isFloatRoundingApprox.cpp

// [email protected]  \(v ` >`)_v
// feel free to use as you see fit, attribution appreciated but not required, not fit for any purpose

// returns TRUE if the printed version of a float is being approximated when we limit the print
// to a certain number of decimal places, as defined by `decimalPlaceLimit`, 
// returns FALSE if the printed version is 100% accurate to the float itself.
// NOTE: This WILL return true for values like 0.1, which ARE approximated at extremely 
//       small fractional parts in floats:  0.1 is actually 0.100000000000000005551115...

// truth table:
// f( val,  dec ) -> ret   
// -----------------------
// f( 0.5,    3 ) ->  0   
// f( 0.25,   3 ) ->  0   
// f( 0.125,  3 ) ->  0   
// f( 0.0625, 3 ) ->  1   

bool isFloatRoundingApprox(float value, uint32_t decimalPlaceLimit) {
	// 0.0 is special, it's the only value for which our assumption about the exponent kind of backfires
	// 1.0 and 0.5 are... not special, these are just kind of common, may as well make quick outs for them
	if(value == 0.f || value == 1.f || (value == 0.5f && decimalPlaceLimit > 0))
		return false; 
	uint32_t bits = *(uint32_t*)(&value);
	uint32_t exponent = (bits>>23)&0xFF;
	uint32_t mantissa = bits&0x7FFFFF;
	uint32_t msb;
	// msb is treated as lsb in the preprocessor'd section
	#ifdef _MSC_VER
		{
			unsigned long result; // has to be this type
			_BitScanForward(&result, mantissa);
			msb = result;
		}
	#elif __GNUC__
		#pragma message ("branch untested, if it works, feel free to delete this!")
		msb = __builtin_ffs(mantissa);
	#else
		#pragma message ("branch untested, if it works, feel free to delete this!")
		#pragma message ("using an unoptimized fallback")
		msb = 0; // treat as lsb until the end
		for (uint32_t i = 0; i < 23; ++i) {
			if((mantissa>>i)&1u)
				break;
			++msb;
		}
		msb = (msb + 1) % 23; // 0 to 22 lsb
	#endif
	msb = (23 - msb);
	if(msb == 23)
		msb = 0;

	// takes advantage of a property of I noticed (that hopefully is true?) regarding float representation,
	// where:
	//		 [index of the most set bit in the mantissa] - ([exponent] - 127)
	// defines how many digits "deep" into the fractional part we travel
	// we can use this to DIRECTLY gather if our decimal point is being rounded due to the fact that...
	// once we reach into any depth of the fractional part, it can NEVER be zero (this isn't true for zero itself tho)

	int32_t depth = int32_t(msb) - (int32_t(exponent) - 127);
	return depth > int32_t(decimalPlaceLimit);
}