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7fd50c04de
drop-in for me and looks substantailly neater than the previous version, so I'll give the floppy tape users a break (but just this once :).
481 lines
13 KiB
C
481 lines
13 KiB
C
/*
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* Copyright (c) 1994 Steve Gerakines
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*
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* This is freely redistributable software. You may do anything you
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* wish with it, so long as the above notice stays intact.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR(S) ``AS IS'' AND ANY EXPRESS
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* OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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* DISCLAIMED. IN NO EVENT SHALL THE AUTHOR(S) BE LIABLE FOR ANY DIRECT,
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* INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
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* IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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*
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* ftecc.c - QIC-40/80 Reed-Solomon error correction
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* 05/30/94 v1.0 ++sg
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* Did some minor optimization. The multiply by 0xc0 was a dog so it
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* was replaced with a table lookup. Fixed a couple of places where
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* bad sectors could go unnoticed. Moved to release.
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*
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* 03/22/94 v0.4
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* Major re-write. It can handle everything required by QIC now.
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*
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* 09/14/93 v0.2 pl01
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* Modified slightly to fit with my driver. Based entirely upon David
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* L. Brown's package.
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*/
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#include <sys/ftape.h>
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/* Inverse matrix */
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struct inv_mat {
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UCHAR log_denom; /* Log of the denominator */
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UCHAR zs[3][3]; /* The matrix */
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};
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/*
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* Powers of x, modulo 255.
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*/
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static UCHAR alpha_power[] = {
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0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80,
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0x87, 0x89, 0x95, 0xad, 0xdd, 0x3d, 0x7a, 0xf4,
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0x6f, 0xde, 0x3b, 0x76, 0xec, 0x5f, 0xbe, 0xfb,
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0x71, 0xe2, 0x43, 0x86, 0x8b, 0x91, 0xa5, 0xcd,
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0x1d, 0x3a, 0x74, 0xe8, 0x57, 0xae, 0xdb, 0x31,
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0x62, 0xc4, 0x0f, 0x1e, 0x3c, 0x78, 0xf0, 0x67,
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0xce, 0x1b, 0x36, 0x6c, 0xd8, 0x37, 0x6e, 0xdc,
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0x3f, 0x7e, 0xfc, 0x7f, 0xfe, 0x7b, 0xf6, 0x6b,
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0xd6, 0x2b, 0x56, 0xac, 0xdf, 0x39, 0x72, 0xe4,
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0x4f, 0x9e, 0xbb, 0xf1, 0x65, 0xca, 0x13, 0x26,
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0x4c, 0x98, 0xb7, 0xe9, 0x55, 0xaa, 0xd3, 0x21,
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0x42, 0x84, 0x8f, 0x99, 0xb5, 0xed, 0x5d, 0xba,
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0xf3, 0x61, 0xc2, 0x03, 0x06, 0x0c, 0x18, 0x30,
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0x60, 0xc0, 0x07, 0x0e, 0x1c, 0x38, 0x70, 0xe0,
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0x47, 0x8e, 0x9b, 0xb1, 0xe5, 0x4d, 0x9a, 0xb3,
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0xe1, 0x45, 0x8a, 0x93, 0xa1, 0xc5, 0x0d, 0x1a,
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0x34, 0x68, 0xd0, 0x27, 0x4e, 0x9c, 0xbf, 0xf9,
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0x75, 0xea, 0x53, 0xa6, 0xcb, 0x11, 0x22, 0x44,
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0x88, 0x97, 0xa9, 0xd5, 0x2d, 0x5a, 0xb4, 0xef,
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0x59, 0xb2, 0xe3, 0x41, 0x82, 0x83, 0x81, 0x85,
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0x8d, 0x9d, 0xbd, 0xfd, 0x7d, 0xfa, 0x73, 0xe6,
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0x4b, 0x96, 0xab, 0xd1, 0x25, 0x4a, 0x94, 0xaf,
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0xd9, 0x35, 0x6a, 0xd4, 0x2f, 0x5e, 0xbc, 0xff,
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0x79, 0xf2, 0x63, 0xc6, 0x0b, 0x16, 0x2c, 0x58,
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0xb0, 0xe7, 0x49, 0x92, 0xa3, 0xc1, 0x05, 0x0a,
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0x14, 0x28, 0x50, 0xa0, 0xc7, 0x09, 0x12, 0x24,
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0x48, 0x90, 0xa7, 0xc9, 0x15, 0x2a, 0x54, 0xa8,
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0xd7, 0x29, 0x52, 0xa4, 0xcf, 0x19, 0x32, 0x64,
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0xc8, 0x17, 0x2e, 0x5c, 0xb8, 0xf7, 0x69, 0xd2,
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0x23, 0x46, 0x8c, 0x9f, 0xb9, 0xf5, 0x6d, 0xda,
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0x33, 0x66, 0xcc, 0x1f, 0x3e, 0x7c, 0xf8, 0x77,
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0xee, 0x5b, 0xb6, 0xeb, 0x51, 0xa2, 0xc3, 0x01
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};
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/*
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* Log table, modulo 255 + 1.
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*/
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static UCHAR alpha_log[] = {
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0xff, 0x00, 0x01, 0x63, 0x02, 0xc6, 0x64, 0x6a,
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0x03, 0xcd, 0xc7, 0xbc, 0x65, 0x7e, 0x6b, 0x2a,
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0x04, 0x8d, 0xce, 0x4e, 0xc8, 0xd4, 0xbd, 0xe1,
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0x66, 0xdd, 0x7f, 0x31, 0x6c, 0x20, 0x2b, 0xf3,
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0x05, 0x57, 0x8e, 0xe8, 0xcf, 0xac, 0x4f, 0x83,
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0xc9, 0xd9, 0xd5, 0x41, 0xbe, 0x94, 0xe2, 0xb4,
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0x67, 0x27, 0xde, 0xf0, 0x80, 0xb1, 0x32, 0x35,
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0x6d, 0x45, 0x21, 0x12, 0x2c, 0x0d, 0xf4, 0x38,
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0x06, 0x9b, 0x58, 0x1a, 0x8f, 0x79, 0xe9, 0x70,
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0xd0, 0xc2, 0xad, 0xa8, 0x50, 0x75, 0x84, 0x48,
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0xca, 0xfc, 0xda, 0x8a, 0xd6, 0x54, 0x42, 0x24,
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0xbf, 0x98, 0x95, 0xf9, 0xe3, 0x5e, 0xb5, 0x15,
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0x68, 0x61, 0x28, 0xba, 0xdf, 0x4c, 0xf1, 0x2f,
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0x81, 0xe6, 0xb2, 0x3f, 0x33, 0xee, 0x36, 0x10,
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0x6e, 0x18, 0x46, 0xa6, 0x22, 0x88, 0x13, 0xf7,
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0x2d, 0xb8, 0x0e, 0x3d, 0xf5, 0xa4, 0x39, 0x3b,
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0x07, 0x9e, 0x9c, 0x9d, 0x59, 0x9f, 0x1b, 0x08,
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0x90, 0x09, 0x7a, 0x1c, 0xea, 0xa0, 0x71, 0x5a,
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0xd1, 0x1d, 0xc3, 0x7b, 0xae, 0x0a, 0xa9, 0x91,
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0x51, 0x5b, 0x76, 0x72, 0x85, 0xa1, 0x49, 0xeb,
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0xcb, 0x7c, 0xfd, 0xc4, 0xdb, 0x1e, 0x8b, 0xd2,
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0xd7, 0x92, 0x55, 0xaa, 0x43, 0x0b, 0x25, 0xaf,
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0xc0, 0x73, 0x99, 0x77, 0x96, 0x5c, 0xfa, 0x52,
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0xe4, 0xec, 0x5f, 0x4a, 0xb6, 0xa2, 0x16, 0x86,
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0x69, 0xc5, 0x62, 0xfe, 0x29, 0x7d, 0xbb, 0xcc,
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0xe0, 0xd3, 0x4d, 0x8c, 0xf2, 0x1f, 0x30, 0xdc,
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0x82, 0xab, 0xe7, 0x56, 0xb3, 0x93, 0x40, 0xd8,
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0x34, 0xb0, 0xef, 0x26, 0x37, 0x0c, 0x11, 0x44,
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0x6f, 0x78, 0x19, 0x9a, 0x47, 0x74, 0xa7, 0xc1,
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0x23, 0x53, 0x89, 0xfb, 0x14, 0x5d, 0xf8, 0x97,
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0x2e, 0x4b, 0xb9, 0x60, 0x0f, 0xed, 0x3e, 0xe5,
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0xf6, 0x87, 0xa5, 0x17, 0x3a, 0xa3, 0x3c, 0xb7
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};
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/*
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* Multiplication table for 0xc0.
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*/
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static UCHAR mult_c0[] = {
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0x00, 0xc0, 0x07, 0xc7, 0x0e, 0xce, 0x09, 0xc9,
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0x1c, 0xdc, 0x1b, 0xdb, 0x12, 0xd2, 0x15, 0xd5,
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0x38, 0xf8, 0x3f, 0xff, 0x36, 0xf6, 0x31, 0xf1,
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0x24, 0xe4, 0x23, 0xe3, 0x2a, 0xea, 0x2d, 0xed,
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0x70, 0xb0, 0x77, 0xb7, 0x7e, 0xbe, 0x79, 0xb9,
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0x6c, 0xac, 0x6b, 0xab, 0x62, 0xa2, 0x65, 0xa5,
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0x48, 0x88, 0x4f, 0x8f, 0x46, 0x86, 0x41, 0x81,
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0x54, 0x94, 0x53, 0x93, 0x5a, 0x9a, 0x5d, 0x9d,
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0xe0, 0x20, 0xe7, 0x27, 0xee, 0x2e, 0xe9, 0x29,
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0xfc, 0x3c, 0xfb, 0x3b, 0xf2, 0x32, 0xf5, 0x35,
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0xd8, 0x18, 0xdf, 0x1f, 0xd6, 0x16, 0xd1, 0x11,
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0xc4, 0x04, 0xc3, 0x03, 0xca, 0x0a, 0xcd, 0x0d,
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0x90, 0x50, 0x97, 0x57, 0x9e, 0x5e, 0x99, 0x59,
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0x8c, 0x4c, 0x8b, 0x4b, 0x82, 0x42, 0x85, 0x45,
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0xa8, 0x68, 0xaf, 0x6f, 0xa6, 0x66, 0xa1, 0x61,
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0xb4, 0x74, 0xb3, 0x73, 0xba, 0x7a, 0xbd, 0x7d,
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0x47, 0x87, 0x40, 0x80, 0x49, 0x89, 0x4e, 0x8e,
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0x5b, 0x9b, 0x5c, 0x9c, 0x55, 0x95, 0x52, 0x92,
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0x7f, 0xbf, 0x78, 0xb8, 0x71, 0xb1, 0x76, 0xb6,
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0x63, 0xa3, 0x64, 0xa4, 0x6d, 0xad, 0x6a, 0xaa,
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0x37, 0xf7, 0x30, 0xf0, 0x39, 0xf9, 0x3e, 0xfe,
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0x2b, 0xeb, 0x2c, 0xec, 0x25, 0xe5, 0x22, 0xe2,
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0x0f, 0xcf, 0x08, 0xc8, 0x01, 0xc1, 0x06, 0xc6,
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0x13, 0xd3, 0x14, 0xd4, 0x1d, 0xdd, 0x1a, 0xda,
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0xa7, 0x67, 0xa0, 0x60, 0xa9, 0x69, 0xae, 0x6e,
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0xbb, 0x7b, 0xbc, 0x7c, 0xb5, 0x75, 0xb2, 0x72,
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0x9f, 0x5f, 0x98, 0x58, 0x91, 0x51, 0x96, 0x56,
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0x83, 0x43, 0x84, 0x44, 0x8d, 0x4d, 0x8a, 0x4a,
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0xd7, 0x17, 0xd0, 0x10, 0xd9, 0x19, 0xde, 0x1e,
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0xcb, 0x0b, 0xcc, 0x0c, 0xc5, 0x05, 0xc2, 0x02,
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0xef, 0x2f, 0xe8, 0x28, 0xe1, 0x21, 0xe6, 0x26,
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0xf3, 0x33, 0xf4, 0x34, 0xfd, 0x3d, 0xfa, 0x3a
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};
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/*
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* Return number of sectors available in a segment.
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*/
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int
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sect_count(ULONG badmap)
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{
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int i, amt;
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for (amt = QCV_BLKSEG, i = 0; i < QCV_BLKSEG; i++)
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if (badmap & (1 << i)) amt--;
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return(amt);
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}
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/*
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* Return number of bytes available in a segment.
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*/
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int
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sect_bytes(ULONG badmap)
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{
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int i, amt;
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for (amt = QCV_SEGSIZE, i = 0; i < QCV_BLKSEG; i++)
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if (badmap & (1 << i)) amt -= QCV_BLKSIZE;
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return(amt);
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}
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/*
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* Multiply two numbers in the field.
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*/
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static inline UCHAR
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multiply(UCHAR a, UCHAR b)
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{
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int tmp;
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if (!a || !b) return(0);
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tmp = alpha_log[a] + alpha_log[b];
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if (tmp > 254) tmp -= 255;
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return(alpha_power[tmp]);
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}
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/*
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* Multiply by an exponent.
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*/
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static inline UCHAR
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multiply_out(UCHAR a, int b)
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{
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int tmp;
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if (!a) return(0);
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tmp = alpha_log[a] + b;
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if (tmp > 254) tmp -= 255;
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return(alpha_power[tmp]);
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}
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/*
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* Divide two numbers.
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*/
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static inline UCHAR
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divide(UCHAR a, UCHAR b)
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{
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int tmp;
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if (!a || !b) return(0);
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tmp = alpha_log[a] - alpha_log[b];
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if (tmp < 0) tmp += 255;
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return (alpha_power[tmp]);
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}
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/*
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* Divide using exponent.
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*/
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static inline UCHAR
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divide_out(UCHAR a, UCHAR b)
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{
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int tmp;
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if (!a) return 0;
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tmp = alpha_log[a] - b;
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if (tmp < 0) tmp += 255;
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return (alpha_power[tmp]);
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}
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/*
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* This returns the value z^{a-b}.
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*/
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static inline UCHAR
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z_of_ab(UCHAR a, UCHAR b)
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{
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int tmp = a - b;
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if (tmp < 0) tmp += 255;
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return(alpha_power[tmp]);
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}
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/*
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* Calculate the inverse matrix for two or three errors. Returns 0
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* if there is no inverse or 1 if successful.
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*/
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static inline int
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calculate_inverse(int nerrs, int *pblk, struct inv_mat *inv)
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{
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/* First some variables to remember some of the results. */
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UCHAR z20, z10, z21, z12, z01, z02;
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UCHAR i0, i1, i2;
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UCHAR iv0, iv1, iv2;
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if (nerrs < 2) return(1);
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if (nerrs > 3) return(0);
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i0 = pblk[0]; i1 = pblk[1]; i2 = pblk[2];
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if (nerrs == 2) {
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/* 2 errs */
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z01 = alpha_power[255 - i0];
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z02 = alpha_power[255 - i1];
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inv->log_denom = (z01 ^ z02);
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if (!inv->log_denom) return(0);
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inv->log_denom = 255 - alpha_log[inv->log_denom];
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inv->zs[0][0] = multiply_out( 1, inv->log_denom);
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inv->zs[0][1] = multiply_out(z02, inv->log_denom);
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inv->zs[1][0] = multiply_out( 1, inv->log_denom);
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inv->zs[1][1] = multiply_out(z01, inv->log_denom);
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} else {
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/* 3 errs */
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z20 = z_of_ab (i2, i0);
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z10 = z_of_ab (i1, i0);
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z21 = z_of_ab (i2, i1);
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z12 = z_of_ab (i1, i2);
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z01 = z_of_ab (i0, i1);
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z02 = z_of_ab (i0, i2);
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inv->log_denom = (z20 ^ z10 ^ z21 ^ z12 ^ z01 ^ z02);
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if (!inv->log_denom) return(0);
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inv->log_denom = 255 - alpha_log[inv->log_denom];
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iv0 = alpha_power[255 - i0];
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iv1 = alpha_power[255 - i1];
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iv2 = alpha_power[255 - i2];
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i0 = alpha_power[i0];
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i1 = alpha_power[i1];
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i2 = alpha_power[i2];
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inv->zs[0][0] = multiply_out(i1 ^ i2, inv->log_denom);
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inv->zs[0][1] = multiply_out(z21 ^ z12, inv->log_denom);
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inv->zs[0][2] = multiply_out(iv1 ^ iv2, inv->log_denom);
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inv->zs[1][0] = multiply_out(i0 ^ i2, inv->log_denom);
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inv->zs[1][1] = multiply_out(z20 ^ z02, inv->log_denom);
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inv->zs[1][2] = multiply_out(iv0 ^ iv2, inv->log_denom);
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inv->zs[2][0] = multiply_out(i0 ^ i1, inv->log_denom);
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inv->zs[2][1] = multiply_out(z10 ^ z01, inv->log_denom);
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inv->zs[2][2] = multiply_out(iv0 ^ iv1, inv->log_denom);
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}
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return(1);
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}
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/*
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* Determine the error magnitudes for a given matrix and syndromes.
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*/
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static inline void
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determine(int nerrs, struct inv_mat *inv, UCHAR *ss, UCHAR *es)
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{
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UCHAR tmp;
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int i, j;
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for (i = 0; i < nerrs; i++) {
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es[i] = 0;
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for (j = 0; j < nerrs; j++)
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es[i] ^= multiply(ss[j], inv->zs[i][j]);
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}
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}
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/*
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* Compute the 3 syndrome values.
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*/
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static inline int
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compute_syndromes(UCHAR *data, int nblks, int col, UCHAR *ss)
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{
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UCHAR r0, r1, r2, t1, t2;
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UCHAR *rptr;
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rptr = data + col;
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data += nblks << 10;
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r0 = r1 = r2 = 0;
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while (rptr < data) {
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t1 = *rptr ^ r0;
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t2 = mult_c0[t1];
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r0 = t2 ^ r1;
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r1 = t2 ^ r2;
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r2 = t1;
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rptr += QCV_BLKSIZE;
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}
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if (r0 || r1 || r2) {
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ss[0] = divide_out(r0 ^ divide_out(r1 ^ divide_out(r2, 1), 1), nblks);
|
|
ss[1] = r0 ^ r1 ^ r2;
|
|
ss[2] = multiply_out(r0 ^ multiply_out(r1 ^ multiply_out(r2, 1), 1), nblks);
|
|
return(0);
|
|
}
|
|
return(1);
|
|
}
|
|
|
|
|
|
/*
|
|
* Calculate the parity bytes for a segment, returns 0 on success (always).
|
|
*/
|
|
int
|
|
set_parity (UCHAR *data, ULONG badmap)
|
|
{
|
|
UCHAR r0, r1, r2, t1, t2;
|
|
UCHAR *rptr;
|
|
int max, row, col;
|
|
|
|
max = sect_count(badmap) - 3;
|
|
col = QCV_BLKSIZE;
|
|
while (col--) {
|
|
rptr = data;
|
|
r0 = r1 = r2 = 0;
|
|
row = max;
|
|
while (row--) {
|
|
t1 = *rptr ^ r0;
|
|
t2 = mult_c0[t1];
|
|
r0 = t2 ^ r1;
|
|
r1 = t2 ^ r2;
|
|
r2 = t1;
|
|
rptr += QCV_BLKSIZE;
|
|
}
|
|
*rptr = r0; rptr += QCV_BLKSIZE;
|
|
*rptr = r1; rptr += QCV_BLKSIZE;
|
|
*rptr = r2;
|
|
data++;
|
|
}
|
|
return(0);
|
|
}
|
|
|
|
|
|
/*
|
|
* Check and correct errors in a block. Returns 0 on success,
|
|
* 1 if failed.
|
|
*/
|
|
int
|
|
check_parity(UCHAR *data, ULONG badmap, ULONG crcmap)
|
|
{
|
|
int crcerrs, eblk[3];
|
|
int col, row;
|
|
int i, j, nblks;
|
|
UCHAR ss[3], es[3];
|
|
int i1, i2, saverrs;
|
|
struct inv_mat inv;
|
|
|
|
nblks = sect_count(badmap);
|
|
|
|
/* Count the number of CRC errors and note their locations. */
|
|
crcerrs = 0;
|
|
if (crcmap) {
|
|
for (i = 0; i < nblks; i++) {
|
|
if (crcmap & (1 << i)) {
|
|
if (crcerrs == 3) return(1);
|
|
eblk[crcerrs++] = i;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Calculate the inverse matrix */
|
|
if (!calculate_inverse(crcerrs, eblk, &inv)) return(1);
|
|
|
|
/* Scan each column for problems and attempt to correct. */
|
|
for (col = 0; col < QCV_BLKSIZE; col++) {
|
|
if (compute_syndromes(data, nblks, col, ss)) continue;
|
|
es[0] = es[1] = es[2] = 0;
|
|
|
|
/* Analyze the error situation. */
|
|
switch (crcerrs) {
|
|
case 0: /* 0 errors >0 failures */
|
|
if (!ss[0]) return(1);
|
|
eblk[crcerrs] = alpha_log[divide(ss[1], ss[0])];
|
|
if (eblk[crcerrs] >= nblks) return(1);
|
|
es[0] = ss[1];
|
|
if (++crcerrs > 3) return(1);
|
|
break;
|
|
|
|
case 1: /* 1 error (+ possible failures) */
|
|
i1 = ss[2] ^ multiply_out(ss[1], eblk[0]);
|
|
i2 = ss[1] ^ multiply_out(ss[0], eblk[0]);
|
|
if (!i1 && !i2) { /* only 1 error */
|
|
inv.zs[0][0] = alpha_power[eblk[0]];
|
|
inv.log_denom = 0;
|
|
} else if (!i1 || !i2) { /* too many errors */
|
|
return(1);
|
|
} else { /* add failure */
|
|
eblk[crcerrs] = alpha_log[divide(i1, i2)];
|
|
if (eblk[crcerrs] >= nblks) return(1);
|
|
if (++crcerrs > 3) return(1);
|
|
if (!calculate_inverse(crcerrs, eblk, &inv)) return(1);
|
|
}
|
|
determine(crcerrs, &inv, ss, es);
|
|
break;
|
|
|
|
case 2: /* 2 errors */
|
|
case 3: /* 3 errors */
|
|
determine(crcerrs, &inv, ss, es);
|
|
break;
|
|
|
|
default:
|
|
return(1);
|
|
}
|
|
|
|
/* Make corrections. */
|
|
for (i = 0; i < crcerrs; i++) {
|
|
data[(eblk[i] << 10) | col] ^= es[i];
|
|
ss[0] ^= divide_out(es[i], eblk[i]);
|
|
ss[1] ^= es[i];
|
|
ss[2] ^= multiply_out(es[i], eblk[i]);
|
|
}
|
|
if (ss[0] || ss[1] || ss[2]) return(1);
|
|
}
|
|
return(0);
|
|
}
|