c/c++: float和double、long double

本文详细解释了单精度和双精度浮点数在计算机中的存储方式,包括指数型式的分解、数符、尾数、指数符及其占用的位数。同时对比了双精度和单精度浮点数在精度、内存消耗和运算速度上的区别,并提供了编程人员在选择使用单精度还是双精度时的建议。

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这两天在写程序,看了一些文章,转过来备忘。原文地址是:

http://topic.youkuaiyun.com/u/20090716/10/ce4a7037-3c0d-40ae-af85-f702c78fcea3.html

单精度浮点数在机内占4个字节,用32位二进制描述。
双精度浮点数在机内占8个字节,用64位二进制描述。

浮点数在机内用指数型式表示,分解为:数符,尾数,指数符,指数四部分。
数符占1位二进制,表示数的正负。
指数符占1位二进制,表示指数的正负。
尾数表示浮点数有效数字,0.xxxxxxx,但不存开头的0和点
指数存指数的有效数字。

指数占多少位,尾数占多少位,由计算机系统决定。
可能是数符加尾数占24位,指数符加指数占8位 -- float.
数符加尾数占48位,指数符加指数占16位 -- double.

知道了这四部分的占位,按二进制估计大小范围,再换算为十进制,就是你想知道的数值范围。

对编程人员来说,double 和 float 的区别是double精度高,有效数字16位,float精度7位。但double消耗内存是float的两倍,double的运算速度比float慢得多,C语言中数学函数名称double 和 float不同,不要写错,能用单精度时不要用双精度(以省内存,加快运算速度)。

 

long double标准是规定它是128位浮点数据的,而double是64位浮点数据,但是编译器不一样也有差别,比如vc中它们都是64位的。总之long double >= double =64位是不会错的。 
a.cpp: In function ‘int main()’: a.cpp:47:17: error: ‘Swap’ was not declared in this scope 47 | Swap(&a, &b); | ^~~~ a.cpp:53:17: error: ‘Swap’ was not declared in this scope 53 | Swap(&a, &b); | ^~~~ a.cpp:59:17: error: ‘Swap’ was not declared in this scope 59 | Swap(&a, &b); | ^~~~ a.cpp:65:17: error: ‘Swap’ was not declared in this scope 65 | Swap(&a, &b); | ^~~~ a.cpp:71:17: error: ‘Swap’ was not declared in this scope 71 | Swap(&a, &b); | ^~~~ a.cpp:78:21: error: no match for ‘operator>>’ (operand types are ‘std::istream’ {aka ‘std::basic_istream<char>’} and ‘char*’) 78 | cin >> a >> b; | ~~~ ^~ ~ | | | | | char* | std::istream {aka std::basic_istream<char>} In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:168:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(bool&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ (near match) 168 | operator>>(bool& __n) | ^~~~~~~~ /usr/include/c++/11/istream:168:7: note: conversion of argument 1 would be ill-formed: a.cpp:78:24: error: cannot bind non-const lvalue reference of type ‘bool&’ to a value of type ‘char*’ 78 | cin >> a >> b; | ^ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:172:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>& std::basic_istream<_CharT, _Traits>::operator>>(short int&) [with _CharT = char; _Traits = std::char_traits<char>]’ (near match) 172 | operator>>(short& __n); | ^~~~~~~~ /usr/include/c++/11/istream:172:7: note: conversion of argument 1 would be ill-formed: a.cpp:78:24: error: invalid conversion from ‘char*’ to ‘short int’ [-fpermissive] 78 | cin >> a >> b; | ^ | | | char* a.cpp:78:24: error: cannot bind rvalue ‘(short int)a’ to ‘short int&’ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:175:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(short unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ (near match) 175 | operator>>(unsigned short& __n) | ^~~~~~~~ /usr/include/c++/11/istream:175:7: note: conversion of argument 1 would be ill-formed: a.cpp:78:24: error: invalid conversion from ‘char*’ to ‘short unsigned int’ [-fpermissive] 78 | cin >> a >> b; | ^ | | | char* a.cpp:78:24: error: cannot bind rvalue ‘(short unsigned int)a’ to ‘short unsigned int&’ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:179:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>& std::basic_istream<_CharT, _Traits>::operator>>(int&) [with _CharT = char; _Traits = std::char_traits<char>]’ (near match) 179 | operator>>(int& __n); | ^~~~~~~~ /usr/include/c++/11/istream:179:7: note: conversion of argument 1 would be ill-formed: a.cpp:78:24: error: invalid conversion from ‘char*’ to ‘int’ [-fpermissive] 78 | cin >> a >> b; | ^ | | | char* a.cpp:78:24: error: cannot bind rvalue ‘(int)a’ to ‘int&’ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:182:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ (near match) 182 | operator>>(unsigned int& __n) | ^~~~~~~~ /usr/include/c++/11/istream:182:7: note: conversion of argument 1 would be ill-formed: a.cpp:78:24: error: invalid conversion from ‘char*’ to ‘unsigned int’ [-fpermissive] 78 | cin >> a >> b; | ^ | | | char* a.cpp:78:24: error: cannot bind rvalue ‘(unsigned int)a’ to ‘unsigned int&’ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:186:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long int&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ (near match) 186 | operator>>(long& __n) | ^~~~~~~~ /usr/include/c++/11/istream:186:7: note: conversion of argument 1 would be ill-formed: a.cpp:78:24: error: invalid conversion from ‘char*’ to ‘long int’ [-fpermissive] 78 | cin >> a >> b; | ^ | | | char* a.cpp:78:24: error: cannot bind rvalue ‘(long int)a’ to ‘long int&’ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:190:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ (near match) 190 | operator>>(unsigned long& __n) | ^~~~~~~~ /usr/include/c++/11/istream:190:7: note: conversion of argument 1 would be ill-formed: a.cpp:78:24: error: invalid conversion from ‘char*’ to ‘long unsigned int’ [-fpermissive] 78 | cin >> a >> b; | ^ | | | char* a.cpp:78:24: error: cannot bind rvalue ‘(long unsigned int)a’ to ‘long unsigned int&’ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:195:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long long int&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ (near match) 195 | operator>>(long long& __n) | ^~~~~~~~ /usr/include/c++/11/istream:195:7: note: conversion of argument 1 would be ill-formed: a.cpp:78:24: error: invalid conversion from ‘char*’ to ‘long long int’ [-fpermissive] 78 | cin >> a >> b; | ^ | | | char* a.cpp:78:24: error: cannot bind rvalue ‘(long long int)a’ to ‘long long int&’ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:199:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long long unsigned int&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ (near match) 199 | operator>>(unsigned long long& __n) | ^~~~~~~~ /usr/include/c++/11/istream:199:7: note: conversion of argument 1 would be ill-formed: a.cpp:78:24: error: invalid conversion from ‘char*’ to ‘long long unsigned int’ [-fpermissive] 78 | cin >> a >> b; | ^ | | | char* a.cpp:78:24: error: cannot bind rvalue ‘(long long unsigned int)a’ to ‘long long unsigned int&’ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:235:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(void*&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ (near match) 235 | operator>>(void*& __p) | ^~~~~~~~ /usr/include/c++/11/istream:235:7: note: conversion of argument 1 would be ill-formed: a.cpp:78:24: error: cannot bind non-const lvalue reference of type ‘void*&’ to an rvalue of type ‘void*’ 78 | cin >> a >> b; | ^ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:120:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(std::basic_istream<_CharT, _Traits>::__istream_type& (*)(std::basic_istream<_CharT, _Traits>::__istream_type&)) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ 120 | operator>>(__istream_type& (*__pf)(__istream_type&)) | ^~~~~~~~ /usr/include/c++/11/istream:120:36: note: no known conversion for argument 1 from ‘char*’ to ‘std::basic_istream<char>::__istream_type& (*)(std::basic_istream<char>::__istream_type&)’ {aka ‘std::basic_istream<char>& (*)(std::basic_istream<char>&)’} 120 | operator>>(__istream_type& (*__pf)(__istream_type&)) | ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~ /usr/include/c++/11/istream:124:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(std::basic_istream<_CharT, _Traits>::__ios_type& (*)(std::basic_istream<_CharT, _Traits>::__ios_type&)) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>; std::basic_istream<_CharT, _Traits>::__ios_type = std::basic_ios<char>]’ 124 | operator>>(__ios_type& (*__pf)(__ios_type&)) | ^~~~~~~~ /usr/include/c++/11/istream:124:32: note: no known conversion for argument 1 from ‘char*’ to ‘std::basic_istream<char>::__ios_type& (*)(std::basic_istream<char>::__ios_type&)’ {aka ‘std::basic_ios<char>& (*)(std::basic_ios<char>&)’} 124 | operator>>(__ios_type& (*__pf)(__ios_type&)) | ~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~ /usr/include/c++/11/istream:131:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(std::ios_base& (*)(std::ios_base&)) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ 131 | operator>>(ios_base& (*__pf)(ios_base&)) | ^~~~~~~~ /usr/include/c++/11/istream:131:30: note: no known conversion for argument 1 from ‘char*’ to ‘std::ios_base& (*)(std::ios_base&)’ 131 | operator>>(ios_base& (*__pf)(ios_base&)) | ~~~~~~~~~~~~^~~~~~~~~~~~~~~~ /usr/include/c++/11/istream:214:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(float&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ 214 | operator>>(float& __f) | ^~~~~~~~ /usr/include/c++/11/istream:214:25: note: no known conversion for argument 1 from ‘char*’ to ‘float&’ 214 | operator>>(float& __f) | ~~~~~~~^~~ /usr/include/c++/11/istream:218:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(double&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ 218 | operator>>(double& __f) | ^~~~~~~~ /usr/include/c++/11/istream:218:26: note: no known conversion for argument 1 from ‘char*’ to ‘double&’ 218 | operator>>(double& __f) | ~~~~~~~~^~~ /usr/include/c++/11/istream:222:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>::__istream_type& std::basic_istream<_CharT, _Traits>::operator>>(long double&) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__istream_type = std::basic_istream<char>]’ 222 | operator>>(long double& __f) | ^~~~~~~~ /usr/include/c++/11/istream:222:31: note: no known conversion for argument 1 from ‘char*’ to ‘long double&’ 222 | operator>>(long double& __f) | ~~~~~~~~~~~~~^~~ /usr/include/c++/11/istream:259:7: note: candidate: ‘std::basic_istream<_CharT, _Traits>& std::basic_istream<_CharT, _Traits>::operator>>(std::basic_istream<_CharT, _Traits>::__streambuf_type*) [with _CharT = char; _Traits = std::char_traits<char>; std::basic_istream<_CharT, _Traits>::__streambuf_type = std::basic_streambuf<char>]’ 259 | operator>>(__streambuf_type* __sb); | ^~~~~~~~ /usr/include/c++/11/istream:259:36: note: no known conversion for argument 1 from ‘char*’ to ‘std::basic_istream<char>::__streambuf_type*’ {aka ‘std::basic_streambuf<char>*’} 259 | operator>>(__streambuf_type* __sb); | ~~~~~~~~~~~~~~~~~~^~~~ In file included from /usr/include/c++/11/string:56, from /usr/include/c++/11/bits/locale_classes.h:40, from /usr/include/c++/11/bits/ios_base.h:41, from /usr/include/c++/11/ios:42, from /usr/include/c++/11/ostream:38, from /usr/include/c++/11/iostream:39, from a.cpp:1: /usr/include/c++/11/bits/basic_string.tcc:1485:5: note: candidate: ‘template<class _CharT, class _Traits, class _Alloc> std::basic_istream<_CharT, _Traits>& std::operator>>(std::basic_istream<_CharT, _Traits>&, std::__cxx11::basic_string<_CharT, _Traits, _Allocator>&)’ 1485 | operator>>(basic_istream<_CharT, _Traits>& __in, | ^~~~~~~~ /usr/include/c++/11/bits/basic_string.tcc:1485:5: note: template argument deduction/substitution failed: a.cpp:78:24: note: mismatched types ‘std::__cxx11::basic_string<_CharT, _Traits, _Allocator>’ and ‘char*’ 78 | cin >> a >> b; | ^ In file included from /usr/include/c++/11/istream:1016, from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/bits/istream.tcc:958:5: note: candidate: ‘template<class _CharT, class _Traits> std::basic_istream<_CharT, _Traits>& std::operator>>(std::basic_istream<_CharT, _Traits>&, _CharT&)’ 958 | operator>>(basic_istream<_CharT, _Traits>& __in, _CharT& __c) | ^~~~~~~~ /usr/include/c++/11/bits/istream.tcc:958:5: note: template argument deduction/substitution failed: a.cpp:78:24: note: deduced conflicting types for parameter ‘_CharT’ (‘char’ and ‘char*’) 78 | cin >> a >> b; | ^ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:756:5: note: candidate: ‘template<class _Traits> std::basic_istream<char, _Traits>& std::operator>>(std::basic_istream<char, _Traits>&, unsigned char&)’ 756 | operator>>(basic_istream<char, _Traits>& __in, unsigned char& __c) | ^~~~~~~~ /usr/include/c++/11/istream:756:5: note: template argument deduction/substitution failed: a.cpp:78:24: note: cannot convert ‘a’ (type ‘char*’) to type ‘unsigned char&’ 78 | cin >> a >> b; | ^ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:761:5: note: candidate: ‘template<class _Traits> std::basic_istream<char, _Traits>& std::operator>>(std::basic_istream<char, _Traits>&, signed char&)’ 761 | operator>>(basic_istream<char, _Traits>& __in, signed char& __c) | ^~~~~~~~ /usr/include/c++/11/istream:761:5: note: template argument deduction/substitution failed: a.cpp:78:24: note: cannot convert ‘a’ (type ‘char*’) to type ‘signed char&’ 78 | cin >> a >> b; | ^ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:859:5: note: candidate: ‘template<class _CharT, class _Traits, long unsigned int _Num> std::basic_istream<_CharT, _Traits>& std::operator>>(std::basic_istream<_CharT, _Traits>&, _CharT (&)[_Num])’ 859 | operator>>(basic_istream<_CharT, _Traits>& __in, _CharT (&__s)[_Num]) | ^~~~~~~~ /usr/include/c++/11/istream:859:5: note: template argument deduction/substitution failed: a.cpp:78:24: note: mismatched types ‘_CharT [_Num]’ and ‘char*’ 78 | cin >> a >> b; | ^ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:868:5: note: candidate: ‘template<class _Traits, long unsigned int _Num> std::basic_istream<char, _Traits>& std::operator>>(std::basic_istream<char, _Traits>&, unsigned char (&)[_Num])’ 868 | operator>>(basic_istream<char, _Traits>& __in, unsigned char (&__s)[_Num]) | ^~~~~~~~ /usr/include/c++/11/istream:868:5: note: template argument deduction/substitution failed: a.cpp:78:24: note: mismatched types ‘unsigned char [_Num]’ and ‘char*’ 78 | cin >> a >> b; | ^ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:873:5: note: candidate: ‘template<class _Traits, long unsigned int _Num> std::basic_istream<char, _Traits>& std::operator>>(std::basic_istream<char, _Traits>&, signed char (&)[_Num])’ 873 | operator>>(basic_istream<char, _Traits>& __in, signed char (&__s)[_Num]) | ^~~~~~~~ /usr/include/c++/11/istream:873:5: note: template argument deduction/substitution failed: a.cpp:78:24: note: mismatched types ‘signed char [_Num]’ and ‘char*’ 78 | cin >> a >> b; | ^ In file included from /usr/include/c++/11/iostream:40, from a.cpp:1: /usr/include/c++/11/istream:1006:5: note: candidate: ‘template<class _Istream, class _Tp> _Istream&& std::operator>>(_Istream&&, _Tp&&)’ 1006 | operator>>(_Istream&& __is, _Tp&& __x) | ^~~~~~~~ /usr/include/c++/11/istream:1006:5: note: template argument deduction/substitution failed: /usr/include/c++/11/istream: In substitution of ‘template<class _Istream, class _Tp> _Istream&& std::operator>>(_Istream&&, _Tp&&) [with _Istream = std::basic_istream<char>&; _Tp = char*&]’: a.cpp:78:10: required from here /usr/include/c++/11/istream:1006:5: error: template constraint failure for ‘template<class _Is, class _Tp> requires (__derived_from_ios_base<_Is>) && requires(_Is& __is, _Tp&& __t) {__is >> (forward<_Tp>)(__t);} using __rvalue_stream_extraction_t = _Is&&’ /usr/include/c++/11/istream:1006:5: note: constraints not satisfied In file included from /usr/include/c++/11/iostream:39, from a.cpp:1: /usr/include/c++/11/ostream: In substitution of ‘template<class _Is, class _Tp> requires (__derived_from_ios_base<_Is>) && requires(_Is& __is, _Tp&& __t) {__is >> (forward<_Tp>)(__t);} using __rvalue_stream_extraction_t = _Is&& [with _Is = std::basic_istream<char>&; _Tp = char*&]’: /usr/include/c++/11/istream:1006:5: required by substitution of ‘template<class _Istream, class _Tp> _Istream&& std::operator>>(_Istream&&, _Tp&&) [with _Istream = std::basic_istream<char>&; _Tp = char*&]’ a.cpp:78:10: required from here /usr/include/c++/11/ostream:717:13: required for the satisfaction of ‘__derived_from_ios_base<_Is>’ [with _Is = std::basic_istream<char, std::char_traits<char> >&] /usr/include/c++/11/ostream:717:39: note: the expression ‘is_class_v<_Tp> [with _Tp = std::basic_istream<char, std::char_traits<char> >&]’ evaluated to ‘false’ 717 | concept __derived_from_ios_base = is_class_v<_Tp> | ^~~~~~~~~~~~~~~ a.cpp:79:17: error: ‘Swap’ was not declared in this scope 79 | Swap(a, b); | ^~~~ a.cpp:42:19: warning: unused variable ‘n’ [-Wunused-variable] 42 | int type, n, i; | ^ a.cpp:42:22: warning: unused variable ‘i’ [-Wunused-variable] 42 | int type, n, i; | ^ 上一个问题的代码出现了上述报错,请修改
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