#include "tommath_private.h" #ifdef BN_MP_SQRT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis */ /* SPDX-License-Identifier: Unlicense */ #ifndef NO_FLOATING_POINT #include #include #if (MP_DIGIT_BIT != 28) || (FLT_RADIX != 2) || (DBL_MANT_DIG != 53) || (DBL_MAX_EXP != 1024) #define NO_FLOATING_POINT #endif #endif /* this function is less generic than mp_n_root, simpler and faster */ mp_err mp_sqrt(const mp_int *arg, mp_int *ret) { mp_err err; mp_int t1, t2; #ifndef NO_FLOATING_POINT int i, j, k; volatile double d; mp_digit dig; #endif /* must be positive */ if (arg->sign == MP_NEG) { return MP_VAL; } /* easy out */ if (MP_IS_ZERO(arg)) { mp_zero(ret); return MP_OKAY; } #ifndef NO_FLOATING_POINT i = (arg->used / 2) - 1; j = 2 * i; if ((err = mp_init_size(&t1, i+2)) != MP_OKAY) { return err; } if ((err = mp_init(&t2)) != MP_OKAY) { goto E2; } for (k = 0; k < i; ++k) { t1.dp[k] = (mp_digit) 0; } /* Estimate the square root using the hardware floating point unit. */ d = 0.0; for (k = arg->used-1; k >= j; --k) { d = ldexp(d, MP_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, -MP_DIGIT_BIT); /* * If the most significant digit is nonzero, find the next digit down * by subtracting MP_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, MP_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 if ((err = mp_init_copy(&t1, arg)) != MP_OKAY) { return err; } if ((err = mp_init(&t2)) != MP_OKAY) { goto E2; } /* First approx. (not very bad for large arg) */ mp_rshd(&t1, t1.used/2); #endif /* t1 > 0 */ if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) { goto E1; } if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) { goto E1; } if ((err = mp_div_2(&t1, &t1)) != MP_OKAY) { goto E1; } /* And now t1 > sqrt(arg) */ do { if ((err = mp_div(arg, &t1, &t2, NULL)) != MP_OKAY) { goto E1; } if ((err = mp_add(&t1, &t2, &t1)) != MP_OKAY) { goto E1; } if ((err = 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 err; } #endif