BcdUnit: what changed

Revision 1 to 2. Removed lines have a minus sign; added lines have a plus sign.

Old	New		Line
1	1		## Welcome
2	2
3	3		Welcome to information page about FMTBcd. Goal of this page is to contain information needed for implementing FPC version of the FMTBcd.
4	4
5	5		------------------------------------------------------------------------
6	6
7	7		FMTBcd unit defines a number of binary-coded decimal (BCD) routines:
8	8
9	9		## Types
10	10
11		-	~~`TBcd = packed record`\~~
12		-	~~` Precision: Byte;`\~~
13		-	~~` SignSpecialPlaces: Byte;`\~~
14		-	~~` Fraction: packed array [0..31] of Byte;`\~~
15		-	~~` end;`~~
	11	+	``` pascal
	12	+	TBcd = packed record
	13	+	Precision: Byte;
	14	+	SignSpecialPlaces: Byte;
	15	+	Fraction: packed array [0..31] of Byte;
	16	+	end;
	17	+	```
16	18
17		-	~~`PBcd: pointer to TBcd`~~
	19	+	```
	20	+	PBcd: pointer to TBcd
	21	+	```
18	22
19	23		### Precision
20	24
21	25		Precision states how many decimal digits are valid out of the 64 nibbles available for use.
22	26
23	27		### SignSpecialPlaces
24	28
25	29		SignSpecialPlaces is three fields packed into a byte.
26	30
27	31		- The first bit is the sign (bit value 128).
28	32		- The second bit is 'Special' (So special, I can't work out what it's for).
29	33		- The third - eights bits contain the number of decimals (less the number of default digits???). 6 bits gives us up to 32 digits.
30	34
31	35		### Fraction
32	36
33	37		array of BCD Nibbles, 00..99 per Byte, high Nibble 1st
34	38
35	39		Can anybody correct the following test cases?
36	40
37	41
38	42
39	43		What do you mean by 'correct'?
40	44
41	45		## test cases
42	46
43	47		### integers
44	48
45	49		If you look at a Tbdc record in the debugger, it will display the Precision as an integer, the SignSpecialPlaces as an interger and the Fraction as an array of integers. The fraction parts of the TBCD are really arrays of nibbles - one nibble per digit, two per byte. Following are some 'debug displays' and their translations. There is a space between bytes. So...
46	50
47	51		zero is boring...
48	52
49		-	~~` 0 -> (Precision: 0;SignSpecialPlaces: 0; Fraction:(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`~~
	53	+	```
	54	+	0 -> (Precision: 0;SignSpecialPlaces: 0; Fraction:(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	55	+	```
50	56
51	57		1..3
52	58
53		-	~~` 1 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
54		-	~~` 1 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(1,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	59	+	```
	60	+	1 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	61	+	1 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(1,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	62	+	```
55	63
56		-	~~` 2 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
57		-	~~` 2 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(2,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	64	+	```
	65	+	2 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(32,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	66	+	2 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(2,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	67	+	```
58	68
59		-	~~` 3 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
60		-	~~` 3 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(3,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	69	+	```
	70	+	3 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(48,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	71	+	3 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(3,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	72	+	```
61	73
62		-	~~`etc...`\~~
63		-	~~` 4 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
64		-	~~` 5 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(80,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
65		-	~~` 6 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(96,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
66		-	~~` 7 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(112,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
67		-	~~` 8 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
68		-	~~` 9 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(144,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`~~
	74	+	```
	75	+	etc...
	76	+	4 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	77	+	5 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(80,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	78	+	6 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(96,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	79	+	7 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(112,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	80	+	8 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(128,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	81	+	9 -> (Precision: 1;SignSpecialPlaces: 0; Fraction:(144,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	82	+	```
69	83
70	84		10 - note: the fractional part is the same as for 1, the precision is now 2. i.e. 10 = 1 * 10^2
71	85
72		-	~~` 10 -> (Precision: 2;SignSpecialPlaces: 0; Fraction:(16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
73		-	~~` 10 -> (Precision: 2;SignSpecialPlaces: 0; Fraction:(1,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	86	+	```
	87	+	10 -> (Precision: 2;SignSpecialPlaces: 0; Fraction:(16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	88	+	10 -> (Precision: 2;SignSpecialPlaces: 0; Fraction:(1,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	89	+	```
74	90
75	91		100 - note: the fractional part is the same as for 1, the precision is now 3. i.e. 10 = 1 * 10^3
76	92
77		-	~~` 100 -> (Precision: 3;SignSpecialPlaces: 0; Fraction:(16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
78		-	~~` 100 -> (Precision: 2;SignSpecialPlaces: 0; Fraction:(1,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`\~~
79		-	~~`etc`\~~
80		-	~~` 1000 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
81		-	~~` 1000 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(1,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	93	+	```
	94	+	100 -> (Precision: 3;SignSpecialPlaces: 0; Fraction:(16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	95	+	100 -> (Precision: 2;SignSpecialPlaces: 0; Fraction:(1,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	96	+	etc
	97	+	1000 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	98	+	1000 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(1,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	99	+	```
82	100
83	101		some more interesting cases:
84	102
85		-	~~` 1111 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(17,17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
86		-	~~` 1111 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(1,1, 1,1, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	103	+	```
	104	+	1111 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(17,17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	105	+	1111 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(1,1, 1,1, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	106	+	```
87	107
88		-	~~` 1234 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(18,52,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
89		-	~~` 1234 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(1,2, 3,4, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	108	+	```
	109	+	1234 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(18,52,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	110	+	1234 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(1,2, 3,4, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	111	+	```
90	112
91		-	~~` -5 -> (Precision: 1;SignSpecialPlaces: 128;Fraction:(80,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
92		-	~~` -5 -> (Precision: 1;SignSpecialPlaces: 128;Fraction:(5,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,... `~~
	113	+	```
	114	+	-5 -> (Precision: 1;SignSpecialPlaces: 128;Fraction:(80,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	115	+	-5 -> (Precision: 1;SignSpecialPlaces: 128;Fraction:(5,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	116	+	```
93	117
94		-	~~` -6 -> (Precision: 1;SignSpecialPlaces: 128;Fraction:(96,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
95		-	~~` -6 -> (Precision: 1;SignSpecialPlaces: 128;Fraction:(6,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,... `~~
	118	+	```
	119	+	-6 -> (Precision: 1;SignSpecialPlaces: 128;Fraction:(96,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	120	+	-6 -> (Precision: 1;SignSpecialPlaces: 128;Fraction:(6,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	121	+	```
96	122
97		-	~~` 9999 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(153,153,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
98		-	~~` 9999 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(9,9, 9,9, 9,9, 9,9, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,... `~~
	123	+	```
	124	+	9999 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(153,153,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	125	+	9999 -> (Precision: 4;SignSpecialPlaces: 0; Fraction:(9,9, 9,9, 9,9, 9,9, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	126	+	```
99	127
100		-	~~` -9999 -> (Precision: 4;SignSpecialPlaces: 128;Fraction:(153,153,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
101		-	~~` -9999 -> (Precision: 4;SignSpecialPlaces: 128; Fraction:(9,9, 9,9, 9,9, 9,9, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,... `~~
	128	+	```
	129	+	-9999 -> (Precision: 4;SignSpecialPlaces: 128;Fraction:(153,153,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	130	+	-9999 -> (Precision: 4;SignSpecialPlaces: 128; Fraction:(9,9, 9,9, 9,9, 9,9, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	131	+	```
102	132
103	133		Displaying the structure in HEX helps...(you should never see any hex digits in the fraction part - only 0..9 is used)
104	134
105		-	~~` 32767 -> (Precision: 5;SignSpecialPlaces: 0; Fraction:($32,$76,$70,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
106		-	~~` 32767 -> (Precision: 5;SignSpecialPlaces: 0; Fraction:(3,2, 7,6, 70,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	135	+	```
	136	+	32767 -> (Precision: 5;SignSpecialPlaces: 0; Fraction:($32,$76,$70,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	137	+	32767 -> (Precision: 5;SignSpecialPlaces: 0; Fraction:(3,2, 7,6, 70,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	138	+	```
107	139
108		-	~~` -32768 -> (Precision: 5;SignSpecialPlaces: 128;Fraction:($32,$76,$80,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
109		-	~~` -32768 -> (Precision: 5;SignSpecialPlaces: 128;Fraction:(3,2, 7,6, 80,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	140	+	```
	141	+	-32768 -> (Precision: 5;SignSpecialPlaces: 128;Fraction:($32,$76,$80,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	142	+	-32768 -> (Precision: 5;SignSpecialPlaces: 128;Fraction:(3,2, 7,6, 80,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	143	+	```
110	144
111		-	~~` 2147483647 -> (Precision:10;SignSpecialPlaces: 0; Fraction:($21,$47,$48,$36,$47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
112		-	~~` 2147483647 -> (Precision:10;SignSpecialPlaces: 0; Fraction:(2,1, 4,7, 4,8, 3,6, 4,7, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	145	+	```
	146	+	2147483647 -> (Precision:10;SignSpecialPlaces: 0; Fraction:($21,$47,$48,$36,$47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	147	+	2147483647 -> (Precision:10;SignSpecialPlaces: 0; Fraction:(2,1, 4,7, 4,8, 3,6, 4,7, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	148	+	```
113	149
114		-	~~` -2147483647 -> (Precision:10;SignSpecialPlaces: 128;Fraction:($21,$47,$48,$36,$47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))`\~~
115		-	~~` -2147483647 -> (Precision:10;SignSpecialPlaces: 128;Fraction:(2,1, 4,7, 4,8, 3,6, 4,7, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...`~~
	150	+	```
	151	+	-2147483647 -> (Precision:10;SignSpecialPlaces: 128;Fraction:($21,$47,$48,$36,$47,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0))
	152	+	-2147483647 -> (Precision:10;SignSpecialPlaces: 128;Fraction:(2,1, 4,7, 4,8, 3,6, 4,7, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0, 0,0,...
	153	+	```
116	154
117	155		### floats
118	156
119		-	~~` -0.01234567 -> (Precision:8; SignSpecialPlaces: 136 {$80+8} Fraction: ( 1,35,69,103, ... 0,0)`~~
	157	+	```
	158	+	-0.01234567 -> (Precision:8; SignSpecialPlaces: 136 {$80+8} Fraction: ( 1,35,69,103, ... 0,0)
	159	+	```
120	160
121	161		## Const
122	162
123		-	~~` NullBcd: TBcd = (Precision: 0; SignSpecialPlaces: 0; Fraction:(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0));`~~
	163	+	```
	164	+	NullBcd: TBcd = (Precision: 0; SignSpecialPlaces: 0; Fraction:(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0));
	165	+	```
124	166
125	167		it's a zero (according to Delphi documentation: "Use NullBcd to indicate an unknown or missing TBcd value. NullBcd is a TBcd with all its fields set to 0. ")
126	168
127	169		## Exceptions
128	170
129		-	~~` EBcdException, EBcdOverflowException`~~
	171	+	```
	172	+	EBcdException, EBcdOverflowException
	173	+	```
130	174
131	175		??
132	176
133		-	~~` EBcdException = Class(Exception);`\~~
134		-	~~` EBcdOverflowException = Class(Exception);`~~
	177	+	```
	178	+	EBcdException = Class(Exception);
	179	+	EBcdOverflowException = Class(Exception);
	180	+	```
135	181
136	182		## Utility
137	183
138		-	~~` function BcdPrecision(const Bcd: TBcd): Word;`\~~
139		-	~~` function BcdScale(const Bcd: TBcd): Word;`\~~
140		-	~~` function IsBcdNegative(const Bcd: TBcd): Boolean;`~~
	184	+	``` pascal
	185	+	function BcdPrecision(const Bcd: TBcd): Word;
	186	+	function BcdScale(const Bcd: TBcd): Word;
	187	+	function IsBcdNegative(const Bcd: TBcd): Boolean;
	188	+	```
141	189
142	190		??
143	191
144	192		## Arithmetic
145	193
146		-	~~` procedure BcdAdd(const bcdIn1, bcdIn2: TBcd; var bcdOut: TBcd);`\~~
147		-	~~` procedure BcdSubtract(const bcdIn1, bcdIn2: TBcd; var bcdOut: TBcd);`\~~
148		-	~~` function NormalizeBcd(const InBcd: TBcd; var OutBcd: TBcd; const Prec, Scale: Word): Boolean;`~~
	194	+	``` pascal
	195	+	procedure BcdAdd(const bcdIn1, bcdIn2: TBcd; var bcdOut: TBcd);
	196	+	procedure BcdSubtract(const bcdIn1, bcdIn2: TBcd; var bcdOut: TBcd);
	197	+	function NormalizeBcd(const InBcd: TBcd; var OutBcd: TBcd; const Prec, Scale: Word): Boolean;
	198	+	```
149	199
150	200		Returns True if successful, False if Int Digits needed to be truncated
151	201
152		-	~~` procedure BcdMultiply(const bcdIn1, bcdIn2: TBcd; var bcdOut: TBcd); overload;`\~~
153		-	~~` procedure BcdMultiply(const bcdIn: TBcd; const DoubleIn: Double; var bcdOut: TBcd); overload;`\~~
154		-	~~` procedure BcdMultiply(const bcdIn: TBcd; const StringIn: string; var bcdOut: TBcd); overload;`\~~
155		-	~~` procedure BcdMultiply(StringIn1, StringIn2: string; var bcdOut: TBcd); overload;`\~~
156		-	~~` procedure BcdDivide(Dividend, Divisor: string; var bcdOut: TBcd); overload;`\~~
157		-	~~` procedure BcdDivide(const Dividend, Divisor: TBcd; var bcdOut: TBcd); overload;`\~~
158		-	~~` procedure BcdDivide(const Dividend: TBcd; const Divisor: Double; var bcdOut: TBcd); overload;`\~~
159		-	~~` procedure BcdDivide(const Dividend: TBcd; const Divisor: string; var bcdOut: TBcd); overload;`~~
	202	+	``` pascal
	203	+	procedure BcdMultiply(const bcdIn1, bcdIn2: TBcd; var bcdOut: TBcd); overload;
	204	+	procedure BcdMultiply(const bcdIn: TBcd; const DoubleIn: Double; var bcdOut: TBcd); overload;
	205	+	procedure BcdMultiply(const bcdIn: TBcd; const StringIn: string; var bcdOut: TBcd); overload;
	206	+	procedure BcdMultiply(StringIn1, StringIn2: string; var bcdOut: TBcd); overload;
	207	+	procedure BcdDivide(Dividend, Divisor: string; var bcdOut: TBcd); overload;
	208	+	procedure BcdDivide(const Dividend, Divisor: TBcd; var bcdOut: TBcd); overload;
	209	+	procedure BcdDivide(const Dividend: TBcd; const Divisor: Double; var bcdOut: TBcd); overload;
	210	+	procedure BcdDivide(const Dividend: TBcd; const Divisor: string; var bcdOut: TBcd); overload;
	211	+	```
160	212
161	213		## Creation
162	214
163		-	~~` procedure VarFMTBcdCreate(var ADest: Variant; const ABcd: TBcd); overload;`\~~
164		-	~~` function VarFMTBcdCreate: Variant; overload;`\~~
165		-	~~` function VarFMTBcdCreate(const AValue: string; Precision, Scale: Word):Variant; overload;`\~~
166		-	~~` function VarFMTBcdCreate(const AValue: Double; Precision: Word; Scale: Word ): Variant; overload;`\~~
167		-	~~` function VarFMTBcdCreate(const ABcd: TBcd): Variant; overload;`\~~
168		-	~~` function VarIsFMTBcd(const AValue: Variant): Boolean; overload;`\~~
169		-	~~` function VarFMTBcd: TVarType;`~~
	215	+	``` pascal
	216	+	procedure VarFMTBcdCreate(var ADest: Variant; const ABcd: TBcd); overload;
	217	+	function VarFMTBcdCreate: Variant; overload;
	218	+	function VarFMTBcdCreate(const AValue: string; Precision, Scale: Word):Variant; overload;
	219	+	function VarFMTBcdCreate(const AValue: Double; Precision: Word; Scale: Word ): Variant; overload;
	220	+	function VarFMTBcdCreate(const ABcd: TBcd): Variant; overload;
	221	+	function VarIsFMTBcd(const AValue: Variant): Boolean; overload;
	222	+	function VarFMTBcd: TVarType;
	223	+	```
170	224
171	225		## Conversions
172	226
173		-	~~` StrToBcd, TryStrToBcd, DoubleToBcd, DoubleToBcd, IntegerToBcd,`\~~
174		-	~~` VarToBcd, CurrToBCD, BcdToStr, BcdToDouble, BcdToInteger,`\~~
175		-	~~` BCDToCurr, BcdToStrF, FormatBcd, BcdCompare`~~
	227	+	```
	228	+	StrToBcd, TryStrToBcd, DoubleToBcd, DoubleToBcd, IntegerToBcd,
	229	+	VarToBcd, CurrToBCD, BcdToStr, BcdToDouble, BcdToInteger,
	230	+	BCDToCurr, BcdToStrF, FormatBcd, BcdCompare
	231	+	```
176	232
177	233		### to BCD
178	234
179	235		Convert String/Double/Integer to BCD struct
180	236
181		-	~~` function StrToBcd(const AValue: string): TBcd;`\~~
182		-	~~` function TryStrToBcd(const AValue: string; var Bcd: TBcd): Boolean;`\~~
183		-	~~` function DoubleToBcd(const AValue: Double): TBcd; overload;`\~~
184		-	~~` procedure DoubleToBcd(const AValue: Double; var bcd: TBcd); overload;`\~~
185		-	~~` function IntegerToBcd(const AValue: Longint): TBcd;`\~~
186		-	~~` function VarToBcd(const AValue: Variant): TBcd;`\~~
187		-	~~` function CurrToBCD(const Curr: Currency; var BCD: TBcd; Precision: Integer; Decimals: Integer): Boolean;`\~~
188		-	~~` `~~
	237	+	``` pascal
	238	+	function StrToBcd(const AValue: string): TBcd;
	239	+	function TryStrToBcd(const AValue: string; var Bcd: TBcd): Boolean;
	240	+	function DoubleToBcd(const AValue: Double): TBcd; overload;
	241	+	procedure DoubleToBcd(const AValue: Double; var bcd: TBcd); overload;
	242	+	function IntegerToBcd(const AValue: Longint): TBcd;
	243	+	function VarToBcd(const AValue: Variant): TBcd;
	244	+	function CurrToBCD(const Curr: Currency; var BCD: TBcd; Precision: Integer; Decimals: Integer): Boolean;
	245	+	```
189	246
190	247		### from BCD
191	248
192	249		Convert Bcd struct to string/Double/Integer
193	250
194		-	~~` function BcdToStr(const Bcd: TBcd): string; overload;`\~~
195		-	~~` function BcdToDouble(const Bcd: TBcd): Double;`\~~
196		-	~~` function BcdToInteger(const Bcd: TBcd; Truncate: Boolean): Longint;`\~~
197		-	~~` function BCDToCurr(const BCD: TBcd; var Curr: Currency): Boolean;`\~~
198		-	~~` function BcdToStrF(const Bcd: TBcd; Format: TFloatFormat; const Precision, Digits: Integer): string;`~~
	251	+	``` pascal
	252	+	function BcdToStr(const Bcd: TBcd): string; overload;
	253	+	function BcdToDouble(const Bcd: TBcd): Double;
	254	+	function BcdToInteger(const Bcd: TBcd; Truncate: Boolean): Longint;
	255	+	function BCDToCurr(const BCD: TBcd; var Curr: Currency): Boolean;
	256	+	function BcdToStrF(const Bcd: TBcd; Format: TFloatFormat; const Precision, Digits: Integer): string;
	257	+	```
199	258
200	259		Formatting Bcd as string
201	260
202		-	~~` function FormatBcd(const Format: string; Bcd: TBcd): string;`\~~
203		-	~~` function BcdCompare(const bcd1, bcd2: TBcd): Integer;`~~
	261	+	``` pascal
	262	+	function FormatBcd(const Format: string; Bcd: TBcd): string;
	263	+	function BcdCompare(const bcd1, bcd2: TBcd): Integer;
	264	+	```
204	265
205	266		Warnings: 1. All these functions can accept integer as a parameter, but they produce a wrong result. For converting integers, use
206	267
207		-	~~` function BCDToInt(Value: Integer):Integer; `~~
	268	+	``` pascal
	269	+	function BCDToInt(Value: Integer):Integer;
	270	+	```
208	271
209	272		from the sysutils unit.
210	273
211	274		2\. Converting invalid BCD arrays cause exceptions.
212	275
213	276		## Resources
214	277
215	278		- [Additional information](http://homepages.borland.com/efg2lab/Library/Delphi/MathInfo/) available from efg's Computer Lab ([archived](https://web.archive.org/web/20080208085333/http://homepages.borland.com/efg2lab/Library/Delphi/MathInfo/) at archive.org).
216	279
217	280		---
218	281		From the Free Pascal wiki, page "BcdUnit", as it stood on 2021-02-17 after a change by Bart, out of the wiki's dump of 2024-05-26. Copyright stays with the author who wrote it, according to the old wiki's [[Licensing]] page. If you have concerns about this material, [message the admin](/wiki-contact).
219	282		Category: FPC
220	283		Category: Proposals

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