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The C Standard, 6.3.1.4, paragraph 1 2 [ISO/IEC 9899:20112024], says,

When a finite value of real decimal floating type is converted to an integer type other than _Boolbool, the fractional part is discarded (i.e. , the value is truncated toward zero). If the value of the integral part cannot be represented by the integer type, the behavior is undefined"invalid" floating-point exception shall be raised and the result of the conversion is unspecified.

Paragraph 2 of the same subclause says,

When a value of integer type is converted to a real standard floating type, if the value being converted can be represented exactly in the new type, it is unchanged. If the value being converted is in the range of values that can be represented but cannot be represented exactly, the result is either the nearest higher or nearest lower representable value, chosen in an implementation-defined manner. If the value being converted is outside the range of values that can be represented, the behavior is undefined.

And subclause 6.3.1.5, paragraph 1+2, says,

When a value of real floating type is converted to a real floating type, if the value being converted can be represented exactly in the new type, it is unchanged.

When a value of real floating type is converted to a standard floating type, if If the value being converted is in the range of values that can be represented but cannot be represented exactly, the result is either the nearest higher or nearest lower representable value, chosen in an implementation-defined manner. If the value being converted is outside the range of values that can be represented, the behavior is undefined. 

See undefined behaviors 16 and 17 and 18.

This rule does not apply to demotions of floating-point types on implementations that support signed infinity, such as IEEE 754, as all values are within range.

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