BigInt Addition

BigInt Addition provides an example for adding two 64-bit arrays. If LeftLength is greater than RightLength, AddByGreaterLength.asm is executed, if equal, AddByEqualLength.asm is executed. AddByEqualLength requires Length additions. If there is a carry value at the end of the addition, the final value of result is 1. AddByEqualLength requires RightLength additions. If there is a carry value at the end of the addition, 1 is added until the carry value becomes zero. If there is any unprocessed digit left from Left, all of these digits are copied to the result.

Decimal digits count of 64-bit arrays

When performing mathematical operations, we may need operations with higher precision than numbers such as double or float. For example, if we want to find the roots of a quartic function as a double, the input of the function must be greater than the double precision.

Length	Byte Count	Decimal Count
128	1024	2467
256	2048	4933
512	4096	9865
1024	8192	19719
2048	16384	39447
32768	262144	631297
65536	524288	1262602

Performance Results

In the performance table below, two random 64-bit numbers of length leftLength and rightLength were multiplied. Each line was run 300 times and the minimum ElapsedTicks values were written with StopWatch(.NET). ExpectedTick(max) belongs to BigInteger(.NET).

leftLength	rightLength	expectedTick(max)	actualTick	Percent
64	64	2	1	50%
64	128	2	1	50%
64	256	2	2	100%
64	512	3	3	100%
64	1024	7	6	85%
64	2048	14	14	100%
64	32768	208	214	102%
64	65536	451	474	105%
128	64	1	1	100%
128	128	2	1	50%
128	256	2	2	100%
128	512	3	2	66%
128	1024	7	6	85%
128	2048	14	13	92%
128	32768	212	220	103%
128	65536	471	458	97%
256	64	1	1	100%
256	128	2	1	50%
256	256	4	2	50%
256	512	5	3	60%
256	1024	9	7	77%
256	2048	16	14	87%
256	32768	218	217	99%
256	65536	461	464	100%
512	64	2	2	100%
512	128	3	2	66%
512	256	5	3	60%
512	512	8	3	37%
512	1024	12	8	66%
512	2048	19	15	78%
512	32768	220	219	99%
512	65536	455	486	106%
1024	64	6	6	100%
1024	128	6	6	100%
1024	256	8	7	87%
1024	512	12	7	58%
1024	1024	19	9	47%
1024	2048	25	16	64%
1024	32768	224	219	97%
1024	65536	478	490	102%
2048	64	14	13	92%
2048	128	14	13	92%
2048	256	16	13	81%
2048	512	19	14	73%
2048	1024	25	15	60%
2048	2048	37	18	48%
2048	32768	236	224	94%
2048	65536	488	464	95%
32768	64	217	221	101%
32768	128	215	220	102%
32768	256	216	218	100%
32768	512	222	217	97%
32768	1024	229	218	95%
32768	2048	244	227	93%
32768	32768	607	327	53%
32768	65536	897	635	70%
65536	64	467	473	101%
65536	128	463	487	105%
65536	256	454	492	108%
65536	512	469	472	100%
65536	1024	472	457	96%
65536	2048	485	448	92%
65536	32768	863	618	71%
65536	65536	1255	781	62%