// 20240227 djb: switching from mode TI to unsigned __int128
// 20240227 djb: changing uint128_t to my_uint128_t
// 20240227 djb: importing load/store fixes from upstream

/* Copyright 2008, Google Inc.
 * All rights reserved.
 *
 * Code released into the public domain.
 *
 * curve25519-donna: Curve25519 elliptic curve, public key function
 * (excerpt for inversion)
 *
 * http://code.google.com/p/curve25519-donna/
 *
 * Adam Langley <agl@imperialviolet.org>
 * Parts optimised by floodyberry
 * Derived from public domain C code by Daniel J. Bernstein <djb@cr.yp.to>
 *
 * More information about curve25519 can be found here
 *   http://cr.yp.to/ecdh.html
 *
 * djb's sample implementation of curve25519 is written in a special assembly
 * language called qhasm and uses the floating point registers.
 *
 * This is, almost, a clean room reimplementation from the curve25519 paper. It
 * uses many of the tricks described therein. Only the crecip function is taken
 * from the sample implementation.
 */

#include <string.h>
#include <stdint.h>
#include "crypto_pow.h"

typedef uint8_t u8;
typedef uint64_t limb;
typedef limb felem[5];
// This is a special gcc mode for 128-bit integers. It's implemented on 64-bit
// platforms only as far as I know.
typedef unsigned __int128 my_uint128_t;

#undef force_inline
#define force_inline __attribute__((always_inline)) inline

/* Multiply two numbers: output = in2 * in
 *
 * output must be distinct to both inputs. The inputs are reduced coefficient
 * form, the output is not.
 *
 * Assumes that in[i] < 2**55 and likewise for in2.
 * On return, output[i] < 2**52
 */
static void force_inline
fmul(felem output, const felem in2, const felem in) {
  my_uint128_t t[5];
  limb r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;

  r0 = in[0];
  r1 = in[1];
  r2 = in[2];
  r3 = in[3];
  r4 = in[4];

  s0 = in2[0];
  s1 = in2[1];
  s2 = in2[2];
  s3 = in2[3];
  s4 = in2[4];

  t[0]  =  ((my_uint128_t) r0) * s0;
  t[1]  =  ((my_uint128_t) r0) * s1 + ((my_uint128_t) r1) * s0;
  t[2]  =  ((my_uint128_t) r0) * s2 + ((my_uint128_t) r2) * s0 + ((my_uint128_t) r1) * s1;
  t[3]  =  ((my_uint128_t) r0) * s3 + ((my_uint128_t) r3) * s0 + ((my_uint128_t) r1) * s2 + ((my_uint128_t) r2) * s1;
  t[4]  =  ((my_uint128_t) r0) * s4 + ((my_uint128_t) r4) * s0 + ((my_uint128_t) r3) * s1 + ((my_uint128_t) r1) * s3 + ((my_uint128_t) r2) * s2;

  r4 *= 19;
  r1 *= 19;
  r2 *= 19;
  r3 *= 19;

  t[0] += ((my_uint128_t) r4) * s1 + ((my_uint128_t) r1) * s4 + ((my_uint128_t) r2) * s3 + ((my_uint128_t) r3) * s2;
  t[1] += ((my_uint128_t) r4) * s2 + ((my_uint128_t) r2) * s4 + ((my_uint128_t) r3) * s3;
  t[2] += ((my_uint128_t) r4) * s3 + ((my_uint128_t) r3) * s4;
  t[3] += ((my_uint128_t) r4) * s4;

                  r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
  t[1] += c;      r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
  t[2] += c;      r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
  t[3] += c;      r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
  t[4] += c;      r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
  r0 +=   c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
  r1 +=   c;      c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
  r2 +=   c;

  output[0] = r0;
  output[1] = r1;
  output[2] = r2;
  output[3] = r3;
  output[4] = r4;
}

static void force_inline
fsquare_times(felem output, const felem in, limb count) {
  my_uint128_t t[5];
  limb r0,r1,r2,r3,r4,c;
  limb d0,d1,d2,d4,d419;

  r0 = in[0];
  r1 = in[1];
  r2 = in[2];
  r3 = in[3];
  r4 = in[4];

  do {
    d0 = r0 * 2;
    d1 = r1 * 2;
    d2 = r2 * 2 * 19;
    d419 = r4 * 19;
    d4 = d419 * 2;

    t[0] = ((my_uint128_t) r0) * r0 + ((my_uint128_t) d4) * r1 + (((my_uint128_t) d2) * (r3     ));
    t[1] = ((my_uint128_t) d0) * r1 + ((my_uint128_t) d4) * r2 + (((my_uint128_t) r3) * (r3 * 19));
    t[2] = ((my_uint128_t) d0) * r2 + ((my_uint128_t) r1) * r1 + (((my_uint128_t) d4) * (r3     ));
    t[3] = ((my_uint128_t) d0) * r3 + ((my_uint128_t) d1) * r2 + (((my_uint128_t) r4) * (d419   ));
    t[4] = ((my_uint128_t) d0) * r4 + ((my_uint128_t) d1) * r3 + (((my_uint128_t) r2) * (r2     ));

                    r0 = (limb)t[0] & 0x7ffffffffffff; c = (limb)(t[0] >> 51);
    t[1] += c;      r1 = (limb)t[1] & 0x7ffffffffffff; c = (limb)(t[1] >> 51);
    t[2] += c;      r2 = (limb)t[2] & 0x7ffffffffffff; c = (limb)(t[2] >> 51);
    t[3] += c;      r3 = (limb)t[3] & 0x7ffffffffffff; c = (limb)(t[3] >> 51);
    t[4] += c;      r4 = (limb)t[4] & 0x7ffffffffffff; c = (limb)(t[4] >> 51);
    r0 +=   c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffff;
    r1 +=   c;      c = r1 >> 51; r1 = r1 & 0x7ffffffffffff;
    r2 +=   c;
  } while(--count);

  output[0] = r0;
  output[1] = r1;
  output[2] = r2;
  output[3] = r3;
  output[4] = r4;
}

/* Load a little-endian 64-bit number  */
static limb
load_limb(const u8 *in) {
  return
    ((limb)in[0]) |
    (((limb)in[1]) << 8) |
    (((limb)in[2]) << 16) |
    (((limb)in[3]) << 24) |
    (((limb)in[4]) << 32) |
    (((limb)in[5]) << 40) |
    (((limb)in[6]) << 48) |
    (((limb)in[7]) << 56);
}

static void
store_limb(u8 *out, limb in) {
  out[0] = in & 0xff;
  out[1] = (in >> 8) & 0xff;
  out[2] = (in >> 16) & 0xff;
  out[3] = (in >> 24) & 0xff;
  out[4] = (in >> 32) & 0xff;
  out[5] = (in >> 40) & 0xff;
  out[6] = (in >> 48) & 0xff;
  out[7] = (in >> 56) & 0xff;
}

/* Take a little-endian, 32-byte number and expand it into polynomial form */
static void
fexpand(limb *output, const u8 *in) {
  output[0] = load_limb(in) & 0x7ffffffffffff;
  output[1] = (load_limb(in+6) >> 3) & 0x7ffffffffffff;
  output[2] = (load_limb(in+12) >> 6) & 0x7ffffffffffff;
  output[3] = (load_limb(in+19) >> 1) & 0x7ffffffffffff;
  output[4] = (load_limb(in+24) >> 12) & 0x7ffffffffffff;
}

/* Take a fully reduced polynomial form number and contract it into a
 * little-endian, 32-byte array
 */
static void
fcontract(u8 *output, const felem input) {
  my_uint128_t t[5];

  t[0] = input[0];
  t[1] = input[1];
  t[2] = input[2];
  t[3] = input[3];
  t[4] = input[4];

  t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
  t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
  t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
  t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
  t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;

  t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
  t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
  t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
  t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
  t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;

  /* now t is between 0 and 2^255-1, properly carried. */
  /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */

  t[0] += 19;

  t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
  t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
  t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
  t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
  t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffff;

  /* now between 19 and 2^255-1 in both cases, and offset by 19. */

  t[0] += 0x8000000000000 - 19;
  t[1] += 0x8000000000000 - 1;
  t[2] += 0x8000000000000 - 1;
  t[3] += 0x8000000000000 - 1;
  t[4] += 0x8000000000000 - 1;

  /* now between 2^255 and 2^256-20, and offset by 2^255. */

  t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffff;
  t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffff;
  t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffff;
  t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffff;
  t[4] &= 0x7ffffffffffff;

  store_limb(output,    t[0] | (t[1] << 51));
  store_limb(output+8,  (t[1] >> 13) | (t[2] << 38));
  store_limb(output+16, (t[2] >> 26) | (t[3] << 25));
  store_limb(output+24, (t[3] >> 39) | (t[4] << 12));
}


// -----------------------------------------------------------------------------
// Shamelessly copied from djb's code, tightened a little
// -----------------------------------------------------------------------------
static void
crecip(felem out, const felem z) {
  felem a,t0,b,c;

  /* 2 */ fsquare_times(a, z, 1); // a = 2
  /* 8 */ fsquare_times(t0, a, 2);
  /* 9 */ fmul(b, t0, z); // b = 9
  /* 11 */ fmul(a, b, a); // a = 11
  /* 22 */ fsquare_times(t0, a, 1);
  /* 2^5 - 2^0 = 31 */ fmul(b, t0, b);
  /* 2^10 - 2^5 */ fsquare_times(t0, b, 5);
  /* 2^10 - 2^0 */ fmul(b, t0, b);
  /* 2^20 - 2^10 */ fsquare_times(t0, b, 10);
  /* 2^20 - 2^0 */ fmul(c, t0, b);
  /* 2^40 - 2^20 */ fsquare_times(t0, c, 20);
  /* 2^40 - 2^0 */ fmul(t0, t0, c);
  /* 2^50 - 2^10 */ fsquare_times(t0, t0, 10);
  /* 2^50 - 2^0 */ fmul(b, t0, b);
  /* 2^100 - 2^50 */ fsquare_times(t0, b, 50);
  /* 2^100 - 2^0 */ fmul(c, t0, b);
  /* 2^200 - 2^100 */ fsquare_times(t0, c, 100);
  /* 2^200 - 2^0 */ fmul(t0, t0, c);
  /* 2^250 - 2^50 */ fsquare_times(t0, t0, 50);
  /* 2^250 - 2^0 */ fmul(t0, t0, b);
  /* 2^255 - 2^5 */ fsquare_times(t0, t0, 5);
  /* 2^255 - 21 */ fmul(out, t0, a);
}

void
crypto_pow(u8 *q, const u8 *p) {
  limb x[5];
  fexpand(x, p);
  crecip(x, x);
  fcontract(q, x);
}