diff options
Diffstat (limited to 'lib/reed_solomon')
| -rw-r--r-- | lib/reed_solomon/Makefile | 6 | ||||
| -rw-r--r-- | lib/reed_solomon/decode_rs.c | 271 | ||||
| -rw-r--r-- | lib/reed_solomon/encode_rs.c | 54 | ||||
| -rw-r--r-- | lib/reed_solomon/reed_solomon.c | 384 |
4 files changed, 715 insertions, 0 deletions
diff --git a/lib/reed_solomon/Makefile b/lib/reed_solomon/Makefile new file mode 100644 index 000000000..c3d713682 --- /dev/null +++ b/lib/reed_solomon/Makefile @@ -0,0 +1,6 @@ +# +# This is a modified version of reed solomon lib, +# + +obj-$(CONFIG_REED_SOLOMON) += reed_solomon.o + diff --git a/lib/reed_solomon/decode_rs.c b/lib/reed_solomon/decode_rs.c new file mode 100644 index 000000000..0ec3f257f --- /dev/null +++ b/lib/reed_solomon/decode_rs.c @@ -0,0 +1,271 @@ +/* + * lib/reed_solomon/decode_rs.c + * + * Overview: + * Generic Reed Solomon encoder / decoder library + * + * Copyright 2002, Phil Karn, KA9Q + * May be used under the terms of the GNU General Public License (GPL) + * + * Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de) + * + * $Id: decode_rs.c,v 1.7 2005/11/07 11:14:59 gleixner Exp $ + * + */ + +/* Generic data width independent code which is included by the + * wrappers. + */ +{ + int deg_lambda, el, deg_omega; + int i, j, r, k, pad; + int nn = rs->nn; + int nroots = rs->nroots; + int fcr = rs->fcr; + int prim = rs->prim; + int iprim = rs->iprim; + uint16_t *alpha_to = rs->alpha_to; + uint16_t *index_of = rs->index_of; + uint16_t u, q, tmp, num1, num2, den, discr_r, syn_error; + /* Err+Eras Locator poly and syndrome poly The maximum value + * of nroots is 8. So the necessary stack size will be about + * 220 bytes max. + */ + uint16_t lambda[nroots + 1], syn[nroots]; + uint16_t b[nroots + 1], t[nroots + 1], omega[nroots + 1]; + uint16_t root[nroots], reg[nroots + 1], loc[nroots]; + int count = 0; + uint16_t msk = (uint16_t) rs->nn; + + /* Check length parameter for validity */ + pad = nn - nroots - len; + BUG_ON(pad < 0 || pad >= nn); + + /* Does the caller provide the syndrome ? */ + if (s != NULL) + goto decode; + + /* form the syndromes; i.e., evaluate data(x) at roots of + * g(x) */ + for (i = 0; i < nroots; i++) + syn[i] = (((uint16_t) data[0]) ^ invmsk) & msk; + + for (j = 1; j < len; j++) { + for (i = 0; i < nroots; i++) { + if (syn[i] == 0) { + syn[i] = (((uint16_t) data[j]) ^ + invmsk) & msk; + } else { + syn[i] = ((((uint16_t) data[j]) ^ + invmsk) & msk) ^ + alpha_to[rs_modnn(rs, index_of[syn[i]] + + (fcr + i) * prim)]; + } + } + } + + for (j = 0; j < nroots; j++) { + for (i = 0; i < nroots; i++) { + if (syn[i] == 0) { + syn[i] = ((uint16_t) par[j]) & msk; + } else { + syn[i] = (((uint16_t) par[j]) & msk) ^ + alpha_to[rs_modnn(rs, index_of[syn[i]] + + (fcr+i)*prim)]; + } + } + } + s = syn; + + /* Convert syndromes to index form, checking for nonzero condition */ + syn_error = 0; + for (i = 0; i < nroots; i++) { + syn_error |= s[i]; + s[i] = index_of[s[i]]; + } + + if (!syn_error) { + /* if syndrome is zero, data[] is a codeword and there are no + * errors to correct. So return data[] unmodified + */ + count = 0; + goto finish; + } + + decode: + memset(&lambda[1], 0, nroots * sizeof(lambda[0])); + lambda[0] = 1; + + if (no_eras > 0) { + /* Init lambda to be the erasure locator polynomial */ + lambda[1] = alpha_to[rs_modnn(rs, + prim * (nn - 1 - eras_pos[0]))]; + for (i = 1; i < no_eras; i++) { + u = rs_modnn(rs, prim * (nn - 1 - eras_pos[i])); + for (j = i + 1; j > 0; j--) { + tmp = index_of[lambda[j - 1]]; + if (tmp != nn) { + lambda[j] ^= + alpha_to[rs_modnn(rs, u + tmp)]; + } + } + } + } + + for (i = 0; i < nroots + 1; i++) + b[i] = index_of[lambda[i]]; + + /* + * Begin Berlekamp-Massey algorithm to determine error+erasure + * locator polynomial + */ + r = no_eras; + el = no_eras; + while (++r <= nroots) { /* r is the step number */ + /* Compute discrepancy at the r-th step in poly-form */ + discr_r = 0; + for (i = 0; i < r; i++) { + if ((lambda[i] != 0) && (s[r - i - 1] != nn)) { + discr_r ^= + alpha_to[rs_modnn(rs, + index_of[lambda[i]] + + s[r - i - 1])]; + } + } + discr_r = index_of[discr_r]; /* Index form */ + if (discr_r == nn) { + /* 2 lines below: B(x) <-- x*B(x) */ + memmove (&b[1], b, nroots * sizeof (b[0])); + b[0] = nn; + } else { + /* 7 lines below: T(x) <-- lambda(x)-discr_r*x*b(x) */ + t[0] = lambda[0]; + for (i = 0; i < nroots; i++) { + if (b[i] != nn) { + t[i + 1] = lambda[i + 1] ^ + alpha_to[rs_modnn(rs, discr_r + + b[i])]; + } else + t[i + 1] = lambda[i + 1]; + } + if (2 * el <= r + no_eras - 1) { + el = r + no_eras - el; + /* + * 2 lines below: B(x) <-- inv(discr_r) * + * lambda(x) + */ + for (i = 0; i <= nroots; i++) { + b[i] = (lambda[i] == 0) ? nn : + rs_modnn(rs, index_of[lambda[i]] + - discr_r + nn); + } + } else { + /* 2 lines below: B(x) <-- x*B(x) */ + memmove(&b[1], b, nroots * sizeof(b[0])); + b[0] = nn; + } + memcpy(lambda, t, (nroots + 1) * sizeof(t[0])); + } + } + + /* Convert lambda to index form and compute deg(lambda(x)) */ + deg_lambda = 0; + for (i = 0; i < nroots + 1; i++) { + lambda[i] = index_of[lambda[i]]; + if (lambda[i] != nn) + deg_lambda = i; + } + /* Find roots of error+erasure locator polynomial by Chien search */ + memcpy(®[1], &lambda[1], nroots * sizeof(reg[0])); + count = 0; /* Number of roots of lambda(x) */ + for (i = 1, k = iprim - 1; i <= nn; i++, k = rs_modnn(rs, k + iprim)) { + q = 1; /* lambda[0] is always 0 */ + for (j = deg_lambda; j > 0; j--) { + if (reg[j] != nn) { + reg[j] = rs_modnn(rs, reg[j] + j); + q ^= alpha_to[reg[j]]; + } + } + if (q != 0) + continue; /* Not a root */ + /* store root (index-form) and error location number */ + root[count] = i; + loc[count] = k; + /* If we've already found max possible roots, + * abort the search to save time + */ + if (++count == deg_lambda) + break; + } + if (deg_lambda != count) { + /* + * deg(lambda) unequal to number of roots => uncorrectable + * error detected + */ + count = -EBADMSG; + goto finish; + } + /* + * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo + * x**nroots). in index form. Also find deg(omega). + */ + deg_omega = deg_lambda - 1; + for (i = 0; i <= deg_omega; i++) { + tmp = 0; + for (j = i; j >= 0; j--) { + if ((s[i - j] != nn) && (lambda[j] != nn)) + tmp ^= + alpha_to[rs_modnn(rs, s[i - j] + lambda[j])]; + } + omega[i] = index_of[tmp]; + } + + /* + * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 = + * inv(X(l))**(fcr-1) and den = lambda_pr(inv(X(l))) all in poly-form + */ + for (j = count - 1; j >= 0; j--) { + num1 = 0; + for (i = deg_omega; i >= 0; i--) { + if (omega[i] != nn) + num1 ^= alpha_to[rs_modnn(rs, omega[i] + + i * root[j])]; + } + num2 = alpha_to[rs_modnn(rs, root[j] * (fcr - 1) + nn)]; + den = 0; + + /* lambda[i+1] for i even is the formal derivative + * lambda_pr of lambda[i] */ + for (i = min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) { + if (lambda[i + 1] != nn) { + den ^= alpha_to[rs_modnn(rs, lambda[i + 1] + + i * root[j])]; + } + } + /* Apply error to data */ + if (num1 != 0 && loc[j] >= pad) { + uint16_t cor = alpha_to[rs_modnn(rs,index_of[num1] + + index_of[num2] + + nn - index_of[den])]; + /* Store the error correction pattern, if a + * correction buffer is available */ + if (corr) { + corr[j] = cor; + } else { + /* If a data buffer is given and the + * error is inside the message, + * correct it */ + if (data && (loc[j] < (nn - nroots))) + data[loc[j] - pad] ^= cor; + } + } + } + +finish: + if (eras_pos != NULL) { + for (i = 0; i < count; i++) + eras_pos[i] = loc[i] - pad; + } + return count; + +} diff --git a/lib/reed_solomon/encode_rs.c b/lib/reed_solomon/encode_rs.c new file mode 100644 index 000000000..0b5b1a672 --- /dev/null +++ b/lib/reed_solomon/encode_rs.c @@ -0,0 +1,54 @@ +/* + * lib/reed_solomon/encode_rs.c + * + * Overview: + * Generic Reed Solomon encoder / decoder library + * + * Copyright 2002, Phil Karn, KA9Q + * May be used under the terms of the GNU General Public License (GPL) + * + * Adaption to the kernel by Thomas Gleixner (tglx@linutronix.de) + * + * $Id: encode_rs.c,v 1.5 2005/11/07 11:14:59 gleixner Exp $ + * + */ + +/* Generic data width independent code which is included by the + * wrappers. + * int encode_rsX (struct rs_control *rs, uintX_t *data, int len, uintY_t *par) + */ +{ + int i, j, pad; + int nn = rs->nn; + int nroots = rs->nroots; + uint16_t *alpha_to = rs->alpha_to; + uint16_t *index_of = rs->index_of; + uint16_t *genpoly = rs->genpoly; + uint16_t fb; + uint16_t msk = (uint16_t) rs->nn; + + /* Check length parameter for validity */ + pad = nn - nroots - len; + if (pad < 0 || pad >= nn) + return -ERANGE; + + for (i = 0; i < len; i++) { + fb = index_of[((((uint16_t) data[i])^invmsk) & msk) ^ par[0]]; + /* feedback term is non-zero */ + if (fb != nn) { + for (j = 1; j < nroots; j++) { + par[j] ^= alpha_to[rs_modnn(rs, fb + + genpoly[nroots - j])]; + } + } + /* Shift */ + memmove(&par[0], &par[1], sizeof(uint16_t) * (nroots - 1)); + if (fb != nn) { + par[nroots - 1] = alpha_to[rs_modnn(rs, + fb + genpoly[0])]; + } else { + par[nroots - 1] = 0; + } + } + return 0; +} diff --git a/lib/reed_solomon/reed_solomon.c b/lib/reed_solomon/reed_solomon.c new file mode 100644 index 000000000..06d04cfa9 --- /dev/null +++ b/lib/reed_solomon/reed_solomon.c @@ -0,0 +1,384 @@ +/* + * lib/reed_solomon/reed_solomon.c + * + * Overview: + * Generic Reed Solomon encoder / decoder library + * + * Copyright (C) 2004 Thomas Gleixner (tglx@linutronix.de) + * + * Reed Solomon code lifted from reed solomon library written by Phil Karn + * Copyright 2002 Phil Karn, KA9Q + * + * $Id: rslib.c,v 1.7 2005/11/07 11:14:59 gleixner Exp $ + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU General Public License version 2 as + * published by the Free Software Foundation. + * + * Description: + * + * The generic Reed Solomon library provides runtime configurable + * encoding / decoding of RS codes. + * Each user must call init_rs to get a pointer to a rs_control + * structure for the given rs parameters. This structure is either + * generated or a already available matching control structure is used. + * If a structure is generated then the polynomial arrays for + * fast encoding / decoding are built. This can take some time so + * make sure not to call this function from a time critical path. + * Usually a module / driver should initialize the necessary + * rs_control structure on module / driver init and release it + * on exit. + * The encoding puts the calculated syndrome into a given syndrome + * buffer. + * The decoding is a two step process. The first step calculates + * the syndrome over the received (data + syndrome) and calls the + * second stage, which does the decoding / error correction itself. + * Many hw encoders provide a syndrome calculation over the received + * data + syndrome and can call the second stage directly. + * + */ + +#include <linux/errno.h> +#include <linux/kernel.h> +#include <linux/init.h> +#include <linux/module.h> +#include <linux/rslib.h> +#include <linux/slab.h> +#include <linux/mutex.h> + +/* This list holds all currently allocated rs control structures */ +static LIST_HEAD (rslist); +/* Protection for the list */ +static DEFINE_MUTEX(rslistlock); + +/** + * rs_init - Initialize a Reed-Solomon codec + * @symsize: symbol size, bits (1-8) + * @gfpoly: Field generator polynomial coefficients + * @gffunc: Field generator function + * @fcr: first root of RS code generator polynomial, index form + * @prim: primitive element to generate polynomial roots + * @nroots: RS code generator polynomial degree (number of roots) + * + * Allocate a control structure and the polynom arrays for faster + * en/decoding. Fill the arrays according to the given parameters. + */ +static struct rs_control *rs_init(int symsize, int gfpoly, int (*gffunc)(int), + int fcr, int prim, int nroots) +{ + struct rs_control *rs; + int i, j, sr, root, iprim; + + /* Allocate the control structure */ + rs = kmalloc(sizeof (struct rs_control), GFP_KERNEL); + if (rs == NULL) + return NULL; + + INIT_LIST_HEAD(&rs->list); + + rs->mm = symsize; + rs->nn = (1 << symsize) - 1; + rs->fcr = fcr; + rs->prim = prim; + rs->nroots = nroots; + rs->gfpoly = gfpoly; + rs->gffunc = gffunc; + + /* Allocate the arrays */ + rs->alpha_to = kmalloc(sizeof(uint16_t) * (rs->nn + 1), GFP_KERNEL); + if (rs->alpha_to == NULL) + goto errrs; + + rs->index_of = kmalloc(sizeof(uint16_t) * (rs->nn + 1), GFP_KERNEL); + if (rs->index_of == NULL) + goto erralp; + + rs->genpoly = kmalloc(sizeof(uint16_t) * (rs->nroots + 1), GFP_KERNEL); + if(rs->genpoly == NULL) + goto erridx; + + /* Generate Galois field lookup tables */ + rs->index_of[0] = rs->nn; /* log(zero) = -inf */ + rs->alpha_to[rs->nn] = 0; /* alpha**-inf = 0 */ + if (gfpoly) { + sr = 1; + for (i = 0; i < rs->nn; i++) { + rs->index_of[sr] = i; + rs->alpha_to[i] = sr; + sr <<= 1; + if (sr & (1 << symsize)) + sr ^= gfpoly; + sr &= rs->nn; + } + } else { + sr = gffunc(0); + for (i = 0; i < rs->nn; i++) { + rs->index_of[sr] = i; + rs->alpha_to[i] = sr; + sr = gffunc(sr); + } + } + /* If it's not primitive, exit */ + if(sr != rs->alpha_to[0]) + goto errpol; + + /* Find prim-th root of 1, used in decoding */ + for(iprim = 1; (iprim % prim) != 0; iprim += rs->nn); + /* prim-th root of 1, index form */ + rs->iprim = iprim / prim; + + /* Form RS code generator polynomial from its roots */ + rs->genpoly[0] = 1; + for (i = 0, root = fcr * prim; i < nroots; i++, root += prim) { + rs->genpoly[i + 1] = 1; + /* Multiply rs->genpoly[] by @**(root + x) */ + for (j = i; j > 0; j--) { + if (rs->genpoly[j] != 0) { + rs->genpoly[j] = rs->genpoly[j -1] ^ + rs->alpha_to[rs_modnn(rs, + rs->index_of[rs->genpoly[j]] + root)]; + } else + rs->genpoly[j] = rs->genpoly[j - 1]; + } + /* rs->genpoly[0] can never be zero */ + rs->genpoly[0] = + rs->alpha_to[rs_modnn(rs, + rs->index_of[rs->genpoly[0]] + root)]; + } + /* convert rs->genpoly[] to index form for quicker encoding */ + for (i = 0; i <= nroots; i++) + rs->genpoly[i] = rs->index_of[rs->genpoly[i]]; + return rs; + + /* Error exit */ +errpol: + kfree(rs->genpoly); +erridx: + kfree(rs->index_of); +erralp: + kfree(rs->alpha_to); +errrs: + kfree(rs); + return NULL; +} + + +/** + * free_rs - Free the rs control structure, if it is no longer used + * @rs: the control structure which is not longer used by the + * caller + */ +void free_rs(struct rs_control *rs) +{ + mutex_lock(&rslistlock); + rs->users--; + if(!rs->users) { + list_del(&rs->list); + kfree(rs->alpha_to); + kfree(rs->index_of); + kfree(rs->genpoly); + kfree(rs); + } + mutex_unlock(&rslistlock); +} + +/** + * init_rs_internal - Find a matching or allocate a new rs control structure + * @symsize: the symbol size (number of bits) + * @gfpoly: the extended Galois field generator polynomial coefficients, + * with the 0th coefficient in the low order bit. The polynomial + * must be primitive; + * @gffunc: pointer to function to generate the next field element, + * or the multiplicative identity element if given 0. Used + * instead of gfpoly if gfpoly is 0 + * @fcr: the first consecutive root of the rs code generator polynomial + * in index form + * @prim: primitive element to generate polynomial roots + * @nroots: RS code generator polynomial degree (number of roots) + */ +static struct rs_control *init_rs_internal(int symsize, int gfpoly, + int (*gffunc)(int), int fcr, + int prim, int nroots) +{ + struct list_head *tmp; + struct rs_control *rs; + + /* Sanity checks */ + if (symsize < 1) + return NULL; + if (fcr < 0 || fcr >= (1<<symsize)) + return NULL; + if (prim <= 0 || prim >= (1<<symsize)) + return NULL; + if (nroots < 0 || nroots >= (1<<symsize)) + return NULL; + + mutex_lock(&rslistlock); + + /* Walk through the list and look for a matching entry */ + list_for_each(tmp, &rslist) { + rs = list_entry(tmp, struct rs_control, list); + if (symsize != rs->mm) + continue; + if (gfpoly != rs->gfpoly) + continue; + if (gffunc != rs->gffunc) + continue; + if (fcr != rs->fcr) + continue; + if (prim != rs->prim) + continue; + if (nroots != rs->nroots) + continue; + /* We have a matching one already */ + rs->users++; + goto out; + } + + /* Create a new one */ + rs = rs_init(symsize, gfpoly, gffunc, fcr, prim, nroots); + if (rs) { + rs->users = 1; + list_add(&rs->list, &rslist); + } +out: + mutex_unlock(&rslistlock); + return rs; +} + +/** + * init_rs - Find a matching or allocate a new rs control structure + * @symsize: the symbol size (number of bits) + * @gfpoly: the extended Galois field generator polynomial coefficients, + * with the 0th coefficient in the low order bit. The polynomial + * must be primitive; + * @fcr: the first consecutive root of the rs code generator polynomial + * in index form + * @prim: primitive element to generate polynomial roots + * @nroots: RS code generator polynomial degree (number of roots) + */ +struct rs_control *init_rs(int symsize, int gfpoly, int fcr, int prim, + int nroots) +{ + return init_rs_internal(symsize, gfpoly, NULL, fcr, prim, nroots); +} + +/** + * init_rs_non_canonical - Find a matching or allocate a new rs control + * structure, for fields with non-canonical + * representation + * @symsize: the symbol size (number of bits) + * @gffunc: pointer to function to generate the next field element, + * or the multiplicative identity element if given 0. Used + * instead of gfpoly if gfpoly is 0 + * @fcr: the first consecutive root of the rs code generator polynomial + * in index form + * @prim: primitive element to generate polynomial roots + * @nroots: RS code generator polynomial degree (number of roots) + */ +struct rs_control *init_rs_non_canonical(int symsize, int (*gffunc)(int), + int fcr, int prim, int nroots) +{ + return init_rs_internal(symsize, 0, gffunc, fcr, prim, nroots); +} + +#ifdef CONFIG_REED_SOLOMON_ENC8 +/** + * encode_rs8 - Calculate the parity for data values (8bit data width) + * @rs: the rs control structure + * @data: data field of a given type + * @len: data length + * @par: parity data, must be initialized by caller (usually all 0) + * @invmsk: invert data mask (will be xored on data) + * + * The parity uses a uint16_t data type to enable + * symbol size > 8. The calling code must take care of encoding of the + * syndrome result for storage itself. + */ +int encode_rs8(struct rs_control *rs, uint8_t *data, int len, uint16_t *par, + uint16_t invmsk) +{ +#include "encode_rs.c" +} +EXPORT_SYMBOL_GPL(encode_rs8); +#endif + +#ifdef CONFIG_REED_SOLOMON_DEC8 +/** + * decode_rs8 - Decode codeword (8bit data width) + * @rs: the rs control structure + * @data: data field of a given type + * @par: received parity data field + * @len: data length + * @s: syndrome data field (if NULL, syndrome is calculated) + * @no_eras: number of erasures + * @eras_pos: position of erasures, can be NULL + * @invmsk: invert data mask (will be xored on data, not on parity!) + * @corr: buffer to store correction bitmask on eras_pos + * + * The syndrome and parity uses a uint16_t data type to enable + * symbol size > 8. The calling code must take care of decoding of the + * syndrome result and the received parity before calling this code. + * Returns the number of corrected bits or -EBADMSG for uncorrectable errors. + */ +int decode_rs8(struct rs_control *rs, uint8_t *data, uint16_t *par, int len, + uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk, + uint16_t *corr) +{ +#include "decode_rs.c" +} +EXPORT_SYMBOL_GPL(decode_rs8); +#endif + +#ifdef CONFIG_REED_SOLOMON_ENC16 +/** + * encode_rs16 - Calculate the parity for data values (16bit data width) + * @rs: the rs control structure + * @data: data field of a given type + * @len: data length + * @par: parity data, must be initialized by caller (usually all 0) + * @invmsk: invert data mask (will be xored on data, not on parity!) + * + * Each field in the data array contains up to symbol size bits of valid data. + */ +int encode_rs16(struct rs_control *rs, uint16_t *data, int len, uint16_t *par, + uint16_t invmsk) +{ +#include "encode_rs.c" +} +EXPORT_SYMBOL_GPL(encode_rs16); +#endif + +#ifdef CONFIG_REED_SOLOMON_DEC16 +/** + * decode_rs16 - Decode codeword (16bit data width) + * @rs: the rs control structure + * @data: data field of a given type + * @par: received parity data field + * @len: data length + * @s: syndrome data field (if NULL, syndrome is calculated) + * @no_eras: number of erasures + * @eras_pos: position of erasures, can be NULL + * @invmsk: invert data mask (will be xored on data, not on parity!) + * @corr: buffer to store correction bitmask on eras_pos + * + * Each field in the data array contains up to symbol size bits of valid data. + * Returns the number of corrected bits or -EBADMSG for uncorrectable errors. + */ +int decode_rs16(struct rs_control *rs, uint16_t *data, uint16_t *par, int len, + uint16_t *s, int no_eras, int *eras_pos, uint16_t invmsk, + uint16_t *corr) +{ +#include "decode_rs.c" +} +EXPORT_SYMBOL_GPL(decode_rs16); +#endif + +EXPORT_SYMBOL_GPL(init_rs); +EXPORT_SYMBOL_GPL(init_rs_non_canonical); +EXPORT_SYMBOL_GPL(free_rs); + +MODULE_LICENSE("GPL"); +MODULE_DESCRIPTION("Reed Solomon encoder/decoder"); +MODULE_AUTHOR("Phil Karn, Thomas Gleixner"); + |