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111
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1 -- CXG2001.A
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2 --
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3 -- Grant of Unlimited Rights
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4 --
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5 -- Under contracts F33600-87-D-0337, F33600-84-D-0280, MDA903-79-C-0687,
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6 -- F08630-91-C-0015, and DCA100-97-D-0025, the U.S. Government obtained
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7 -- unlimited rights in the software and documentation contained herein.
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8 -- Unlimited rights are defined in DFAR 252.227-7013(a)(19). By making
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9 -- this public release, the Government intends to confer upon all
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10 -- recipients unlimited rights equal to those held by the Government.
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11 -- These rights include rights to use, duplicate, release or disclose the
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12 -- released technical data and computer software in whole or in part, in
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13 -- any manner and for any purpose whatsoever, and to have or permit others
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14 -- to do so.
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15 --
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16 -- DISCLAIMER
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17 --
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18 -- ALL MATERIALS OR INFORMATION HEREIN RELEASED, MADE AVAILABLE OR
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19 -- DISCLOSED ARE AS IS. THE GOVERNMENT MAKES NO EXPRESS OR IMPLIED
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20 -- WARRANTY AS TO ANY MATTER WHATSOEVER, INCLUDING THE CONDITIONS OF THE
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21 -- SOFTWARE, DOCUMENTATION OR OTHER INFORMATION RELEASED, MADE AVAILABLE
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22 -- OR DISCLOSED, OR THE OWNERSHIP, MERCHANTABILITY, OR FITNESS FOR A
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23 -- PARTICULAR PURPOSE OF SAID MATERIAL.
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24 --*
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25 --
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26 -- OBJECTIVE:
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27 -- Check that the floating point attributes Model_Mantissa,
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28 -- Machine_Mantissa, Machine_Radix, and Machine_Rounds
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29 -- are properly reported.
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30 --
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31 -- TEST DESCRIPTION:
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32 -- This test uses a generic package to compute and check the
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33 -- values of the Machine_ attributes listed above. The
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34 -- generic package is instantiated with the standard FLOAT
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35 -- type and a floating point type for the maximum number
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36 -- of digits of precision.
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37 --
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38 -- APPLICABILITY CRITERIA:
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39 -- This test applies only to implementations supporting the
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40 -- Numerics Annex.
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41 --
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42 --
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43 -- CHANGE HISTORY:
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44 -- 26 JAN 96 SAIC Initial Release for 2.1
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45 --
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46 --!
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47
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48 -- References:
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49 --
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50 -- "Algorithms To Reveal Properties of Floating-Point Arithmetic"
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51 -- Michael A. Malcolm; CACM November 1972; pgs 949-951.
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52 --
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53 -- Software Manual for Elementary Functions; W. J. Cody and W. Waite;
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54 -- Prentice-Hall; 1980
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55 -----------------------------------------------------------------------
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56 --
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57 -- This test relies upon the fact that
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58 -- (A+2.0)-A is not necessarily 2.0. If A is large enough then adding
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59 -- a small value to A does not change the value of A. Consider the case
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60 -- where we have a decimal based floating point representation with 4
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61 -- digits of precision. A floating point number would logically be
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62 -- represented as "DDDD * 10 ** exp" where D is a value in the range 0..9.
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63 -- The first loop of the test starts A at 2.0 and doubles it until
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64 -- ((A+1.0)-A)-1.0 is no longer zero. For our decimal floating point
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65 -- number this will be 1638 * 10**1 (the value 16384 rounded or truncated
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66 -- to fit in 4 digits).
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67 -- The second loop starts B at 2.0 and keeps doubling B until (A+B)-A is
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68 -- no longer 0. This will keep looping until B is 8.0 because that is
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69 -- the first value where rounding (assuming our machine rounds and addition
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70 -- employs a guard digit) will change the upper 4 digits of the result:
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71 -- 1638_
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72 -- + 8
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73 -- -------
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74 -- 1639_
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75 -- Without rounding the second loop will continue until
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76 -- B is 16:
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77 -- 1638_
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78 -- + 16
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79 -- -------
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80 -- 1639_
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81 --
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82 -- The radix is then determined by (A+B)-A which will give 10.
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83 --
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84 -- The use of Tmp and ITmp in the test is to force values to be
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85 -- stored into memory in the event that register precision is greater
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86 -- than the stored precision of the floating point values.
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87 --
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88 --
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89 -- The test for rounding is (ignoring the temporary variables used to
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90 -- get the stored precision) is
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91 -- Rounds := A + Radix/2.0 - A /= 0.0 ;
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92 -- where A is the value determined in the first step that is the smallest
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93 -- power of 2 such that A + 1.0 = A. This means that the true value of
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94 -- A has one more digit in its value than 'Machine_Mantissa.
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95 -- This check will detect the case where a value is always rounded.
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96 -- There is an additional case where values are rounded to the nearest
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97 -- even value. That is referred to as IEEE style rounding in the test.
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98 --
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99 -----------------------------------------------------------------------
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100
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101 with System;
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102 with Report;
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103 with Ada.Numerics.Generic_Elementary_Functions;
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104 procedure CXG2001 is
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105 Verbose : constant Boolean := False;
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106
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107 -- if one of the attribute computation loops exceeds Max_Iterations
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108 -- it is most likely due to the compiler reordering an expression
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109 -- that should not be reordered.
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110 Illegal_Optimization : exception;
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111 Max_Iterations : constant := 10_000;
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112
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113 generic
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114 type Real is digits <>;
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115 package Chk_Attrs is
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116 procedure Do_Test;
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117 end Chk_Attrs;
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118
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119 package body Chk_Attrs is
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120 package EF is new Ada.Numerics.Generic_Elementary_Functions (Real);
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121 function Log (X : Real) return Real renames EF.Log;
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122
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123
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124 -- names used in paper
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125 Radix : Integer; -- Beta
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126 Mantissa_Digits : Integer; -- t
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127 Rounds : Boolean; -- RND
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128
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129 -- made global to Determine_Attributes to help thwart optimization
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130 A, B : Real := 2.0;
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131 Tmp, Tmpa, Tmp1 : Real;
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132 ITmp : Integer;
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133 Half_Radix : Real;
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134
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135 -- special constants - not declared as constants so that
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136 -- the "stored" precision will be used instead of a "register"
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137 -- precision.
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138 Zero : Real := 0.0;
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139 One : Real := 1.0;
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140 Two : Real := 2.0;
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141
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142
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143 procedure Thwart_Optimization is
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144 -- the purpose of this procedure is to reference the
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145 -- global variables used by Determine_Attributes so
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146 -- that the compiler is not likely to keep them in
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147 -- a higher precision register for their entire lifetime.
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148 begin
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149 if Report.Ident_Bool (False) then
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150 -- never executed
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151 A := A + 5.0;
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152 B := B + 6.0;
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153 Tmp := Tmp + 1.0;
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154 Tmp1 := Tmp1 + 2.0;
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155 Tmpa := Tmpa + 2.0;
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156 One := 12.34; Two := 56.78; Zero := 90.12;
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157 end if;
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158 end Thwart_Optimization;
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159
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160
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161 -- determines values for Radix, Mantissa_Digits, and Rounds
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162 -- This is mostly a straight translation of the C code.
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163 -- The only significant addition is the iteration count
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164 -- to prevent endless looping if things are really screwed up.
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165 procedure Determine_Attributes is
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166 Iterations : Integer;
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167 begin
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168 Rounds := True;
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169
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170 Iterations := 0;
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171 Tmp := Real'Machine (((A + One) - A) - One);
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172 while Tmp = Zero loop
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173 A := Real'Machine(A + A);
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174 Tmp := Real'Machine(A + One);
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175 Tmp1 := Real'Machine(Tmp - A);
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176 Tmp := Real'Machine(Tmp1 - One);
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177
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178 Iterations := Iterations + 1;
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179 if Iterations > Max_Iterations then
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180 raise Illegal_Optimization;
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181 end if;
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182 end loop;
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183
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184 Iterations := 0;
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185 Tmp := Real'Machine(A + B);
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186 ITmp := Integer (Tmp - A);
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187 while ITmp = 0 loop
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188 B := Real'Machine(B + B);
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189 Tmp := Real'Machine(A + B);
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190 ITmp := Integer (Tmp - A);
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191
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192 Iterations := Iterations + 1;
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193 if Iterations > Max_Iterations then
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194 raise Illegal_Optimization;
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195 end if;
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196 end loop;
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197
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198 Radix := ITmp;
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199
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200 Mantissa_Digits := 0;
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201 B := 1.0;
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202 Tmp := Real'Machine(((B + One) - B) - One);
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203 Iterations := 0;
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204 while (Tmp = Zero) loop
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205 Mantissa_Digits := Mantissa_Digits + 1;
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206 B := B * Real (Radix);
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207 Tmp := Real'Machine(B + One);
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208 Tmp1 := Real'Machine(Tmp - B);
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209 Tmp := Real'Machine(Tmp1 - One);
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210
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211 Iterations := Iterations + 1;
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212 if Iterations > Max_Iterations then
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213 raise Illegal_Optimization;
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214 end if;
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215 end loop;
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216
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217 Rounds := False;
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218 Half_Radix := Real (Radix) / Two;
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219 Tmp := Real'Machine(A + Half_Radix);
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220 Tmp1 := Real'Machine(Tmp - A);
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221 if (Tmp1 /= Zero) then
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222 Rounds := True;
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223 end if;
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224 Tmpa := Real'Machine(A + Real (Radix));
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225 Tmp := Real'Machine(Tmpa + Half_Radix);
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226 if not Rounds and (Tmp - TmpA /= Zero) then
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227 Rounds := True;
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228 if Verbose then
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229 Report.Comment ("IEEE style rounding");
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230 end if;
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231 end if;
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232
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233 exception
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234 when others =>
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235 Thwart_Optimization;
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236 raise;
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237 end Determine_Attributes;
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238
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239
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240 procedure Do_Test is
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241 Show_Results : Boolean := Verbose;
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242 Min_Mantissa_Digits : Integer;
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243 begin
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244 -- compute the actual Machine_* attribute values
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245 Determine_Attributes;
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246
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247 if Real'Machine_Radix /= Radix then
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248 Report.Failed ("'Machine_Radix incorrectly reports" &
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249 Integer'Image (Real'Machine_Radix));
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250 Show_Results := True;
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251 end if;
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252
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253 if Real'Machine_Mantissa /= Mantissa_Digits then
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254 Report.Failed ("'Machine_Mantissa incorrectly reports" &
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255 Integer'Image (Real'Machine_Mantissa));
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256 Show_Results := True;
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257 end if;
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258
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259 if Real'Machine_Rounds /= Rounds then
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260 Report.Failed ("'Machine_Rounds incorrectly reports " &
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261 Boolean'Image (Real'Machine_Rounds));
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262 Show_Results := True;
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263 end if;
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264
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265 if Show_Results then
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266 Report.Comment ("computed Machine_Mantissa is" &
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267 Integer'Image (Mantissa_Digits));
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268 Report.Comment ("computed Radix is" &
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269 Integer'Image (Radix));
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270 Report.Comment ("computed Rounds is " &
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271 Boolean'Image (Rounds));
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272 end if;
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273
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274 -- check the model attributes against the machine attributes
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275 -- G.2.2(3)/3;6.0
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276 if Real'Model_Mantissa > Real'Machine_Mantissa then
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277 Report.Failed ("model mantissa > machine mantissa");
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278 end if;
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279
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280 -- G.2.2(3)/2;6.0
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281 -- 'Model_Mantissa >= ceiling(d*log(10)/log(radix))+1
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282 Min_Mantissa_Digits :=
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283 Integer (
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284 Real'Ceiling (
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285 Real(Real'Digits) * Log(10.0) / Log(Real(Real'Machine_Radix))
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286 ) ) + 1;
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287 if Real'Model_Mantissa < Min_Mantissa_Digits then
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288 Report.Failed ("Model_Mantissa [" &
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289 Integer'Image (Real'Model_Mantissa) &
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290 "] < minimum mantissa digits [" &
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291 Integer'Image (Min_Mantissa_Digits) &
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292 "]");
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293 end if;
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294
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295 exception
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296 when Illegal_Optimization =>
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297 Report.Failed ("illegal optimization of" &
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298 " floating point expression");
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299 end Do_Test;
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300 end Chk_Attrs;
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301
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302 package Chk_Float is new Chk_Attrs (Float);
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303
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304 -- check the floating point type with the most digits
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305 type A_Long_Float is digits System.Max_Digits;
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306 package Chk_A_Long_Float is new Chk_Attrs (A_Long_Float);
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307 begin
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308 Report.Test ("CXG2001",
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309 "Check the attributes Model_Mantissa," &
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310 " Machine_Mantissa, Machine_Radix," &
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311 " and Machine_Rounds");
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312
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313 Report.Comment ("checking Standard.Float");
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314 Chk_Float.Do_Test;
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315
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316 Report.Comment ("checking a digits" &
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317 Integer'Image (System.Max_Digits) &
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318 " floating point type");
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319 Chk_A_Long_Float.Do_Test;
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320
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321 Report.Result;
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322 end CXG2001;
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