codekingpro/portable-devtools

1// Copyright 2009 The Go Authors. All rights reserved.2// Use of this source code is governed by a BSD-style3// license that can be found in the LICENSE file.4 5package math6 7// Floor returns the greatest integer value less than or equal to x.8//9// Special cases are:10//11//	Floor(±0) = ±012//	Floor(±Inf) = ±Inf13//	Floor(NaN) = NaN14func Floor(x float64) float64 {15	if haveArchFloor {16		return archFloor(x)17	}18	return floor(x)19}20 21func floor(x float64) float64 {22	if x == 0 || IsNaN(x) || IsInf(x, 0) {23		return x24	}25	if x < 0 {26		d, fract := Modf(-x)27		if fract != 0.0 {28			d = d + 129		}30		return -d31	}32	d, _ := Modf(x)33	return d34}35 36// Ceil returns the least integer value greater than or equal to x.37//38// Special cases are:39//40//	Ceil(±0) = ±041//	Ceil(±Inf) = ±Inf42//	Ceil(NaN) = NaN43func Ceil(x float64) float64 {44	if haveArchCeil {45		return archCeil(x)46	}47	return ceil(x)48}49 50func ceil(x float64) float64 {51	return -Floor(-x)52}53 54// Trunc returns the integer value of x.55//56// Special cases are:57//58//	Trunc(±0) = ±059//	Trunc(±Inf) = ±Inf60//	Trunc(NaN) = NaN61func Trunc(x float64) float64 {62	if haveArchTrunc {63		return archTrunc(x)64	}65	return trunc(x)66}67 68func trunc(x float64) float64 {69	if Abs(x) < 1 {70		return Copysign(0, x)71	}72 73	b := Float64bits(x)74	e := uint(b>>shift)&mask - bias75 76	// Keep the top 12+e bits, the integer part; clear the rest.77	if e < 64-12 {78		b &^= 1<<(64-12-e) - 179	}80	return Float64frombits(b)81}82 83// Round returns the nearest integer, rounding half away from zero.84//85// Special cases are:86//87//	Round(±0) = ±088//	Round(±Inf) = ±Inf89//	Round(NaN) = NaN90func Round(x float64) float64 {91	// Round is a faster implementation of:92	//93	// func Round(x float64) float64 {94	//   t := Trunc(x)95	//   if Abs(x-t) >= 0.5 {96	//     return t + Copysign(1, x)97	//   }98	//   return t99	// }100	bits := Float64bits(x)101	e := uint(bits>>shift) & mask102	if e < bias {103		// Round abs(x) < 1 including denormals.104		bits &= signMask // +-0105		if e == bias-1 {106			bits |= uvone // +-1107		}108	} else if e < bias+shift {109		// Round any abs(x) >= 1 containing a fractional component [0,1).110		//111		// Numbers with larger exponents are returned unchanged since they112		// must be either an integer, infinity, or NaN.113		const half = 1 << (shift - 1)114		e -= bias115		bits += half >> e116		bits &^= fracMask >> e117	}118	return Float64frombits(bits)119}120 121// RoundToEven returns the nearest integer, rounding ties to even.122//123// Special cases are:124//125//	RoundToEven(±0) = ±0126//	RoundToEven(±Inf) = ±Inf127//	RoundToEven(NaN) = NaN128func RoundToEven(x float64) float64 {129	// RoundToEven is a faster implementation of:130	//131	// func RoundToEven(x float64) float64 {132	//   t := math.Trunc(x)133	//   odd := math.Remainder(t, 2) != 0134	//   if d := math.Abs(x - t); d > 0.5 || (d == 0.5 && odd) {135	//     return t + math.Copysign(1, x)136	//   }137	//   return t138	// }139	bits := Float64bits(x)140	e := uint(bits>>shift) & mask141	if e >= bias {142		// Round abs(x) >= 1.143		// - Large numbers without fractional components, infinity, and NaN are unchanged.144		// - Add 0.499.. or 0.5 before truncating depending on whether the truncated145		//   number is even or odd (respectively).146		const halfMinusULP = (1 << (shift - 1)) - 1147		e -= bias148		bits += (halfMinusULP + (bits>>(shift-e))&1) >> e149		bits &^= fracMask >> e150	} else if e == bias-1 && bits&fracMask != 0 {151		// Round 0.5 < abs(x) < 1.152		bits = bits&signMask | uvone // +-1153	} else {154		// Round abs(x) <= 0.5 including denormals.155		bits &= signMask // +-0156	}157	return Float64frombits(bits)158}159