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Vector-based pocket calculator for Tcl, implemented in C++

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vecexpr

Vector-based pocket calculator for Tcl implemented in C++ : a much faster alternative to long loops calling expr over vector data.

Compiling and loading vecexpr

Compile using the Makefile provided (amending the Tcl lib path). Run tests from the shell: tclsh test.tcl Start Tcl interpreter: tclsh Then load into Tcl interpreter: load vecexpr.so

Syntax

Uses reverse Polish syntax (operands followed by operators). Uses a LIFO stack, plus an extra register (used via store and recall) Arguments: scalars, vectors (Tcl lists), matrices (flattened, row-major) and built-in operators.

Examples:

% set vec "1 2 3"
% vecexpr $vec "4 5 6" add >othervec
% puts $othervec
5.0 7.0 9.0

vecexpr "1.2 -2.3 3.2" floor >integers; puts $integers (prints 1.0 -3.0 3.0)

Operators

nullary

pi (constant), height (current stack height, for debugging), <varName (push Tcl var - can be done with $varName as well), recall (after calling store)

unary

abs cos sin tan exp floor log mean min max round sq sqrt sum >varName (pop into Tcl var), &varName (copy floor values to an int variable), store (recall is 0-ary) dup (duplicate in the stack), pop

binary

add sub mult matmult (see below) dot div concat swap atan2

All binary functions except dot and matmult accept mixed scalar/vector operands. Vector lengths must match, except for concat and swap.

Example usage of atan2, converting result to degrees (note order of operands: y, x):

% vecexpr 5 0 atan2 pi div 180 mult
90.0

Quaternary: bin

vecexpr <data> <xmin> <dx> <nbins> where xmin, dx and nbins are scalars. Will push on the stack a histogram of the data, with nbins bins of width dx starting at xmin. The histogram can be saved as an integer-typed Tcl list using the '&' operator:

% vecexpr "1.1 2.1 2.2 3.5 4.1" 0. 1. 5 bin &histogram
1.1 2.1 2.2 3.5 4.1
% puts $histogram
0 1 2 1 1

Matrix operations

Matrices are stored unrolled (in row-major order). "Unary" matrix operations (min_ew, transp) are binary because they require the shape of the matrix, provided as the number of lines at the top of the stack.

Transposing a (2,3) matrix:

vecexpr "1 2 3 4 5 6" 2 transp -> 1.0 4.0 2.0 5.0 3.0 6.0

Transposing the (3,2) matrix with the same (flattened) elements:

vecexpr "1 2 3 4 5 6" 3 transp -> 1.0 3.0 5.0 2.0 4.0 6.0

For matrix multiplication, push both matrices on the stack, then the common dimension:

vecexpr "1 0 0 1" "1 2" 2 matmult -> "1.0 2.0"

vecexpr "1 0 0 1" "1 2" 1 matmult -> "1.0 2.0 0.0 0.0 0.0 0.0 1.0 2.0"

Complete table of operators

This table lists each operator, the number of operands it uses (top n vectors on the stack), and the change in stack height after execution, that is, how many items are added or removed.

Operator n. operands Stack chg. Action
<varName 0 +1 push Tcl var. varName on the stack (in practice, $varName is faster)
>varName 1 -1 pop into Tcl var. varName
&varName 1 0 copy integer-typed floor values to variable varName
abs 1 0 absolute value
add 2 -1 add 2 same-length vectors, or vector and scalar (element-wise), or column-vector and matrix, or matrix and row-vector
atan2 2 -1 given vectors y and x, push element-wise arctangent of y / x (in radians)
bin 4 -3 push on the stack a histogram of the data, with nbins bins of width dx starting at xmin
concat 2 -1 concatenate two top vectors
cos 1 0 cosine (angles in radians)
div 2 -1 division (same-length vectors or vector by scalar or scalar by vector)
dot 2 -1 dot product
dup 1 +1 push copy of top vector onto stack                                                                            
exp 1 0 exponential
floor 1 0 floor (type: double)
height 0 0 push current stack height
log 1 0 natural log
matmult 3 0 multiply matrices, using 3 args: M1 M2 n, where n is the common dimension
max 1 +1 push max element of top vector
mean 1 +1 push mean of top vector
min 1 +1 push min of top vector
min_ew 2 -1 element-wise minimum between lines of the top matrix (M, n, where n is the number of lines)
mult 2 -1 element-wise multiply vectors, or multiply vector and scalar
pi 0 +1 push pi constant onto stack
pop 1 -1 remove top vector from stack
recall 0 +1 push stored data (register)
round 1 0 round all elements to nearest integer (keep double type)
sin 1 0 sine (angles in radians)
sq 1 0 square
sqrt 1 0 square root
store 1 0 copy top vector to register
sub 2 -1 subtract (see add for details)
sum 1 +1 push sum of values of top vector
swap 2 0 swap top two vectors of stack
tan 1 0 tangent (angles in radians)
transp 2 -1 transpose top matrix (M, n, where n is the number of lines)

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