tools: import new curve25519 implementations

1 files changed, 1423 insertions, 1129 deletions

diff --git a/src/tools/curve25519.c b/src/tools/curve25519.c
index 3e770b2..ee7df84 100644
--- a/src/tools/curve25519.c
+++ b/src/tools/curve25519.c
@@ -1,1277 +1,1571 @@
 /* SPDX-License-Identifier: GPL-2.0
  *
- * Copyright (C) 2008 Google Inc. All Rights Reserved.
- * Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ * Copyright (C) 2016-2017 INRIA and Microsoft Corporation.
+ * Copyright (C) 2015-2016 The fiat-crypto Authors.
+ * Copyright (C) 2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
  *
- * Original author: Adam Langley <agl@imperialviolet.org>
+ * This is a machine-generated formally verified implementation of curve25519 DH from:
+ * https://github.com/mitls/hacl-star and https://github.com/mit-plv/fiat-crypto
  */
 
 #include "curve25519.h"
 
 #include <stdint.h>
 #include <string.h>
+#include <endian.h>
 
 #ifndef __always_inline
 #define __always_inline __inline __attribute__((__always_inline__))
 #endif
 
+#ifndef __aligned
+#define __aligned(x) __attribute__((aligned(x)))
+#endif
+
 #ifdef __SIZEOF_INT128__
-typedef uint64_t limb;
-typedef limb felem[5];
 typedef __uint128_t uint128_t;
 
-/* Sum two numbers: output += in */
-static __always_inline void fsum(limb *output, const limb *in)
+static __always_inline uint64_t uint64_t_eq_mask(uint64_t x, uint64_t y)
 {
-	output[0] += in[0];
-	output[1] += in[1];
-	output[2] += in[2];
-	output[3] += in[3];
-	output[4] += in[4];
+	x = ~(x ^ y);
+	x &= x << 32;
+	x &= x << 16;
+	x &= x << 8;
+	x &= x << 4;
+	x &= x << 2;
+	x &= x << 1;
+	return ((int64_t)x) >> 63;
 }
 
-/* Find the difference of two numbers: output = in - output
- * (note the order of the arguments!)
- *
- * Assumes that out[i] < 2**52
- * On return, out[i] < 2**55
- */
-static __always_inline void fdifference_backwards(felem out, const felem in)
+static __always_inline uint64_t uint64_t_gte_mask(uint64_t x, uint64_t y)
 {
-	/* 152 is 19 << 3 */
-	static const limb two54m152 = (((limb)1) << 54) - 152;
-	static const limb two54m8 = (((limb)1) << 54) - 8;
+	uint64_t low63 = ~((uint64_t)((int64_t)((int64_t)(x & 0x7fffffffffffffffLLU) - (int64_t)(y & 0x7fffffffffffffffLLU)) >> 63));
+	uint64_t high_bit = ~((uint64_t)((int64_t)((int64_t)(x & 0x8000000000000000LLU) - (int64_t)(y & 0x8000000000000000LLU)) >> 63));
+	return low63 & high_bit;
+}
 
-	out[0] = in[0] + two54m152 - out[0];
-	out[1] = in[1] + two54m8 - out[1];
-	out[2] = in[2] + two54m8 - out[2];
-	out[3] = in[3] + two54m8 - out[3];
-	out[4] = in[4] + two54m8 - out[4];
+static __always_inline void modulo_carry_top(uint64_t *b)
+{
+	uint64_t b4 = b[4];
+	uint64_t b0 = b[0];
+	uint64_t b4_ = b4 & 0x7ffffffffffffLLU;
+	uint64_t b0_ = b0 + 19 * (b4 >> 51);
+	b[4] = b4_;
+	b[0] = b0_;
 }
 
-/* Multiply a number by a scalar: output = in * scalar */
-static __always_inline void fscalar_product(felem output, const felem in, const limb scalar)
+static __always_inline void fproduct_copy_from_wide_(uint64_t *output, uint128_t *input)
 {
-	uint128_t a;
+	{
+		uint128_t xi = input[0];
+		output[0] = ((uint64_t)(xi));
+	}
+	{
+		uint128_t xi = input[1];
+		output[1] = ((uint64_t)(xi));
+	}
+	{
+		uint128_t xi = input[2];
+		output[2] = ((uint64_t)(xi));
+	}
+	{
+		uint128_t xi = input[3];
+		output[3] = ((uint64_t)(xi));
+	}
+	{
+		uint128_t xi = input[4];
+		output[4] = ((uint64_t)(xi));
+	}
+}
 
-	a = ((uint128_t) in[0]) * scalar;
-	output[0] = ((limb)a) & 0x7ffffffffffffUL;
+static __always_inline void fproduct_sum_scalar_multiplication_(uint128_t *output, uint64_t *input, uint64_t s)
+{
+	uint32_t i;
+	for (i = 0; i < 5; ++i) {
+		uint128_t xi = output[i];
+		uint64_t yi = input[i];
+		output[i] = ((xi) + (((uint128_t)(yi) * (s))));
+	}
+}
 
-	a = ((uint128_t) in[1]) * scalar + ((limb) (a >> 51));
-	output[1] = ((limb)a) & 0x7ffffffffffffUL;
+static __always_inline void fproduct_carry_wide_(uint128_t *tmp)
+{
+	uint32_t i;
+	for (i = 0; i < 4; ++i) {
+		uint32_t ctr = i;
+		uint128_t tctr = tmp[ctr];
+		uint128_t tctrp1 = tmp[ctr + 1];
+		uint64_t r0 = ((uint64_t)(tctr)) & 0x7ffffffffffffLLU;
+		uint128_t c = ((tctr) >> (51));
+		tmp[ctr] = ((uint128_t)(r0));
+		tmp[ctr + 1] = ((tctrp1) + (c));
+	}
+}
 
-	a = ((uint128_t) in[2]) * scalar + ((limb) (a >> 51));
-	output[2] = ((limb)a) & 0x7ffffffffffffUL;
+static __always_inline void fmul_shift_reduce(uint64_t *output)
+{
+	uint64_t tmp = output[4];
+	uint64_t b0;
+	{
+		uint32_t ctr = 5 - 0 - 1;
+		uint64_t z = output[ctr - 1];
+		output[ctr] = z;
+	}
+	{
+		uint32_t ctr = 5 - 1 - 1;
+		uint64_t z = output[ctr - 1];
+		output[ctr] = z;
+	}
+	{
+		uint32_t ctr = 5 - 2 - 1;
+		uint64_t z = output[ctr - 1];
+		output[ctr] = z;
+	}
+	{
+		uint32_t ctr = 5 - 3 - 1;
+		uint64_t z = output[ctr - 1];
+		output[ctr] = z;
+	}
+	output[0] = tmp;
+	b0 = output[0];
+	output[0] = 19 * b0;
+}
 
-	a = ((uint128_t) in[3]) * scalar + ((limb) (a >> 51));
-	output[3] = ((limb)a) & 0x7ffffffffffffUL;
+static __always_inline void fmul_mul_shift_reduce_(uint128_t *output, uint64_t *input, uint64_t *input21)
+{
+	uint32_t i;
+	uint64_t input2i;
+	{
+		uint64_t input2i = input21[0];
+		fproduct_sum_scalar_multiplication_(output, input, input2i);
+		fmul_shift_reduce(input);
+	}
+	{
+		uint64_t input2i = input21[1];
+		fproduct_sum_scalar_multiplication_(output, input, input2i);
+		fmul_shift_reduce(input);
+	}
+	{
+		uint64_t input2i = input21[2];
+		fproduct_sum_scalar_multiplication_(output, input, input2i);
+		fmul_shift_reduce(input);
+	}
+	{
+		uint64_t input2i = input21[3];
+		fproduct_sum_scalar_multiplication_(output, input, input2i);
+		fmul_shift_reduce(input);
+	}
+	i = 4;
+	input2i = input21[i];
+	fproduct_sum_scalar_multiplication_(output, input, input2i);
+}
 
-	a = ((uint128_t) in[4]) * scalar + ((limb) (a >> 51));
-	output[4] = ((limb)a) & 0x7ffffffffffffUL;
+static __always_inline void fmul_fmul(uint64_t *output, uint64_t *input, uint64_t *input21)
+{
+	uint64_t tmp[5];
+	memcpy(tmp, input, 5 * sizeof(*input));
+	{
+		uint128_t b4;
+		uint128_t b0;
+		uint128_t b4_;
+		uint128_t b0_;
+		uint64_t i0;
+		uint64_t i1;
+		uint64_t i0_;
+		uint64_t i1_;
+		uint128_t t[5];
+		{
+			uint32_t _i;
+			for (_i = 0; _i < 5; ++_i)
+				t[_i] = ((uint128_t)(0));
+		}
+		fmul_mul_shift_reduce_(t, tmp, input21);
+		fproduct_carry_wide_(t);
+		b4 = t[4];
+		b0 = t[0];
+		b4_ = ((b4) & (((uint128_t)(0x7ffffffffffffLLU))));
+		b0_ = ((b0) + (((uint128_t)(19) * (((uint64_t)(((b4) >> (51))))))));
+		t[4] = b4_;
+		t[0] = b0_;
+		fproduct_copy_from_wide_(output, t);
+		i0 = output[0];
+		i1 = output[1];
+		i0_ = i0 & 0x7ffffffffffffLLU;
+		i1_ = i1 + (i0 >> 51);
+		output[0] = i0_;
+		output[1] = i1_;
+	}
+}
 
-	output[0] += (a >> 51) * 19;
+static __always_inline void fsquare_fsquare__(uint128_t *tmp, uint64_t *output)
+{
+	uint64_t r0 = output[0];
+	uint64_t r1 = output[1];
+	uint64_t r2 = output[2];
+	uint64_t r3 = output[3];
+	uint64_t r4 = output[4];
+	uint64_t d0 = r0 * 2;
+	uint64_t d1 = r1 * 2;
+	uint64_t d2 = r2 * 2 * 19;
+	uint64_t d419 = r4 * 19;
+	uint64_t d4 = d419 * 2;
+	uint128_t s0 = ((((((uint128_t)(r0) * (r0))) + (((uint128_t)(d4) * (r1))))) + (((uint128_t)(d2) * (r3))));
+	uint128_t s1 = ((((((uint128_t)(d0) * (r1))) + (((uint128_t)(d4) * (r2))))) + (((uint128_t)(r3 * 19) * (r3))));
+	uint128_t s2 = ((((((uint128_t)(d0) * (r2))) + (((uint128_t)(r1) * (r1))))) + (((uint128_t)(d4) * (r3))));
+	uint128_t s3 = ((((((uint128_t)(d0) * (r3))) + (((uint128_t)(d1) * (r2))))) + (((uint128_t)(r4) * (d419))));
+	uint128_t s4 = ((((((uint128_t)(d0) * (r4))) + (((uint128_t)(d1) * (r3))))) + (((uint128_t)(r2) * (r2))));
+	tmp[0] = s0;
+	tmp[1] = s1;
+	tmp[2] = s2;
+	tmp[3] = s3;
+	tmp[4] = s4;
 }
 
-/* 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 __always_inline void fmul(felem output, const felem in2, const felem in)
+static __always_inline void fsquare_fsquare_(uint128_t *tmp, uint64_t *output)
 {
-	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]  =  ((uint128_t) r0) * s0;
-	t[1]  =  ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0;
-	t[2]  =  ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1;
-	t[3]  =  ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1;
-	t[4]  =  ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2;
-
-	r4 *= 19;
-	r1 *= 19;
-	r2 *= 19;
-	r3 *= 19;
-
-	t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2;
-	t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3;
-	t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4;
-	t[3] += ((uint128_t) r4) * s4;
-
-			r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
-	t[1] += c;      r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
-	t[2] += c;      r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
-	t[3] += c;      r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
-	t[4] += c;      r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
-	r0 +=   c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
-	r1 +=   c;      c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
-	r2 +=   c;
-
-	output[0] = r0;
-	output[1] = r1;
-	output[2] = r2;
-	output[3] = r3;
-	output[4] = r4;
-}
-
-static __always_inline void fsquare_times(felem output, const felem in, limb count)
+	uint128_t b4;
+	uint128_t b0;
+	uint128_t b4_;
+	uint128_t b0_;
+	uint64_t i0;
+	uint64_t i1;
+	uint64_t i0_;
+	uint64_t i1_;
+	fsquare_fsquare__(tmp, output);
+	fproduct_carry_wide_(tmp);
+	b4 = tmp[4];
+	b0 = tmp[0];
+	b4_ = ((b4) & (((uint128_t)(0x7ffffffffffffLLU))));
+	b0_ = ((b0) + (((uint128_t)(19) * (((uint64_t)(((b4) >> (51))))))));
+	tmp[4] = b4_;
+	tmp[0] = b0_;
+	fproduct_copy_from_wide_(output, tmp);
+	i0 = output[0];
+	i1 = output[1];
+	i0_ = i0 & 0x7ffffffffffffLLU;
+	i1_ = i1 + (i0 >> 51);
+	output[0] = i0_;
+	output[1] = i1_;
+}
+
+static __always_inline void fsquare_fsquare_times_(uint64_t *input, uint128_t *tmp, uint32_t count1)
 {
-	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] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3     ));
-		t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
-		t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3     ));
-		t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419   ));
-		t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2     ));
-
-				r0 = (limb)t[0] & 0x7ffffffffffffUL; c = (limb)(t[0] >> 51);
-		t[1] += c;      r1 = (limb)t[1] & 0x7ffffffffffffUL; c = (limb)(t[1] >> 51);
-		t[2] += c;      r2 = (limb)t[2] & 0x7ffffffffffffUL; c = (limb)(t[2] >> 51);
-		t[3] += c;      r3 = (limb)t[3] & 0x7ffffffffffffUL; c = (limb)(t[3] >> 51);
-		t[4] += c;      r4 = (limb)t[4] & 0x7ffffffffffffUL; c = (limb)(t[4] >> 51);
-		r0 +=   c * 19; c = r0 >> 51; r0 = r0 & 0x7ffffffffffffUL;
-		r1 +=   c;      c = r1 >> 51; r1 = r1 & 0x7ffffffffffffUL;
-		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 uint8_t *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(uint8_t *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 uint8_t *in)
-{
-	output[0] = load_limb(in) & 0x7ffffffffffffUL;
-	output[1] = (load_limb(in+6) >> 3) & 0x7ffffffffffffUL;
-	output[2] = (load_limb(in+12) >> 6) & 0x7ffffffffffffUL;
-	output[3] = (load_limb(in+19) >> 1) & 0x7ffffffffffffUL;
-	output[4] = (load_limb(in+24) >> 12) & 0x7ffffffffffffUL;
-}
-
-/* Take a fully reduced polynomial form number and contract it into a
- * little-endian, 32-byte array
- */
-static void fcontract(uint8_t *output, const felem input)
+	uint32_t i;
+	fsquare_fsquare_(tmp, input);
+	for (i = 1; i < count1; ++i)
+		fsquare_fsquare_(tmp, input);
+}
+
+static __always_inline void fsquare_fsquare_times(uint64_t *output, uint64_t *input, uint32_t count1)
 {
 	uint128_t t[5];
+	{
+		uint32_t _i;
+		for (_i = 0; _i < 5; ++_i)
+			t[_i] = ((uint128_t)(0));
+	}
+	memcpy(output, input, 5 * sizeof(*input));
+	fsquare_fsquare_times_(output, t, count1);
+}
 
-	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] &= 0x7ffffffffffffUL;
-	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
-	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
-	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
-	t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
-
-	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
-	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
-	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
-	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
-	t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
+static __always_inline void fsquare_fsquare_times_inplace(uint64_t *output, uint32_t count1)
+{
+	uint128_t t[5];
+	{
+		uint32_t _i;
+		for (_i = 0; _i < 5; ++_i)
+			t[_i] = ((uint128_t)(0));
+	}
+	fsquare_fsquare_times_(output, t, count1);
+}
 
-	/* 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. */
+static __always_inline void crecip_crecip(uint64_t *out, uint64_t *z)
+{
+	uint64_t buf[20] = { 0 };
+	uint64_t *a0 = buf;
+	uint64_t *t00 = buf + 5;
+	uint64_t *b0 = buf + 10;
+	uint64_t *t01;
+	uint64_t *b1;
+	uint64_t *c0;
+	uint64_t *a;
+	uint64_t *t0;
+	uint64_t *b;
+	uint64_t *c;
+	fsquare_fsquare_times(a0, z, 1);
+	fsquare_fsquare_times(t00, a0, 2);
+	fmul_fmul(b0, t00, z);
+	fmul_fmul(a0, b0, a0);
+	fsquare_fsquare_times(t00, a0, 1);
+	fmul_fmul(b0, t00, b0);
+	fsquare_fsquare_times(t00, b0, 5);
+	t01 = buf + 5;
+	b1 = buf + 10;
+	c0 = buf + 15;
+	fmul_fmul(b1, t01, b1);
+	fsquare_fsquare_times(t01, b1, 10);
+	fmul_fmul(c0, t01, b1);
+	fsquare_fsquare_times(t01, c0, 20);
+	fmul_fmul(t01, t01, c0);
+	fsquare_fsquare_times_inplace(t01, 10);
+	fmul_fmul(b1, t01, b1);
+	fsquare_fsquare_times(t01, b1, 50);
+	a = buf;
+	t0 = buf + 5;
+	b = buf + 10;
+	c = buf + 15;
+	fmul_fmul(c, t0, b);
+	fsquare_fsquare_times(t0, c, 100);
+	fmul_fmul(t0, t0, c);
+	fsquare_fsquare_times_inplace(t0, 50);
+	fmul_fmul(t0, t0, b);
+	fsquare_fsquare_times_inplace(t0, 5);
+	fmul_fmul(out, t0, a);
+}
 
-	t[0] += 19;
+static __always_inline void fsum(uint64_t *a, uint64_t *b)
+{
+	uint32_t i;
+	for (i = 0; i < 5; ++i) {
+		uint64_t xi = a[i];
+		uint64_t yi = b[i];
+		a[i] = xi + yi;
+	}
+}
 
-	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
-	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
-	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
-	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
-	t[0] += 19 * (t[4] >> 51); t[4] &= 0x7ffffffffffffUL;
+static __always_inline void fdifference(uint64_t *a, uint64_t *b)
+{
+	uint64_t tmp[5] = { 0 };
+	uint64_t b0;
+	uint64_t b1;
+	uint64_t b2;
+	uint64_t b3;
+	uint64_t b4;
+	memcpy(tmp, b, 5 * sizeof(*b));
+	b0 = tmp[0];
+	b1 = tmp[1];
+	b2 = tmp[2];
+	b3 = tmp[3];
+	b4 = tmp[4];
+	tmp[0] = b0 + 0x3fffffffffff68LLU;
+	tmp[1] = b1 + 0x3ffffffffffff8LLU;
+	tmp[2] = b2 + 0x3ffffffffffff8LLU;
+	tmp[3] = b3 + 0x3ffffffffffff8LLU;
+	tmp[4] = b4 + 0x3ffffffffffff8LLU;
+	{
+		uint64_t xi = a[0];
+		uint64_t yi = tmp[0];
+		a[0] = yi - xi;
+	}
+	{
+		uint64_t xi = a[1];
+		uint64_t yi = tmp[1];
+		a[1] = yi - xi;
+	}
+	{
+		uint64_t xi = a[2];
+		uint64_t yi = tmp[2];
+		a[2] = yi - xi;
+	}
+	{
+		uint64_t xi = a[3];
+		uint64_t yi = tmp[3];
+		a[3] = yi - xi;
+	}
+	{
+		uint64_t xi = a[4];
+		uint64_t yi = tmp[4];
+		a[4] = yi - xi;
+	}
+}
 
-	/* now between 19 and 2^255-1 in both cases, and offset by 19. */
+static __always_inline void fscalar(uint64_t *output, uint64_t *b, uint64_t s)
+{
+	uint128_t tmp[5];
+	uint128_t b4;
+	uint128_t b0;
+	uint128_t b4_;
+	uint128_t b0_;
+	{
+		uint64_t xi = b[0];
+		tmp[0] = ((uint128_t)(xi) * (s));
+	}
+	{
+		uint64_t xi = b[1];
+		tmp[1] = ((uint128_t)(xi) * (s));
+	}
+	{
+		uint64_t xi = b[2];
+		tmp[2] = ((uint128_t)(xi) * (s));
+	}
+	{
+		uint64_t xi = b[3];
+		tmp[3] = ((uint128_t)(xi) * (s));
+	}
+	{
+		uint64_t xi = b[4];
+		tmp[4] = ((uint128_t)(xi) * (s));
+	}
+	fproduct_carry_wide_(tmp);
+	b4 = tmp[4];
+	b0 = tmp[0];
+	b4_ = ((b4) & (((uint128_t)(0x7ffffffffffffLLU))));
+	b0_ = ((b0) + (((uint128_t)(19) * (((uint64_t)(((b4) >> (51))))))));
+	tmp[4] = b4_;
+	tmp[0] = b0_;
+	fproduct_copy_from_wide_(output, tmp);
+}
 
-	t[0] += 0x8000000000000UL - 19;
-	t[1] += 0x8000000000000UL - 1;
-	t[2] += 0x8000000000000UL - 1;
-	t[3] += 0x8000000000000UL - 1;
-	t[4] += 0x8000000000000UL - 1;
+static __always_inline void fmul(uint64_t *output, uint64_t *a, uint64_t *b)
+{
+	fmul_fmul(output, a, b);
+}
 
-	/* now between 2^255 and 2^256-20, and offset by 2^255. */
+static __always_inline void crecip(uint64_t *output, uint64_t *input)
+{
+	crecip_crecip(output, input);
+}
 
-	t[1] += t[0] >> 51; t[0] &= 0x7ffffffffffffUL;
-	t[2] += t[1] >> 51; t[1] &= 0x7ffffffffffffUL;
-	t[3] += t[2] >> 51; t[2] &= 0x7ffffffffffffUL;
-	t[4] += t[3] >> 51; t[3] &= 0x7ffffffffffffUL;
-	t[4] &= 0x7ffffffffffffUL;
+static __always_inline void point_swap_conditional_step(uint64_t *a, uint64_t *b, uint64_t swap1, uint32_t ctr)
+{
+	uint32_t i = ctr - 1;
+	uint64_t ai = a[i];
+	uint64_t bi = b[i];
+	uint64_t x = swap1 & (ai ^ bi);
+	uint64_t ai1 = ai ^ x;
+	uint64_t bi1 = bi ^ x;
+	a[i] = ai1;
+	b[i] = bi1;
+}
 
-	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));
+static __always_inline void point_swap_conditional_(uint64_t *a, uint64_t *b, uint64_t swap1, uint32_t ctr)
+{
+	uint32_t i;
+	for (i = ctr; i > 0; --i)
+		point_swap_conditional_step(a, b, swap1, i);
 }
 
-/* Input: Q, Q', Q-Q'
- * Output: 2Q, Q+Q'
- *
- *   x2 z3: long form
- *   x3 z3: long form
- *   x z: short form, destroyed
- *   xprime zprime: short form, destroyed
- *   qmqp: short form, preserved
- */
-static void fmonty(limb *x2, limb *z2, /* output 2Q */
-			 limb *x3, limb *z3, /* output Q + Q' */
-			 limb *x, limb *z,   /* input Q */
-			 limb *xprime, limb *zprime, /* input Q' */
+static __always_inline void point_swap_conditional(uint64_t *a, uint64_t *b, uint64_t iswap)
+{
+	uint64_t swap1 = 0 - iswap;
+	point_swap_conditional_(a, b, swap1, 5);
+	point_swap_conditional_(a + 5, b + 5, swap1, 5);
+}
 
-			 const limb *qmqp /* input Q - Q' */)
+static __always_inline void point_copy(uint64_t *output, uint64_t *input)
 {
-	limb origx[5], origxprime[5], zzz[5], xx[5], zz[5], xxprime[5], zzprime[5], zzzprime[5];
+	memcpy(output, input, 5 * sizeof(*input));
+	memcpy(output + 5, input + 5, 5 * sizeof(*input));
+}
 
-	memcpy(origx, x, 5 * sizeof(limb));
+static __always_inline void addanddouble_fmonty(uint64_t *pp, uint64_t *ppq, uint64_t *p, uint64_t *pq, uint64_t *qmqp)
+{
+	uint64_t *qx = qmqp;
+	uint64_t *x2 = pp;
+	uint64_t *z2 = pp + 5;
+	uint64_t *x3 = ppq;
+	uint64_t *z3 = ppq + 5;
+	uint64_t *x = p;
+	uint64_t *z = p + 5;
+	uint64_t *xprime = pq;
+	uint64_t *zprime = pq + 5;
+	uint64_t buf[40] = { 0 };
+	uint64_t *origx = buf;
+	uint64_t *origxprime0 = buf + 5;
+	uint64_t *xxprime0;
+	uint64_t *zzprime0;
+	uint64_t *origxprime;
+	xxprime0 = buf + 25;
+	zzprime0 = buf + 30;
+	memcpy(origx, x, 5 * sizeof(*x));
 	fsum(x, z);
-	fdifference_backwards(z, origx);  // does x - z
-
-	memcpy(origxprime, xprime, sizeof(limb) * 5);
+	fdifference(z, origx);
+	memcpy(origxprime0, xprime, 5 * sizeof(*xprime));
 	fsum(xprime, zprime);
-	fdifference_backwards(zprime, origxprime);
-	fmul(xxprime, xprime, z);
-	fmul(zzprime, x, zprime);
-	memcpy(origxprime, xxprime, sizeof(limb) * 5);
-	fsum(xxprime, zzprime);
-	fdifference_backwards(zzprime, origxprime);
-	fsquare_times(x3, xxprime, 1);
-	fsquare_times(zzzprime, zzprime, 1);
-	fmul(z3, zzzprime, qmqp);
-
-	fsquare_times(xx, x, 1);
-	fsquare_times(zz, z, 1);
-	fmul(x2, xx, zz);
-	fdifference_backwards(zz, xx);  // does zz = xx - zz
-	fscalar_product(zzz, zz, 121665);
-	fsum(zzz, xx);
-	fmul(z2, zz, zzz);
-}
-
-/* Maybe swap the contents of two limb arrays (@a and @b), each @len elements
- * long. Perform the swap iff @swap is non-zero.
- *
- * This function performs the swap without leaking any side-channel
- * information.
- */
-static void swap_conditional(limb a[static 5], limb b[static 5], limb iswap)
+	fdifference(zprime, origxprime0);
+	fmul(xxprime0, xprime, z);
+	fmul(zzprime0, x, zprime);
+	origxprime = buf + 5;
+	{
+		uint64_t *xx0;
+		uint64_t *zz0;
+		uint64_t *xxprime;
+		uint64_t *zzprime;
+		uint64_t *zzzprime;
+		xx0 = buf + 15;
+		zz0 = buf + 20;
+		xxprime = buf + 25;
+		zzprime = buf + 30;
+		zzzprime = buf + 35;
+		memcpy(origxprime, xxprime, 5 * sizeof(*xxprime));
+		fsum(xxprime, zzprime);
+		fdifference(zzprime, origxprime);
+		fsquare_fsquare_times(x3, xxprime, 1);
+		fsquare_fsquare_times(zzzprime, zzprime, 1);
+		fmul(z3, zzzprime, qx);
+		fsquare_fsquare_times(xx0, x, 1);
+		fsquare_fsquare_times(zz0, z, 1);
+		{
+			uint64_t *zzz;
+			uint64_t *xx;
+			uint64_t *zz;
+			uint64_t scalar;
+			zzz = buf + 10;
+			xx = buf + 15;
+			zz = buf + 20;
+			fmul(x2, xx, zz);
+			fdifference(zz, xx);
+			scalar = 121665;
+			fscalar(zzz, zz, scalar);
+			fsum(zzz, xx);
+			fmul(z2, zzz, zz);
+		}
+	}
+}
+
+static __always_inline void ladder_smallloop_cmult_small_loop_step(uint64_t *nq, uint64_t *nqpq, uint64_t *nq2, uint64_t *nqpq2, uint64_t *q, uint8_t byt)
 {
-	unsigned int i;
-	const limb swap = -iswap;
+	uint64_t bit0 = (uint64_t)(byt >> 7);
+	uint64_t bit;
+	point_swap_conditional(nq, nqpq, bit0);
+	addanddouble_fmonty(nq2, nqpq2, nq, nqpq, q);
+	bit = (uint64_t)(byt >> 7);
+	point_swap_conditional(nq2, nqpq2, bit);
+}
 
-	for (i = 0; i < 5; ++i) {
-		const limb x = swap & (a[i] ^ b[i]);
+static __always_inline void ladder_smallloop_cmult_small_loop_double_step(uint64_t *nq, uint64_t *nqpq, uint64_t *nq2, uint64_t *nqpq2, uint64_t *q, uint8_t byt)
+{
+	uint8_t byt1;
+	ladder_smallloop_cmult_small_loop_step(nq, nqpq, nq2, nqpq2, q, byt);
+	byt1 = byt << 1;
+	ladder_smallloop_cmult_small_loop_step(nq2, nqpq2, nq, nqpq, q, byt1);
+}
 
-		a[i] ^= x;
-		b[i] ^= x;
+static __always_inline void ladder_smallloop_cmult_small_loop(uint64_t *nq, uint64_t *nqpq, uint64_t *nq2, uint64_t *nqpq2, uint64_t *q, uint8_t byt, uint32_t i)
+{
+	while (i--) {
+		ladder_smallloop_cmult_small_loop_double_step(nq, nqpq, nq2, nqpq2, q, byt);
+		byt <<= 2;
 	}
 }
 
-/* Calculates nQ where Q is the x-coordinate of a point on the curve
- *
- *   resultx/resultz: the x coordinate of the resulting curve point (short form)
- *   n: a little endian, 32-byte number
- *   q: a point of the curve (short form)
- */
-static void cmult(limb *resultx, limb *resultz, const uint8_t *n, const limb *q)
-{
-	limb a[5] = {0}, b[5] = {1}, c[5] = {1}, d[5] = {0};
-	limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
-	limb e[5] = {0}, f[5] = {1}, g[5] = {0}, h[5] = {1};
-	limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
-
-	unsigned int i, j;
-
-	memcpy(nqpqx, q, sizeof(limb) * 5);
-
-	for (i = 0; i < 32; ++i) {
-		uint8_t byte = n[31 - i];
-
-		for (j = 0; j < 8; ++j) {
-			const limb bit = byte >> 7;
-
-			swap_conditional(nqx, nqpqx, bit);
-			swap_conditional(nqz, nqpqz, bit);
-			fmonty(nqx2, nqz2,
-						 nqpqx2, nqpqz2,
-						 nqx, nqz,
-						 nqpqx, nqpqz,
-						 q);
-			swap_conditional(nqx2, nqpqx2, bit);
-			swap_conditional(nqz2, nqpqz2, bit);
-
-			t = nqx;
-			nqx = nqx2;
-			nqx2 = t;
-			t = nqz;
-			nqz = nqz2;
-			nqz2 = t;
-			t = nqpqx;
-			nqpqx = nqpqx2;
-			nqpqx2 = t;
-			t = nqpqz;
-			nqpqz = nqpqz2;
-			nqpqz2 = t;
-
-			byte <<= 1;
-		}
+static __always_inline void ladder_bigloop_cmult_big_loop(uint8_t *n1, uint64_t *nq, uint64_t *nqpq, uint64_t *nq2, uint64_t *nqpq2, uint64_t *q, uint32_t i)
+{
+	while (i--) {
+		uint8_t byte = n1[i];
+		ladder_smallloop_cmult_small_loop(nq, nqpq, nq2, nqpq2, q, byte, 4);
 	}
-
-	memcpy(resultx, nqx, sizeof(limb) * 5);
-	memcpy(resultz, nqz, sizeof(limb) * 5);
-}
-
-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 curve25519(uint8_t mypublic[static CURVE25519_POINT_SIZE], const uint8_t secret[static CURVE25519_POINT_SIZE], const uint8_t basepoint[static CURVE25519_POINT_SIZE])
+static __always_inline void ladder_cmult(uint64_t *result, uint8_t *n1, uint64_t *q)
 {
-	limb bp[5], x[5], z[5], zmone[5];
-	uint8_t e[32];
+	uint64_t point_buf[40] = { 0 };
+	uint64_t *nq = point_buf;
+	uint64_t *nqpq = point_buf + 10;
+	uint64_t *nq2 = point_buf + 20;
+	uint64_t *nqpq2 = point_buf + 30;
+	point_copy(nqpq, q);
+	nq[0] = 1;
+	ladder_bigloop_cmult_big_loop(n1, nq, nqpq, nq2, nqpq2, q, 32);
+	point_copy(result, nq);
+}
 
-	memcpy(e, secret, 32);
-	curve25519_normalize_secret(e);
+static __always_inline void format_fexpand(uint64_t *output, const uint8_t *input)
+{
+	const uint8_t *x00 = input + 6;
+	const uint8_t *x01 = input + 12;
+	const uint8_t *x02 = input + 19;
+	const uint8_t *x0 = input + 24;
+	uint64_t i0, i1, i2, i3, i4, output0, output1, output2, output3, output4;
+	i0 = le64toh(*(uint64_t *)input);
+	i1 = le64toh(*(uint64_t *)x00);
+	i2 = le64toh(*(uint64_t *)x01);
+	i3 = le64toh(*(uint64_t *)x02);
+	i4 = le64toh(*(uint64_t *)x0);
+	output0 = i0 & 0x7ffffffffffffLLU;
+	output1 = i1 >> 3 & 0x7ffffffffffffLLU;
+	output2 = i2 >> 6 & 0x7ffffffffffffLLU;
+	output3 = i3 >> 1 & 0x7ffffffffffffLLU;
+	output4 = i4 >> 12 & 0x7ffffffffffffLLU;
+	output[0] = output0;
+	output[1] = output1;
+	output[2] = output2;
+	output[3] = output3;
+	output[4] = output4;
+}
 
-	fexpand(bp, basepoint);
-	cmult(x, z, e, bp);
-	crecip(zmone, z);
-	fmul(z, x, zmone);
-	fcontract(mypublic, z);
+static __always_inline void format_fcontract_first_carry_pass(uint64_t *input)
+{
+	uint64_t t0 = input[0];
+	uint64_t t1 = input[1];
+	uint64_t t2 = input[2];
+	uint64_t t3 = input[3];
+	uint64_t t4 = input[4];
+	uint64_t t1_ = t1 + (t0 >> 51);
+	uint64_t t0_ = t0 & 0x7ffffffffffffLLU;
+	uint64_t t2_ = t2 + (t1_ >> 51);
+	uint64_t t1__ = t1_ & 0x7ffffffffffffLLU;
+	uint64_t t3_ = t3 + (t2_ >> 51);
+	uint64_t t2__ = t2_ & 0x7ffffffffffffLLU;
+	uint64_t t4_ = t4 + (t3_ >> 51);
+	uint64_t t3__ = t3_ & 0x7ffffffffffffLLU;
+	input[0] = t0_;
+	input[1] = t1__;
+	input[2] = t2__;
+	input[3] = t3__;
+	input[4] = t4_;
 }
 
-#else
-typedef int64_t limb;
+static __always_inline void format_fcontract_first_carry_full(uint64_t *input)
+{
+	format_fcontract_first_carry_pass(input);
+	modulo_carry_top(input);
+}
 
-/* Field element representation:
- *
- * Field elements are written as an array of signed, 64-bit limbs, least
- * significant first. The value of the field element is:
- *   x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
- *
- * i.e. the limbs are 26, 25, 26, 25, ... bits wide.
- */
+static __always_inline void format_fcontract_second_carry_pass(uint64_t *input)
+{
+	uint64_t t0 = input[0];
+	uint64_t t1 = input[1];
+	uint64_t t2 = input[2];
+	uint64_t t3 = input[3];
+	uint64_t t4 = input[4];
+	uint64_t t1_ = t1 + (t0 >> 51);
+	uint64_t t0_ = t0 & 0x7ffffffffffffLLU;
+	uint64_t t2_ = t2 + (t1_ >> 51);
+	uint64_t t1__ = t1_ & 0x7ffffffffffffLLU;
+	uint64_t t3_ = t3 + (t2_ >> 51);
+	uint64_t t2__ = t2_ & 0x7ffffffffffffLLU;
+	uint64_t t4_ = t4 + (t3_ >> 51);
+	uint64_t t3__ = t3_ & 0x7ffffffffffffLLU;
+	input[0] = t0_;
+	input[1] = t1__;
+	input[2] = t2__;
+	input[3] = t3__;
+	input[4] = t4_;
+}
 
-/* Sum two numbers: output += in */
-static void fsum(limb *output, const limb *in)
+static __always_inline void format_fcontract_second_carry_full(uint64_t *input)
 {
-	unsigned int i;
+	uint64_t i0;
+	uint64_t i1;
+	uint64_t i0_;
+	uint64_t i1_;
+	format_fcontract_second_carry_pass(input);
+	modulo_carry_top(input);
+	i0 = input[0];
+	i1 = input[1];
+	i0_ = i0 & 0x7ffffffffffffLLU;
+	i1_ = i1 + (i0 >> 51);
+	input[0] = i0_;
+	input[1] = i1_;
+}
 
-	for (i = 0; i < 10; i += 2) {
-		output[0 + i] = output[0 + i] + in[0 + i];
-		output[1 + i] = output[1 + i] + in[1 + i];
-	}
+static __always_inline void format_fcontract_trim(uint64_t *input)
+{
+	uint64_t a0 = input[0];
+	uint64_t a1 = input[1];
+	uint64_t a2 = input[2];
+	uint64_t a3 = input[3];
+	uint64_t a4 = input[4];
+	uint64_t mask0 = uint64_t_gte_mask(a0, 0x7ffffffffffedLLU);
+	uint64_t mask1 = uint64_t_eq_mask(a1, 0x7ffffffffffffLLU);
+	uint64_t mask2 = uint64_t_eq_mask(a2, 0x7ffffffffffffLLU);
+	uint64_t mask3 = uint64_t_eq_mask(a3, 0x7ffffffffffffLLU);
+	uint64_t mask4 = uint64_t_eq_mask(a4, 0x7ffffffffffffLLU);
+	uint64_t mask = (((mask0 & mask1) & mask2) & mask3) & mask4;
+	uint64_t a0_ = a0 - (0x7ffffffffffedLLU & mask);
+	uint64_t a1_ = a1 - (0x7ffffffffffffLLU & mask);
+	uint64_t a2_ = a2 - (0x7ffffffffffffLLU & mask);
+	uint64_t a3_ = a3 - (0x7ffffffffffffLLU & mask);
+	uint64_t a4_ = a4 - (0x7ffffffffffffLLU & mask);
+	input[0] = a0_;
+	input[1] = a1_;
+	input[2] = a2_;
+	input[3] = a3_;
+	input[4] = a4_;
 }
 
-/* Find the difference of two numbers: output = in - output
- * (note the order of the arguments!).
- */
-static void fdifference(limb *output, const limb *in)
+static __always_inline void format_fcontract_store(uint8_t *output, uint64_t *input)
 {
-	unsigned int i;
+	uint64_t t0 = input[0];
+	uint64_t t1 = input[1];
+	uint64_t t2 = input[2];
+	uint64_t t3 = input[3];
+	uint64_t t4 = input[4];
+	uint64_t o0 = t1 << 51 | t0;
+	uint64_t o1 = t2 << 38 | t1 >> 13;
+	uint64_t o2 = t3 << 25 | t2 >> 26;
+	uint64_t o3 = t4 << 12 | t3 >> 39;
+	uint8_t *b0 = output;
+	uint8_t *b1 = output + 8;
+	uint8_t *b2 = output + 16;
+	uint8_t *b3 = output + 24;
+	*(uint64_t *)b0 = htole64(o0);
+	*(uint64_t *)b1 = htole64(o1);
+	*(uint64_t *)b2 = htole64(o2);
+	*(uint64_t *)b3 = htole64(o3);
+}
 
-	for (i = 0; i < 10; ++i) {
-		output[i] = in[i] - output[i];
-	}
+static __always_inline void format_fcontract(uint8_t *output, uint64_t *input)
+{
+	format_fcontract_first_carry_full(input);
+	format_fcontract_second_carry_full(input);
+	format_fcontract_trim(input);
+	format_fcontract_store(output, input);
 }
 
-/* Multiply a number by a scalar: output = in * scalar */
-static void fscalar_product(limb *output, const limb *in, const limb scalar)
+static __always_inline void format_scalar_of_point(uint8_t *scalar, uint64_t *point)
 {
-	unsigned int i;
+	uint64_t *x = point;
+	uint64_t *z = point + 5;
+	uint64_t buf[10] __aligned(32) = { 0 };
+	uint64_t *zmone = buf;
+	uint64_t *sc = buf + 5;
+	crecip(zmone, z);
+	fmul(sc, x, zmone);
+	format_fcontract(scalar, sc);
+}
 
-	for (i = 0; i < 10; ++i) {
-		output[i] = in[i] * scalar;
+void curve25519(uint8_t mypublic[static CURVE25519_POINT_SIZE], const uint8_t secret[static CURVE25519_POINT_SIZE], const uint8_t basepoint[static CURVE25519_POINT_SIZE])
+{
+	uint64_t buf0[10] __aligned(32) = { 0 };
+	uint64_t *x0 = buf0;
+	uint64_t *z = buf0 + 5;
+	uint64_t *q;
+	format_fexpand(x0, basepoint);
+	z[0] = 1;
+	q = buf0;
+	{
+		uint8_t e[32] __aligned(32) = { 0 };
+		uint8_t *scalar;
+		memcpy(e, secret, 32);
+		curve25519_normalize_secret(e);
+		scalar = e;
+		{
+			uint64_t buf[15] = { 0 };
+			uint64_t *nq = buf;
+			uint64_t *x = nq;
+			x[0] = 1;
+			ladder_cmult(nq, scalar, q);
+			format_scalar_of_point(mypublic, nq);
+		}
 	}
 }
-
-/* Multiply two numbers: output = in2 * in
- *
- * output must be distinct to both inputs. The inputs are reduced coefficient
- * form, the output is not.
- *
- * output[x] <= 14 * the largest product of the input limbs.
- */
-static void fproduct(limb *output, const limb *in2, const limb *in)
-{
-	output[0] =       ((limb) ((int32_t) in2[0])) * ((int32_t) in[0]);
-	output[1] =       ((limb) ((int32_t) in2[0])) * ((int32_t) in[1]) +
-					    ((limb) ((int32_t) in2[1])) * ((int32_t) in[0]);
-	output[2] =  2 *  ((limb) ((int32_t) in2[1])) * ((int32_t) in[1]) +
-					    ((limb) ((int32_t) in2[0])) * ((int32_t) in[2]) +
-					    ((limb) ((int32_t) in2[2])) * ((int32_t) in[0]);
-	output[3] =       ((limb) ((int32_t) in2[1])) * ((int32_t) in[2]) +
-					    ((limb) ((int32_t) in2[2])) * ((int32_t) in[1]) +
-					    ((limb) ((int32_t) in2[0])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in2[3])) * ((int32_t) in[0]);
-	output[4] =       ((limb) ((int32_t) in2[2])) * ((int32_t) in[2]) +
-				       2 * (((limb) ((int32_t) in2[1])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in2[3])) * ((int32_t) in[1])) +
-					    ((limb) ((int32_t) in2[0])) * ((int32_t) in[4]) +
-					    ((limb) ((int32_t) in2[4])) * ((int32_t) in[0]);
-	output[5] =       ((limb) ((int32_t) in2[2])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in2[3])) * ((int32_t) in[2]) +
-					    ((limb) ((int32_t) in2[1])) * ((int32_t) in[4]) +
-					    ((limb) ((int32_t) in2[4])) * ((int32_t) in[1]) +
-					    ((limb) ((int32_t) in2[0])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in2[5])) * ((int32_t) in[0]);
-	output[6] =  2 * (((limb) ((int32_t) in2[3])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in2[1])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in2[5])) * ((int32_t) in[1])) +
-					    ((limb) ((int32_t) in2[2])) * ((int32_t) in[4]) +
-					    ((limb) ((int32_t) in2[4])) * ((int32_t) in[2]) +
-					    ((limb) ((int32_t) in2[0])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in2[6])) * ((int32_t) in[0]);
-	output[7] =       ((limb) ((int32_t) in2[3])) * ((int32_t) in[4]) +
-					    ((limb) ((int32_t) in2[4])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in2[2])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in2[5])) * ((int32_t) in[2]) +
-					    ((limb) ((int32_t) in2[1])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in2[6])) * ((int32_t) in[1]) +
-					    ((limb) ((int32_t) in2[0])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in2[7])) * ((int32_t) in[0]);
-	output[8] =       ((limb) ((int32_t) in2[4])) * ((int32_t) in[4]) +
-				       2 * (((limb) ((int32_t) in2[3])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in2[5])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in2[1])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in2[7])) * ((int32_t) in[1])) +
-					    ((limb) ((int32_t) in2[2])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in2[6])) * ((int32_t) in[2]) +
-					    ((limb) ((int32_t) in2[0])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in2[8])) * ((int32_t) in[0]);
-	output[9] =       ((limb) ((int32_t) in2[4])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in2[5])) * ((int32_t) in[4]) +
-					    ((limb) ((int32_t) in2[3])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in2[6])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in2[2])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in2[7])) * ((int32_t) in[2]) +
-					    ((limb) ((int32_t) in2[1])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in2[8])) * ((int32_t) in[1]) +
-					    ((limb) ((int32_t) in2[0])) * ((int32_t) in[9]) +
-					    ((limb) ((int32_t) in2[9])) * ((int32_t) in[0]);
-	output[10] = 2 * (((limb) ((int32_t) in2[5])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in2[3])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in2[7])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in2[1])) * ((int32_t) in[9]) +
-					    ((limb) ((int32_t) in2[9])) * ((int32_t) in[1])) +
-					    ((limb) ((int32_t) in2[4])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in2[6])) * ((int32_t) in[4]) +
-					    ((limb) ((int32_t) in2[2])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in2[8])) * ((int32_t) in[2]);
-	output[11] =      ((limb) ((int32_t) in2[5])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in2[6])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in2[4])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in2[7])) * ((int32_t) in[4]) +
-					    ((limb) ((int32_t) in2[3])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in2[8])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in2[2])) * ((int32_t) in[9]) +
-					    ((limb) ((int32_t) in2[9])) * ((int32_t) in[2]);
-	output[12] =      ((limb) ((int32_t) in2[6])) * ((int32_t) in[6]) +
-				       2 * (((limb) ((int32_t) in2[5])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in2[7])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in2[3])) * ((int32_t) in[9]) +
-					    ((limb) ((int32_t) in2[9])) * ((int32_t) in[3])) +
-					    ((limb) ((int32_t) in2[4])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in2[8])) * ((int32_t) in[4]);
-	output[13] =      ((limb) ((int32_t) in2[6])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in2[7])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in2[5])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in2[8])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in2[4])) * ((int32_t) in[9]) +
-					    ((limb) ((int32_t) in2[9])) * ((int32_t) in[4]);
-	output[14] = 2 * (((limb) ((int32_t) in2[7])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in2[5])) * ((int32_t) in[9]) +
-					    ((limb) ((int32_t) in2[9])) * ((int32_t) in[5])) +
-					    ((limb) ((int32_t) in2[6])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in2[8])) * ((int32_t) in[6]);
-	output[15] =      ((limb) ((int32_t) in2[7])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in2[8])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in2[6])) * ((int32_t) in[9]) +
-					    ((limb) ((int32_t) in2[9])) * ((int32_t) in[6]);
-	output[16] =      ((limb) ((int32_t) in2[8])) * ((int32_t) in[8]) +
-				       2 * (((limb) ((int32_t) in2[7])) * ((int32_t) in[9]) +
-					    ((limb) ((int32_t) in2[9])) * ((int32_t) in[7]));
-	output[17] =      ((limb) ((int32_t) in2[8])) * ((int32_t) in[9]) +
-					    ((limb) ((int32_t) in2[9])) * ((int32_t) in[8]);
-	output[18] = 2 *  ((limb) ((int32_t) in2[9])) * ((int32_t) in[9]);
-}
-
-/* Reduce a long form to a short form by taking the input mod 2^255 - 19.
- *
- * On entry: |output[i]| < 14*2^54
- * On exit: |output[0..8]| < 280*2^54
+#else
+/* 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].
+ * fe limbs are bounded by 1.125*2^26,1.125*2^25,1.125*2^26,1.125*2^25,etc.
+ * Multiplication and carrying produce fe from fe_loose.
  */
-static void freduce_degree(limb *output)
-{
-	/* Each of these shifts and adds ends up multiplying the value by 19.
-	 *
-	 * For output[0..8], the absolute entry value is < 14*2^54 and we add, at
-	 * most, 19*14*2^54 thus, on exit, |output[0..8]| < 280*2^54.
-	 */
-	output[8] += output[18] << 4;
-	output[8] += output[18] << 1;
-	output[8] += output[18];
-	output[7] += output[17] << 4;
-	output[7] += output[17] << 1;
-	output[7] += output[17];
-	output[6] += output[16] << 4;
-	output[6] += output[16] << 1;
-	output[6] += output[16];
-	output[5] += output[15] << 4;
-	output[5] += output[15] << 1;
-	output[5] += output[15];
-	output[4] += output[14] << 4;
-	output[4] += output[14] << 1;
-	output[4] += output[14];
-	output[3] += output[13] << 4;
-	output[3] += output[13] << 1;
-	output[3] += output[13];
-	output[2] += output[12] << 4;
-	output[2] += output[12] << 1;
-	output[2] += output[12];
-	output[1] += output[11] << 4;
-	output[1] += output[11] << 1;
-	output[1] += output[11];
-	output[0] += output[10] << 4;
-	output[0] += output[10] << 1;
-	output[0] += output[10];
-}
-
-#if (-1 & 3) != 3
-#error "This code only works on a two's complement system"
-#endif
+typedef struct fe { uint32_t v[10]; } fe;
 
-/* return v / 2^26, using only shifts and adds.
- *
- * On entry: v can take any value.
+/* fe_loose limbs are bounded by 3.375*2^26,3.375*2^25,3.375*2^26,3.375*2^25,etc.
+ * Addition and subtraction produce fe_loose from (fe, fe).
  */
-static inline limb div_by_2_26(const limb v)
+typedef struct fe_loose { uint32_t v[10]; } fe_loose;
+
+static __always_inline void fe_frombytes_impl(uint32_t h[10], const uint8_t *s)
 {
-	/* High word of v; no shift needed. */
-	const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
-	/* Set to all 1s if v was negative; else set to 0s. */
-	const int32_t sign = ((int32_t) highword) >> 31;
-	/* Set to 0x3ffffff if v was negative; else set to 0. */
-	const int32_t roundoff = ((uint32_t) sign) >> 6;
-	/* Should return v / (1<<26) */
-	return (v + roundoff) >> 26;
+	/* Ignores top bit of s. */
+	uint32_t a0 = le32toh(*(uint32_t *)(s));
+	uint32_t a1 = le32toh(*(uint32_t *)(s+4));
+	uint32_t a2 = le32toh(*(uint32_t *)(s+8));
+	uint32_t a3 = le32toh(*(uint32_t *)(s+12));
+	uint32_t a4 = le32toh(*(uint32_t *)(s+16));
+	uint32_t a5 = le32toh(*(uint32_t *)(s+20));
+	uint32_t a6 = le32toh(*(uint32_t *)(s+24));
+	uint32_t a7 = le32toh(*(uint32_t *)(s+28));
+	h[0] = a0&((1<<26)-1);                    /* 26 used, 32-26 left.   26 */
+	h[1] = (a0>>26) | ((a1&((1<<19)-1))<< 6); /* (32-26) + 19 =  6+19 = 25 */
+	h[2] = (a1>>19) | ((a2&((1<<13)-1))<<13); /* (32-19) + 13 = 13+13 = 26 */
+	h[3] = (a2>>13) | ((a3&((1<< 6)-1))<<19); /* (32-13) +  6 = 19+ 6 = 25 */
+	h[4] = (a3>> 6);                          /* (32- 6)              = 26 */
+	h[5] = a4&((1<<25)-1);                    /*                        25 */
+	h[6] = (a4>>25) | ((a5&((1<<19)-1))<< 7); /* (32-25) + 19 =  7+19 = 26 */
+	h[7] = (a5>>19) | ((a6&((1<<12)-1))<<13); /* (32-19) + 12 = 13+12 = 25 */
+	h[8] = (a6>>12) | ((a7&((1<< 6)-1))<<20); /* (32-12) +  6 = 20+ 6 = 26 */
+	h[9] = (a7>> 6)&((1<<25)-1); /*                                     25 */
 }
 
-/* return v / (2^25), using only shifts and adds.
- *
- * On entry: v can take any value.
- */
-static inline limb div_by_2_25(const limb v)
+static __always_inline void fe_frombytes(fe *h, const uint8_t *s)
 {
-	/* High word of v; no shift needed*/
-	const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
-	/* Set to all 1s if v was negative; else set to 0s. */
-	const int32_t sign = ((int32_t) highword) >> 31;
-	/* Set to 0x1ffffff if v was negative; else set to 0. */
-	const int32_t roundoff = ((uint32_t) sign) >> 7;
-	/* Should return v / (1<<25) */
-	return (v + roundoff) >> 25;
+	fe_frombytes_impl(h->v, s);
 }
 
-/* Reduce all coefficients of the short form input so that |x| < 2^26.
- *
- * On entry: |output[i]| < 280*2^54
- */
-static void freduce_coefficients(limb *output)
+static __always_inline uint8_t /*bool*/ addcarryx_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
 {
-	unsigned int i;
-
-	output[10] = 0;
-
-	for (i = 0; i < 10; i += 2) {
-		limb over = div_by_2_26(output[i]);
-		/* The entry condition (that |output[i]| < 280*2^54) means that over is, at
-		 * most, 280*2^28 in the first iteration of this loop. This is added to the
-		 * next limb and we can approximate the resulting bound of that limb by
-		 * 281*2^54.
-		 */
-		output[i] -= over << 26;
-		output[i+1] += over;
-
-		/* For the first iteration, |output[i+1]| < 281*2^54, thus |over| <
-		 * 281*2^29. When this is added to the next limb, the resulting bound can
-		 * be approximated as 281*2^54.
-		 *
-		 * For subsequent iterations of the loop, 281*2^54 remains a conservative
-		 * bound and no overflow occurs.
-		 */
-		over = div_by_2_25(output[i+1]);
-		output[i+1] -= over << 25;
-		output[i+2] += over;
-	}
-	/* Now |output[10]| < 281*2^29 and all other coefficients are reduced. */
-	output[0] += output[10] << 4;
-	output[0] += output[10] << 1;
-	output[0] += output[10];
-
-	output[10] = 0;
-
-	/* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19*281*2^29
-	 * So |over| will be no more than 2^16.
+	/* This function extracts 25 bits of result and 1 bit of carry (26 total), so
+	 * a 32-bit intermediate is sufficient.
 	 */
-	{
-		limb over = div_by_2_26(output[0]);
-
-		output[0] -= over << 26;
-		output[1] += over;
-	}
+	uint32_t x = a + b + c;
+	*low = x & ((1 << 25) - 1);
+	return (x >> 25) & 1;
+}
 
-	/* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 2^16 < 2^26. The
-	 * bound on |output[1]| is sufficient to meet our needs.
+static __always_inline uint8_t /*bool*/ addcarryx_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
+{
+	/* This function extracts 26 bits of result and 1 bit of carry (27 total), so
+	 * a 32-bit intermediate is sufficient.
 	 */
+	uint32_t x = a + b + c;
+	*low = x & ((1 << 26) - 1);
+	return (x >> 26) & 1;
 }
 
-/* A helpful wrapper around fproduct: output = in * in2.
- *
- * On entry: |in[i]| < 2^27 and |in2[i]| < 2^27.
- *
- * output must be distinct to both inputs. The output is reduced degree
- * (indeed, one need only provide storage for 10 limbs) and |output[i]| < 2^26.
- */
-static void fmul(limb *output, const limb *in, const limb *in2)
+static __always_inline uint8_t /*bool*/ subborrow_u25(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
 {
-	limb t[19];
-
-	fproduct(t, in, in2);
-	/* |t[i]| < 14*2^54 */
-	freduce_degree(t);
-	freduce_coefficients(t);
-	/* |t[i]| < 2^26 */
-	memcpy(output, t, sizeof(limb) * 10);
+	/* This function extracts 25 bits of result and 1 bit of borrow (26 total), so
+	 * a 32-bit intermediate is sufficient.
+	 */
+	uint32_t x = a - b - c;
+	*low = x & ((1 << 25) - 1);
+	return x >> 31;
 }
 
-/* Square a number: output = in**2
- *
- * output must be distinct from the input. The inputs are reduced coefficient
- * form, the output is not.
- *
- * output[x] <= 14 * the largest product of the input limbs.
- */
-static void fsquare_inner(limb *output, const limb *in)
-{
-	output[0] =       ((limb) ((int32_t) in[0])) * ((int32_t) in[0]);
-	output[1] =  2 *  ((limb) ((int32_t) in[0])) * ((int32_t) in[1]);
-	output[2] =  2 * (((limb) ((int32_t) in[1])) * ((int32_t) in[1]) +
-					    ((limb) ((int32_t) in[0])) * ((int32_t) in[2]));
-	output[3] =  2 * (((limb) ((int32_t) in[1])) * ((int32_t) in[2]) +
-					    ((limb) ((int32_t) in[0])) * ((int32_t) in[3]));
-	output[4] =       ((limb) ((int32_t) in[2])) * ((int32_t) in[2]) +
-				       4 *  ((limb) ((int32_t) in[1])) * ((int32_t) in[3]) +
-				       2 *  ((limb) ((int32_t) in[0])) * ((int32_t) in[4]);
-	output[5] =  2 * (((limb) ((int32_t) in[2])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in[1])) * ((int32_t) in[4]) +
-					    ((limb) ((int32_t) in[0])) * ((int32_t) in[5]));
-	output[6] =  2 * (((limb) ((int32_t) in[3])) * ((int32_t) in[3]) +
-					    ((limb) ((int32_t) in[2])) * ((int32_t) in[4]) +
-					    ((limb) ((int32_t) in[0])) * ((int32_t) in[6]) +
-				       2 *  ((limb) ((int32_t) in[1])) * ((int32_t) in[5]));
-	output[7] =  2 * (((limb) ((int32_t) in[3])) * ((int32_t) in[4]) +
-					    ((limb) ((int32_t) in[2])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in[1])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in[0])) * ((int32_t) in[7]));
-	output[8] =       ((limb) ((int32_t) in[4])) * ((int32_t) in[4]) +
-				       2 * (((limb) ((int32_t) in[2])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in[0])) * ((int32_t) in[8]) +
-				       2 * (((limb) ((int32_t) in[1])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in[3])) * ((int32_t) in[5])));
-	output[9] =  2 * (((limb) ((int32_t) in[4])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in[3])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in[2])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in[1])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in[0])) * ((int32_t) in[9]));
-	output[10] = 2 * (((limb) ((int32_t) in[5])) * ((int32_t) in[5]) +
-					    ((limb) ((int32_t) in[4])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in[2])) * ((int32_t) in[8]) +
-				       2 * (((limb) ((int32_t) in[3])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in[1])) * ((int32_t) in[9])));
-	output[11] = 2 * (((limb) ((int32_t) in[5])) * ((int32_t) in[6]) +
-					    ((limb) ((int32_t) in[4])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in[3])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in[2])) * ((int32_t) in[9]));
-	output[12] =      ((limb) ((int32_t) in[6])) * ((int32_t) in[6]) +
-				       2 * (((limb) ((int32_t) in[4])) * ((int32_t) in[8]) +
-				       2 * (((limb) ((int32_t) in[5])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in[3])) * ((int32_t) in[9])));
-	output[13] = 2 * (((limb) ((int32_t) in[6])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in[5])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in[4])) * ((int32_t) in[9]));
-	output[14] = 2 * (((limb) ((int32_t) in[7])) * ((int32_t) in[7]) +
-					    ((limb) ((int32_t) in[6])) * ((int32_t) in[8]) +
-				       2 *  ((limb) ((int32_t) in[5])) * ((int32_t) in[9]));
-	output[15] = 2 * (((limb) ((int32_t) in[7])) * ((int32_t) in[8]) +
-					    ((limb) ((int32_t) in[6])) * ((int32_t) in[9]));
-	output[16] =      ((limb) ((int32_t) in[8])) * ((int32_t) in[8]) +
-				       4 *  ((limb) ((int32_t) in[7])) * ((int32_t) in[9]);
-	output[17] = 2 *  ((limb) ((int32_t) in[8])) * ((int32_t) in[9]);
-	output[18] = 2 *  ((limb) ((int32_t) in[9])) * ((int32_t) in[9]);
-}
-
-/* fsquare sets output = in^2.
- *
- * On entry: The |in| argument is in reduced coefficients form and |in[i]| <
- * 2^27.
- *
- * On exit: The |output| argument is in reduced coefficients form (indeed, one
- * need only provide storage for 10 limbs) and |out[i]| < 2^26.
- */
-static void fsquare(limb *output, const limb *in)
+static __always_inline uint8_t /*bool*/ subborrow_u26(uint8_t /*bool*/ c, uint32_t a, uint32_t b, uint32_t *low)
 {
-	limb t[19];
-
-	fsquare_inner(t, in);
-	/* |t[i]| < 14*2^54 because the largest product of two limbs will be <
-	 * 2^(27+27) and fsquare_inner adds together, at most, 14 of those
-	 * products.
+	/* This function extracts 26 bits of result and 1 bit of borrow (27 total), so
+	 * a 32-bit intermediate is sufficient.
 	 */
-	freduce_degree(t);
-	freduce_coefficients(t);
-	/* |t[i]| < 2^26 */
-	memcpy(output, t, sizeof(limb) * 10);
-}
-
-/* Take a little-endian, 32-byte number and expand it into polynomial form */
-static void fexpand(limb *output, const uint8_t *input)
-{
-#define F(n, start, shift, mask) \
-	output[n] = ((((limb) input[start + 0]) | \
-		      ((limb) input[start + 1]) << 8 | \
-		      ((limb) input[start + 2]) << 16 | \
-		      ((limb) input[start + 3]) << 24) >> shift) & mask;
-	F(0, 0, 0, 0x3ffffff);
-	F(1, 3, 2, 0x1ffffff);
-	F(2, 6, 3, 0x3ffffff);
-	F(3, 9, 5, 0x1ffffff);
-	F(4, 12, 6, 0x3ffffff);
-	F(5, 16, 0, 0x1ffffff);
-	F(6, 19, 1, 0x3ffffff);
-	F(7, 22, 3, 0x1ffffff);
-	F(8, 25, 4, 0x3ffffff);
-	F(9, 28, 6, 0x1ffffff);
-#undef F
-}
-
-#if (-32 >> 1) != -16
-#error "This code only works when >> does sign-extension on negative numbers"
-#endif
+	uint32_t x = a - b - c;
+	*low = x & ((1 << 26) - 1);
+	return x >> 31;
+}
 
-/* int32_t_eq returns 0xffffffff iff a == b and zero otherwise. */
-static int32_t int32_t_eq(int32_t a, int32_t b)
+static __always_inline uint32_t cmovznz32(uint32_t t, uint32_t z, uint32_t nz)
 {
-	a = ~(a ^ b);
-	a &= a << 16;
-	a &= a << 8;
-	a &= a << 4;
-	a &= a << 2;
-	a &= a << 1;
-	return a >> 31;
+	t = -!!t; /* all set if nonzero, 0 if 0 */
+	return (t&nz) | ((~t)&z);
 }
 
-/* int32_t_gte returns 0xffffffff if a >= b and zero otherwise, where a and b are
- * both non-negative.
- */
-static int32_t int32_t_gte(int32_t a, int32_t b)
+static __always_inline void fe_freeze(uint32_t out[10], const uint32_t in1[10])
 {
-	a -= b;
-	/* a >= 0 iff a >= b. */
-	return ~(a >> 31);
+	{ const uint32_t x17 = in1[9];
+	{ const uint32_t x18 = in1[8];
+	{ const uint32_t x16 = in1[7];
+	{ const uint32_t x14 = in1[6];
+	{ const uint32_t x12 = in1[5];
+	{ const uint32_t x10 = in1[4];
+	{ const uint32_t x8 = in1[3];
+	{ const uint32_t x6 = in1[2];
+	{ const uint32_t x4 = in1[1];
+	{ const uint32_t x2 = in1[0];
+	{ uint32_t x20; uint8_t/*bool*/ x21 = subborrow_u26(0x0, x2, 0x3ffffed, &x20);
+	{ uint32_t x23; uint8_t/*bool*/ x24 = subborrow_u25(x21, x4, 0x1ffffff, &x23);
+	{ uint32_t x26; uint8_t/*bool*/ x27 = subborrow_u26(x24, x6, 0x3ffffff, &x26);
+	{ uint32_t x29; uint8_t/*bool*/ x30 = subborrow_u25(x27, x8, 0x1ffffff, &x29);
+	{ uint32_t x32; uint8_t/*bool*/ x33 = subborrow_u26(x30, x10, 0x3ffffff, &x32);
+	{ uint32_t x35; uint8_t/*bool*/ x36 = subborrow_u25(x33, x12, 0x1ffffff, &x35);
+	{ uint32_t x38; uint8_t/*bool*/ x39 = subborrow_u26(x36, x14, 0x3ffffff, &x38);
+	{ uint32_t x41; uint8_t/*bool*/ x42 = subborrow_u25(x39, x16, 0x1ffffff, &x41);
+	{ uint32_t x44; uint8_t/*bool*/ x45 = subborrow_u26(x42, x18, 0x3ffffff, &x44);
+	{ uint32_t x47; uint8_t/*bool*/ x48 = subborrow_u25(x45, x17, 0x1ffffff, &x47);
+	{ uint32_t x49 = cmovznz32(x48, 0x0, 0xffffffff);
+	{ uint32_t x50 = (x49 & 0x3ffffed);
+	{ uint32_t x52; uint8_t/*bool*/ x53 = addcarryx_u26(0x0, x20, x50, &x52);
+	{ uint32_t x54 = (x49 & 0x1ffffff);
+	{ uint32_t x56; uint8_t/*bool*/ x57 = addcarryx_u25(x53, x23, x54, &x56);
+	{ uint32_t x58 = (x49 & 0x3ffffff);
+	{ uint32_t x60; uint8_t/*bool*/ x61 = addcarryx_u26(x57, x26, x58, &x60);
+	{ uint32_t x62 = (x49 & 0x1ffffff);
+	{ uint32_t x64; uint8_t/*bool*/ x65 = addcarryx_u25(x61, x29, x62, &x64);
+	{ uint32_t x66 = (x49 & 0x3ffffff);
+	{ uint32_t x68; uint8_t/*bool*/ x69 = addcarryx_u26(x65, x32, x66, &x68);
+	{ uint32_t x70 = (x49 & 0x1ffffff);
+	{ uint32_t x72; uint8_t/*bool*/ x73 = addcarryx_u25(x69, x35, x70, &x72);
+	{ uint32_t x74 = (x49 & 0x3ffffff);
+	{ uint32_t x76; uint8_t/*bool*/ x77 = addcarryx_u26(x73, x38, x74, &x76);
+	{ uint32_t x78 = (x49 & 0x1ffffff);
+	{ uint32_t x80; uint8_t/*bool*/ x81 = addcarryx_u25(x77, x41, x78, &x80);
+	{ uint32_t x82 = (x49 & 0x3ffffff);
+	{ uint32_t x84; uint8_t/*bool*/ x85 = addcarryx_u26(x81, x44, x82, &x84);
+	{ uint32_t x86 = (x49 & 0x1ffffff);
+	{ uint32_t x88; addcarryx_u25(x85, x47, x86, &x88);
+	out[0] = x52;
+	out[1] = x56;
+	out[2] = x60;
+	out[3] = x64;
+	out[4] = x68;
+	out[5] = x72;
+	out[6] = x76;
+	out[7] = x80;
+	out[8] = x84;
+	out[9] = x88;
+	}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
 }
 
-/* Take a fully reduced polynomial form number and contract it into a
- * little-endian, 32-byte array.
- *
- * On entry: |input_limbs[i]| < 2^26
- */
-static void fcontract(uint8_t *output, limb *input_limbs)
+static __always_inline void fe_tobytes(uint8_t s[32], const fe *f)
 {
-	int i;
-	int j;
-	int32_t input[10];
-	int32_t mask;
-
-	/* |input_limbs[i]| < 2^26, so it's valid to convert to an int32_t. */
-	for (i = 0; i < 10; i++) {
-		input[i] = input_limbs[i];
-	}
-
-	for (j = 0; j < 2; ++j) {
-		for (i = 0; i < 9; ++i) {
-			if ((i & 1) == 1) {
-				/* This calculation is a time-invariant way to make input[i]
-				 * non-negative by borrowing from the next-larger limb.
-				 */
-				const int32_t mask = input[i] >> 31;
-				const int32_t carry = -((input[i] & mask) >> 25);
-
-				input[i] = input[i] + (carry << 25);
-				input[i+1] = input[i+1] - carry;
-			} else {
-				const int32_t mask = input[i] >> 31;
-				const int32_t carry = -((input[i] & mask) >> 26);
-
-				input[i] = input[i] + (carry << 26);
-				input[i+1] = input[i+1] - carry;
-			}
-		}
+	uint32_t h[10];
+	fe_freeze(h, f->v);
+	s[0] = h[0] >> 0;
+	s[1] = h[0] >> 8;
+	s[2] = h[0] >> 16;
+	s[3] = (h[0] >> 24) | (h[1] << 2);
+	s[4] = h[1] >> 6;
+	s[5] = h[1] >> 14;
+	s[6] = (h[1] >> 22) | (h[2] << 3);
+	s[7] = h[2] >> 5;
+	s[8] = h[2] >> 13;
+	s[9] = (h[2] >> 21) | (h[3] << 5);
+	s[10] = h[3] >> 3;
+	s[11] = h[3] >> 11;
+	s[12] = (h[3] >> 19) | (h[4] << 6);
+	s[13] = h[4] >> 2;
+	s[14] = h[4] >> 10;
+	s[15] = h[4] >> 18;
+	s[16] = h[5] >> 0;
+	s[17] = h[5] >> 8;
+	s[18] = h[5] >> 16;
+	s[19] = (h[5] >> 24) | (h[6] << 1);
+	s[20] = h[6] >> 7;
+	s[21] = h[6] >> 15;
+	s[22] = (h[6] >> 23) | (h[7] << 3);
+	s[23] = h[7] >> 5;
+	s[24] = h[7] >> 13;
+	s[25] = (h[7] >> 21) | (h[8] << 4);
+	s[26] = h[8] >> 4;
+	s[27] = h[8] >> 12;
+	s[28] = (h[8] >> 20) | (h[9] << 6);
+	s[29] = h[9] >> 2;
+	s[30] = h[9] >> 10;
+	s[31] = h[9] >> 18;
+}
 
-		/* There's no greater limb for input[9] to borrow from, but we can multiply
-		 * by 19 and borrow from input[0], which is valid mod 2^255-19.
-		 */
-		{
-			const int32_t mask = input[9] >> 31;
-			const int32_t carry = -((input[9] & mask) >> 25);
+/* h = f */
+static __always_inline void fe_copy(fe *h, const fe *f)
+{
+	memmove(h, f, sizeof(uint32_t) * 10);
+}
 
-			input[9] = input[9] + (carry << 25);
-			input[0] = input[0] - (carry * 19);
-		}
+static __always_inline void fe_copy_lt(fe_loose *h, const fe *f)
+{
+	memmove(h, f, sizeof(uint32_t) * 10);
+}
 
-		/* After the first iteration, input[1..9] are non-negative and fit within
-		 * 25 or 26 bits, depending on position. However, input[0] may be
-		 * negative.
-		 */
-	}
+/* h = 0 */
+static __always_inline void fe_0(fe *h)
+{
+	memset(h, 0, sizeof(uint32_t) * 10);
+}
 
-	/* The first borrow-propagation pass above ended with every limb
-		 except (possibly) input[0] non-negative.
-		 If input[0] was negative after the first pass, then it was because of a
-		 carry from input[9]. On entry, input[9] < 2^26 so the carry was, at most,
-		 one, since (2**26-1) >> 25 = 1. Thus input[0] >= -19.
-		 In the second pass, each limb is decreased by at most one. Thus the second
-		 borrow-propagation pass could only have wrapped around to decrease
-		 input[0] again if the first pass left input[0] negative *and* input[1]
-		 through input[9] were all zero.  In that case, input[1] is now 2^25 - 1,
-		 and this last borrow-propagation step will leave input[1] non-negative. */
-	{
-		const int32_t mask = input[0] >> 31;
-		const int32_t carry = -((input[0] & mask) >> 26);
+/* h = 1 */
+static __always_inline void fe_1(fe *h)
+{
+	memset(h, 0, sizeof(uint32_t) * 10);
+	h->v[0] = 1;
+}
 
-		input[0] = input[0] + (carry << 26);
-		input[1] = input[1] - carry;
-	}
+static __always_inline void fe_add_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10])
+{
+	{ const uint32_t x20 = in1[9];
+	{ const uint32_t x21 = in1[8];
+	{ const uint32_t x19 = in1[7];
+	{ const uint32_t x17 = in1[6];
+	{ const uint32_t x15 = in1[5];
+	{ const uint32_t x13 = in1[4];
+	{ const uint32_t x11 = in1[3];
+	{ const uint32_t x9 = in1[2];
+	{ const uint32_t x7 = in1[1];
+	{ const uint32_t x5 = in1[0];
+	{ const uint32_t x38 = in2[9];
+	{ const uint32_t x39 = in2[8];
+	{ const uint32_t x37 = in2[7];
+	{ const uint32_t x35 = in2[6];
+	{ const uint32_t x33 = in2[5];
+	{ const uint32_t x31 = in2[4];
+	{ const uint32_t x29 = in2[3];
+	{ const uint32_t x27 = in2[2];
+	{ const uint32_t x25 = in2[1];
+	{ const uint32_t x23 = in2[0];
+	out[0] = (x5 + x23);
+	out[1] = (x7 + x25);
+	out[2] = (x9 + x27);
+	out[3] = (x11 + x29);
+	out[4] = (x13 + x31);
+	out[5] = (x15 + x33);
+	out[6] = (x17 + x35);
+	out[7] = (x19 + x37);
+	out[8] = (x21 + x39);
+	out[9] = (x20 + x38);
+	}}}}}}}}}}}}}}}}}}}}
+}
 
-	/* All input[i] are now non-negative. However, there might be values between
-	 * 2^25 and 2^26 in a limb which is, nominally, 25 bits wide.
-	 */
-	for (j = 0; j < 2; j++) {
-		for (i = 0; i < 9; i++) {
-			if ((i & 1) == 1) {
-				const int32_t carry = input[i] >> 25;
-
-				input[i] &= 0x1ffffff;
-				input[i+1] += carry;
-			} else {
-				const int32_t carry = input[i] >> 26;
-
-				input[i] &= 0x3ffffff;
-				input[i+1] += carry;
-			}
-		}
+/* h = f + g
+ * Can overlap h with f or g.
+ */
+static __always_inline void fe_add(fe_loose *h, const fe *f, const fe *g)
+{
+	fe_add_impl(h->v, f->v, g->v);
+}
 
-		{
-			const int32_t carry = input[9] >> 25;
+static __always_inline void fe_sub_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10])
+{
+	{ const uint32_t x20 = in1[9];
+	{ const uint32_t x21 = in1[8];
+	{ const uint32_t x19 = in1[7];
+	{ const uint32_t x17 = in1[6];
+	{ const uint32_t x15 = in1[5];
+	{ const uint32_t x13 = in1[4];
+	{ const uint32_t x11 = in1[3];
+	{ const uint32_t x9 = in1[2];
+	{ const uint32_t x7 = in1[1];
+	{ const uint32_t x5 = in1[0];
+	{ const uint32_t x38 = in2[9];
+	{ const uint32_t x39 = in2[8];
+	{ const uint32_t x37 = in2[7];
+	{ const uint32_t x35 = in2[6];
+	{ const uint32_t x33 = in2[5];
+	{ const uint32_t x31 = in2[4];
+	{ const uint32_t x29 = in2[3];
+	{ const uint32_t x27 = in2[2];
+	{ const uint32_t x25 = in2[1];
+	{ const uint32_t x23 = in2[0];
+	out[0] = ((0x7ffffda + x5) - x23);
+	out[1] = ((0x3fffffe + x7) - x25);
+	out[2] = ((0x7fffffe + x9) - x27);
+	out[3] = ((0x3fffffe + x11) - x29);
+	out[4] = ((0x7fffffe + x13) - x31);
+	out[5] = ((0x3fffffe + x15) - x33);
+	out[6] = ((0x7fffffe + x17) - x35);
+	out[7] = ((0x3fffffe + x19) - x37);
+	out[8] = ((0x7fffffe + x21) - x39);
+	out[9] = ((0x3fffffe + x20) - x38);
+	}}}}}}}}}}}}}}}}}}}}
+}
 
-			input[9] &= 0x1ffffff;
-			input[0] += 19*carry;
-		}
-	}
+/* h = f - g
+ * Can overlap h with f or g.
+ */
+static __always_inline void fe_sub(fe_loose *h, const fe *f, const fe *g)
+{
+	fe_sub_impl(h->v, f->v, g->v);
+}
 
-	/* If the first carry-chain pass, just above, ended up with a carry from
-	 * input[9], and that caused input[0] to be out-of-bounds, then input[0] was
-	 * < 2^26 + 2*19, because the carry was, at most, two.
-	 *
-	 * If the second pass carried from input[9] again then input[0] is < 2*19 and
-	 * the input[9] -> input[0] carry didn't push input[0] out of bounds.
-	 */
+static __always_inline void fe_mul_impl(uint32_t out[10], const uint32_t in1[10], const uint32_t in2[10])
+{
+	{ const uint32_t x20 = in1[9];
+	{ const uint32_t x21 = in1[8];
+	{ const uint32_t x19 = in1[7];
+	{ const uint32_t x17 = in1[6];
+	{ const uint32_t x15 = in1[5];
+	{ const uint32_t x13 = in1[4];
+	{ const uint32_t x11 = in1[3];
+	{ const uint32_t x9 = in1[2];
+	{ const uint32_t x7 = in1[1];
+	{ const uint32_t x5 = in1[0];
+	{ const uint32_t x38 = in2[9];
+	{ const uint32_t x39 = in2[8];
+	{ const uint32_t x37 = in2[7];
+	{ const uint32_t x35 = in2[6];
+	{ const uint32_t x33 = in2[5];
+	{ const uint32_t x31 = in2[4];
+	{ const uint32_t x29 = in2[3];
+	{ const uint32_t x27 = in2[2];
+	{ const uint32_t x25 = in2[1];
+	{ const uint32_t x23 = in2[0];
+	{ uint64_t x40 = ((uint64_t)x23 * x5);
+	{ uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+	{ uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+	{ uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+	{ uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+	{ uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+	{ uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+	{ uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+	{ uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+	{ uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+	{ uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+	{ uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+	{ uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+	{ uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+	{ uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+	{ uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+	{ uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+	{ uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+	{ uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+	{ uint64_t x59 = (x48 + (x58 << 0x4));
+	{ uint64_t x60 = (x59 + (x58 << 0x1));
+	{ uint64_t x61 = (x60 + x58);
+	{ uint64_t x62 = (x47 + (x57 << 0x4));
+	{ uint64_t x63 = (x62 + (x57 << 0x1));
+	{ uint64_t x64 = (x63 + x57);
+	{ uint64_t x65 = (x46 + (x56 << 0x4));
+	{ uint64_t x66 = (x65 + (x56 << 0x1));
+	{ uint64_t x67 = (x66 + x56);
+	{ uint64_t x68 = (x45 + (x55 << 0x4));
+	{ uint64_t x69 = (x68 + (x55 << 0x1));
+	{ uint64_t x70 = (x69 + x55);
+	{ uint64_t x71 = (x44 + (x54 << 0x4));
+	{ uint64_t x72 = (x71 + (x54 << 0x1));
+	{ uint64_t x73 = (x72 + x54);
+	{ uint64_t x74 = (x43 + (x53 << 0x4));
+	{ uint64_t x75 = (x74 + (x53 << 0x1));
+	{ uint64_t x76 = (x75 + x53);
+	{ uint64_t x77 = (x42 + (x52 << 0x4));
+	{ uint64_t x78 = (x77 + (x52 << 0x1));
+	{ uint64_t x79 = (x78 + x52);
+	{ uint64_t x80 = (x41 + (x51 << 0x4));
+	{ uint64_t x81 = (x80 + (x51 << 0x1));
+	{ uint64_t x82 = (x81 + x51);
+	{ uint64_t x83 = (x40 + (x50 << 0x4));
+	{ uint64_t x84 = (x83 + (x50 << 0x1));
+	{ uint64_t x85 = (x84 + x50);
+	{ uint64_t x86 = (x85 >> 0x1a);
+	{ uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+	{ uint64_t x88 = (x86 + x82);
+	{ uint64_t x89 = (x88 >> 0x19);
+	{ uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+	{ uint64_t x91 = (x89 + x79);
+	{ uint64_t x92 = (x91 >> 0x1a);
+	{ uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+	{ uint64_t x94 = (x92 + x76);
+	{ uint64_t x95 = (x94 >> 0x19);
+	{ uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+	{ uint64_t x97 = (x95 + x73);
+	{ uint64_t x98 = (x97 >> 0x1a);
+	{ uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+	{ uint64_t x100 = (x98 + x70);
+	{ uint64_t x101 = (x100 >> 0x19);
+	{ uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+	{ uint64_t x103 = (x101 + x67);
+	{ uint64_t x104 = (x103 >> 0x1a);
+	{ uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+	{ uint64_t x106 = (x104 + x64);
+	{ uint64_t x107 = (x106 >> 0x19);
+	{ uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+	{ uint64_t x109 = (x107 + x61);
+	{ uint64_t x110 = (x109 >> 0x1a);
+	{ uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+	{ uint64_t x112 = (x110 + x49);
+	{ uint64_t x113 = (x112 >> 0x19);
+	{ uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+	{ uint64_t x115 = (x87 + (0x13 * x113));
+	{ uint32_t x116 = (uint32_t) (x115 >> 0x1a);
+	{ uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+	{ uint32_t x118 = (x116 + x90);
+	{ uint32_t x119 = (x118 >> 0x19);
+	{ uint32_t x120 = (x118 & 0x1ffffff);
+	out[0] = x117;
+	out[1] = x120;
+	out[2] = (x119 + x93);
+	out[3] = x96;
+	out[4] = x99;
+	out[5] = x102;
+	out[6] = x105;
+	out[7] = x108;
+	out[8] = x111;
+	out[9] = x114;
+	}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+}
 
-	/* It still remains the case that input might be between 2^255-19 and 2^255.
-	 * In this case, input[1..9] must take their maximum value and input[0] must
-	 * be >= (2^255-19) & 0x3ffffff, which is 0x3ffffed.
-	 */
-	mask = int32_t_gte(input[0], 0x3ffffed);
-	for (i = 1; i < 10; i++) {
-		if ((i & 1) == 1) {
-			mask &= int32_t_eq(input[i], 0x1ffffff);
-		} else {
-			mask &= int32_t_eq(input[i], 0x3ffffff);
-		}
-	}
+static __always_inline void fe_mul_ttt(fe *h, const fe *f, const fe *g)
+{
+	fe_mul_impl(h->v, f->v, g->v);
+}
 
-	/* mask is either 0xffffffff (if input >= 2^255-19) and zero otherwise. Thus
-	 * this conditionally subtracts 2^255-19.
-	 */
-	input[0] -= mask & 0x3ffffed;
+static __always_inline void fe_mul_tlt(fe *h, const fe_loose *f, const fe *g)
+{
+	fe_mul_impl(h->v, f->v, g->v);
+}
 
-	for (i = 1; i < 10; i++) {
-		if ((i & 1) == 1) {
-			input[i] -= mask & 0x1ffffff;
-		} else {
-			input[i] -= mask & 0x3ffffff;
-		}
-	}
+static __always_inline void fe_mul_tll(fe *h, const fe_loose *f, const fe_loose *g)
+{
+	fe_mul_impl(h->v, f->v, g->v);
+}
 
-	input[1] <<= 2;
-	input[2] <<= 3;
-	input[3] <<= 5;
-	input[4] <<= 6;
-	input[6] <<= 1;
-	input[7] <<= 3;
-	input[8] <<= 4;
-	input[9] <<= 6;
-#define F(i, s) \
-	output[s+0] |=  input[i] & 0xff; \
-	output[s+1]  = (input[i] >> 8) & 0xff; \
-	output[s+2]  = (input[i] >> 16) & 0xff; \
-	output[s+3]  = (input[i] >> 24) & 0xff;
-	output[0] = 0;
-	output[16] = 0;
-	F(0, 0);
-	F(1, 3);
-	F(2, 6);
-	F(3, 9);
-	F(4, 12);
-	F(5, 16);
-	F(6, 19);
-	F(7, 22);
-	F(8, 25);
-	F(9, 28);
-#undef F
-}
-
-/* Input: Q, Q', Q-Q'
- * Output: 2Q, Q+Q'
- *
- *   x2 z3: long form
- *   x3 z3: long form
- *   x z: short form, destroyed
- *   xprime zprime: short form, destroyed
- *   qmqp: short form, preserved
- *
- * On entry and exit, the absolute value of the limbs of all inputs and outputs
- * are < 2^26.
- */
-static void fmonty(limb *x2, limb *z2,  /* output 2Q */
-		   limb *x3, limb *z3,  /* output Q + Q' */
-		   limb *x, limb *z,    /* input Q */
-		   limb *xprime, limb *zprime,  /* input Q' */
+static __always_inline void fe_sqr_impl(uint32_t out[10], const uint32_t in1[10])
+{
+	{ const uint32_t x17 = in1[9];
+	{ const uint32_t x18 = in1[8];
+	{ const uint32_t x16 = in1[7];
+	{ const uint32_t x14 = in1[6];
+	{ const uint32_t x12 = in1[5];
+	{ const uint32_t x10 = in1[4];
+	{ const uint32_t x8 = in1[3];
+	{ const uint32_t x6 = in1[2];
+	{ const uint32_t x4 = in1[1];
+	{ const uint32_t x2 = in1[0];
+	{ uint64_t x19 = ((uint64_t)x2 * x2);
+	{ uint64_t x20 = ((uint64_t)(0x2 * x2) * x4);
+	{ uint64_t x21 = (0x2 * (((uint64_t)x4 * x4) + ((uint64_t)x2 * x6)));
+	{ uint64_t x22 = (0x2 * (((uint64_t)x4 * x6) + ((uint64_t)x2 * x8)));
+	{ uint64_t x23 = ((((uint64_t)x6 * x6) + ((uint64_t)(0x4 * x4) * x8)) + ((uint64_t)(0x2 * x2) * x10));
+	{ uint64_t x24 = (0x2 * ((((uint64_t)x6 * x8) + ((uint64_t)x4 * x10)) + ((uint64_t)x2 * x12)));
+	{ uint64_t x25 = (0x2 * (((((uint64_t)x8 * x8) + ((uint64_t)x6 * x10)) + ((uint64_t)x2 * x14)) + ((uint64_t)(0x2 * x4) * x12)));
+	{ uint64_t x26 = (0x2 * (((((uint64_t)x8 * x10) + ((uint64_t)x6 * x12)) + ((uint64_t)x4 * x14)) + ((uint64_t)x2 * x16)));
+	{ uint64_t x27 = (((uint64_t)x10 * x10) + (0x2 * ((((uint64_t)x6 * x14) + ((uint64_t)x2 * x18)) + (0x2 * (((uint64_t)x4 * x16) + ((uint64_t)x8 * x12))))));
+	{ uint64_t x28 = (0x2 * ((((((uint64_t)x10 * x12) + ((uint64_t)x8 * x14)) + ((uint64_t)x6 * x16)) + ((uint64_t)x4 * x18)) + ((uint64_t)x2 * x17)));
+	{ uint64_t x29 = (0x2 * (((((uint64_t)x12 * x12) + ((uint64_t)x10 * x14)) + ((uint64_t)x6 * x18)) + (0x2 * (((uint64_t)x8 * x16) + ((uint64_t)x4 * x17)))));
+	{ uint64_t x30 = (0x2 * (((((uint64_t)x12 * x14) + ((uint64_t)x10 * x16)) + ((uint64_t)x8 * x18)) + ((uint64_t)x6 * x17)));
+	{ uint64_t x31 = (((uint64_t)x14 * x14) + (0x2 * (((uint64_t)x10 * x18) + (0x2 * (((uint64_t)x12 * x16) + ((uint64_t)x8 * x17))))));
+	{ uint64_t x32 = (0x2 * ((((uint64_t)x14 * x16) + ((uint64_t)x12 * x18)) + ((uint64_t)x10 * x17)));
+	{ uint64_t x33 = (0x2 * ((((uint64_t)x16 * x16) + ((uint64_t)x14 * x18)) + ((uint64_t)(0x2 * x12) * x17)));
+	{ uint64_t x34 = (0x2 * (((uint64_t)x16 * x18) + ((uint64_t)x14 * x17)));
+	{ uint64_t x35 = (((uint64_t)x18 * x18) + ((uint64_t)(0x4 * x16) * x17));
+	{ uint64_t x36 = ((uint64_t)(0x2 * x18) * x17);
+	{ uint64_t x37 = ((uint64_t)(0x2 * x17) * x17);
+	{ uint64_t x38 = (x27 + (x37 << 0x4));
+	{ uint64_t x39 = (x38 + (x37 << 0x1));
+	{ uint64_t x40 = (x39 + x37);
+	{ uint64_t x41 = (x26 + (x36 << 0x4));
+	{ uint64_t x42 = (x41 + (x36 << 0x1));
+	{ uint64_t x43 = (x42 + x36);
+	{ uint64_t x44 = (x25 + (x35 << 0x4));
+	{ uint64_t x45 = (x44 + (x35 << 0x1));
+	{ uint64_t x46 = (x45 + x35);
+	{ uint64_t x47 = (x24 + (x34 << 0x4));
+	{ uint64_t x48 = (x47 + (x34 << 0x1));
+	{ uint64_t x49 = (x48 + x34);
+	{ uint64_t x50 = (x23 + (x33 << 0x4));
+	{ uint64_t x51 = (x50 + (x33 << 0x1));
+	{ uint64_t x52 = (x51 + x33);
+	{ uint64_t x53 = (x22 + (x32 << 0x4));
+	{ uint64_t x54 = (x53 + (x32 << 0x1));
+	{ uint64_t x55 = (x54 + x32);
+	{ uint64_t x56 = (x21 + (x31 << 0x4));
+	{ uint64_t x57 = (x56 + (x31 << 0x1));
+	{ uint64_t x58 = (x57 + x31);
+	{ uint64_t x59 = (x20 + (x30 << 0x4));
+	{ uint64_t x60 = (x59 + (x30 << 0x1));
+	{ uint64_t x61 = (x60 + x30);
+	{ uint64_t x62 = (x19 + (x29 << 0x4));
+	{ uint64_t x63 = (x62 + (x29 << 0x1));
+	{ uint64_t x64 = (x63 + x29);
+	{ uint64_t x65 = (x64 >> 0x1a);
+	{ uint32_t x66 = ((uint32_t)x64 & 0x3ffffff);
+	{ uint64_t x67 = (x65 + x61);
+	{ uint64_t x68 = (x67 >> 0x19);
+	{ uint32_t x69 = ((uint32_t)x67 & 0x1ffffff);
+	{ uint64_t x70 = (x68 + x58);
+	{ uint64_t x71 = (x70 >> 0x1a);
+	{ uint32_t x72 = ((uint32_t)x70 & 0x3ffffff);
+	{ uint64_t x73 = (x71 + x55);
+	{ uint64_t x74 = (x73 >> 0x19);
+	{ uint32_t x75 = ((uint32_t)x73 & 0x1ffffff);
+	{ uint64_t x76 = (x74 + x52);
+	{ uint64_t x77 = (x76 >> 0x1a);
+	{ uint32_t x78 = ((uint32_t)x76 & 0x3ffffff);
+	{ uint64_t x79 = (x77 + x49);
+	{ uint64_t x80 = (x79 >> 0x19);
+	{ uint32_t x81 = ((uint32_t)x79 & 0x1ffffff);
+	{ uint64_t x82 = (x80 + x46);
+	{ uint64_t x83 = (x82 >> 0x1a);
+	{ uint32_t x84 = ((uint32_t)x82 & 0x3ffffff);
+	{ uint64_t x85 = (x83 + x43);
+	{ uint64_t x86 = (x85 >> 0x19);
+	{ uint32_t x87 = ((uint32_t)x85 & 0x1ffffff);
+	{ uint64_t x88 = (x86 + x40);
+	{ uint64_t x89 = (x88 >> 0x1a);
+	{ uint32_t x90 = ((uint32_t)x88 & 0x3ffffff);
+	{ uint64_t x91 = (x89 + x28);
+	{ uint64_t x92 = (x91 >> 0x19);
+	{ uint32_t x93 = ((uint32_t)x91 & 0x1ffffff);
+	{ uint64_t x94 = (x66 + (0x13 * x92));
+	{ uint32_t x95 = (uint32_t) (x94 >> 0x1a);
+	{ uint32_t x96 = ((uint32_t)x94 & 0x3ffffff);
+	{ uint32_t x97 = (x95 + x69);
+	{ uint32_t x98 = (x97 >> 0x19);
+	{ uint32_t x99 = (x97 & 0x1ffffff);
+	out[0] = x96;
+	out[1] = x99;
+	out[2] = (x98 + x72);
+	out[3] = x75;
+	out[4] = x78;
+	out[5] = x81;
+	out[6] = x84;
+	out[7] = x87;
+	out[8] = x90;
+	out[9] = x93;
+	}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+}
 
-		   const limb *qmqp /* input Q - Q' */)
+static __always_inline void fe_sq_tl(fe *h, const fe_loose *f)
 {
-	limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19],
-				zzprime[19], zzzprime[19], xxxprime[19];
+	fe_sqr_impl(h->v, f->v);
+}
 
-	memcpy(origx, x, 10 * sizeof(limb));
-	fsum(x, z);
-	/* |x[i]| < 2^27 */
-	fdifference(z, origx);  /* does x - z */
-	/* |z[i]| < 2^27 */
+static __always_inline void fe_sq_tt(fe *h, const fe *f)
+{
+	fe_sqr_impl(h->v, f->v);
+}
 
-	memcpy(origxprime, xprime, sizeof(limb) * 10);
-	fsum(xprime, zprime);
-	/* |xprime[i]| < 2^27 */
-	fdifference(zprime, origxprime);
-	/* |zprime[i]| < 2^27 */
-	fproduct(xxprime, xprime, z);
-	/* |xxprime[i]| < 14*2^54: the largest product of two limbs will be <
-	 * 2^(27+27) and fproduct adds together, at most, 14 of those products.
-	 * (Approximating that to 2^58 doesn't work out.)
-	 */
-	fproduct(zzprime, x, zprime);
-	/* |zzprime[i]| < 14*2^54 */
-	freduce_degree(xxprime);
-	freduce_coefficients(xxprime);
-	/* |xxprime[i]| < 2^26 */
-	freduce_degree(zzprime);
-	freduce_coefficients(zzprime);
-	/* |zzprime[i]| < 2^26 */
-	memcpy(origxprime, xxprime, sizeof(limb) * 10);
-	fsum(xxprime, zzprime);
-	/* |xxprime[i]| < 2^27 */
-	fdifference(zzprime, origxprime);
-	/* |zzprime[i]| < 2^27 */
-	fsquare(xxxprime, xxprime);
-	/* |xxxprime[i]| < 2^26 */
-	fsquare(zzzprime, zzprime);
-	/* |zzzprime[i]| < 2^26 */
-	fproduct(zzprime, zzzprime, qmqp);
-	/* |zzprime[i]| < 14*2^52 */
-	freduce_degree(zzprime);
-	freduce_coefficients(zzprime);
-	/* |zzprime[i]| < 2^26 */
-	memcpy(x3, xxxprime, sizeof(limb) * 10);
-	memcpy(z3, zzprime, sizeof(limb) * 10);
-
-	fsquare(xx, x);
-	/* |xx[i]| < 2^26 */
-	fsquare(zz, z);
-	/* |zz[i]| < 2^26 */
-	fproduct(x2, xx, zz);
-	/* |x2[i]| < 14*2^52 */
-	freduce_degree(x2);
-	freduce_coefficients(x2);
-	/* |x2[i]| < 2^26 */
-	fdifference(zz, xx);  // does zz = xx - zz
-	/* |zz[i]| < 2^27 */
-	memset(zzz + 10, 0, sizeof(limb) * 9);
-	fscalar_product(zzz, zz, 121665);
-	/* |zzz[i]| < 2^(27+17) */
-	/* No need to call freduce_degree here:
-		 fscalar_product doesn't increase the degree of its input. */
-	freduce_coefficients(zzz);
-	/* |zzz[i]| < 2^26 */
-	fsum(zzz, xx);
-	/* |zzz[i]| < 2^27 */
-	fproduct(z2, zz, zzz);
-	/* |z2[i]| < 14*2^(26+27) */
-	freduce_degree(z2);
-	freduce_coefficients(z2);
-	/* |z2|i| < 2^26 */
-}
-
-/* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
- * them unchanged if 'iswap' is 0.  Runs in data-invariant time to avoid
- * side-channel attacks.
- *
- * NOTE that this function requires that 'iswap' be 1 or 0; other values give
- * wrong results.  Also, the two limb arrays must be in reduced-coefficient,
- * reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
- * and all all values in a[0..9],b[0..9] must have magnitude less than
- * INT32_MAX.
- */
-static void swap_conditional(limb a[static 19], limb b[static 19], limb iswap)
+static __always_inline void fe_loose_invert(fe *out, const fe_loose *z)
 {
-	unsigned int i;
-	const int32_t swap = (int32_t) -iswap;
+	fe t0;
+	fe t1;
+	fe t2;
+	fe t3;
+	int i;
 
-	for (i = 0; i < 10; ++i) {
-		const int32_t x = swap & (((int32_t)a[i]) ^ ((int32_t)b[i]));
+	fe_sq_tl(&t0, z);
+	fe_sq_tt(&t1, &t0);
+	for (i = 1; i < 2; ++i)
+		fe_sq_tt(&t1, &t1);
+	fe_mul_tlt(&t1, z, &t1);
+	fe_mul_ttt(&t0, &t0, &t1);
+	fe_sq_tt(&t2, &t0);
+	fe_mul_ttt(&t1, &t1, &t2);
+	fe_sq_tt(&t2, &t1);
+	for (i = 1; i < 5; ++i)
+		fe_sq_tt(&t2, &t2);
+	fe_mul_ttt(&t1, &t2, &t1);
+	fe_sq_tt(&t2, &t1);
+	for (i = 1; i < 10; ++i)
+		fe_sq_tt(&t2, &t2);
+	fe_mul_ttt(&t2, &t2, &t1);
+	fe_sq_tt(&t3, &t2);
+	for (i = 1; i < 20; ++i)
+		fe_sq_tt(&t3, &t3);
+	fe_mul_ttt(&t2, &t3, &t2);
+	fe_sq_tt(&t2, &t2);
+	for (i = 1; i < 10; ++i)
+		fe_sq_tt(&t2, &t2);
+	fe_mul_ttt(&t1, &t2, &t1);
+	fe_sq_tt(&t2, &t1);
+	for (i = 1; i < 50; ++i)
+		fe_sq_tt(&t2, &t2);
+	fe_mul_ttt(&t2, &t2, &t1);
+	fe_sq_tt(&t3, &t2);
+	for (i = 1; i < 100; ++i)
+		fe_sq_tt(&t3, &t3);
+	fe_mul_ttt(&t2, &t3, &t2);
+	fe_sq_tt(&t2, &t2);
+	for (i = 1; i < 50; ++i)
+		fe_sq_tt(&t2, &t2);
+	fe_mul_ttt(&t1, &t2, &t1);
+	fe_sq_tt(&t1, &t1);
+	for (i = 1; i < 5; ++i)
+		fe_sq_tt(&t1, &t1);
+	fe_mul_ttt(out, &t1, &t0);
+}
 
-		a[i] = ((int32_t)a[i]) ^ x;
-		b[i] = ((int32_t)b[i]) ^ x;
-	}
+static __always_inline void fe_invert(fe *out, const fe *z)
+{
+	fe_loose l;
+	fe_copy_lt(&l, z);
+	fe_loose_invert(out, &l);
 }
 
-/* Calculates nQ where Q is the x-coordinate of a point on the curve
+/* Replace (f,g) with (g,f) if b == 1;
+ * replace (f,g) with (f,g) if b == 0.
  *
- *   resultx/resultz: the x coordinate of the resulting curve point (short form)
- *   n: a little endian, 32-byte number
- *   q: a point of the curve (short form)
+ * Preconditions: b in {0,1}
  */
-static void cmult(limb *resultx, limb *resultz, const uint8_t *n, const limb *q)
-{
-	limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
-	limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
-	limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
-	limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
-
-	unsigned int i, j;
-
-	memcpy(nqpqx, q, sizeof(limb) * 10);
-
-	for (i = 0; i < 32; ++i) {
-		uint8_t byte = n[31 - i];
-
-		for (j = 0; j < 8; ++j) {
-			const limb bit = byte >> 7;
-
-			swap_conditional(nqx, nqpqx, bit);
-			swap_conditional(nqz, nqpqz, bit);
-			fmonty(nqx2, nqz2,
-			       nqpqx2, nqpqz2,
-			       nqx, nqz,
-			       nqpqx, nqpqz,
-			       q);
-			swap_conditional(nqx2, nqpqx2, bit);
-			swap_conditional(nqz2, nqpqz2, bit);
-
-			t = nqx;
-			nqx = nqx2;
-			nqx2 = t;
-			t = nqz;
-			nqz = nqz2;
-			nqz2 = t;
-			t = nqpqx;
-			nqpqx = nqpqx2;
-			nqpqx2 = t;
-			t = nqpqz;
-			nqpqz = nqpqz2;
-			nqpqz2 = t;
-
-			byte <<= 1;
-		}
+static __always_inline void fe_cswap(fe *f, fe *g, unsigned int b)
+{
+	unsigned i;
+	b = 0-b;
+	for (i = 0; i < 10; i++) {
+		uint32_t x = f->v[i] ^ g->v[i];
+		x &= b;
+		f->v[i] ^= x;
+		g->v[i] ^= x;
 	}
-
-	memcpy(resultx, nqx, sizeof(limb) * 10);
-	memcpy(resultz, nqz, sizeof(limb) * 10);
 }
 
-static void crecip(limb *out, const limb *z)
+/* NOTE: based on fiat-crypto fe_mul, edited for in2=121666, 0, 0.*/
+static __always_inline void fe_mul_121666_impl(uint32_t out[10], const uint32_t in1[10])
 {
-	limb z2[10];
-	limb z9[10];
-	limb z11[10];
-	limb z2_5_0[10];
-	limb z2_10_0[10];
-	limb z2_20_0[10];
-	limb z2_50_0[10];
-	limb z2_100_0[10];
-	limb t0[10];
-	limb t1[10];
-	int i;
+	{ const uint32_t x20 = in1[9];
+	{ const uint32_t x21 = in1[8];
+	{ const uint32_t x19 = in1[7];
+	{ const uint32_t x17 = in1[6];
+	{ const uint32_t x15 = in1[5];
+	{ const uint32_t x13 = in1[4];
+	{ const uint32_t x11 = in1[3];
+	{ const uint32_t x9 = in1[2];
+	{ const uint32_t x7 = in1[1];
+	{ const uint32_t x5 = in1[0];
+	{ const uint32_t x38 = 0;
+	{ const uint32_t x39 = 0;
+	{ const uint32_t x37 = 0;
+	{ const uint32_t x35 = 0;
+	{ const uint32_t x33 = 0;
+	{ const uint32_t x31 = 0;
+	{ const uint32_t x29 = 0;
+	{ const uint32_t x27 = 0;
+	{ const uint32_t x25 = 0;
+	{ const uint32_t x23 = 121666;
+	{ uint64_t x40 = ((uint64_t)x23 * x5);
+	{ uint64_t x41 = (((uint64_t)x23 * x7) + ((uint64_t)x25 * x5));
+	{ uint64_t x42 = ((((uint64_t)(0x2 * x25) * x7) + ((uint64_t)x23 * x9)) + ((uint64_t)x27 * x5));
+	{ uint64_t x43 = (((((uint64_t)x25 * x9) + ((uint64_t)x27 * x7)) + ((uint64_t)x23 * x11)) + ((uint64_t)x29 * x5));
+	{ uint64_t x44 = (((((uint64_t)x27 * x9) + (0x2 * (((uint64_t)x25 * x11) + ((uint64_t)x29 * x7)))) + ((uint64_t)x23 * x13)) + ((uint64_t)x31 * x5));
+	{ uint64_t x45 = (((((((uint64_t)x27 * x11) + ((uint64_t)x29 * x9)) + ((uint64_t)x25 * x13)) + ((uint64_t)x31 * x7)) + ((uint64_t)x23 * x15)) + ((uint64_t)x33 * x5));
+	{ uint64_t x46 = (((((0x2 * ((((uint64_t)x29 * x11) + ((uint64_t)x25 * x15)) + ((uint64_t)x33 * x7))) + ((uint64_t)x27 * x13)) + ((uint64_t)x31 * x9)) + ((uint64_t)x23 * x17)) + ((uint64_t)x35 * x5));
+	{ uint64_t x47 = (((((((((uint64_t)x29 * x13) + ((uint64_t)x31 * x11)) + ((uint64_t)x27 * x15)) + ((uint64_t)x33 * x9)) + ((uint64_t)x25 * x17)) + ((uint64_t)x35 * x7)) + ((uint64_t)x23 * x19)) + ((uint64_t)x37 * x5));
+	{ uint64_t x48 = (((((((uint64_t)x31 * x13) + (0x2 * (((((uint64_t)x29 * x15) + ((uint64_t)x33 * x11)) + ((uint64_t)x25 * x19)) + ((uint64_t)x37 * x7)))) + ((uint64_t)x27 * x17)) + ((uint64_t)x35 * x9)) + ((uint64_t)x23 * x21)) + ((uint64_t)x39 * x5));
+	{ uint64_t x49 = (((((((((((uint64_t)x31 * x15) + ((uint64_t)x33 * x13)) + ((uint64_t)x29 * x17)) + ((uint64_t)x35 * x11)) + ((uint64_t)x27 * x19)) + ((uint64_t)x37 * x9)) + ((uint64_t)x25 * x21)) + ((uint64_t)x39 * x7)) + ((uint64_t)x23 * x20)) + ((uint64_t)x38 * x5));
+	{ uint64_t x50 = (((((0x2 * ((((((uint64_t)x33 * x15) + ((uint64_t)x29 * x19)) + ((uint64_t)x37 * x11)) + ((uint64_t)x25 * x20)) + ((uint64_t)x38 * x7))) + ((uint64_t)x31 * x17)) + ((uint64_t)x35 * x13)) + ((uint64_t)x27 * x21)) + ((uint64_t)x39 * x9));
+	{ uint64_t x51 = (((((((((uint64_t)x33 * x17) + ((uint64_t)x35 * x15)) + ((uint64_t)x31 * x19)) + ((uint64_t)x37 * x13)) + ((uint64_t)x29 * x21)) + ((uint64_t)x39 * x11)) + ((uint64_t)x27 * x20)) + ((uint64_t)x38 * x9));
+	{ uint64_t x52 = (((((uint64_t)x35 * x17) + (0x2 * (((((uint64_t)x33 * x19) + ((uint64_t)x37 * x15)) + ((uint64_t)x29 * x20)) + ((uint64_t)x38 * x11)))) + ((uint64_t)x31 * x21)) + ((uint64_t)x39 * x13));
+	{ uint64_t x53 = (((((((uint64_t)x35 * x19) + ((uint64_t)x37 * x17)) + ((uint64_t)x33 * x21)) + ((uint64_t)x39 * x15)) + ((uint64_t)x31 * x20)) + ((uint64_t)x38 * x13));
+	{ uint64_t x54 = (((0x2 * ((((uint64_t)x37 * x19) + ((uint64_t)x33 * x20)) + ((uint64_t)x38 * x15))) + ((uint64_t)x35 * x21)) + ((uint64_t)x39 * x17));
+	{ uint64_t x55 = (((((uint64_t)x37 * x21) + ((uint64_t)x39 * x19)) + ((uint64_t)x35 * x20)) + ((uint64_t)x38 * x17));
+	{ uint64_t x56 = (((uint64_t)x39 * x21) + (0x2 * (((uint64_t)x37 * x20) + ((uint64_t)x38 * x19))));
+	{ uint64_t x57 = (((uint64_t)x39 * x20) + ((uint64_t)x38 * x21));
+	{ uint64_t x58 = ((uint64_t)(0x2 * x38) * x20);
+	{ uint64_t x59 = (x48 + (x58 << 0x4));
+	{ uint64_t x60 = (x59 + (x58 << 0x1));
+	{ uint64_t x61 = (x60 + x58);
+	{ uint64_t x62 = (x47 + (x57 << 0x4));
+	{ uint64_t x63 = (x62 + (x57 << 0x1));
+	{ uint64_t x64 = (x63 + x57);
+	{ uint64_t x65 = (x46 + (x56 << 0x4));
+	{ uint64_t x66 = (x65 + (x56 << 0x1));
+	{ uint64_t x67 = (x66 + x56);
+	{ uint64_t x68 = (x45 + (x55 << 0x4));
+	{ uint64_t x69 = (x68 + (x55 << 0x1));
+	{ uint64_t x70 = (x69 + x55);
+	{ uint64_t x71 = (x44 + (x54 << 0x4));
+	{ uint64_t x72 = (x71 + (x54 << 0x1));
+	{ uint64_t x73 = (x72 + x54);
+	{ uint64_t x74 = (x43 + (x53 << 0x4));
+	{ uint64_t x75 = (x74 + (x53 << 0x1));
+	{ uint64_t x76 = (x75 + x53);
+	{ uint64_t x77 = (x42 + (x52 << 0x4));
+	{ uint64_t x78 = (x77 + (x52 << 0x1));
+	{ uint64_t x79 = (x78 + x52);
+	{ uint64_t x80 = (x41 + (x51 << 0x4));
+	{ uint64_t x81 = (x80 + (x51 << 0x1));
+	{ uint64_t x82 = (x81 + x51);
+	{ uint64_t x83 = (x40 + (x50 << 0x4));
+	{ uint64_t x84 = (x83 + (x50 << 0x1));
+	{ uint64_t x85 = (x84 + x50);
+	{ uint64_t x86 = (x85 >> 0x1a);
+	{ uint32_t x87 = ((uint32_t)x85 & 0x3ffffff);
+	{ uint64_t x88 = (x86 + x82);
+	{ uint64_t x89 = (x88 >> 0x19);
+	{ uint32_t x90 = ((uint32_t)x88 & 0x1ffffff);
+	{ uint64_t x91 = (x89 + x79);
+	{ uint64_t x92 = (x91 >> 0x1a);
+	{ uint32_t x93 = ((uint32_t)x91 & 0x3ffffff);
+	{ uint64_t x94 = (x92 + x76);
+	{ uint64_t x95 = (x94 >> 0x19);
+	{ uint32_t x96 = ((uint32_t)x94 & 0x1ffffff);
+	{ uint64_t x97 = (x95 + x73);
+	{ uint64_t x98 = (x97 >> 0x1a);
+	{ uint32_t x99 = ((uint32_t)x97 & 0x3ffffff);
+	{ uint64_t x100 = (x98 + x70);
+	{ uint64_t x101 = (x100 >> 0x19);
+	{ uint32_t x102 = ((uint32_t)x100 & 0x1ffffff);
+	{ uint64_t x103 = (x101 + x67);
+	{ uint64_t x104 = (x103 >> 0x1a);
+	{ uint32_t x105 = ((uint32_t)x103 & 0x3ffffff);
+	{ uint64_t x106 = (x104 + x64);
+	{ uint64_t x107 = (x106 >> 0x19);
+	{ uint32_t x108 = ((uint32_t)x106 & 0x1ffffff);
+	{ uint64_t x109 = (x107 + x61);
+	{ uint64_t x110 = (x109 >> 0x1a);
+	{ uint32_t x111 = ((uint32_t)x109 & 0x3ffffff);
+	{ uint64_t x112 = (x110 + x49);
+	{ uint64_t x113 = (x112 >> 0x19);
+	{ uint32_t x114 = ((uint32_t)x112 & 0x1ffffff);
+	{ uint64_t x115 = (x87 + (0x13 * x113));
+	{ uint32_t x116 = (uint32_t) (x115 >> 0x1a);
+	{ uint32_t x117 = ((uint32_t)x115 & 0x3ffffff);
+	{ uint32_t x118 = (x116 + x90);
+	{ uint32_t x119 = (x118 >> 0x19);
+	{ uint32_t x120 = (x118 & 0x1ffffff);
+	out[0] = x117;
+	out[1] = x120;
+	out[2] = (x119 + x93);
+	out[3] = x96;
+	out[4] = x99;
+	out[5] = x102;
+	out[6] = x105;
+	out[7] = x108;
+	out[8] = x111;
+	out[9] = x114;
+	}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
+}
 
-	/* 2 */ fsquare(z2, z);
-	/* 4 */ fsquare(t1, z2);
-	/* 8 */ fsquare(t0, t1);
-	/* 9 */ fmul(z9, t0, z);
-	/* 11 */ fmul(z11, z9, z2);
-	/* 22 */ fsquare(t0, z11);
-	/* 2^5 - 2^0 = 31 */ fmul(z2_5_0, t0, z9);
-
-	/* 2^6 - 2^1 */ fsquare(t0, z2_5_0);
-	/* 2^7 - 2^2 */ fsquare(t1, t0);
-	/* 2^8 - 2^3 */ fsquare(t0, t1);
-	/* 2^9 - 2^4 */ fsquare(t1, t0);
-	/* 2^10 - 2^5 */ fsquare(t0, t1);
-	/* 2^10 - 2^0 */ fmul(z2_10_0, t0, z2_5_0);
-
-	/* 2^11 - 2^1 */ fsquare(t0, z2_10_0);
-	/* 2^12 - 2^2 */ fsquare(t1, t0);
-	/* 2^20 - 2^10 */ for (i = 2; i < 10; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
-	/* 2^20 - 2^0 */ fmul(z2_20_0, t1, z2_10_0);
-
-	/* 2^21 - 2^1 */ fsquare(t0, z2_20_0);
-	/* 2^22 - 2^2 */ fsquare(t1, t0);
-	/* 2^40 - 2^20 */ for (i = 2; i < 20; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
-	/* 2^40 - 2^0 */ fmul(t0, t1, z2_20_0);
-
-	/* 2^41 - 2^1 */ fsquare(t1, t0);
-	/* 2^42 - 2^2 */ fsquare(t0, t1);
-	/* 2^50 - 2^10 */ for (i = 2; i < 10; i += 2) { fsquare(t1, t0); fsquare(t0, t1); }
-	/* 2^50 - 2^0 */ fmul(z2_50_0, t0, z2_10_0);
-
-	/* 2^51 - 2^1 */ fsquare(t0, z2_50_0);
-	/* 2^52 - 2^2 */ fsquare(t1, t0);
-	/* 2^100 - 2^50 */ for (i = 2; i < 50; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
-	/* 2^100 - 2^0 */ fmul(z2_100_0, t1, z2_50_0);
-
-	/* 2^101 - 2^1 */ fsquare(t1, z2_100_0);
-	/* 2^102 - 2^2 */ fsquare(t0, t1);
-	/* 2^200 - 2^100 */ for (i = 2; i < 100; i += 2) { fsquare(t1, t0); fsquare(t0, t1); }
-	/* 2^200 - 2^0 */ fmul(t1, t0, z2_100_0);
-
-	/* 2^201 - 2^1 */ fsquare(t0, t1);
-	/* 2^202 - 2^2 */ fsquare(t1, t0);
-	/* 2^250 - 2^50 */ for (i = 2; i < 50; i += 2) { fsquare(t0, t1); fsquare(t1, t0); }
-	/* 2^250 - 2^0 */ fmul(t0, t1, z2_50_0);
-
-	/* 2^251 - 2^1 */ fsquare(t1, t0);
-	/* 2^252 - 2^2 */ fsquare(t0, t1);
-	/* 2^253 - 2^3 */ fsquare(t1, t0);
-	/* 2^254 - 2^4 */ fsquare(t0, t1);
-	/* 2^255 - 2^5 */ fsquare(t1, t0);
-	/* 2^255 - 21 */ fmul(out, t1, z11);
+static __always_inline void fe_mul121666(fe *h, const fe_loose *f)
+{
+	fe_mul_121666_impl(h->v, f->v);
 }
 
-void curve25519(uint8_t mypublic[static CURVE25519_POINT_SIZE], const uint8_t secret[static CURVE25519_POINT_SIZE], const uint8_t basepoint[static CURVE25519_POINT_SIZE])
+void curve25519(uint8_t out[static CURVE25519_POINT_SIZE], const uint8_t scalar[static CURVE25519_POINT_SIZE], const uint8_t point[static CURVE25519_POINT_SIZE])
 {
-	limb bp[10], x[10], z[11], zmone[10];
+	fe x1, x2, z2, x3, z3, tmp0, tmp1;
+	fe_loose x2l, z2l, x3l, tmp0l, tmp1l;
+	unsigned swap = 0;
+	int pos;
 	uint8_t e[32];
 
-	memcpy(e, secret, 32);
+	memcpy(e, scalar, 32);
 	curve25519_normalize_secret(e);
 
-	fexpand(bp, basepoint);
-	cmult(x, z, e, bp);
-	crecip(zmone, z);
-	fmul(z, x, zmone);
-	fcontract(mypublic, z);
+	/* The following implementation was transcribed to Coq and proven to
+	 * correspond to unary scalar multiplication in affine coordinates given that
+	 * x1 != 0 is the x coordinate of some point on the curve. It was also checked
+	 * in Coq that doing a ladderstep with x1 = x3 = 0 gives z2' = z3' = 0, and z2
+	 * = z3 = 0 gives z2' = z3' = 0. The statement was quantified over the
+	 * underlying field, so it applies to Curve25519 itself and the quadratic
+	 * twist of Curve25519. It was not proven in Coq that prime-field arithmetic
+	 * correctly simulates extension-field arithmetic on prime-field values.
+	 * The decoding of the byte array representation of e was not considered.
+	 * Specification of Montgomery curves in affine coordinates:
+	 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Spec/MontgomeryCurve.v#L27>
+	 * Proof that these form a group that is isomorphic to a Weierstrass curve:
+	 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/AffineProofs.v#L35>
+	 * Coq transcription and correctness proof of the loop (where scalarbits=255):
+	 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L118>
+	 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L278>
+	 * preconditions: 0 <= e < 2^255 (not necessarily e < order), fe_invert(0) = 0
+	 */
+	fe_frombytes(&x1, point);
+	fe_1(&x2);
+	fe_0(&z2);
+	fe_copy(&x3, &x1);
+	fe_1(&z3);
+
+	for (pos = 254; pos >= 0; --pos) {
+		/* loop invariant as of right before the test, for the case where x1 != 0:
+		 *   pos >= -1; if z2 = 0 then x2 is nonzero; if z3 = 0 then x3 is nonzero
+		 *   let r := e >> (pos+1) in the following equalities of projective points:
+		 *   to_xz (r*P)     === if swap then (x3, z3) else (x2, z2)
+		 *   to_xz ((r+1)*P) === if swap then (x2, z2) else (x3, z3)
+		 *   x1 is the nonzero x coordinate of the nonzero point (r*P-(r+1)*P)
+		 */
+		unsigned b = 1 & (e[pos / 8] >> (pos & 7));
+		swap ^= b;
+		fe_cswap(&x2, &x3, swap);
+		fe_cswap(&z2, &z3, swap);
+		swap = b;
+		/* Coq transcription of ladderstep formula (called from transcribed loop):
+		 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZ.v#L89>
+		 * <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L131>
+		 * x1 != 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L217>
+		 * x1  = 0 <https://github.com/mit-plv/fiat-crypto/blob/2456d821825521f7e03e65882cc3521795b0320f/src/Curves/Montgomery/XZProofs.v#L147>
+		 */
+		fe_sub(&tmp0l, &x3, &z3);
+		fe_sub(&tmp1l, &x2, &z2);
+		fe_add(&x2l, &x2, &z2);
+		fe_add(&z2l, &x3, &z3);
+		fe_mul_tll(&z3, &tmp0l, &x2l);
+		fe_mul_tll(&z2, &z2l, &tmp1l);
+		fe_sq_tl(&tmp0, &tmp1l);
+		fe_sq_tl(&tmp1, &x2l);
+		fe_add(&x3l, &z3, &z2);
+		fe_sub(&z2l, &z3, &z2);
+		fe_mul_ttt(&x2, &tmp1, &tmp0);
+		fe_sub(&tmp1l, &tmp1, &tmp0);
+		fe_sq_tl(&z2, &z2l);
+		fe_mul121666(&z3, &tmp1l);
+		fe_sq_tl(&x3, &x3l);
+		fe_add(&tmp0l, &tmp0, &z3);
+		fe_mul_ttt(&z3, &x1, &z2);
+		fe_mul_tll(&z2, &tmp1l, &tmp0l);
+	}
+	/* here pos=-1, so r=e, so to_xz (e*P) === if swap then (x3, z3) else (x2, z2) */
+	fe_cswap(&x2, &x3, swap);
+	fe_cswap(&z2, &z3, swap);
+
+	fe_invert(&z2, &z2);
+	fe_mul_ttt(&x2, &x2, &z2);
+	fe_tobytes(out, &x2);
 }
 #endif