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annotate lib/round.c @ 17342:c75939cb6254

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author Michael Goffioul <michael.goffioul@gmail.com>
date Thu, 21 Feb 2013 14:57:31 +0000
parents e542fd46ad6f
children
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1 /* Round toward nearest, breaking ties away from zero.
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2 Copyright (C) 2007, 2010-2013 Free Software Foundation, Inc.
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3
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4 This program is free software; you can redistribute it and/or modify
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5 it under the terms of the GNU General Public License as published by
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6 the Free Software Foundation; either version 2, or (at your option)
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7 any later version.
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8
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9 This program is distributed in the hope that it will be useful,
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10 but WITHOUT ANY WARRANTY; without even the implied warranty of
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11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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12 GNU General Public License for more details.
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13
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14 You should have received a copy of the GNU General Public License along
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15 with this program; if not, see <http://www.gnu.org/licenses/>. */
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16
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17 /* Written by Ben Pfaff <blp@gnu.org>, 2007.
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18 Based heavily on code by Bruno Haible. */
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19
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20 #if ! defined USE_LONG_DOUBLE
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21 # include <config.h>
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22 #endif
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23
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24 /* Specification. */
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25 #include <math.h>
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26
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27 #include <float.h>
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28
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29 #undef MIN
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30
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31 #ifdef USE_LONG_DOUBLE
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32 # define ROUND roundl
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33 # define FLOOR floorl
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34 # define CEIL ceill
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35 # define DOUBLE long double
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36 # define MANT_DIG LDBL_MANT_DIG
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37 # define MIN LDBL_MIN
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38 # define L_(literal) literal##L
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39 # define HAVE_FLOOR_AND_CEIL HAVE_FLOORL_AND_CEILL
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40 #elif ! defined USE_FLOAT
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41 # define ROUND round
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42 # define FLOOR floor
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43 # define CEIL ceil
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44 # define DOUBLE double
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45 # define MANT_DIG DBL_MANT_DIG
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46 # define MIN DBL_MIN
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47 # define L_(literal) literal
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48 # define HAVE_FLOOR_AND_CEIL 1
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49 #else /* defined USE_FLOAT */
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50 # define ROUND roundf
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51 # define FLOOR floorf
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52 # define CEIL ceilf
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53 # define DOUBLE float
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54 # define MANT_DIG FLT_MANT_DIG
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55 # define MIN FLT_MIN
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56 # define L_(literal) literal##f
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57 # define HAVE_FLOOR_AND_CEIL HAVE_FLOORF_AND_CEILF
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58 #endif
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59
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60 /* -0.0. See minus-zero.h. */
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61 #if defined __hpux || defined __sgi || defined __ICC
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62 # define MINUS_ZERO (-MIN * MIN)
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63 #else
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64 # define MINUS_ZERO L_(-0.0)
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65 #endif
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66
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67 /* MSVC with option -fp:strict refuses to compile constant initializers that
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68 contain floating-point operations. Pacify this compiler. */
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69 #ifdef _MSC_VER
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70 # pragma fenv_access (off)
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71 #endif
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72
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73 /* If we're being included from test-round2[f].c, it already defined names for
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74 our round implementations. Otherwise, pick the preferred implementation for
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75 this machine. */
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76 #if !defined FLOOR_BASED_ROUND && !defined FLOOR_FREE_ROUND
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77 # if HAVE_FLOOR_AND_CEIL
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78 # define FLOOR_BASED_ROUND ROUND
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79 # else
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80 # define FLOOR_FREE_ROUND ROUND
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81 # endif
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82 #endif
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83
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84 #ifdef FLOOR_BASED_ROUND
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85 /* An implementation of the C99 round function based on floor and ceil. We use
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86 this when floor and ceil are available, on the assumption that they are
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87 faster than the open-coded versions below. */
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88 DOUBLE
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89 FLOOR_BASED_ROUND (DOUBLE x)
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90 {
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91 if (x >= L_(0.0))
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92 {
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93 DOUBLE y = FLOOR (x);
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94 if (x - y >= L_(0.5))
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95 y += L_(1.0);
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96 return y;
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97 }
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98 else
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99 {
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100 DOUBLE y = CEIL (x);
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101 if (y - x >= L_(0.5))
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102 y -= L_(1.0);
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103 return y;
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104 }
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105 }
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106 #endif /* FLOOR_BASED_ROUND */
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107
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108 #ifdef FLOOR_FREE_ROUND
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109 /* An implementation of the C99 round function without floor or ceil.
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110 We use this when floor or ceil is missing. */
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111 DOUBLE
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112 FLOOR_FREE_ROUND (DOUBLE x)
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113 {
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114 /* 2^(MANT_DIG-1). */
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115 static const DOUBLE TWO_MANT_DIG =
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116 /* Assume MANT_DIG <= 5 * 31.
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117 Use the identity
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118 n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5). */
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119 (DOUBLE) (1U << ((MANT_DIG - 1) / 5))
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120 * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
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121 * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
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122 * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
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123 * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
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124
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125 /* The use of 'volatile' guarantees that excess precision bits are dropped at
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126 each addition step and before the following comparison at the caller's
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127 site. It is necessary on x86 systems where double-floats are not IEEE
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128 compliant by default, to avoid that the results become platform and
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129 compiler option dependent. 'volatile' is a portable alternative to gcc's
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130 -ffloat-store option. */
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131 volatile DOUBLE y = x;
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132 volatile DOUBLE z = y;
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133
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134 if (z > L_(0.0))
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135 {
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136 /* Avoid rounding error for x = 0.5 - 2^(-MANT_DIG-1). */
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137 if (z < L_(0.5))
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138 z = L_(0.0);
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139 /* Avoid rounding errors for values near 2^k, where k >= MANT_DIG-1. */
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140 else if (z < TWO_MANT_DIG)
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141 {
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142 /* Add 0.5 to the absolute value. */
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143 y = z += L_(0.5);
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144 /* Round to the next integer (nearest or up or down, doesn't
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145 matter). */
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146 z += TWO_MANT_DIG;
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147 z -= TWO_MANT_DIG;
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148 /* Enforce rounding down. */
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149 if (z > y)
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150 z -= L_(1.0);
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151 }
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152 }
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153 else if (z < L_(0.0))
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154 {
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155 /* Avoid rounding error for x = -(0.5 - 2^(-MANT_DIG-1)). */
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156 if (z > - L_(0.5))
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157 z = MINUS_ZERO;
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158 /* Avoid rounding errors for values near -2^k, where k >= MANT_DIG-1. */
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159 else if (z > -TWO_MANT_DIG)
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160 {
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161 /* Add 0.5 to the absolute value. */
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162 y = z -= L_(0.5);
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163 /* Round to the next integer (nearest or up or down, doesn't
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164 matter). */
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165 z -= TWO_MANT_DIG;
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166 z += TWO_MANT_DIG;
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167 /* Enforce rounding up. */
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168 if (z < y)
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169 z += L_(1.0);
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170 }
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171 }
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172 return z;
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173 }
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174 #endif /* FLOOR_FREE_ROUND */