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[英]Why does C# allow dividing a non-zero number by zero in floating-point type?
[英]C# compiler does not limit the number of digits of fractional part of a floating-point literal
這僅用於學術目的。
我注意到對於整數文字,我們可以聲明最多18446744073709551615
,即2^64-1
或ulong.MaxValue
。 定義大於此值會產生編譯時錯誤。
對於浮點文字,我們可以用999...999
( 9
重復308次)的整數部分聲明它們。 再次使用更多數字聲明整數部分會產生編譯時錯誤。 我感興趣的一件事是編譯器似乎允許我們指定小數部分無限數字的位數。 實際上,小數部分的無限數字位數沒有意義。
問題:
是否有一個常量表示C#編譯器內部定義的最大位數,用於浮點數的小數部分?
如果存在這樣的常量,當用戶指定超出其限制的小數部分時,為什么C#編譯器不會拋出編譯時錯誤?
namespace FloatingPoint
{
class Program
{
static void Main(string[] args)
{
const ulong @ulong = 18446744073709551615;
const double @double = 99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999;
}
}
}
using System;
namespace FloatingPoint
{
class Program
{
static void Main(string[] args)
{
const double x01 = 0.9;
const double x02 = 0.99;
const double x03 = 0.999;
const double x04 = 0.9999;
const double x05 = 0.99999;
const double x06 = 0.999999;
const double x07 = 0.9999999;
const double x08 = 0.99999999;
const double x09 = 0.999999999;
const double x10 = 0.9999999999;
const double x11 = 0.99999999999;
const double x12 = 0.999999999999;
const double x13 = 0.9999999999999;
const double x14 = 0.99999999999999;
const double x15 = 0.999999999999999;
const double x16 = 0.9999999999999999;
const double x17 = 0.99999999999999999;
const double x18 = 0.999999999999999999;
const double x19 = 0.9999999999999999999;
const double x20 = 0.99999999999999999999;
Console.WriteLine(x01);
Console.WriteLine(x02);
Console.WriteLine(x03);
Console.WriteLine(x04);
Console.WriteLine(x05);
Console.WriteLine(x06);
Console.WriteLine(x07);
Console.WriteLine(x08);
Console.WriteLine(x09);
Console.WriteLine(x10);
Console.WriteLine(x11);
Console.WriteLine(x12);
Console.WriteLine(x13);
Console.WriteLine(x14);
Console.WriteLine(x15);
Console.WriteLine(x16);
Console.WriteLine(x17);
Console.WriteLine(x18);
Console.WriteLine(x19);
Console.WriteLine(x20);
}
}
}
/* output:
0.9
0.99
0.999
0.9999
0.99999
0.999999
0.9999999
0.99999999
0.999999999
0.9999999999
0.99999999999
0.999999999999
0.9999999999999
0.99999999999999
0.999999999999999
1
1
1
1
1
*/
IL:
.method private hidebysig static void Main(string[] args) cil managed
{
.entrypoint
// Code size 302 (0x12e)
.maxstack 1
IL_0000: nop
IL_0001: ldc.r8 0.90000000000000002
IL_000a: call void [mscorlib]System.Console::WriteLine(float64)
IL_000f: nop
IL_0010: ldc.r8 0.98999999999999999
IL_0019: call void [mscorlib]System.Console::WriteLine(float64)
IL_001e: nop
IL_001f: ldc.r8 0.999
IL_0028: call void [mscorlib]System.Console::WriteLine(float64)
IL_002d: nop
IL_002e: ldc.r8 0.99990000000000001
IL_0037: call void [mscorlib]System.Console::WriteLine(float64)
IL_003c: nop
IL_003d: ldc.r8 0.99999000000000005
IL_0046: call void [mscorlib]System.Console::WriteLine(float64)
IL_004b: nop
IL_004c: ldc.r8 0.99999899999999997
IL_0055: call void [mscorlib]System.Console::WriteLine(float64)
IL_005a: nop
IL_005b: ldc.r8 0.99999990000000005
IL_0064: call void [mscorlib]System.Console::WriteLine(float64)
IL_0069: nop
IL_006a: ldc.r8 0.99999998999999995
IL_0073: call void [mscorlib]System.Console::WriteLine(float64)
IL_0078: nop
IL_0079: ldc.r8 0.99999999900000003
IL_0082: call void [mscorlib]System.Console::WriteLine(float64)
IL_0087: nop
IL_0088: ldc.r8 0.99999999989999999
IL_0091: call void [mscorlib]System.Console::WriteLine(float64)
IL_0096: nop
IL_0097: ldc.r8 0.99999999999
IL_00a0: call void [mscorlib]System.Console::WriteLine(float64)
IL_00a5: nop
IL_00a6: ldc.r8 0.99999999999900002
IL_00af: call void [mscorlib]System.Console::WriteLine(float64)
IL_00b4: nop
IL_00b5: ldc.r8 0.99999999999989997
IL_00be: call void [mscorlib]System.Console::WriteLine(float64)
IL_00c3: nop
IL_00c4: ldc.r8 0.99999999999999001
IL_00cd: call void [mscorlib]System.Console::WriteLine(float64)
IL_00d2: nop
IL_00d3: ldc.r8 0.999999999999999
IL_00dc: call void [mscorlib]System.Console::WriteLine(float64)
IL_00e1: nop
IL_00e2: ldc.r8 0.99999999999999989
IL_00eb: call void [mscorlib]System.Console::WriteLine(float64)
IL_00f0: nop
IL_00f1: ldc.r8 1.
IL_00fa: call void [mscorlib]System.Console::WriteLine(float64)
IL_00ff: nop
IL_0100: ldc.r8 1.
IL_0109: call void [mscorlib]System.Console::WriteLine(float64)
IL_010e: nop
IL_010f: ldc.r8 1.
IL_0118: call void [mscorlib]System.Console::WriteLine(float64)
IL_011d: nop
IL_011e: ldc.r8 1.
IL_0127: call void [mscorlib]System.Console::WriteLine(float64)
IL_012c: nop
IL_012d: ret
} // end of method Program::Main
0.3
已經需要近似值。 在大多數情況下,浮點數無論如何都將是所需實際值的近似值(除非它恰好是可以精確表示的值之一)。 此外,近似是明確定義的:簡單地舍入到最接近的可表示值。 另一方面,沒有有用的方法將整數(或實數的整數部分)舍入到最接近的可表示值。 例如,將2 ^ 100舍入到2 ^ 64-1是什么意思?
我不知道浮點文字中允許的小數位數有任何限制,雖然測試這樣的限制是否確實存在應該相對簡單,但如果確實存在,它可能更多地取決於編譯器內部而不是特定的任何內容。無論如何,要浮點值。 但是我認為值得思考是否有必要限制文字中的小數位數。 我認為這里的關鍵點是無法表示的數字之間的差異,因為它們超出了雙數據類型支持的范圍 (由編譯器選取),以及無法在數據類型中准確表示的數字。
確實有許多十進制數字不能完全表示為雙精度數(例如0.1),但編譯器默默地接受它們,將它們轉換為最接近的可表示值,如果不這樣做,則會帶來很大的不便。 那么為什么一個超過小數的文字應該被區別對待呢?
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