The R13B03 release.OTP_R13B03

1 files changed, 131 insertions, 0 deletions

diff --git a/lib/ssh/src/ssh_math.erl b/lib/ssh/src/ssh_math.erl
new file mode 100755
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+++ b/lib/ssh/src/ssh_math.erl
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+%%
+%% %CopyrightBegin%
+%% 
+%% Copyright Ericsson AB 2005-2009. All Rights Reserved.
+%% 
+%% The contents of this file are subject to the Erlang Public License,
+%% Version 1.1, (the "License"); you may not use this file except in
+%% compliance with the License. You should have received a copy of the
+%% Erlang Public License along with this software. If not, it can be
+%% retrieved online at http://www.erlang.org/.
+%% 
+%% Software distributed under the License is distributed on an "AS IS"
+%% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
+%% the License for the specific language governing rights and limitations
+%% under the License.
+%% 
+%% %CopyrightEnd%
+%%
+
+%%
+
+%%% Description: SSH math utilities
+
+-module(ssh_math).
+
+-export([ilog2/1, ipow/3, invert/2, ipow2/3]).
+	 
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%
+%% INTEGER utils
+%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%% number of bits (used) in a integer = isize(N) = |log2(N)|+1
+ilog2(N) ->
+    ssh_bits:isize(N) - 1.
+
+
+%% calculate A^B mod M
+ipow(A, B, M) when M > 0, B >= 0 ->
+    crypto:mod_exp(A, B, M).
+
+ipow2(A, B, M) when M > 0, B >= 0 ->
+    if A == 1 -> 
+ 	    1;
+       true -> 
+ 	    ipow2(A, B, M, 1)
+    end.
+
+ipow2(A, 1, M, Prod) ->
+    (A*Prod) rem M;
+ipow2(_A, 0, _M, Prod) ->
+    Prod;
+ipow2(A, B, M, Prod)  ->
+    B1 = B bsr 1,
+    A1 = (A*A) rem M,
+    if B - B1 == B1 ->
+	    ipow2(A1, B1, M, Prod);
+       true ->
+	    ipow2(A1, B1, M, (A*Prod) rem M)
+    end.
+
+%% %%
+%% %% Normal gcd
+%% %%
+%% gcd(R, Q) when abs(Q) < abs(R) -> gcd1(Q,R);
+%% gcd(R, Q) -> gcd1(R,Q).
+
+%% gcd1(0, Q) -> Q;
+%% gcd1(R, Q) ->
+%%     gcd1(Q rem R, R).
+
+
+%% %%
+%% %% Least common multiple of (R,Q)
+%% %%
+%% lcm(0, _Q) -> 0;
+%% lcm(_R, 0) -> 0;
+%% lcm(R, Q) ->
+%%     (Q div gcd(R, Q)) * R.
+
+%% %%
+%% %% Extended gcd gcd(R,Q) -> {G, {A,B}} such that G == R*A + Q*B
+%% %%
+%% %% Here we could have use for a bif divrem(Q, R) -> {Quote, Remainder}
+%% %%
+%% egcd(R,Q) when abs(Q) < abs(R) -> egcd1(Q,R,1,0,0,1);
+%% egcd(R,Q) -> egcd1(R,Q,0,1,1,0).
+
+%% egcd1(0,Q,_,_,Q1,Q2) -> {Q, {Q2,Q1}};
+%% egcd1(R,Q,R1,R2,Q1,Q2) ->
+%%     D = Q div R,
+%%     egcd1(Q rem R, R, Q1-D*R1, Q2-D*R2, R1, R2).
+
+%%
+%% Invert an element X mod P
+%% Calculated as {1, {A,B}} = egcd(X,P),
+%%   1 == P*A + X*B == X*B (mod P) i.e B is the inverse element
+%%
+%% X > 0, P > 0, X < P   (P should be prime)
+%%
+invert(X,P) when X > 0, P > 0, X < P ->
+    I = inv(X,P,1,0),
+    if 
+        I < 0 -> P + I;
+        true -> I
+    end.
+
+inv(0,_,_,Q) -> Q;
+inv(X,P,R1,Q1) ->
+    D = P div X,
+    inv(P rem X, X, Q1 - D*R1, R1).
+
+
+%% %%
+%% %% Integer square root
+%% %%
+
+%% isqrt(0) -> 0;
+%% isqrt(1) -> 1;
+%% isqrt(X) when X >= 0 ->
+%%     R = X div 2,
+%%     isqrt(X div R, R, X).
+
+%% isqrt(Q,R,X) when Q < R ->
+%%     R1 = (R+Q) div 2,
+%%     isqrt(X div R1, R1, X);
+%% isqrt(_, R, _) -> R.
+
+