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// Copyright 2015 The Ramp Developers // // Licensed under the Apache License, Version 2.0 (the "License"); // you may not use this file except in compliance with the License. // You may obtain a copy of the License at // // http://www.apache.org/licenses/LICENSE-2.0 // // Unless required by applicable law or agreed to in writing, software // distributed under the License is distributed on an "AS IS" BASIS, // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. // See the License for the specific language governing permissions and // limitations under the License. use ll; use ll::limb::Limb; use mem; use ll::limb_ptr::{Limbs, LimbsMut}; /** * Takes `{ap, an}` to the power of `exp` and stores the result to `wp`. `wp` is * assumed to have enough space to store the result (which can be calculated using * `num_pow_limbs` * * `{wp, an*exp}` must be disjoint from `{ap, an}`. * `{ap, an}` must not be zero. * `exp` must be greater than 2 */ pub unsafe fn pow(mut wp: LimbsMut, mut ap: Limbs, mut an: i32, mut exp: u32) { debug_assert!(exp > 2); debug_assert!(!ll::is_zero(ap, an)); let mut wn = num_pow_limbs(ap, an, exp); debug_assert!(!ll::overlap(wp, wn, ap, an)); let mut tmp = mem::TmpAllocator::new(); ll::zero(wp, wn); // (m * 2**K)**exp == m**exp * 2**(K*exp) while *ap == 0 { ap = ap.offset(1); an -= 1; wp = wp.offset(exp as isize); wn -= exp as i32; } let trailing = (*ap).trailing_zeros() as u32; let sz = wn as usize; // An extra limb of scratch space is needed because the length // estimation is precise: if you're doing something like x**7, the // final multiplication is ``x**3 * x**4`. These could have // lengths, like, say, 30 and 40 limbs, so the multiplication can // take at most 30 + 40 + 1 limbs, and the multiplication // algorithm will write to all of them, possibly putting a zero in // the very highest limb... however, the x**7 length estimator may // work out that the final result actually fits into only 70 // limbs, so if we don't account for this mismatch we risk memory // corruption. // // (Examples of such x are 2**(k L), where k > 0 is an integer and // L is the number of bits in a limb.) let (bp, scratch) = tmp.allocate_2(sz, sz + 1); let mut bn = an; if trailing > 0 { ll::shr(bp, ap, an, trailing); } else { ll::copy_incr(ap, bp, an); } // Calculate the amount we'll need to shift by at the end, // we need to adjust wp here because the shift functions only // work with shifts of < Limb::BITS let mut shift = trailing * exp; while shift >= Limb::BITS as u32 { shift -= Limb::BITS as u32; wp = wp.offset(1); } *wp = Limb(1); let mut wn = 1; loop { if (exp & 1) == 1 { if wn > bn { ll::mul(scratch, wp.as_const(), wn, bp.as_const(), bn); } else { ll::mul(scratch, bp.as_const(), bn, wp.as_const(), wn); } wn = ll::normalize(scratch.as_const(), wn + bn); ll::copy_incr(scratch.as_const(), wp, wn); } exp >>= 1; // Do this check before the base multiplication so we don't // end up needing more space than necessary if exp == 0 { break; } ll::sqr(scratch, bp.as_const(), bn); bn = ll::normalize(scratch.as_const(), bn + bn); ll::copy_incr(scratch.as_const(), bp, bn); } if shift > 0 { let v = ll::shl(wp, wp.as_const(), wn, shift); if v > 0 { *wp.offset(wn as isize) = v; } } } /// Calculates the number of limbs required to store the result of taking /// `{xp, xn}` to the power of `exp` pub unsafe fn num_pow_limbs(xp: Limbs, xn: i32, exp: u32) -> i32 { // This is a better approximation of log_b(x^e) than simply using the // the number of digits, n. // Instead it uses the most significant digit, a, to calculate // e*log_b(a*b^(n-1)), which is e*(log_b(a) + n - 1) let n = xn - 1; let high_limb = *xp.offset(n as isize); // Calculate log_2(a), this is because floor(log_b(a)) will always be // 0 let lg2 = Limb::BITS as u32 - high_limb.leading_zeros() as u32; // Get e*log_2(a) let lg2e = exp as i32 * lg2 as i32; // Now convert it to log_b using the formula // log_a(x) = log_b(x) / log_b(a) let elog_b = lg2e / Limb::BITS as i32; // Add a final 1 to account for the error in the estimate elog_b + (exp as i32 * n) + 1 }