1 | // One modification by macko in FormatScientific(): use 3 digits of exponent only if necessary (e+123), otherwise use two if necessary (e+45), otherwise use one (e+6)
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2 | // This is consistent with java and javascript, and partially with python (which never uses one digit, only two or three).
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3 |
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4 |
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5 | /******************************************************************************
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6 | Copyright (c) 2014 Ryan Juckett
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7 | http://www.ryanjuckett.com/
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8 |
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9 | This software is provided 'as-is', without any express or implied
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10 | warranty. In no event will the authors be held liable for any damages
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11 | arising from the use of this software.
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12 |
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13 | Permission is granted to anyone to use this software for any purpose,
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14 | including commercial applications, and to alter it and redistribute it
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15 | freely, subject to the following restrictions:
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16 |
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17 | 1. The origin of this software must not be misrepresented; you must not
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18 | claim that you wrote the original software. If you use this software
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19 | in a product, an acknowledgment in the product documentation would be
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20 | appreciated but is not required.
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21 |
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22 | 2. Altered source versions must be plainly marked as such, and must not be
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23 | misrepresented as being the original software.
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24 |
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25 | 3. This notice may not be removed or altered from any source
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26 | distribution.
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27 | ******************************************************************************/
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28 |
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29 | #include "PrintFloat.h"
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30 | #include "Dragon4.h"
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31 | #include "Math.h"
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32 |
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33 | #include <string.h>
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34 |
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35 | //******************************************************************************
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36 | // Helper union to decompose a 32-bit IEEE float.
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37 | // sign: 1 bit
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38 | // exponent: 8 bits
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39 | // mantissa: 23 bits
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40 | //******************************************************************************
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41 | union tFloatUnion32
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42 | {
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43 | tB IsNegative() const { return (m_integer >> 31) != 0; }
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44 | tU32 GetExponent() const { return (m_integer >> 23) & 0xFF; }
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45 | tU32 GetMantissa() const { return m_integer & 0x7FFFFF; }
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46 |
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47 | tF32 m_floatingPoint;
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48 | tU32 m_integer;
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49 | };
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50 |
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51 | //******************************************************************************
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52 | // Helper union to decompose a 64-bit IEEE float.
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53 | // sign: 1 bit
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54 | // exponent: 11 bits
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55 | // mantissa: 52 bits
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56 | //******************************************************************************
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57 | union tFloatUnion64
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58 | {
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59 | tB IsNegative() const { return (m_integer >> 63) != 0; }
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60 | tU32 GetExponent() const { return (m_integer >> 52) & 0x7FF; }
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61 | tU64 GetMantissa() const { return m_integer & 0xFFFFFFFFFFFFFull; }
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62 |
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63 | tF64 m_floatingPoint;
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64 | tU64 m_integer;
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65 | };
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66 |
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67 | //******************************************************************************
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68 | // Outputs the positive number with positional notation: ddddd.dddd
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69 | // The output is always NUL terminated and the output length (not including the
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70 | // NUL) is returned.
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71 | //******************************************************************************
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72 | tU32 FormatPositional
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73 | (
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74 | tC8 * pOutBuffer, // buffer to output into
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75 | tU32 bufferSize, // maximum characters that can be printed to pOutBuffer
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76 | tU64 mantissa, // value significand
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77 | tS32 exponent, // value exponent in base 2
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78 | tU32 mantissaHighBitIdx, // index of the highest set mantissa bit
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79 | tB hasUnequalMargins, // is the high margin twice as large as the low margin
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80 | tS32 precision // Negative prints as many digits as are needed for a unique
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81 | // number. Positive specifies the maximum number of
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82 | // significant digits to print past the decimal point.
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83 | )
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84 | {
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85 | RJ_ASSERT(bufferSize > 0);
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86 |
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87 | tS32 printExponent;
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88 | tU32 numPrintDigits;
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89 |
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90 | tU32 maxPrintLen = bufferSize - 1;
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91 |
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92 | if (precision < 0)
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93 | {
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94 | numPrintDigits = Dragon4( mantissa,
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95 | exponent,
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96 | mantissaHighBitIdx,
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97 | hasUnequalMargins,
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98 | CutoffMode_Unique,
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99 | 0,
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100 | pOutBuffer,
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101 | maxPrintLen,
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102 | &printExponent );
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103 | }
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104 | else
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105 | {
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106 | numPrintDigits = Dragon4( mantissa,
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107 | exponent,
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108 | mantissaHighBitIdx,
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109 | hasUnequalMargins,
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110 | CutoffMode_FractionLength,
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111 | precision,
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112 | pOutBuffer,
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113 | maxPrintLen,
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114 | &printExponent );
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115 | }
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116 |
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117 | RJ_ASSERT( numPrintDigits > 0 );
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118 | RJ_ASSERT( numPrintDigits <= bufferSize );
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119 |
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120 | // track the number of digits past the decimal point that have been printed
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121 | tU32 numFractionDigits = 0;
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122 |
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123 | // if output has a whole number
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124 | if (printExponent >= 0)
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125 | {
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126 | // leave the whole number at the start of the buffer
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127 | tU32 numWholeDigits = printExponent+1;
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128 | if (numPrintDigits < numWholeDigits)
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129 | {
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130 | // don't overflow the buffer
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131 | if (numWholeDigits > maxPrintLen)
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132 | numWholeDigits = maxPrintLen;
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133 |
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134 | // add trailing zeros up to the decimal point
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135 | for ( ; numPrintDigits < numWholeDigits; ++numPrintDigits )
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136 | pOutBuffer[numPrintDigits] = '0';
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137 | }
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138 | // insert the decimal point prior to the fraction
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139 | else if (numPrintDigits > (tU32)numWholeDigits)
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140 | {
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141 | numFractionDigits = numPrintDigits - numWholeDigits;
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142 | tU32 maxFractionDigits = maxPrintLen - numWholeDigits - 1;
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143 | if (numFractionDigits > maxFractionDigits)
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144 | numFractionDigits = maxFractionDigits;
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145 |
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146 | memmove(pOutBuffer + numWholeDigits + 1, pOutBuffer + numWholeDigits, numFractionDigits);
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147 | pOutBuffer[numWholeDigits] = '.';
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148 | numPrintDigits = numWholeDigits + 1 + numFractionDigits;
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149 | }
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150 | }
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151 | else
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152 | {
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153 | // shift out the fraction to make room for the leading zeros
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154 | if (maxPrintLen > 2)
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155 | {
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156 | tU32 numFractionZeros = (tU32)-printExponent - 1;
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157 | tU32 maxFractionZeros = maxPrintLen - 2;
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158 | if (numFractionZeros > maxFractionZeros)
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159 | numFractionZeros = maxFractionZeros;
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160 |
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161 | tU32 digitsStartIdx = 2 + numFractionZeros;
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162 |
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163 | // shift the significant digits right such that there is room for leading zeros
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164 | numFractionDigits = numPrintDigits;
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165 | tU32 maxFractionDigits = maxPrintLen - digitsStartIdx;
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166 | if (numFractionDigits > maxFractionDigits)
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167 | numFractionDigits = maxFractionDigits;
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168 |
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169 | memmove(pOutBuffer + digitsStartIdx, pOutBuffer, numFractionDigits);
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170 |
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171 | // insert the leading zeros
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172 | for (tU32 i = 2; i < digitsStartIdx; ++i)
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173 | pOutBuffer[i] = '0';
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174 |
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175 | // update the counts
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176 | numFractionDigits += numFractionZeros;
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177 | numPrintDigits = numFractionDigits;
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178 | }
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179 |
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180 | // add the decimal point
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181 | if (maxPrintLen > 1)
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182 | {
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183 | pOutBuffer[1] = '.';
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184 | numPrintDigits += 1;
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185 | }
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186 |
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187 | // add the initial zero
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188 | if (maxPrintLen > 0)
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189 | {
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190 | pOutBuffer[0] = '0';
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191 | numPrintDigits += 1;
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192 | }
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193 | }
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194 |
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195 | // add trailing zeros up to precision length
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196 | if (precision > (tS32)numFractionDigits && numPrintDigits < maxPrintLen)
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197 | {
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198 | // add a decimal point if this is the first fractional digit we are printing
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199 | if (numFractionDigits == 0)
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200 | {
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201 | pOutBuffer[numPrintDigits++] = '.';
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202 | }
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203 |
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204 | // compute the number of trailing zeros needed
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205 | tU32 totalDigits = numPrintDigits + (precision - numFractionDigits);
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206 | if (totalDigits > maxPrintLen)
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207 | totalDigits = maxPrintLen;
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208 |
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209 | for ( ; numPrintDigits < totalDigits; ++numPrintDigits )
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210 | pOutBuffer[numPrintDigits] = '0';
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211 | }
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212 |
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213 | // terminate the buffer
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214 | RJ_ASSERT( numPrintDigits <= maxPrintLen );
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215 | pOutBuffer[numPrintDigits] = '\0';
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216 |
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217 | return numPrintDigits;
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218 | }
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219 |
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220 | //******************************************************************************
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221 | // Outputs the positive number with scientific notation: d.dddde[sign]ddd
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222 | // The output is always NUL terminated and the output length (not including the
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223 | // NUL) is returned.
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224 | //******************************************************************************
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225 | tU32 FormatScientific
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226 | (
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227 | tC8 * pOutBuffer, // buffer to output into
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228 | tU32 bufferSize, // maximum characters that can be printed to pOutBuffer
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229 | tU64 mantissa, // value significand
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230 | tS32 exponent, // value exponent in base 2
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231 | tU32 mantissaHighBitIdx, // index of the highest set mantissa bit
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232 | tB hasUnequalMargins, // is the high margin twice as large as the low margin
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233 | tS32 precision // Negative prints as many digits as are needed for a unique
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234 | // number. Positive specifies the maximum number of
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235 | // significant digits to print past the decimal point.
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236 | )
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237 | {
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238 | RJ_ASSERT(bufferSize > 0);
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239 |
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240 | tS32 printExponent;
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241 | tU32 numPrintDigits;
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242 |
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243 | if (precision < 0)
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244 | {
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245 | numPrintDigits = Dragon4( mantissa,
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246 | exponent,
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247 | mantissaHighBitIdx,
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248 | hasUnequalMargins,
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249 | CutoffMode_Unique,
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250 | 0,
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251 | pOutBuffer,
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252 | bufferSize,
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253 | &printExponent );
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254 | }
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255 | else
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256 | {
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257 | numPrintDigits = Dragon4( mantissa,
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258 | exponent,
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259 | mantissaHighBitIdx,
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260 | hasUnequalMargins,
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261 | CutoffMode_TotalLength,
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262 | precision + 1,
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263 | pOutBuffer,
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264 | bufferSize,
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265 | &printExponent );
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266 | }
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267 |
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268 | RJ_ASSERT( numPrintDigits > 0 );
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269 | RJ_ASSERT( numPrintDigits <= bufferSize );
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270 |
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271 | tC8 * pCurOut = pOutBuffer;
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272 |
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273 | // keep the whole number as the first digit
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274 | if (bufferSize > 1)
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275 | {
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276 | pCurOut += 1;
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277 | bufferSize -= 1;
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278 | }
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279 |
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280 | // insert the decimal point prior to the fractional number
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281 | tU32 numFractionDigits = numPrintDigits-1;
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282 | if (numFractionDigits > 0 && bufferSize > 1)
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283 | {
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284 | tU32 maxFractionDigits = bufferSize-2;
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285 | if (numFractionDigits > maxFractionDigits)
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286 | numFractionDigits = maxFractionDigits;
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287 |
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288 | memmove(pCurOut + 1, pCurOut, numFractionDigits);
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289 | pCurOut[0] = '.';
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290 | pCurOut += (1 + numFractionDigits);
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291 | bufferSize -= (1 + numFractionDigits);
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292 | }
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293 |
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294 | // add trailing zeros up to precision length
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295 | if (precision > (tS32)numFractionDigits && bufferSize > 1)
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296 | {
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297 | // add a decimal point if this is the first fractional digit we are printing
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298 | if (numFractionDigits == 0)
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299 | {
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300 | *pCurOut = '.';
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301 | ++pCurOut;
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302 | --bufferSize;
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303 | }
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304 |
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305 | // compute the number of trailing zeros needed
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306 | tU32 numZeros = (precision - numFractionDigits);
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307 | if (numZeros > bufferSize-1)
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308 | numZeros = bufferSize-1;
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309 |
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310 | for (tC8 * pEnd = pCurOut + numZeros; pCurOut < pEnd; ++pCurOut )
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311 | *pCurOut = '0';
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312 | }
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313 |
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314 | // print the exponent into a local buffer and copy into output buffer
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315 | if (bufferSize > 1)
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316 | {
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317 | tC8 exponentBuffer[5]; //we will need 3, 4 or 5 chars
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318 | exponentBuffer[0] = 'e';
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319 | if (printExponent >= 0)
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320 | {
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321 | exponentBuffer[1] = '+';
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322 | }
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323 | else
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324 | {
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325 | exponentBuffer[1] = '-';
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326 | printExponent = -printExponent;
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327 | }
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328 |
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329 | RJ_ASSERT(printExponent < 1000);
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330 | tU32 hundredsPlace = printExponent / 100;
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331 | tU32 tensPlace = (printExponent - hundredsPlace*100) / 10;
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332 | tU32 onesPlace = (printExponent - hundredsPlace*100 - tensPlace*10);
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333 |
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334 | // modified by macko: use 3 digits of exponent only if necessary (e+123), otherwise use two if necessary (e+45), otherwise use one (e+6)
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335 | unsigned int bufferIndex = 2;
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336 | if (hundredsPlace != 0) //3 digits needed
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337 | exponentBuffer[bufferIndex++] = (tC8)('0' + hundredsPlace);
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338 | if (hundredsPlace != 0 || tensPlace != 0) //2 digits needed
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339 | exponentBuffer[bufferIndex++] = (tC8)('0' + tensPlace);
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340 | exponentBuffer[bufferIndex++] = (tC8)('0' + onesPlace);
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341 | // now bufferIndex indicates how many characters of exponentBuffer were used
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342 |
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343 | // copy the exponent buffer into the output
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344 | tU32 maxExponentSize = bufferSize - 1;
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345 | tU32 exponentSize = (bufferIndex < maxExponentSize) ? bufferIndex : maxExponentSize;
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346 | memcpy( pCurOut, exponentBuffer, exponentSize );
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347 |
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348 | pCurOut += exponentSize;
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349 | bufferSize -= exponentSize;
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350 | }
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351 |
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352 | RJ_ASSERT( bufferSize > 0 );
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353 | pCurOut[0] = '\0';
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354 |
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355 | return pCurOut - pOutBuffer;
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356 | }
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357 |
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358 | //******************************************************************************
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359 | // Print a hexadecimal value with a given width.
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360 | // The output string is always NUL terminated and the string length (not
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361 | // including the NUL) is returned.
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362 | //******************************************************************************
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363 | static tU32 PrintHex(tC8 * pOutBuffer, tU32 bufferSize, tU64 value, tU32 width)
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364 | {
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365 | const tC8 digits[] = "0123456789abcdef";
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366 |
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367 | RJ_ASSERT(bufferSize > 0);
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368 |
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369 | tU32 maxPrintLen = bufferSize-1;
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370 | if (width > maxPrintLen)
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371 | width = maxPrintLen;
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372 |
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373 | tC8 * pCurOut = pOutBuffer;
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374 | while (width > 0)
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375 | {
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376 | --width;
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377 |
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378 | tU8 digit = (tU8)((value >> 4ull*(tU64)width) & 0xF);
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379 | *pCurOut = digits[digit];
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380 |
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381 | ++pCurOut;
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382 | }
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383 |
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384 | *pCurOut = '\0';
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385 | return pCurOut - pOutBuffer;
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386 | }
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387 |
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388 | //******************************************************************************
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389 | // Print special case values for infinities and NaNs.
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390 | // The output string is always NUL terminated and the string length (not
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391 | // including the NUL) is returned.
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392 | //******************************************************************************
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393 | static tU32 PrintInfNan(tC8 * pOutBuffer, tU32 bufferSize, tU64 mantissa, tU32 mantissaHexWidth)
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394 | {
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395 | RJ_ASSERT(bufferSize > 0);
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396 |
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397 | tU32 maxPrintLen = bufferSize-1;
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398 |
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399 | // Check for infinity
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400 | if (mantissa == 0)
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401 | {
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402 | // copy and make sure the buffer is terminated
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403 | tU32 printLen = (3 < maxPrintLen) ? 3 : maxPrintLen;
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404 | ::memcpy( pOutBuffer, "Inf", printLen );
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405 | pOutBuffer[printLen] = '\0';
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406 | return printLen;
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407 | }
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408 | else
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409 | {
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410 | // copy and make sure the buffer is terminated
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411 | tU32 printLen = (3 < maxPrintLen) ? 3 : maxPrintLen;
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412 | ::memcpy( pOutBuffer, "NaN", printLen );
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413 | pOutBuffer[printLen] = '\0';
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414 |
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415 | // append HEX value
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416 | if (maxPrintLen > 3)
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417 | printLen += PrintHex(pOutBuffer+3, bufferSize-3, mantissa, mantissaHexWidth);
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418 |
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419 | return printLen;
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420 | }
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421 | }
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422 |
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423 | //******************************************************************************
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424 | // Print a 32-bit floating-point number as a decimal string.
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425 | // The output string is always NUL terminated and the string length (not
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426 | // including the NUL) is returned.
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427 | //******************************************************************************
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428 | tU32 PrintFloat32
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429 | (
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430 | tC8 * pOutBuffer, // buffer to output into
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431 | tU32 bufferSize, // size of pOutBuffer
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432 | tF32 value, // value to print
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433 | tPrintFloatFormat format, // format to print with
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434 | tS32 precision // If negative, the minimum number of digits to represent a
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435 | // unique 32-bit floating point value is output. Otherwise,
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436 | // this is the number of digits to print past the decimal point.
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437 | )
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438 | {
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439 | if (bufferSize == 0)
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440 | return 0;
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441 |
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442 | if (bufferSize == 1)
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443 | {
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444 | pOutBuffer[0] = '\0';
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445 | return 0;
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446 | }
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447 |
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448 | // deconstruct the floating point value
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449 | tFloatUnion32 floatUnion;
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450 | floatUnion.m_floatingPoint = value;
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451 | tU32 floatExponent = floatUnion.GetExponent();
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452 | tU32 floatMantissa = floatUnion.GetMantissa();
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453 | tU32 prefixLength = 0;
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454 |
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455 | // output the sign
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456 | if (floatUnion.IsNegative())
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457 | {
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458 | pOutBuffer[0] = '-';
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459 | ++pOutBuffer;
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460 | --bufferSize;
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461 | ++prefixLength;
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462 | RJ_ASSERT(bufferSize > 0);
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463 | }
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464 |
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465 | // if this is a special value
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466 | if (floatExponent == 0xFF)
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467 | {
|
---|
468 | return PrintInfNan(pOutBuffer, bufferSize, floatMantissa, 6) + prefixLength;
|
---|
469 | }
|
---|
470 | // else this is a number
|
---|
471 | else
|
---|
472 | {
|
---|
473 | // factor the value into its parts
|
---|
474 | tU32 mantissa;
|
---|
475 | tS32 exponent;
|
---|
476 | tU32 mantissaHighBitIdx;
|
---|
477 | tB hasUnequalMargins;
|
---|
478 | if (floatExponent != 0)
|
---|
479 | {
|
---|
480 | // normalized
|
---|
481 | // The floating point equation is:
|
---|
482 | // value = (1 + mantissa/2^23) * 2 ^ (exponent-127)
|
---|
483 | // We convert the integer equation by factoring a 2^23 out of the exponent
|
---|
484 | // value = (1 + mantissa/2^23) * 2^23 * 2 ^ (exponent-127-23)
|
---|
485 | // value = (2^23 + mantissa) * 2 ^ (exponent-127-23)
|
---|
486 | // Because of the implied 1 in front of the mantissa we have 24 bits of precision.
|
---|
487 | // m = (2^23 + mantissa)
|
---|
488 | // e = (exponent-127-23)
|
---|
489 | mantissa = (1UL << 23) | floatMantissa;
|
---|
490 | exponent = floatExponent - 127 - 23;
|
---|
491 | mantissaHighBitIdx = 23;
|
---|
492 | hasUnequalMargins = (floatExponent != 1) && (floatMantissa == 0);
|
---|
493 | }
|
---|
494 | else
|
---|
495 | {
|
---|
496 | // denormalized
|
---|
497 | // The floating point equation is:
|
---|
498 | // value = (mantissa/2^23) * 2 ^ (1-127)
|
---|
499 | // We convert the integer equation by factoring a 2^23 out of the exponent
|
---|
500 | // value = (mantissa/2^23) * 2^23 * 2 ^ (1-127-23)
|
---|
501 | // value = mantissa * 2 ^ (1-127-23)
|
---|
502 | // We have up to 23 bits of precision.
|
---|
503 | // m = (mantissa)
|
---|
504 | // e = (1-127-23)
|
---|
505 | mantissa = floatMantissa;
|
---|
506 | exponent = 1 - 127 - 23;
|
---|
507 | mantissaHighBitIdx = LogBase2(mantissa);
|
---|
508 | hasUnequalMargins = false;
|
---|
509 | }
|
---|
510 |
|
---|
511 | // format the value
|
---|
512 | switch (format)
|
---|
513 | {
|
---|
514 | case PrintFloatFormat_Positional:
|
---|
515 | return FormatPositional( pOutBuffer,
|
---|
516 | bufferSize,
|
---|
517 | mantissa,
|
---|
518 | exponent,
|
---|
519 | mantissaHighBitIdx,
|
---|
520 | hasUnequalMargins,
|
---|
521 | precision ) + prefixLength;
|
---|
522 |
|
---|
523 | case PrintFloatFormat_Scientific:
|
---|
524 | return FormatScientific( pOutBuffer,
|
---|
525 | bufferSize,
|
---|
526 | mantissa,
|
---|
527 | exponent,
|
---|
528 | mantissaHighBitIdx,
|
---|
529 | hasUnequalMargins,
|
---|
530 | precision ) + prefixLength;
|
---|
531 |
|
---|
532 | default:
|
---|
533 | pOutBuffer[0] = '\0';
|
---|
534 | return 0;
|
---|
535 | }
|
---|
536 | }
|
---|
537 | }
|
---|
538 |
|
---|
539 | //******************************************************************************
|
---|
540 | // Print a 64-bit floating-point number as a decimal string.
|
---|
541 | // The output string is always NUL terminated and the string length (not
|
---|
542 | // including the NUL) is returned.
|
---|
543 | //******************************************************************************
|
---|
544 | tU32 PrintFloat64
|
---|
545 | (
|
---|
546 | tC8 * pOutBuffer, // buffer to output into
|
---|
547 | tU32 bufferSize, // size of pOutBuffer
|
---|
548 | tF64 value, // value to print
|
---|
549 | tPrintFloatFormat format, // format to print with
|
---|
550 | tS32 precision // If negative, the minimum number of digits to represent a
|
---|
551 | // unique 64-bit floating point value is output. Otherwise,
|
---|
552 | // this is the number of digits to print past the decimal point.
|
---|
553 | )
|
---|
554 | {
|
---|
555 | if (bufferSize == 0)
|
---|
556 | return 0;
|
---|
557 |
|
---|
558 | if (bufferSize == 1)
|
---|
559 | {
|
---|
560 | pOutBuffer[0] = '\0';
|
---|
561 | return 0;
|
---|
562 | }
|
---|
563 |
|
---|
564 | // deconstruct the floating point value
|
---|
565 | tFloatUnion64 floatUnion;
|
---|
566 | floatUnion.m_floatingPoint = value;
|
---|
567 | tU32 floatExponent = floatUnion.GetExponent();
|
---|
568 | tU64 floatMantissa = floatUnion.GetMantissa();
|
---|
569 | tU32 prefixLength = 0;
|
---|
570 |
|
---|
571 | // output the sign
|
---|
572 | if (floatUnion.IsNegative())
|
---|
573 | {
|
---|
574 | pOutBuffer[0] = '-';
|
---|
575 | ++pOutBuffer;
|
---|
576 | --bufferSize;
|
---|
577 | ++prefixLength;
|
---|
578 | RJ_ASSERT(bufferSize > 0);
|
---|
579 | }
|
---|
580 |
|
---|
581 | // if this is a special value
|
---|
582 | if (floatExponent == 0x7FF)
|
---|
583 | {
|
---|
584 | return PrintInfNan(pOutBuffer, bufferSize, floatMantissa, 13) + prefixLength;
|
---|
585 | }
|
---|
586 | // else this is a number
|
---|
587 | else
|
---|
588 | {
|
---|
589 | // factor the value into its parts
|
---|
590 | tU64 mantissa;
|
---|
591 | tS32 exponent;
|
---|
592 | tU32 mantissaHighBitIdx;
|
---|
593 | tB hasUnequalMargins;
|
---|
594 |
|
---|
595 | if (floatExponent != 0)
|
---|
596 | {
|
---|
597 | // normal
|
---|
598 | // The floating point equation is:
|
---|
599 | // value = (1 + mantissa/2^52) * 2 ^ (exponent-1023)
|
---|
600 | // We convert the integer equation by factoring a 2^52 out of the exponent
|
---|
601 | // value = (1 + mantissa/2^52) * 2^52 * 2 ^ (exponent-1023-52)
|
---|
602 | // value = (2^52 + mantissa) * 2 ^ (exponent-1023-52)
|
---|
603 | // Because of the implied 1 in front of the mantissa we have 53 bits of precision.
|
---|
604 | // m = (2^52 + mantissa)
|
---|
605 | // e = (exponent-1023+1-53)
|
---|
606 | mantissa = (1ull << 52) | floatMantissa;
|
---|
607 | exponent = floatExponent - 1023 - 52;
|
---|
608 | mantissaHighBitIdx = 52;
|
---|
609 | hasUnequalMargins = (floatExponent != 1) && (floatMantissa == 0);
|
---|
610 | }
|
---|
611 | else
|
---|
612 | {
|
---|
613 | // subnormal
|
---|
614 | // The floating point equation is:
|
---|
615 | // value = (mantissa/2^52) * 2 ^ (1-1023)
|
---|
616 | // We convert the integer equation by factoring a 2^52 out of the exponent
|
---|
617 | // value = (mantissa/2^52) * 2^52 * 2 ^ (1-1023-52)
|
---|
618 | // value = mantissa * 2 ^ (1-1023-52)
|
---|
619 | // We have up to 52 bits of precision.
|
---|
620 | // m = (mantissa)
|
---|
621 | // e = (1-1023-52)
|
---|
622 | mantissa = floatMantissa;
|
---|
623 | exponent = 1 - 1023 - 52;
|
---|
624 | mantissaHighBitIdx = LogBase2(mantissa);
|
---|
625 | hasUnequalMargins = false;
|
---|
626 | }
|
---|
627 |
|
---|
628 | // format the value
|
---|
629 | switch (format)
|
---|
630 | {
|
---|
631 | case PrintFloatFormat_Positional:
|
---|
632 | return FormatPositional( pOutBuffer,
|
---|
633 | bufferSize,
|
---|
634 | mantissa,
|
---|
635 | exponent,
|
---|
636 | mantissaHighBitIdx,
|
---|
637 | hasUnequalMargins,
|
---|
638 | precision ) + prefixLength;
|
---|
639 |
|
---|
640 | case PrintFloatFormat_Scientific:
|
---|
641 | return FormatScientific( pOutBuffer,
|
---|
642 | bufferSize,
|
---|
643 | mantissa,
|
---|
644 | exponent,
|
---|
645 | mantissaHighBitIdx,
|
---|
646 | hasUnequalMargins,
|
---|
647 | precision ) + prefixLength;
|
---|
648 |
|
---|
649 | default:
|
---|
650 | pOutBuffer[0] = '\0';
|
---|
651 | return 0;
|
---|
652 | }
|
---|
653 | }
|
---|
654 | }
|
---|