This is Info file pm.info, produced by Makeinfo version 1.68 from the input file bigpm.texi.  File: pm.info, Node: Math/Round, Next: Math/SO3, Prev: Math/Random, Up: Module List Perl extension for rounding numbers *********************************** NAME ==== Math::Round - Perl extension for rounding numbers SYNOPSIS ======== use Math::Round qw(...those desired... or :all); $rounded = round($scalar); @rounded = round(LIST...); $rounded = nearest($target, $scalar); @rounded = nearest($target, LIST...); # and other functions as described below DESCRIPTION =========== *Math::Round* supplies functions that will round numbers in different ways. The functions round and nearest are exported by default; others are available as described below. "use ... qw(:all)" exports all functions. FUNCTIONS ========= round LIST Rounds the number(s) to the nearest integer. In scalar context, returns a single value; in list context, returns a list of values. Numbers that are halfway between two integers are rounded "to infinity"; i.e., positive values are rounded up (e.g., 2.5 becomes 3) and negative values down (e.g., -2.5 becomes -3). round_even LIST Rounds the number(s) to the nearest integer. In scalar context, returns a single value; in list context, returns a list of values. Numbers that are halfway between two integers are rounded to the nearest even number; e.g., 2.5 becomes 2, 3.5 becomes 4, and -2.5 becomes -2. round_odd LIST Rounds the number(s) to the nearest integer. In scalar context, returns a single value; in list context, returns a list of values. Numbers that are halfway between two integers are rounded to the nearest odd number; e.g., 3.5 becomes 3, 4.5 becomes 5, and -3.5 becomes -3. round_rand LIST Rounds the number(s) to the nearest integer. In scalar context, returns a single value; in list context, returns a list of values. Numbers that are halfway between two integers are rounded up or down in a random fashion. For example, in a large number of trials, 2.5 will become 2 half the time and 3 half the time. nearest TARGET, LIST Rounds the number(s) to the nearest multiple of the target value. TARGET must be positive. In scalar context, returns a single value; in list context, returns a list of values. Numbers that are halfway between two multiples of the target will be rounded to infinity. For example: nearest(10, 44) yields 40 nearest(10, 46) 50 nearest(10, 45) 50 nearest(25, 328) 325 nearest(.1, 4.567) 4.6 nearest(10, -45) -50 nearest_rand TARGET, LIST Rounds the number(s) to the nearest multiple of the target value. TARGET must be positive. In scalar context, returns a single value; in list context, returns a list of values. Numbers that are halfway between two multiples of the target will be rounded up or down in a random fashion. For example, in a large number of trials, nearest(10, 45) will yield 40 half the time and 50 half the time. STANDARD FLOATING-POINT DISCLAIMER ================================== If the numbers to be rounded are stored as floating-point, they will be subject, as usual, to the mercies of your hardware, your C compiler, etc. Thus, numbers that are supposed to be halfway between two others may be stored in a slightly different way and thus behave surprisingly. AUTHOR ====== Math::Round was written by Geoffrey Rommel in October 2000.  File: pm.info, Node: Math/SO3, Next: Math/SigFigs, Prev: Math/Round, Up: Module List Perl extension for SO3 rotations ******************************** NAME ==== Math::SO3 - Perl extension for SO3 rotations (Useful for: implementing orientation in 3d scenes. One major nice feature of this package is to prevent numerical drift that makes rotation matrices nonorthogonal when combining lots of them. And no, this is a direct implementation, of SO3 it does not use quaternions and SU2->SO3 homomorphism.) SYNOPSIS ======== use Math::SO3; $rotation=Math::SO3->new("zr" => 3.14159/2, "xr" => 3.14159/4, "zr" => 3.14159/8); $rotation=Math::SO3->new("zd" => 90, "xd" => 90, "zr" => 3.14159/6); $rotation->invert(); $rotation->turn("zr" => 3.14159/2, "xr" => 3.14159/4); $rotation->turn_round_axis((pack "d3", 1,1,1), 30, "degrees"); $rotation->combine($rotation_after); $rotation->translate_vectors($vec1, $vec2, $vec3, $vec4, @more_vectors); $rotation->inv_translate_vectors($vec1, $vec2, $vec3, $vec4, @more_vectors); ($angle, $dir)=$rotation->turning_angle_and_dir("d"); ($phi, $theta, $psi)=$rotation->euler_angles_zxz("d"); ($heading, $pitch, $roll)=$rotation->euler_angles_yxz("d"); $rotation->format_matrix(); $rotation->format_matrix("%16.8f"); $rotation->format_eigenvector(); $rotation->format_eigenvector("%16.8f"); $rotation->format_euler_zxz(); $rotation->format_euler_zxz("%16.8f"); $rotation->format_euler_yxz(); $rotation->format_euler_yxz("%16.8f"); DESCRIPTION =========== Internal representation: SO3s are blessed refs to strings of size 3*3*sizeof(double) which contain the rotation matrix elements in standard C order. THIS IS PART OF THE OFFICIAL INTERFACE, so you may use this information, if you want. (It simply doesn't make much sense to inherit from purely mathematical data types like this one, so this doesn't hurt.) Note: whenever the text below says "d" is used for angles in degrees, any string starting with a lowercase "d" will work. Same goes for "r" for rad. If you entirely leave it away, default is "r". So you have much freedom in choosing those terms which are most descriptive and most readable. Note: some textbooks on Mechanics (like the very good and very influential one by Goldstein) follow the convention (e1') ( ) (e1) (e2') = ( M ) (e2) (e3') ( ) (e3) This is not very fortunate, since it introduces some nasty ambiguity: it's easy to misinterpret the "vector-rotation matrix" M as the coefficient-rotation matrix, which, however, is just M^T. Matrix/vector calculus is exploited best if one agrees to write coefficient vectors as column vectors and the "array of base vectors" as a row vector (e1 e2 e3). Just look here: (a1) a1*e1 + a2*e2 + a3*e3 = (e1 e2 e3) (a2) (a3) Therefore, WE use the convention (a1') ( ) (a1) (a2') = ( M ) (a2) (a3') ( ) (a3) ( ) (e1 e2 e3) = (e1' e2' e3') ( M ) ( ) For details, see e.g. "Misner, Thorne, Wheeler: Gravitation". Unfortunately, the "wrong way" is rather widespread. Even OpenGL seems to want us to think this way. Please try not to get too confused about this; or better, if you are confused: yes, it's not entirely trivial what's going on here. Our three-dimensional space *is* a bit complicated. But there is a recipe to master it: practice. Once you can think of one constellation in two different coordinate systems, you have won. In rigid body mechanics, it's best to think of this M as the matrix, which, when multiplied-right with a column space-coordinate vector (cscv) gives the corresponding column body-coordinate vector (cbcv). $rotation=Math::SO3->new("zr" => 3.14159/2, "xr" => 3.14159/4, "zr" => 3.14159/8); Create a new SO3-rotation matrix. You may specify an arbitrary number of rotations performed on the identity matrix. In the above case, if you think of $rotation as the matrix translating column-space-coordinate-vectors to column-body-coordinate-vectors (from here on called cscv->cbcv), these rotations you specify here will be applied to the body, rotating the body round one of its body axes. Important: Leftmost rotation will be applied first. "zr" means rotate round z-axis, angle is in rad (full turn= 2pi rad); "xd" would mean: rotate round x-axis, angle is in degrees (full turn=360 degrees). Can be mixed. May also act as a copying constructor, as in: $copy=$rotation->new(). $rotation->invert(); Invert a rotation. $rotation->turn("zr" => 3.14159/2, "xr" => 3.14159/4); Just as you can specify rotations at SO3 creation, you may add a few more later on. Although "numerical drift" can build up, it is not possible for the rotation to get noticeably non-orthogonal. $rotation->turn_round_axis((pack "d3", 1,1,1), 30, "degrees"); Turn the body round the axis given in space coordinates. $rotation->combine($rotation_after); left-multiplies with $rotation_after, that is, executes $rotation_after after $rotation, in the sense defined above. $rotation->translate_vectors($vec1, $vec2, $vec3, $vec4, @other_vectors); Destructively replace each single one of a list of cscv's by the corresponding cbcv's. Note that vectors must be packed-double-strings: $vec=pack("d3",$xcoord,$ycoord,$zcoord); Note: if vectors are "longer", say, like pack("d4", 5,8,10,1), only the first three coordinates will be replaced. This is very useful when working with homogenous coordinates. $rotation->inv_translate_vectors($vec1, $vec2, $vec3, $vec4, @other_vectors); Just the other way round, going cbcv -> cscv. ($angle, $dir)=$rotation->turning_angle_and_dir("d"); Euler's theorem states that in three dimensions, every combination of rotations may be expressed as a single rotation round a given direction. This determines angle and direction Say "d" if you want degrees, "r" for rad. FIXME code for this function is a bit weird and really should be reviewed. So please, you NASA guys, don't use it to compute RTG-satellite trajectories. ($phi, $theta, $psi)=$rotation->euler_angles_zxz("d"); Returns just the famous Euler angles corresponding to a rotation. Specify "d" if you want degrees, "r" for rad. Note: this is designed for speed, and may, for a very small fraction of all possible angles, give bad results due to division by a small quantity. ($heading, $pitch, $roll)=$rotation->euler_angles_yxz("d"); Standard zxz euler angles have one problem: if theta is very small, phi and psi rotations nearly go in the same direction, therefore, it's a bit difficult to see from coordinates if two rotations are very similar or are absolutely not. This is an alternative angle specification which is very common in aeronautics. Probably just the thing you need if you want to build a flight simulator. Note: accuracy see above. $rotation->format_matrix(); $rotation->format_matrix("%16.8f"); Computes a string "[[m00 m01 m02][m10 m11 m12][m20 m21 m22]]" displaying the matrix elements. Optionally, a sprintf format-string may be specified for the matrix elements. Default is "%10.5f". $rotation->format_eigenvector(); $rotation->format_eigenvector("%16.8f"); Similarly, computes a string like "" $rotation->format_euler_zxz(); $rotation->format_euler_zxz("%16.8f"); Similarly, computes a string like "" $rotation->format_euler_yxz(); $rotation->format_euler_yxz("%16.8f"); Just the same, but string is like "" Basically, these functions were added as a quick way to get debugging info. Therefore, all angles are given in degrees, since these are more readable. AUTHOR AND LICENSE ================== Copyright 1999 Thomas Fischbacher (tf@cip.physik.uni-muenchen.de) License: GNU Lesser General Public License (aka GNU LGPL) Copy of the LGPL not included, since it should come with your copy of perl. You may find it at http://www.gnu.org/copyleft/lesser.html SEE ALSO ======== perl(1).  File: pm.info, Node: Math/SigFigs, Next: Math/Spline, Prev: Math/SO3, Up: Module List do math with correct handling of significant figures **************************************************** NAME ==== Math::SigFigs - do math with correct handling of significant figures SYNOPSIS ======== If you only need to use CountSigFigs and FormatSigFigs, use the first form. If you are going to be doing arithmetic, use the second line. use Math::SigFigs; use Math::SigFigs qw(:all); The following routines do simple counting/formatting: $n=&CountSigFigs($num); $num=&FormatSigFigs($num,$n); Use the following routines to do arithmetic operations. $num=&addSF($n1,$n2); $num=&subSF($n1,$n2); $num=&multSF($n1,$n2); $num=&divSF($n1,$n2); DESCRIPTION =========== In many scientific applications, it is often useful to be able to format numbers with a given number of significant figures, or to do math in such a way as to maintain the correct number of significant figures. The rules for significant figures are too complicated to be handled solely using the sprintf function (unless you happen to be Randal Schwartz :-). These routines allow you to correctly handle significan figures. It can count the number of significan figures, format a number to a given number of significant figures, and do basic arithmetic. ROUTINES ======== CountSigFigs $n=&CountSigFigs($N); This returns the number of significant figures in a number. It returns () if $N is not a number. $N $n ----- -- 240 2 240. 3 241 3 0240 2 0.03 1 0 0 0.0 0 FormatSigFigs $str=&FormatSigFigs($N,$n) This returns a string containing $N formatted to $n significant figures. This will work for all cases except something like "2400" formatted to 3 significant figures. $N $n $str ------ -- ------- 2400 1 2000 2400 2 2400 2400 3 2400 2400 4 2400. 2400 5 2400.0 141 3 141. 141 2 140 0.039 1 0.04 0.039 2 0.039 9.9 1 10 9.9 2 9.9 9.9 3 9.90 addSF, subSF, multSF, divSF These routines add/subtract/multiply/divide two numbers while maintaining the proper number of significant figures. KNOWN PROBLEMS ============== These routines do not work with scientific notation (exponents). As a result, it is impossible to unambiguously format some numbers. For example, $str=&FormatSigFigs("2400",3); will by necessity return the string "2400" which does NOT have 3 significant figures. This is not a bug. It is simply a fundamental problem with working with significant figures when not using scientific notation. AUTHOR ====== Sullivan Beck (sbeck@cise.ufl.edu)  File: pm.info, Node: Math/Spline, Next: Math/Trig, Prev: Math/SigFigs, Up: Module List SYNOPSIS require Math::Spline; $spline=new Math::Spline(\@x,\@y) $y_interp=$spline->evaluate($x); ================================================================================================================== use Math::Spline qw(spline linsearch binsearch); use Math::Derivative qw(Derivative2); @y2=Derivative2(\@x,\@y); $index=binsearch(\@x,$x); $index=linsearch(\@x,$x,$index); $y_interp=spline(\@x,\@y,\@y2,$index,$x); DESCRIPTION =========== This package provides cubic spline interpolation of numeric data. The data is passed as references to two arrays containing the x and y ordinates. It may be used as an exporter of the numerical functions or, more easily as a class module. The *Math::Spline* class constructor new takes references to the arrays of x and y ordinates of the data. An interpolation is performed using the evaluate method, which, when given an x ordinate returns the interpolate y ordinate at that value. The *spline* function takes as arguments references to the x and y ordinate array, a reference to the 2nd derivatives (calculated using *Derivative2*, the low index of the interval in which to interpolate and the x ordinate in that interval. Returned is the interpolated y ordinate. Two functions are provided to look up the appropriate index in the array of x data. For random calls *binsearch* can be used - give a reference to the x ordinates and the x loopup value it returns the low index of the interval in the data in which the value lies. Where the lookups are strictly in ascending sequence (e.g. if interpolating to produce a higher resolution data set to draw a curve) the *linsearch* function may more efficiently be used. It performs like *binsearch*, but requires a third argument being the previous index value, which is incremented if necessary. NOTE ==== requires Math::Derivative module EXAMPLE ======= require Math::Spline; my @x=(1,3,8,10); my @y=(1,2,3,4); $spline=new Math::Spline(\@x,\@y); print $spline->evaluate(5)."\n"; produces the output 2.44 HISTORY ======= $Log: Spline.pm,v $ Revision 1.1 1995/12/26 17:28:17 willijar Initial revision BUGS ==== Bug reports or constructive comments are welcome. AUTHOR ====== John A.R. Williams SEE ALSO ======== "Numerical Recipies: The Art of Scientific Computing" W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling. Cambridge University Press. ISBN 0 521 30811 9.  File: pm.info, Node: Math/Trig, Next: Math/TrulyRandom, Prev: Math/Spline, Up: Module List trigonometric functions *********************** NAME ==== Math::Trig - trigonometric functions SYNOPSIS ======== use Math::Trig; $x = tan(0.9); $y = acos(3.7); $z = asin(2.4); $halfpi = pi/2; $rad = deg2rad(120); DESCRIPTION =========== Math::Trig defines many trigonometric functions not defined by the core Perl which defines only the `sin()' and `cos()'. The constant pi is also defined as are a few convenience functions for angle conversions. TRIGONOMETRIC FUNCTIONS ======================= The tangent tan The cofunctions of the sine, cosine, and tangent (cosec/csc and cotan/cot are aliases) *csc*, *cosec*, sec, sec, *cot*, *cotan* The arcus (also known as the inverse) functions of the sine, cosine, and tangent asin, acos, atan The principal value of the arc tangent of y/x atan2(y, x) The arcus cofunctions of the sine, cosine, and tangent (acosec/acsc and acotan/acot are aliases) *acsc*, *acosec*, *asec*, *acot*, *acotan* The hyperbolic sine, cosine, and tangent sinh, cosh, tanh The cofunctions of the hyperbolic sine, cosine, and tangent (cosech/csch and cotanh/coth are aliases) *csch*, *cosech*, *sech*, *coth*, *cotanh* The arcus (also known as the inverse) functions of the hyperbolic sine, cosine, and tangent asinh, acosh, atanh The arcus cofunctions of the hyperbolic sine, cosine, and tangent (acsch/acosech and acoth/acotanh are aliases) *acsch*, *acosech*, *asech*, *acoth*, *acotanh* The trigonometric constant pi is also defined. $pi2 = 2 * pi; ERRORS DUE TO DIVISION BY ZERO ------------------------------ The following functions acoth acsc acsch asec asech atanh cot coth csc csch sec sech tan tanh cannot be computed for all arguments because that would mean dividing by zero or taking logarithm of zero. These situations cause fatal runtime errors looking like this cot(0): Division by zero. (Because in the definition of cot(0), the divisor sin(0) is 0) Died at ... or atanh(-1): Logarithm of zero. Died at... For the `csc', `cot', `asec', `acsc', `acot', `csch', `coth', `asech', `acsch', the argument cannot be 0 (zero). For the atanh, `acoth', the argument cannot be 1 (one). For the atanh, `acoth', the argument cannot be `-1' (minus one). For the tan, sec, tanh, `sech', the argument cannot be *pi/2 + k * pi*, where k is any integer. SIMPLE (REAL) ARGUMENTS, COMPLEX RESULTS ---------------------------------------- Please note that some of the trigonometric functions can break out from the *real axis* into the *complex plane*. For example `asin(2)' has no definition for plain real numbers but it has definition for complex numbers. In Perl terms this means that supplying the usual Perl numbers (also known as scalars, please see *Note Perldata: (perl.info)perldata,) as input for the trigonometric functions might produce as output results that no more are simple real numbers: instead they are complex numbers. The Math::Trig handles this by using the Math::Complex package which knows how to handle complex numbers, please see *Note Math/Complex: Math/Complex, for more information. In practice you need not to worry about getting complex numbers as results because the Math::Complex takes care of details like for example how to display complex numbers. For example: print asin(2), "\n"; should produce something like this (take or leave few last decimals): 1.5707963267949-1.31695789692482i That is, a complex number with the real part of approximately `1.571' and the imaginary part of approximately `-1.317'. PLANE ANGLE CONVERSIONS ======================= (Plane, 2-dimensional) angles may be converted with the following functions. $radians = deg2rad($degrees); $radians = grad2rad($gradians); $degrees = rad2deg($radians); $degrees = grad2deg($gradians); $gradians = deg2grad($degrees); $gradians = rad2grad($radians); The full circle is 2 pi radians or *360* degrees or *400* gradians. RADIAL COORDINATE CONVERSIONS ============================= *Radial coordinate systems* are the *spherical* and the *cylindrical* systems, explained shortly in more detail. You can import radial coordinate conversion functions by using the `:radial' tag: use Math::Trig ':radial'; ($rho, $theta, $z) = cartesian_to_cylindrical($x, $y, $z); ($rho, $theta, $phi) = cartesian_to_spherical($x, $y, $z); ($x, $y, $z) = cylindrical_to_cartesian($rho, $theta, $z); ($rho_s, $theta, $phi) = cylindrical_to_spherical($rho_c, $theta, $z); ($x, $y, $z) = spherical_to_cartesian($rho, $theta, $phi); ($rho_c, $theta, $z) = spherical_to_cylindrical($rho_s, $theta, $phi); *All angles are in radians*. COORDINATE SYSTEMS ------------------ *Cartesian* coordinates are the usual rectangular *(x, y, z)*-coordinates. Spherical coordinates, *(rho, theta, pi)*, are three-dimensional coordinates which define a point in three-dimensional space. They are based on a sphere surface. The radius of the sphere is *rho*, also known as the *radial* coordinate. The angle in the *xy*-plane (around the z-axis) is *theta*, also known as the *azimuthal* coordinate. The angle from the z-axis is *phi*, also known as the *polar* coordinate. The `North Pole' is therefore *0, 0, rho*, and the `Bay of Guinea' (think of the missing big chunk of Africa) *0, pi/2, rho*. In geographical terms *phi* is latitude (northward positive, southward negative) and *theta* is longitude (eastward positive, westward negative). *BEWARE*: some texts define *theta* and *phi* the other way round, some texts define the *phi* to start from the horizontal plane, some texts use r in place of *rho*. Cylindrical coordinates, *(rho, theta, z)*, are three-dimensional coordinates which define a point in three-dimensional space. They are based on a cylinder surface. The radius of the cylinder is *rho*, also known as the *radial* coordinate. The angle in the *xy*-plane (around the z-axis) is *theta*, also known as the *azimuthal* coordinate. The third coordinate is the z, pointing up from the *theta*-plane. 3-D ANGLE CONVERSIONS --------------------- Conversions to and from spherical and cylindrical coordinates are available. Please notice that the conversions are not necessarily reversible because of the equalities like pi angles being equal to *-pi* angles. cartesian_to_cylindrical ($rho, $theta, $z) = cartesian_to_cylindrical($x, $y, $z); cartesian_to_spherical ($rho, $theta, $phi) = cartesian_to_spherical($x, $y, $z); cylindrical_to_cartesian ($x, $y, $z) = cylindrical_to_cartesian($rho, $theta, $z); cylindrical_to_spherical ($rho_s, $theta, $phi) = cylindrical_to_spherical($rho_c, $theta, $z); Notice that when `$z' is not 0 `$rho_s' is not equal to `$rho_c'. spherical_to_cartesian ($x, $y, $z) = spherical_to_cartesian($rho, $theta, $phi); spherical_to_cylindrical ($rho_c, $theta, $z) = spherical_to_cylindrical($rho_s, $theta, $phi); Notice that when `$z' is not 0 `$rho_c' is not equal to `$rho_s'. GREAT CIRCLE DISTANCES ====================== You can compute spherical distances, called *great circle distances*, by importing the `great_circle_distance' function: use Math::Trig 'great_circle_distance' $distance = great_circle_distance($theta0, $phi0, $theta1, $phi1, [, $rho]); The *great circle distance* is the shortest distance between two points on a sphere. The distance is in `$rho' units. The `$rho' is optional, it defaults to 1 (the unit sphere), therefore the distance defaults to radians. If you think geographically the *theta* are longitudes: zero at the Greenwhich meridian, eastward positive, westward negative-and the *phi* are latitudes: zero at the North Pole, northward positive, southward negative. NOTE: this formula thinks in mathematics, not geographically: the *phi* zero is at the North Pole, not at the Equator on the west coast of Africa (Bay of Guinea). You need to subtract your geographical coordinates from *pi/2* (also known as 90 degrees). $distance = great_circle_distance($lon0, pi/2 - $lat0, $lon1, pi/2 - $lat1, $rho); EXAMPLES ======== To calculate the distance between London (51.3N 0.5W) and Tokyo (35.7N 139.8E) in kilometers: use Math::Trig qw(great_circle_distance deg2rad); # Notice the 90 - latitude: phi zero is at the North Pole. @L = (deg2rad(-0.5), deg2rad(90 - 51.3)); @T = (deg2rad(139.8),deg2rad(90 - 35.7)); $km = great_circle_distance(@L, @T, 6378); The answer may be off by few percentages because of the irregular (slightly aspherical) form of the Earth. The used formula lat0 = 90 degrees - phi0 lat1 = 90 degrees - phi1 d = R * arccos(cos(lat0) * cos(lat1) * cos(lon1 - lon01) + sin(lat0) * sin(lat1)) is also somewhat unreliable for small distances (for locations separated less than about five degrees) because it uses arc cosine which is rather ill-conditioned for values close to zero. BUGS ==== Saying `use Math::Trig;' exports many mathematical routines in the caller environment and even overrides some (sin, cos). This is construed as a feature by the Authors, actually... ;-) The code is not optimized for speed, especially because we use Math::Complex and thus go quite near complex numbers while doing the computations even when the arguments are not. This, however, cannot be completely avoided if we want things like `asin(2)' to give an answer instead of giving a fatal runtime error. AUTHORS ======= Jarkko Hietaniemi <`jhi@iki.fi'> and Raphael Manfredi <`Raphael_Manfredi@pobox.com'>.  File: pm.info, Node: Math/TrulyRandom, Next: Math/Units, Prev: Math/Trig, Up: Module List Perl interface to a truly random number generator function ********************************************************** NAME ==== TrulyRandom - Perl interface to a truly random number generator function SYNOPSIS ======== use Math::TrulyRandom; $random = truly_random_value(); DESCRIPTION =========== The *TrulyRandom* module provides an ability to generate truly random numbers from within Perl programs. The source of the randomness is from interrupt timing discrepancies. EXAMPLE ======= $random = truly_random_value(); BUGS ==== The random numbers take a long time (in computer terms) to generate, so are only really useful for seeding pseudo random sequence generators. COPYRIGHT ========= This implementation derives from the truly random number generator function developed by Matt Blaze and Don Mitchell, and is copyright of AT&T. Other parts of this perl extension are copyright of Systemics Ltd ( http://www.systemics.com/ ).  File: pm.info, Node: Math/Units, Next: Math/VecStat, Prev: Math/TrulyRandom, Up: Module List Unit conversion *************** NAME ==== Math::Units - Unit conversion SYNOPSIS ======== use Math::Units qw(convert); my $out_value = convert($in_value, 'in unit', 'out unit'); DESCRIPTION =========== The Math::Units module converts a numeric value in one unit of measurement to some other unit. The units must be compatible, i.e. length can not be converted to volume. If a conversion can not be made an exception is thrown. A combination chaining and reduction algorithm is used to perform the most direct unit conversion possible. Units may be written in several different styles. An abbreviation table is used to convert from common long-form unit names to the (more or less) standard abbreviations that the units module uses internally. All multiplicative unit conversions are cached so that future conversions can be performed very quickly. Too many units, prefixes and abbreviations are supported to list here. See the source code for a complete listing. EXAMPLES ======== print "5 mm == ", convert(5, 'mm', 'in'), " inches\n"; print "72 degrees Farenheit == ", convert(72, 'F', 'C'), " degrees Celsius\n"; print "1 gallon == ", convert(1, 'gallon', 'cm^3'), " cubic centimeters\n"; print "4500 rpm == ", convert(4500, 'rpm', 'Hz'), " Hertz\n";  File: pm.info, Node: Math/VecStat, Next: Mcrypt, Prev: Math/Units, Up: Module List Some basic numeric stats on vectors *********************************** NAME ==== Math::VecStat - Some basic numeric stats on vectors SYNOPSIS ======== use Math::VecStat qw(max min maxabs minabs sum average); $max=max(@vector); $max=max(\@vector); ($max,$imax)=max(@vector); ($max,$imax)=max(\@vector); $min=min(@vector); $min=min(\@vector); ($max,$imin)=min(@vector); ($max,$imin)=min(\@vector); $max=maxabs(@vector); $max=maxabs(\@vector); ($max,$imax)=maxabs(@vector); ($max,$imax)=maxabs(\@vector); $min=minabs(@vector); $min=minabs(\@vector); ($max,$imin)=minabs(@vector); ($max,$imin)=minabs(\@vector); $sum=sum($v1,$v2,...); $sum=sum(@vector); $sum=sum(\@vector); $average=average($v1,$v2,...); $av=average(@vector); $av=average(\@vector); $ref=vecprod($scalar,\@vector); $ok=ordered(@vector); $ok=ordered(\@vector); $ref=sumbyelement(\@vector1,\@vector2); $ref=diffbyelement(\@vector1,\@vector2); $ok=allequal(\@vector1,\@vector2); $ref=convolute(\@vector1,\@vector2); DESCRIPTION =========== This package provides some basic statistics on numerical vectors. All the subroutines can take a reference to the vector to be operated on. In some cases a copy of the vector is acceptable, but is not recommended for efficiency. max(@vector), max(\@vector) return the maximum value of given values or vector. In an array context returns the value and the index in the array where it occurs. min(@vector), min(\@vector) return the minimum value of given values or vector, In an array context returns the value and the index in the array where it occurs. maxabs(@vector), maxabs(\@vector) return the maximum value of absolute of the given values or vector. In an array context returns the value and the index in the array where it occurs. minabs(@vector), minabs(\@vector) return the minimum value of the absolute of the given values or vector. In an array context returns the value and the index in the array where it occurs. sum($v1,$v2,...), sum(@vector), sum(\@vector) return the sum of the given values or vector average($v1,$v2,..), average(@vector), average(\@vector) return the average of the given values or vector vecprod($a,$v1,$v2,..), vecprod($a,@vector), vecprod( $a, \@vector ) return a vector built by multiplying the scalar $a by each element of the @vector. ordered($v1,$v2,..), ordered(@vector), ordered(\@vector) return nonzero iff the vector is nondecreasing with respect to its index. To be used like if( ordered( $lowBound, $value, $highBound ) ){ instead of the (slightly) more clumsy if( ($lowBound <= $value) && ($value <= $highBound) ) { sumbyelement( \@array1, \@array2 ), diffbyelement(\@array1,\@array2) return the element-by-element sum or difference of two identically-sized vectors. Given $s = sumbyelement( [10,20,30], [1,2,3] ); $d = diffbyelement( [10,20,30], [1,2,3] ); $s will be `[11,22,33]', $d will be `[9,18,27]'. allequal( \@array1, \@array2 ) returns true if and only if the two arrays are numerically identical. convolute( \@array1, \@array2 ) return a reference to an array containing the element-by-element product of the two input arrays. I.e., $r = convolute( [1,2,3], [-1,2,1] ); returns a reference to [-1,4,3] HISTORY ======= $Log: VecStat.pm,v $ Revision 1.7 2000/10/24 15:28:00 spinellia@acm.org Added functions allequal diffbyelement Created a reasonable test suite. Revision 1.6 2000/06/29 16:06:37 spinellia@acm.org Added functions vecprod, convolute, sumbyelement Revision 1.5 1997/02/26 17:20:37 willijar Added line before pod header so pod2man installs man page correctly Revision 1.4 1996/02/20 07:53:10 willijar Added ability to return index in array contex to max and min functions. Added minabs and maxabs functions. Thanks to Mark Borges for these suggestions. Revision 1.3 1996/01/06 11:03:30 willijar Fixed stupid bug that crept into looping in min and max functions Revision 1.2 1995/12/26 09:56:38 willijar Oops - removed xy data functions. Revision 1.1 1995/12/26 09:39:07 willijar Initial revision BUGS ==== Let me know. I welcome any appropriate additions for this package. AUTHORS ======= John A.R. Williams Andrea Spinelli  File: pm.info, Node: Mcrypt, Next: MegaHAL, Prev: Math/VecStat, Up: Module List Perl extension for the Mcrypt cryptography library ************************************************** NAME ==== Mcrypt - Perl extension for the Mcrypt cryptography library SYNOPSIS ======== use Mcrypt; # Procedural routines $td = Mcrypt::mcrypt_load($algorithm, $algorithm_dir, $mode, $mode_dir); Mcrypt::mcrypt_get_key_size($td); # in bytes Mcrypt::mcrypt_get_iv_size($td); # in bytes Mcrypt::mcrypt_get_block_size($td); # in bytes Mcrypt::mcrypt_init($td, $key, $iv); $encryptedstr = Mcrypt::mcrypt_encrypt($td, $decryptedstr); $decryptedstr = Mcrypt::mcrypt_decrypt($td, $encryptedstr); Mcrypt::mcrypt_end($td); # Object-oriented methods $td = Mcrypt->new( algorithm => $algorithm, mode => $mode ); $keysize = $td->{KEY_SIZE}; $ivsize = $td->{IV_SIZE}; $blksize = $td->{BLOCK_SIZE}; $td->init($key, $iv); $encryptedstr = $td->encrypt($decryptedstr); $decryptedstr = $td->decrypt($encryptedstr); # If the $td goes out of context, # the destructor will do this for you $td->end(); DESCRIPTION =========== This module wraps the libmcrypt encryption library for easy and convenient use from within perl. Encryption and decryption using a variety of algorithms is as easy as a few simple lines of perl. Exported constants ================== The predefined groups of exports in the use statements are as follows: use Mcrypt qw(:ALGORITHMS); Exports the BLOWFISH DES 3DES 3WAY GOST SAFER_SK64 SAFER_SK128 CAST_128 XTEA RC2 TWOFISH CAST_256 SAFERPLUS LOKI97 SERPENT RIJNDAEL_128 RIJNDAEL_192 RIJNDAEL_256 ENIGMA ARCFOUR WAKE libmcrypt algorithms. See the mcrypt(3) man page for more details. use Mcrypt qw(:MODES); Exports the CBC ECB CFB OFB bOFB STREAM modes of encryption. See the mcrypt(3) man page for more details. use Mcrypt qw(:FUNCS); Exports the following functions: mcrypt_load, mcrypt_unload, mcrypt_init, mcrypt_end, mcrypt_encrypt, mcrypt_decrypt, mcrypt_get_block_size, mcrypt_get_iv_size, mcrypt_get_key_size. EXAMPLES ======== # Procedural approach: # create an ecryption descriptor: # ALGORITHM: blowfish (256 bit key + 16 byte IV) # MODE: cfb # The user application has set: # $method to either "encrypt" or "decrypt" # $infile to the input filename # $outfile to the output filename my($td) = Mcrypt::mcrypt_load( Mcrypt::BLOWFISH, '', Mcrypt::CFB, '' ); my($key) = "32 bytes of your apps secret key"; # secret key my($iv) = "16 bytes of rand"; # shared initialization vector Mcrypt::mcrypt_init($td, $key, $iv) || die "Could not initialize td"; print Mcrypt::mcrypt_encrypt($td, $_) while(<>); Mcrypt::mcrypt_end($td); # OO approach of the above except decrypting my($td) = Mcrypt->new( algorithm => Mcrypt::BLOWFISH, mode => Mcrypt::CFB, verbose => 0 ); my($key) = "k" x $td->{KEY_SIZE}; my($iv) = "i" x $td->{IV_SIZE}; $td->init($key, $iv); print $td->decrypt($_) while (<>); $td->end(); AUTHOR ====== Theo Schlossnagle SEE ALSO ======== The libmcrypt man page: mcrypt(3). Other libmcrypt information is available at http://mcrypt.hellug.gr/.  File: pm.info, Node: MegaHAL, Next: MemHandle, Prev: Mcrypt, Up: Module List Perl interface to the MegaHAL natural language conversation simulator. ********************************************************************************** NAME ==== MegaHAL - Perl interface to the MegaHAL natural language conversation simulator. SYNOPSIS ======== use MegaHAL; $megahal = new MegaHAL('Path' => './', 'Banner' => 0, 'Prompt' => 0, 'Wrap' => 0, 'AutoSave' => 0); $text = $megahal->initial_greeting(); $text = $megahal->do_reply($message); DESCRIPTION =========== Conversation simulators are computer programs which give the appearance of conversing with a user in natural language. Such programs are effective because they exploit the fact that human beings tend to read much more meaning into what is said than is actually there; we are fooled into reading structure into chaos, and we interpret non-sequitur as valid conversation. This package provides a Perl interface to the MegaHAL conversation simulator written by Jason Hutchens. USAGE ===== $megahal = new MegaHAL('Path' => './', 'Banner' => 0, 'Prompt' => 0, 'Wrap' => 0, 'AutoSave' => 0); Creates a new MegaHAL object. The object constructor can optionaly receive the following named parameters: 'Path' - The path to MegaHALs brain or training file (megahal.brn and megahal.trn respectively). If 'Path' is not specified the current working directory is assumed. 'Banner' - A flag which enables/disables the banner which is displayed when MegaHAL starts up. The default is to disable the banner. 'Prompt' - A flag which enables/disables the prompt. This flag is only useful when MegaHAL is run interactively and is disabled by default. 'Wrap' - A flag which enables/disables word wrapping of MegaHALs responses when the lines exceed 80 characters in length. The default is to disable word wrapping. $text = $megahal->initial_greeting(); Returns a string containing the initial greeting which is created by MegaHAL at startup. $text = $megahal->do_reply($message); Generates reply $text to a given message $message. BUGS ==== None known at this time. AUTHORS ======= The Perl MegaHAL interface was written by Cory Spencer MegaHAL was originally written by and is copyright Jason Hutchens  File: pm.info, Node: MemHandle, Next: MemHandle/Tie, Prev: MegaHAL, Up: Module List supply memory-based FILEHANDLE methods ************************************** NAME ==== MemHandle - supply memory-based FILEHANDLE methods SYNOPSIS ======== use MemHandle; use IO::Seekable; my $mh = new MemHandle; print $mh "foo\n"; $mh->print( "bar\n" ); printf $mh "This is a number: %d\n", 10; $mh->printf( "a string: \"%s\"\n", "all strings come to those who wait" ); my $len = $mh->tell(); # Use $mh->tell(); # tell( $mh ) will NOT work! $mh->seek(0, SEEK_SET); # Use $mh->seek($where, $whence) # seek($mh, $where, $whence) # will NOT work! my $memory = $mh->mem(); Here's the real meat: my $mh = new MemHandle; my $old = select( $mh ); . . . print "foo bar\n"; print "baz\n"; &MyPrintSub(); select( $old ); print "here it all is: ", $mh->mem(), "\n"; DESCRIPTION =========== Generates inherits from IO::Handle and IO::Seekable. It provides an interface to the file routines which uses memory instead. See perldoc IO::Handle, and perldoc IO::Seekable as well as *Note Perlfunc: (perl.info)perlfunc, for more detailed descriptions of the provided built-in functions: print printf readline sysread syswrite getc gets The following functions are provided, but tie doesn't allow them to be tied to the built in functions. They should be used by calling the appropriate method on the MemHandle object. seek tell call them like this: my $mh = new MemHandle(); . . . my $pos = $mh->tell(); $mh->seek( 0, SEEK_SET ); CONSTRUCTOR =========== new( [mem] ) Creates a `MemHandle', which is a reference to a newly created symbol (see the Symbol package). It then ties the FILEHANDLE to `MemHandle::Tie' (see `"Tying FileHandles"', *Note Perltie: (perl.info)perltie,). Tied methods in `MemHandle::Tie' translate file operations into reads/writes into a string, which can be accessed by calling `MemHandle::mem'. METHODS ======= seek( POS, WHENCE ) Sets the read/write position to WHENCE + POS. WHENCE is one of the constants which are available from IO::Seekable or POSIX: SEEK_SET # absolute position from the beginning. SEEK_CUR # offset from the current location. SEEK_END # from the end (POS can be negative). tell() Returns the current position of the mem-file, similiar to the way tell would. (See *Note Perlfunc: (perl.info)perlfunc,). mem( [mem] ) gets or sets the memory. If called with a parameter, it copies it to the memory and sets the position to be immediately after (so if you write more to it, you append the string). Returns the current value of memory. AUTHOR ====== "Sheridan C. Rawlins" SEE ALSO ======== *Note Perl: (perl.info)perl,. *Note Perlfunc: (perl.info)perlfunc,. `"Tying FileHandles"', *Note Perltie: (perl.info)perltie,. perldoc IO::Handle. perldoc IO::Seekable. perldoc Symbol.  File: pm.info, Node: MemHandle/Tie, Next: Memoize, Prev: MemHandle, Up: Module List The package which ties the MemHandle to memory. *********************************************** NAME ==== MemHandle::Tie - The package which ties the MemHandle to memory. SYNOPSIS ======== DESCRIPTION =========== This should not be used except by MemHandle. It provides functions for tie-ing a FILEHANDLE. See `"Tying FileHandles"', *Note Perltie: (perl.info)perltie, for more detail. AUTHOR ====== "Sheridan C. Rawlins" SEE ALSO ======== *Note Perl: (perl.info)perl,. *Note Perlfunc: (perl.info)perlfunc,. `"Tying FileHandles"', *Note Perltie: (perl.info)perltie,. perldoc MemHandle.  File: pm.info, Node: Memoize, Next: Memoize/Expire, Prev: MemHandle/Tie, Up: Module List Make your functions faster by trading space for time **************************************************** NAME ==== Memoize - Make your functions faster by trading space for time SYNOPSIS ======== use Memoize; memoize('slow_function'); slow_function(arguments); # Is faster than it was before This is normally all you need to know. However, many options are available: memoize(function, options...); Options include: NORMALIZER => function INSTALL => new_name SCALAR_CACHE => 'MEMORY' SCALAR_CACHE => ['TIE', Module, arguments...] SCALAR_CACHE => ['HASH', \%cache_hash ] SCALAR_CACHE => 'FAULT' SCALAR_CACHE => 'MERGE' LIST_CACHE => 'MEMORY' LIST_CACHE => ['TIE', Module, arguments...] LIST_CACHE => ['HASH', \%cache_hash ] LIST_CACHE => 'FAULT' LIST_CACHE => 'MERGE' DESCRIPTION =========== `Memoizing' a function makes it faster by trading space for time. It does this by caching the return values of the function in a table. If you call the function again with the same arguments, `memoize' jmups in and gives you the value out of the table, instead of letting the function compute the value all over again. Here is an extreme example. Consider the Fibonacci sequence, defined by the following function: # Compute Fibonacci numbers sub fib { my $n = shift; return $n if $n < 2; fib($n-1) + fib($n-2); } This function is very slow. Why? To compute fib(14), it first wants to compute fib(13) and fib(12), and add the results. But to compute fib(13), it first has to compute fib(12) and fib(11), and then it comes back and computes fib(12) all over again even though the answer is the same. And both of the times that it wants to compute fib(12), it has to compute fib(11) from scratch, and then it has to do it again each time it wants to compute fib(13). This function does so much recomputing of old results that it takes a really long time to run--fib(14) makes 1,200 extra recursive calls to itself, to compute and recompute things that it already computed. This function is a good candidate for memoization. If you memoize the `fib' function above, it will compute fib(14) exactly once, the first time it needs to, and then save the result in a table. Then if you ask for fib(14) again, it gives you the result out of the table. While computing fib(14), instead of computing fib(12) twice, it does it once; the second time it needs the value it gets it from the table. It doesn't compute fib(11) four times; it computes it once, getting it from the table the next three times. Instead of making 1,200 recursive calls to `fib', it makes 15. This makes the function about 150 times faster. You could do the memoization yourself, by rewriting the function, like this: # Compute Fibonacci numbers, memoized version { my @fib; sub fib { my $n = shift; return $fib[$n] if defined $fib[$n]; return $fib[$n] = $n if $n < 2; $fib[$n] = fib($n-1) + fib($n-2); } } Or you could use this module, like this: use Memoize; memoize('fib'); # Rest of the fib function just like the original version. This makes it easy to turn memoizing on and off. Here's an even simpler example: I wrote a simple ray tracer; the program would look in a certain direction, figure out what it was looking at, and then convert the `color' value (typically a string like `red') of that object to a red, green, and blue pixel value, like this: for ($direction = 0; $direction < 300; $direction++) { # Figure out which object is in direction $direction $color = $object->{color}; ($r, $g, $b) = @{&ColorToRGB($color)}; ... } Since there are relatively few objects in a picture, there are only a few colors, which get looked up over and over again. Memoizing `ColorToRGB' speeded up the program by several percent. DETAILS ======= This module exports exactly one function, `memoize'. The rest of the functions in this package are None of Your Business. You should say memoize(function) where function is the name of the function you want to memoize, or a reference to it. `memoize' returns a reference to the new, memoized version of the function, or undef on a non-fatal error. At present, there are no non-fatal errors, but there might be some in the future. If function was the name of a function, then `memoize' hides the old version and installs the new memoized version under the old name, so that `&function(...)' actually invokes the memoized version. OPTIONS ======= There are some optional options you can pass to `memoize' to change the way it behaves a little. To supply options, invoke `memoize' like this: memoize(function, NORMALIZER => function, INSTALL => newname, SCALAR_CACHE => option, LIST_CACHE => option ); Each of these options is optional; you can include some, all, or none of them. INSTALL ------- If you supply a function name with INSTALL, memoize will install the new, memoized version of the function under the name you give. For example, memoize('fib', INSTALL => 'fastfib') installs the memoized version of `fib' as `fastfib'; without the INSTALL option it would have replaced the old `fib' with the memoized version. To prevent `memoize' from installing the memoized version anywhere, use `INSTALL => undef'. NORMALIZER ---------- Suppose your function looks like this: # Typical call: f('aha!', A => 11, B => 12); sub f { my $a = shift; my %hash = @_; $hash{B} ||= 2; # B defaults to 2 $hash{C} ||= 7; # C defaults to 7 # Do something with $a, %hash } Now, the following calls to your function are all completely equivalent: f(OUCH); f(OUCH, B => 2); f(OUCH, C => 7); f(OUCH, B => 2, C => 7); f(OUCH, C => 7, B => 2); (etc.) However, unless you tell `Memoize' that these calls are equivalent, it will not know that, and it will compute the values for these invocations of your function separately, and store them separately. To prevent this, supply a NORMALIZER function that turns the program arguments into a string in a way that equivalent arguments turn into the same string. A NORMALIZER function for f above might look like this: sub normalize_f { my $a = shift; my %hash = @_; $hash{B} ||= 2; $hash{C} ||= 7; join($;, $a, map ($_ => $hash{$_}) sort keys %hash); } Each of the argument lists above comes out of the `normalize_f' function looking exactly the same, like this: OUCH^\B^\2^\C^\7 You would tell `Memoize' to use this normalizer this way: memoize('f', NORMALIZER => 'normalize_f'); `memoize' knows that if the normalized version of the arguments is the same for two argument lists, then it can safely look up the value that it computed for one argument list and return it as the result of calling the function with the other argument list, even if the argument lists look different. The default normalizer just concatenates the arguments with $; in between. This always works correctly for functions with only one argument, and also when the arguments never contain $; (which is normally character #28, control-\. ) However, it can confuse certain argument lists: normalizer("a\034", "b") normalizer("a", "\034b") normalizer("a\034\034b") for example. The default normalizer also won't work when the function's arguments are references. For exampple, consider a function g which gets two arguments: A number, and a reference to an array of numbers: g(13, [1,2,3,4,5,6,7]); The default normalizer will turn this into something like `"13\024ARRAY(0x436c1f)"'. That would be all right, except that a subsequent array of numbers might be stored at a different location even though it contains the same data. If this happens, `Memoize' will think that the arguments are different, even though they are equivalent. In this case, a normalizer like this is appropriate: sub normalize { join ' ', $_[0], @{$_[1]} } For the example above, this produces the key "13 1 2 3 4 5 6 7". Another use for normalizers is when the function depends on data other than those in its arguments. Suppose you have a function which returns a value which depends on the current hour of the day: sub on_duty { my ($problem_type) = @_; my $hour = (localtime)[2]; open my $fh, "$DIR/$problem_type" or die...; my $line; while ($hour-- > 0) $line = <$fh>; } return $line; } At 10:23, this function generates the tenth line of a data file; at 3:45 PM it generates the 15th line instead. By default, `Memoize' will only see the $problem_type argument. To fix this, include the current hour in the normalizer: sub normalize { join ' ', (localtime)[2], @_ } The calling context of the function (scalar or list context) is propagated to the normalizer. This means that if the memoized function will treat its arguments differently in list context than it would in scalar context, you can have the normalizer function select its behavior based on the results of wantarray. Even if called in a list context, a normalizer should still return a single string. `SCALAR_CACHE', `LIST_CACHE' ---------------------------- Normally, `Memoize' caches your function's return values into an ordinary Perl hash variable. However, you might like to have the values cached on the disk, so that they persist from one run of your program to the next, or you might like to associate some other interesting semantics with the cached values. There's a slight complication under the hood of `Memoize': There are actually *two* caches, one for scalar values and one for list values. When your function is called in scalar context, its return value is cached in one hash, and when your function is called in list context, its value is cached in the other hash. You can control the caching behavior of both contexts independently with these options. The argument to `LIST_CACHE' or `SCALAR_CACHE' must either be one of the following five strings: MEMORY TIE FAULT MERGE HASH or else it must be a reference to a list whose first element is one of these four strings, such as `[TIE, arguments...]'. MEMORY MEMORY means that return values from the function will be cached in an ordinary Perl hash variable. The hash variable will not persist after the program exits. This is the default. TIE TIE means that the function's return values will be cached in a tied hash. A tied hash can have any semantics at all. It is typically tied to an on-disk database, so that cached values are stored in the database and retrieved from it again when needed, and the disk file typically persists after your pogram has exited. If TIE is specified as the first element of a list, the remaining list elements are taken as arguments to the tie call that sets up the tied hash. For example, SCALAR_CACHE => [TIE, DB_File, $filename, O_RDWR | O_CREAT, 0666] says to tie the hash into the DB_File package, and to pass the $filename, `O_RDWR | O_CREAT', and `0666' arguments to the tie call. This has the effect of storing the cache in a DB_File database whose name is in $filename. Other typical uses of TIE: LIST_CACHE => [TIE, GDBM_File, $filename, O_RDWR | O_CREAT, 0666] SCALAR_CACHE => [TIE, MLDBM, DB_File, $filename, O_RDWR|O_CREAT, 0666] LIST_CACHE => [TIE, My_Package, $tablename, $key_field, $val_field] This last might tie the cache hash to a package that you wrote yourself that stores the cache in a SQL-accessible database. A useful use of this feature: You can construct a batch program that runs in the background and populates the memo table, and then when you come to run your real program the memoized function will be screamingly fast because all its results have been precomputed. HASH HASH allows you to specify that a particular hash that you supply will be used as the cache. You can tie this hash beforehand to give it any behavior you want. `FAULT' `FAULT' means that you never expect to call the function in scalar (or list) context, and that if `Memoize' detects such a call, it should abort the program. The error message is one of `foo' function called in forbidden list context at line ... `foo' function called in forbidden scalar context at line ... `MERGE' `MERGE' normally means the function does not distinguish between list and sclar context, and that return values in both contexts should be stored together. `LIST_CACHE => MERGE' means that list context return values should be stored in the same hash that is used for scalar context returns, and `SCALAR_CACHE => MERGE' means the same, mutatis mutandis. It is an error to specify `MERGE' for both, but it probably does something useful. Consider this function: sub pi { 3; } Normally, the following code will result in two calls to pi: $x = pi(); ($y) = pi(); $z = pi(); The first call caches the value 3 in the scalar cache; the second caches the list (3) in the list cache. The third call doesn't call the real pi function; it gets the value from the scalar cache. Obviously, the second call to pi is a waste of time, and storing its return value is a waste of space. Specifying `LIST_CACHE => MERGE' will make `memoize' use the same cache for scalar and list context return values, so that the second call uses the scalar cache that was populated by the first call. pi ends up being cvalled only once, and both subsequent calls return 3 from the cache, regardless of the calling context. Another use for `MERGE' is when you want both kinds of return values stored in the same disk file; this saves you from having to deal with two disk files instead of one. You can use a normalizer function to keep the two sets of return values separate. For example: memoize 'myfunc', NORMALIZER => 'n', SCALAR_CACHE => [TIE, MLDBM, DB_File, $filename, ...], LIST_CACHE => MERGE, ; sub n { my $context = wantarray() ? 'L' : 'S'; # ... now compute the hash key from the arguments ... $hashkey = "$context:$hashkey"; } This normalizer function will store scalar context return values in the disk file under keys that begin with `S:', and list context return values under keys that begin with `L:'. OTHER FACILITIES ================ `unmemoize' ----------- There's an `unmemoize' function that you can import if you want to. Why would you want to? Here's an example: Suppose you have your cache tied to a DBM file, and you want to make sure that the cache is written out to disk if someone interrupts the program. If the program exits normally, this will happen anyway, but if someone types control-C or something then the program will terminate immediately without synchronizing the database. So what you can do instead is $SIG{INT} = sub { unmemoize 'function' }; Thanks to Jonathan Roy for discovering a use for `unmemoize'. `unmemoize' accepts a reference to, or the name of a previously memoized function, and undoes whatever it did to provide the memoized version in the first place, including making the name refer to the unmemoized version if appropriate. It returns a reference to the unmemoized version of the function. If you ask it to unmemoize a function that was never memoized, it croaks. flush_cache ----------- `flush_cache(function)' will flush out the caches, discarding all the cached data. The argument may be a funciton name or a reference to a function. For finer control over when data is discarded or expired, see the documentation for `Memoize::Expire', included in this package. Note that if the cache is a tied hash, flush_cache will attempt to invoke the CLEAR method on the hash. If there is no CLEAR method, this will cause a run-time error. An alternative approach to cache flushing is to use the HASH option (see above) to request that `Memoize' use a particular hash variable as its cache. Then you can examine or modify the hash at any time in any way you desire. CAVEATS ======= Memoization is not a cure-all: * Do not memoize a function whose behavior depends on program state other than its own arguments, such as global variables, the time of day, or file input. These functions will not produce correct results when memoized. For a particularly easy example: sub f { time; } This function takes no arguments, and as far as `Memoize' is concerned, it always returns the same result. `Memoize' is wrong, of course, and the memoized version of this function will call time once to get the current time, and it will return that same time every time you call it after that. * Do not memoize a function with side effects. sub f { my ($a, $b) = @_; my $s = $a + $b; print "$a + $b = $s.\n"; } This function accepts two arguments, adds them, and prints their sum. Its return value is the numuber of characters it printed, but you probably didn't care about that. But `Memoize' doesn't understand that. If you memoize this function, you will get the result you expect the first time you ask it to print the sum of 2 and 3, but subsequent calls will return 1 (the return value of print) without actually printing anything. * Do not memoize a function that returns a data structure that is modified by its caller. Consider these functions: `getusers' returns a list of users somehow, and then main throws away the first user on the list and prints the rest: sub main { my $userlist = getusers(); shift @$userlist; foreach $u (@$userlist) { print "User $u\n"; } } sub getusers { my @users; # Do something to get a list of users; \@users; # Return reference to list. } If you memoize `getusers' here, it will work right exactly once. The reference to the users list will be stored in the memo table. main will discard the first element from the referenced list. The next time you invoke main, `Memoize' will not call `getusers'; it will just return the same reference to the same list it got last time. But this time the list has already had its head removed; main will erroneously remove another element from it. The list will get shorter and shorter every time you call main. Similarly, this: $u1 = getusers(); $u2 = getusers(); pop @$u1; will modify $u2 as well as $u1, because both variables are references to the same array. Had `getusers' not been memoized, $u1 and $u2 would have referred to different arrays. PERSISTENT CACHE SUPPORT ======================== You can tie the cache tables to any sort of tied hash that you want to, as long as it supports TIEHASH, FETCH, STORE, and EXISTS. For example, memoize 'function', SCALAR_CACHE => [TIE, GDBM_File, $filename, O_RDWR|O_CREAT, 0666]; works just fine. For some storage methods, you need a little glue. SDBM_File doesn't supply an EXISTS method, so included in this package is a glue module called `Memoize::SDBM_File' which does provide one. Use this instead of plain SDBM_File to store your cache table on disk in an SDBM_File database: memoize 'function', SCALAR_CACHE => [TIE, Memoize::SDBM_File, $filename, O_RDWR|O_CREAT, 0666]; `NDBM_File' has the same problem and the same solution. Storable isn't a tied hash class at all. You can use it to store a hash to disk and retrieve it again, but you can't modify the hash while it's on the disk. So if you want to store your cache table in a Storable database, use `Memoize::Storable', which puts a hashlike front-end onto Storable. The hash table is actually kept in memory, and is loaded from your Storable file at the time you memoize the function, and stored back at the time you unmemoize the function (or when your program exits): memoize 'function', SCALAR_CACHE => [TIE, Memoize::Storable, $filename]; memoize 'function', SCALAR_CACHE => [TIE, Memoize::Storable, $filename, 'nstore']; Include the `nstore' option to have the Storable database written in `network order'. (See *Note Storable: Storable, for more details about this.) EXPIRATION SUPPORT ================== See Memoize::Expire, which is a plug-in module that adds expiration functionality to Memoize. If you don't like the kinds of policies that Memoize::Expire implements, it is easy to write your own plug-in module to implement whatever policy you desire. BUGS ==== The test suite is much better, but always needs improvement. There used to be some problem with the way `goto &f' works under threaded Perl, because of the lexical scoping of `@_'. This is a bug in Perl, and until it is resolved, Memoize won't work with these Perls. This is probably still the case, although I have not been able to try it out. If you encounter this problem, you can fix it by chopping the source code a little. Find the comment in the source code that says `--- THREADED PERL COMMENT---' and comment out the active line and uncomment the commented one. Then try it again. Here's a bug that isn't my fault: Some versions of DB_File won't let you store data under a key of length 0. That means that if you have a function f which you memoized and the cache is in a DB_File database, then the value of `f()' (f called with no arguments) will not be memoized. Let us all breathe deeply and repeat this mantra: "Gosh, Keith, that sure was a stupid thing to do." MAILING LIST ============ To join a very low-traffic mailing list for announcements about `Memoize', send an empty note to `mjd-perl-memoize-request@plover.com'. AUTHOR ====== Mark-Jason Dominus (`mjd-perl-memoize+@plover.com'), Plover Systems co. See the `Memoize.pm' Page at http://www.plover.com/~mjd/perl/Memoize/ for news and upgrades. Near this page, at http://www.plover.com/~mjd/perl/MiniMemoize/ there is an article about memoization and about the internals of Memoize that appeared in The Perl Journal, issue #13. (This article is also included in the Memoize distribution as `article.html'.) To join a mailing list for announcements about `Memoize', send an empty message to `mjd-perl-memoize-request@plover.com'. This mailing list is for announcements only and has extremely low traffic--about four messages per year. THANK YOU ========= Many thanks to Jonathan Roy for bug reports and suggestions, to Michael Schwern for other bug reports and patches, to Mike Cariaso for helping me to figure out the Right Thing to Do About Expiration, to Joshua Gerth, Joshua Chamas, Jonathan Roy, Mark D. Anderson, and Andrew Johnson for more suggestions about expiration, to Ariel Scolnikov for delightful messages about the Fibonacci function, to Dion Almaer for thought-provoking suggestions about the default normalizer, to Walt Mankowski and Kurt Starsinic for much help investigating problems under threaded Perl, to Alex Dudkevich for reporting the bug in prototyped functions and for checking my patch, to Tony Bass for many helpful suggestions, to Philippe Verdret for enlightening discussion of Hook::PrePostCall, to Nat Torkington for advice I ignored, to Chris Nandor for portability advice, to Randal Schwartz for suggesting the 'flush_cache function, and to Jenda Krynicky for being a light in the world.