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1 /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*- vi:set ts=8 sts=4 sw=4: */
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2
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3 /*
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4 Sonic Visualiser
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5 An audio file viewer and annotation editor.
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6 Centre for Digital Music, Queen Mary, University of London.
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7 This file copyright 2006-2017 Chris Cannam and QMUL.
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8
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9 This program is free software; you can redistribute it and/or
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10 modify it under the terms of the GNU General Public License as
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11 published by the Free Software Foundation; either version 2 of the
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12 License, or (at your option) any later version. See the file
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13 COPYING included with this distribution for more information.
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14 */
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15
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16 #ifndef SV_SCALE_TICK_INTERVALS_H
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17 #define SV_SCALE_TICK_INTERVALS_H
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18
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19 #include <string>
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20 #include <vector>
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21 #include <cmath>
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22
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23 #define DEBUG_SCALE_TICK_INTERVALS 1
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24
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25 #ifdef DEBUG_SCALE_TICK_INTERVALS
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26 #include <iostream>
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27 #endif
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28
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29 #include "LogRange.h"
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30
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31 class ScaleTickIntervals
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32 {
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33 public:
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34 struct Range {
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35 double min; // start of value range
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36 double max; // end of value range
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37 int n; // number of divisions (approximate only)
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38 };
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39
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40 struct Tick {
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41 double value; // value this tick represents
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42 std::string label; // value as written
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43 };
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44
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45 typedef std::vector<Tick> Ticks;
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46
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47 /**
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48 * Return a set of ticks that divide the range r linearly into
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49 * roughly r.n equal divisions, in such a way as to yield
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50 * reasonably human-readable labels.
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51 */
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52 static Ticks linear(Range r) {
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53 return linearTicks(r);
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54 }
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55
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56 /**
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57 * Return a set of ticks that divide the range r into roughly r.n
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58 * logarithmic divisions, in such a way as to yield reasonably
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59 * human-readable labels.
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60 */
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61 static Ticks logarithmic(Range r) {
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62 LogRange::mapRange(r.min, r.max);
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63 return logarithmicAlready(r);
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64 }
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65
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66 /**
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67 * Return a set of ticks that divide the range r into roughly r.n
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68 * logarithmic divisions, on the asssumption that r.min and r.max
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69 * already represent the logarithms of the boundary values rather
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70 * than the values themselves.
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71 */
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72 static Ticks logarithmicAlready(Range r) {
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73 return logTicks(r);
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74 }
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75
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76 private:
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77 enum Display {
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78 Fixed,
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79 Scientific,
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80 Auto
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81 };
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82
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83 struct Instruction {
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84 double initial; // value of first tick
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85 double limit; // max from original range
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86 double spacing; // increment between ticks
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87 double roundTo; // what all displayed values should be rounded to
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88 Display display; // whether to use fixed precision (%e, %f, or %g)
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89 int precision; // number of dp (%f) or sf (%e)
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90 bool logUnmap; // true if values represent logs of display values
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91 };
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92
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93 static Instruction linearInstruction(Range r)
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94 {
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95 Display display = Auto;
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96
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97 if (r.max < r.min) {
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98 return linearInstruction({ r.max, r.min, r.n });
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99 }
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100 if (r.n < 1 || r.max == r.min) {
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101 return { r.min, r.min, 1.0, r.min, display, 1, false };
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102 }
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103
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104 double inc = (r.max - r.min) / r.n;
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105
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106 double digInc = log10(inc);
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107 double digMax = log10(fabs(r.max));
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108 double digMin = log10(fabs(r.min));
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109
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110 int precInc = int(floor(digInc));
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111 double roundTo = pow(10.0, precInc);
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112
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113 if (precInc > -4 && precInc < 4) {
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114 display = Fixed;
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115 } else if ((digMax >= -2.0 && digMax <= 3.0) &&
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116 (digMin >= -3.0 && digMin <= 3.0)) {
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117 display = Fixed;
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118 } else {
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119 display = Scientific;
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120 }
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121
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122 int precRange = int(ceil(digMax - digInc));
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123
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124 int prec = 1;
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125
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126 if (display == Fixed) {
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127 if (digInc < 0) {
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128 prec = -precInc;
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129 } else {
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130 prec = 0;
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131 }
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132 } else {
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133 prec = precRange;
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134 }
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135
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136 #ifdef DEBUG_SCALE_TICK_INTERVALS
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137 std::cerr << "\nmin = " << r.min << ", max = " << r.max << ", n = " << r.n
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138 << ", inc = " << inc << std::endl;
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139 std::cerr << "digMax = " << digMax << ", digInc = " << digInc
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140 << std::endl;
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141 std::cerr << "display = " << display << ", inc = " << inc
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142 << ", precInc = " << precInc << ", precRange = " << precRange
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143 << ", prec = " << prec << std::endl;
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144 std::cerr << "roundTo = " << roundTo << std::endl;
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145 #endif
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146
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147 double min = r.min;
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148
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149 if (roundTo != 0.0) {
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150 inc = round(inc / roundTo) * roundTo;
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151 if (inc < roundTo) inc = roundTo;
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152 min = ceil(min / roundTo) * roundTo;
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153 if (min > r.max) min = r.max;
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154 }
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155
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156 if (display == Scientific && min != 0.0) {
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157 double digNewMin = log10(fabs(min));
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158 if (digNewMin < digInc) {
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159 prec = int(ceil(digMax - digNewMin));
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160 #ifdef DEBUG_SCALE_TICK_INTERVALS
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161 std::cerr << "min is smaller than increment, adjusting prec to "
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162 << prec << std::endl;
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163 #endif
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164 }
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165 }
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166
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167 return { min, r.max, inc, roundTo, display, prec, false };
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168 }
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169
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170 static Instruction logInstruction(Range r)
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171 {
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172 Display display = Auto;
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173
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174 if (r.n < 1) {
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175 return {};
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176 }
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177 if (r.max < r.min) {
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178 return logInstruction({ r.max, r.min, r.n });
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179 }
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180 if (r.max == r.min) {
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181 return { r.min, r.max, 1.0, r.min, display, 1, true };
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182 }
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183
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184 double inc = (r.max - r.min) / r.n;
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185
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186 double digInc = log10(inc);
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187 int precInc = int(floor(digInc));
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188 double roundTo = pow(10.0, precInc);
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189
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190 if (roundTo != 0.0) {
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191 inc = round(inc / roundTo) * roundTo;
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192 if (inc < roundTo) inc = roundTo;
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193 }
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194
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195 // if inc is close to giving us powers of two, nudge it
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196 if (fabs(inc - 0.301) < 0.01) {
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197 inc = log10(2.0);
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198 }
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199
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200 // smallest increment as displayed
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201 double minDispInc =
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202 LogRange::unmap(r.min + inc) - LogRange::unmap(r.min);
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203
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204 int prec = 1;
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205
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206 if (minDispInc > 0.0) {
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207 prec = int(floor(log10(minDispInc)));
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208 if (prec < 0) prec = -prec;
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209 }
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210
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211 if (r.max >= -2.0 && r.max <= 3.0 &&
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212 r.min >= -3.0 && r.min <= 3.0) {
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213 display = Fixed;
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214 if (prec == 0) prec = 1;
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215 }
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216
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217 #ifdef DEBUG_SCALE_TICK_INTERVALS
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218 std::cerr << "\nmin = " << r.min << ", max = " << r.max << ", n = " << r.n
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219 << ", inc = " << inc << ", minDispInc = " << minDispInc
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220 << ", digInc = " << digInc << std::endl;
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221 std::cerr << "display = " << display << ", inc = " << inc
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222 << ", precInc = " << precInc
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223 << ", prec = " << prec << std::endl;
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224 std::cerr << "roundTo = " << roundTo << std::endl;
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225 #endif
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226
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227 double min = r.min;
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228 if (inc != 0.0) {
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229 min = ceil(r.min / inc) * inc;
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230 if (min > r.max) min = r.max;
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231 }
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232
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233 return { min, r.max, inc, 0.0, display, prec, true };
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234 }
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235
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236 static Ticks linearTicks(Range r) {
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237 Instruction instruction = linearInstruction(r);
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238 Ticks ticks = explode(instruction);
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239 return ticks;
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240 }
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241
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242 static Ticks logTicks(Range r) {
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243 Instruction instruction = logInstruction(r);
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244 Ticks ticks = explode(instruction);
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245 return ticks;
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246 }
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247
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248 static Tick makeTick(Display display, int precision, double value) {
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249 const int buflen = 40;
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250 char buffer[buflen];
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251 snprintf(buffer, buflen,
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252 display == Auto ? "%.*g" :
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253 display == Fixed ? "%.*f" :
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254 "%.*e",
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255 precision, value);
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256 return Tick({ value, std::string(buffer) });
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257 }
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258
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259 static Ticks explode(Instruction instruction) {
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260
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261 #ifdef DEBUG_SCALE_TICK_INTERVALS
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262 std::cerr << "initial = " << instruction.initial
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263 << ", limit = " << instruction.limit
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264 << ", spacing = " << instruction.spacing
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265 << ", roundTo = " << instruction.roundTo
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266 << ", display = " << instruction.display
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267 << ", precision = " << instruction.precision
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268 << ", logUnmap = " << instruction.logUnmap
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269 << std::endl;
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270 #endif
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271
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272 if (instruction.spacing == 0.0) {
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273 return {};
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274 }
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275
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276 double eps = 1e-7;
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277 if (instruction.spacing < eps * 10.0) {
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278 eps = instruction.spacing / 10.0;
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279 }
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280
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281 double max = instruction.limit;
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282 int n = 0;
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283
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284 Ticks ticks;
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285
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286 while (true) {
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287 double value = instruction.initial + n * instruction.spacing;
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288 if (value >= max + eps) {
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289 break;
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290 }
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291 if (instruction.logUnmap) {
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292 value = pow(10.0, value);
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293 }
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294 if (instruction.roundTo != 0.0) {
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295 value = instruction.roundTo * round(value / instruction.roundTo);
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296 }
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297 ticks.push_back(makeTick(instruction.display,
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298 instruction.precision,
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299 value));
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300 ++n;
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301 }
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302
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303 return ticks;
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304 }
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305 };
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306
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307 #endif
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