) < 0;
         if ($str_format eq 'S' && $format =~ /^U/) {
             $event = "Signed number encountered when unsigned specified.\ntData::SecsPack::pack_int-3\n";
         }
         if (Math::BigInt->new($_)->bcmp(0) == 0) {
             push @integers, [0];
             next;
         }
         if (Math::BigInt->new($_)->bcmp(-1) == 0) {
             push @integers, [0xFF];
             next;
         }
         @bytes = int2bytes($_);

         #######
         # Positive number in negative number range
         #
         if($str_format eq 'S' && Math::BigInt->new($_)->bcmp($pos_range) > 0) {
              my $i = $max_bytes;
              while($i--) {
                  unshift @bytes, '0';
              }           
         }
         $num_bytes = scalar(@bytes);
         if($max_bytes < $num_bytes) {
             $max_bytes = $num_bytes;
             if($str_format eq 'S') {
                 $pos_range = Math::BigInt->new(1)->blsft(($max_bytes << 3) - 1);
                 $pos_range = $pos_range->bdec()->bstr();
             }
         }
         push @integers, [@bytes];
     }
     unless(@integers) {
         $event = "No integers in the input.\ntData::SecsPack::pack_int-4\n";
     }

     ####
     # Round up the max length to the nearest power of 2 boundary.
     #
     if( $max_bytes  <= 1) {
         $max_bytes  = 1; 
     }
     elsif( $max_bytes  <= 2) {
         $max_bytes  = 2; 
     }
     elsif( $max_bytes  <= 4) {
         $max_bytes  = 4; 
     }
     elsif( $max_bytes  <= 8) {
         $max_bytes  = 8; 
     }
     else {
         return ("Integer or float out of SECS-II range.\n",undef);
     }
     if ($format_length) {
         if( $format_length < $max_bytes ) {
                 $event = "Integer bigger than format length of $max_bytes bytes.\ntData::SecsPack::pack_int-5\n";
         }
         $max_bytes  = $format_length;
     }

     $format = $str_format if $format eq 'I';
     my $signed = $format eq 'S' ? 1 : 0;
     my ($i, $fill, $length, $integers);
     foreach (@integers) {
         @bytes = @{$_};
         $length = $max_bytes - scalar @bytes;
         if($length) {
             $fill =  $signed && $bytes[0] >= 128 ? 0xFF : 0;
             for($i=0; $i< $length; $i++) {
                 unshift @bytes,$fill;
             }
         }
         $integers .= pack ("C$max_bytes",  @bytes);
     }
     $format .= $max_bytes;
     no integer;

     return ($format, $integers);

EVENT:
   if($options->{warnings} ) {
       warn($event);
   }
   elsif($options->{die}) {
       die($event);
   }
   (undef,$event);
   
}


#####
#  Pack a list of integers, twos complement, MSB first order.
#  Assumming the native computer does two's arith.
#
sub pack_num
{
     my $event;
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     $default_options = Data::SecsPack->new() unless ref($default_options);
     unless(defined($_[0])) {
         $event = "No inputs\ntData::SecsPack::float2binary-1\n";
         goto EVENT;
     }
     my $options = ref($_[-1]) ? $default_options->override(pop @_ ) : $default_options ;

     my $format = shift;
     ($format, my $format_length) = $format =~ /([FSUIT])(\d)?/;
     unless($format) {
         my $event = "Format $format is not an integer or floating point format.\ntData::SecsPack::pack_num-2\n";
         goto EVENT;
     }

     my ($str,@nums,$nums);
     if($format =~ /^F/) {
         ($str, @nums) = Data::Str2Num->str2float(@nums, $str);
         $nums = pack_float($format, @nums, $options);  
     }
     else {
         ($str, @nums) = Data::Str2Num->str2integer(@_);
         my $format_hint = $format;
         ($format, $nums) = pack_int($format, @nums, $options) if @nums;

         if($format_hint eq 'I') {
             if((!$options->{nomix} && @$str != 0 && ${$str}[0] =~ /^\s*-?\s*\d+[\.E]/) ||
                     0 == @nums) {
                 my ($float_str, @float_nums) = Data::Str2Num->str2float(@nums, @$str);
                 if(@float_nums) {
                     my ($float_format,$float_nums) = pack_float('F', @float_nums, $options);
                     if( $float_format && $float_format =~ /^F/ &&  $float_nums) {
                         $format = $float_format;
                         $nums = $float_nums;
                         $str = $float_str;
                     }
                 }
                 else {
                     $event = "No numbers in the input.\ntData::SecsPack::pack_num-3\n";
                     goto EVENT;
                 }
             }
         } 
     }
     return ($format,$nums,@$str);

EVENT:
    if($options->{warnings} ) {
        warn($event);
    }
    elsif($options->{die}) {
        die($event);
    }
    (undef,$event);

}



######
# Covert a string to floats.
#
sub str2float 
{ 
    shift if UNIVERSAL::isa($_[0],__PACKAGE__);
    Data::Str2Num->str2float(@_)
}


######
# Convert number (oct, bin, hex, decimal) to decimal
#
sub str2int 
{ 
    shift if UNIVERSAL::isa($_[0],__PACKAGE__);
    Data::Str2Num->str2integer(@_) 
}

#####
#  Unpack a list of floats, IEEC 754-1985, sign bit first.
#
sub unpack_float
{
     my $event;
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     unless(defined($_[0])) {
         $event = "No inputs\ntData::SecsPack::float2binary-1\n";
         goto EVENT;
     }

     my $format_in = shift;
     unless($format_in eq 'F4' || $format_in eq 'F8') {
         $event = "Format $format_in not supported.\n\tData::SecsPack::unpack_float-2\n";
         goto EVENT;
     }
     my ($format, $format_length) = $format_in =~ /(F)(\d)?/;
     my (@bytes,$float);
     my @floats = ();
     my ($binary_magnitude,$sign,$binary_exponent,$decimal_magnitude,$decimal_exponent,$binary_divider);
     my $secsii_floats = shift @_;

     $default_options = Data::SecsPack->new() unless ref($default_options);
     my $options = $default_options->override(@_);

     while ($secsii_floats) {
         @bytes = unpack "C$format_length",$secsii_floats;
         $secsii_floats = substr($secsii_floats,$format_length);
         $sign = $bytes[0] & 0x80 ? '-' : '';
         $bytes[0] &= 0x7F;
         if($format_length == 4) {
             $binary_exponent = (bytes2int($bytes[0],$bytes[1]) >> 7) - 127;
             shift @bytes;
             $bytes[0] &= 0x7F;
             $binary_magnitude = bytes2int(@bytes);
             $binary_magnitude <<= 1;
             $binary_divider =  2 ** 24; # decode into 3 bytes, not 23 bits

         }
         else {
             $binary_exponent = (bytes2int($bytes[0],$bytes[1]) >> 4) - 1023;
             shift @bytes;
             $bytes[0] &= 0x0F;
             $binary_magnitude = bytes2int(@bytes);
             $binary_magnitude = Math::BigInt->new($binary_magnitude)->blsft(4);
             $binary_divider = '72057594037927036';  # 2 ** 56  -  bytes integer too big for Perl
         }

         if($binary_magnitude) {
             $decimal_magnitude = $binary_magnitude . '0'x20; # twenty digit decimal results
             $decimal_magnitude = Math::BigInt->new(bytes2int($decimal_magnitude))->bdiv($binary_divider)->bstr();
         }
         else {
             $decimal_magnitude = 0;
         }

         #########
         # Let Perl do the arith, doing an automatic convert to float if needed.
         # The accuracy suffers again if Perl must convert to float to get the answer.
         #  
         $float = Math::BigFloat->new(2,20)->bpow($binary_exponent)->bmul("${sign}1.$decimal_magnitude")->bsstr();
         ($sign,$decimal_magnitude,$decimal_exponent) = $float =~ /([-+]?)(\d+)E([-+]?\d+)/i;
         $sign = '' unless $sign;
         $decimal_exponent += length($decimal_magnitude) - 1;
         $float = $sign . substr($decimal_magnitude,0,1) . '.' . substr($decimal_magnitude,1) . 'E' . $decimal_exponent;
         push @floats, $float;

     }
     no integer;
     return \@floats;

EVENT:
    if($options->{warnings} ) {
        warn($event);
    }
    elsif($options->{die}) {
        die($event);
    }
    $event;
}


#####
#  Unpack a list of integers, twos complement, MSB first order.
#  Assumming the native computer does two's arith.
#
sub unpack_int
{
     my $event;
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     unless(defined($_[0])) {
         $event = "No inputs\ntData::SecsPack::float2binary-1\n";
         goto EVENT;
     }

     my $format_in = shift;
     unless($format_in =~ /(T|U1|U2|U4|U8|S1|S2|S4|S8)/) {
         $event = "Format $format_in not supported.\n\tData::SecsPack::unpack_int-2\n";
         goto EVENT;
     }
     my ($format, $format_length) = $format_in =~ /([TSU])(\d)?/;
     $format_length = 1 if $format eq 'T';
     my $signed = $format =~ /S/ ? 1 : 0;
     my ($twos_complement, @bytes, $int);
     my @integers = ();
     my $secsii_ints = shift @_;

     $default_options = Data::SecsPack->new() unless ref($default_options);
     my $options = $default_options->override(@_);

     if($signed) {
         $twos_complement = Math::BigInt->new(1)->blsft($format_length << 3);
     }
     while ($secsii_ints) {
         @bytes = unpack "C$format_length",$secsii_ints;
         $secsii_ints = substr($secsii_ints,$format_length);
         $int = bytes2int(@bytes);
         if($signed) {
             if(128 <= $bytes[0]) {       
                 $int = Math::BigInt->new($int)->bsub($twos_complement)->bstr();
             }
         }         
         push @integers, $int;
     }
     return \@integers;

EVENT:
    if($options->{warnings} ) {
        warn($event);
    }
    elsif($options->{die}) {
        die($event);
    }
    return ($event);

}


#####
#  Unpack a list of numbers, twos complement, MSB first order.
#  Assumming the native computer does two's arith.
#
sub unpack_num
{
     shift if UNIVERSAL::isa($_[0],__PACKAGE__);
     $default_options = Data::SecsPack->new() unless ref($default_options);
     my $options = ref($_[-1]) ? $default_options->override(pop @_) : $default_options;
     return unpack_float(@_, $options) if($_[0] =~ /^F/);
     unpack_int(@_, $options);
}


1

__END__



### end of script  ######