浮点的下界
C 中的浮点类型有下限吗？就像整数类型有下限（int 至少 16 位）？
Are there any lower bounds for floating point types in C? Like there are lower bounds for integral types (int being at least 16 bits)?
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是的。
float.h包含常量，例如：FLT_EPSILON、DBL_EPSILON、LDBL_EPSILON这是可用float表示的最小非零值，double和long double表示形式。FLT_MAX和FLT_MIN表示float可以表示的极端正数和负数。类似的DBL_和LDBL_也可用。FLT_DIG、DBL_DIG、LDBL_DIG定义为十进制位数精度。您要求提供
xxx_MIN或xxx_EPSILON值。沿着这些思路，这里有一个问题，其中 我发布了一些显示 64 位 IEEE-754 浮点数内部结构的代码。
Yes.
float.hcontains constants such as:FLT_EPSILON, DBL_EPSILON, LDBL_EPSILONthis is the least magnitude non-zero value which can be represented byfloat,double, andlong doublerepresentations.FLT_MAXandFLT_MINrepresent the extreme positive and negative numbers which can be represented forfloat. SimilarDBL_andLDBL_are available.FLT_DIG, DBL_DIG, LDBL_DIGare defined as the number of decimal digits precision.You are asking for either the
xxx_MINor thexxx_EPSILONvalue.Along these lines, here is a question wherein I posted some code which displays the internals of a 64-bit IEEE-754 floating-point number.
float.h包含许多描述浮点类型各种属性的宏（包括FLT_MIN和DBL_MIN）。标准中给出了
float.h中限制要求的描述（C90 或 C99 - 5.2.4.2.2“浮点类型的特性”）。特别是，根据标准，任何实现都必须支持
float或double的下限至少为1E-37。但实现可以做得比这更好（并在FLT_MIN和DBL_MIN中指出它的作用）。如果需要，请参阅此问题，了解如何获取标准文档副本的信息：
float.hcontains many macros describing various properties of the floating types (includingFLT_MINandDBL_MIN).The description of the requirements of the limits in
float.his given in the standard (C90 or C99 - 5.2.4.2.2 "Characteristics of floating types").In particular, according to the standard any implementation must support a lower-bound of at least
1E-37forfloatordouble. But an implementation is free to do better than that (and indicate what it does inFLT_MINandDBL_MIN).See this question for information on where to get a copy of the standards documents if you need one:
这里有用的参考是每个计算机科学家应该了解浮点知识算术。
浮点数的本质——它的大小、精度、限制——实际上是由硬件定义的，而不是由编程语言定义的。 x86 上的单精度浮点与 C、C#、Java 和任何其他实用编程语言中的单精度浮点相同。 （例外是在软件中实现奇数宽度浮点数的深奥编程语言。）
A useful reference here is What Every Computer Scientist Should Know About Floating-Point Arithmetic.
The nature of a floating point number — its size, precision, limits — is really defined by the hardware, rather than the programming language. A single-precision float on an x86 is the same in C, C#, Java, and any other practical programming language. (The exception is esoteric programming languages that implement odd widths of floating point number in software.)
标准草案 (n1401.pdf) 摘录
Annex F (normative) IEC 60559 floating-point arithmetic F.1 Introduction 1 ... An implementation that defines _ _STDC_IEC_559_ _ shall conform to the specifications in this annex. ... F.2 Types 1 The C floating types match the IEC 60559 formats as follows: -- The float type matches the IEC 60559 single format. -- The double type matches the IEC 60559 double format. -- The long double type matches an IEC 60559 extended format ...Wikipedia 有 一篇关于 IEC 559（或更确切地说 IEEE 754）的文章-1985）你可能会觉得有趣。
Excerpts from the Standard draft (n1401.pdf)
Annex F (normative) IEC 60559 floating-point arithmetic F.1 Introduction 1 ... An implementation that defines _ _STDC_IEC_559_ _ shall conform to the specifications in this annex. ... F.2 Types 1 The C floating types match the IEC 60559 formats as follows: -- The float type matches the IEC 60559 single format. -- The double type matches the IEC 60559 double format. -- The long double type matches an IEC 60559 extended format ...Wikipedia has an article about IEC 559 (or rather IEEE 754-1985) you might find interesting.