Approach for determining max and min values of various types

I wrote a custom atoi function and wanted to write some tests for the types int32_t,uint32_t,int,double to know it is doing the conversion correct. For the test I'll give it the maximum and min values and see if the conversion is correct.What I would like to know is if the approach I am taking to determining the max and min values of the type are correct.

This is my approach : To confirm the sizes of types I am using this link Now the link states that the size of int_32_t (which by default is signed) will be 16 bits in LP32 .So max 16 bit no is 65535. But since its signed we will get a max of 65535/2 = 32767.5 so I am assuming its range will be -32767 to 32767 ? Am I correct ? And similarly for uint32_t the size is will be 16 bits in LP32 .So max 16 bit no is 65535 so range will be 0 to 65535 ? Am I correct ? Also what is the difference between LP32 and ILP32 which one should I be following ?