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-rw-r--r--libtommath/bn_mp_sqrt.c142
1 files changed, 142 insertions, 0 deletions
diff --git a/libtommath/bn_mp_sqrt.c b/libtommath/bn_mp_sqrt.c
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+++ b/libtommath/bn_mp_sqrt.c
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+#include <tommath.h>
+
+#ifdef BN_MP_SQRT_C
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
+ */
+
+#ifndef NO_FLOATING_POINT
+#include <math.h>
+#endif
+
+/* this function is less generic than mp_n_root, simpler and faster */
+int mp_sqrt(mp_int *arg, mp_int *ret)
+{
+ int res;
+ mp_int t1,t2;
+ int i, j, k;
+#ifndef NO_FLOATING_POINT
+ volatile double d;
+ mp_digit dig;
+#endif
+
+ /* must be positive */
+ if (arg->sign == MP_NEG) {
+ return MP_VAL;
+ }
+
+ /* easy out */
+ if (mp_iszero(arg) == MP_YES) {
+ mp_zero(ret);
+ return MP_OKAY;
+ }
+
+ i = (arg->used / 2) - 1;
+ j = 2 * i;
+ if ((res = mp_init_size(&t1, i+2)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init(&t2)) != MP_OKAY) {
+ goto E2;
+ }
+
+ for (k = 0; k < i; ++k) {
+ t1.dp[k] = (mp_digit) 0;
+ }
+
+#ifndef NO_FLOATING_POINT
+
+ /* Estimate the square root using the hardware floating point unit. */
+
+ d = 0.0;
+ for (k = arg->used-1; k >= j; --k) {
+ d = ldexp(d, DIGIT_BIT) + (double) (arg->dp[k]);
+ }
+
+ /*
+ * At this point, d is the nearest floating point number to the most
+ * significant 1 or 2 mp_digits of arg. Extract its square root.
+ */
+
+ d = sqrt(d);
+
+ /* dig is the most significant mp_digit of the square root */
+
+ dig = (mp_digit) ldexp(d, -DIGIT_BIT);
+
+ /*
+ * If the most significant digit is nonzero, find the next digit down
+ * by subtracting DIGIT_BIT times thie most significant digit.
+ * Subtract one from the result so that our initial estimate is always
+ * low.
+ */
+
+ if (dig) {
+ t1.used = i+2;
+ d -= ldexp((double) dig, DIGIT_BIT);
+ if (d >= 1.0) {
+ t1.dp[i+1] = dig;
+ t1.dp[i] = ((mp_digit) d) - 1;
+ } else {
+ t1.dp[i+1] = dig-1;
+ t1.dp[i] = MP_DIGIT_MAX;
+ }
+ } else {
+ t1.used = i+1;
+ t1.dp[i] = ((mp_digit) d) - 1;
+ }
+
+#else
+
+ /* Estimate the square root as having 1 in the most significant place. */
+
+ t1.used = i + 2;
+ t1.dp[i+1] = (mp_digit) 1;
+ t1.dp[i] = (mp_digit) 0;
+
+#endif
+
+ /* t1 > 0 */
+ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ /* And now t1 > sqrt(arg) */
+ do {
+ if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
+ goto E1;
+ }
+ /* t1 >= sqrt(arg) >= t2 at this point */
+ } while (mp_cmp_mag(&t1,&t2) == MP_GT);
+
+ mp_exch(&t1,ret);
+
+E1: mp_clear(&t2);
+E2: mp_clear(&t1);
+ return res;
+}
+
+#endif