1// Copyright 2015 The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5package runtime
6
7// fastlog2 implements a fast approximation to the base 2 log of a
8// float64. This is used to compute a geometric distribution for heap
9// sampling, without introducing dependencies into package math. This
10// uses a very rough approximation using the float64 exponent and the
11// first 25 bits of the mantissa. The top 5 bits of the mantissa are
12// used to load limits from a table of constants and the rest are used
13// to scale linearly between them.
14func fastlog2(x float64) float64 {
15	const fastlogScaleBits = 20
16	const fastlogScaleRatio = 1.0 / (1 << fastlogScaleBits)
17
18	xBits := float64bits(x)
19	// Extract the exponent from the IEEE float64, and index a constant
20	// table with the first 10 bits from the mantissa.
21	xExp := int64((xBits>>52)&0x7FF) - 1023
22	xManIndex := (xBits >> (52 - fastlogNumBits)) % (1 << fastlogNumBits)
23	xManScale := (xBits >> (52 - fastlogNumBits - fastlogScaleBits)) % (1 << fastlogScaleBits)
24
25	low, high := fastlog2Table[xManIndex], fastlog2Table[xManIndex+1]
26	return float64(xExp) + low + (high-low)*float64(xManScale)*fastlogScaleRatio
27}
28