floor.go

     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
     6  
     7  // Floor returns the greatest integer value less than or equal to x.
     8  //
     9  // Special cases are:
    10  //
    11  //	Floor(±0) = ±0
    12  //	Floor(±Inf) = ±Inf
    13  //	Floor(NaN) = NaN
    14  func Floor(x float64) float64 {
    15  	if haveArchFloor {
    16  		return archFloor(x)
    17  	}
    18  	return floor(x)
    19  }
    20  
    21  func floor(x float64) float64 {
    22  	if x == 0 || IsNaN(x) || IsInf(x, 0) {
    23  		return x
    24  	}
    25  	if x < 0 {
    26  		d, fract := Modf(-x)
    27  		if fract != 0.0 {
    28  			d = d + 1
    29  		}
    30  		return -d
    31  	}
    32  	d, _ := Modf(x)
    33  	return d
    34  }
    35  
    36  // Ceil returns the least integer value greater than or equal to x.
    37  //
    38  // Special cases are:
    39  //
    40  //	Ceil(±0) = ±0
    41  //	Ceil(±Inf) = ±Inf
    42  //	Ceil(NaN) = NaN
    43  func Ceil(x float64) float64 {
    44  	if haveArchCeil {
    45  		return archCeil(x)
    46  	}
    47  	return ceil(x)
    48  }
    49  
    50  func 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) = ±0
    59  //	Trunc(±Inf) = ±Inf
    60  //	Trunc(NaN) = NaN
    61  func Trunc(x float64) float64 {
    62  	if haveArchTrunc {
    63  		return archTrunc(x)
    64  	}
    65  	return trunc(x)
    66  }
    67  
    68  func trunc(x float64) float64 {
    69  	if x == 0 || IsNaN(x) || IsInf(x, 0) {
    70  		return x
    71  	}
    72  	d, _ := Modf(x)
    73  	return d
    74  }
    75  
    76  // Round returns the nearest integer, rounding half away from zero.
    77  //
    78  // Special cases are:
    79  //
    80  //	Round(±0) = ±0
    81  //	Round(±Inf) = ±Inf
    82  //	Round(NaN) = NaN
    83  func Round(x float64) float64 {
    84  	// Round is a faster implementation of:
    85  	//
    86  	// func Round(x float64) float64 {
    87  	//   t := Trunc(x)
    88  	//   if Abs(x-t) >= 0.5 {
    89  	//     return t + Copysign(1, x)
    90  	//   }
    91  	//   return t
    92  	// }
    93  	bits := Float64bits(x)
    94  	e := uint(bits>>shift) & mask
    95  	if e < bias {
    96  		// Round abs(x) < 1 including denormals.
    97  		bits &= signMask // +-0
    98  		if e == bias-1 {
    99  			bits |= uvone // +-1
   100  		}
   101  	} else if e < bias+shift {
   102  		// Round any abs(x) >= 1 containing a fractional component [0,1).
   103  		//
   104  		// Numbers with larger exponents are returned unchanged since they
   105  		// must be either an integer, infinity, or NaN.
   106  		const half = 1 << (shift - 1)
   107  		e -= bias
   108  		bits += half >> e
   109  		bits &^= fracMask >> e
   110  	}
   111  	return Float64frombits(bits)
   112  }
   113  
   114  // RoundToEven returns the nearest integer, rounding ties to even.
   115  //
   116  // Special cases are:
   117  //
   118  //	RoundToEven(±0) = ±0
   119  //	RoundToEven(±Inf) = ±Inf
   120  //	RoundToEven(NaN) = NaN
   121  func RoundToEven(x float64) float64 {
   122  	// RoundToEven is a faster implementation of:
   123  	//
   124  	// func RoundToEven(x float64) float64 {
   125  	//   t := math.Trunc(x)
   126  	//   odd := math.Remainder(t, 2) != 0
   127  	//   if d := math.Abs(x - t); d > 0.5 || (d == 0.5 && odd) {
   128  	//     return t + math.Copysign(1, x)
   129  	//   }
   130  	//   return t
   131  	// }
   132  	bits := Float64bits(x)
   133  	e := uint(bits>>shift) & mask
   134  	if e >= bias {
   135  		// Round abs(x) >= 1.
   136  		// - Large numbers without fractional components, infinity, and NaN are unchanged.
   137  		// - Add 0.499.. or 0.5 before truncating depending on whether the truncated
   138  		//   number is even or odd (respectively).
   139  		const halfMinusULP = (1 << (shift - 1)) - 1
   140  		e -= bias
   141  		bits += (halfMinusULP + (bits>>(shift-e))&1) >> e
   142  		bits &^= fracMask >> e
   143  	} else if e == bias-1 && bits&fracMask != 0 {
   144  		// Round 0.5 < abs(x) < 1.
   145  		bits = bits&signMask | uvone // +-1
   146  	} else {
   147  		// Round abs(x) <= 0.5 including denormals.
   148  		bits &= signMask // +-0
   149  	}
   150  	return Float64frombits(bits)
   151  }
   152
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