1// Copyright 2009 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
5// Package math provides basic constants and mathematical functions.
6//
7// This package does not guarantee bit-identical results across architectures.
8package math
9
10// Mathematical constants.
11const (
12	E   = 2.71828182845904523536028747135266249775724709369995957496696763 // https://oeis.org/A001113
13	Pi  = 3.14159265358979323846264338327950288419716939937510582097494459 // https://oeis.org/A000796
14	Phi = 1.61803398874989484820458683436563811772030917980576286213544862 // https://oeis.org/A001622
15
16	Sqrt2   = 1.41421356237309504880168872420969807856967187537694807317667974 // https://oeis.org/A002193
17	SqrtE   = 1.64872127070012814684865078781416357165377610071014801157507931 // https://oeis.org/A019774
18	SqrtPi  = 1.77245385090551602729816748334114518279754945612238712821380779 // https://oeis.org/A002161
19	SqrtPhi = 1.27201964951406896425242246173749149171560804184009624861664038 // https://oeis.org/A139339
20
21	Ln2    = 0.693147180559945309417232121458176568075500134360255254120680009 // https://oeis.org/A002162
22	Log2E  = 1 / Ln2
23	Ln10   = 2.30258509299404568401799145468436420760110148862877297603332790 // https://oeis.org/A002392
24	Log10E = 1 / Ln10
25)
26
27// Floating-point limit values.
28// Max is the largest finite value representable by the type.
29// SmallestNonzero is the smallest positive, non-zero value representable by the type.
30const (
31	MaxFloat32             = 0x1p127 * (1 + (1 - 0x1p-23)) // 3.40282346638528859811704183484516925440e+38
32	SmallestNonzeroFloat32 = 0x1p-126 * 0x1p-23            // 1.401298464324817070923729583289916131280e-45
33
34	MaxFloat64             = 0x1p1023 * (1 + (1 - 0x1p-52)) // 1.79769313486231570814527423731704356798070e+308
35	SmallestNonzeroFloat64 = 0x1p-1022 * 0x1p-52            // 4.9406564584124654417656879286822137236505980e-324
36)
37
38// Integer limit values.
39const (
40	intSize = 32 << (^uint(0) >> 63) // 32 or 64
41
42	MaxInt    = 1<<(intSize-1) - 1
43	MinInt    = -1 << (intSize - 1)
44	MaxInt8   = 1<<7 - 1
45	MinInt8   = -1 << 7
46	MaxInt16  = 1<<15 - 1
47	MinInt16  = -1 << 15
48	MaxInt32  = 1<<31 - 1
49	MinInt32  = -1 << 31
50	MaxInt64  = 1<<63 - 1
51	MinInt64  = -1 << 63
52	MaxUint   = 1<<intSize - 1
53	MaxUint8  = 1<<8 - 1
54	MaxUint16 = 1<<16 - 1
55	MaxUint32 = 1<<32 - 1
56	MaxUint64 = 1<<64 - 1
57)
58