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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
这仅用于学术目的。
我注意到对于整数文字,我们可以声明最多18446744073709551615
,即2^64-1
或ulong.MaxValue
。 定义大于此值会产生编译时错误。
对于浮点文字,我们可以用999...999
( 9
重复308次)的整数部分声明它们。 再次使用更多数字声明整数部分会产生编译时错误。 我感兴趣的一件事是编译器似乎允许我们指定小数部分无限数字的位数。 实际上,小数部分的无限数字位数没有意义。
问题:
是否有一个常量表示C#编译器内部定义的最大位数,用于浮点数的小数部分?
如果存在这样的常量,当用户指定超出其限制的小数部分时,为什么C#编译器不会抛出编译时错误?
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
已经需要近似值。 在大多数情况下,浮点数无论如何都将是所需实际值的近似值(除非它恰好是可以精确表示的值之一)。 此外,近似是明确定义的:简单地舍入到最接近的可表示值。 另一方面,没有有用的方法将整数(或实数的整数部分)舍入到最接近的可表示值。 例如,将2 ^ 100舍入到2 ^ 64-1是什么意思?
我不知道浮点文字中允许的小数位数有任何限制,虽然测试这样的限制是否确实存在应该相对简单,但如果确实存在,它可能更多地取决于编译器内部而不是特定的任何内容。无论如何,要浮点值。 但是我认为值得思考是否有必要限制文字中的小数位数。 我认为这里的关键点是无法表示的数字之间的差异,因为它们超出了双数据类型支持的范围 (由编译器选取),以及无法在数据类型中准确表示的数字。
确实有许多十进制数字不能完全表示为双精度数(例如0.1),但编译器默默地接受它们,将它们转换为最接近的可表示值,如果不这样做,则会带来很大的不便。 那么为什么一个超过小数的文字应该被区别对待呢?
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