struct.ref

任意精度的数学库

============================================================================
          This file describes the format of the internal representation 
	  of an MAPM number in the M_APM data structure
          M. Ring   June 1, 1999
============================================================================

struct  M_APM_struct {
	long	m_apm_id;
	int	m_apm_malloclength;
	int	m_apm_datalength;
	int	m_apm_exponent;
	int	m_apm_sign;
	UCHAR	*m_apm_data;
};


The internal representation of the number is in base 100. Each byte in 
'm_apm_data' can store the values 0-99 (out of a possible 0-255). All 
numbers mentioned here will be in decimal unless otherwise noted. Base 100
was used since that is the largest power of 10 that will fit in one byte.
A base that is a power of 10 was chosen since it is real convienent when 
translating to/from the internal format.

All math operations will result in a 'normalized' number. In this context,
normalized means 2 things; the first nibble of the first byte of data will
be non-zero, and all trailing zero's will be ignored. As an example, 25 * 4
would normally yield 100, or the digits '1', '0', '0' an have a 'datalength'
of 3. Since the trailing zeros carry no information, the datalength will
simply be truncated to 1. Note that this assumes the exponent is adjusted
accordingly, which we of course do.

The decimal point of the number is implied to be before the first byte of
data. See the examples below.


'm_apm_id'            : Set during m_apm_init to M_APM_IDENT. Used to 
			validate the structure before the call to 'free'.

'm_apm_malloclength'  : Keeps track of how many bytes were allocated in the
			malloc call to m_apm_data. If a given math operation
			will yield a result that won't fit into the existing
			m_apm_data array, we will realloc m_apm_data so it 
			will be guaranteed to hold the result.

'm_apm_datalength'    : The number of base 10 digits in the number. In other
			words, the number 5678 will have a datalength of 4
			(which will fit into 2 bytes). The number 1234567 will
			have a datalength of 7 (which requires 4 bytes to
			store).

'm_apm_exponent'      : The exponent of the number, can be up to sizeof(int)

'm_apm_sign'          : The sign of the number. sign = -1 is a negative 
			number. sign = +1 is a positive number. sign = 0 is 
			a number that is exactly 0. This feature is used 
			extensively in the library for fast comparisons to 0.

'm_apm_data'          : An array to hold the digits. The byte at offset 0 will
			contain the the first 2 digits of the number, the next
			byte will contain the 3rd and 4th digits, etc. If the 
			number has an odd number of digits, the least 
			significant nibble in the last byte of data will be 0.

--------
Examples
--------

number          sign  datalength  exponent  data: [byte 0,1,2, etc]
-----------------------------------------------------------------------
0                 0       1           0     00

4.0              +1       1          +1     40       (data = 28h)

-0.07            -1       1          -1     70       (data = 46h)

31.6             +1       3          +2     31, 60   (data = 1Fh, 3Ch)

-52338.226       -1       8          +5     52, 33, 82, 26  

0.0007621        +1       4          -3     76, 21

3.75900064E+18   +1       9         +19     37, 59, 00, 06, 40

-6.1289E-7       -1       5          -6     61, 28, 90

0.872394         +1       6           0     87, 23, 94