Reconsider string representation of floating points for parameter files and parameter maps

[N-Dekker]

It seems more convenient to represent floating point (double) parameter values the same way for parameter files and parameter maps. Elastix currently uses scientific format, and default precision for parameter maps, and fixed (showpoint) format with a precision of 10 for parameter files. Both formats are lossy. C++11 allows specifying a lossless precision by max_digits10.

The following tables could be helpful. Related to issue #217 the "Origin" precision in TransformParameters is not high enough by @GouZi2019

Format	Precision	Length	String representation of 0
scientific	6 (default)	1	0
scientific	10 (elastix-txt-file)	1	0
scientific	15 (digits10)	1	0
scientific	17 (max_digits10)	1	0
fixed (showpoint)	6 (default)	8	0.000000
fixed (showpoint)	10 (elastix-txt-file)	12	0.0000000000
fixed (showpoint)	15 (digits10)	17	0.000000000000000
fixed (showpoint)	17 (max_digits10)	19	0.00000000000000000

Format	Precision	Length	String representation of 1
scientific	6 (default)	1	1
scientific	10 (elastix-txt-file)	1	1
scientific	15 (digits10)	1	1
scientific	17 (max_digits10)	1	1
fixed (showpoint)	6 (default)	8	1.000000
fixed (showpoint)	10 (elastix-txt-file)	12	1.0000000000
fixed (showpoint)	15 (digits10)	17	1.000000000000000
fixed (showpoint)	17 (max_digits10)	19	1.00000000000000000

Format	Precision	Length	String representation of 0.1
scientific	6 (default)	3	0.1
scientific	10 (elastix-txt-file)	3	0.1
scientific	15 (digits10)	3	0.1
scientific	17 (max_digits10)	19	0.10000000000000001
fixed (showpoint)	6 (default)	8	0.100000
fixed (showpoint)	10 (elastix-txt-file)	12	0.1000000000
fixed (showpoint)	15 (digits10)	17	0.100000000000000
fixed (showpoint)	17 (max_digits10)	19	0.10000000000000001

Format	Precision	Length	String representation of 1.0 / 3.0
scientific	6 (default)	8	0.333333
scientific	10 (elastix-txt-file)	12	0.3333333333
scientific	15 (digits10)	17	0.333333333333333
scientific	17 (max_digits10)	19	0.33333333333333331
fixed (showpoint)	6 (default)	8	0.333333
fixed (showpoint)	10 (elastix-txt-file)	12	0.3333333333
fixed (showpoint)	15 (digits10)	17	0.333333333333333
fixed (showpoint)	17 (max_digits10)	19	0.33333333333333331

Format	Precision	Length	String representation of 1e-10
scientific	6 (default)	5	1e-10
scientific	10 (elastix-txt-file)	5	1e-10
scientific	15 (digits10)	5	1e-10
scientific	17 (max_digits10)	5	1e-10
fixed (showpoint)	6 (default)	8	0.000000
fixed (showpoint)	10 (elastix-txt-file)	12	0.0000000001
fixed (showpoint)	15 (digits10)	17	0.000000000100000
fixed (showpoint)	17 (max_digits10)	19	0.00000000010000000

Format	Precision	Length	String representation of 1e+10
scientific	6 (default)	5	1e+10
scientific	10 (elastix-txt-file)	5	1e+10
scientific	15 (digits10)	11	10000000000
scientific	17 (max_digits10)	11	10000000000
fixed (showpoint)	6 (default)	18	10000000000.000000
fixed (showpoint)	10 (elastix-txt-file)	22	10000000000.0000000000
fixed (showpoint)	15 (digits10)	27	10000000000.000000000000000
fixed (showpoint)	17 (max_digits10)	29	10000000000.00000000000000000

Format	Precision	Length	String representation of 1e+10 - 1
scientific	6 (default)	5	1e+10
scientific	10 (elastix-txt-file)	10	9999999999
scientific	15 (digits10)	10	9999999999
scientific	17 (max_digits10)	10	9999999999
fixed (showpoint)	6 (default)	17	9999999999.000000
fixed (showpoint)	10 (elastix-txt-file)	21	9999999999.0000000000
fixed (showpoint)	15 (digits10)	26	9999999999.000000000000000
fixed (showpoint)	17 (max_digits10)	28	9999999999.00000000000000000

Format	Precision	Length	String representation of M_PI
scientific	6 (default)	7	3.14159
scientific	10 (elastix-txt-file)	11	3.141592654
scientific	15 (digits10)	16	3.14159265358979
scientific	17 (max_digits10)	18	3.1415926535897931
fixed (showpoint)	6 (default)	8	3.141593
fixed (showpoint)	10 (elastix-txt-file)	12	3.1415926536
fixed (showpoint)	15 (digits10)	17	3.141592653589793
fixed (showpoint)	17 (max_digits10)	19	3.14159265358979312

Format	Precision	Length	String representation of DBL_MIN
scientific	6 (default)	12	2.22507e-308
scientific	10 (elastix-txt-file)	16	2.225073859e-308
scientific	15 (digits10)	20	2.2250738585072e-308
scientific	17 (max_digits10)	23	2.2250738585072014e-308
fixed (showpoint)	6 (default)	8	0.000000
fixed (showpoint)	10 (elastix-txt-file)	12	0.0000000000
fixed (showpoint)	15 (digits10)	17	0.000000000000000
fixed (showpoint)	17 (max_digits10)	19	0.00000000000000000

Format	Precision	Length	String representation of DBL_EPSILON
scientific	6 (default)	11	2.22045e-16
scientific	10 (elastix-txt-file)	15	2.220446049e-16
scientific	15 (digits10)	20	2.22044604925031e-16
scientific	17 (max_digits10)	22	2.2204460492503131e-16
fixed (showpoint)	6 (default)	8	0.000000
fixed (showpoint)	10 (elastix-txt-file)	12	0.0000000000
fixed (showpoint)	15 (digits10)	17	0.000000000000000
fixed (showpoint)	17 (max_digits10)	19	0.00000000000000022

Format	Precision	Length	String representation of DBL_MAX
scientific	6 (default)	12	1.79769e+308
scientific	10 (elastix-txt-file)	16	1.797693135e+308
scientific	15 (digits10)	21	1.79769313486232e+308
scientific	17 (max_digits10)	23	1.7976931348623157e+308
fixed (showpoint)	6 (default)	316	1797693134...4124858368.000000
fixed (showpoint)	10 (elastix-txt-file)	320	1797693134...4124858368.0000000000
fixed (showpoint)	15 (digits10)	325	1797693134...4124858368.000000000000000
fixed (showpoint)	17 (max_digits10)	327	1797693134...4124858368.00000000000000000

[N-Dekker]

Code that produced the tables: https://rextester.com/JHSNQ26951

// Niels Dekker, LKEB, Leiden University Medical Center, 2021

#define _USE_MATH_DEFINES
#include <cmath>
#include <iostream>
#include <iomanip>
#include <sstream>
#include <limits>
#include <string>

const std::string separator = " | ";

std::string GetPrecisionAsString(const long long i)
{
	return std::to_string(i) + " (" +
		((i == std::ostringstream{}.precision()) ? "default" :
			(i == 10) ? "elastix-txt-file" :
			(i == std::numeric_limits<double>::digits10) ? "digits10" :
			(i == std::numeric_limits<double>::max_digits10) ? "max_digits10" :
			" ") + ")";
};


template <bool FixedFormat>
void Print(const double& x)
{
	std::ostringstream outputStringStreams[4];

	outputStringStreams[1] << std::setprecision(10);
	outputStringStreams[2] << std::setprecision(std::numeric_limits<double>::digits10);
	outputStringStreams[3] << std::setprecision(std::numeric_limits<double>::max_digits10);

	for (auto& outputStringStream : outputStringStreams)
	{
		if (FixedFormat)
		{
			outputStringStream << std::showpoint << std::fixed;
		}
		outputStringStream << x;
		const auto str = outputStringStream.str();
		std::cout << (FixedFormat ? "fixed (showpoint)" : "scientific")
			<< separator << GetPrecisionAsString(outputStringStream.precision())
			<< separator << str.length()
			<< separator << str << '\n';
	}
}

void Print(const double& x, const std::string& str)
{
	const auto dashes = " --- ";
	std::cout
		<< ("Format" + separator + "Precision" + separator + "Length" + separator + "String representation of " + str + '\n')
		<< (dashes + separator + dashes + separator + dashes + separator + dashes + '\n');
	Print<false>(x);
	Print<true>(x);
	std::cout << '\n';
}

#define PRINT_MACRO(x) Print(x, #x);

int main()
{
	PRINT_MACRO(0);
	PRINT_MACRO(1);
	PRINT_MACRO(0.1);
	PRINT_MACRO(1.0 / 3.0);
	PRINT_MACRO(1e-10);
	PRINT_MACRO(1e+10);
	PRINT_MACRO(1e+10 - 1);
	PRINT_MACRO(M_PI);
	PRINT_MACRO(DBL_MIN);
	PRINT_MACRO(DBL_EPSILON);
	PRINT_MACRO(DBL_MAX);
}

[N-Dekker]

For the record, ITK's itk::TransformFileWriter uses Google's double-conversion library to write transform parameters to file, like:

Parameters: 0 1 0.1 0.3333333333333333 1e-10 10000000000

and for 1e+10 - 1, M_PI, DBL_MIN, DBL_EPSILON, DBL_MAX:

Parameters: 9999999999 3.141592653589793 2.2250738585072014e-308 2.220446049250313e-16 1.7976931348623157e+308

[N-Dekker]

If both the elastix parameter file and the parameterMap would use the very same floating point format and precision, elastix Transform::WriteToFile member functions could simply write the values from the parameterMap directly to file. I think that would be preferable to the current situation (with parameterMap being "out of sync" with the parameter file).

[N-Dekker]

For the record, at the internal weekly elastix sprint this afternoon, Marius (@mstaring) and I agreed that it is worth adjusting the behavior of both Transform::WriteToFileand CreateTransformParametersMap to produce floating point values in the same format as ITK's itk::TransformFileWriter. So it is not necessary anymore to always write those numbers with 10 "fixed" decimals.

We agreed that it would be OK for Transform::WriteToFile to just call CreateTransformParametersMap, and then write the content of the map to file (in alphabetic order of the keys). It should be noted that string values that do not represent numeric values should get double-quotes, when written to file.