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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
    }

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