Source: fastlog2.go in package runtime


package runtime

fastlog2 implements a fast approximation to the base 2 log of a float64. This is used to compute a geometric distribution for heap sampling, without introducing dependencies into package math. This uses a very rough approximation using the float64 exponent and the first 25 bits of the mantissa. The top 5 bits of the mantissa are used to load limits from a table of constants and the rest are used to scale linearly between them.

func fastlog2(x float64) float64 {
	const fastlogScaleBits = 20
	const fastlogScaleRatio = 1.0 / (1 << fastlogScaleBits)

Extract the exponent from the IEEE float64, and index a constant table with the first 10 bits from the mantissa.

	xExp := int64((xBits>>52)&0x7FF) - 1023
	xManIndex := (xBits >> (52 - fastlogNumBits)) % (1 << fastlogNumBits)
	xManScale := (xBits >> (52 - fastlogNumBits - fastlogScaleBits)) % (1 << fastlogScaleBits)

	low, high := fastlog2Table[xManIndex], fastlog2Table[xManIndex+1]
	return float64(xExp) + low + (high-low)*float64(xManScale)*fastlogScaleRatio