BigReal

An arbitrary size and precision rational number stored using two BigIntegers.

Usage

Create from fixed-size numbers:

Console.WriteLine(new BigReal(100)); // 100
Console.WriteLine((BigReal)3.14); // 3.14
Console.WriteLine(new BigReal(4, 3).ToString(4)); // 1.3333

Perform basic operations:

Console.WriteLine((BigReal)3 * (BigReal)5); // 15
Console.WriteLine(BigReal.Pow(3.4, 2)); // 11.559999999999999

Parse from string:

Console.WriteLine(BigReal.Parse("12.34")); // 12.34
Console.WriteLine(BigReal.Parse("2e2.5").ToString(2)); // 632.45

Trigonometry:

Console.WriteLine(BigReal.Sin(100).ToString(20)); // -0.5063656411097587906

Performance

Basic operations comparing BigReal, BigDecimal, and BigFloat:

• Add: 10 + 3
• Divide: 10 / 3
• DivideToString: (10 / 3).ToString()
• Parse: Parse("12345.6789")
• FromFloat: 123.45f

Method	Mean	Error	StdDev	Gen0	Allocated
Add_BigReal	20.342 ns	0.0616 ns	0.0514 ns	-	-
Add_BigDecimal	373.701 ns	2.4290 ns	2.0284 ns	0.0739	464 B
Add_BigFloat	21.680 ns	0.0568 ns	0.0504 ns	-	-
Divide_BigReal	9.109 ns	0.0228 ns	0.0190 ns	-	-
Divide_BigDecimal	28,783.122 ns	134.7718 ns	112.5406 ns	5.2185	32832 B
Divide_BigFloat	14.687 ns	0.3137 ns	0.3356 ns	-	-
DivideToString_BigReal	1,165.798 ns	3.4006 ns	3.1809 ns	0.0534	344 B
DivideToString_BigDecimal	2,822.685 ns	24.7819 ns	19.3481 ns	0.5226	3296 B
DivideToString_BigFloat	1,385.152 ns	19.1418 ns	16.9687 ns	0.1869	1176 B
Parse_BigReal	272.192 ns	1.9640 ns	1.6400 ns	0.0062	40 B
Parse_BigDecimal	243.745 ns	1.3348 ns	1.0421 ns	0.0291	184 B
Parse_BigFloat	311.843 ns	5.5915 ns	4.9568 ns	0.0062	40 B
FromFloat_BigReal	110.971 ns	0.3906 ns	0.3262 ns	-	-
FromFloat_BigDecimal	322.433 ns	0.9244 ns	0.7719 ns	0.0329	208 B
FromFloat_BigFloat	1,609.420 ns	5.7215 ns	4.7777 ns	0.1068	672 B

Notes:

• Whereas BigDecimal divides by calculating the decimal digits at a certain precision, BigReal stores a fraction so the digits are only calculated at ToString.

Background

BigReal is made by Joyless and based on BigFloat by FaustVX. Some inspiration was taken from BigDecimal by AdamWhiteHat.

Gotchas

• The default value of BigReal is NaN, since 0 / 0 is NaN.
• Dividing by 0 gives positive or negative infinity depending on the numerator.