pyrtsa · February 14, 2016 12:43 · Feb 14, 2016
diff --git a/approx.m b/approx.m
@@ -0,0 +1,15 @@
+function y = approx(x, n)
+% APPROX  Round the number to 1+n significant digits.
+%   y = APPROX(x) shorthand for round(x, 4, 'significant').
+%   y = APPROX(x, n) shorthand for round(x, 1 + n, 'significant').
+
+%   Copyright 2016 Pyry Jahkola
+
+if nargin < 2
+    n = 3;
+end
+
+m = floor(log10(abs(x)));
+unit = 10 .^ (max(m) - n);
+y = bsxfun(@times, round(bsxfun(@rdivide, x, unit)), unit);
+
diff --git a/concise.m b/concise.m
@@ -0,0 +1,41 @@
+function str = concise(x, d)
+% CONCISE  Concise representation of a quantity value x ± d.
+%   str = CONCISE(x, d) returns the concise form string representation of
+%   x ± d where the precision in x is kept up to the two most significant
+%   digits of d and those two digits are shown in parentheses.
+%
+%   The result is shown with power-of-ten representation which is omitted
+%   if the exponent is zero.
+%
+% Examples
+%
+%   CONCISE(3.14159, 0.0485) %=> '3.142(49)'
+%   CONCISE(6.02214129e23, 2.7e16) %=> '6.02214129(27) × 10^23'
+%   CONCISE(6.67408e-11, 3.1e-15) %=> '6.67408(31) × 10^-11'
+
+%   Copyright 2016 Pyry Jahkola
+
+xmag = floor(log10(abs(x)));
+dmag = floor(log10(abs(d)));
+mag = max(xmag, dmag);
+prec = mag - dmag + 1;
+x = round(x, 1 - dmag);
+if dmag >= 0
+    D = round(d / 10 ^ (dmag - 1));
+else
+    D = round(d * 10 ^ (1 - dmag));
+end
+
+if mag > 0
+    X = x / 10 ^ mag;
+    fmt = sprintf('%%.%df(%%02d) × 10^%%d', prec);
+    str = sprintf(fmt, X, D, mag);
+elseif mag < 0
+    X = x * 10 ^ -mag;
+    fmt = sprintf('%%.%df(%%02d) × 10^%%d', prec);
+    str = sprintf(fmt, X, D, mag);
+else
+    X = x / 10 ^ mag;
+    fmt = sprintf('%%.%df(%%02d)', prec);
+    str = sprintf(fmt, X, D);
+end
diff --git a/magnitude.m b/magnitude.m
@@ -0,0 +1,9 @@
+function m = magnitude(x)
+% MAGNITUDE  Get the power-of-ten order of a number.
+%   m = MAGNITUDE(x) returns the largest integer m where 10^m <= abs(x).
+%   m = MAGNITUDE(0) returns -Inf.
+
+%   Copyright 2016 Pyry Jahkola
+
+m = floor(log10(abs(x)));
+
diff --git a/plusminus.m b/plusminus.m
@@ -0,0 +1,39 @@
+function str = plusminus(x, d)
+% PLUSMINUS  Full representation of quantity value x ± d
+%   str = PLUSMINUS(x, d) returns the value x ± d as a string of
+%   form of either '(x ± d) × 10^e' or 'x ± d', keeping precision
+%   up to two most significant digits of d, and omitting the
+%   power-of-ten representation for values within range [0.1, 1000).
+%
+% Examples
+%
+%   PLUSMINUS(3.14159, 0.0485)       %=> '3.142 ± 0.049'
+%   PLUSMINUS(6.02214129e23, 2.7e16) %=> '(6.02214129 ± 0.00000027) × 10^23'
+%   PLUSMINUS(6.67408e-11, 3.1e-15)  %=> '(6.67408 ± 0.00031) × 10^-11'
+
+%   Copyright 2016 Pyry Jahkola
+
+xmag = floor(log10(abs(x)));
+dmag = floor(log10(abs(d)));
+mag = max(xmag, dmag);
+prec = mag - dmag + 1;
+x = round(x, 1 - dmag);
+d = round(d, 1 - dmag);
+
+if mag > 3
+    X = x / 10 ^ mag;
+    D = d / 10 ^ mag;
+    fmt = sprintf('(%%.%df ± %%.%df) × 10^%%d', prec, prec);
+    str = sprintf(fmt, X, D, mag);
+elseif mag < -2
+    X = x * 10 ^ -mag;
+    D = d * 10 ^ -mag;
+    fmt = sprintf('(%%.%df ± %%.%df) × 10^%%d', prec, prec);
+    str = sprintf(fmt, X, D, mag);
+elseif xmag > dmag && mag < 0
+    fmt = sprintf('%%#.%dg ± %%.%dg', prec + 1, prec + 1);
+    str = sprintf(fmt, x, d);
+else
+    fmt = sprintf('%%.%df ± %%.%df', max(0, 1 - dmag), max(0, 1 - dmag));
+    str = sprintf(fmt, x, d);
+end
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