remainder.go

     1  // Copyright 2010 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  // The original C code and the comment below are from
     8  // FreeBSD's /usr/src/lib/msun/src/e_remainder.c and came
     9  // with this notice. The go code is a simplified version of
    10  // the original C.
    11  //
    12  // ====================================================
    13  // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
    14  //
    15  // Developed at SunPro, a Sun Microsystems, Inc. business.
    16  // Permission to use, copy, modify, and distribute this
    17  // software is freely granted, provided that this notice
    18  // is preserved.
    19  // ====================================================
    20  //
    21  // __ieee754_remainder(x,y)
    22  // Return :
    23  //      returns  x REM y  =  x - [x/y]*y  as if in infinite
    24  //      precision arithmetic, where [x/y] is the (infinite bit)
    25  //      integer nearest x/y (in half way cases, choose the even one).
    26  // Method :
    27  //      Based on Mod() returning  x - [x/y]chopped * y  exactly.
    28  
    29  // Remainder returns the IEEE 754 floating-point remainder of x/y.
    30  //
    31  // Special cases are:
    32  //	Remainder(±Inf, y) = NaN
    33  //	Remainder(NaN, y) = NaN
    34  //	Remainder(x, 0) = NaN
    35  //	Remainder(x, ±Inf) = x
    36  //	Remainder(x, NaN) = NaN
    37  func Remainder(x, y float64) float64 {
    38  	if haveArchRemainder {
    39  		return archRemainder(x, y)
    40  	}
    41  	return remainder(x, y)
    42  }
    43  
    44  func remainder(x, y float64) float64 {
    45  	const (
    46  		Tiny    = 4.45014771701440276618e-308 // 0x0020000000000000
    47  		HalfMax = MaxFloat64 / 2
    48  	)
    49  	// special cases
    50  	switch {
    51  	case IsNaN(x) || IsNaN(y) || IsInf(x, 0) || y == 0:
    52  		return NaN()
    53  	case IsInf(y, 0):
    54  		return x
    55  	}
    56  	sign := false
    57  	if x < 0 {
    58  		x = -x
    59  		sign = true
    60  	}
    61  	if y < 0 {
    62  		y = -y
    63  	}
    64  	if x == y {
    65  		if sign {
    66  			zero := 0.0
    67  			return -zero
    68  		}
    69  		return 0
    70  	}
    71  	if y <= HalfMax {
    72  		x = Mod(x, y+y) // now x < 2y
    73  	}
    74  	if y < Tiny {
    75  		if x+x > y {
    76  			x -= y
    77  			if x+x >= y {
    78  				x -= y
    79  			}
    80  		}
    81  	} else {
    82  		yHalf := 0.5 * y
    83  		if x > yHalf {
    84  			x -= y
    85  			if x >= yHalf {
    86  				x -= y
    87  			}
    88  		}
    89  	}
    90  	if sign {
    91  		x = -x
    92  	}
    93  	return x
    94  }
    95
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