Lua - Are numbers floats or doubles?

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The Lua documentation says that Lua represents values of type number using a double, which allows all long integer values to be correctly represented using a floating point number.

However I see in the code that lua_Number is actually a float. Which is giving me the following warning :

warning C4244: 'argument' : conversion from 'double' to 'lua_Number', possible loss of data

For :

double fVarVal = 0.0;
lua_pushnumber( L, fVarVal );

So how are the values of type number represented in Lua ? float or double ? If they are using floats, can't this create problems when integer values, like array indexes, are being used ?

I'm using Lua 5.3.2 for Windows CE.

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