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If a floating-point value is to be demoted to a floating-point value of a smaller range and precision or to an integer type, or if an integer type is to be converted to a floating-point type, the value must be represented in the new type.

Section Subclause 6.3.1.4 of the C Standard [ISO/IEC 9899:2011] says,

When a finite value of real floating type is converted to an integer type other than _Bool, 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.

When a value of integer type is converted to a real 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 section subclause 6.3.1.5 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. 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.

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

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float f_a;
int i_a;

/* initializeInitialize float f_a */

i_a = f_a; /* Undefined if the integral part of f_a > INT_MAX */

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float f_a;
int i_a;

/* initializeInitialize float f_a */

if (f_a > (float) INT_MAX || f_a < (float) INT_MIN) {
  /* Handle error */
} else {
  i_a = f_a;
}

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This noncompliant code example contains conversions that may be outside of the range of the demoted types:

long double big_d;
double d_a;
double d_b;
float f_a;
float f_b;

/* initializationsInitializations */

f_a = (float)d_a;
f_b = (float)big_d;
d_b = (double)big_d;

As a result of these conversions, it is possible that d_a is outside the range of values that can be represented by a float or that big_d is outside the range of values that can be represented as either a float or a double. If this is the case, the result is undefined.

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