//! Curve25519 elliptic curve

use crate::util::fixed_time_eq;
use core::cmp::{min, Eq, Ordering, PartialEq};
use core::ops::{Add, Mul, Sub};

/*
fe means field element.
Here the field is \Z/(2^255-19).
An element t, entries t[0]...t[9], represents the integer
t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
Bounds on each t[i] vary depending on context.
*/

#[derive(Clone)]
pub struct Fe(pub [i32; 10]);

impl PartialEq for Fe {
    fn eq(&self, other: &Fe) -> bool {
        let &Fe(self_elems) = self;
        let &Fe(other_elems) = other;
        self_elems.to_vec() == other_elems.to_vec()
    }
}
impl Eq for Fe {}

static FE_ZERO: Fe = Fe([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]);
static FE_ONE: Fe = Fe([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]);
static FE_SQRTM1: Fe = Fe([
    -32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482,
]);
static FE_D: Fe = Fe([
    -10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448,
    -12055116,
]);
static FE_D2: Fe = Fe([
    -21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968,
    9444199,
]);

fn load_4u(s: &[u8]) -> u64 {
    (s[0] as u64) | ((s[1] as u64) << 8) | ((s[2] as u64) << 16) | ((s[3] as u64) << 24)
}
fn load_4i(s: &[u8]) -> i64 {
    load_4u(s) as i64
}
fn load_3u(s: &[u8]) -> u64 {
    (s[0] as u64) | ((s[1] as u64) << 8) | ((s[2] as u64) << 16)
}
fn load_3i(s: &[u8]) -> i64 {
    load_3u(s) as i64
}

impl Add for Fe {
    type Output = Fe;
    fn add(self, rhs: Fe) -> Fe {
        &self + &rhs
    }
}

impl Add for &Fe {
    type Output = Fe;

    /*
    h = f + g
    Can overlap h with f or g.

    Preconditions:
       |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
       |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

    Postconditions:
       |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
    */
    fn add(self, _rhs: &Fe) -> Fe {
        let Fe(f) = self;
        let Fe(g) = _rhs;

        let f0 = f[0];
        let f1 = f[1];
        let f2 = f[2];
        let f3 = f[3];
        let f4 = f[4];
        let f5 = f[5];
        let f6 = f[6];
        let f7 = f[7];
        let f8 = f[8];
        let f9 = f[9];
        let g0 = g[0];
        let g1 = g[1];
        let g2 = g[2];
        let g3 = g[3];
        let g4 = g[4];
        let g5 = g[5];
        let g6 = g[6];
        let g7 = g[7];
        let g8 = g[8];
        let g9 = g[9];
        let h0 = f0 + g0;
        let h1 = f1 + g1;
        let h2 = f2 + g2;
        let h3 = f3 + g3;
        let h4 = f4 + g4;
        let h5 = f5 + g5;
        let h6 = f6 + g6;
        let h7 = f7 + g7;
        let h8 = f8 + g8;
        let h9 = f9 + g9;
        Fe([h0, h1, h2, h3, h4, h5, h6, h7, h8, h9])
    }
}

impl Sub for Fe {
    type Output = Fe;
    fn sub(self, rhs: Fe) -> Fe {
        &self - &rhs
    }
}

impl Sub for &Fe {
    type Output = Fe;

    /*
    h = f - g
    Can overlap h with f or g.

    Preconditions:
       |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
       |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

    Postconditions:
       |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
    */
    fn sub(self, rhs: &Fe) -> Fe {
        let Fe(f) = self;
        let Fe(g) = rhs;

        let f0 = f[0];
        let f1 = f[1];
        let f2 = f[2];
        let f3 = f[3];
        let f4 = f[4];
        let f5 = f[5];
        let f6 = f[6];
        let f7 = f[7];
        let f8 = f[8];
        let f9 = f[9];
        let g0 = g[0];
        let g1 = g[1];
        let g2 = g[2];
        let g3 = g[3];
        let g4 = g[4];
        let g5 = g[5];
        let g6 = g[6];
        let g7 = g[7];
        let g8 = g[8];
        let g9 = g[9];
        let h0 = f0 - g0;
        let h1 = f1 - g1;
        let h2 = f2 - g2;
        let h3 = f3 - g3;
        let h4 = f4 - g4;
        let h5 = f5 - g5;
        let h6 = f6 - g6;
        let h7 = f7 - g7;
        let h8 = f8 - g8;
        let h9 = f9 - g9;
        Fe([h0, h1, h2, h3, h4, h5, h6, h7, h8, h9])
    }
}

impl Mul for Fe {
    type Output = Fe;
    fn mul(self, rhs: Fe) -> Fe {
        &self * &rhs
    }
}

impl Mul for &Fe {
    type Output = Fe;

    /*
    h = f * g
    Can overlap h with f or g.

    Preconditions:
       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
       |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

    Postconditions:
       |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
    */

    /*
    Notes on implementation strategy:

    Using schoolbook multiplication.
    Karatsuba would save a little in some cost models.

    Most multiplications by 2 and 19 are 32-bit precomputations;
    cheaper than 64-bit postcomputations.

    There is one remaining multiplication by 19 in the carry chain;
    one *19 precomputation can be merged into this,
    but the resulting data flow is considerably less clean.

    There are 12 carries below.
    10 of them are 2-way parallelizable and vectorizable.
    Can get away with 11 carries, but then data flow is much deeper.

    With tighter constraints on inputs can squeeze carries into int32.
    */
    #[rustfmt::skip]
    #[allow(clippy::suspicious_arithmetic_impl)]
    fn mul(self, _rhs: &Fe) -> Fe {
        let Fe(f) = self;
        let Fe(g) = _rhs;
        let f0 = f[0];
        let f1 = f[1];
        let f2 = f[2];
        let f3 = f[3];
        let f4 = f[4];
        let f5 = f[5];
        let f6 = f[6];
        let f7 = f[7];
        let f8 = f[8];
        let f9 = f[9];
        let g0 = g[0];
        let g1 = g[1];
        let g2 = g[2];
        let g3 = g[3];
        let g4 = g[4];
        let g5 = g[5];
        let g6 = g[6];
        let g7 = g[7];
        let g8 = g[8];
        let g9 = g[9];
        let g1_19 = 19 * g1; /* 1.4*2^29 */
        let g2_19 = 19 * g2; /* 1.4*2^30; still ok */
        let g3_19 = 19 * g3;
        let g4_19 = 19 * g4;
        let g5_19 = 19 * g5;
        let g6_19 = 19 * g6;
        let g7_19 = 19 * g7;
        let g8_19 = 19 * g8;
        let g9_19 = 19 * g9;
        let f1_2 = 2 * f1;
        let f3_2 = 2 * f3;
        let f5_2 = 2 * f5;
        let f7_2 = 2 * f7;
        let f9_2 = 2 * f9;
        let f0g0    = (f0   as i64) * (g0 as i64);
        let f0g1    = (f0   as i64) * (g1 as i64);
        let f0g2    = (f0   as i64) * (g2 as i64);
        let f0g3    = (f0   as i64) * (g3 as i64);
        let f0g4    = (f0   as i64) * (g4 as i64);
        let f0g5    = (f0   as i64) * (g5 as i64);
        let f0g6    = (f0   as i64) * (g6 as i64);
        let f0g7    = (f0   as i64) * (g7 as i64);
        let f0g8    = (f0   as i64) * (g8 as i64);
        let f0g9    = (f0   as i64) * (g9 as i64);
        let f1g0    = (f1   as i64) * (g0 as i64);
        let f1g1_2  = (f1_2 as i64) * (g1 as i64);
        let f1g2    = (f1   as i64) * (g2 as i64);
        let f1g3_2  = (f1_2 as i64) * (g3 as i64);
        let f1g4    = (f1   as i64) * (g4 as i64);
        let f1g5_2  = (f1_2 as i64) * (g5 as i64);
        let f1g6    = (f1   as i64) * (g6 as i64);
        let f1g7_2  = (f1_2 as i64) * (g7 as i64);
        let f1g8    = (f1   as i64) * (g8 as i64);
        let f1g9_38 = (f1_2 as i64) * (g9_19 as i64);
        let f2g0    = (f2   as i64) * (g0 as i64);
        let f2g1    = (f2   as i64) * (g1 as i64);
        let f2g2    = (f2   as i64) * (g2 as i64);
        let f2g3    = (f2   as i64) * (g3 as i64);
        let f2g4    = (f2   as i64) * (g4 as i64);
        let f2g5    = (f2   as i64) * (g5 as i64);
        let f2g6    = (f2   as i64) * (g6 as i64);
        let f2g7    = (f2   as i64) * (g7 as i64);
        let f2g8_19 = (f2   as i64) * (g8_19 as i64);
        let f2g9_19 = (f2   as i64) * (g9_19 as i64);
        let f3g0    = (f3   as i64) * (g0 as i64);
        let f3g1_2  = (f3_2 as i64) * (g1 as i64);
        let f3g2    = (f3   as i64) * (g2 as i64);
        let f3g3_2  = (f3_2 as i64) * (g3 as i64);
        let f3g4    = (f3   as i64) * (g4 as i64);
        let f3g5_2  = (f3_2 as i64) * (g5 as i64);
        let f3g6    = (f3   as i64) * (g6 as i64);
        let f3g7_38 = (f3_2 as i64) * (g7_19 as i64);
        let f3g8_19 = (f3   as i64) * (g8_19 as i64);
        let f3g9_38 = (f3_2 as i64) * (g9_19 as i64);
        let f4g0    = (f4   as i64) * (g0 as i64);
        let f4g1    = (f4   as i64) * (g1 as i64);
        let f4g2    = (f4   as i64) * (g2 as i64);
        let f4g3    = (f4   as i64) * (g3 as i64);
        let f4g4    = (f4   as i64) * (g4 as i64);
        let f4g5    = (f4   as i64) * (g5 as i64);
        let f4g6_19 = (f4   as i64) * (g6_19 as i64);
        let f4g7_19 = (f4   as i64) * (g7_19 as i64);
        let f4g8_19 = (f4   as i64) * (g8_19 as i64);
        let f4g9_19 = (f4   as i64) * (g9_19 as i64);
        let f5g0    = (f5   as i64) * (g0 as i64);
        let f5g1_2  = (f5_2 as i64) * (g1 as i64);
        let f5g2    = (f5   as i64) * (g2 as i64);
        let f5g3_2  = (f5_2 as i64) * (g3 as i64);
        let f5g4    = (f5   as i64) * (g4 as i64);
        let f5g5_38 = (f5_2 as i64) * (g5_19 as i64);
        let f5g6_19 = (f5   as i64) * (g6_19 as i64);
        let f5g7_38 = (f5_2 as i64) * (g7_19 as i64);
        let f5g8_19 = (f5   as i64) * (g8_19 as i64);
        let f5g9_38 = (f5_2 as i64) * (g9_19 as i64);
        let f6g0    = (f6   as i64) * (g0 as i64);
        let f6g1    = (f6   as i64) * (g1 as i64);
        let f6g2    = (f6   as i64) * (g2 as i64);
        let f6g3    = (f6   as i64) * (g3 as i64);
        let f6g4_19 = (f6   as i64) * (g4_19 as i64);
        let f6g5_19 = (f6   as i64) * (g5_19 as i64);
        let f6g6_19 = (f6   as i64) * (g6_19 as i64);
        let f6g7_19 = (f6   as i64) * (g7_19 as i64);
        let f6g8_19 = (f6   as i64) * (g8_19 as i64);
        let f6g9_19 = (f6   as i64) * (g9_19 as i64);
        let f7g0    = (f7   as i64) * (g0 as i64);
        let f7g1_2  = (f7_2 as i64) * (g1 as i64);
        let f7g2    = (f7   as i64) * (g2 as i64);
        let f7g3_38 = (f7_2 as i64) * (g3_19 as i64);
        let f7g4_19 = (f7   as i64) * (g4_19 as i64);
        let f7g5_38 = (f7_2 as i64) * (g5_19 as i64);
        let f7g6_19 = (f7   as i64) * (g6_19 as i64);
        let f7g7_38 = (f7_2 as i64) * (g7_19 as i64);
        let f7g8_19 = (f7   as i64) * (g8_19 as i64);
        let f7g9_38 = (f7_2 as i64) * (g9_19 as i64);
        let f8g0    = (f8   as i64) * (g0 as i64);
        let f8g1    = (f8   as i64) * (g1 as i64);
        let f8g2_19 = (f8   as i64) * (g2_19 as i64);
        let f8g3_19 = (f8   as i64) * (g3_19 as i64);
        let f8g4_19 = (f8   as i64) * (g4_19 as i64);
        let f8g5_19 = (f8   as i64) * (g5_19 as i64);
        let f8g6_19 = (f8   as i64) * (g6_19 as i64);
        let f8g7_19 = (f8   as i64) * (g7_19 as i64);
        let f8g8_19 = (f8   as i64) * (g8_19 as i64);
        let f8g9_19 = (f8   as i64) * (g9_19 as i64);
        let f9g0    = (f9   as i64) * (g0 as i64);
        let f9g1_38 = (f9_2 as i64) * (g1_19 as i64);
        let f9g2_19 = (f9   as i64) * (g2_19 as i64);
        let f9g3_38 = (f9_2 as i64) * (g3_19 as i64);
        let f9g4_19 = (f9   as i64) * (g4_19 as i64);
        let f9g5_38 = (f9_2 as i64) * (g5_19 as i64);
        let f9g6_19 = (f9   as i64) * (g6_19 as i64);
        let f9g7_38 = (f9_2 as i64) * (g7_19 as i64);
        let f9g8_19 = (f9   as i64) * (g8_19 as i64);
        let f9g9_38 = (f9_2 as i64) * (g9_19 as i64);
        let mut h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
        let mut h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
        let mut h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
        let mut h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
        let mut h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
        let mut h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
        let mut h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
        let mut h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
        let mut h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
        let mut h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
        let mut carry0;
        let carry1;
        let carry2;
        let carry3;
        let mut carry4;
        let carry5;
        let carry6;
        let carry7;
        let carry8;
        let carry9;

        /*
        |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
          i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
        |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
          i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
        */

        carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
        carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
        /* |h0| <= 2^25 */
        /* |h4| <= 2^25 */
        /* |h1| <= 1.51*2^58 */
        /* |h5| <= 1.51*2^58 */

        carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
        carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
        /* |h1| <= 2^24; from now on fits into int32 */
        /* |h5| <= 2^24; from now on fits into int32 */
        /* |h2| <= 1.21*2^59 */
        /* |h6| <= 1.21*2^59 */

        carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
        carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
        /* |h2| <= 2^25; from now on fits into int32 unchanged */
        /* |h6| <= 2^25; from now on fits into int32 unchanged */
        /* |h3| <= 1.51*2^58 */
        /* |h7| <= 1.51*2^58 */

        carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
        carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
        /* |h3| <= 2^24; from now on fits into int32 unchanged */
        /* |h7| <= 2^24; from now on fits into int32 unchanged */
        /* |h4| <= 1.52*2^33 */
        /* |h8| <= 1.52*2^33 */

        carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
        carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
        /* |h4| <= 2^25; from now on fits into int32 unchanged */
        /* |h8| <= 2^25; from now on fits into int32 unchanged */
        /* |h5| <= 1.01*2^24 */
        /* |h9| <= 1.51*2^58 */

        carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
        /* |h9| <= 2^24; from now on fits into int32 unchanged */
        /* |h0| <= 1.8*2^37 */

        carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
        /* |h0| <= 2^25; from now on fits into int32 unchanged */
        /* |h1| <= 1.01*2^24 */

        Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
            h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
    }
}

impl Fe {
    #[rustfmt::skip]
    pub fn from_bytes(s: &[u8]) -> Fe {
        let mut h0 = load_4i(&s[0..4]);
        let mut h1 = load_3i(&s[4..7]) << 6;
        let mut h2 = load_3i(&s[7..10]) << 5;
        let mut h3 = load_3i(&s[10..13]) << 3;
        let mut h4 = load_3i(&s[13..16]) << 2;
        let mut h5 = load_4i(&s[16..20]);
        let mut h6 = load_3i(&s[20..23]) << 7;
        let mut h7 = load_3i(&s[23..26]) << 5;
        let mut h8 = load_3i(&s[26..29]) << 4;
        let mut h9 = (load_3i(&s[29..32]) & 8388607) << 2;

        let carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
        let carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
        let carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
        let carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
        let carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;

        let carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
        let carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
        let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
        let carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
        let carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;

        Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
            h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
    }

    /*
    Preconditions:
      |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

    Write p=2^255-19; q=floor(h/p).
    Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).

    Proof:
      Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
      Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.

      Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
      Then 0<y<1.

      Write r=h-pq.
      Have 0<=r<=p-1=2^255-20.
      Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.

      Write x=r+19(2^-255)r+y.
      Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.

      Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
      so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
    */

    #[rustfmt::skip]
    pub fn to_bytes(&self) -> [u8; 32] {
        let &Fe(es) = self;
        let mut h0 = es[0];
        let mut h1 = es[1];
        let mut h2 = es[2];
        let mut h3 = es[3];
        let mut h4 = es[4];
        let mut h5 = es[5];
        let mut h6 = es[6];
        let mut h7 = es[7];
        let mut h8 = es[8];
        let mut h9 = es[9];
        let mut q;

        q = (19 * h9 + (1 << 24)) >> 25;
        q = (h0 + q) >> 26;
        q = (h1 + q) >> 25;
        q = (h2 + q) >> 26;
        q = (h3 + q) >> 25;
        q = (h4 + q) >> 26;
        q = (h5 + q) >> 25;
        q = (h6 + q) >> 26;
        q = (h7 + q) >> 25;
        q = (h8 + q) >> 26;
        q = (h9 + q) >> 25;

        /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
        h0 += 19 * q;
        /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */

        let carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
        let carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
        let carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
        let carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
        let carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
        let carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
        let carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
        let carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
        let carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
        let carry9 = h9 >> 25;               h9 -= carry9 << 25;
                            /* h10 = carry9 */

        /*
        Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
        Have h0+...+2^230 h9 between 0 and 2^255-1;
        evidently 2^255 h10-2^255 q = 0.
        Goal: Output h0+...+2^230 h9.
        */
        [
            (h0 >> 0) as u8,
            (h0 >> 8) as u8,
            (h0 >> 16) as u8,
            ((h0 >> 24) | (h1 << 2)) as u8,
            (h1 >> 6) as u8,
            (h1 >> 14) as u8,
            ((h1 >> 22) | (h2 << 3)) as u8,
            (h2 >> 5) as u8,
            (h2 >> 13) as u8,
            ((h2 >> 21) | (h3 << 5)) as u8,
            (h3 >> 3) as u8,
            (h3 >> 11) as u8,
            ((h3 >> 19) | (h4 << 6)) as u8,
            (h4 >> 2) as u8,
            (h4 >> 10) as u8,
            (h4 >> 18) as u8,
            (h5 >> 0) as u8,
            (h5 >> 8) as u8,
            (h5 >> 16) as u8,
            ((h5 >> 24) | (h6 << 1)) as u8,
            (h6 >> 7) as u8,
            (h6 >> 15) as u8,
            ((h6 >> 23) | (h7 << 3)) as u8,
            (h7 >> 5) as u8,
            (h7 >> 13) as u8,
            ((h7 >> 21) | (h8 << 4)) as u8,
            (h8 >> 4) as u8,
            (h8 >> 12) as u8,
            ((h8 >> 20) | (h9 << 6)) as u8,
            (h9 >> 2) as u8,
            (h9 >> 10) as u8,
            (h9 >> 18) as u8,
        ]
    }

    pub fn maybe_swap_with(&mut self, other: &mut Fe, do_swap: i32) {
        let &mut Fe(f) = self;
        let &mut Fe(g) = other;
        let f0 = f[0];
        let f1 = f[1];
        let f2 = f[2];
        let f3 = f[3];
        let f4 = f[4];
        let f5 = f[5];
        let f6 = f[6];
        let f7 = f[7];
        let f8 = f[8];
        let f9 = f[9];
        let g0 = g[0];
        let g1 = g[1];
        let g2 = g[2];
        let g3 = g[3];
        let g4 = g[4];
        let g5 = g[5];
        let g6 = g[6];
        let g7 = g[7];
        let g8 = g[8];
        let g9 = g[9];
        let mut x0 = f0 ^ g0;
        let mut x1 = f1 ^ g1;
        let mut x2 = f2 ^ g2;
        let mut x3 = f3 ^ g3;
        let mut x4 = f4 ^ g4;
        let mut x5 = f5 ^ g5;
        let mut x6 = f6 ^ g6;
        let mut x7 = f7 ^ g7;
        let mut x8 = f8 ^ g8;
        let mut x9 = f9 ^ g9;
        let b = -do_swap;
        x0 &= b;
        x1 &= b;
        x2 &= b;
        x3 &= b;
        x4 &= b;
        x5 &= b;
        x6 &= b;
        x7 &= b;
        x8 &= b;
        x9 &= b;
        *self = Fe([
            f0 ^ x0,
            f1 ^ x1,
            f2 ^ x2,
            f3 ^ x3,
            f4 ^ x4,
            f5 ^ x5,
            f6 ^ x6,
            f7 ^ x7,
            f8 ^ x8,
            f9 ^ x9,
        ]);
        *other = Fe([
            g0 ^ x0,
            g1 ^ x1,
            g2 ^ x2,
            g3 ^ x3,
            g4 ^ x4,
            g5 ^ x5,
            g6 ^ x6,
            g7 ^ x7,
            g8 ^ x8,
            g9 ^ x9,
        ]);
    }

    pub fn maybe_set(&mut self, other: &Fe, do_swap: i32) {
        let &mut Fe(f) = self;
        let &Fe(g) = other;
        let f0 = f[0];
        let f1 = f[1];
        let f2 = f[2];
        let f3 = f[3];
        let f4 = f[4];
        let f5 = f[5];
        let f6 = f[6];
        let f7 = f[7];
        let f8 = f[8];
        let f9 = f[9];
        let g0 = g[0];
        let g1 = g[1];
        let g2 = g[2];
        let g3 = g[3];
        let g4 = g[4];
        let g5 = g[5];
        let g6 = g[6];
        let g7 = g[7];
        let g8 = g[8];
        let g9 = g[9];
        let mut x0 = f0 ^ g0;
        let mut x1 = f1 ^ g1;
        let mut x2 = f2 ^ g2;
        let mut x3 = f3 ^ g3;
        let mut x4 = f4 ^ g4;
        let mut x5 = f5 ^ g5;
        let mut x6 = f6 ^ g6;
        let mut x7 = f7 ^ g7;
        let mut x8 = f8 ^ g8;
        let mut x9 = f9 ^ g9;
        let b = -do_swap;
        x0 &= b;
        x1 &= b;
        x2 &= b;
        x3 &= b;
        x4 &= b;
        x5 &= b;
        x6 &= b;
        x7 &= b;
        x8 &= b;
        x9 &= b;
        *self = Fe([
            f0 ^ x0,
            f1 ^ x1,
            f2 ^ x2,
            f3 ^ x3,
            f4 ^ x4,
            f5 ^ x5,
            f6 ^ x6,
            f7 ^ x7,
            f8 ^ x8,
            f9 ^ x9,
        ]);
    }

    /*
    h = f * 121666
    Can overlap h with f.

    Preconditions:
       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

    Postconditions:
       |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
    */

    #[rustfmt::skip]
    fn mul_121666(&self) -> Fe {
        let &Fe(f) = self;

        let mut h0 = (f[0] as i64) * 121666;
        let mut h1 = (f[1] as i64) * 121666;
        let mut h2 = (f[2] as i64) * 121666;
        let mut h3 = (f[3] as i64) * 121666;
        let mut h4 = (f[4] as i64) * 121666;
        let mut h5 = (f[5] as i64) * 121666;
        let mut h6 = (f[6] as i64) * 121666;
        let mut h7 = (f[7] as i64) * 121666;
        let mut h8 = (f[8] as i64) * 121666;
        let mut h9 = (f[9] as i64) * 121666;

        let carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
        let carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
        let carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
        let carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
        let carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;

        let carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
        let carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
        let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
        let carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
        let carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;

        Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
            h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
    }

    /*
    h = f * f
    Can overlap h with f.

    Preconditions:
       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

    Postconditions:
       |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
    */

    /*
    See fe_mul.c for discussion of implementation strategy.
    */
    #[rustfmt::skip]
    fn square(&self) -> Fe {
        let &Fe(f) = self;

        let f0 = f[0];
        let f1 = f[1];
        let f2 = f[2];
        let f3 = f[3];
        let f4 = f[4];
        let f5 = f[5];
        let f6 = f[6];
        let f7 = f[7];
        let f8 = f[8];
        let f9 = f[9];
        let f0_2 = 2 * f0;
        let f1_2 = 2 * f1;
        let f2_2 = 2 * f2;
        let f3_2 = 2 * f3;
        let f4_2 = 2 * f4;
        let f5_2 = 2 * f5;
        let f6_2 = 2 * f6;
        let f7_2 = 2 * f7;
        let f5_38 = 38 * f5; /* 1.31*2^30 */
        let f6_19 = 19 * f6; /* 1.31*2^30 */
        let f7_38 = 38 * f7; /* 1.31*2^30 */
        let f8_19 = 19 * f8; /* 1.31*2^30 */
        let f9_38 = 38 * f9; /* 1.31*2^30 */
        let f0f0    = (f0   as i64) * (f0 as i64);
        let f0f1_2  = (f0_2 as i64) * (f1 as i64);
        let f0f2_2  = (f0_2 as i64) * (f2 as i64);
        let f0f3_2  = (f0_2 as i64) * (f3 as i64);
        let f0f4_2  = (f0_2 as i64) * (f4 as i64);
        let f0f5_2  = (f0_2 as i64) * (f5 as i64);
        let f0f6_2  = (f0_2 as i64) * (f6 as i64);
        let f0f7_2  = (f0_2 as i64) * (f7 as i64);
        let f0f8_2  = (f0_2 as i64) * (f8 as i64);
        let f0f9_2  = (f0_2 as i64) * (f9 as i64);
        let f1f1_2  = (f1_2 as i64) * (f1 as i64);
        let f1f2_2  = (f1_2 as i64) * (f2 as i64);
        let f1f3_4  = (f1_2 as i64) * (f3_2 as i64);
        let f1f4_2  = (f1_2 as i64) * (f4 as i64);
        let f1f5_4  = (f1_2 as i64) * (f5_2 as i64);
        let f1f6_2  = (f1_2 as i64) * (f6 as i64);
        let f1f7_4  = (f1_2 as i64) * (f7_2 as i64);
        let f1f8_2  = (f1_2 as i64) * (f8 as i64);
        let f1f9_76 = (f1_2 as i64) * (f9_38 as i64);
        let f2f2    = (f2   as i64) * (f2 as i64);
        let f2f3_2  = (f2_2 as i64) * (f3 as i64);
        let f2f4_2  = (f2_2 as i64) * (f4 as i64);
        let f2f5_2  = (f2_2 as i64) * (f5 as i64);
        let f2f6_2  = (f2_2 as i64) * (f6 as i64);
        let f2f7_2  = (f2_2 as i64) * (f7 as i64);
        let f2f8_38 = (f2_2 as i64) * (f8_19 as i64);
        let f2f9_38 = (f2   as i64) * (f9_38 as i64);
        let f3f3_2  = (f3_2 as i64) * (f3 as i64);
        let f3f4_2  = (f3_2 as i64) * (f4 as i64);
        let f3f5_4  = (f3_2 as i64) * (f5_2 as i64);
        let f3f6_2  = (f3_2 as i64) * (f6 as i64);
        let f3f7_76 = (f3_2 as i64) * (f7_38 as i64);
        let f3f8_38 = (f3_2 as i64) * (f8_19 as i64);
        let f3f9_76 = (f3_2 as i64) * (f9_38 as i64);
        let f4f4    = (f4   as i64) * (f4 as i64);
        let f4f5_2  = (f4_2 as i64) * (f5 as i64);
        let f4f6_38 = (f4_2 as i64) * (f6_19 as i64);
        let f4f7_38 = (f4   as i64) * (f7_38 as i64);
        let f4f8_38 = (f4_2 as i64) * (f8_19 as i64);
        let f4f9_38 = (f4   as i64) * (f9_38 as i64);
        let f5f5_38 = (f5   as i64) * (f5_38 as i64);
        let f5f6_38 = (f5_2 as i64) * (f6_19 as i64);
        let f5f7_76 = (f5_2 as i64) * (f7_38 as i64);
        let f5f8_38 = (f5_2 as i64) * (f8_19 as i64);
        let f5f9_76 = (f5_2 as i64) * (f9_38 as i64);
        let f6f6_19 = (f6   as i64) * (f6_19 as i64);
        let f6f7_38 = (f6   as i64) * (f7_38 as i64);
        let f6f8_38 = (f6_2 as i64) * (f8_19 as i64);
        let f6f9_38 = (f6   as i64) * (f9_38 as i64);
        let f7f7_38 = (f7   as i64) * (f7_38 as i64);
        let f7f8_38 = (f7_2 as i64) * (f8_19 as i64);
        let f7f9_76 = (f7_2 as i64) * (f9_38 as i64);
        let f8f8_19 = (f8   as i64) * (f8_19 as i64);
        let f8f9_38 = (f8   as i64) * (f9_38 as i64);
        let f9f9_38 = (f9   as i64) * (f9_38 as i64);
        let mut h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
        let mut h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
        let mut h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
        let mut h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
        let mut h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
        let mut h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
        let mut h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
        let mut h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
        let mut h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
        let mut h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;

        let carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
        let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;

        let carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
        let carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;

        let carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
        let carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;

        let carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
        let carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;

        let carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
        let carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;

        let carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;

        let carrya = (h0 + (1<<25)) >> 26; h1 += carrya; h0 -= carrya << 26;

        Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
            h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
    }

    #[rustfmt::skip]
    fn square_and_double(&self) -> Fe {
        let &Fe(f) = self;

        let f0 = f[0];
        let f1 = f[1];
        let f2 = f[2];
        let f3 = f[3];
        let f4 = f[4];
        let f5 = f[5];
        let f6 = f[6];
        let f7 = f[7];
        let f8 = f[8];
        let f9 = f[9];
        let f0_2 = 2 * f0;
        let f1_2 = 2 * f1;
        let f2_2 = 2 * f2;
        let f3_2 = 2 * f3;
        let f4_2 = 2 * f4;
        let f5_2 = 2 * f5;
        let f6_2 = 2 * f6;
        let f7_2 = 2 * f7;
        let f5_38 = 38 * f5; /* 1.959375*2^30 */
        let f6_19 = 19 * f6; /* 1.959375*2^30 */
        let f7_38 = 38 * f7; /* 1.959375*2^30 */
        let f8_19 = 19 * f8; /* 1.959375*2^30 */
        let f9_38 = 38 * f9; /* 1.959375*2^30 */
        let f0f0    = (f0    as i64) * (f0 as i64);
        let f0f1_2  = (f0_2  as i64) * (f1 as i64);
        let f0f2_2  = (f0_2  as i64) * (f2 as i64);
        let f0f3_2  = (f0_2  as i64) * (f3 as i64);
        let f0f4_2  = (f0_2  as i64) * (f4 as i64);
        let f0f5_2  = (f0_2  as i64) * (f5 as i64);
        let f0f6_2  = (f0_2  as i64) * (f6 as i64);
        let f0f7_2  = (f0_2  as i64) * (f7 as i64);
        let f0f8_2  = (f0_2  as i64) * (f8 as i64);
        let f0f9_2  = (f0_2  as i64) * (f9 as i64);
        let f1f1_2  = (f1_2  as i64) * (f1 as i64);
        let f1f2_2  = (f1_2  as i64) * (f2 as i64);
        let f1f3_4  = (f1_2  as i64) * (f3_2 as i64);
        let f1f4_2  = (f1_2  as i64) * (f4 as i64);
        let f1f5_4  = (f1_2  as i64) * (f5_2 as i64);
        let f1f6_2  = (f1_2  as i64) * (f6 as i64);
        let f1f7_4  = (f1_2  as i64) * (f7_2 as i64);
        let f1f8_2  = (f1_2  as i64) * (f8 as i64);
        let f1f9_76 = (f1_2  as i64) * (f9_38 as i64);
        let f2f2    = (f2    as i64) * (f2 as i64);
        let f2f3_2  = (f2_2  as i64) * (f3 as i64);
        let f2f4_2  = (f2_2  as i64) * (f4 as i64);
        let f2f5_2  = (f2_2  as i64) * (f5 as i64);
        let f2f6_2  = (f2_2  as i64) * (f6 as i64);
        let f2f7_2  = (f2_2  as i64) * (f7 as i64);
        let f2f8_38 = (f2_2  as i64) * (f8_19 as i64);
        let f2f9_38 = (f2    as i64) * (f9_38 as i64);
        let f3f3_2  = (f3_2  as i64) * (f3 as i64);
        let f3f4_2  = (f3_2  as i64) * (f4 as i64);
        let f3f5_4  = (f3_2  as i64) * (f5_2 as i64);
        let f3f6_2  = (f3_2  as i64) * (f6 as i64);
        let f3f7_76 = (f3_2  as i64) * (f7_38 as i64);
        let f3f8_38 = (f3_2  as i64) * (f8_19 as i64);
        let f3f9_76 = (f3_2  as i64) * (f9_38 as i64);
        let f4f4    = (f4    as i64) * (f4 as i64);
        let f4f5_2  = (f4_2  as i64) * (f5 as i64);
        let f4f6_38 = (f4_2  as i64) * (f6_19 as i64);
        let f4f7_38 = (f4    as i64) * (f7_38 as i64);
        let f4f8_38 = (f4_2  as i64) * (f8_19 as i64);
        let f4f9_38 = (f4    as i64) * (f9_38 as i64);
        let f5f5_38 = (f5    as i64) * (f5_38 as i64);
        let f5f6_38 = (f5_2  as i64) * (f6_19 as i64);
        let f5f7_76 = (f5_2  as i64) * (f7_38 as i64);
        let f5f8_38 = (f5_2  as i64) * (f8_19 as i64);
        let f5f9_76 = (f5_2  as i64) * (f9_38 as i64);
        let f6f6_19 = (f6    as i64) * (f6_19 as i64);
        let f6f7_38 = (f6    as i64) * (f7_38 as i64);
        let f6f8_38 = (f6_2  as i64) * (f8_19 as i64);
        let f6f9_38 = (f6    as i64) * (f9_38 as i64);
        let f7f7_38 = (f7    as i64) * (f7_38 as i64);
        let f7f8_38 = (f7_2  as i64) * (f8_19 as i64);
        let f7f9_76 = (f7_2  as i64) * (f9_38 as i64);
        let f8f8_19 = (f8    as i64) * (f8_19 as i64);
        let f8f9_38 = (f8    as i64) * (f9_38 as i64);
        let f9f9_38 = (f9    as i64) * (f9_38 as i64);
        let mut h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
        let mut h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
        let mut h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
        let mut h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
        let mut h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
        let mut h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
        let mut h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
        let mut h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
        let mut h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
        let mut h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
        let mut carry0: i64;
        let carry1: i64;
        let carry2: i64;
        let carry3: i64;
        let mut carry4: i64;
        let carry5: i64;
        let carry6: i64;
        let carry7: i64;
        let carry8: i64;
        let carry9: i64;

        h0 += h0;
        h1 += h1;
        h2 += h2;
        h3 += h3;
        h4 += h4;
        h5 += h5;
        h6 += h6;
        h7 += h7;
        h8 += h8;
        h9 += h9;

        carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
        carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;

        carry1 = (h1 + (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
        carry5 = (h5 + (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;

        carry2 = (h2 + (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
        carry6 = (h6 + (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;

        carry3 = (h3 + (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
        carry7 = (h7 + (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;

        carry4 = (h4 + (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
        carry8 = (h8 + (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;

        carry9 = (h9 + (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;

        carry0 = (h0 + (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;

        Fe([h0 as i32, h1 as i32, h2 as i32, h3 as i32, h4 as i32,
            h5 as i32, h6 as i32, h7 as i32, h8 as i32, h9 as i32])
    }

    pub fn invert(&self) -> Fe {
        let z1 = self.clone();

        /* qhasm: z2 = z1^2^1 */
        let z2 = z1.square();
        /* qhasm: z8 = z2^2^2 */
        let z8 = z2.square().square();
        /* qhasm: z9 = z1*z8 */
        let z9 = z1 * z8;

        /* qhasm: z11 = z2*z9 */
        let z11 = &z2 * &z9;

        /* qhasm: z22 = z11^2^1 */
        let z22 = z11.square();

        /* qhasm: z_5_0 = z9*z22 */
        let z_5_0 = &z9 * &z22;

        /* qhasm: z_10_5 = z_5_0^2^5 */
        let z_10_5 = (0..5).fold(z_5_0.clone(), |z_5_n, _| z_5_n.square());

        /* qhasm: z_10_0 = z_10_5*z_5_0 */
        let z_10_0 = &z_10_5 * &z_5_0;

        /* qhasm: z_20_10 = z_10_0^2^10 */
        let z_20_10 = (0..10).fold(z_10_0.clone(), |x, _| x.square());

        /* qhasm: z_20_0 = z_20_10*z_10_0 */
        let z_20_0 = &z_20_10 * &z_10_0;

        /* qhasm: z_40_20 = z_20_0^2^20 */
        let z_40_20 = (0..20).fold(z_20_0.clone(), |x, _| x.square());

        /* qhasm: z_40_0 = z_40_20*z_20_0 */
        let z_40_0 = &z_40_20 * &z_20_0;

        /* qhasm: z_50_10 = z_40_0^2^10 */
        let z_50_10 = (0..10).fold(z_40_0, |x, _| x.square());

        /* qhasm: z_50_0 = z_50_10*z_10_0 */
        let z_50_0 = &z_50_10 * &z_10_0;

        /* qhasm: z_100_50 = z_50_0^2^50 */
        let z_100_50 = (0..50).fold(z_50_0.clone(), |x, _| x.square());

        /* qhasm: z_100_0 = z_100_50*z_50_0 */
        let z_100_0 = &z_100_50 * &z_50_0;

        /* qhasm: z_200_100 = z_100_0^2^100 */
        let z_200_100 = (0..100).fold(z_100_0.clone(), |x, _| x.square());

        /* qhasm: z_200_0 = z_200_100*z_100_0 */
        /* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
        /* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
        let z_200_0 = &z_200_100 * &z_100_0;

        /* qhasm: z_250_50 = z_200_0^2^50 */
        let z_250_50 = (0..50).fold(z_200_0, |x, _| x.square());

        /* qhasm: z_250_0 = z_250_50*z_50_0 */
        let z_250_0 = &z_250_50 * &z_50_0;

        /* qhasm: z_255_5 = z_250_0^2^5 */
        let z_255_5 = (0..5).fold(z_250_0, |x, _| x.square());

        /* qhasm: z_255_21 = z_255_5*z11 */
        /* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
        /* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
        let z_255_21 = z_255_5 * z11;

        z_255_21
    }

    fn is_nonzero(&self) -> bool {
        let bs = self.to_bytes();
        let zero = [0; 32];
        !fixed_time_eq(bs.as_ref(), zero.as_ref())
    }

    fn is_negative(&self) -> bool {
        (self.to_bytes()[0] & 1) != 0
    }

    fn neg(&self) -> Fe {
        let &Fe(f) = self;
        Fe([
            -f[0], -f[1], -f[2], -f[3], -f[4], -f[5], -f[6], -f[7], -f[8], -f[9],
        ])
    }

    fn pow25523(&self) -> Fe {
        let z2 = self.square();
        let z8 = (0..2).fold(z2.clone(), |x, _| x.square());
        let z9 = self.clone() * z8;
        let z11 = &z2 * &z9;
        let z22 = z11.square();
        let z_5_0 = &z9 * &z22;
        let z_10_5 = (0..5).fold(z_5_0.clone(), |x, _| x.square());
        let z_10_0 = &z_10_5 * &z_5_0;
        let z_20_10 = (0..10).fold(z_10_0.clone(), |x, _| x.square());
        let z_20_0 = &z_20_10 * &z_10_0;
        let z_40_20 = (0..20).fold(z_20_0.clone(), |x, _| x.square());
        let z_40_0 = &z_40_20 * &z_20_0;
        let z_50_10 = (0..10).fold(z_40_0, |x, _| x.square());
        let z_50_0 = &z_50_10 * &z_10_0;
        let z_100_50 = (0..50).fold(z_50_0.clone(), |x, _| x.square());
        let z_100_0 = &z_100_50 * &z_50_0;
        let z_200_100 = (0..100).fold(z_100_0.clone(), |x, _| x.square());
        let z_200_0 = &z_200_100 * &z_100_0;
        let z_250_50 = (0..50).fold(z_200_0, |x, _| x.square());
        let z_250_0 = &z_250_50 * &z_50_0;
        let z_252_2 = (0..2).fold(z_250_0, |x, _| x.square());
        let z_252_3 = z_252_2 * self.clone();

        z_252_3
    }
}

#[derive(Clone)]
pub struct GeP2 {
    x: Fe,
    y: Fe,
    z: Fe,
}

#[derive(Clone)]
pub struct GeP3 {
    x: Fe,
    y: Fe,
    z: Fe,
    t: Fe,
}

#[derive(Clone)]
pub struct GeP1P1 {
    x: Fe,
    y: Fe,
    z: Fe,
    t: Fe,
}

#[derive(Clone)]
pub struct GePrecomp {
    y_plus_x: Fe,
    y_minus_x: Fe,
    xy2d: Fe,
}

#[derive(Clone)]
pub struct GeCached {
    y_plus_x: Fe,
    y_minus_x: Fe,
    z: Fe,
    t2d: Fe,
}

impl GeP1P1 {
    pub fn to_p2(&self) -> GeP2 {
        GeP2 {
            x: &self.x * &self.t,
            y: &self.y * &self.z,
            z: &self.z * &self.t,
        }
    }

    fn to_p3(&self) -> GeP3 {
        GeP3 {
            x: &self.x * &self.t,
            y: &self.y * &self.z,
            z: &self.z * &self.t,
            t: &self.x * &self.y,
        }
    }
}

impl GeP2 {
    fn zero() -> GeP2 {
        GeP2 {
            x: FE_ZERO.clone(),
            y: FE_ONE.clone(),
            z: FE_ONE.clone(),
        }
    }

    pub fn to_bytes(&self) -> [u8; 32] {
        let recip = self.z.invert();
        let x = &self.x * &recip;
        let y = &self.y * &recip;
        let mut bs = y.to_bytes();
        bs[31] ^= (if x.is_negative() { 1 } else { 0 }) << 7;
        bs
    }

    fn dbl(&self) -> GeP1P1 {
        let xx = self.x.square();
        let yy = self.y.square();
        let b = self.z.square_and_double();
        let a = &self.x + &self.y;
        let aa = a.square();
        let y3 = &yy + &xx;
        let z3 = &yy - &xx;
        let x3 = &aa - &y3;
        let t3 = &b - &z3;

        GeP1P1 {
            x: x3,
            y: y3,
            z: z3,
            t: t3,
        }
    }

    #[allow(clippy::needless_range_loop)]
    fn slide(a: &[u8]) -> [i8; 256] {
        let mut r = [0i8; 256];
        for i in 0..256 {
            r[i] = (1 & (a[i >> 3] >> (i & 7))) as i8;
        }
        for i in 0..256 {
            if r[i] != 0 {
                for b in 1..min(7, 256 - i) {
                    if r[i + b] != 0 {
                        if r[i] + (r[i + b] << b) <= 15 {
                            r[i] += r[i + b] << b;
                            r[i + b] = 0;
                        } else if r[i] - (r[i + b] << b) >= -15 {
                            r[i] -= r[i + b] << b;
                            for k in i + b..256 {
                                if r[k] == 0 {
                                    r[k] = 1;
                                    break;
                                }
                                r[k] = 0;
                            }
                        } else {
                            break;
                        }
                    }
                }
            }
        }

        r
    }

    /*
    r = a * A + b * B
    where a = a[0]+256*a[1]+...+256^31 a[31].
    and b = b[0]+256*b[1]+...+256^31 b[31].
    B is the Ed25519 base point (x,4/5) with x positive.
    */
    pub fn double_scalarmult_vartime(a_scalar: &[u8], a_point: GeP3, b_scalar: &[u8]) -> GeP2 {
        let aslide = GeP2::slide(a_scalar);
        let bslide = GeP2::slide(b_scalar);

        let a1 = a_point.to_cached();
        let a2 = a_point.dbl().to_p3();
        let a3 = (&a2 + &a1).to_p3().to_cached();
        let a5 = (&a2 + &a3).to_p3().to_cached();
        let a7 = (&a2 + &a5).to_p3().to_cached();
        let a9 = (&a2 + &a7).to_p3().to_cached();
        let a11 = (&a2 + &a9).to_p3().to_cached();
        let a13 = (&a2 + &a11).to_p3().to_cached();
        let a15 = (&a2 + &a13).to_p3().to_cached();

        let ai: [GeCached; 8] = [a1, a3, a5, a7, a9, a11, a13, a15];

        let mut r = GeP2::zero();

        let mut i: usize = 255;
        loop {
            if aslide[i] != 0 || bslide[i] != 0 {
                break;
            }
            if i == 0 {
                return r;
            }
            i -= 1;
        }

        loop {
            let mut t = r.dbl();
            match aslide[i].cmp(&0) {
                Ordering::Greater => t = &t.to_p3() + &ai[(aslide[i] / 2) as usize],
                Ordering::Less => t = &t.to_p3() - &ai[(-aslide[i] / 2) as usize],
                Ordering::Equal => {}
            }

            match bslide[i].cmp(&0) {
                Ordering::Greater => t = &t.to_p3() + &BI[(bslide[i] / 2) as usize],
                Ordering::Less => t = &t.to_p3() - &BI[(-bslide[i] / 2) as usize],
                Ordering::Equal => {}
            }

            r = t.to_p2();

            if i == 0 {
                return r;
            }
            i -= 1;
        }
    }
}

impl GeP3 {
    pub fn from_bytes_negate_vartime(s: &[u8]) -> Option<GeP3> {
        let y = Fe::from_bytes(s);
        let z = FE_ONE.clone();
        let y_squared = y.square();
        let u = &y_squared - &FE_ONE;
        let v = &(&y_squared * &FE_D) + &FE_ONE;
        let v_raise_3 = &v.square() * &v;
        let v_raise_7 = &v_raise_3.square() * &v;
        let uv7 = &v_raise_7 * &u; // Is this commutative? u comes second in the code, but not in the notation...

        let mut x = &(&uv7.pow25523() * &v_raise_3) * &u;

        let vxx = x.square() * v;
        let check = &vxx - &u;
        if check.is_nonzero() {
            let check2 = vxx + u;
            if check2.is_nonzero() {
                return None;
            }
            x = &x * &FE_SQRTM1;
        }

        if x.is_negative() == ((s[31] >> 7) != 0) {
            x = x.neg();
        }

        let t = &x * &y;

        Some(GeP3 {
            x: x,
            y: y,
            z: z,
            t: t,
        })
    }

    fn to_p2(&self) -> GeP2 {
        GeP2 {
            x: self.x.clone(),
            y: self.y.clone(),
            z: self.z.clone(),
        }
    }

    pub fn to_cached(&self) -> GeCached {
        GeCached {
            y_plus_x: &self.y + &self.x,
            y_minus_x: &self.y - &self.x,
            z: self.z.clone(),
            t2d: &self.t * &FE_D2,
        }
    }

    fn zero() -> GeP3 {
        GeP3 {
            x: FE_ZERO.clone(),
            y: FE_ONE.clone(),
            z: FE_ONE.clone(),
            t: FE_ZERO.clone(),
        }
    }

    fn dbl(&self) -> GeP1P1 {
        self.to_p2().dbl()
    }

    pub fn to_bytes(&self) -> [u8; 32] {
        let recip = self.z.invert();
        let x = &self.x * &recip;
        let y = &self.y * &recip;
        let mut bs = y.to_bytes();
        bs[31] ^= (if x.is_negative() { 1 } else { 0 }) << 7;
        bs
    }
}

impl Add<GeCached> for GeP3 {
    type Output = GeP1P1;
    fn add(self, rhs: GeCached) -> GeP1P1 {
        &self + &rhs
    }
}

impl Add<&GeCached> for &GeP3 {
    type Output = GeP1P1;

    #[allow(clippy::suspicious_arithmetic_impl)]
    fn add(self, _rhs: &GeCached) -> GeP1P1 {
        let y1_plus_x1 = &self.y + &self.x;
        let y1_minus_x1 = &self.y - &self.x;
        let a = &y1_plus_x1 * &_rhs.y_plus_x;
        let b = &y1_minus_x1 * &_rhs.y_minus_x;
        let c = &_rhs.t2d * &self.t;
        let zz = &self.z * &_rhs.z;
        let d = &zz + &zz;
        let x3 = &a - &b;
        let y3 = &a + &b;
        let z3 = &d + &c;
        let t3 = &d - &c;

        GeP1P1 {
            x: x3,
            y: y3,
            z: z3,
            t: t3,
        }
    }
}

impl Add<GePrecomp> for GeP3 {
    type Output = GeP1P1;

    fn add(self, rhs: GePrecomp) -> GeP1P1 {
        &self + &rhs
    }
}

impl Add<&GePrecomp> for &GeP3 {
    type Output = GeP1P1;

    #[allow(clippy::suspicious_arithmetic_impl)]
    fn add(self, _rhs: &GePrecomp) -> GeP1P1 {
        let y1_plus_x1 = &self.y + &self.x;
        let y1_minus_x1 = &self.y - &self.x;
        let a = &y1_plus_x1 * &_rhs.y_plus_x;
        let b = &y1_minus_x1 * &_rhs.y_minus_x;
        let c = &_rhs.xy2d * &self.t;
        let d = &self.z + &self.z;
        let x3 = &a - &b;
        let y3 = &a + &b;
        let z3 = &d + &c;
        let t3 = &d - &c;

        GeP1P1 {
            x: x3,
            y: y3,
            z: z3,
            t: t3,
        }
    }
}

impl Sub<GeCached> for GeP3 {
    type Output = GeP1P1;

    fn sub(self, rhs: GeCached) -> GeP1P1 {
        &self - &rhs
    }
}

impl Sub<&GeCached> for &GeP3 {
    type Output = GeP1P1;

    #[allow(clippy::suspicious_arithmetic_impl)]
    fn sub(self, _rhs: &GeCached) -> GeP1P1 {
        let y1_plus_x1 = &self.y + &self.x;
        let y1_minus_x1 = &self.y - &self.x;
        let a = &y1_plus_x1 * &_rhs.y_minus_x;
        let b = &y1_minus_x1 * &_rhs.y_plus_x;
        let c = &_rhs.t2d * &self.t;
        let zz = &self.z * &_rhs.z;
        let d = &zz + &zz;
        let x3 = &a - &b;
        let y3 = &a + &b;
        let z3 = &d - &c;
        let t3 = &d + &c;

        GeP1P1 {
            x: x3,
            y: y3,
            z: z3,
            t: t3,
        }
    }
}

impl Sub<GePrecomp> for GeP3 {
    type Output = GeP1P1;

    fn sub(self, rhs: GePrecomp) -> GeP1P1 {
        &self - &rhs
    }
}

impl Sub<&GePrecomp> for &GeP3 {
    type Output = GeP1P1;

    #[allow(clippy::suspicious_arithmetic_impl)]
    fn sub(self, _rhs: &GePrecomp) -> GeP1P1 {
        let y1_plus_x1 = &self.y + &self.x;
        let y1_minus_x1 = &self.y - &self.x;
        let a = &y1_plus_x1 * &_rhs.y_minus_x;
        let b = &y1_minus_x1 * &_rhs.y_plus_x;
        let c = &_rhs.xy2d * &self.t;
        let d = &self.z + &self.z;
        let x3 = &a - &b;
        let y3 = &a + &b;
        let z3 = &d - &c;
        let t3 = &d + &c;

        GeP1P1 {
            x: x3,
            y: y3,
            z: z3,
            t: t3,
        }
    }
}

fn equal(b: u8, c: u8) -> i32 {
    let x = b ^ c; /* 0: yes; 1..255: no */
    let mut y = x as u32; /* 0: yes; 1..255: no */
    y = y.wrapping_sub(1); /* 4294967295: yes; 0..254: no */
    y >>= 31; /* 1: yes; 0: no */
    y as i32
}

impl GePrecomp {
    fn zero() -> GePrecomp {
        GePrecomp {
            y_plus_x: FE_ONE.clone(),
            y_minus_x: FE_ONE.clone(),
            xy2d: FE_ZERO.clone(),
        }
    }

    pub fn maybe_set(&mut self, other: &GePrecomp, do_swap: i32) {
        self.y_plus_x.maybe_set(&other.y_plus_x, do_swap);
        self.y_minus_x.maybe_set(&other.y_minus_x, do_swap);
        self.xy2d.maybe_set(&other.xy2d, do_swap);
    }

    pub fn select(pos: usize, b: i8) -> GePrecomp {
        let bnegative = (b as u8) >> 7;
        let babs: u8 = (b - (((-(bnegative as i8)) & b) << 1)) as u8;
        let mut t = GePrecomp::zero();
        t.maybe_set(&GE_PRECOMP_BASE[pos][0], equal(babs, 1));
        t.maybe_set(&GE_PRECOMP_BASE[pos][1], equal(babs, 2));
        t.maybe_set(&GE_PRECOMP_BASE[pos][2], equal(babs, 3));
        t.maybe_set(&GE_PRECOMP_BASE[pos][3], equal(babs, 4));
        t.maybe_set(&GE_PRECOMP_BASE[pos][4], equal(babs, 5));
        t.maybe_set(&GE_PRECOMP_BASE[pos][5], equal(babs, 6));
        t.maybe_set(&GE_PRECOMP_BASE[pos][6], equal(babs, 7));
        t.maybe_set(&GE_PRECOMP_BASE[pos][7], equal(babs, 8));
        let minus_t = GePrecomp {
            y_plus_x: t.y_minus_x.clone(),
            y_minus_x: t.y_plus_x.clone(),
            xy2d: t.xy2d.neg(),
        };
        t.maybe_set(&minus_t, bnegative as i32);
        t
    }
}

/*
h = a * B
where a = a[0]+256*a[1]+...+256^31 a[31]
B is the Ed25519 base point (x,4/5) with x positive.

Preconditions:
  a[31] <= 127
*/
pub fn ge_scalarmult_base(a: &[u8]) -> GeP3 {
    let mut es: [i8; 64] = [0; 64];
    let mut r: GeP1P1;
    let mut s: GeP2;
    let mut t: GePrecomp;

    for i in 0..32 {
        es[2 * i + 0] = ((a[i] >> 0) & 15) as i8;
        es[2 * i + 1] = ((a[i] >> 4) & 15) as i8;
    }
    /* each es[i] is between 0 and 15 */
    /* es[63] is between 0 and 7 */

    let mut carry: i8 = 0;
    for esi in es[0..63].iter_mut() {
        *esi += carry;
        carry = *esi + 8;
        carry >>= 4;
        *esi -= carry << 4;
    }
    es[63] += carry;
    /* each es[i] is between -8 and 8 */

    let mut h = GeP3::zero();
    for j in 0..32 {
        let i = j * 2 + 1;
        t = GePrecomp::select(j, es[i]);
        r = h + t;
        h = r.to_p3();
    }

    r = h.dbl();
    s = r.to_p2();
    r = s.dbl();
    s = r.to_p2();
    r = s.dbl();
    s = r.to_p2();
    r = s.dbl();
    h = r.to_p3();

    for j in 0..32 {
        let i = j * 2;
        t = GePrecomp::select(j, es[i]);
        r = h + t;
        h = r.to_p3();
    }

    h
}
/*
Input:
    s[0]+256*s[1]+...+256^63*s[63] = s

Output:
    s[0]+256*s[1]+...+256^31*s[31] = s mod l
    where l = 2^252 + 27742317777372353535851937790883648493.
    Overwrites s in place.
*/
#[rustfmt::skip]
pub fn sc_reduce(s: &mut [u8]) {
    let mut s0: i64 = 2097151 & load_3i(s);
    let mut s1: i64 = 2097151 & (load_4i(&s[2..6]) >> 5);
    let mut s2: i64 = 2097151 & (load_3i(&s[5..8]) >> 2);
    let mut s3: i64 = 2097151 & (load_4i(&s[7..11]) >> 7);
    let mut s4: i64 = 2097151 & (load_4i(&s[10..14]) >> 4);
    let mut s5: i64 = 2097151 & (load_3i(&s[13..16]) >> 1);
    let mut s6: i64 = 2097151 & (load_4i(&s[15..19]) >> 6);
    let mut s7: i64 = 2097151 & (load_3i(&s[18..21]) >> 3);
    let mut s8: i64 = 2097151 & load_3i(&s[21..24]);
    let mut s9: i64 = 2097151 & (load_4i(&s[23..27]) >> 5);
    let mut s10: i64 = 2097151 & (load_3i(&s[26..29]) >> 2);
    let mut s11: i64 = 2097151 & (load_4i(&s[28..32]) >> 7);
    let mut s12: i64 = 2097151 & (load_4i(&s[31..35]) >> 4);
    let mut s13: i64 = 2097151 & (load_3i(&s[34..37]) >> 1);
    let mut s14: i64 = 2097151 & (load_4i(&s[36..40]) >> 6);
    let mut s15: i64 = 2097151 & (load_3i(&s[39..42]) >> 3);
    let mut s16: i64 = 2097151 & load_3i(&s[42..45]);
    let mut s17: i64 = 2097151 & (load_4i(&s[44..48]) >> 5);
    let s18: i64 = 2097151 & (load_3i(&s[47..50]) >> 2);
    let s19: i64 = 2097151 & (load_4i(&s[49..53]) >> 7);
    let s20: i64 = 2097151 & (load_4i(&s[52..56]) >> 4);
    let s21: i64 = 2097151 & (load_3i(&s[55..58]) >> 1);
    let s22: i64 = 2097151 & (load_4i(&s[57..61]) >> 6);
    let s23: i64 = load_4i(&s[60..64]) >> 3;
    let mut carry0: i64;
    let mut carry1: i64;
    let mut carry2: i64;
    let mut carry3: i64;
    let mut carry4: i64;
    let mut carry5: i64;
    let mut carry6: i64;
    let mut carry7: i64;
    let mut carry8: i64;
    let mut carry9: i64;
    let mut carry10: i64;
    let mut carry11: i64;
    let carry12: i64;
    let carry13: i64;
    let carry14: i64;
    let carry15: i64;
    let carry16: i64;

    s11 += s23 * 666643;
    s12 += s23 * 470296;
    s13 += s23 * 654183;
    s14 -= s23 * 997805;
    s15 += s23 * 136657;
    s16 -= s23 * 683901;


    s10 += s22 * 666643;
    s11 += s22 * 470296;
    s12 += s22 * 654183;
    s13 -= s22 * 997805;
    s14 += s22 * 136657;
    s15 -= s22 * 683901;


    s9 += s21 * 666643;
    s10 += s21 * 470296;
    s11 += s21 * 654183;
    s12 -= s21 * 997805;
    s13 += s21 * 136657;
    s14 -= s21 * 683901;


    s8 += s20 * 666643;
    s9 += s20 * 470296;
    s10 += s20 * 654183;
    s11 -= s20 * 997805;
    s12 += s20 * 136657;
    s13 -= s20 * 683901;


    s7 += s19 * 666643;
    s8 += s19 * 470296;
    s9 += s19 * 654183;
    s10 -= s19 * 997805;
    s11 += s19 * 136657;
    s12 -= s19 * 683901;


    s6 += s18 * 666643;
    s7 += s18 * 470296;
    s8 += s18 * 654183;
    s9 -= s18 * 997805;
    s10 += s18 * 136657;
    s11 -= s18 * 683901;


    carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
    carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
    carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
    carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
    carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
    carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;

    carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
    carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
    carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
    carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
    carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;

    s5 += s17 * 666643;
    s6 += s17 * 470296;
    s7 += s17 * 654183;
    s8 -= s17 * 997805;
    s9 += s17 * 136657;
    s10 -= s17 * 683901;


    s4 += s16 * 666643;
    s5 += s16 * 470296;
    s6 += s16 * 654183;
    s7 -= s16 * 997805;
    s8 += s16 * 136657;
    s9 -= s16 * 683901;


    s3 += s15 * 666643;
    s4 += s15 * 470296;
    s5 += s15 * 654183;
    s6 -= s15 * 997805;
    s7 += s15 * 136657;
    s8 -= s15 * 683901;


    s2 += s14 * 666643;
    s3 += s14 * 470296;
    s4 += s14 * 654183;
    s5 -= s14 * 997805;
    s6 += s14 * 136657;
    s7 -= s14 * 683901;


    s1 += s13 * 666643;
    s2 += s13 * 470296;
    s3 += s13 * 654183;
    s4 -= s13 * 997805;
    s5 += s13 * 136657;
    s6 -= s13 * 683901;


    s0 += s12 * 666643;
    s1 += s12 * 470296;
    s2 += s12 * 654183;
    s3 -= s12 * 997805;
    s4 += s12 * 136657;
    s5 -= s12 * 683901;
    s12 = 0;

    carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
    carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
    carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
    carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
    carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
    carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;

    carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
    carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
    carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
    carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
    carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
    carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;

    s0 += s12 * 666643;
    s1 += s12 * 470296;
    s2 += s12 * 654183;
    s3 -= s12 * 997805;
    s4 += s12 * 136657;
    s5 -= s12 * 683901;
    s12 = 0;

    carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
    carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
    carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
    carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
    carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
    carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
    carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
    carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
    carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
    carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
    carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
    carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;

    s0 += s12 * 666643;
    s1 += s12 * 470296;
    s2 += s12 * 654183;
    s3 -= s12 * 997805;
    s4 += s12 * 136657;
    s5 -= s12 * 683901;


    carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
    carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
    carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
    carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
    carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
    carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
    carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
    carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
    carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
    carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
    carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;

    s[0] = (s0 >> 0) as u8;
    s[1] = (s0 >> 8) as u8;
    s[2] = ((s0 >> 16) | (s1 << 5)) as u8;
    s[3] = (s1 >> 3) as u8;
    s[4] = (s1 >> 11) as u8;
    s[5] = ((s1 >> 19) | (s2 << 2)) as u8;
    s[6] = (s2 >> 6) as u8;
    s[7] = ((s2 >> 14) | (s3 << 7)) as u8;
    s[8] = (s3 >> 1) as u8;
    s[9] = (s3 >> 9) as u8;
    s[10] = ((s3 >> 17) | (s4 << 4)) as u8;
    s[11] = (s4 >> 4) as u8;
    s[12] = (s4 >> 12) as u8;
    s[13] = ((s4 >> 20) | (s5 << 1)) as u8;
    s[14] = (s5 >> 7) as u8;
    s[15] = ((s5 >> 15) | (s6 << 6)) as u8;
    s[16] = (s6 >> 2) as u8;
    s[17] = (s6 >> 10) as u8;
    s[18] = ((s6 >> 18) | (s7 << 3)) as u8;
    s[19] = (s7 >> 5) as u8;
    s[20] = (s7 >> 13) as u8;
    s[21] = (s8 >> 0) as u8;
    s[22] = (s8 >> 8) as u8;
    s[23] = ((s8 >> 16) | (s9 << 5)) as u8;
    s[24] = (s9 >> 3) as u8;
    s[25] = (s9 >> 11) as u8;
    s[26] = ((s9 >> 19) | (s10 << 2)) as u8;
    s[27] = (s10 >> 6) as u8;
    s[28] = ((s10 >> 14) | (s11 << 7)) as u8;
    s[29] = (s11 >> 1) as u8;
    s[30] = (s11 >> 9) as u8;
    s[31] = (s11 >> 17) as u8;
}

/*
Input:
    a[0]+256*a[1]+...+256^31*a[31] = a
    b[0]+256*b[1]+...+256^31*b[31] = b
    c[0]+256*c[1]+...+256^31*c[31] = c

Output:
    s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
    where l = 2^252 + 27742317777372353535851937790883648493.
*/
#[rustfmt::skip]
pub fn sc_muladd(s: &mut[u8], a: &[u8], b: &[u8], c: &[u8]) {
    let a0 = 2097151 & load_3i(&a[0..3]);
    let a1 = 2097151 & (load_4i(&a[2..6]) >> 5);
    let a2 = 2097151 & (load_3i(&a[5..8]) >> 2);
    let a3 = 2097151 & (load_4i(&a[7..11]) >> 7);
    let a4 = 2097151 & (load_4i(&a[10..14]) >> 4);
    let a5 = 2097151 & (load_3i(&a[13..16]) >> 1);
    let a6 = 2097151 & (load_4i(&a[15..19]) >> 6);
    let a7 = 2097151 & (load_3i(&a[18..21]) >> 3);
    let a8 = 2097151 & load_3i(&a[21..24]);
    let a9 = 2097151 & (load_4i(&a[23..27]) >> 5);
    let a10 = 2097151 & (load_3i(&a[26..29]) >> 2);
    let a11 = load_4i(&a[28..32]) >> 7;
    let b0 = 2097151 & load_3i(&b[0..3]);
    let b1 = 2097151 & (load_4i(&b[2..6]) >> 5);
    let b2 = 2097151 & (load_3i(&b[5..8]) >> 2);
    let b3 = 2097151 & (load_4i(&b[7..11]) >> 7);
    let b4 = 2097151 & (load_4i(&b[10..14]) >> 4);
    let b5 = 2097151 & (load_3i(&b[13..16]) >> 1);
    let b6 = 2097151 & (load_4i(&b[15..19]) >> 6);
    let b7 = 2097151 & (load_3i(&b[18..21]) >> 3);
    let b8 = 2097151 & load_3i(&b[21..24]);
    let b9 = 2097151 & (load_4i(&b[23..27]) >> 5);
    let b10 = 2097151 & (load_3i(&b[26..29]) >> 2);
    let b11 = load_4i(&b[28..32]) >> 7;
    let c0 = 2097151 & load_3i(&c[0..3]);
    let c1 = 2097151 & (load_4i(&c[2..6]) >> 5);
    let c2 = 2097151 & (load_3i(&c[5..8]) >> 2);
    let c3 = 2097151 & (load_4i(&c[7..11]) >> 7);
    let c4 = 2097151 & (load_4i(&c[10..14]) >> 4);
    let c5 = 2097151 & (load_3i(&c[13..16]) >> 1);
    let c6 = 2097151 & (load_4i(&c[15..19]) >> 6);
    let c7 = 2097151 & (load_3i(&c[18..21]) >> 3);
    let c8 = 2097151 & load_3i(&c[21..24]);
    let c9 = 2097151 & (load_4i(&c[23..27]) >> 5);
    let c10 = 2097151 & (load_3i(&c[26..29]) >> 2);
    let c11 = load_4i(&c[28..32]) >> 7;
    let mut s0: i64;
    let mut s1: i64;
    let mut s2: i64;
    let mut s3: i64;
    let mut s4: i64;
    let mut s5: i64;
    let mut s6: i64;
    let mut s7: i64;
    let mut s8: i64;
    let mut s9: i64;
    let mut s10: i64;
    let mut s11: i64;
    let mut s12: i64;
    let mut s13: i64;
    let mut s14: i64;
    let mut s15: i64;
    let mut s16: i64;
    let mut s17: i64;
    let mut s18: i64;
    let mut s19: i64;
    let mut s20: i64;
    let mut s21: i64;
    let mut s22: i64;
    let mut s23: i64;
    let mut carry0: i64;
    let mut carry1: i64;
    let mut carry2: i64;
    let mut carry3: i64;
    let mut carry4: i64;
    let mut carry5: i64;
    let mut carry6: i64;
    let mut carry7: i64;
    let mut carry8: i64;
    let mut carry9: i64;
    let mut carry10: i64;
    let mut carry11: i64;
    let mut carry12: i64;
    let mut carry13: i64;
    let mut carry14: i64;
    let mut carry15: i64;
    let mut carry16: i64;
    let carry17: i64;
    let carry18: i64;
    let carry19: i64;
    let carry20: i64;
    let carry21: i64;
    let carry22: i64;

    s0 = c0 + a0*b0;
    s1 = c1 + a0*b1 + a1*b0;
    s2 = c2 + a0*b2 + a1*b1 + a2*b0;
    s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0;
    s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0;
    s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0;
    s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0;
    s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0;
    s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0;
    s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0;
    s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0;
    s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0;
    s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1;
    s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2;
    s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3;
    s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4;
    s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5;
    s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6;
    s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7;
    s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8;
    s20 = a9*b11 + a10*b10 + a11*b9;
    s21 = a10*b11 + a11*b10;
    s22 = a11*b11;
    s23 = 0;

    carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
    carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
    carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
    carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
    carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
    carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
    carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
    carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
    carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
    carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
    carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
    carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;

    carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
    carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
    carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
    carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
    carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
    carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
    carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
    carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
    carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
    carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
    carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;

    s11 += s23 * 666643;
    s12 += s23 * 470296;
    s13 += s23 * 654183;
    s14 -= s23 * 997805;
    s15 += s23 * 136657;
    s16 -= s23 * 683901;


    s10 += s22 * 666643;
    s11 += s22 * 470296;
    s12 += s22 * 654183;
    s13 -= s22 * 997805;
    s14 += s22 * 136657;
    s15 -= s22 * 683901;


    s9 += s21 * 666643;
    s10 += s21 * 470296;
    s11 += s21 * 654183;
    s12 -= s21 * 997805;
    s13 += s21 * 136657;
    s14 -= s21 * 683901;


    s8 += s20 * 666643;
    s9 += s20 * 470296;
    s10 += s20 * 654183;
    s11 -= s20 * 997805;
    s12 += s20 * 136657;
    s13 -= s20 * 683901;


    s7 += s19 * 666643;
    s8 += s19 * 470296;
    s9 += s19 * 654183;
    s10 -= s19 * 997805;
    s11 += s19 * 136657;
    s12 -= s19 * 683901;


    s6 += s18 * 666643;
    s7 += s18 * 470296;
    s8 += s18 * 654183;
    s9 -= s18 * 997805;
    s10 += s18 * 136657;
    s11 -= s18 * 683901;


    carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
    carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
    carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
    carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
    carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
    carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;

    carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
    carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
    carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
    carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
    carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;

    s5 += s17 * 666643;
    s6 += s17 * 470296;
    s7 += s17 * 654183;
    s8 -= s17 * 997805;
    s9 += s17 * 136657;
    s10 -= s17 * 683901;


    s4 += s16 * 666643;
    s5 += s16 * 470296;
    s6 += s16 * 654183;
    s7 -= s16 * 997805;
    s8 += s16 * 136657;
    s9 -= s16 * 683901;


    s3 += s15 * 666643;
    s4 += s15 * 470296;
    s5 += s15 * 654183;
    s6 -= s15 * 997805;
    s7 += s15 * 136657;
    s8 -= s15 * 683901;


    s2 += s14 * 666643;
    s3 += s14 * 470296;
    s4 += s14 * 654183;
    s5 -= s14 * 997805;
    s6 += s14 * 136657;
    s7 -= s14 * 683901;


    s1 += s13 * 666643;
    s2 += s13 * 470296;
    s3 += s13 * 654183;
    s4 -= s13 * 997805;
    s5 += s13 * 136657;
    s6 -= s13 * 683901;


    s0 += s12 * 666643;
    s1 += s12 * 470296;
    s2 += s12 * 654183;
    s3 -= s12 * 997805;
    s4 += s12 * 136657;
    s5 -= s12 * 683901;
    s12 = 0;

    carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
    carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
    carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
    carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
    carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
    carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;

    carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
    carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
    carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
    carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
    carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
    carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;

    s0 += s12 * 666643;
    s1 += s12 * 470296;
    s2 += s12 * 654183;
    s3 -= s12 * 997805;
    s4 += s12 * 136657;
    s5 -= s12 * 683901;
    s12 = 0;

    carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
    carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
    carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
    carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
    carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
    carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
    carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
    carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
    carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
    carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
    carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
    carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;

    s0 += s12 * 666643;
    s1 += s12 * 470296;
    s2 += s12 * 654183;
    s3 -= s12 * 997805;
    s4 += s12 * 136657;
    s5 -= s12 * 683901;


    carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
    carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
    carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
    carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
    carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
    carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
    carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
    carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
    carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
    carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
    carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;

    s[0] = (s0 >> 0) as u8;
    s[1] = (s0 >> 8) as u8;
    s[2] = ((s0 >> 16) | (s1 << 5)) as u8;
    s[3] = (s1 >> 3) as u8;
    s[4] = (s1 >> 11) as u8;
    s[5] = ((s1 >> 19) | (s2 << 2)) as u8;
    s[6] = (s2 >> 6) as u8;
    s[7] = ((s2 >> 14) | (s3 << 7)) as u8;
    s[8] = (s3 >> 1) as u8;
    s[9] = (s3 >> 9) as u8;
    s[10] = ((s3 >> 17) | (s4 << 4)) as u8;
    s[11] = (s4 >> 4) as u8;
    s[12] = (s4 >> 12) as u8;
    s[13] = ((s4 >> 20) | (s5 << 1)) as u8;
    s[14] = (s5 >> 7) as u8;
    s[15] = ((s5 >> 15) | (s6 << 6)) as u8;
    s[16] = (s6 >> 2) as u8;
    s[17] = (s6 >> 10) as u8;
    s[18] = ((s6 >> 18) | (s7 << 3)) as u8;
    s[19] = (s7 >> 5) as u8;
    s[20] = (s7 >> 13) as u8;
    s[21] = (s8 >> 0) as u8;
    s[22] = (s8 >> 8) as u8;
    s[23] = ((s8 >> 16) | (s9 << 5)) as u8;
    s[24] = (s9 >> 3) as u8;
    s[25] = (s9 >> 11) as u8;
    s[26] = ((s9 >> 19) | (s10 << 2)) as u8;
    s[27] = (s10 >> 6) as u8;
    s[28] = ((s10 >> 14) | (s11 << 7)) as u8;
    s[29] = (s11 >> 1) as u8;
    s[30] = (s11 >> 9) as u8;
    s[31] = (s11 >> 17) as u8;
}

pub fn curve25519(n: &[u8], p: &[u8]) -> [u8; 32] {
    let mut e = [0u8; 32];
    let mut x2;
    let mut z2;
    let mut x3;
    let mut z3;
    let mut swap: i32;
    let mut b: i32;

    for (d, s) in e.iter_mut().zip(n.iter()) {
        *d = *s;
    }
    e[0] &= 248;
    e[31] &= 127;
    e[31] |= 64;
    let x1 = Fe::from_bytes(p);
    x2 = FE_ONE.clone();
    z2 = FE_ZERO.clone();
    x3 = x1.clone();
    z3 = FE_ONE.clone();

    swap = 0;
    // pos starts at 254 and goes down to 0
    for pos in (0usize..255).rev() {
        b = (e[pos / 8] >> (pos & 7)) as i32;
        b &= 1;
        swap ^= b;
        x2.maybe_swap_with(&mut x3, swap);
        z2.maybe_swap_with(&mut z3, swap);
        swap = b;

        let d = &x3 - &z3;
        let b = &x2 - &z2;
        let a = &x2 + &z2;
        let c = &x3 + &z3;
        let da = &d * &a;
        let cb = &c * &b;
        let bb = b.square();
        let aa = a.square();
        let t0 = &da + &cb;
        let t1 = &da - &cb;
        let x4 = &aa * &bb;
        let e = &aa - &bb;
        let t2 = t1.square();
        let t3 = e.mul_121666();
        let x5 = t0.square();
        let t4 = &bb + &t3;
        let z5 = &x1 * &t2;
        let z4 = &e * &t4;

        z2 = z4;
        z3 = z5;
        x2 = x4;
        x3 = x5;
    }
    x2.maybe_swap_with(&mut x3, swap);
    z2.maybe_swap_with(&mut z3, swap);

    (z2.invert() * x2).to_bytes()
}

pub fn curve25519_base(x: &[u8]) -> [u8; 32] {
    let mut base: [u8; 32] = [0; 32];
    base[0] = 9;
    curve25519(x, base.as_ref())
}

#[cfg(test)]
mod tests {
    use super::{curve25519_base, Fe};
    use alloc::vec::Vec;

    #[test]
    fn from_to_bytes_preserves() {
        for i in 0..50 {
            let mut e: Vec<u8> = (0u32..32)
                .map(|idx| (idx * (1289 + i * 761)) as u8)
                .collect();
            e[0] &= 248;
            e[31] &= 127;
            e[31] |= 64;
            let fe = Fe::from_bytes(e.as_ref());
            let e_preserved = fe.to_bytes();
            assert!(e == e_preserved.to_vec());
        }
    }

    #[test]
    fn swap_test() {
        let f_initial = Fe([10, 20, 30, 40, 50, 60, 70, 80, 90, 100]);
        let g_initial = Fe([11, 21, 31, 41, 51, 61, 71, 81, 91, 101]);
        let mut f = f_initial.clone();
        let mut g = g_initial.clone();
        f.maybe_swap_with(&mut g, 0);
        assert!(f == f_initial);
        assert!(g == g_initial);

        f.maybe_swap_with(&mut g, 1);
        assert!(f == g_initial);
        assert!(g == f_initial);
    }

    struct CurveGen {
        which: u32,
    }
    impl CurveGen {
        fn new(seed: u32) -> CurveGen {
            CurveGen { which: seed }
        }
    }
    impl Iterator for CurveGen {
        type Item = Fe;

        fn next(&mut self) -> Option<Fe> {
            let mut e: Vec<u8> = (0..32)
                .map(|idx| (idx * (1289 + self.which * 761)) as u8)
                .collect();
            e[0] &= 248;
            e[31] &= 127;
            e[31] |= 64;
            Some(Fe::from_bytes(e.as_ref()))
        }
    }

    #[test]
    #[allow(clippy::eq_op)]
    fn mul_commutes() {
        for (x, y) in CurveGen::new(1).zip(CurveGen::new(2)).take(40) {
            assert!(&x * &y == &y * &x);
        }
    }

    #[test]
    fn mul_assoc() {
        for (x, (y, z)) in CurveGen::new(1)
            .zip(CurveGen::new(2).zip(CurveGen::new(3)))
            .take(40)
        {
            assert!(&(&x * &y) * &z == &x * &(&y * &z));
        }
    }

    #[test]
    fn invert_inverts() {
        for x in CurveGen::new(1).take(40) {
            assert!(x.invert().invert() == x);
        }
    }

    #[test]
    fn square_by_mul() {
        for x in CurveGen::new(1).take(40) {
            assert!(&x * &x == x.square());
        }
    }

    #[test]
    fn base_example() {
        let sk: [u8; 32] = [
            0x77, 0x07, 0x6d, 0x0a, 0x73, 0x18, 0xa5, 0x7d, 0x3c, 0x16, 0xc1, 0x72, 0x51, 0xb2,
            0x66, 0x45, 0xdf, 0x4c, 0x2f, 0x87, 0xeb, 0xc0, 0x99, 0x2a, 0xb1, 0x77, 0xfb, 0xa5,
            0x1d, 0xb9, 0x2c, 0x2a,
        ];
        let pk = curve25519_base(sk.as_ref());
        let correct: [u8; 32] = [
            0x85, 0x20, 0xf0, 0x09, 0x89, 0x30, 0xa7, 0x54, 0x74, 0x8b, 0x7d, 0xdc, 0xb4, 0x3e,
            0xf7, 0x5a, 0x0d, 0xbf, 0x3a, 0x0d, 0x26, 0x38, 0x1a, 0xf4, 0xeb, 0xa4, 0xa9, 0x8e,
            0xaa, 0x9b, 0x4e, 0x6a,
        ];
        assert_eq!(pk.to_vec(), correct.to_vec());
    }
}

#[rustfmt::skip]
static BI: [GePrecomp; 8] = [
    GePrecomp {
        y_plus_x: Fe([ 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 ]),
        y_minus_x: Fe([ -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 ]),
        xy2d: Fe([ -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 ]),
    },
    GePrecomp {
        y_plus_x: Fe([ 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 ]),
        y_minus_x: Fe([ 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 ]),
        xy2d: Fe([ 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 ]),
    },
    GePrecomp {
        y_plus_x: Fe([ 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 ]),
        y_minus_x: Fe([ 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 ]),
        xy2d: Fe([ 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 ]),
    },
    GePrecomp {
        y_plus_x: Fe([ 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 ]),
        y_minus_x: Fe([ -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 ]),
        xy2d: Fe([ 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 ]),
    },
    GePrecomp {
        y_plus_x: Fe([ -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 ]),
        y_minus_x: Fe([ -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 ]),
        xy2d: Fe([ 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 ]),
    },
    GePrecomp {
        y_plus_x: Fe([ -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 ]),
        y_minus_x: Fe([ 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 ]),
        xy2d: Fe([ 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 ]),
    },
    GePrecomp {
        y_plus_x: Fe([ -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 ]),
        y_minus_x: Fe([ -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 ]),
        xy2d: Fe([ -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 ]),
    },
    GePrecomp {
        y_plus_x: Fe([ -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 ]),
        y_minus_x: Fe([ -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 ]),
        xy2d: Fe([ -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 ]),
    },
];

static GE_PRECOMP_BASE: [[GePrecomp; 8]; 32] = [
    [
        GePrecomp {
            y_plus_x: Fe([
                25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271,
                -6079156, 2047605,
            ]),
            y_minus_x: Fe([
                -12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384,
                19500929, -15469378,
            ]),
            xy2d: Fe([
                -8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899,
                -24514362, -4438546,
            ]),
        },
        GePrecomp {
            y_plus_x: Fe([
                -12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903,
                -3814571, -358445, -10211303,
            ]),
            y_minus_x: Fe([
                -21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268,
                -26829678, -5319081,
            ]),
            xy2d: Fe([
                26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118,
                -15472047, -4166697,
            ]),
        },
        GePrecomp {
            y_plus_x: Fe([
                15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189,
                28944400, -1550024,
            ]),
            y_minus_x: Fe([
                16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962,
                7689662, 11199574,
            ]),
            xy2d: Fe([
                30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326,
                -17749093, -9920357,
            ]),
        },
        GePrecomp {
            y_plus_x: Fe([
                -17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023,
                3284568, -6276540,
            ]),
            y_minus_x: Fe([
                23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445,
                13059162, 10374397,
            ]),
            xy2d: Fe([
                7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045,
                -641708, -101325,
            ]),
        },
        GePrecomp {
            y_plus_x: Fe([
                10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107,
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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        GePrecomp {
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