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1 2 ============================================================================ 3 This file describes the format of the internal representation 4 of an MAPM number in the M_APM data structure 5 M. Ring Nov 10, 2002 6 ============================================================================ 7 8 struct M_APM_struct { 9 UCHAR *m_apm_data; 10 long m_apm_id; 11 int m_apm_refcount; 12 int m_apm_malloclength; 13 int m_apm_datalength; 14 int m_apm_exponent; 15 int m_apm_sign; 16 }; 17 18 19 The internal representation of the number is in base 100. Each byte in 20 'm_apm_data' can store the values 0-99 (out of a possible 0-255). All 21 numbers mentioned here will be in decimal unless otherwise noted. Base 100 22 was used since that is the largest power of 10 that will fit in one byte. 23 A base that is a power of 10 was chosen since it is real convienent when 24 translating to/from the internal format. 25 26 All math operations will result in a 'normalized' number. In this context, 27 normalized means 2 things; the first nibble of the first byte of data will 28 be non-zero, and all trailing zero's will be ignored. As an example, 25 * 4 29 would normally yield 100, or the digits '1', '0', '0' an have a 'datalength' 30 of 3. Since the trailing zeros carry no information, the datalength will 31 simply be truncated to 1. Note that this assumes the exponent is adjusted 32 accordingly, which we of course do. 33 34 The decimal point of the number is implied to be before the first byte of 35 data. See the examples below. 36 37 'm_apm_data' : An array to hold the digits. The byte at offset 0 will 38 contain the the first 2 (base 10) digits of the number 39 (or 1 base 100 digit), the next byte will contain the 40 3rd and 4th digits, etc. If the number has an odd 41 number of digits, the least significant nibble in the 42 last byte of data will be 0. 43 44 'm_apm_id' : Set during m_apm_init to M_APM_IDENT. Used to 45 validate the structure before the call to 'free'. 46 47 'm_apm_refcount' : NOT used by the basic M_APM. It was added to support 48 the C++ MAPM wrapper class. (However, we do initialize 49 this element to 1). 50 51 'm_apm_malloclength' : Keeps track of how many bytes were allocated in the 52 malloc call to m_apm_data. If a given math operation 53 will yield a result that won't fit into the existing 54 m_apm_data array, we will realloc m_apm_data so it 55 will be guaranteed to hold the result. 56 57 'm_apm_datalength' : The number of base 10 digits in the number. In other 58 words, the number 5678 will have a datalength of 4 59 (which will fit into 2 bytes). The number 1234567 will 60 have a datalength of 7 (which requires 4 bytes to 61 store). 62 63 'm_apm_exponent' : The exponent of the number, can be up to sizeof(int) 64 65 'm_apm_sign' : The sign of the number. sign = -1 is a negative 66 number. sign = +1 is a positive number. sign = 0 is 67 a number that is exactly 0. This feature is used 68 extensively in the library for fast comparisons to 0. 69 70 -------- 71 Examples 72 -------- 73 74 number sign datalength exponent data: [byte 0,1,2, etc] 75 ----------------------------------------------------------------------- 76 0 0 1 0 00 77 78 4.0 +1 1 +1 40 (data = 28h) 79 80 -0.07 -1 1 -1 70 (data = 46h) 81 82 31.6 +1 3 +2 31, 60 (data = 1Fh, 3Ch) 83 84 -52338.226 -1 8 +5 52, 33, 82, 26 85 86 0.0007621 +1 4 -3 76, 21 87 88 3.75900064E+18 +1 9 +19 37, 59, 00, 06, 40 89 90 -6.1289E-7 -1 5 -6 61, 28, 90 91 92 0.872394 +1 6 0 87, 23, 94 93