hcrypto/libtommath/tommath.tex

168 \subsection{What is Multiple Precision Arithmetic?}
182 \subsection{The Need for Multiple Precision Arithmetic}
230 \subsection{Benefits of Multiple Precision Arithmetic}
284 \subsection{Notation}
307 \subsection{Precision Notation}
331 \subsection{Algorithm Inputs and Outputs}
336 \subsection{Mathematical Expressions}
347 \subsection{Work Effort}
429 \subsection{What is LibTomMath?}
439 \subsection{Goals of LibTomMath}
469 \subsection{Code Base}
484 \subsection{API Simplicity}
498 \subsection{Optimizations}
509 \subsection{Portability and Stability}
518 \subsection{Choice}
586 \subsection{The mp\_int Structure}
734 \subsection{Initializing an mp\_int}
814 \subsection{Clearing an mp\_int}
881 \subsection{Augmenting an mp\_int's Precision}
941 \subsection{Initializing Variable Precision mp\_ints}
998 \subsection{Multiple Integer Initializations and Clearings}
1045 \subsection{Clamping Excess Digits}
1135 \subsection{Copying an mp\_int}
1254 \subsection{Creating a Clone}
1326 \subsection{Absolute Value}
1363 \subsection{Integer Negation}
1406 \subsection{Setting Small Constants}
1451 \subsection{Setting Large Constants}
1498 \subsection{Unsigned Comparisions}
1565 \subsection{Signed Comparisons}
1648 \subsection{Low Level Addition}
1746 \subsection{Low Level Subtraction}
1849 \subsection{High Level Addition}
1938 \subsection{High Level Subtraction}
2018 \subsection{Multiplication by Two}
2081 \subsection{Division by Two}
2140 \subsection{Multiplication by $x$}
2209 \subsection{Division by $x$}
2272 \subsection{Multiplication by Power of Two}
2340 \subsection{Division by Power of Two}
2395 \subsection{Remainder of Division by Power of Two}
2498 \subsection{The Baseline Multiplication}
2631 \subsection{Faster Multiplication by the ``Comba'' Method}
2823 \subsection{Polynomial Basis Multiplication}
2919 \subsection{Karatsuba Multiplication}
3032 \subsection{Toom-Cook $3$-Way Multiplication}
3165 \subsection{Signed Multiplication}
3252 \subsection{The Baseline Squaring Algorithm}
3326 \subsection{Faster Squaring by the ``Comba'' Method}
3408 \subsection{Polynomial Basis Squaring}
3413 \subsection{Karatsuba Squaring}
3527 \subsection{Toom-Cook Squaring}
3532 \subsection{High Level Squaring}
3631 \subsection{Fixed Point Arithmetic}
3685 \subsection{Choosing a Radix Point}
3726 \subsection{Trimming the Quotient}
3740 \subsection{Trimming the Residue}
3754 \subsection{The Barrett Algorithm}
3830 \subsection{The Barrett Setup Algorithm}
3992 \subsection{Digit Based Montgomery Reduction}
4050 \subsection{Baseline Montgomery Reduction}
4128 \subsection{Faster ``Comba'' Montgomery Reduction}
4225 \subsection{Montgomery Setup}
4373 \subsection{Choice of Moduli}
4390 \subsection{Choice of $k$}
4395 \subsection{Restricted Diminished Radix Reduction}
4531 \subsection{Unrestricted Diminished Radix Reduction}
4783 \subsection{Single Digit Exponentiation}
4875 \subsection{Optimal Values of $k$}
4902 \subsection{Sliding-Window Exponentiation}
5037 \subsection{Barrett Modular Exponentiation}
5300 \subsection{Quotient Estimation}
5344 \subsection{Normalized Integers}
5356 \subsection{Radix-$\beta$ Division with Remainder}
5523 \subsection{Single Digit Addition and Subtraction}
5561 \subsection{Single Digit Multiplication}
5609 \subsection{Single Digit Division}
5668 \subsection{Single Digit Root Extraction}
5781 \subsection{Reading Radix-n Input}
5858 \subsection{Generating Radix-$n$ Output}
6036 \subsection{Complete Greatest Common Divisor}
6208 \subsection{Jacobi Symbol}
6369 \subsection{General Case}
6466 \subsection{Trial Division}
6529 \subsection{The Fermat Test}
6572 \subsection{The Miller-Rabin Test}