diff --git a/lib/des/imath/imrat.c b/lib/des/imath/imrat.c deleted file mode 100755 index fb63f6279..000000000 --- a/lib/des/imath/imrat.c +++ /dev/null @@ -1,1092 +0,0 @@ -/* - Name: imrat.c - Purpose: Arbitrary precision rational arithmetic routines. - Author: M. J. Fromberger - Info: $Id$ - - Copyright (C) 2002 Michael J. Fromberger, All Rights Reserved. - - Permission is hereby granted, free of charge, to any person - obtaining a copy of this software and associated documentation files - (the "Software"), to deal in the Software without restriction, - including without limitation the rights to use, copy, modify, merge, - publish, distribute, sublicense, and/or sell copies of the Software, - and to permit persons to whom the Software is furnished to do so, - subject to the following conditions: - - The above copyright notice and this permission notice shall be - included in all copies or substantial portions of the Software. - - THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, - EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF - MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND - NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS - BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN - ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN - CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE - SOFTWARE. - */ - -#include "imrat.h" -#include -#include -#include -#include - -/* {{{ Useful macros */ - -#define TEMP(K) (temp + (K)) -#define SETUP(E, C) \ -do{if((res = (E)) != MP_OK) goto CLEANUP; ++(C);}while(0) - -/* Argument checking: - Use CHECK() where a return value is required; NRCHECK() elsewhere */ -#define CHECK(TEST) assert(TEST) -#define NRCHECK(TEST) assert(TEST) - -/* }}} */ - -/* Reduce the given rational, in place, to lowest terms and canonical - form. Zero is represented as 0/1, one as 1/1. Signs are adjusted - so that the sign of the numerator is definitive. */ -static mp_result s_rat_reduce(mp_rat r); - -/* Common code for addition and subtraction operations on rationals. */ -static mp_result s_rat_combine(mp_rat a, mp_rat b, mp_rat c, - mp_result (*comb_f)(mp_int, mp_int, mp_int)); - -/* {{{ mp_rat_init(r) */ - -mp_result mp_rat_init(mp_rat r) -{ - return mp_rat_init_size(r, 0, 0); -} - -/* }}} */ - -/* {{{ mp_rat_alloc() */ - -mp_rat mp_rat_alloc(void) -{ - mp_rat out = malloc(sizeof(*out)); - - if(out != NULL) { - if(mp_rat_init(out) != MP_OK) { - free(out); - return NULL; - } - } - - return out; -} - -/* }}} */ - -/* {{{ mp_rat_init_size(r, n_prec, d_prec) */ - -mp_result mp_rat_init_size(mp_rat r, mp_size n_prec, mp_size d_prec) -{ - mp_result res; - - if((res = mp_int_init_size(MP_NUMER_P(r), n_prec)) != MP_OK) - return res; - if((res = mp_int_init_size(MP_DENOM_P(r), d_prec)) != MP_OK) { - mp_int_clear(MP_NUMER_P(r)); - return res; - } - - return mp_int_set_value(MP_DENOM_P(r), 1); -} - -/* }}} */ - -/* {{{ mp_rat_init_copy(r, old) */ - -mp_result mp_rat_init_copy(mp_rat r, mp_rat old) -{ - mp_result res; - - if((res = mp_int_init_copy(MP_NUMER_P(r), MP_NUMER_P(old))) != MP_OK) - return res; - if((res = mp_int_init_copy(MP_DENOM_P(r), MP_DENOM_P(old))) != MP_OK) - mp_int_clear(MP_NUMER_P(r)); - - return res; -} - -/* }}} */ - -/* {{{ mp_rat_set_value(r, numer, denom) */ - -mp_result mp_rat_set_value(mp_rat r, int numer, int denom) -{ - mp_result res; - - if(denom == 0) - return MP_UNDEF; - - if((res = mp_int_set_value(MP_NUMER_P(r), numer)) != MP_OK) - return res; - if((res = mp_int_set_value(MP_DENOM_P(r), denom)) != MP_OK) - return res; - - return s_rat_reduce(r); -} - -/* }}} */ - -/* {{{ mp_rat_clear(r) */ - -void mp_rat_clear(mp_rat r) -{ - mp_int_clear(MP_NUMER_P(r)); - mp_int_clear(MP_DENOM_P(r)); - -} - -/* }}} */ - -/* {{{ mp_rat_free(r) */ - -void mp_rat_free(mp_rat r) -{ - NRCHECK(r != NULL); - - if(r->num.digits != NULL) - mp_rat_clear(r); - - free(r); -} - -/* }}} */ - -/* {{{ mp_rat_numer(r, z) */ - -mp_result mp_rat_numer(mp_rat r, mp_int z) -{ - return mp_int_copy(MP_NUMER_P(r), z); -} - -/* }}} */ - -/* {{{ mp_rat_denom(r, z) */ - -mp_result mp_rat_denom(mp_rat r, mp_int z) -{ - return mp_int_copy(MP_DENOM_P(r), z); -} - -/* }}} */ - -/* {{{ mp_rat_sign(r) */ - -mp_sign mp_rat_sign(mp_rat r) -{ - return MP_SIGN(MP_NUMER_P(r)); -} - -/* }}} */ - -/* {{{ mp_rat_copy(a, c) */ - -mp_result mp_rat_copy(mp_rat a, mp_rat c) -{ - mp_result res; - - if((res = mp_int_copy(MP_NUMER_P(a), MP_NUMER_P(c))) != MP_OK) - return res; - - res = mp_int_copy(MP_DENOM_P(a), MP_DENOM_P(c)); - return res; -} - -/* }}} */ - -/* {{{ mp_rat_zero(r) */ - -void mp_rat_zero(mp_rat r) -{ - mp_int_zero(MP_NUMER_P(r)); - mp_int_set_value(MP_DENOM_P(r), 1); - -} - -/* }}} */ - -/* {{{ mp_rat_abs(a, c) */ - -mp_result mp_rat_abs(mp_rat a, mp_rat c) -{ - mp_result res; - - if((res = mp_int_abs(MP_NUMER_P(a), MP_NUMER_P(c))) != MP_OK) - return res; - - res = mp_int_abs(MP_DENOM_P(a), MP_DENOM_P(c)); - return res; -} - -/* }}} */ - -/* {{{ mp_rat_neg(a, c) */ - -mp_result mp_rat_neg(mp_rat a, mp_rat c) -{ - mp_result res; - - if((res = mp_int_neg(MP_NUMER_P(a), MP_NUMER_P(c))) != MP_OK) - return res; - - res = mp_int_copy(MP_DENOM_P(a), MP_DENOM_P(c)); - return res; -} - -/* }}} */ - -/* {{{ mp_rat_recip(a, c) */ - -mp_result mp_rat_recip(mp_rat a, mp_rat c) -{ - mp_result res; - - if(mp_rat_compare_zero(a) == 0) - return MP_UNDEF; - - if((res = mp_rat_copy(a, c)) != MP_OK) - return res; - - mp_int_swap(MP_NUMER_P(c), MP_DENOM_P(c)); - - /* Restore the signs of the swapped elements */ - { - mp_sign tmp = MP_SIGN(MP_NUMER_P(c)); - - MP_SIGN(MP_NUMER_P(c)) = MP_SIGN(MP_DENOM_P(c)); - MP_SIGN(MP_DENOM_P(c)) = tmp; - } - - return MP_OK; -} - -/* }}} */ - -/* {{{ mp_rat_add(a, b, c) */ - -mp_result mp_rat_add(mp_rat a, mp_rat b, mp_rat c) -{ - return s_rat_combine(a, b, c, mp_int_add); - -} - -/* }}} */ - -/* {{{ mp_rat_sub(a, b, c) */ - -mp_result mp_rat_sub(mp_rat a, mp_rat b, mp_rat c) -{ - return s_rat_combine(a, b, c, mp_int_sub); - -} - -/* }}} */ - -/* {{{ mp_rat_mul(a, b, c) */ - -mp_result mp_rat_mul(mp_rat a, mp_rat b, mp_rat c) -{ - mp_result res; - - if((res = mp_int_mul(MP_NUMER_P(a), MP_NUMER_P(b), MP_NUMER_P(c))) != MP_OK) - return res; - - if(mp_int_compare_zero(MP_NUMER_P(c)) != 0) { - if((res = mp_int_mul(MP_DENOM_P(a), MP_DENOM_P(b), MP_DENOM_P(c))) != MP_OK) - return res; - } - - return s_rat_reduce(c); -} - -/* }}} */ - -/* {{{ mp_int_div(a, b, c) */ - -mp_result mp_rat_div(mp_rat a, mp_rat b, mp_rat c) -{ - mp_result res = MP_OK; - - if(mp_rat_compare_zero(b) == 0) - return MP_UNDEF; - - if(c == a || c == b) { - mpz_t tmp; - - if((res = mp_int_init(&tmp)) != MP_OK) return res; - if((res = mp_int_mul(MP_NUMER_P(a), MP_DENOM_P(b), &tmp)) != MP_OK) - goto CLEANUP; - if((res = mp_int_mul(MP_DENOM_P(a), MP_NUMER_P(b), MP_DENOM_P(c))) != MP_OK) - goto CLEANUP; - res = mp_int_copy(&tmp, MP_NUMER_P(c)); - - CLEANUP: - mp_int_clear(&tmp); - } - else { - if((res = mp_int_mul(MP_NUMER_P(a), MP_DENOM_P(b), MP_NUMER_P(c))) != MP_OK) - return res; - if((res = mp_int_mul(MP_DENOM_P(a), MP_NUMER_P(b), MP_DENOM_P(c))) != MP_OK) - return res; - } - - if(res != MP_OK) - return res; - else - return s_rat_reduce(c); -} - -/* }}} */ - -/* {{{ mp_rat_add_int(a, b, c) */ - -mp_result mp_rat_add_int(mp_rat a, mp_int b, mp_rat c) -{ - mpz_t tmp; - mp_result res; - - if((res = mp_int_init_copy(&tmp, b)) != MP_OK) - return res; - - if((res = mp_int_mul(&tmp, MP_DENOM_P(a), &tmp)) != MP_OK) - goto CLEANUP; - - if((res = mp_rat_copy(a, c)) != MP_OK) - goto CLEANUP; - - if((res = mp_int_add(MP_NUMER_P(c), &tmp, MP_NUMER_P(c))) != MP_OK) - goto CLEANUP; - - res = s_rat_reduce(c); - - CLEANUP: - mp_int_clear(&tmp); - return res; -} - -/* }}} */ - -/* {{{ mp_rat_sub_int(a, b, c) */ - -mp_result mp_rat_sub_int(mp_rat a, mp_int b, mp_rat c) -{ - mpz_t tmp; - mp_result res; - - if((res = mp_int_init_copy(&tmp, b)) != MP_OK) - return res; - - if((res = mp_int_mul(&tmp, MP_DENOM_P(a), &tmp)) != MP_OK) - goto CLEANUP; - - if((res = mp_rat_copy(a, c)) != MP_OK) - goto CLEANUP; - - if((res = mp_int_sub(MP_NUMER_P(c), &tmp, MP_NUMER_P(c))) != MP_OK) - goto CLEANUP; - - res = s_rat_reduce(c); - - CLEANUP: - mp_int_clear(&tmp); - return res; -} - -/* }}} */ - -/* {{{ mp_rat_mul_int(a, b, c) */ - -mp_result mp_rat_mul_int(mp_rat a, mp_int b, mp_rat c) -{ - mp_result res; - - if((res = mp_rat_copy(a, c)) != MP_OK) - return res; - - if((res = mp_int_mul(MP_NUMER_P(c), b, MP_NUMER_P(c))) != MP_OK) - return res; - - return s_rat_reduce(c); -} - -/* }}} */ - -/* {{{ mp_rat_div_int(a, b, c) */ - -mp_result mp_rat_div_int(mp_rat a, mp_int b, mp_rat c) -{ - mp_result res; - - if(mp_int_compare_zero(b) == 0) - return MP_UNDEF; - - if((res = mp_rat_copy(a, c)) != MP_OK) - return res; - - if((res = mp_int_mul(MP_DENOM_P(c), b, MP_DENOM_P(c))) != MP_OK) - return res; - - return s_rat_reduce(c); -} - -/* }}} */ - -/* {{{ mp_rat_expt(a, b, c) */ - -mp_result mp_rat_expt(mp_rat a, int b, mp_rat c) -{ - mp_result res; - - /* Special cases for easy powers. */ - if(b == 0) - return mp_rat_set_value(c, 1, 1); - else if(b == 1) - return mp_rat_copy(a, c); - - /* Since rationals are always stored in lowest terms, it is not - necessary to reduce again when raising to an integer power. */ - if((res = mp_int_expt(MP_NUMER_P(a), b, MP_NUMER_P(c))) != MP_OK) - return res; - - return mp_int_expt(MP_DENOM_P(a), b, MP_DENOM_P(c)); -} - -/* }}} */ - -/* {{{ mp_rat_compare(a, b) */ - -int mp_rat_compare(mp_rat a, mp_rat b) -{ - /* Quick check for opposite signs. Works because the sign of the - numerator is always definitive. */ - if(MP_SIGN(MP_NUMER_P(a)) != MP_SIGN(MP_NUMER_P(b))) { - if(MP_SIGN(MP_NUMER_P(a)) == MP_ZPOS) - return 1; - else - return -1; - } - else { - /* Compare absolute magnitudes; if both are positive, the answer - stands, otherwise it needs to be reflected about zero. */ - int cmp = mp_rat_compare_unsigned(a, b); - - if(MP_SIGN(MP_NUMER_P(a)) == MP_ZPOS) - return cmp; - else - return -cmp; - } -} - -/* }}} */ - -/* {{{ mp_rat_compare_unsigned(a, b) */ - -int mp_rat_compare_unsigned(mp_rat a, mp_rat b) -{ - /* If the denominators are equal, we can quickly compare numerators - without multiplying. Otherwise, we actually have to do some work. */ - if(mp_int_compare_unsigned(MP_DENOM_P(a), MP_DENOM_P(b)) == 0) - return mp_int_compare_unsigned(MP_NUMER_P(a), MP_NUMER_P(b)); - - else { - mpz_t temp[2]; - mp_result res; - int cmp = INT_MAX, last = 0; - - /* t0 = num(a) * den(b), t1 = num(b) * den(a) */ - SETUP(mp_int_init_copy(TEMP(last), MP_NUMER_P(a)), last); - SETUP(mp_int_init_copy(TEMP(last), MP_NUMER_P(b)), last); - - if((res = mp_int_mul(TEMP(0), MP_DENOM_P(b), TEMP(0))) != MP_OK || - (res = mp_int_mul(TEMP(1), MP_DENOM_P(a), TEMP(1))) != MP_OK) - goto CLEANUP; - - cmp = mp_int_compare_unsigned(TEMP(0), TEMP(1)); - - CLEANUP: - while(--last >= 0) - mp_int_clear(TEMP(last)); - - return cmp; - } -} - -/* }}} */ - -/* {{{ mp_rat_compare_zero(r) */ - -int mp_rat_compare_zero(mp_rat r) -{ - return mp_int_compare_zero(MP_NUMER_P(r)); - -} - -/* }}} */ - -/* {{{ mp_rat_compare_value(r, n, d) */ - -int mp_rat_compare_value(mp_rat r, int n, int d) -{ - mpq_t tmp; - mp_result res; - int out = INT_MAX; - - if((res = mp_rat_init(&tmp)) != MP_OK) - return out; - if((res = mp_rat_set_value(&tmp, n, d)) != MP_OK) - goto CLEANUP; - - out = mp_rat_compare(r, &tmp); - - CLEANUP: - mp_rat_clear(&tmp); - return out; -} - -/* }}} */ - -/* {{{ mp_rat_is_integer(r) */ - -int mp_rat_is_integer(mp_rat r) -{ - return (mp_int_compare_value(MP_DENOM_P(r), 1) == 0); -} - -/* }}} */ - -/* {{{ mp_rat_to_ints(r, *num, *den) */ - -mp_result mp_rat_to_ints(mp_rat r, int *num, int *den) -{ - mp_result res; - - if((res = mp_int_to_int(MP_NUMER_P(r), num)) != MP_OK) - return res; - - res = mp_int_to_int(MP_DENOM_P(r), den); - return res; -} - -/* }}} */ - -/* {{{ mp_rat_to_string(r, radix, *str, limit) */ - -mp_result mp_rat_to_string(mp_rat r, mp_size radix, char *str, int limit) -{ - char *start; - int len; - mp_result res; - - /* Write the numerator. The sign of the rational number is written - by the underlying integer implementation. */ - if((res = mp_int_to_string(MP_NUMER_P(r), radix, str, limit)) != MP_OK) - return res; - - /* If the value is zero, don't bother writing any denominator */ - if(mp_int_compare_zero(MP_NUMER_P(r)) == 0) - return MP_OK; - - /* Locate the end of the numerator, and make sure we are not going to - exceed the limit by writing a slash. */ - len = strlen(str); - start = str + len; - limit -= len; - if(limit == 0) - return MP_TRUNC; - - *start++ = '/'; - limit -= 1; - - res = mp_int_to_string(MP_DENOM_P(r), radix, start, limit); - return res; -} - -/* }}} */ - -/* {{{ mp_rat_to_decimal(r, radix, prec, *str, limit) */ -mp_result mp_rat_to_decimal(mp_rat r, mp_size radix, mp_size prec, - mp_round_mode round, char *str, int limit) -{ - mpz_t temp[3]; - mp_result res; - char *start = str; - int len, lead_0, left = limit, last = 0; - - SETUP(mp_int_init_copy(TEMP(last), MP_NUMER_P(r)), last); - SETUP(mp_int_init(TEMP(last)), last); - SETUP(mp_int_init(TEMP(last)), last); - - /* Get the unsigned integer part by dividing denominator into the - absolute value of the numerator. */ - mp_int_abs(TEMP(0), TEMP(0)); - if((res = mp_int_div(TEMP(0), MP_DENOM_P(r), TEMP(0), TEMP(1))) != MP_OK) - goto CLEANUP; - - /* Now: T0 = integer portion, unsigned; - T1 = remainder, from which fractional part is computed. */ - - /* Count up leading zeroes after the radix point. */ - for(lead_0 = 0; lead_0 < prec && mp_int_compare(TEMP(1), MP_DENOM_P(r)) < 0; - ++lead_0) { - if((res = mp_int_mul_value(TEMP(1), radix, TEMP(1))) != MP_OK) - goto CLEANUP; - } - - /* Multiply remainder by a power of the radix sufficient to get the - right number of significant figures. */ - if(prec > lead_0) { - if((res = mp_int_expt_value(radix, prec - lead_0, TEMP(2))) != MP_OK) - goto CLEANUP; - if((res = mp_int_mul(TEMP(1), TEMP(2), TEMP(1))) != MP_OK) - goto CLEANUP; - } - if((res = mp_int_div(TEMP(1), MP_DENOM_P(r), TEMP(1), TEMP(2))) != MP_OK) - goto CLEANUP; - - /* Now: T1 = significant digits of fractional part; - T2 = leftovers, to use for rounding. - - At this point, what we do depends on the rounding mode. The - default is MP_ROUND_DOWN, for which everything is as it should be - already. - */ - switch(round) { - int cmp; - - case MP_ROUND_UP: - if(mp_int_compare_zero(TEMP(2)) != 0) { - if(prec == 0) - res = mp_int_add_value(TEMP(0), 1, TEMP(0)); - else - res = mp_int_add_value(TEMP(1), 1, TEMP(1)); - } - break; - - case MP_ROUND_HALF_UP: - case MP_ROUND_HALF_DOWN: - if((res = mp_int_mul_pow2(TEMP(2), 1, TEMP(2))) != MP_OK) - goto CLEANUP; - - cmp = mp_int_compare(TEMP(2), MP_DENOM_P(r)); - - if(round == MP_ROUND_HALF_UP) - cmp += 1; - - if(cmp > 0) { - if(prec == 0) - res = mp_int_add_value(TEMP(0), 1, TEMP(0)); - else - res = mp_int_add_value(TEMP(1), 1, TEMP(1)); - } - break; - - case MP_ROUND_DOWN: - break; /* No action required */ - - default: - return MP_BADARG; /* Invalid rounding specifier */ - } - - /* The sign of the output should be the sign of the numerator, but - if all the displayed digits will be zero due to the precision, a - negative shouldn't be shown. */ - if(MP_SIGN(MP_NUMER_P(r)) == MP_NEG && - (mp_int_compare_zero(TEMP(0)) != 0 || - mp_int_compare_zero(TEMP(1)) != 0)) { - *start++ = '-'; - left -= 1; - } - - if((res = mp_int_to_string(TEMP(0), radix, start, left)) != MP_OK) - goto CLEANUP; - - len = strlen(start); - start += len; - left -= len; - - if(prec == 0) - goto CLEANUP; - - *start++ = '.'; - left -= 1; - - if(left < prec + 1) { - res = MP_TRUNC; - goto CLEANUP; - } - - memset(start, '0', lead_0 - 1); - left -= lead_0; - start += lead_0 - 1; - - res = mp_int_to_string(TEMP(1), radix, start, left); - - CLEANUP: - while(--last >= 0) - mp_int_clear(TEMP(last)); - - return res; -} - -/* }}} */ - -/* {{{ mp_rat_string_len(r, radix) */ - -mp_result mp_rat_string_len(mp_rat r, mp_size radix) -{ - mp_result n_len, d_len = 0; - - n_len = mp_int_string_len(MP_NUMER_P(r), radix); - - if(mp_int_compare_zero(MP_NUMER_P(r)) != 0) - d_len = mp_int_string_len(MP_DENOM_P(r), radix); - - /* Though simplistic, this formula is correct. Space for the sign - flag is included in n_len, and the space for the NUL that is - counted in n_len counts for the separator here. The space for - the NUL counted in d_len counts for the final terminator here. */ - - return n_len + d_len; - -} - -/* }}} */ - -/* {{{ mp_rat_decimal_len(r, radix, prec) */ - -mp_result mp_rat_decimal_len(mp_rat r, mp_size radix, mp_size prec) -{ - int z_len, f_len; - - z_len = mp_int_string_len(MP_NUMER_P(r), radix); - - if(prec == 0) - f_len = 1; /* terminator only */ - else - f_len = 1 + prec + 1; /* decimal point, digits, terminator */ - - return z_len + f_len; -} - -/* }}} */ - -/* {{{ mp_rat_read_string(r, radix, *str) */ - -mp_result mp_rat_read_string(mp_rat r, mp_size radix, const char *str) -{ - return mp_rat_read_cstring(r, radix, str, NULL); -} - -/* }}} */ - -/* {{{ mp_rat_read_cstring(r, radix, *str, **end) */ - -mp_result mp_rat_read_cstring(mp_rat r, mp_size radix, const char *str, - char **end) -{ - mp_result res; - char *endp; - - if((res = mp_int_read_cstring(MP_NUMER_P(r), radix, str, &endp)) != MP_OK && - (res != MP_TRUNC)) - return res; - - /* Skip whitespace between numerator and (possible) separator */ - while(isspace((unsigned char) *endp)) - ++endp; - - /* If there is no separator, we will stop reading at this point. */ - if(*endp != '/') { - mp_int_set_value(MP_DENOM_P(r), 1); - if(end != NULL) - *end = endp; - return res; - } - - ++endp; /* skip separator */ - if((res = mp_int_read_cstring(MP_DENOM_P(r), radix, endp, end)) != MP_OK) - return res; - - /* Make sure the value is well-defined */ - if(mp_int_compare_zero(MP_DENOM_P(r)) == 0) - return MP_UNDEF; - - /* Reduce to lowest terms */ - return s_rat_reduce(r); -} - -/* }}} */ - -/* {{{ mp_rat_read_ustring(r, radix, *str, **end) */ - -/* Read a string and figure out what format it's in. The radix may be - supplied as zero to use "default" behaviour. - - This function will accept either a/b notation or decimal notation. - */ -mp_result mp_rat_read_ustring(mp_rat r, mp_size radix, const char *str, - char **end) -{ - char *endp; - mp_result res; - - if(radix == 0) - radix = 10; /* default to decimal input */ - - if((res = mp_rat_read_cstring(r, radix, str, &endp)) != MP_OK) { - if(res == MP_TRUNC) { - if(*endp == '.') - res = mp_rat_read_cdecimal(r, radix, str, &endp); - } - else - return res; - } - - if(end != NULL) - *end = endp; - - return res; -} - -/* }}} */ - -/* {{{ mp_rat_read_decimal(r, radix, *str) */ - -mp_result mp_rat_read_decimal(mp_rat r, mp_size radix, const char *str) -{ - return mp_rat_read_cdecimal(r, radix, str, NULL); -} - -/* }}} */ - -/* {{{ mp_rat_read_cdecimal(r, radix, *str, **end) */ - -mp_result mp_rat_read_cdecimal(mp_rat r, mp_size radix, const char *str, - char **end) -{ - mp_result res; - mp_sign osign; - char *endp; - - while(isspace((unsigned char) *str)) - ++str; - - switch(*str) { - case '-': - osign = MP_NEG; - break; - default: - osign = MP_ZPOS; - } - - if((res = mp_int_read_cstring(MP_NUMER_P(r), radix, str, &endp)) != MP_OK && - (res != MP_TRUNC)) - return res; - - /* This needs to be here. */ - (void) mp_int_set_value(MP_DENOM_P(r), 1); - - if(*endp != '.') { - if(end != NULL) - *end = endp; - return res; - } - - /* If the character following the decimal point is whitespace or a - sign flag, we will consider this a truncated value. This special - case is because mp_int_read_string() will consider whitespace or - sign flags to be valid starting characters for a value, and we do - not want them following the decimal point. - - Once we have done this check, it is safe to read in the value of - the fractional piece as a regular old integer. - */ - ++endp; - if(*endp == '\0') { - if(end != NULL) - *end = endp; - return MP_OK; - } - else if(isspace((unsigned char) *endp) || *endp == '-' || *endp == '+') { - return MP_TRUNC; - } - else { - mpz_t frac; - mp_result save_res; - char *save = endp; - int num_lz = 0; - - /* Make a temporary to hold the part after the decimal point. */ - if((res = mp_int_init(&frac)) != MP_OK) - return res; - - if((res = mp_int_read_cstring(&frac, radix, endp, &endp)) != MP_OK && - (res != MP_TRUNC)) - goto CLEANUP; - - /* Save this response for later. */ - save_res = res; - - if(mp_int_compare_zero(&frac) == 0) - goto FINISHED; - - /* Discard trailing zeroes (somewhat inefficiently) */ - while(mp_int_divisible_value(&frac, radix)) - if((res = mp_int_div_value(&frac, radix, &frac, NULL)) != MP_OK) - goto CLEANUP; - - /* Count leading zeros after the decimal point */ - while(save[num_lz] == '0') - ++num_lz; - - /* Find the least power of the radix that is at least as large as - the significant value of the fractional part, ignoring leading - zeroes. */ - (void) mp_int_set_value(MP_DENOM_P(r), radix); - - while(mp_int_compare(MP_DENOM_P(r), &frac) < 0) { - if((res = mp_int_mul_value(MP_DENOM_P(r), radix, MP_DENOM_P(r))) != MP_OK) - goto CLEANUP; - } - - /* Also shift by enough to account for leading zeroes */ - while(num_lz > 0) { - if((res = mp_int_mul_value(MP_DENOM_P(r), radix, MP_DENOM_P(r))) != MP_OK) - goto CLEANUP; - - --num_lz; - } - - /* Having found this power, shift the numerator leftward that - many, digits, and add the nonzero significant digits of the - fractional part to get the result. */ - if((res = mp_int_mul(MP_NUMER_P(r), MP_DENOM_P(r), MP_NUMER_P(r))) != MP_OK) - goto CLEANUP; - - { /* This addition needs to be unsigned. */ - MP_SIGN(MP_NUMER_P(r)) = MP_ZPOS; - if((res = mp_int_add(MP_NUMER_P(r), &frac, MP_NUMER_P(r))) != MP_OK) - goto CLEANUP; - - MP_SIGN(MP_NUMER_P(r)) = osign; - } - if((res = s_rat_reduce(r)) != MP_OK) - goto CLEANUP; - - /* At this point, what we return depends on whether reading the - fractional part was truncated or not. That information is - saved from when we called mp_int_read_string() above. */ - FINISHED: - res = save_res; - if(end != NULL) - *end = endp; - - CLEANUP: - mp_int_clear(&frac); - - return res; - } -} - -/* }}} */ - -/* Private functions for internal use. Make unchecked assumptions - about format and validity of inputs. */ - -/* {{{ s_rat_reduce(r) */ - -static mp_result s_rat_reduce(mp_rat r) -{ - mpz_t gcd; - mp_result res = MP_OK; - - if(mp_int_compare_zero(MP_NUMER_P(r)) == 0) { - mp_int_set_value(MP_DENOM_P(r), 1); - return MP_OK; - } - - /* If the greatest common divisor of the numerator and denominator - is greater than 1, divide it out. */ - if((res = mp_int_init(&gcd)) != MP_OK) - return res; - - if((res = mp_int_gcd(MP_NUMER_P(r), MP_DENOM_P(r), &gcd)) != MP_OK) - goto CLEANUP; - - if(mp_int_compare_value(&gcd, 1) != 0) { - if((res = mp_int_div(MP_NUMER_P(r), &gcd, MP_NUMER_P(r), NULL)) != MP_OK) - goto CLEANUP; - if((res = mp_int_div(MP_DENOM_P(r), &gcd, MP_DENOM_P(r), NULL)) != MP_OK) - goto CLEANUP; - } - - /* Fix up the signs of numerator and denominator */ - if(MP_SIGN(MP_NUMER_P(r)) == MP_SIGN(MP_DENOM_P(r))) - MP_SIGN(MP_NUMER_P(r)) = MP_SIGN(MP_DENOM_P(r)) = MP_ZPOS; - else { - MP_SIGN(MP_NUMER_P(r)) = MP_NEG; - MP_SIGN(MP_DENOM_P(r)) = MP_ZPOS; - } - - CLEANUP: - mp_int_clear(&gcd); - - return res; -} - -/* }}} */ - -/* {{{ s_rat_combine(a, b, c, comb_f) */ - -static mp_result s_rat_combine(mp_rat a, mp_rat b, mp_rat c, - mp_result (*comb_f)(mp_int, mp_int, mp_int)) -{ - mp_result res; - - /* Shortcut when denominators are already common */ - if(mp_int_compare(MP_DENOM_P(a), MP_DENOM_P(b)) == 0) { - if((res = (comb_f)(MP_NUMER_P(a), MP_NUMER_P(b), MP_NUMER_P(c))) != MP_OK) - return res; - if((res = mp_int_copy(MP_DENOM_P(a), MP_DENOM_P(c))) != MP_OK) - return res; - - return s_rat_reduce(c); - } - else { - mpz_t temp[2]; - int last = 0; - - SETUP(mp_int_init_copy(TEMP(last), MP_NUMER_P(a)), last); - SETUP(mp_int_init_copy(TEMP(last), MP_NUMER_P(b)), last); - - if((res = mp_int_mul(TEMP(0), MP_DENOM_P(b), TEMP(0))) != MP_OK) - goto CLEANUP; - if((res = mp_int_mul(TEMP(1), MP_DENOM_P(a), TEMP(1))) != MP_OK) - goto CLEANUP; - if((res = (comb_f)(TEMP(0), TEMP(1), MP_NUMER_P(c))) != MP_OK) - goto CLEANUP; - - res = mp_int_mul(MP_DENOM_P(a), MP_DENOM_P(b), MP_DENOM_P(c)); - - CLEANUP: - while(--last >= 0) - mp_int_clear(TEMP(last)); - - if(res == MP_OK) - return s_rat_reduce(c); - else - return res; - } -} - -/* }}} */ - -/* Here there be dragons */ diff --git a/lib/des/imath/imrat.h b/lib/des/imath/imrat.h deleted file mode 100755 index 71b0c84f3..000000000 --- a/lib/des/imath/imrat.h +++ /dev/null @@ -1,123 +0,0 @@ -/* - Name: imrat.h - Purpose: Arbitrary precision rational arithmetic routines. - Author: M. J. Fromberger - Info: $Id$ - - Copyright (C) 2002 Michael J. Fromberger, All Rights Reserved. - - Permission is hereby granted, free of charge, to any person - obtaining a copy of this software and associated documentation files - (the "Software"), to deal in the Software without restriction, - including without limitation the rights to use, copy, modify, merge, - publish, distribute, sublicense, and/or sell copies of the Software, - and to permit persons to whom the Software is furnished to do so, - subject to the following conditions: - - The above copyright notice and this permission notice shall be - included in all copies or substantial portions of the Software. - - THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, - EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF - MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND - NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS - BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN - ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN - CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE - SOFTWARE. - */ - -#ifndef IMRAT_H_ -#define IMRAT_H_ - -#include "imath.h" - -#ifdef __cplusplus -extern "C" { -#endif - -typedef struct mpq { - mpz_t num; /* Numerator */ - mpz_t den; /* Denominator, <> 0 */ -} mpq_t, *mp_rat; - -#define MP_NUMER_P(Q) (&((Q)->num)) /* Pointer to numerator */ -#define MP_DENOM_P(Q) (&((Q)->den)) /* Pointer to denominator */ - -/* Rounding constants */ -typedef enum { - MP_ROUND_DOWN, - MP_ROUND_HALF_UP, - MP_ROUND_UP, - MP_ROUND_HALF_DOWN -} mp_round_mode; - -mp_result mp_rat_init(mp_rat r); -mp_rat mp_rat_alloc(void); -mp_result mp_rat_init_size(mp_rat r, mp_size n_prec, mp_size d_prec); -mp_result mp_rat_init_copy(mp_rat r, mp_rat old); -mp_result mp_rat_set_value(mp_rat r, int numer, int denom); -void mp_rat_clear(mp_rat r); -void mp_rat_free(mp_rat r); -mp_result mp_rat_numer(mp_rat r, mp_int z); /* z = num(r) */ -mp_result mp_rat_denom(mp_rat r, mp_int z); /* z = den(r) */ -mp_sign mp_rat_sign(mp_rat r); - -mp_result mp_rat_copy(mp_rat a, mp_rat c); /* c = a */ -void mp_rat_zero(mp_rat r); /* r = 0 */ -mp_result mp_rat_abs(mp_rat a, mp_rat c); /* c = |a| */ -mp_result mp_rat_neg(mp_rat a, mp_rat c); /* c = -a */ -mp_result mp_rat_recip(mp_rat a, mp_rat c); /* c = 1 / a */ -mp_result mp_rat_add(mp_rat a, mp_rat b, mp_rat c); /* c = a + b */ -mp_result mp_rat_sub(mp_rat a, mp_rat b, mp_rat c); /* c = a - b */ -mp_result mp_rat_mul(mp_rat a, mp_rat b, mp_rat c); /* c = a * b */ -mp_result mp_rat_div(mp_rat a, mp_rat b, mp_rat c); /* c = a / b */ - -mp_result mp_rat_add_int(mp_rat a, mp_int b, mp_rat c); /* c = a + b */ -mp_result mp_rat_sub_int(mp_rat a, mp_int b, mp_rat c); /* c = a - b */ -mp_result mp_rat_mul_int(mp_rat a, mp_int b, mp_rat c); /* c = a * b */ -mp_result mp_rat_div_int(mp_rat a, mp_int b, mp_rat c); /* c = a / b */ -mp_result mp_rat_expt(mp_rat a, int b, mp_rat c); /* c = a ^ b */ - -int mp_rat_compare(mp_rat a, mp_rat b); /* a <=> b */ -int mp_rat_compare_unsigned(mp_rat a, mp_rat b); /* |a| <=> |b| */ -int mp_rat_compare_zero(mp_rat r); /* r <=> 0 */ -int mp_rat_compare_value(mp_rat r, int n, int d); /* r <=> n/d */ -int mp_rat_is_integer(mp_rat r); - -/* Convert to integers, if representable (returns MP_RANGE if not). */ -mp_result mp_rat_to_ints(mp_rat r, int *num, int *den); - -/* Convert to nul-terminated string with the specified radix, writing - at most limit characters including the nul terminator. */ -mp_result mp_rat_to_string(mp_rat r, mp_size radix, char *str, int limit); - -/* Convert to decimal format in the specified radix and precision, - writing at most limit characters including a nul terminator. */ -mp_result mp_rat_to_decimal(mp_rat r, mp_size radix, mp_size prec, - mp_round_mode round, char *str, int limit); - -/* Return the number of characters required to represent r in the given - radix. May over-estimate. */ -mp_result mp_rat_string_len(mp_rat r, mp_size radix); - -/* Return the number of characters required to represent r in decimal - format with the given radix and precision. May over-estimate. */ -mp_result mp_rat_decimal_len(mp_rat r, mp_size radix, mp_size prec); - -/* Read zero-terminated string into r */ -mp_result mp_rat_read_string(mp_rat r, mp_size radix, const char *str); -mp_result mp_rat_read_cstring(mp_rat r, mp_size radix, const char *str, - char **end); -mp_result mp_rat_read_ustring(mp_rat r, mp_size radix, const char *str, - char **end); - -/* Read zero-terminated string in decimal format into r */ -mp_result mp_rat_read_decimal(mp_rat r, mp_size radix, const char *str); -mp_result mp_rat_read_cdecimal(mp_rat r, mp_size radix, const char *str, - char **end); - -#ifdef __cplusplus -} -#endif -#endif /* IMRAT_H_ */ diff --git a/lib/des/imath/rsamath.c b/lib/des/imath/rsamath.c deleted file mode 100755 index dbdf6254d..000000000 --- a/lib/des/imath/rsamath.c +++ /dev/null @@ -1,205 +0,0 @@ -/* - Name: rsamath.c - Purpose: Implements part of PKCS#1, v. 2.1, June 14, 2002 (RSA Labs) - Author: M. J. Fromberger - Copyright (C) 2002 Michael J. Fromberger, All Rights Reserved. - Info: $Id$ - - Permission is hereby granted, free of charge, to any person - obtaining a copy of this software and associated documentation files - (the "Software"), to deal in the Software without restriction, - including without limitation the rights to use, copy, modify, merge, - publish, distribute, sublicense, and/or sell copies of the Software, - and to permit persons to whom the Software is furnished to do so, - subject to the following conditions: - - The above copyright notice and this permission notice shall be - included in all copies or substantial portions of the Software. - - THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, - EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF - MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND - NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS - BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN - ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN - CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE - SOFTWARE. - */ - -#include "rsamath.h" - -#include -#include - -static mp_result s_rsa_transform(mp_int msg, mp_int exp, - mp_int mod, mp_int out); - -/* {{{ rsa_i2osp(z, out, len) */ - -/* Convert integer to octet string, per PKCS#1 v.2.1 */ -mp_result rsa_i2osp(mp_int z, unsigned char *out, int len) -{ - int excess_len = mp_int_binary_len(z); - - if(excess_len < len) - return MP_RANGE; - - memset(out, 0, len); - - excess_len -= len; - mp_int_to_binary(z, out + excess_len, len); - - return MP_OK; -} - -/* }}} */ - -/* {{{ rsa_os2ip(z, in, len) */ - -/* Convert octet string to integer, per PKCS#1 v.2.1 */ -mp_result rsa_os2ip(mp_int z, unsigned char *in, int len) -{ - return mp_int_read_binary(z, in, len); -} - -/* }}} */ - -/* {{{ rsa_rsaep(msg, exp, mod, cipher) */ - -/* Primitive RSA encryption operation */ -mp_result rsa_rsaep(mp_int msg, mp_int exp, mp_int mod, mp_int cipher) -{ - return s_rsa_transform(msg, exp, mod, cipher); -} - -/* }}} */ - -/* {{{ rsa_rsadp(cipher, exp, mod, msg) */ - -/* Primitive RSA decryption operation */ -mp_result rsa_rsadp(mp_int cipher, mp_int exp, mp_int mod, mp_int msg) -{ - return s_rsa_transform(cipher, exp, mod, msg); -} - -/* }}} */ - -/* {{{ rsa_rsasp(msg, exp, mod, signature) */ - -/* Primitive RSA signing operation */ -mp_result rsa_rsasp(mp_int msg, mp_int exp, mp_int mod, mp_int signature) -{ - return s_rsa_transform(msg, exp, mod, signature); -} - -/* }}} */ - -/* {{{ rsa_rsavp(signature, exp, mod, msg) */ - -/* Primitive RSA verification operation */ -mp_result rsa_rsavp(mp_int signature, mp_int exp, mp_int mod, mp_int msg) -{ - return s_rsa_transform(signature, exp, mod, msg); -} - -/* }}} */ - -/* {{{ rsa_max_message_len(mod) */ - -/* Compute the maximum length in bytes a message can have using PKCS#1 - v.1.5 encoding with the given modulus */ -int rsa_max_message_len(mp_int mod) -{ - int num_bits = mp_int_count_bits(mod); - int num_bytes = num_bits / CHAR_BIT; - - if(num_bytes < 11) - return 0; /* at least eleven bytes are required for padding */ - else - return num_bytes - 11; -} - -/* }}} */ - -/* {{{ rsa_pkcs1v15_encode(buf, msg_len, buf_len, tag, filler) */ - -mp_result rsa_pkcs1v15_encode(unsigned char *buf, int msg_len, - int buf_len, int tag, random_f filler) -{ - int pad_len, msg_start; - - /* Make sure there is enough space for the encoded output */ - if(msg_len > (buf_len - 11)) - return MP_RANGE; - - msg_start = buf_len - msg_len; - pad_len = msg_start - 3; - - /* Move message to top of buffer -- these might overlap, so we rely - on the semantics of memmove() here */ - memmove(buf + msg_start, buf, msg_len); - - /* Set initial bytes as required by the specification */ - buf[0] = 0x00; - buf[1] = (unsigned char)tag; - - /* Fill with random padding. We'll just assume the filler function - does the right thing and only writes the requested number of - nonzero bytes */ - (filler)(buf + 2, pad_len); - - /* Write separator between pad and message body */ - buf[msg_start - 1] = 0x00; - - return MP_OK; -} - -/* }}} */ - -/* {{{ rsa_pkcs1v15_decode(buf, buf_len, *msg_len) */ - -mp_result rsa_pkcs1v15_decode(unsigned char *buf, int buf_len, - int tag, int *msg_len) -{ - int pad_len = 0, data_len, data_start, i; - - /* Make sure the buffer is syntactically valid */ - if(buf_len < 11 || buf[0] != 0x00 || buf[1] != (unsigned char)tag) - return MP_UNDEF; - - /* Figure out how many bytes of random padding there are */ - i = 2; - while(buf[i++] != '\0') - ++pad_len; - - data_start = i; - data_len = buf_len - data_start; - - /* Shift the message to the front of the buffer */ - memmove(buf, buf + data_start, data_len); - - /* Zero out the rest of the buffer */ - memset(buf + data_len, 0, pad_len + 3); - - *msg_len = data_len; - - return MP_OK; -} - -/* }}} */ - -/* {{{ s_rsa_transform(msg, exp, mod, out) */ - -static mp_result s_rsa_transform(mp_int msg, mp_int exp, - mp_int mod, mp_int out) -{ - if(mp_int_compare_zero(msg) < 0 || - mp_int_compare(msg, mod) >= 0) - return MP_RANGE; - - return mp_int_exptmod(msg, exp, mod, out); -} - -/* }}} */ - -/* Here there be dragons */ diff --git a/lib/des/imath/rsamath.h b/lib/des/imath/rsamath.h deleted file mode 100755 index abd105d13..000000000 --- a/lib/des/imath/rsamath.h +++ /dev/null @@ -1,97 +0,0 @@ -/* - Name: rsamath.h - Purpose: Implements part of PKCS#1, v. 2.1, June 14, 2002 (RSA Labs) - Author: M. J. Fromberger - Info: $Id$ - - Copyright (C) 2002 Michael J. Fromberger, All Rights Reserved. - - Permission is hereby granted, free of charge, to any person - obtaining a copy of this software and associated documentation files - (the "Software"), to deal in the Software without restriction, - including without limitation the rights to use, copy, modify, merge, - publish, distribute, sublicense, and/or sell copies of the Software, - and to permit persons to whom the Software is furnished to do so, - subject to the following conditions: - - The above copyright notice and this permission notice shall be - included in all copies or substantial portions of the Software. - - THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, - EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF - MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND - NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS - BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN - ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN - CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE - SOFTWARE. - */ - -#ifndef RSAMATH_H_ -#define RSAMATH_H_ - -#include "imath.h" - -#ifdef __cplusplus -extern "C" { -#endif - -/* Function to fill a buffer with nonzero random bytes */ -typedef void (*random_f)(unsigned char *, int); - -/* Convert integer to octet string, per PKCS#1 v.2.1 */ -mp_result rsa_i2osp(mp_int z, unsigned char *out, int len); - -/* Convert octet string to integer, per PKCS#1 v.2.1 */ -mp_result rsa_os2ip(mp_int z, unsigned char *in, int len); - -/* The following operations assume that you have converted your keys - and message data into mp_int values somehow. */ - -/* Primitive RSA encryption operation */ -mp_result rsa_rsaep(mp_int msg, mp_int exp, mp_int mod, mp_int cipher); - -/* Primitive RSA decryption operation */ -mp_result rsa_rsadp(mp_int cipher, mp_int exp, mp_int mod, mp_int msg); - -/* Primitive RSA signing operation */ -mp_result rsa_rsasp(mp_int msg, mp_int exp, mp_int mod, mp_int signature); - -/* Primitive RSA verification operation */ -mp_result rsa_rsavp(mp_int signature, mp_int exp, mp_int mod, mp_int msg); - -/* Compute the maximum length in bytes a message can have using PKCS#1 - v.1.5 encoding with the given modulus */ -int rsa_max_message_len(mp_int mod); - -/* Encode a raw message per PKCS#1 v.1.5 - buf - the buffer containing the message - msg_len - the length in bytes of the message - buf_len - the size in bytes of the buffer - tag - the message tag (nonzero byte) - filler - function to generate pseudorandom nonzero padding - - On input, the message is in the first msg_len bytes of the buffer; - on output, the contents of the buffer are replaced by the padded - message. If there is not enough room, MP_RANGE is returned. - */ -mp_result rsa_pkcs1v15_encode(unsigned char *buf, int msg_len, - int buf_len, int tag, random_f filler); - -/* Decode a PKCS#1 v.1.5 message back to its raw form - buf - the buffer containing the encoded message - buf_len - the length in bytes of the buffer - tag - the expected message tag (nonzero byte) - msg_len - on output, receives the length of the message content - - On output, the message is packed into the first msg_len bytes of - the buffer, and the rest of the buffer is zeroed. If the buffer is - not of the correct form, MP_UNDEF is returned and msg_len is undefined. - */ -mp_result rsa_pkcs1v15_decode(unsigned char *buf, int buf_len, - int tag, int *msg_len); - -#ifdef __cplusplus -} -#endif -#endif /* end RSAMATH_H_ */