linux下 比较简单，这里不在说明，
windows下 相对复杂一点，用SetUnhandledExceptionFilter 来捕获 MiniDumpWriteDump 来写dmp文件，这种方法还不够完全，一些错误 一样无法捕获 比如 多次 delete ，可修改注册表 crash自动生成dmp 而不用代码去控制 结合代码控制 一起使用
#if _WIN32
#include <windows.h>
#include <dbghelp.h>
#pragma comment(lib, "dbghelp.lib")
void myInvalidParameterHandler(const wchar_t* expression,
const wchar_t* function,
const wchar_t* file,
unsigned int line,
uintptr_t pReserved)
{
throw 1;
}
LONG CustomCrashHandledExceptionFilter(_EXCEPTION_POINTERS *ExceptionInfo)
{
CHAR strDumpFile[MAX_PATH] = { 0 };
SYSTEMTIME tm;
HANDLE hFile = NULL;
time_t rawtime;
struct tm * t;
time(&rawtime);
t = localtime(&rawtime);
sprintf(strDumpFile, "%d%s%d-%04d-%02d-%02d-%02d-%02d-%02d.dmp", sid, name.c_str(), g_Inner_id, t->tm_year + 1900, t->tm_mon + 1, t->tm_mday, t->tm_hour, t->www.boyunylpt1.com tm_min, t->tm_sec);
hFile = CreateFileA(strDumpFile, GENERIC_WRITE, FILE_SHARE_WRITE, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL);
if (hFile != INVALID_HANDLE_VALUE)
{
MINIDUMP_EXCEPTION_INFORMATION ExInfo;
ExInfo.ThreadId = GetCurrentThreadId();
ExInfo.ExceptionPointers www.maituyul1.cn = ExceptionInfo;
ExInfo.ClientPointers = NULL;
BOOL bOK = MiniDumpWriteDump(
GetCurrentProcess(www.furongpt.com),
GetCurrentProcessId(www.dashuju2.cn),
hFile,
MiniDumpNormal,
&ExInfo,
NULL,
NULL);
CloseHandle(hFile);
}
return EXCEPTION_CONTINUE_SEARCH;
}
LPTOP_LEVEL_EXCEPTION_FILTER WINAPI EmptySetUnhandledExceptionFilter(
LPTOP_LEVEL_EXCEPTION_www.yingka178.com FILTER lpTopLevelExceptionFilter)
{
return NULL;
}
void myPurecallHandler(void)
{
throw 1;
}
BOOL HookSetUnhandledExceptionFilter()
{
HMODULE hKernel32 = LoadLibraryA(("kernel32.dll"));
if (hKernel32 == NULL) return FALSE;
void *pOrgEntry = GetProcAddress(hKernel32, "SetUnhandledExceptionFilter");
if (pOrgEntry == www.yongshi123.cn NULL) return FALSE;
unsigned char newJump[100];
DWORD dwOrgEntryAddr = (DWORD)pOrgEntry;
dwOrgEntryAddr +www.yongshiyule178.com= 5; // add 5 for 5 op-codes for jmp far
void *pNewFunc = &EmptySetUnhandledExceptionFilter;
DWORD dwNewEntryAddr www.michenggw.com= (DWORD)pNewFunc;
DWORD dwRelativeAddr =www.dfgjpt.com dwNewEntryAddr - dwOrgEntryAddr;
newJump[0] = 0xE9; // JMP absolute
memcpy(&newJump[1], &dwRelativeAddr, sizeof(pNewFunc));
SIZE_T bytesWritten;
BOOL bRet = WriteProcessMemory(GetCurrentProcess(),
pOrgEntry, newJump, sizeof(pNewFunc) + 1, &bytesWritten);
return bRet;
}
class CrashHandler
{
public:
CrashHandler()
{
//SetErrorMode(SEM_FAILCRITICALERRORS);
SetUnhandledExceptionFilter((LPTOP_LEVEL_EXCEPTION_FILTER)CustomCrashHandledExceptionFilter);
_purecall_handler old_pure_handle;
old_pure_handle = _set_purecall_handler(myPurecallHandler);
_invalid_parameter_handler oldHandler;
oldHandler = _set_invalid_parameter_handler(myInvalidParameterHandler);
HookSetUnhandledExceptionFilter();
在高阶导数的时候说过，如果两个函数每一阶导数都相等，那么"理论上"两个函数是相等的。
因为我们有cos′(x)=−sin(x)、cos′′(x)=−cos(x)、cos′′′(x)=sin(x)、cos′′′′(x)=cos(x)
此后就是−sin(x)、−cos(x)、sin(x)、cos(x)循环，求导次数x，其xmod 4=1,2,3,0的时候分别对应这四个。
cos(0)=1⇒f(x)=a0+∑ni=1ai⋅0=a0=1
cos′(0)=0⇒f′(x)=1⋅a1+∑ni=2(i−1)ai⋅0=1!⋅a1=0
cos′′(0)=−1⇒f′′(x)=1⋅2⋅a2+∑ni=3(i−1)⋅(i−2)ai=2!⋅a2=−1
cos′′′(0)=0⇒f′′′(x)=1⋅2⋅3a3+∑ni=4(i−1)⋅(i−2)⋅(i−3)ai=3!⋅a3=0
cos′′′′(0)=1⇒f′′′′(x)=1⋅2⋅3⋅4a4+∑ni=5(i−1)⋅(i−2)⋅(i−3)⋅(i−4)ai=4!⋅a4=1
可以发现规律了，假设取了i次导数，且有i=2n。
n是奇数有：i!⋅ai=−1⇒ai=−1i!
n是偶数有：i!⋅ai=1⇒ai=1i!
也就是cos(x)=1−x22!+x44!−x66!+x48!−⋯
同样的思路可以证明sin(x)=∑∞i=2n+1,n∈N(−1)nxii!=x−x33!+x55!−x77!+⋯
证明ex=⋯比这更容易，根据定义(ex)′=ex，重复上述过程即可。
麦克劳林展开式
ex=∑∞i=0xii!=1+x11!+x22!+x33!+x44!+⋯
sin(x)=∑∞i=2n+1,n∈N(−1)nxii!=x−x33!+x55!−x77!+⋯
cos(x)=∑∞i=2n,n∈N(−1)nxii!=1−x22!+x44!−x66!+⋯
本文正题
eix=1+(ix)11!+(ix)22!+(ix)33!+(ix)44!+(ix)55!=1+ix1!−x22!−ix33!+x44!+ix55!−⋯
把带有i的提出来有：
eix=1−x22!+x44!−x66!+⋯+i(x−x33!+x55!−x77!)=cos(x)+i×sin(x)
当x=π的时候
eiπ=cos(π)+i×sin(π)=−1
所以