added libtommath-0.38
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Tom St Denis
Steffen Jaeckel
parent
fde740eae0
commit
21adca01da
2
bn.tex
2
bn.tex
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@ -49,7 +49,7 @@
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\begin{document}
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\frontmatter
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\pagestyle{empty}
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\title{LibTomMath User Manual \\ v0.37}
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\title{LibTomMath User Manual \\ v0.38}
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\author{Tom St Denis \\ tomstdenis@iahu.ca}
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\maketitle
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This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been
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@ -78,10 +78,7 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
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/* make next carry */
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_W = _W >> ((mp_word)DIGIT_BIT);
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}
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/* store final carry */
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W[ix] = (mp_digit)(_W & MP_MASK);
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}
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/* setup dest */
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olduse = c->used;
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@ -70,9 +70,6 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
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_W = _W >> ((mp_word)DIGIT_BIT);
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}
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/* store final carry */
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W[ix] = (mp_digit)(_W & MP_MASK);
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/* setup dest */
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olduse = c->used;
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c->used = pa;
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@ -1,3 +1,7 @@
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Jan 26th, 2006
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v0.38 -- broken makefile.shared fixed
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-- removed some carry stores that were not required [updated text]
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November 18th, 2005
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v0.37 -- [Don Porter] reported on a TCL list [HEY SEND ME BUGREPORTS ALREADY!!!] that mp_add_d() would compute -0 with some inputs. Fixed.
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-- [rinick@gmail.com] reported the makefile.bcc was messed up. Fixed.
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2
makefile
2
makefile
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@ -3,7 +3,7 @@
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#Tom St Denis
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#version of library
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VERSION=0.37
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VERSION=0.38
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CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare
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@ -1,7 +1,7 @@
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#Makefile for GCC
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#
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#Tom St Denis
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VERSION=0:37
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VERSION=0:38
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CC = libtool --mode=compile gcc
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BIN
poster.pdf
BIN
poster.pdf
Binary file not shown.
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@ -458,10 +458,7 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
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/* make next carry */
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_W = _W >> ((mp_word)DIGIT_BIT);
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}
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/* store final carry */
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W[ix] = (mp_digit)(_W & MP_MASK);
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}
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/* setup dest */
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olduse = c->used;
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@ -564,9 +561,6 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
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_W = _W >> ((mp_word)DIGIT_BIT);
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}
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/* store final carry */
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W[ix] = (mp_digit)(_W & MP_MASK);
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/* setup dest */
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olduse = c->used;
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c->used = pa;
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BIN
tommath.pdf
BIN
tommath.pdf
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23
tommath.src
23
tommath.src
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@ -66,7 +66,7 @@ QUALCOMM Australia \\
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}
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}
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\maketitle
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This text has been placed in the public domain. This text corresponds to the v0.37 release of the
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This text has been placed in the public domain. This text corresponds to the v0.38 release of the
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LibTomMath project.
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\begin{alltt}
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@ -77,7 +77,7 @@ K2L 1C3
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Canada
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Phone: 1-613-836-3160
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Email: tomstdenis@iahu.ca
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Email: tomstdenis@gmail.com
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\end{alltt}
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This text is formatted to the international B5 paper size of 176mm wide by 250mm tall using the \LaTeX{}
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@ -2190,7 +2190,7 @@ left.
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After the digits have been shifted appropriately at most $lg(\beta) - 1$ shifts are left to perform. Step 5 calculates the number of remaining shifts
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required. If it is non-zero a modified shift loop is used to calculate the remaining product.
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Essentially the loop is a generic version of algorith mp\_mul2 designed to handle any shift count in the range $1 \le x < lg(\beta)$. The $mask$
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Essentially the loop is a generic version of algorithm mp\_mul\_2 designed to handle any shift count in the range $1 \le x < lg(\beta)$. The $mask$
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variable is used to extract the upper $d$ bits to form the carry for the next iteration.
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This algorithm is loosely measured as a $O(2n)$ algorithm which means that if the input is $n$-digits that it takes $2n$ ``time'' to
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@ -2611,17 +2611,16 @@ Place an array of \textbf{MP\_WARRAY} single precision digits named $W$ on the s
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\hspace{6mm}5.4.1 $\_ \hat W \leftarrow \_ \hat W + a_{tx+iy}b_{ty-iy}$ \\
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\hspace{3mm}5.5 $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$\\
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\hspace{3mm}5.6 $\_ \hat W \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\
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6. $W_{pa} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\
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\\
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7. $oldused \leftarrow c.used$ \\
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8. $c.used \leftarrow digs$ \\
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9. for $ix$ from $0$ to $pa$ do \\
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\hspace{3mm}9.1 $c_{ix} \leftarrow W_{ix}$ \\
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10. for $ix$ from $pa + 1$ to $oldused - 1$ do \\
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\hspace{3mm}10.1 $c_{ix} \leftarrow 0$ \\
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6. $oldused \leftarrow c.used$ \\
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7. $c.used \leftarrow digs$ \\
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8. for $ix$ from $0$ to $pa$ do \\
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\hspace{3mm}8.1 $c_{ix} \leftarrow W_{ix}$ \\
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9. for $ix$ from $pa + 1$ to $oldused - 1$ do \\
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\hspace{3mm}9.1 $c_{ix} \leftarrow 0$ \\
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\\
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11. Clamp $c$. \\
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12. Return MP\_OKAY. \\
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10. Clamp $c$. \\
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11. Return MP\_OKAY. \\
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\hline
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\end{tabular}
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\end{center}
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74
tommath.tex
74
tommath.tex
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@ -66,7 +66,7 @@ QUALCOMM Australia \\
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}
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}
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\maketitle
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This text has been placed in the public domain. This text corresponds to the v0.37 release of the
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This text has been placed in the public domain. This text corresponds to the v0.38 release of the
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LibTomMath project.
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\begin{alltt}
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@ -77,7 +77,7 @@ K2L 1C3
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Canada
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Phone: 1-613-836-3160
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Email: tomstdenis@iahu.ca
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Email: tomstdenis@gmail.com
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\end{alltt}
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This text is formatted to the international B5 paper size of 176mm wide by 250mm tall using the \LaTeX{}
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@ -3169,7 +3169,7 @@ left.
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After the digits have been shifted appropriately at most $lg(\beta) - 1$ shifts are left to perform. Step 5 calculates the number of remaining shifts
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required. If it is non-zero a modified shift loop is used to calculate the remaining product.
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Essentially the loop is a generic version of algorith mp\_mul2 designed to handle any shift count in the range $1 \le x < lg(\beta)$. The $mask$
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Essentially the loop is a generic version of algorithm mp\_mul\_2 designed to handle any shift count in the range $1 \le x < lg(\beta)$. The $mask$
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variable is used to extract the upper $d$ bits to form the carry for the next iteration.
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This algorithm is loosely measured as a $O(2n)$ algorithm which means that if the input is $n$-digits that it takes $2n$ ``time'' to
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@ -3864,17 +3864,16 @@ Place an array of \textbf{MP\_WARRAY} single precision digits named $W$ on the s
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\hspace{6mm}5.4.1 $\_ \hat W \leftarrow \_ \hat W + a_{tx+iy}b_{ty-iy}$ \\
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\hspace{3mm}5.5 $W_{ix} \leftarrow \_ \hat W (\mbox{mod }\beta)$\\
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\hspace{3mm}5.6 $\_ \hat W \leftarrow \lfloor \_ \hat W / \beta \rfloor$ \\
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6. $W_{pa} \leftarrow \_ \hat W (\mbox{mod }\beta)$ \\
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\\
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7. $oldused \leftarrow c.used$ \\
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8. $c.used \leftarrow digs$ \\
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9. for $ix$ from $0$ to $pa$ do \\
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\hspace{3mm}9.1 $c_{ix} \leftarrow W_{ix}$ \\
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10. for $ix$ from $pa + 1$ to $oldused - 1$ do \\
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\hspace{3mm}10.1 $c_{ix} \leftarrow 0$ \\
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6. $oldused \leftarrow c.used$ \\
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7. $c.used \leftarrow digs$ \\
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8. for $ix$ from $0$ to $pa$ do \\
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\hspace{3mm}8.1 $c_{ix} \leftarrow W_{ix}$ \\
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9. for $ix$ from $pa + 1$ to $oldused - 1$ do \\
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\hspace{3mm}9.1 $c_{ix} \leftarrow 0$ \\
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\\
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11. Clamp $c$. \\
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12. Return MP\_OKAY. \\
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10. Clamp $c$. \\
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11. Return MP\_OKAY. \\
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\hline
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\end{tabular}
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\end{center}
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@ -3977,33 +3976,30 @@ and addition operations in the nested loop in parallel.
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077
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078 /* make next carry */
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079 _W = _W >> ((mp_word)DIGIT_BIT);
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080 \}
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080 \}
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081
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082 /* store final carry */
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083 W[ix] = (mp_digit)(_W & MP_MASK);
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084
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085 /* setup dest */
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086 olduse = c->used;
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087 c->used = pa;
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088
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089 \{
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090 register mp_digit *tmpc;
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091 tmpc = c->dp;
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092 for (ix = 0; ix < pa+1; ix++) \{
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093 /* now extract the previous digit [below the carry] */
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094 *tmpc++ = W[ix];
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095 \}
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096
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097 /* clear unused digits [that existed in the old copy of c] */
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098 for (; ix < olduse; ix++) \{
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099 *tmpc++ = 0;
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100 \}
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101 \}
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102 mp_clamp (c);
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103 return MP_OKAY;
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104 \}
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105 #endif
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106
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082 /* setup dest */
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083 olduse = c->used;
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084 c->used = pa;
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085
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086 \{
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087 register mp_digit *tmpc;
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088 tmpc = c->dp;
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089 for (ix = 0; ix < pa+1; ix++) \{
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090 /* now extract the previous digit [below the carry] */
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091 *tmpc++ = W[ix];
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092 \}
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093
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094 /* clear unused digits [that existed in the old copy of c] */
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095 for (; ix < olduse; ix++) \{
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096 *tmpc++ = 0;
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097 \}
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098 \}
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099 mp_clamp (c);
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100 return MP_OKAY;
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101 \}
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102 #endif
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103
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\end{alltt}
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\end{small}
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@ -4020,7 +4016,7 @@ slower and also often doesn't exist. This new algorithm only performs two reads
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compiler has aliased $\_ \hat W$ to a CPU register.
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After the inner loop we store the current accumulator in $W$ and shift $\_ \hat W$ (lines 76, 79) to forward it as
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a carry for the next pass. After the outer loop we use the final carry (line 83) as the last digit of the product.
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a carry for the next pass. After the outer loop we use the final carry (line 76) as the last digit of the product.
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\subsection{Polynomial Basis Multiplication}
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To break the $O(n^2)$ barrier in multiplication requires a completely different look at integer multiplication. In the following algorithms
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