memset, memcpy, sizeof consistency fixes
[openssl.git] / crypto / ec / ecp_nistp521.c
index 7ff3a0b..6e572f1 100644 (file)
 #include <openssl/opensslconf.h>
 #ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
 
-#ifndef OPENSSL_SYS_VMS
-#include <stdint.h>
-#else
-#include <inttypes.h>
-#endif
+# ifndef OPENSSL_SYS_VMS
+#  include <stdint.h>
+# else
+#  include <inttypes.h>
+# endif
 
-#include <string.h>
-#include <openssl/err.h>
-#include "ec_lcl.h"
+# include <string.h>
+# include <openssl/err.h>
+# include "ec_lcl.h"
 
-#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
+# if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1))
   /* even with gcc, the typedef won't work for 32-bit platforms */
-  typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */
-#else
-  #error "Need GCC 3.1 or later to define type uint128_t"
-#endif
+typedef __uint128_t uint128_t;  /* nonstandard; implemented by gcc on 64-bit
+                                 * platforms */
+# else
+#  error "Need GCC 3.1 or later to define type uint128_t"
+# endif
 
 typedef uint8_t u8;
 typedef uint64_t u64;
 typedef int64_t s64;
 
-/* The underlying field.
- *
- * P521 operates over GF(2^521-1). We can serialise an element of this field
- * into 66 bytes where the most significant byte contains only a single bit. We
- * call this an felem_bytearray. */
+/*
+ * The underlying field. P521 operates over GF(2^521-1). We can serialise an
+ * element of this field into 66 bytes where the most significant byte
+ * contains only a single bit. We call this an felem_bytearray.
+ */
 
 typedef u8 felem_bytearray[66];
 
-/* These are the parameters of P521, taken from FIPS 186-3, section D.1.2.5.
- * These values are big-endian. */
-static const felem_bytearray nistp521_curve_params[5] =
-       {
-       {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,  /* p */
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff},
-       {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,  /* a = -3 */
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
-        0xff, 0xfc},
-       {0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c,  /* b */
-        0x9a, 0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85,
-        0x40, 0xee, 0xa2, 0xda, 0x72, 0x5b, 0x99, 0xb3,
-        0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1,
-        0x09, 0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e,
-        0x93, 0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1,
-        0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c,
-        0x34, 0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50,
-        0x3f, 0x00},
-       {0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04,  /* x */
-        0xe9, 0xcd, 0x9e, 0x3e, 0xcb, 0x66, 0x23, 0x95,
-        0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f,
-        0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d,
-        0x3d, 0xba, 0xa1, 0x4b, 0x5e, 0x77, 0xef, 0xe7,
-        0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff,
-        0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a,
-        0x42, 0x9b, 0xf9, 0x7e, 0x7e, 0x31, 0xc2, 0xe5,
-        0xbd, 0x66},
-       {0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b,  /* y */
-        0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d,
-        0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b,
-        0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e,
-        0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4,
-        0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad,
-        0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72,
-        0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1,
-        0x66, 0x50}
-       };
+/*
+ * These are the parameters of P521, taken from FIPS 186-3, section D.1.2.5.
+ * These values are big-endian.
+ */
+static const felem_bytearray nistp521_curve_params[5] = {
+    {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* p */
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff},
+    {0x01, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, /* a = -3 */
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xfc},
+    {0x00, 0x51, 0x95, 0x3e, 0xb9, 0x61, 0x8e, 0x1c, /* b */
+     0x9a, 0x1f, 0x92, 0x9a, 0x21, 0xa0, 0xb6, 0x85,
+     0x40, 0xee, 0xa2, 0xda, 0x72, 0x5b, 0x99, 0xb3,
+     0x15, 0xf3, 0xb8, 0xb4, 0x89, 0x91, 0x8e, 0xf1,
+     0x09, 0xe1, 0x56, 0x19, 0x39, 0x51, 0xec, 0x7e,
+     0x93, 0x7b, 0x16, 0x52, 0xc0, 0xbd, 0x3b, 0xb1,
+     0xbf, 0x07, 0x35, 0x73, 0xdf, 0x88, 0x3d, 0x2c,
+     0x34, 0xf1, 0xef, 0x45, 0x1f, 0xd4, 0x6b, 0x50,
+     0x3f, 0x00},
+    {0x00, 0xc6, 0x85, 0x8e, 0x06, 0xb7, 0x04, 0x04, /* x */
+     0xe9, 0xcd, 0x9e, 0x3e, 0xcb, 0x66, 0x23, 0x95,
+     0xb4, 0x42, 0x9c, 0x64, 0x81, 0x39, 0x05, 0x3f,
+     0xb5, 0x21, 0xf8, 0x28, 0xaf, 0x60, 0x6b, 0x4d,
+     0x3d, 0xba, 0xa1, 0x4b, 0x5e, 0x77, 0xef, 0xe7,
+     0x59, 0x28, 0xfe, 0x1d, 0xc1, 0x27, 0xa2, 0xff,
+     0xa8, 0xde, 0x33, 0x48, 0xb3, 0xc1, 0x85, 0x6a,
+     0x42, 0x9b, 0xf9, 0x7e, 0x7e, 0x31, 0xc2, 0xe5,
+     0xbd, 0x66},
+    {0x01, 0x18, 0x39, 0x29, 0x6a, 0x78, 0x9a, 0x3b, /* y */
+     0xc0, 0x04, 0x5c, 0x8a, 0x5f, 0xb4, 0x2c, 0x7d,
+     0x1b, 0xd9, 0x98, 0xf5, 0x44, 0x49, 0x57, 0x9b,
+     0x44, 0x68, 0x17, 0xaf, 0xbd, 0x17, 0x27, 0x3e,
+     0x66, 0x2c, 0x97, 0xee, 0x72, 0x99, 0x5e, 0xf4,
+     0x26, 0x40, 0xc5, 0x50, 0xb9, 0x01, 0x3f, 0xad,
+     0x07, 0x61, 0x35, 0x3c, 0x70, 0x86, 0xa2, 0x72,
+     0xc2, 0x40, 0x88, 0xbe, 0x94, 0x76, 0x9f, 0xd1,
+     0x66, 0x50}
+};
 
 /*-
  * The representation of field elements.
@@ -123,7 +125,7 @@ static const felem_bytearray nistp521_curve_params[5] =
  * A field element with 64-bit limbs is an 'felem'. One with 128-bit limbs is a
  * 'largefelem' */
 
-#define NLIMBS 9
+# define NLIMBS 9
 
 typedef uint64_t limb;
 typedef limb felem[NLIMBS];
@@ -132,165 +134,168 @@ typedef uint128_t largefelem[NLIMBS];
 static const limb bottom57bits = 0x1ffffffffffffff;
 static const limb bottom58bits = 0x3ffffffffffffff;
 
-/* bin66_to_felem takes a little-endian byte array and converts it into felem
- * form. This assumes that the CPU is little-endian. */
+/*
+ * bin66_to_felem takes a little-endian byte array and converts it into felem
+ * form. This assumes that the CPU is little-endian.
+ */
 static void bin66_to_felem(felem out, const u8 in[66])
-       {
-       out[0] = (*((limb*) &in[0])) & bottom58bits;
-       out[1] = (*((limb*) &in[7]) >> 2) & bottom58bits;
-       out[2] = (*((limb*) &in[14]) >> 4) & bottom58bits;
-       out[3] = (*((limb*) &in[21]) >> 6) & bottom58bits;
-       out[4] = (*((limb*) &in[29])) & bottom58bits;
-       out[5] = (*((limb*) &in[36]) >> 2) & bottom58bits;
-       out[6] = (*((limb*) &in[43]) >> 4) & bottom58bits;
-       out[7] = (*((limb*) &in[50]) >> 6) & bottom58bits;
-       out[8] = (*((limb*) &in[58])) & bottom57bits;
-       }
-
-/* felem_to_bin66 takes an felem and serialises into a little endian, 66 byte
- * array. This assumes that the CPU is little-endian. */
+{
+    out[0] = (*((limb *) & in[0])) & bottom58bits;
+    out[1] = (*((limb *) & in[7]) >> 2) & bottom58bits;
+    out[2] = (*((limb *) & in[14]) >> 4) & bottom58bits;
+    out[3] = (*((limb *) & in[21]) >> 6) & bottom58bits;
+    out[4] = (*((limb *) & in[29])) & bottom58bits;
+    out[5] = (*((limb *) & in[36]) >> 2) & bottom58bits;
+    out[6] = (*((limb *) & in[43]) >> 4) & bottom58bits;
+    out[7] = (*((limb *) & in[50]) >> 6) & bottom58bits;
+    out[8] = (*((limb *) & in[58])) & bottom57bits;
+}
+
+/*
+ * felem_to_bin66 takes an felem and serialises into a little endian, 66 byte
+ * array. This assumes that the CPU is little-endian.
+ */
 static void felem_to_bin66(u8 out[66], const felem in)
-       {
-       memset(out, 0, 66);
-       (*((limb*) &out[0])) = in[0];
-       (*((limb*) &out[7])) |= in[1] << 2;
-       (*((limb*) &out[14])) |= in[2] << 4;
-       (*((limb*) &out[21])) |= in[3] << 6;
-       (*((limb*) &out[29])) = in[4];
-       (*((limb*) &out[36])) |= in[5] << 2;
-       (*((limb*) &out[43])) |= in[6] << 4;
-       (*((limb*) &out[50])) |= in[7] << 6;
-       (*((limb*) &out[58])) = in[8];
-       }
+{
+    memset(out, 0, 66);
+    (*((limb *) & out[0])) = in[0];
+    (*((limb *) & out[7])) |= in[1] << 2;
+    (*((limb *) & out[14])) |= in[2] << 4;
+    (*((limb *) & out[21])) |= in[3] << 6;
+    (*((limb *) & out[29])) = in[4];
+    (*((limb *) & out[36])) |= in[5] << 2;
+    (*((limb *) & out[43])) |= in[6] << 4;
+    (*((limb *) & out[50])) |= in[7] << 6;
+    (*((limb *) & out[58])) = in[8];
+}
 
 /* To preserve endianness when using BN_bn2bin and BN_bin2bn */
 static void flip_endian(u8 *out, const u8 *in, unsigned len)
-       {
-       unsigned i;
-       for (i = 0; i < len; ++i)
-               out[i] = in[len-1-i];
-       }
+{
+    unsigned i;
+    for (i = 0; i < len; ++i)
+        out[i] = in[len - 1 - i];
+}
 
 /* BN_to_felem converts an OpenSSL BIGNUM into an felem */
 static int BN_to_felem(felem out, const BIGNUM *bn)
-       {
-       felem_bytearray b_in;
-       felem_bytearray b_out;
-       unsigned num_bytes;
-
-       /* BN_bn2bin eats leading zeroes */
-       memset(b_out, 0, sizeof b_out);
-       num_bytes = BN_num_bytes(bn);
-       if (num_bytes > sizeof b_out)
-               {
-               ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
-               return 0;
-               }
-       if (BN_is_negative(bn))
-               {
-               ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
-               return 0;
-               }
-       num_bytes = BN_bn2bin(bn, b_in);
-       flip_endian(b_out, b_in, num_bytes);
-       bin66_to_felem(out, b_out);
-       return 1;
-       }
+{
+    felem_bytearray b_in;
+    felem_bytearray b_out;
+    unsigned num_bytes;
+
+    /* BN_bn2bin eats leading zeroes */
+    memset(b_out, 0, sizeof(b_out));
+    num_bytes = BN_num_bytes(bn);
+    if (num_bytes > sizeof b_out) {
+        ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
+        return 0;
+    }
+    if (BN_is_negative(bn)) {
+        ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE);
+        return 0;
+    }
+    num_bytes = BN_bn2bin(bn, b_in);
+    flip_endian(b_out, b_in, num_bytes);
+    bin66_to_felem(out, b_out);
+    return 1;
+}
 
 /* felem_to_BN converts an felem into an OpenSSL BIGNUM */
 static BIGNUM *felem_to_BN(BIGNUM *out, const felem in)
-       {
-       felem_bytearray b_in, b_out;
-       felem_to_bin66(b_in, in);
-       flip_endian(b_out, b_in, sizeof b_out);
-       return BN_bin2bn(b_out, sizeof b_out, out);
-       }
-
+{
+    felem_bytearray b_in, b_out;
+    felem_to_bin66(b_in, in);
+    flip_endian(b_out, b_in, sizeof b_out);
+    return BN_bin2bn(b_out, sizeof b_out, out);
+}
 
-/* Field operations
- * ---------------- */
+/*-
+ * Field operations
+ * ----------------
+ */
 
 static void felem_one(felem out)
-       {
-       out[0] = 1;
-       out[1] = 0;
-       out[2] = 0;
-       out[3] = 0;
-       out[4] = 0;
-       out[5] = 0;
-       out[6] = 0;
-       out[7] = 0;
-       out[8] = 0;
-       }
+{
+    out[0] = 1;
+    out[1] = 0;
+    out[2] = 0;
+    out[3] = 0;
+    out[4] = 0;
+    out[5] = 0;
+    out[6] = 0;
+    out[7] = 0;
+    out[8] = 0;
+}
 
 static void felem_assign(felem out, const felem in)
-       {
-       out[0] = in[0];
-       out[1] = in[1];
-       out[2] = in[2];
-       out[3] = in[3];
-       out[4] = in[4];
-       out[5] = in[5];
-       out[6] = in[6];
-       out[7] = in[7];
-       out[8] = in[8];
-       }
+{
+    out[0] = in[0];
+    out[1] = in[1];
+    out[2] = in[2];
+    out[3] = in[3];
+    out[4] = in[4];
+    out[5] = in[5];
+    out[6] = in[6];
+    out[7] = in[7];
+    out[8] = in[8];
+}
 
 /* felem_sum64 sets out = out + in. */
 static void felem_sum64(felem out, const felem in)
-       {
-       out[0] += in[0];
-       out[1] += in[1];
-       out[2] += in[2];
-       out[3] += in[3];
-       out[4] += in[4];
-       out[5] += in[5];
-       out[6] += in[6];
-       out[7] += in[7];
-       out[8] += in[8];
-       }
+{
+    out[0] += in[0];
+    out[1] += in[1];
+    out[2] += in[2];
+    out[3] += in[3];
+    out[4] += in[4];
+    out[5] += in[5];
+    out[6] += in[6];
+    out[7] += in[7];
+    out[8] += in[8];
+}
 
 /* felem_scalar sets out = in * scalar */
 static void felem_scalar(felem out, const felem in, limb scalar)
-       {
-       out[0] = in[0] * scalar;
-       out[1] = in[1] * scalar;
-       out[2] = in[2] * scalar;
-       out[3] = in[3] * scalar;
-       out[4] = in[4] * scalar;
-       out[5] = in[5] * scalar;
-       out[6] = in[6] * scalar;
-       out[7] = in[7] * scalar;
-       out[8] = in[8] * scalar;
-       }
+{
+    out[0] = in[0] * scalar;
+    out[1] = in[1] * scalar;
+    out[2] = in[2] * scalar;
+    out[3] = in[3] * scalar;
+    out[4] = in[4] * scalar;
+    out[5] = in[5] * scalar;
+    out[6] = in[6] * scalar;
+    out[7] = in[7] * scalar;
+    out[8] = in[8] * scalar;
+}
 
 /* felem_scalar64 sets out = out * scalar */
 static void felem_scalar64(felem out, limb scalar)
-       {
-       out[0] *= scalar;
-       out[1] *= scalar;
-       out[2] *= scalar;
-       out[3] *= scalar;
-       out[4] *= scalar;
-       out[5] *= scalar;
-       out[6] *= scalar;
-       out[7] *= scalar;
-       out[8] *= scalar;
-       }
+{
+    out[0] *= scalar;
+    out[1] *= scalar;
+    out[2] *= scalar;
+    out[3] *= scalar;
+    out[4] *= scalar;
+    out[5] *= scalar;
+    out[6] *= scalar;
+    out[7] *= scalar;
+    out[8] *= scalar;
+}
 
 /* felem_scalar128 sets out = out * scalar */
 static void felem_scalar128(largefelem out, limb scalar)
-       {
-       out[0] *= scalar;
-       out[1] *= scalar;
-       out[2] *= scalar;
-       out[3] *= scalar;
-       out[4] *= scalar;
-       out[5] *= scalar;
-       out[6] *= scalar;
-       out[7] *= scalar;
-       out[8] *= scalar;
-       }
+{
+    out[0] *= scalar;
+    out[1] *= scalar;
+    out[2] *= scalar;
+    out[3] *= scalar;
+    out[4] *= scalar;
+    out[5] *= scalar;
+    out[6] *= scalar;
+    out[7] *= scalar;
+    out[8] *= scalar;
+}
 
 /*-
  * felem_neg sets |out| to |-in|
@@ -300,21 +305,21 @@ static void felem_scalar128(largefelem out, limb scalar)
  *   out[i] < 2^62
  */
 static void felem_neg(felem out, const felem in)
-       {
-       /* In order to prevent underflow, we subtract from 0 mod p. */
-       static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5);
-       static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4);
-
-       out[0] = two62m3 - in[0];
-       out[1] = two62m2 - in[1];
-       out[2] = two62m2 - in[2];
-       out[3] = two62m2 - in[3];
-       out[4] = two62m2 - in[4];
-       out[5] = two62m2 - in[5];
-       out[6] = two62m2 - in[6];
-       out[7] = two62m2 - in[7];
-       out[8] = two62m2 - in[8];
-       }
+{
+    /* In order to prevent underflow, we subtract from 0 mod p. */
+    static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5);
+    static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4);
+
+    out[0] = two62m3 - in[0];
+    out[1] = two62m2 - in[1];
+    out[2] = two62m2 - in[2];
+    out[3] = two62m2 - in[3];
+    out[4] = two62m2 - in[4];
+    out[5] = two62m2 - in[5];
+    out[6] = two62m2 - in[6];
+    out[7] = two62m2 - in[7];
+    out[8] = two62m2 - in[8];
+}
 
 /*-
  * felem_diff64 subtracts |in| from |out|
@@ -324,21 +329,23 @@ static void felem_neg(felem out, const felem in)
  *   out[i] < out[i] + 2^62
  */
 static void felem_diff64(felem out, const felem in)
-       {
-       /* In order to prevent underflow, we add 0 mod p before subtracting. */
-       static const limb two62m3 = (((limb)1) << 62) - (((limb)1) << 5);
-       static const limb two62m2 = (((limb)1) << 62) - (((limb)1) << 4);
-
-       out[0] += two62m3 - in[0];
-       out[1] += two62m2 - in[1];
-       out[2] += two62m2 - in[2];
-       out[3] += two62m2 - in[3];
-       out[4] += two62m2 - in[4];
-       out[5] += two62m2 - in[5];
-       out[6] += two62m2 - in[6];
-       out[7] += two62m2 - in[7];
-       out[8] += two62m2 - in[8];
-       }
+{
+    /*
+     * In order to prevent underflow, we add 0 mod p before subtracting.
+     */
+    static const limb two62m3 = (((limb) 1) << 62) - (((limb) 1) << 5);
+    static const limb two62m2 = (((limb) 1) << 62) - (((limb) 1) << 4);
+
+    out[0] += two62m3 - in[0];
+    out[1] += two62m2 - in[1];
+    out[2] += two62m2 - in[2];
+    out[3] += two62m2 - in[3];
+    out[4] += two62m2 - in[4];
+    out[5] += two62m2 - in[5];
+    out[6] += two62m2 - in[6];
+    out[7] += two62m2 - in[7];
+    out[8] += two62m2 - in[8];
+}
 
 /*-
  * felem_diff_128_64 subtracts |in| from |out|
@@ -348,21 +355,23 @@ static void felem_diff64(felem out, const felem in)
  *   out[i] < out[i] + 2^63
  */
 static void felem_diff_128_64(largefelem out, const felem in)
-       {
-       /* In order to prevent underflow, we add 0 mod p before subtracting. */
-       static const limb two63m6 = (((limb)1) << 62) - (((limb)1) << 5);
-       static const limb two63m5 = (((limb)1) << 62) - (((limb)1) << 4);
-
-       out[0] += two63m6 - in[0];
-       out[1] += two63m5 - in[1];
-       out[2] += two63m5 - in[2];
-       out[3] += two63m5 - in[3];
-       out[4] += two63m5 - in[4];
-       out[5] += two63m5 - in[5];
-       out[6] += two63m5 - in[6];
-       out[7] += two63m5 - in[7];
-       out[8] += two63m5 - in[8];
-       }
+{
+    /*
+     * In order to prevent underflow, we add 0 mod p before subtracting.
+     */
+    static const limb two63m6 = (((limb) 1) << 62) - (((limb) 1) << 5);
+    static const limb two63m5 = (((limb) 1) << 62) - (((limb) 1) << 4);
+
+    out[0] += two63m6 - in[0];
+    out[1] += two63m5 - in[1];
+    out[2] += two63m5 - in[2];
+    out[3] += two63m5 - in[3];
+    out[4] += two63m5 - in[4];
+    out[5] += two63m5 - in[5];
+    out[6] += two63m5 - in[6];
+    out[7] += two63m5 - in[7];
+    out[8] += two63m5 - in[8];
+}
 
 /*-
  * felem_diff_128_64 subtracts |in| from |out|
@@ -372,21 +381,25 @@ static void felem_diff_128_64(largefelem out, const felem in)
  *   out[i] < out[i] + 2^127 - 2^69
  */
 static void felem_diff128(largefelem out, const largefelem in)
-       {
-       /* In order to prevent underflow, we add 0 mod p before subtracting. */
-       static const uint128_t two127m70 = (((uint128_t)1) << 127) - (((uint128_t)1) << 70);
-       static const uint128_t two127m69 = (((uint128_t)1) << 127) - (((uint128_t)1) << 69);
-
-       out[0] += (two127m70 - in[0]);
-       out[1] += (two127m69 - in[1]);
-       out[2] += (two127m69 - in[2]);
-       out[3] += (two127m69 - in[3]);
-       out[4] += (two127m69 - in[4]);
-       out[5] += (two127m69 - in[5]);
-       out[6] += (two127m69 - in[6]);
-       out[7] += (two127m69 - in[7]);
-       out[8] += (two127m69 - in[8]);
-       }
+{
+    /*
+     * In order to prevent underflow, we add 0 mod p before subtracting.
+     */
+    static const uint128_t two127m70 =
+        (((uint128_t) 1) << 127) - (((uint128_t) 1) << 70);
+    static const uint128_t two127m69 =
+        (((uint128_t) 1) << 127) - (((uint128_t) 1) << 69);
+
+    out[0] += (two127m70 - in[0]);
+    out[1] += (two127m69 - in[1]);
+    out[2] += (two127m69 - in[2]);
+    out[3] += (two127m69 - in[3]);
+    out[4] += (two127m69 - in[4]);
+    out[5] += (two127m69 - in[5]);
+    out[6] += (two127m69 - in[6]);
+    out[7] += (two127m69 - in[7]);
+    out[8] += (two127m69 - in[8]);
+}
 
 /*-
  * felem_square sets |out| = |in|^2
@@ -396,90 +409,80 @@ static void felem_diff128(largefelem out, const largefelem in)
  *   out[i] < 17 * max(in[i]) * max(in[i])
  */
 static void felem_square(largefelem out, const felem in)
-       {
-       felem inx2, inx4;
-       felem_scalar(inx2, in, 2);
-       felem_scalar(inx4, in, 4);
-
-       /*-
-        * We have many cases were we want to do
-        *   in[x] * in[y] +
-        *   in[y] * in[x]
-        * This is obviously just
-        *   2 * in[x] * in[y]
-        * However, rather than do the doubling on the 128 bit result, we
-        * double one of the inputs to the multiplication by reading from
-        * |inx2| */
-
-       out[0] = ((uint128_t) in[0]) * in[0];
-       out[1] = ((uint128_t) in[0]) * inx2[1];
-       out[2] = ((uint128_t) in[0]) * inx2[2] +
-                ((uint128_t) in[1]) * in[1];
-       out[3] = ((uint128_t) in[0]) * inx2[3] +
-                ((uint128_t) in[1]) * inx2[2];
-       out[4] = ((uint128_t) in[0]) * inx2[4] +
-                ((uint128_t) in[1]) * inx2[3] +
-                ((uint128_t) in[2]) * in[2];
-       out[5] = ((uint128_t) in[0]) * inx2[5] +
-                ((uint128_t) in[1]) * inx2[4] +
-                ((uint128_t) in[2]) * inx2[3];
-       out[6] = ((uint128_t) in[0]) * inx2[6] +
-                ((uint128_t) in[1]) * inx2[5] +
-                ((uint128_t) in[2]) * inx2[4] +
-                ((uint128_t) in[3]) * in[3];
-       out[7] = ((uint128_t) in[0]) * inx2[7] +
-                ((uint128_t) in[1]) * inx2[6] +
-                ((uint128_t) in[2]) * inx2[5] +
-                ((uint128_t) in[3]) * inx2[4];
-       out[8] = ((uint128_t) in[0]) * inx2[8] +
-                ((uint128_t) in[1]) * inx2[7] +
-                ((uint128_t) in[2]) * inx2[6] +
-                ((uint128_t) in[3]) * inx2[5] +
-                ((uint128_t) in[4]) * in[4];
-
-       /* The remaining limbs fall above 2^521, with the first falling at
-        * 2^522. They correspond to locations one bit up from the limbs
-        * produced above so we would have to multiply by two to align them.
-        * Again, rather than operate on the 128-bit result, we double one of
-        * the inputs to the multiplication. If we want to double for both this
-        * reason, and the reason above, then we end up multiplying by four. */
-
-       /* 9 */
-       out[0] += ((uint128_t) in[1]) * inx4[8] +
-                 ((uint128_t) in[2]) * inx4[7] +
-                 ((uint128_t) in[3]) * inx4[6] +
-                 ((uint128_t) in[4]) * inx4[5];
-
-       /* 10 */
-       out[1] += ((uint128_t) in[2]) * inx4[8] +
-                 ((uint128_t) in[3]) * inx4[7] +
-                 ((uint128_t) in[4]) * inx4[6] +
-                 ((uint128_t) in[5]) * inx2[5];
-
-       /* 11 */
-       out[2] += ((uint128_t) in[3]) * inx4[8] +
-                 ((uint128_t) in[4]) * inx4[7] +
-                 ((uint128_t) in[5]) * inx4[6];
-
-       /* 12 */
-       out[3] += ((uint128_t) in[4]) * inx4[8] +
-                 ((uint128_t) in[5]) * inx4[7] +
-                 ((uint128_t) in[6]) * inx2[6];
-
-       /* 13 */
-       out[4] += ((uint128_t) in[5]) * inx4[8] +
-                 ((uint128_t) in[6]) * inx4[7];
-
-       /* 14 */
-       out[5] += ((uint128_t) in[6]) * inx4[8] +
-                 ((uint128_t) in[7]) * inx2[7];
-
-       /* 15 */
-       out[6] += ((uint128_t) in[7]) * inx4[8];
-
-       /* 16 */
-       out[7] += ((uint128_t) in[8]) * inx2[8];
-       }
+{
+    felem inx2, inx4;
+    felem_scalar(inx2, in, 2);
+    felem_scalar(inx4, in, 4);
+
+    /*-
+     * We have many cases were we want to do
+     *   in[x] * in[y] +
+     *   in[y] * in[x]
+     * This is obviously just
+     *   2 * in[x] * in[y]
+     * However, rather than do the doubling on the 128 bit result, we
+     * double one of the inputs to the multiplication by reading from
+     * |inx2|
+     */
+
+    out[0] = ((uint128_t) in[0]) * in[0];
+    out[1] = ((uint128_t) in[0]) * inx2[1];
+    out[2] = ((uint128_t) in[0]) * inx2[2] + ((uint128_t) in[1]) * in[1];
+    out[3] = ((uint128_t) in[0]) * inx2[3] + ((uint128_t) in[1]) * inx2[2];
+    out[4] = ((uint128_t) in[0]) * inx2[4] +
+             ((uint128_t) in[1]) * inx2[3] + ((uint128_t) in[2]) * in[2];
+    out[5] = ((uint128_t) in[0]) * inx2[5] +
+             ((uint128_t) in[1]) * inx2[4] + ((uint128_t) in[2]) * inx2[3];
+    out[6] = ((uint128_t) in[0]) * inx2[6] +
+             ((uint128_t) in[1]) * inx2[5] +
+             ((uint128_t) in[2]) * inx2[4] + ((uint128_t) in[3]) * in[3];
+    out[7] = ((uint128_t) in[0]) * inx2[7] +
+             ((uint128_t) in[1]) * inx2[6] +
+             ((uint128_t) in[2]) * inx2[5] + ((uint128_t) in[3]) * inx2[4];
+    out[8] = ((uint128_t) in[0]) * inx2[8] +
+             ((uint128_t) in[1]) * inx2[7] +
+             ((uint128_t) in[2]) * inx2[6] +
+             ((uint128_t) in[3]) * inx2[5] + ((uint128_t) in[4]) * in[4];
+
+    /*
+     * The remaining limbs fall above 2^521, with the first falling at 2^522.
+     * They correspond to locations one bit up from the limbs produced above
+     * so we would have to multiply by two to align them. Again, rather than
+     * operate on the 128-bit result, we double one of the inputs to the
+     * multiplication. If we want to double for both this reason, and the
+     * reason above, then we end up multiplying by four.
+     */
+
+    /* 9 */
+    out[0] += ((uint128_t) in[1]) * inx4[8] +
+              ((uint128_t) in[2]) * inx4[7] +
+              ((uint128_t) in[3]) * inx4[6] + ((uint128_t) in[4]) * inx4[5];
+
+    /* 10 */
+    out[1] += ((uint128_t) in[2]) * inx4[8] +
+              ((uint128_t) in[3]) * inx4[7] +
+              ((uint128_t) in[4]) * inx4[6] + ((uint128_t) in[5]) * inx2[5];
+
+    /* 11 */
+    out[2] += ((uint128_t) in[3]) * inx4[8] +
+              ((uint128_t) in[4]) * inx4[7] + ((uint128_t) in[5]) * inx4[6];
+
+    /* 12 */
+    out[3] += ((uint128_t) in[4]) * inx4[8] +
+              ((uint128_t) in[5]) * inx4[7] + ((uint128_t) in[6]) * inx2[6];
+
+    /* 13 */
+    out[4] += ((uint128_t) in[5]) * inx4[8] + ((uint128_t) in[6]) * inx4[7];
+
+    /* 14 */
+    out[5] += ((uint128_t) in[6]) * inx4[8] + ((uint128_t) in[7]) * inx2[7];
+
+    /* 15 */
+    out[6] += ((uint128_t) in[7]) * inx4[8];
+
+    /* 16 */
+    out[7] += ((uint128_t) in[8]) * inx2[8];
+}
 
 /*-
  * felem_mul sets |out| = |in1| * |in2|
@@ -490,110 +493,110 @@ static void felem_square(largefelem out, const felem in)
  *   out[i] < 17 * max(in1[i]) * max(in2[i])
  */
 static void felem_mul(largefelem out, const felem in1, const felem in2)
-       {
-       felem in2x2;
-       felem_scalar(in2x2, in2, 2);
-
-       out[0] = ((uint128_t) in1[0]) * in2[0];
-
-       out[1] = ((uint128_t) in1[0]) * in2[1] +
-                ((uint128_t) in1[1]) * in2[0];
-
-       out[2] = ((uint128_t) in1[0]) * in2[2] +
-                ((uint128_t) in1[1]) * in2[1] +
-                ((uint128_t) in1[2]) * in2[0];
-
-       out[3] = ((uint128_t) in1[0]) * in2[3] +
-                ((uint128_t) in1[1]) * in2[2] +
-                ((uint128_t) in1[2]) * in2[1] +
-                ((uint128_t) in1[3]) * in2[0];
-
-       out[4] = ((uint128_t) in1[0]) * in2[4] +
-                ((uint128_t) in1[1]) * in2[3] +
-                ((uint128_t) in1[2]) * in2[2] +
-                ((uint128_t) in1[3]) * in2[1] +
-                ((uint128_t) in1[4]) * in2[0];
-
-       out[5] = ((uint128_t) in1[0]) * in2[5] +
-                ((uint128_t) in1[1]) * in2[4] +
-                ((uint128_t) in1[2]) * in2[3] +
-                ((uint128_t) in1[3]) * in2[2] +
-                ((uint128_t) in1[4]) * in2[1] +
-                ((uint128_t) in1[5]) * in2[0];
-
-       out[6] = ((uint128_t) in1[0]) * in2[6] +
-                ((uint128_t) in1[1]) * in2[5] +
-                ((uint128_t) in1[2]) * in2[4] +
-                ((uint128_t) in1[3]) * in2[3] +
-                ((uint128_t) in1[4]) * in2[2] +
-                ((uint128_t) in1[5]) * in2[1] +
-                ((uint128_t) in1[6]) * in2[0];
-
-       out[7] = ((uint128_t) in1[0]) * in2[7] +
-                ((uint128_t) in1[1]) * in2[6] +
-                ((uint128_t) in1[2]) * in2[5] +
-                ((uint128_t) in1[3]) * in2[4] +
-                ((uint128_t) in1[4]) * in2[3] +
-                ((uint128_t) in1[5]) * in2[2] +
-                ((uint128_t) in1[6]) * in2[1] +
-                ((uint128_t) in1[7]) * in2[0];
-
-       out[8] = ((uint128_t) in1[0]) * in2[8] +
-                ((uint128_t) in1[1]) * in2[7] +
-                ((uint128_t) in1[2]) * in2[6] +
-                ((uint128_t) in1[3]) * in2[5] +
-                ((uint128_t) in1[4]) * in2[4] +
-                ((uint128_t) in1[5]) * in2[3] +
-                ((uint128_t) in1[6]) * in2[2] +
-                ((uint128_t) in1[7]) * in2[1] +
-                ((uint128_t) in1[8]) * in2[0];
-
-       /* See comment in felem_square about the use of in2x2 here */
-
-       out[0] += ((uint128_t) in1[1]) * in2x2[8] +
-                 ((uint128_t) in1[2]) * in2x2[7] +
-                 ((uint128_t) in1[3]) * in2x2[6] +
-                 ((uint128_t) in1[4]) * in2x2[5] +
-                 ((uint128_t) in1[5]) * in2x2[4] +
-                 ((uint128_t) in1[6]) * in2x2[3] +
-                 ((uint128_t) in1[7]) * in2x2[2] +
-                 ((uint128_t) in1[8]) * in2x2[1];
-
-       out[1] += ((uint128_t) in1[2]) * in2x2[8] +
-                 ((uint128_t) in1[3]) * in2x2[7] +
-                 ((uint128_t) in1[4]) * in2x2[6] +
-                 ((uint128_t) in1[5]) * in2x2[5] +
-                 ((uint128_t) in1[6]) * in2x2[4] +
-                 ((uint128_t) in1[7]) * in2x2[3] +
-                 ((uint128_t) in1[8]) * in2x2[2];
-
-       out[2] += ((uint128_t) in1[3]) * in2x2[8] +
-                 ((uint128_t) in1[4]) * in2x2[7] +
-                 ((uint128_t) in1[5]) * in2x2[6] +
-                 ((uint128_t) in1[6]) * in2x2[5] +
-                 ((uint128_t) in1[7]) * in2x2[4] +
-                 ((uint128_t) in1[8]) * in2x2[3];
-
-       out[3] += ((uint128_t) in1[4]) * in2x2[8] +
-                 ((uint128_t) in1[5]) * in2x2[7] +
-                 ((uint128_t) in1[6]) * in2x2[6] +
-                 ((uint128_t) in1[7]) * in2x2[5] +
-                 ((uint128_t) in1[8]) * in2x2[4];
-
-       out[4] += ((uint128_t) in1[5]) * in2x2[8] +
-                 ((uint128_t) in1[6]) * in2x2[7] +
-                 ((uint128_t) in1[7]) * in2x2[6] +
-                 ((uint128_t) in1[8]) * in2x2[5];
-
-       out[5] += ((uint128_t) in1[6]) * in2x2[8] +
-                 ((uint128_t) in1[7]) * in2x2[7] +
-                 ((uint128_t) in1[8]) * in2x2[6];
-
-       out[6] += ((uint128_t) in1[7]) * in2x2[8] +
-                 ((uint128_t) in1[8]) * in2x2[7];
-
-       out[7] += ((uint128_t) in1[8]) * in2x2[8];
-       }
+{
+    felem in2x2;
+    felem_scalar(in2x2, in2, 2);
+
+    out[0] = ((uint128_t) in1[0]) * in2[0];
+
+    out[1] = ((uint128_t) in1[0]) * in2[1] +
+             ((uint128_t) in1[1]) * in2[0];
+
+    out[2] = ((uint128_t) in1[0]) * in2[2] +
+             ((uint128_t) in1[1]) * in2[1] +
+             ((uint128_t) in1[2]) * in2[0];
+
+    out[3] = ((uint128_t) in1[0]) * in2[3] +
+             ((uint128_t) in1[1]) * in2[2] +
+             ((uint128_t) in1[2]) * in2[1] +
+             ((uint128_t) in1[3]) * in2[0];
+
+    out[4] = ((uint128_t) in1[0]) * in2[4] +
+             ((uint128_t) in1[1]) * in2[3] +
+             ((uint128_t) in1[2]) * in2[2] +
+             ((uint128_t) in1[3]) * in2[1] +
+             ((uint128_t) in1[4]) * in2[0];
+
+    out[5] = ((uint128_t) in1[0]) * in2[5] +
+             ((uint128_t) in1[1]) * in2[4] +
+             ((uint128_t) in1[2]) * in2[3] +
+             ((uint128_t) in1[3]) * in2[2] +
+             ((uint128_t) in1[4]) * in2[1] +
+             ((uint128_t) in1[5]) * in2[0];
+
+    out[6] = ((uint128_t) in1[0]) * in2[6] +
+             ((uint128_t) in1[1]) * in2[5] +
+             ((uint128_t) in1[2]) * in2[4] +
+             ((uint128_t) in1[3]) * in2[3] +
+             ((uint128_t) in1[4]) * in2[2] +
+             ((uint128_t) in1[5]) * in2[1] +
+             ((uint128_t) in1[6]) * in2[0];
+
+    out[7] = ((uint128_t) in1[0]) * in2[7] +
+             ((uint128_t) in1[1]) * in2[6] +
+             ((uint128_t) in1[2]) * in2[5] +
+             ((uint128_t) in1[3]) * in2[4] +
+             ((uint128_t) in1[4]) * in2[3] +
+             ((uint128_t) in1[5]) * in2[2] +
+             ((uint128_t) in1[6]) * in2[1] +
+             ((uint128_t) in1[7]) * in2[0];
+
+    out[8] = ((uint128_t) in1[0]) * in2[8] +
+             ((uint128_t) in1[1]) * in2[7] +
+             ((uint128_t) in1[2]) * in2[6] +
+             ((uint128_t) in1[3]) * in2[5] +
+             ((uint128_t) in1[4]) * in2[4] +
+             ((uint128_t) in1[5]) * in2[3] +
+             ((uint128_t) in1[6]) * in2[2] +
+             ((uint128_t) in1[7]) * in2[1] +
+             ((uint128_t) in1[8]) * in2[0];
+
+    /* See comment in felem_square about the use of in2x2 here */
+
+    out[0] += ((uint128_t) in1[1]) * in2x2[8] +
+              ((uint128_t) in1[2]) * in2x2[7] +
+              ((uint128_t) in1[3]) * in2x2[6] +
+              ((uint128_t) in1[4]) * in2x2[5] +
+              ((uint128_t) in1[5]) * in2x2[4] +
+              ((uint128_t) in1[6]) * in2x2[3] +
+              ((uint128_t) in1[7]) * in2x2[2] +
+              ((uint128_t) in1[8]) * in2x2[1];
+
+    out[1] += ((uint128_t) in1[2]) * in2x2[8] +
+              ((uint128_t) in1[3]) * in2x2[7] +
+              ((uint128_t) in1[4]) * in2x2[6] +
+              ((uint128_t) in1[5]) * in2x2[5] +
+              ((uint128_t) in1[6]) * in2x2[4] +
+              ((uint128_t) in1[7]) * in2x2[3] +
+              ((uint128_t) in1[8]) * in2x2[2];
+
+    out[2] += ((uint128_t) in1[3]) * in2x2[8] +
+              ((uint128_t) in1[4]) * in2x2[7] +
+              ((uint128_t) in1[5]) * in2x2[6] +
+              ((uint128_t) in1[6]) * in2x2[5] +
+              ((uint128_t) in1[7]) * in2x2[4] +
+              ((uint128_t) in1[8]) * in2x2[3];
+
+    out[3] += ((uint128_t) in1[4]) * in2x2[8] +
+              ((uint128_t) in1[5]) * in2x2[7] +
+              ((uint128_t) in1[6]) * in2x2[6] +
+              ((uint128_t) in1[7]) * in2x2[5] +
+              ((uint128_t) in1[8]) * in2x2[4];
+
+    out[4] += ((uint128_t) in1[5]) * in2x2[8] +
+              ((uint128_t) in1[6]) * in2x2[7] +
+              ((uint128_t) in1[7]) * in2x2[6] +
+              ((uint128_t) in1[8]) * in2x2[5];
+
+    out[5] += ((uint128_t) in1[6]) * in2x2[8] +
+              ((uint128_t) in1[7]) * in2x2[7] +
+              ((uint128_t) in1[8]) * in2x2[6];
+
+    out[6] += ((uint128_t) in1[7]) * in2x2[8] +
+              ((uint128_t) in1[8]) * in2x2[7];
+
+    out[7] += ((uint128_t) in1[8]) * in2x2[8];
+}
 
 static const limb bottom52bits = 0xfffffffffffff;
 
@@ -605,86 +608,93 @@ static const limb bottom52bits = 0xfffffffffffff;
  *   out[i] < 2^59 + 2^14
  */
 static void felem_reduce(felem out, const largefelem in)
-       {
-       u64 overflow1, overflow2;
-
-       out[0] = ((limb) in[0]) & bottom58bits;
-       out[1] = ((limb) in[1]) & bottom58bits;
-       out[2] = ((limb) in[2]) & bottom58bits;
-       out[3] = ((limb) in[3]) & bottom58bits;
-       out[4] = ((limb) in[4]) & bottom58bits;
-       out[5] = ((limb) in[5]) & bottom58bits;
-       out[6] = ((limb) in[6]) & bottom58bits;
-       out[7] = ((limb) in[7]) & bottom58bits;
-       out[8] = ((limb) in[8]) & bottom58bits;
-
-       /* out[i] < 2^58 */
-
-       out[1] += ((limb) in[0]) >> 58;
-       out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6;
-       /* out[1] < 2^58 + 2^6 + 2^58
-        *        = 2^59 + 2^6 */
-       out[2] += ((limb) (in[0] >> 64)) >> 52;
-
-       out[2] += ((limb) in[1]) >> 58;
-       out[2] += (((limb) (in[1] >> 64)) & bottom52bits) << 6;
-       out[3] += ((limb) (in[1] >> 64)) >> 52;
-
-       out[3] += ((limb) in[2]) >> 58;
-       out[3] += (((limb) (in[2] >> 64)) & bottom52bits) << 6;
-       out[4] += ((limb) (in[2] >> 64)) >> 52;
-
-       out[4] += ((limb) in[3]) >> 58;
-       out[4] += (((limb) (in[3] >> 64)) & bottom52bits) << 6;
-       out[5] += ((limb) (in[3] >> 64)) >> 52;
-
-       out[5] += ((limb) in[4]) >> 58;
-       out[5] += (((limb) (in[4] >> 64)) & bottom52bits) << 6;
-       out[6] += ((limb) (in[4] >> 64)) >> 52;
-
-       out[6] += ((limb) in[5]) >> 58;
-       out[6] += (((limb) (in[5] >> 64)) & bottom52bits) << 6;
-       out[7] += ((limb) (in[5] >> 64)) >> 52;
-
-       out[7] += ((limb) in[6]) >> 58;
-       out[7] += (((limb) (in[6] >> 64)) & bottom52bits) << 6;
-       out[8] += ((limb) (in[6] >> 64)) >> 52;
-
-       out[8] += ((limb) in[7]) >> 58;
-       out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6;
-       /* out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12
-        *            < 2^59 + 2^13 */
-       overflow1 = ((limb) (in[7] >> 64)) >> 52;
-
-       overflow1 += ((limb) in[8]) >> 58;
-       overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6;
-       overflow2 = ((limb) (in[8] >> 64)) >> 52;
-
-       overflow1 <<= 1;  /* overflow1 < 2^13 + 2^7 + 2^59 */
-       overflow2 <<= 1;  /* overflow2 < 2^13 */
-
-       out[0] += overflow1;  /* out[0] < 2^60 */
-       out[1] += overflow2;  /* out[1] < 2^59 + 2^6 + 2^13 */
-
-       out[1] += out[0] >> 58; out[0] &= bottom58bits;
-       /* out[0] < 2^58
-        * out[1] < 2^59 + 2^6 + 2^13 + 2^2
-        *        < 2^59 + 2^14 */
-       }
+{
+    u64 overflow1, overflow2;
+
+    out[0] = ((limb) in[0]) & bottom58bits;
+    out[1] = ((limb) in[1]) & bottom58bits;
+    out[2] = ((limb) in[2]) & bottom58bits;
+    out[3] = ((limb) in[3]) & bottom58bits;
+    out[4] = ((limb) in[4]) & bottom58bits;
+    out[5] = ((limb) in[5]) & bottom58bits;
+    out[6] = ((limb) in[6]) & bottom58bits;
+    out[7] = ((limb) in[7]) & bottom58bits;
+    out[8] = ((limb) in[8]) & bottom58bits;
+
+    /* out[i] < 2^58 */
+
+    out[1] += ((limb) in[0]) >> 58;
+    out[1] += (((limb) (in[0] >> 64)) & bottom52bits) << 6;
+    /*-
+     * out[1] < 2^58 + 2^6 + 2^58
+     *        = 2^59 + 2^6
+     */
+    out[2] += ((limb) (in[0] >> 64)) >> 52;
+
+    out[2] += ((limb) in[1]) >> 58;
+    out[2] += (((limb) (in[1] >> 64)) & bottom52bits) << 6;
+    out[3] += ((limb) (in[1] >> 64)) >> 52;
+
+    out[3] += ((limb) in[2]) >> 58;
+    out[3] += (((limb) (in[2] >> 64)) & bottom52bits) << 6;
+    out[4] += ((limb) (in[2] >> 64)) >> 52;
+
+    out[4] += ((limb) in[3]) >> 58;
+    out[4] += (((limb) (in[3] >> 64)) & bottom52bits) << 6;
+    out[5] += ((limb) (in[3] >> 64)) >> 52;
+
+    out[5] += ((limb) in[4]) >> 58;
+    out[5] += (((limb) (in[4] >> 64)) & bottom52bits) << 6;
+    out[6] += ((limb) (in[4] >> 64)) >> 52;
+
+    out[6] += ((limb) in[5]) >> 58;
+    out[6] += (((limb) (in[5] >> 64)) & bottom52bits) << 6;
+    out[7] += ((limb) (in[5] >> 64)) >> 52;
+
+    out[7] += ((limb) in[6]) >> 58;
+    out[7] += (((limb) (in[6] >> 64)) & bottom52bits) << 6;
+    out[8] += ((limb) (in[6] >> 64)) >> 52;
+
+    out[8] += ((limb) in[7]) >> 58;
+    out[8] += (((limb) (in[7] >> 64)) & bottom52bits) << 6;
+    /*-
+     * out[x > 1] < 2^58 + 2^6 + 2^58 + 2^12
+     *            < 2^59 + 2^13
+     */
+    overflow1 = ((limb) (in[7] >> 64)) >> 52;
+
+    overflow1 += ((limb) in[8]) >> 58;
+    overflow1 += (((limb) (in[8] >> 64)) & bottom52bits) << 6;
+    overflow2 = ((limb) (in[8] >> 64)) >> 52;
+
+    overflow1 <<= 1;            /* overflow1 < 2^13 + 2^7 + 2^59 */
+    overflow2 <<= 1;            /* overflow2 < 2^13 */
+
+    out[0] += overflow1;        /* out[0] < 2^60 */
+    out[1] += overflow2;        /* out[1] < 2^59 + 2^6 + 2^13 */
+
+    out[1] += out[0] >> 58;
+    out[0] &= bottom58bits;
+    /*-
+     * out[0] < 2^58
+     * out[1] < 2^59 + 2^6 + 2^13 + 2^2
+     *        < 2^59 + 2^14
+     */
+}
 
 static void felem_square_reduce(felem out, const felem in)
-       {
-       largefelem tmp;
-       felem_square(tmp, in);
-       felem_reduce(out, tmp);
-       }
+{
+    largefelem tmp;
+    felem_square(tmp, in);
+    felem_reduce(out, tmp);
+}
 
 static void felem_mul_reduce(felem out, const felem in1, const felem in2)
-       {
-       largefelem tmp;
-       felem_mul(tmp, in1, in2);
-       felem_reduce(out, tmp);
-       }
+{
+    largefelem tmp;
+    felem_mul(tmp, in1, in2);
+    felem_reduce(out, tmp);
+}
 
 /*-
  * felem_inv calculates |out| = |in|^{-1}
@@ -695,89 +705,111 @@ static void felem_mul_reduce(felem out, const felem in1, const felem in2)
  *   a^{p-2} = a^{-1} (mod p)
  */
 static void felem_inv(felem out, const felem in)
-       {
-       felem ftmp, ftmp2, ftmp3, ftmp4;
-       largefelem tmp;
-       unsigned i;
-
-       felem_square(tmp, in); felem_reduce(ftmp, tmp);         /* 2^1 */
-       felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp);      /* 2^2 - 2^0 */
-       felem_assign(ftmp2, ftmp);
-       felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);       /* 2^3 - 2^1 */
-       felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp);      /* 2^3 - 2^0 */
-       felem_square(tmp, ftmp); felem_reduce(ftmp, tmp);       /* 2^4 - 2^1 */
-
-       felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp);     /* 2^3 - 2^1 */
-       felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^4 - 2^2 */
-       felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^4 - 2^0 */
-
-       felem_assign(ftmp2, ftmp3);
-       felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^5 - 2^1 */
-       felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^6 - 2^2 */
-       felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^7 - 2^3 */
-       felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^8 - 2^4 */
-       felem_assign(ftmp4, ftmp3);
-       felem_mul(tmp, ftmp3, ftmp); felem_reduce(ftmp4, tmp);  /* 2^8 - 2^1 */
-       felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp);     /* 2^9 - 2^2 */
-       felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^8 - 2^0 */
-       felem_assign(ftmp2, ftmp3);
-
-       for (i = 0; i < 8; i++)
-               {
-               felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^16 - 2^8 */
-               }
-       felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^16 - 2^0 */
-       felem_assign(ftmp2, ftmp3);
-
-       for (i = 0; i < 16; i++)
-               {
-               felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^32 - 2^16 */
-               }
-       felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^32 - 2^0 */
-       felem_assign(ftmp2, ftmp3);
-
-       for (i = 0; i < 32; i++)
-               {
-               felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^64 - 2^32 */
-               }
-       felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^64 - 2^0 */
-       felem_assign(ftmp2, ftmp3);
-
-       for (i = 0; i < 64; i++)
-               {
-               felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^128 - 2^64 */
-               }
-       felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^128 - 2^0 */
-       felem_assign(ftmp2, ftmp3);
-
-       for (i = 0; i < 128; i++)
-               {
-               felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^256 - 2^128 */
-               }
-       felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^256 - 2^0 */
-       felem_assign(ftmp2, ftmp3);
-
-       for (i = 0; i < 256; i++)
-               {
-               felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^512 - 2^256 */
-               }
-       felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^512 - 2^0 */
-
-       for (i = 0; i < 9; i++)
-               {
-               felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp);     /* 2^521 - 2^9 */
-               }
-       felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^512 - 2^2 */
-       felem_mul(tmp, ftmp3, in); felem_reduce(out, tmp);      /* 2^512 - 3 */
+{
+    felem ftmp, ftmp2, ftmp3, ftmp4;
+    largefelem tmp;
+    unsigned i;
+
+    felem_square(tmp, in);
+    felem_reduce(ftmp, tmp);    /* 2^1 */
+    felem_mul(tmp, in, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^2 - 2^0 */
+    felem_assign(ftmp2, ftmp);
+    felem_square(tmp, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^3 - 2^1 */
+    felem_mul(tmp, in, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^3 - 2^0 */
+    felem_square(tmp, ftmp);
+    felem_reduce(ftmp, tmp);    /* 2^4 - 2^1 */
+
+    felem_square(tmp, ftmp2);
+    felem_reduce(ftmp3, tmp);   /* 2^3 - 2^1 */
+    felem_square(tmp, ftmp3);
+    felem_reduce(ftmp3, tmp);   /* 2^4 - 2^2 */
+    felem_mul(tmp, ftmp3, ftmp2);
+    felem_reduce(ftmp3, tmp);   /* 2^4 - 2^0 */
+
+    felem_assign(ftmp2, ftmp3);
+    felem_square(tmp, ftmp3);
+    felem_reduce(ftmp3, tmp);   /* 2^5 - 2^1 */
+    felem_square(tmp, ftmp3);
+    felem_reduce(ftmp3, tmp);   /* 2^6 - 2^2 */
+    felem_square(tmp, ftmp3);
+    felem_reduce(ftmp3, tmp);   /* 2^7 - 2^3 */
+    felem_square(tmp, ftmp3);
+    felem_reduce(ftmp3, tmp);   /* 2^8 - 2^4 */
+    felem_assign(ftmp4, ftmp3);
+    felem_mul(tmp, ftmp3, ftmp);
+    felem_reduce(ftmp4, tmp);   /* 2^8 - 2^1 */
+    felem_square(tmp, ftmp4);
+    felem_reduce(ftmp4, tmp);   /* 2^9 - 2^2 */
+    felem_mul(tmp, ftmp3, ftmp2);
+    felem_reduce(ftmp3, tmp);   /* 2^8 - 2^0 */
+    felem_assign(ftmp2, ftmp3);
+
+    for (i = 0; i < 8; i++) {
+        felem_square(tmp, ftmp3);
+        felem_reduce(ftmp3, tmp); /* 2^16 - 2^8 */
+    }
+    felem_mul(tmp, ftmp3, ftmp2);
+    felem_reduce(ftmp3, tmp);   /* 2^16 - 2^0 */
+    felem_assign(ftmp2, ftmp3);
+
+    for (i = 0; i < 16; i++) {
+        felem_square(tmp, ftmp3);
+        felem_reduce(ftmp3, tmp); /* 2^32 - 2^16 */
+    }
+    felem_mul(tmp, ftmp3, ftmp2);
+    felem_reduce(ftmp3, tmp);   /* 2^32 - 2^0 */
+    felem_assign(ftmp2, ftmp3);
+
+    for (i = 0; i < 32; i++) {
+        felem_square(tmp, ftmp3);
+        felem_reduce(ftmp3, tmp); /* 2^64 - 2^32 */
+    }
+    felem_mul(tmp, ftmp3, ftmp2);
+    felem_reduce(ftmp3, tmp);   /* 2^64 - 2^0 */
+    felem_assign(ftmp2, ftmp3);
+
+    for (i = 0; i < 64; i++) {
+        felem_square(tmp, ftmp3);
+        felem_reduce(ftmp3, tmp); /* 2^128 - 2^64 */
+    }
+    felem_mul(tmp, ftmp3, ftmp2);
+    felem_reduce(ftmp3, tmp);   /* 2^128 - 2^0 */
+    felem_assign(ftmp2, ftmp3);
+
+    for (i = 0; i < 128; i++) {
+        felem_square(tmp, ftmp3);
+        felem_reduce(ftmp3, tmp); /* 2^256 - 2^128 */
+    }
+    felem_mul(tmp, ftmp3, ftmp2);
+    felem_reduce(ftmp3, tmp);   /* 2^256 - 2^0 */
+    felem_assign(ftmp2, ftmp3);
+
+    for (i = 0; i < 256; i++) {
+        felem_square(tmp, ftmp3);
+        felem_reduce(ftmp3, tmp); /* 2^512 - 2^256 */
+    }
+    felem_mul(tmp, ftmp3, ftmp2);
+    felem_reduce(ftmp3, tmp);   /* 2^512 - 2^0 */
+
+    for (i = 0; i < 9; i++) {
+        felem_square(tmp, ftmp3);
+        felem_reduce(ftmp3, tmp); /* 2^521 - 2^9 */
+    }
+    felem_mul(tmp, ftmp3, ftmp4);
+    felem_reduce(ftmp3, tmp);   /* 2^512 - 2^2 */
+    felem_mul(tmp, ftmp3, in);
+    felem_reduce(out, tmp);     /* 2^512 - 3 */
 }
 
 /* This is 2^521-1, expressed as an felem */
-static const felem kPrime =
-       {
-       0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff,
-       0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff,
-       0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff
-       };
+static const felem kPrime = {
+    0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff,
+    0x03ffffffffffffff, 0x03ffffffffffffff, 0x03ffffffffffffff,
+    0x03ffffffffffffff, 0x03ffffffffffffff, 0x01ffffffffffffff
+};
 
 /*-
  * felem_is_zero returns a limb with all bits set if |in| == 0 (mod p) and 0
@@ -786,64 +818,77 @@ static const felem kPrime =
  *   in[i] < 2^59 + 2^14
  */
 static limb felem_is_zero(const felem in)
-       {
-       felem ftmp;
-       limb is_zero, is_p;
-       felem_assign(ftmp, in);
-
-       ftmp[0] += ftmp[8] >> 57; ftmp[8] &= bottom57bits;
-       /* ftmp[8] < 2^57 */
-       ftmp[1] += ftmp[0] >> 58; ftmp[0] &= bottom58bits;
-       ftmp[2] += ftmp[1] >> 58; ftmp[1] &= bottom58bits;
-       ftmp[3] += ftmp[2] >> 58; ftmp[2] &= bottom58bits;
-       ftmp[4] += ftmp[3] >> 58; ftmp[3] &= bottom58bits;
-       ftmp[5] += ftmp[4] >> 58; ftmp[4] &= bottom58bits;
-       ftmp[6] += ftmp[5] >> 58; ftmp[5] &= bottom58bits;
-       ftmp[7] += ftmp[6] >> 58; ftmp[6] &= bottom58bits;
-       ftmp[8] += ftmp[7] >> 58; ftmp[7] &= bottom58bits;
-       /* ftmp[8] < 2^57 + 4 */
-
-       /* The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is
-        * greater than our bound for ftmp[8]. Therefore we only have to check
-        * if the zero is zero or 2^521-1. */
-
-       is_zero = 0;
-       is_zero |= ftmp[0];
-       is_zero |= ftmp[1];
-       is_zero |= ftmp[2];
-       is_zero |= ftmp[3];
-       is_zero |= ftmp[4];
-       is_zero |= ftmp[5];
-       is_zero |= ftmp[6];
-       is_zero |= ftmp[7];
-       is_zero |= ftmp[8];
-
-       is_zero--;
-       /* We know that ftmp[i] < 2^63, therefore the only way that the top bit
-        * can be set is if is_zero was 0 before the decrement. */
-       is_zero = ((s64) is_zero) >> 63;
-
-       is_p = ftmp[0] ^ kPrime[0];
-       is_p |= ftmp[1] ^ kPrime[1];
-       is_p |= ftmp[2] ^ kPrime[2];
-       is_p |= ftmp[3] ^ kPrime[3];
-       is_p |= ftmp[4] ^ kPrime[4];
-       is_p |= ftmp[5] ^ kPrime[5];
-       is_p |= ftmp[6] ^ kPrime[6];
-       is_p |= ftmp[7] ^ kPrime[7];
-       is_p |= ftmp[8] ^ kPrime[8];
-
-       is_p--;
-       is_p = ((s64) is_p) >> 63;
-
-       is_zero |= is_p;
-       return is_zero;
-       }
+{
+    felem ftmp;
+    limb is_zero, is_p;
+    felem_assign(ftmp, in);
+
+    ftmp[0] += ftmp[8] >> 57;
+    ftmp[8] &= bottom57bits;
+    /* ftmp[8] < 2^57 */
+    ftmp[1] += ftmp[0] >> 58;
+    ftmp[0] &= bottom58bits;
+    ftmp[2] += ftmp[1] >> 58;
+    ftmp[1] &= bottom58bits;
+    ftmp[3] += ftmp[2] >> 58;
+    ftmp[2] &= bottom58bits;
+    ftmp[4] += ftmp[3] >> 58;
+    ftmp[3] &= bottom58bits;
+    ftmp[5] += ftmp[4] >> 58;
+    ftmp[4] &= bottom58bits;
+    ftmp[6] += ftmp[5] >> 58;
+    ftmp[5] &= bottom58bits;
+    ftmp[7] += ftmp[6] >> 58;
+    ftmp[6] &= bottom58bits;
+    ftmp[8] += ftmp[7] >> 58;
+    ftmp[7] &= bottom58bits;
+    /* ftmp[8] < 2^57 + 4 */
+
+    /*
+     * The ninth limb of 2*(2^521-1) is 0x03ffffffffffffff, which is greater
+     * than our bound for ftmp[8]. Therefore we only have to check if the
+     * zero is zero or 2^521-1.
+     */
+
+    is_zero = 0;
+    is_zero |= ftmp[0];
+    is_zero |= ftmp[1];
+    is_zero |= ftmp[2];
+    is_zero |= ftmp[3];
+    is_zero |= ftmp[4];
+    is_zero |= ftmp[5];
+    is_zero |= ftmp[6];
+    is_zero |= ftmp[7];
+    is_zero |= ftmp[8];
+
+    is_zero--;
+    /*
+     * We know that ftmp[i] < 2^63, therefore the only way that the top bit
+     * can be set is if is_zero was 0 before the decrement.
+     */
+    is_zero = ((s64) is_zero) >> 63;
+
+    is_p = ftmp[0] ^ kPrime[0];
+    is_p |= ftmp[1] ^ kPrime[1];
+    is_p |= ftmp[2] ^ kPrime[2];
+    is_p |= ftmp[3] ^ kPrime[3];
+    is_p |= ftmp[4] ^ kPrime[4];
+    is_p |= ftmp[5] ^ kPrime[5];
+    is_p |= ftmp[6] ^ kPrime[6];
+    is_p |= ftmp[7] ^ kPrime[7];
+    is_p |= ftmp[8] ^ kPrime[8];
+
+    is_p--;
+    is_p = ((s64) is_p) >> 63;
+
+    is_zero |= is_p;
+    return is_zero;
+}
 
 static int felem_is_zero_int(const felem in)
-       {
-       return (int) (felem_is_zero(in) & ((limb)1));
-       }
+{
+    return (int)(felem_is_zero(in) & ((limb) 1));
+}
 
 /*-
  * felem_contract converts |in| to its unique, minimal representation.
@@ -851,96 +896,133 @@ static int felem_is_zero_int(const felem in)
  *   in[i] < 2^59 + 2^14
  */
 static void felem_contract(felem out, const felem in)
-       {
-       limb is_p, is_greater, sign;
-       static const limb two58 = ((limb)1) << 58;
-
-       felem_assign(out, in);
-
-       out[0] += out[8] >> 57; out[8] &= bottom57bits;
-       /* out[8] < 2^57 */
-       out[1] += out[0] >> 58; out[0] &= bottom58bits;
-       out[2] += out[1] >> 58; out[1] &= bottom58bits;
-       out[3] += out[2] >> 58; out[2] &= bottom58bits;
-       out[4] += out[3] >> 58; out[3] &= bottom58bits;
-       out[5] += out[4] >> 58; out[4] &= bottom58bits;
-       out[6] += out[5] >> 58; out[5] &= bottom58bits;
-       out[7] += out[6] >> 58; out[6] &= bottom58bits;
-       out[8] += out[7] >> 58; out[7] &= bottom58bits;
-       /* out[8] < 2^57 + 4 */
-
-       /* If the value is greater than 2^521-1 then we have to subtract
-        * 2^521-1 out. See the comments in felem_is_zero regarding why we
-        * don't test for other multiples of the prime. */
-
-       /* First, if |out| is equal to 2^521-1, we subtract it out to get zero. */
-
-       is_p = out[0] ^ kPrime[0];
-       is_p |= out[1] ^ kPrime[1];
-       is_p |= out[2] ^ kPrime[2];
-       is_p |= out[3] ^ kPrime[3];
-       is_p |= out[4] ^ kPrime[4];
-       is_p |= out[5] ^ kPrime[5];
-       is_p |= out[6] ^ kPrime[6];
-       is_p |= out[7] ^ kPrime[7];
-       is_p |= out[8] ^ kPrime[8];
-
-       is_p--;
-       is_p &= is_p << 32;
-       is_p &= is_p << 16;
-       is_p &= is_p << 8;
-       is_p &= is_p << 4;
-       is_p &= is_p << 2;
-       is_p &= is_p << 1;
-       is_p = ((s64) is_p) >> 63;
-       is_p = ~is_p;
-
-       /* is_p is 0 iff |out| == 2^521-1 and all ones otherwise */
-
-       out[0] &= is_p;
-       out[1] &= is_p;
-       out[2] &= is_p;
-       out[3] &= is_p;
-       out[4] &= is_p;
-       out[5] &= is_p;
-       out[6] &= is_p;
-       out[7] &= is_p;
-       out[8] &= is_p;
-
-       /* In order to test that |out| >= 2^521-1 we need only test if out[8]
-        * >> 57 is greater than zero as (2^521-1) + x >= 2^522 */
-       is_greater = out[8] >> 57;
-       is_greater |= is_greater << 32;
-       is_greater |= is_greater << 16;
-       is_greater |= is_greater << 8;
-       is_greater |= is_greater << 4;
-       is_greater |= is_greater << 2;
-       is_greater |= is_greater << 1;
-       is_greater = ((s64) is_greater) >> 63;
-
-       out[0] -= kPrime[0] & is_greater;
-       out[1] -= kPrime[1] & is_greater;
-       out[2] -= kPrime[2] & is_greater;
-       out[3] -= kPrime[3] & is_greater;
-       out[4] -= kPrime[4] & is_greater;
-       out[5] -= kPrime[5] & is_greater;
-       out[6] -= kPrime[6] & is_greater;
-       out[7] -= kPrime[7] & is_greater;
-       out[8] -= kPrime[8] & is_greater;
-
-       /* Eliminate negative coefficients */
-       sign = -(out[0] >> 63); out[0] += (two58 & sign); out[1] -= (1 & sign);
-       sign = -(out[1] >> 63); out[1] += (two58 & sign); out[2] -= (1 & sign);
-       sign = -(out[2] >> 63); out[2] += (two58 & sign); out[3] -= (1 & sign);
-       sign = -(out[3] >> 63); out[3] += (two58 & sign); out[4] -= (1 & sign);
-       sign = -(out[4] >> 63); out[4] += (two58 & sign); out[5] -= (1 & sign);
-       sign = -(out[0] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign);
-       sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign);
-       sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign);
-       sign = -(out[5] >> 63); out[5] += (two58 & sign); out[6] -= (1 & sign);
-       sign = -(out[6] >> 63); out[6] += (two58 & sign); out[7] -= (1 & sign);
-       sign = -(out[7] >> 63); out[7] += (two58 & sign); out[8] -= (1 & sign);
-       }
+{
+    limb is_p, is_greater, sign;
+    static const limb two58 = ((limb) 1) << 58;
+
+    felem_assign(out, in);
+
+    out[0] += out[8] >> 57;
+    out[8] &= bottom57bits;
+    /* out[8] < 2^57 */
+    out[1] += out[0] >> 58;
+    out[0] &= bottom58bits;
+    out[2] += out[1] >> 58;
+    out[1] &= bottom58bits;
+    out[3] += out[2] >> 58;
+    out[2] &= bottom58bits;
+    out[4] += out[3] >> 58;
+    out[3] &= bottom58bits;
+    out[5] += out[4] >> 58;
+    out[4] &= bottom58bits;
+    out[6] += out[5] >> 58;
+    out[5] &= bottom58bits;
+    out[7] += out[6] >> 58;
+    out[6] &= bottom58bits;
+    out[8] += out[7] >> 58;
+    out[7] &= bottom58bits;
+    /* out[8] < 2^57 + 4 */
+
+    /*
+     * If the value is greater than 2^521-1 then we have to subtract 2^521-1
+     * out. See the comments in felem_is_zero regarding why we don't test for
+     * other multiples of the prime.
+     */
+
+    /*
+     * First, if |out| is equal to 2^521-1, we subtract it out to get zero.
+     */
+
+    is_p = out[0] ^ kPrime[0];
+    is_p |= out[1] ^ kPrime[1];
+    is_p |= out[2] ^ kPrime[2];
+    is_p |= out[3] ^ kPrime[3];
+    is_p |= out[4] ^ kPrime[4];
+    is_p |= out[5] ^ kPrime[5];
+    is_p |= out[6] ^ kPrime[6];
+    is_p |= out[7] ^ kPrime[7];
+    is_p |= out[8] ^ kPrime[8];
+
+    is_p--;
+    is_p &= is_p << 32;
+    is_p &= is_p << 16;
+    is_p &= is_p << 8;
+    is_p &= is_p << 4;
+    is_p &= is_p << 2;
+    is_p &= is_p << 1;
+    is_p = ((s64) is_p) >> 63;
+    is_p = ~is_p;
+
+    /* is_p is 0 iff |out| == 2^521-1 and all ones otherwise */
+
+    out[0] &= is_p;
+    out[1] &= is_p;
+    out[2] &= is_p;
+    out[3] &= is_p;
+    out[4] &= is_p;
+    out[5] &= is_p;
+    out[6] &= is_p;
+    out[7] &= is_p;
+    out[8] &= is_p;
+
+    /*
+     * In order to test that |out| >= 2^521-1 we need only test if out[8] >>
+     * 57 is greater than zero as (2^521-1) + x >= 2^522
+     */
+    is_greater = out[8] >> 57;
+    is_greater |= is_greater << 32;
+    is_greater |= is_greater << 16;
+    is_greater |= is_greater << 8;
+    is_greater |= is_greater << 4;
+    is_greater |= is_greater << 2;
+    is_greater |= is_greater << 1;
+    is_greater = ((s64) is_greater) >> 63;
+
+    out[0] -= kPrime[0] & is_greater;
+    out[1] -= kPrime[1] & is_greater;
+    out[2] -= kPrime[2] & is_greater;
+    out[3] -= kPrime[3] & is_greater;
+    out[4] -= kPrime[4] & is_greater;
+    out[5] -= kPrime[5] & is_greater;
+    out[6] -= kPrime[6] & is_greater;
+    out[7] -= kPrime[7] & is_greater;
+    out[8] -= kPrime[8] & is_greater;
+
+    /* Eliminate negative coefficients */
+    sign = -(out[0] >> 63);
+    out[0] += (two58 & sign);
+    out[1] -= (1 & sign);
+    sign = -(out[1] >> 63);
+    out[1] += (two58 & sign);
+    out[2] -= (1 & sign);
+    sign = -(out[2] >> 63);
+    out[2] += (two58 & sign);
+    out[3] -= (1 & sign);
+    sign = -(out[3] >> 63);
+    out[3] += (two58 & sign);
+    out[4] -= (1 & sign);
+    sign = -(out[4] >> 63);
+    out[4] += (two58 & sign);
+    out[5] -= (1 & sign);
+    sign = -(out[0] >> 63);
+    out[5] += (two58 & sign);
+    out[6] -= (1 & sign);
+    sign = -(out[6] >> 63);
+    out[6] += (two58 & sign);
+    out[7] -= (1 & sign);
+    sign = -(out[7] >> 63);
+    out[7] += (two58 & sign);
+    out[8] -= (1 & sign);
+    sign = -(out[5] >> 63);
+    out[5] += (two58 & sign);
+    out[6] -= (1 & sign);
+    sign = -(out[6] >> 63);
+    out[6] += (two58 & sign);
+    out[7] -= (1 & sign);
+    sign = -(out[7] >> 63);
+    out[7] += (two58 & sign);
+    out[8] -= (1 & sign);
+}
 
 /*-
  * Group operations
@@ -960,111 +1042,111 @@ static void felem_contract(felem out, const felem in)
  * while x_out == y_in is not (maybe this works, but it's not tested). */
 static void
 point_double(felem x_out, felem y_out, felem z_out,
-            const felem x_in, const felem y_in, const felem z_in)
-       {
-       largefelem tmp, tmp2;
-       felem delta, gamma, beta, alpha, ftmp, ftmp2;
-
-       felem_assign(ftmp, x_in);
-       felem_assign(ftmp2, x_in);
-
-       /* delta = z^2 */
-       felem_square(tmp, z_in);
-       felem_reduce(delta, tmp);  /* delta[i] < 2^59 + 2^14 */
-
-       /* gamma = y^2 */
-       felem_square(tmp, y_in);
-       felem_reduce(gamma, tmp);  /* gamma[i] < 2^59 + 2^14 */
-
-       /* beta = x*gamma */
-       felem_mul(tmp, x_in, gamma);
-       felem_reduce(beta, tmp);  /* beta[i] < 2^59 + 2^14 */
-
-       /* alpha = 3*(x-delta)*(x+delta) */
-       felem_diff64(ftmp, delta);
-       /* ftmp[i] < 2^61 */
-       felem_sum64(ftmp2, delta);
-       /* ftmp2[i] < 2^60 + 2^15 */
-       felem_scalar64(ftmp2, 3);
-       /* ftmp2[i] < 3*2^60 + 3*2^15 */
-       felem_mul(tmp, ftmp, ftmp2);
-       /*-
-        * tmp[i] < 17(3*2^121 + 3*2^76)
-        *        = 61*2^121 + 61*2^76
-        *        < 64*2^121 + 64*2^76
-        *        = 2^127 + 2^82
-        *        < 2^128 
-        */
-       felem_reduce(alpha, tmp);
-
-       /* x' = alpha^2 - 8*beta */
-       felem_square(tmp, alpha);
-       /* tmp[i] < 17*2^120
-        *        < 2^125 */
-       felem_assign(ftmp, beta);
-       felem_scalar64(ftmp, 8);
-       /* ftmp[i] < 2^62 + 2^17 */
-       felem_diff_128_64(tmp, ftmp);
-       /* tmp[i] < 2^125 + 2^63 + 2^62 + 2^17 */
-       felem_reduce(x_out, tmp);
-
-       /* z' = (y + z)^2 - gamma - delta */
-       felem_sum64(delta, gamma);
-       /* delta[i] < 2^60 + 2^15 */
-       felem_assign(ftmp, y_in);
-       felem_sum64(ftmp, z_in);
-       /* ftmp[i] < 2^60 + 2^15 */
-       felem_square(tmp, ftmp);
-       /* tmp[i] < 17(2^122)
-        *        < 2^127 */
-       felem_diff_128_64(tmp, delta);
-       /* tmp[i] < 2^127 + 2^63 */
-       felem_reduce(z_out, tmp);
-
-       /* y' = alpha*(4*beta - x') - 8*gamma^2 */
-       felem_scalar64(beta, 4);
-       /* beta[i] < 2^61 + 2^16 */
-       felem_diff64(beta, x_out);
-       /* beta[i] < 2^61 + 2^60 + 2^16 */
-       felem_mul(tmp, alpha, beta);
-       /*-
-        * tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16))
-        *        = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30) 
-        *        = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30)
-        *        < 2^128 
-        */
-       felem_square(tmp2, gamma);
-       /*-
-        * tmp2[i] < 17*(2^59 + 2^14)^2
-        *         = 17*(2^118 + 2^74 + 2^28) 
-        */
-       felem_scalar128(tmp2, 8);
-       /*- 
-        * tmp2[i] < 8*17*(2^118 + 2^74 + 2^28)
-        *         = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31
-        *         < 2^126 
-        */
-       felem_diff128(tmp, tmp2);
-       /*-
-        * tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30)
-        *        = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 +
-        *          2^74 + 2^69 + 2^34 + 2^30
-        *        < 2^128 
-        */
-       felem_reduce(y_out, tmp);
-       }
+             const felem x_in, const felem y_in, const felem z_in)
+{
+    largefelem tmp, tmp2;
+    felem delta, gamma, beta, alpha, ftmp, ftmp2;
+
+    felem_assign(ftmp, x_in);
+    felem_assign(ftmp2, x_in);
+
+    /* delta = z^2 */
+    felem_square(tmp, z_in);
+    felem_reduce(delta, tmp);   /* delta[i] < 2^59 + 2^14 */
+
+    /* gamma = y^2 */
+    felem_square(tmp, y_in);
+    felem_reduce(gamma, tmp);   /* gamma[i] < 2^59 + 2^14 */
+
+    /* beta = x*gamma */
+    felem_mul(tmp, x_in, gamma);
+    felem_reduce(beta, tmp);    /* beta[i] < 2^59 + 2^14 */
+
+    /* alpha = 3*(x-delta)*(x+delta) */
+    felem_diff64(ftmp, delta);
+    /* ftmp[i] < 2^61 */
+    felem_sum64(ftmp2, delta);
+    /* ftmp2[i] < 2^60 + 2^15 */
+    felem_scalar64(ftmp2, 3);
+    /* ftmp2[i] < 3*2^60 + 3*2^15 */
+    felem_mul(tmp, ftmp, ftmp2);
+    /*-
+     * tmp[i] < 17(3*2^121 + 3*2^76)
+     *        = 61*2^121 + 61*2^76
+     *        < 64*2^121 + 64*2^76
+     *        = 2^127 + 2^82
+     *        < 2^128
+     */
+    felem_reduce(alpha, tmp);
+
+    /* x' = alpha^2 - 8*beta */
+    felem_square(tmp, alpha);
+    /*
+     * tmp[i] < 17*2^120 < 2^125
+     */
+    felem_assign(ftmp, beta);
+    felem_scalar64(ftmp, 8);
+    /* ftmp[i] < 2^62 + 2^17 */
+    felem_diff_128_64(tmp, ftmp);
+    /* tmp[i] < 2^125 + 2^63 + 2^62 + 2^17 */
+    felem_reduce(x_out, tmp);
+
+    /* z' = (y + z)^2 - gamma - delta */
+    felem_sum64(delta, gamma);
+    /* delta[i] < 2^60 + 2^15 */
+    felem_assign(ftmp, y_in);
+    felem_sum64(ftmp, z_in);
+    /* ftmp[i] < 2^60 + 2^15 */
+    felem_square(tmp, ftmp);
+    /*
+     * tmp[i] < 17(2^122) < 2^127
+     */
+    felem_diff_128_64(tmp, delta);
+    /* tmp[i] < 2^127 + 2^63 */
+    felem_reduce(z_out, tmp);
+
+    /* y' = alpha*(4*beta - x') - 8*gamma^2 */
+    felem_scalar64(beta, 4);
+    /* beta[i] < 2^61 + 2^16 */
+    felem_diff64(beta, x_out);
+    /* beta[i] < 2^61 + 2^60 + 2^16 */
+    felem_mul(tmp, alpha, beta);
+    /*-
+     * tmp[i] < 17*((2^59 + 2^14)(2^61 + 2^60 + 2^16))
+     *        = 17*(2^120 + 2^75 + 2^119 + 2^74 + 2^75 + 2^30)
+     *        = 17*(2^120 + 2^119 + 2^76 + 2^74 + 2^30)
+     *        < 2^128
+     */
+    felem_square(tmp2, gamma);
+    /*-
+     * tmp2[i] < 17*(2^59 + 2^14)^2
+     *         = 17*(2^118 + 2^74 + 2^28)
+     */
+    felem_scalar128(tmp2, 8);
+    /*-
+     * tmp2[i] < 8*17*(2^118 + 2^74 + 2^28)
+     *         = 2^125 + 2^121 + 2^81 + 2^77 + 2^35 + 2^31
+     *         < 2^126
+     */
+    felem_diff128(tmp, tmp2);
+    /*-
+     * tmp[i] < 2^127 - 2^69 + 17(2^120 + 2^119 + 2^76 + 2^74 + 2^30)
+     *        = 2^127 + 2^124 + 2^122 + 2^120 + 2^118 + 2^80 + 2^78 + 2^76 +
+     *          2^74 + 2^69 + 2^34 + 2^30
+     *        < 2^128
+     */
+    felem_reduce(y_out, tmp);
+}
 
 /* copy_conditional copies in to out iff mask is all ones. */
-static void
-copy_conditional(felem out, const felem in, limb mask)
-       {
-       unsigned i;
-       for (i = 0; i < NLIMBS; ++i)
-               {
-               const limb tmp = mask & (in[i] ^ out[i]);
-               out[i] ^= tmp;
-               }
-       }
+static void copy_conditional(felem out, const felem in, limb mask)
+{
+    unsigned i;
+    for (i = 0; i < NLIMBS; ++i) {
+        const limb tmp = mask & (in[i] ^ out[i]);
+        out[i] ^= tmp;
+    }
+}
 
 /*-
  * point_add calcuates (x1, y1, z1) + (x2, y2, z2)
@@ -1078,157 +1160,159 @@ copy_conditional(felem out, const felem in, limb mask)
  * happens during single point multiplication, so there is no timing leak for
  * ECDH or ECDSA signing. */
 static void point_add(felem x3, felem y3, felem z3,
-       const felem x1, const felem y1, const felem z1,
-       const int mixed, const felem x2, const felem y2, const felem z2)
-       {
-       felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out;
-       largefelem tmp, tmp2;
-       limb x_equal, y_equal, z1_is_zero, z2_is_zero;
-
-       z1_is_zero = felem_is_zero(z1);
-       z2_is_zero = felem_is_zero(z2);
-
-       /* ftmp = z1z1 = z1**2 */
-       felem_square(tmp, z1);
-       felem_reduce(ftmp, tmp);
-
-       if (!mixed)
-               {
-               /* ftmp2 = z2z2 = z2**2 */
-               felem_square(tmp, z2);
-               felem_reduce(ftmp2, tmp);
-
-               /* u1 = ftmp3 = x1*z2z2 */
-               felem_mul(tmp, x1, ftmp2);
-               felem_reduce(ftmp3, tmp);
-
-               /* ftmp5 = z1 + z2 */
-               felem_assign(ftmp5, z1);
-               felem_sum64(ftmp5, z2);
-               /* ftmp5[i] < 2^61 */
-
-               /* ftmp5 = (z1 + z2)**2 - z1z1 - z2z2 = 2*z1z2 */
-               felem_square(tmp, ftmp5);
-               /* tmp[i] < 17*2^122 */
-               felem_diff_128_64(tmp, ftmp);
-               /* tmp[i] < 17*2^122 + 2^63 */
-               felem_diff_128_64(tmp, ftmp2);
-               /* tmp[i] < 17*2^122 + 2^64 */
-               felem_reduce(ftmp5, tmp);
-
-               /* ftmp2 = z2 * z2z2 */
-               felem_mul(tmp, ftmp2, z2);
-               felem_reduce(ftmp2, tmp);
-
-               /* s1 = ftmp6 = y1 * z2**3 */
-               felem_mul(tmp, y1, ftmp2);
-               felem_reduce(ftmp6, tmp);
-               }
-       else
-               {
-               /* We'll assume z2 = 1 (special case z2 = 0 is handled later) */
-
-               /* u1 = ftmp3 = x1*z2z2 */
-               felem_assign(ftmp3, x1);
-
-               /* ftmp5 = 2*z1z2 */
-               felem_scalar(ftmp5, z1, 2);
-
-               /* s1 = ftmp6 = y1 * z2**3 */
-               felem_assign(ftmp6, y1);
-               }
-
-       /* u2 = x2*z1z1 */
-       felem_mul(tmp, x2, ftmp);
-       /* tmp[i] < 17*2^120 */
-
-       /* h = ftmp4 = u2 - u1 */
-       felem_diff_128_64(tmp, ftmp3);
-       /* tmp[i] < 17*2^120 + 2^63 */
-       felem_reduce(ftmp4, tmp);
-
-       x_equal = felem_is_zero(ftmp4);
-
-       /* z_out = ftmp5 * h */
-       felem_mul(tmp, ftmp5, ftmp4);
-       felem_reduce(z_out, tmp);
-
-       /* ftmp = z1 * z1z1 */
-       felem_mul(tmp, ftmp, z1);
-       felem_reduce(ftmp, tmp);
-
-       /* s2 = tmp = y2 * z1**3 */
-       felem_mul(tmp, y2, ftmp);
-       /* tmp[i] < 17*2^120 */
-
-       /* r = ftmp5 = (s2 - s1)*2 */
-       felem_diff_128_64(tmp, ftmp6);
-       /* tmp[i] < 17*2^120 + 2^63 */
-       felem_reduce(ftmp5, tmp);
-       y_equal = felem_is_zero(ftmp5);
-       felem_scalar64(ftmp5, 2);
-       /* ftmp5[i] < 2^61 */
-
-       if (x_equal && y_equal && !z1_is_zero && !z2_is_zero)
-               {
-               point_double(x3, y3, z3, x1, y1, z1);
-               return;
-               }
-
-       /* I = ftmp = (2h)**2 */
-       felem_assign(ftmp, ftmp4);
-       felem_scalar64(ftmp, 2);
-       /* ftmp[i] < 2^61 */
-       felem_square(tmp, ftmp);
-       /* tmp[i] < 17*2^122 */
-       felem_reduce(ftmp, tmp);
-
-       /* J = ftmp2 = h * I */
-       felem_mul(tmp, ftmp4, ftmp);
-       felem_reduce(ftmp2, tmp);
-
-       /* V = ftmp4 = U1 * I */
-       felem_mul(tmp, ftmp3, ftmp);
-       felem_reduce(ftmp4, tmp);
-
-       /* x_out = r**2 - J - 2V */
-       felem_square(tmp, ftmp5);
-       /* tmp[i] < 17*2^122 */
-       felem_diff_128_64(tmp, ftmp2);
-       /* tmp[i] < 17*2^122 + 2^63 */
-       felem_assign(ftmp3, ftmp4);
-       felem_scalar64(ftmp4, 2);
-       /* ftmp4[i] < 2^61 */
-       felem_diff_128_64(tmp, ftmp4);
-       /* tmp[i] < 17*2^122 + 2^64 */
-       felem_reduce(x_out, tmp);
-
-       /* y_out = r(V-x_out) - 2 * s1 * J */
-       felem_diff64(ftmp3, x_out);
-       /* ftmp3[i] < 2^60 + 2^60
-        *          = 2^61 */
-       felem_mul(tmp, ftmp5, ftmp3);
-       /* tmp[i] < 17*2^122 */
-       felem_mul(tmp2, ftmp6, ftmp2);
-       /* tmp2[i] < 17*2^120 */
-       felem_scalar128(tmp2, 2);
-       /* tmp2[i] < 17*2^121 */
-       felem_diff128(tmp, tmp2);
-       /* tmp[i] < 2^127 - 2^69 + 17*2^122
-        *        = 2^126 - 2^122 - 2^6 - 2^2 - 1
-        *        < 2^127 */
-       felem_reduce(y_out, tmp);
-
-       copy_conditional(x_out, x2, z1_is_zero);
-       copy_conditional(x_out, x1, z2_is_zero);
-       copy_conditional(y_out, y2, z1_is_zero);
-       copy_conditional(y_out, y1, z2_is_zero);
-       copy_conditional(z_out, z2, z1_is_zero);
-       copy_conditional(z_out, z1, z2_is_zero);
-       felem_assign(x3, x_out);
-       felem_assign(y3, y_out);
-       felem_assign(z3, z_out);
-       }
+                      const felem x1, const felem y1, const felem z1,
+                      const int mixed, const felem x2, const felem y2,
+                      const felem z2)
+{
+    felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, ftmp6, x_out, y_out, z_out;
+    largefelem tmp, tmp2;
+    limb x_equal, y_equal, z1_is_zero, z2_is_zero;
+
+    z1_is_zero = felem_is_zero(z1);
+    z2_is_zero = felem_is_zero(z2);
+
+    /* ftmp = z1z1 = z1**2 */
+    felem_square(tmp, z1);
+    felem_reduce(ftmp, tmp);
+
+    if (!mixed) {
+        /* ftmp2 = z2z2 = z2**2 */
+        felem_square(tmp, z2);
+        felem_reduce(ftmp2, tmp);
+
+        /* u1 = ftmp3 = x1*z2z2 */
+        felem_mul(tmp, x1, ftmp2);
+        felem_reduce(ftmp3, tmp);
+
+        /* ftmp5 = z1 + z2 */
+        felem_assign(ftmp5, z1);
+        felem_sum64(ftmp5, z2);
+        /* ftmp5[i] < 2^61 */
+
+        /* ftmp5 = (z1 + z2)**2 - z1z1 - z2z2 = 2*z1z2 */
+        felem_square(tmp, ftmp5);
+        /* tmp[i] < 17*2^122 */
+        felem_diff_128_64(tmp, ftmp);
+        /* tmp[i] < 17*2^122 + 2^63 */
+        felem_diff_128_64(tmp, ftmp2);
+        /* tmp[i] < 17*2^122 + 2^64 */
+        felem_reduce(ftmp5, tmp);
+
+        /* ftmp2 = z2 * z2z2 */
+        felem_mul(tmp, ftmp2, z2);
+        felem_reduce(ftmp2, tmp);
+
+        /* s1 = ftmp6 = y1 * z2**3 */
+        felem_mul(tmp, y1, ftmp2);
+        felem_reduce(ftmp6, tmp);
+    } else {
+        /*
+         * We'll assume z2 = 1 (special case z2 = 0 is handled later)
+         */
+
+        /* u1 = ftmp3 = x1*z2z2 */
+        felem_assign(ftmp3, x1);
+
+        /* ftmp5 = 2*z1z2 */
+        felem_scalar(ftmp5, z1, 2);
+
+        /* s1 = ftmp6 = y1 * z2**3 */
+        felem_assign(ftmp6, y1);
+    }
+
+    /* u2 = x2*z1z1 */
+    felem_mul(tmp, x2, ftmp);
+    /* tmp[i] < 17*2^120 */
+
+    /* h = ftmp4 = u2 - u1 */
+    felem_diff_128_64(tmp, ftmp3);
+    /* tmp[i] < 17*2^120 + 2^63 */
+    felem_reduce(ftmp4, tmp);
+
+    x_equal = felem_is_zero(ftmp4);
+
+    /* z_out = ftmp5 * h */
+    felem_mul(tmp, ftmp5, ftmp4);
+    felem_reduce(z_out, tmp);
+
+    /* ftmp = z1 * z1z1 */
+    felem_mul(tmp, ftmp, z1);
+    felem_reduce(ftmp, tmp);
+
+    /* s2 = tmp = y2 * z1**3 */
+    felem_mul(tmp, y2, ftmp);
+    /* tmp[i] < 17*2^120 */
+
+    /* r = ftmp5 = (s2 - s1)*2 */
+    felem_diff_128_64(tmp, ftmp6);
+    /* tmp[i] < 17*2^120 + 2^63 */
+    felem_reduce(ftmp5, tmp);
+    y_equal = felem_is_zero(ftmp5);
+    felem_scalar64(ftmp5, 2);
+    /* ftmp5[i] < 2^61 */
+
+    if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
+        point_double(x3, y3, z3, x1, y1, z1);
+        return;
+    }
+
+    /* I = ftmp = (2h)**2 */
+    felem_assign(ftmp, ftmp4);
+    felem_scalar64(ftmp, 2);
+    /* ftmp[i] < 2^61 */
+    felem_square(tmp, ftmp);
+    /* tmp[i] < 17*2^122 */
+    felem_reduce(ftmp, tmp);
+
+    /* J = ftmp2 = h * I */
+    felem_mul(tmp, ftmp4, ftmp);
+    felem_reduce(ftmp2, tmp);
+
+    /* V = ftmp4 = U1 * I */
+    felem_mul(tmp, ftmp3, ftmp);
+    felem_reduce(ftmp4, tmp);
+
+    /* x_out = r**2 - J - 2V */
+    felem_square(tmp, ftmp5);
+    /* tmp[i] < 17*2^122 */
+    felem_diff_128_64(tmp, ftmp2);
+    /* tmp[i] < 17*2^122 + 2^63 */
+    felem_assign(ftmp3, ftmp4);
+    felem_scalar64(ftmp4, 2);
+    /* ftmp4[i] < 2^61 */
+    felem_diff_128_64(tmp, ftmp4);
+    /* tmp[i] < 17*2^122 + 2^64 */
+    felem_reduce(x_out, tmp);
+
+    /* y_out = r(V-x_out) - 2 * s1 * J */
+    felem_diff64(ftmp3, x_out);
+    /*
+     * ftmp3[i] < 2^60 + 2^60 = 2^61
+     */
+    felem_mul(tmp, ftmp5, ftmp3);
+    /* tmp[i] < 17*2^122 */
+    felem_mul(tmp2, ftmp6, ftmp2);
+    /* tmp2[i] < 17*2^120 */
+    felem_scalar128(tmp2, 2);
+    /* tmp2[i] < 17*2^121 */
+    felem_diff128(tmp, tmp2);
+        /*-
+         * tmp[i] < 2^127 - 2^69 + 17*2^122
+         *        = 2^126 - 2^122 - 2^6 - 2^2 - 1
+         *        < 2^127
+         */
+    felem_reduce(y_out, tmp);
+
+    copy_conditional(x_out, x2, z1_is_zero);
+    copy_conditional(x_out, x1, z2_is_zero);
+    copy_conditional(y_out, y2, z1_is_zero);
+    copy_conditional(y_out, y1, z2_is_zero);
+    copy_conditional(z_out, z2, z1_is_zero);
+    copy_conditional(z_out, z1, z2_is_zero);
+    felem_assign(x3, x_out);
+    felem_assign(y3, y_out);
+    felem_assign(z3, z_out);
+}
 
 /*-
  * Base point pre computation
@@ -1265,787 +1349,806 @@ static void point_add(felem x3, felem y3, felem z3,
  * Tables for other points have table[i] = iG for i in 0 .. 16. */
 
 /* gmul is the table of precomputed base points */
-static const felem gmul[16][3] =
-       {{{0, 0, 0, 0, 0, 0, 0, 0, 0},
-         {0, 0, 0, 0, 0, 0, 0, 0, 0},
-         {0, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334,
-          0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8,
-          0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404},
-         {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353,
-          0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45,
-          0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad,
-          0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e,
-          0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5},
-         {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58,
-          0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c,
-          0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873,
-          0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c,
-          0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9},
-         {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52,
-          0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e,
-          0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2,
-          0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561,
-          0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065},
-         {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a,
-          0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e,
-          0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6,
-          0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51,
-          0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe},
-         {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d,
-          0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c,
-          0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27,
-          0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f,
-          0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256},
-         {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa,
-          0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2,
-          0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890,
-          0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74,
-          0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23},
-         {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516,
-          0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1,
-          0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce,
-          0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7,
-          0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5},
-         {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318,
-          0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83,
-          0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae,
-          0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef,
-          0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203},
-         {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447,
-          0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283,
-          0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5,
-          0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c,
-          0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a},
-         {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df,
-          0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645,
-          0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292,
-          0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422,
-          0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b},
-         {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30,
-          0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb,
-          0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767,
-          0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3,
-          0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf},
-         {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2,
-          0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692,
-          0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3,
-          0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade,
-          0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684},
-         {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8,
-          0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a,
-          0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608,
-          0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610,
-          0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d},
-         {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006,
-          0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86,
-          0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42},
-         {1, 0, 0, 0, 0, 0, 0, 0, 0}},
-        {{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c,
-          0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9,
-          0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f},
-         {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7,
-          0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c,
-          0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055},
-        {1, 0, 0, 0, 0, 0, 0, 0, 0}}};
-
-/* select_point selects the |idx|th point from a precomputation table and
- * copies it to out. */
-static void select_point(const limb idx, unsigned int size, const felem pre_comp[/* size */][3],
-                        felem out[3])
-       {
-       unsigned i, j;
-       limb *outlimbs = &out[0][0];
-       memset(outlimbs, 0, 3 * sizeof(felem));
-
-       for (i = 0; i < size; i++)
-               {
-               const limb *inlimbs = &pre_comp[i][0][0];
-               limb mask = i ^ idx;
-               mask |= mask >> 4;
-               mask |= mask >> 2;
-               mask |= mask >> 1;
-               mask &= 1;
-               mask--;
-               for (j = 0; j < NLIMBS * 3; j++)
-                       outlimbs[j] |= inlimbs[j] & mask;
-               }
-       }
+static const felem gmul[16][3] = {
+{{0, 0, 0, 0, 0, 0, 0, 0, 0},
+ {0, 0, 0, 0, 0, 0, 0, 0, 0},
+ {0, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x017e7e31c2e5bd66, 0x022cf0615a90a6fe, 0x00127a2ffa8de334,
+  0x01dfbf9d64a3f877, 0x006b4d3dbaa14b5e, 0x014fed487e0a2bd8,
+  0x015b4429c6481390, 0x03a73678fb2d988e, 0x00c6858e06b70404},
+ {0x00be94769fd16650, 0x031c21a89cb09022, 0x039013fad0761353,
+  0x02657bd099031542, 0x03273e662c97ee72, 0x01e6d11a05ebef45,
+  0x03d1bd998f544495, 0x03001172297ed0b1, 0x011839296a789a3b},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x0373faacbc875bae, 0x00f325023721c671, 0x00f666fd3dbde5ad,
+  0x01a6932363f88ea7, 0x01fc6d9e13f9c47b, 0x03bcbffc2bbf734e,
+  0x013ee3c3647f3a92, 0x029409fefe75d07d, 0x00ef9199963d85e5},
+ {0x011173743ad5b178, 0x02499c7c21bf7d46, 0x035beaeabb8b1a58,
+  0x00f989c4752ea0a3, 0x0101e1de48a9c1a3, 0x01a20076be28ba6c,
+  0x02f8052e5eb2de95, 0x01bfe8f82dea117c, 0x0160074d3c36ddb7},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x012f3fc373393b3b, 0x03d3d6172f1419fa, 0x02adc943c0b86873,
+  0x00d475584177952b, 0x012a4d1673750ee2, 0x00512517a0f13b0c,
+  0x02b184671a7b1734, 0x0315b84236f1a50a, 0x00a4afc472edbdb9},
+ {0x00152a7077f385c4, 0x03044007d8d1c2ee, 0x0065829d61d52b52,
+  0x00494ff6b6631d0d, 0x00a11d94d5f06bcf, 0x02d2f89474d9282e,
+  0x0241c5727c06eeb9, 0x0386928710fbdb9d, 0x01f883f727b0dfbe},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x019b0c3c9185544d, 0x006243a37c9d97db, 0x02ee3cbe030a2ad2,
+  0x00cfdd946bb51e0d, 0x0271c00932606b91, 0x03f817d1ec68c561,
+  0x03f37009806a369c, 0x03c1f30baf184fd5, 0x01091022d6d2f065},
+ {0x0292c583514c45ed, 0x0316fca51f9a286c, 0x00300af507c1489a,
+  0x0295f69008298cf1, 0x02c0ed8274943d7b, 0x016509b9b47a431e,
+  0x02bc9de9634868ce, 0x005b34929bffcb09, 0x000c1a0121681524},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x0286abc0292fb9f2, 0x02665eee9805b3f7, 0x01ed7455f17f26d6,
+  0x0346355b83175d13, 0x006284944cd0a097, 0x0191895bcdec5e51,
+  0x02e288370afda7d9, 0x03b22312bfefa67a, 0x01d104d3fc0613fe},
+ {0x0092421a12f7e47f, 0x0077a83fa373c501, 0x03bd25c5f696bd0d,
+  0x035c41e4d5459761, 0x01ca0d1742b24f53, 0x00aaab27863a509c,
+  0x018b6de47df73917, 0x025c0b771705cd01, 0x01fd51d566d760a7},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x01dd92ff6b0d1dbd, 0x039c5e2e8f8afa69, 0x0261ed13242c3b27,
+  0x0382c6e67026e6a0, 0x01d60b10be2089f9, 0x03c15f3dce86723f,
+  0x03c764a32d2a062d, 0x017307eac0fad056, 0x018207c0b96c5256},
+ {0x0196a16d60e13154, 0x03e6ce74c0267030, 0x00ddbf2b4e52a5aa,
+  0x012738241bbf31c8, 0x00ebe8dc04685a28, 0x024c2ad6d380d4a2,
+  0x035ee062a6e62d0e, 0x0029ed74af7d3a0f, 0x00eef32aec142ebd},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x00c31ec398993b39, 0x03a9f45bcda68253, 0x00ac733c24c70890,
+  0x00872b111401ff01, 0x01d178c23195eafb, 0x03bca2c816b87f74,
+  0x0261a9af46fbad7a, 0x0324b2a8dd3d28f9, 0x00918121d8f24e23},
+ {0x032bc8c1ca983cd7, 0x00d869dfb08fc8c6, 0x01693cb61fce1516,
+  0x012a5ea68f4e88a8, 0x010869cab88d7ae3, 0x009081ad277ceee1,
+  0x033a77166d064cdc, 0x03955235a1fb3a95, 0x01251a4a9b25b65e},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x00148a3a1b27f40b, 0x0123186df1b31fdc, 0x00026e7beaad34ce,
+  0x01db446ac1d3dbba, 0x0299c1a33437eaec, 0x024540610183cbb7,
+  0x0173bb0e9ce92e46, 0x02b937e43921214b, 0x01ab0436a9bf01b5},
+ {0x0383381640d46948, 0x008dacbf0e7f330f, 0x03602122bcc3f318,
+  0x01ee596b200620d6, 0x03bd0585fda430b3, 0x014aed77fd123a83,
+  0x005ace749e52f742, 0x0390fe041da2b842, 0x0189a8ceb3299242},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x012a19d6b3282473, 0x00c0915918b423ce, 0x023a954eb94405ae,
+  0x00529f692be26158, 0x0289fa1b6fa4b2aa, 0x0198ae4ceea346ef,
+  0x0047d8cdfbdedd49, 0x00cc8c8953f0f6b8, 0x001424abbff49203},
+ {0x0256732a1115a03a, 0x0351bc38665c6733, 0x03f7b950fb4a6447,
+  0x000afffa94c22155, 0x025763d0a4dab540, 0x000511e92d4fc283,
+  0x030a7e9eda0ee96c, 0x004c3cd93a28bf0a, 0x017edb3a8719217f},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x011de5675a88e673, 0x031d7d0f5e567fbe, 0x0016b2062c970ae5,
+  0x03f4a2be49d90aa7, 0x03cef0bd13822866, 0x03f0923dcf774a6c,
+  0x0284bebc4f322f72, 0x016ab2645302bb2c, 0x01793f95dace0e2a},
+ {0x010646e13527a28f, 0x01ca1babd59dc5e7, 0x01afedfd9a5595df,
+  0x01f15785212ea6b1, 0x0324e5d64f6ae3f4, 0x02d680f526d00645,
+  0x0127920fadf627a7, 0x03b383f75df4f684, 0x0089e0057e783b0a},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x00f334b9eb3c26c6, 0x0298fdaa98568dce, 0x01c2d24843a82292,
+  0x020bcb24fa1b0711, 0x02cbdb3d2b1875e6, 0x0014907598f89422,
+  0x03abe3aa43b26664, 0x02cbf47f720bc168, 0x0133b5e73014b79b},
+ {0x034aab5dab05779d, 0x00cdc5d71fee9abb, 0x0399f16bd4bd9d30,
+  0x03582fa592d82647, 0x02be1cdfb775b0e9, 0x0034f7cea32e94cb,
+  0x0335a7f08f56f286, 0x03b707e9565d1c8b, 0x0015c946ea5b614f},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x024676f6cff72255, 0x00d14625cac96378, 0x00532b6008bc3767,
+  0x01fc16721b985322, 0x023355ea1b091668, 0x029de7afdc0317c3,
+  0x02fc8a7ca2da037c, 0x02de1217d74a6f30, 0x013f7173175b73bf},
+ {0x0344913f441490b5, 0x0200f9e272b61eca, 0x0258a246b1dd55d2,
+  0x03753db9ea496f36, 0x025e02937a09c5ef, 0x030cbd3d14012692,
+  0x01793a67e70dc72a, 0x03ec1d37048a662e, 0x006550f700c32a8d},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x00d3f48a347eba27, 0x008e636649b61bd8, 0x00d3b93716778fb3,
+  0x004d1915757bd209, 0x019d5311a3da44e0, 0x016d1afcbbe6aade,
+  0x0241bf5f73265616, 0x0384672e5d50d39b, 0x005009fee522b684},
+ {0x029b4fab064435fe, 0x018868ee095bbb07, 0x01ea3d6936cc92b8,
+  0x000608b00f78a2f3, 0x02db911073d1c20f, 0x018205938470100a,
+  0x01f1e4964cbe6ff2, 0x021a19a29eed4663, 0x01414485f42afa81},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x01612b3a17f63e34, 0x03813992885428e6, 0x022b3c215b5a9608,
+  0x029b4057e19f2fcb, 0x0384059a587af7e6, 0x02d6400ace6fe610,
+  0x029354d896e8e331, 0x00c047ee6dfba65e, 0x0037720542e9d49d},
+ {0x02ce9eed7c5e9278, 0x0374ed703e79643b, 0x01316c54c4072006,
+  0x005aaa09054b2ee8, 0x002824000c840d57, 0x03d4eba24771ed86,
+  0x0189c50aabc3bdae, 0x0338c01541e15510, 0x00466d56e38eed42},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}},
+{{0x007efd8330ad8bd6, 0x02465ed48047710b, 0x0034c6606b215e0c,
+  0x016ae30c53cbf839, 0x01fa17bd37161216, 0x018ead4e61ce8ab9,
+  0x005482ed5f5dee46, 0x037543755bba1d7f, 0x005e5ac7e70a9d0f},
+ {0x0117e1bb2fdcb2a2, 0x03deea36249f40c4, 0x028d09b4a6246cb7,
+  0x03524b8855bcf756, 0x023d7d109d5ceb58, 0x0178e43e3223ef9c,
+  0x0154536a0c6e966a, 0x037964d1286ee9fe, 0x0199bcd90e125055},
+ {1, 0, 0, 0, 0, 0, 0, 0, 0}}
+};
+
+/*
+ * select_point selects the |idx|th point from a precomputation table and
+ * copies it to out.
+ */
+ /* pre_comp below is of the size provided in |size| */
+static void select_point(const limb idx, unsigned int size,
+                         const felem pre_comp[][3], felem out[3])
+{
+    unsigned i, j;
+    limb *outlimbs = &out[0][0];
+
+    memset(out, 0, sizeof(out));
+
+    for (i = 0; i < size; i++) {
+        const limb *inlimbs = &pre_comp[i][0][0];
+        limb mask = i ^ idx;
+        mask |= mask >> 4;
+        mask |= mask >> 2;
+        mask |= mask >> 1;
+        mask &= 1;
+        mask--;
+        for (j = 0; j < NLIMBS * 3; j++)
+            outlimbs[j] |= inlimbs[j] & mask;
+    }
+}
 
 /* get_bit returns the |i|th bit in |in| */
 static char get_bit(const felem_bytearray in, int i)
-       {
-       if (i < 0)
-               return 0;
-       return (in[i >> 3] >> (i & 7)) & 1;
-       }
-
-/* Interleaved point multiplication using precomputed point multiples:
- * The small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[],
- * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple
- * of the generator, using certain (large) precomputed multiples in g_pre_comp.
- * Output point (X, Y, Z) is stored in x_out, y_out, z_out */
-static void batch_mul(felem x_out, felem y_out, felem z_out,
-       const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar,
-       const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[16][3])
-       {
-       int i, skip;
-       unsigned num, gen_mul = (g_scalar != NULL);
-       felem nq[3], tmp[4];
-       limb bits;
-       u8 sign, digit;
-
-       /* set nq to the point at infinity */
-       memset(nq, 0, 3 * sizeof(felem));
-
-       /* Loop over all scalars msb-to-lsb, interleaving additions
-        * of multiples of the generator (last quarter of rounds)
-        * and additions of other points multiples (every 5th round).
-        */
-       skip = 1; /* save two point operations in the first round */
-       for (i = (num_points ? 520 : 130); i >= 0; --i)
-               {
-               /* double */
-               if (!skip)
-                       point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
-
-               /* add multiples of the generator */
-               if (gen_mul && (i <= 130))
-                       {
-                       bits = get_bit(g_scalar, i + 390) << 3;
-                       if (i < 130)
-                               {
-                               bits |= get_bit(g_scalar, i + 260) << 2;
-                               bits |= get_bit(g_scalar, i + 130) << 1;
-                               bits |= get_bit(g_scalar, i);
-                               }
-                       /* select the point to add, in constant time */
-                       select_point(bits, 16, g_pre_comp, tmp);
-                       if (!skip)
-                               {
-                               point_add(nq[0], nq[1], nq[2],
-                                       nq[0], nq[1], nq[2],
-                                       1 /* mixed */, tmp[0], tmp[1], tmp[2]);
-                               }
-                       else
-                               {
-                               memcpy(nq, tmp, 3 * sizeof(felem));
-                               skip = 0;
-                               }
-                       }
-
-               /* do other additions every 5 doublings */
-               if (num_points && (i % 5 == 0))
-                       {
-                       /* loop over all scalars */
-                       for (num = 0; num < num_points; ++num)
-                               {
-                               bits = get_bit(scalars[num], i + 4) << 5;
-                               bits |= get_bit(scalars[num], i + 3) << 4;
-                               bits |= get_bit(scalars[num], i + 2) << 3;
-                               bits |= get_bit(scalars[num], i + 1) << 2;
-                               bits |= get_bit(scalars[num], i) << 1;
-                               bits |= get_bit(scalars[num], i - 1);
-                               ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
-
-                               /* select the point to add or subtract, in constant time */
-                               select_point(digit, 17, pre_comp[num], tmp);
-                               felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative point */
-                               copy_conditional(tmp[1], tmp[3], (-(limb) sign));
-
-                               if (!skip)
-                                       {
-                                       point_add(nq[0], nq[1], nq[2],
-                                               nq[0], nq[1], nq[2],
-                                               mixed, tmp[0], tmp[1], tmp[2]);
-                                       }
-                               else
-                                       {
-                                       memcpy(nq, tmp, 3 * sizeof(felem));
-                                       skip = 0;
-                                       }
-                               }
-                       }
-               }
-       felem_assign(x_out, nq[0]);
-       felem_assign(y_out, nq[1]);
-       felem_assign(z_out, nq[2]);
-       }
+{
+    if (i < 0)
+        return 0;
+    return (in[i >> 3] >> (i & 7)) & 1;
+}
 
+/*
+ * Interleaved point multiplication using precomputed point multiples: The
+ * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars
+ * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the
+ * generator, using certain (large) precomputed multiples in g_pre_comp.
+ * Output point (X, Y, Z) is stored in x_out, y_out, z_out
+ */
+static void batch_mul(felem x_out, felem y_out, felem z_out,
+                      const felem_bytearray scalars[],
+                      const unsigned num_points, const u8 *g_scalar,
+                      const int mixed, const felem pre_comp[][17][3],
+                      const felem g_pre_comp[16][3])
+{
+    int i, skip;
+    unsigned num, gen_mul = (g_scalar != NULL);
+    felem nq[3], tmp[4];
+    limb bits;
+    u8 sign, digit;
+
+    /* set nq to the point at infinity */
+    memset(nq, 0, sizeof(nq));
+
+    /*
+     * Loop over all scalars msb-to-lsb, interleaving additions of multiples
+     * of the generator (last quarter of rounds) and additions of other
+     * points multiples (every 5th round).
+     */
+    skip = 1;                   /* save two point operations in the first
+                                 * round */
+    for (i = (num_points ? 520 : 130); i >= 0; --i) {
+        /* double */
+        if (!skip)
+            point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
+
+        /* add multiples of the generator */
+        if (gen_mul && (i <= 130)) {
+            bits = get_bit(g_scalar, i + 390) << 3;
+            if (i < 130) {
+                bits |= get_bit(g_scalar, i + 260) << 2;
+                bits |= get_bit(g_scalar, i + 130) << 1;
+                bits |= get_bit(g_scalar, i);
+            }
+            /* select the point to add, in constant time */
+            select_point(bits, 16, g_pre_comp, tmp);
+            if (!skip) {
+                /* The 1 argument below is for "mixed" */
+                point_add(nq[0], nq[1], nq[2],
+                          nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]);
+            } else {
+                memcpy(nq, tmp, 3 * sizeof(felem));
+                skip = 0;
+            }
+        }
+
+        /* do other additions every 5 doublings */
+        if (num_points && (i % 5 == 0)) {
+            /* loop over all scalars */
+            for (num = 0; num < num_points; ++num) {
+                bits = get_bit(scalars[num], i + 4) << 5;
+                bits |= get_bit(scalars[num], i + 3) << 4;
+                bits |= get_bit(scalars[num], i + 2) << 3;
+                bits |= get_bit(scalars[num], i + 1) << 2;
+                bits |= get_bit(scalars[num], i) << 1;
+                bits |= get_bit(scalars[num], i - 1);
+                ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
+
+                /*
+                 * select the point to add or subtract, in constant time
+                 */
+                select_point(digit, 17, pre_comp[num], tmp);
+                felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative
+                                            * point */
+                copy_conditional(tmp[1], tmp[3], (-(limb) sign));
+
+                if (!skip) {
+                    point_add(nq[0], nq[1], nq[2],
+                              nq[0], nq[1], nq[2],
+                              mixed, tmp[0], tmp[1], tmp[2]);
+                } else {
+                    memcpy(nq, tmp, 3 * sizeof(felem));
+                    skip = 0;
+                }
+            }
+        }
+    }
+    felem_assign(x_out, nq[0]);
+    felem_assign(y_out, nq[1]);
+    felem_assign(z_out, nq[2]);
+}
 
 /* Precomputation for the group generator. */
 typedef struct {
-       felem g_pre_comp[16][3];
-       int references;
+    felem g_pre_comp[16][3];
+    int references;
 } NISTP521_PRE_COMP;
 
 const EC_METHOD *EC_GFp_nistp521_method(void)
-       {
-       static const EC_METHOD ret = {
-               EC_FLAGS_DEFAULT_OCT,
-               NID_X9_62_prime_field,
-               ec_GFp_nistp521_group_init,
-               ec_GFp_simple_group_finish,
-               ec_GFp_simple_group_clear_finish,
-               ec_GFp_nist_group_copy,
-               ec_GFp_nistp521_group_set_curve,
-               ec_GFp_simple_group_get_curve,
-               ec_GFp_simple_group_get_degree,
-               ec_GFp_simple_group_check_discriminant,
-               ec_GFp_simple_point_init,
-               ec_GFp_simple_point_finish,
-               ec_GFp_simple_point_clear_finish,
-               ec_GFp_simple_point_copy,
-               ec_GFp_simple_point_set_to_infinity,
-               ec_GFp_simple_set_Jprojective_coordinates_GFp,
-               ec_GFp_simple_get_Jprojective_coordinates_GFp,
-               ec_GFp_simple_point_set_affine_coordinates,
-               ec_GFp_nistp521_point_get_affine_coordinates,
-               0 /* point_set_compressed_coordinates */,
-               0 /* point2oct */,
-               0 /* oct2point */,
-               ec_GFp_simple_add,
-               ec_GFp_simple_dbl,
-               ec_GFp_simple_invert,
-               ec_GFp_simple_is_at_infinity,
-               ec_GFp_simple_is_on_curve,
-               ec_GFp_simple_cmp,
-               ec_GFp_simple_make_affine,
-               ec_GFp_simple_points_make_affine,
-               ec_GFp_nistp521_points_mul,
-               ec_GFp_nistp521_precompute_mult,
-               ec_GFp_nistp521_have_precompute_mult,
-               ec_GFp_nist_field_mul,
-               ec_GFp_nist_field_sqr,
-               0 /* field_div */,
-               0 /* field_encode */,
-               0 /* field_decode */,
-               0 /* field_set_to_one */ };
-
-       return &ret;
-       }
-
+{
+    static const EC_METHOD ret = {
+        EC_FLAGS_DEFAULT_OCT,
+        NID_X9_62_prime_field,
+        ec_GFp_nistp521_group_init,
+        ec_GFp_simple_group_finish,
+        ec_GFp_simple_group_clear_finish,
+        ec_GFp_nist_group_copy,
+        ec_GFp_nistp521_group_set_curve,
+        ec_GFp_simple_group_get_curve,
+        ec_GFp_simple_group_get_degree,
+        ec_GFp_simple_group_check_discriminant,
+        ec_GFp_simple_point_init,
+        ec_GFp_simple_point_finish,
+        ec_GFp_simple_point_clear_finish,
+        ec_GFp_simple_point_copy,
+        ec_GFp_simple_point_set_to_infinity,
+        ec_GFp_simple_set_Jprojective_coordinates_GFp,
+        ec_GFp_simple_get_Jprojective_coordinates_GFp,
+        ec_GFp_simple_point_set_affine_coordinates,
+        ec_GFp_nistp521_point_get_affine_coordinates,
+        0 /* point_set_compressed_coordinates */ ,
+        0 /* point2oct */ ,
+        0 /* oct2point */ ,
+        ec_GFp_simple_add,
+        ec_GFp_simple_dbl,
+        ec_GFp_simple_invert,
+        ec_GFp_simple_is_at_infinity,
+        ec_GFp_simple_is_on_curve,
+        ec_GFp_simple_cmp,
+        ec_GFp_simple_make_affine,
+        ec_GFp_simple_points_make_affine,
+        ec_GFp_nistp521_points_mul,
+        ec_GFp_nistp521_precompute_mult,
+        ec_GFp_nistp521_have_precompute_mult,
+        ec_GFp_nist_field_mul,
+        ec_GFp_nist_field_sqr,
+        0 /* field_div */ ,
+        0 /* field_encode */ ,
+        0 /* field_decode */ ,
+        0                       /* field_set_to_one */
+    };
+
+    return &ret;
+}
 
 /******************************************************************************/
-/*                    FUNCTIONS TO MANAGE PRECOMPUTATION
+/*
+ * FUNCTIONS TO MANAGE PRECOMPUTATION
  */
 
 static NISTP521_PRE_COMP *nistp521_pre_comp_new()
-       {
-       NISTP521_PRE_COMP *ret = NULL;
-       ret = (NISTP521_PRE_COMP *)OPENSSL_malloc(sizeof(NISTP521_PRE_COMP));
-       if (!ret)
-               {
-               ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
-               return ret;
-               }
-       memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
-       ret->references = 1;
-       return ret;
-       }
+{
+    NISTP521_PRE_COMP *ret = OPENSSL_malloc(sizeof(*ret));
+
+    if (!ret) {
+        ECerr(EC_F_NISTP521_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
+        return ret;
+    }
+    memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp));
+    ret->references = 1;
+    return ret;
+}
 
 static void *nistp521_pre_comp_dup(void *src_)
-       {
-       NISTP521_PRE_COMP *src = src_;
+{
+    NISTP521_PRE_COMP *src = src_;
 
-       /* no need to actually copy, these objects never change! */
-       CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
+    /* no need to actually copy, these objects never change! */
+    CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
 
-       return src_;
-       }
+    return src_;
+}
 
 static void nistp521_pre_comp_free(void *pre_)
-       {
-       int i;
-       NISTP521_PRE_COMP *pre = pre_;
+{
+    int i;
+    NISTP521_PRE_COMP *pre = pre_;
 
-       if (!pre)
-               return;
+    if (!pre)
+        return;
 
-       i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
-       if (i > 0)
-               return;
+    i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
+    if (i > 0)
+        return;
 
-       OPENSSL_free(pre);
-       }
+    OPENSSL_free(pre);
+}
 
 static void nistp521_pre_comp_clear_free(void *pre_)
-       {
-       int i;
-       NISTP521_PRE_COMP *pre = pre_;
+{
+    int i;
+    NISTP521_PRE_COMP *pre = pre_;
 
-       if (!pre)
-               return;
+    if (!pre)
+        return;
 
-       i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
-       if (i > 0)
-               return;
+    i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
+    if (i > 0)
+        return;
 
-       OPENSSL_cleanse(pre, sizeof(*pre));
-       OPENSSL_free(pre);
-       }
+    OPENSSL_clear_free(pre, sizeof(*pre));
+}
 
 /******************************************************************************/
-/*                        OPENSSL EC_METHOD FUNCTIONS
+/*
+ * OPENSSL EC_METHOD FUNCTIONS
  */
 
 int ec_GFp_nistp521_group_init(EC_GROUP *group)
-       {
-       int ret;
-       ret = ec_GFp_simple_group_init(group);
-       group->a_is_minus3 = 1;
-       return ret;
-       }
+{
+    int ret;
+    ret = ec_GFp_simple_group_init(group);
+    group->a_is_minus3 = 1;
+    return ret;
+}
 
 int ec_GFp_nistp521_group_set_curve(EC_GROUP *group, const BIGNUM *p,
-       const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
-       {
-       int ret = 0;
-       BN_CTX *new_ctx = NULL;
-       BIGNUM *curve_p, *curve_a, *curve_b;
-
-       if (ctx == NULL)
-               if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
-       BN_CTX_start(ctx);
-       if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
-               ((curve_a = BN_CTX_get(ctx)) == NULL) ||
-               ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err;
-       BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p);
-       BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a);
-       BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b);
-       if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) ||
-               (BN_cmp(curve_b, b)))
-               {
-               ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE,
-                       EC_R_WRONG_CURVE_PARAMETERS);
-               goto err;
-               }
-       group->field_mod_func = BN_nist_mod_521;
-       ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
-err:
-       BN_CTX_end(ctx);
-       if (new_ctx != NULL)
-               BN_CTX_free(new_ctx);
-       return ret;
-       }
-
-/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns
- * (X', Y') = (X/Z^2, Y/Z^3) */
+                                    const BIGNUM *a, const BIGNUM *b,
+                                    BN_CTX *ctx)
+{
+    int ret = 0;
+    BN_CTX *new_ctx = NULL;
+    BIGNUM *curve_p, *curve_a, *curve_b;
+
+    if (ctx == NULL)
+        if ((ctx = new_ctx = BN_CTX_new()) == NULL)
+            return 0;
+    BN_CTX_start(ctx);
+    if (((curve_p = BN_CTX_get(ctx)) == NULL) ||
+        ((curve_a = BN_CTX_get(ctx)) == NULL) ||
+        ((curve_b = BN_CTX_get(ctx)) == NULL))
+        goto err;
+    BN_bin2bn(nistp521_curve_params[0], sizeof(felem_bytearray), curve_p);
+    BN_bin2bn(nistp521_curve_params[1], sizeof(felem_bytearray), curve_a);
+    BN_bin2bn(nistp521_curve_params[2], sizeof(felem_bytearray), curve_b);
+    if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) {
+        ECerr(EC_F_EC_GFP_NISTP521_GROUP_SET_CURVE,
+              EC_R_WRONG_CURVE_PARAMETERS);
+        goto err;
+    }
+    group->field_mod_func = BN_nist_mod_521;
+    ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx);
+ err:
+    BN_CTX_end(ctx);
+    BN_CTX_free(new_ctx);
+    return ret;
+}
+
+/*
+ * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') =
+ * (X/Z^2, Y/Z^3)
+ */
 int ec_GFp_nistp521_point_get_affine_coordinates(const EC_GROUP *group,
-       const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
-       {
-       felem z1, z2, x_in, y_in, x_out, y_out;
-       largefelem tmp;
-
-       if (EC_POINT_is_at_infinity(group, point))
-               {
-               ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES,
-                       EC_R_POINT_AT_INFINITY);
-               return 0;
-               }
-       if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) ||
-               (!BN_to_felem(z1, &point->Z))) return 0;
-       felem_inv(z2, z1);
-       felem_square(tmp, z2); felem_reduce(z1, tmp);
-       felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp);
-       felem_contract(x_out, x_in);
-       if (x != NULL)
-               {
-               if (!felem_to_BN(x, x_out))
-                       {
-                       ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
-                       return 0;
-                       }
-               }
-       felem_mul(tmp, z1, z2); felem_reduce(z1, tmp);
-       felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp);
-       felem_contract(y_out, y_in);
-       if (y != NULL)
-               {
-               if (!felem_to_BN(y, y_out))
-                       {
-                       ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES, ERR_R_BN_LIB);
-                       return 0;
-                       }
-               }
-       return 1;
-       }
-
-static void make_points_affine(size_t num, felem points[/* num */][3], felem tmp_felems[/* num+1 */])
-       {
-       /* Runs in constant time, unless an input is the point at infinity
-        * (which normally shouldn't happen). */
-       ec_GFp_nistp_points_make_affine_internal(
-               num,
-               points,
-               sizeof(felem),
-               tmp_felems,
-               (void (*)(void *)) felem_one,
-               (int (*)(const void *)) felem_is_zero_int,
-               (void (*)(void *, const void *)) felem_assign,
-               (void (*)(void *, const void *)) felem_square_reduce,
-               (void (*)(void *, const void *, const void *)) felem_mul_reduce,
-               (void (*)(void *, const void *)) felem_inv,
-               (void (*)(void *, const void *)) felem_contract);
-       }
-
-/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values
- * Result is stored in r (r can equal one of the inputs). */
+                                                 const EC_POINT *point,
+                                                 BIGNUM *x, BIGNUM *y,
+                                                 BN_CTX *ctx)
+{
+    felem z1, z2, x_in, y_in, x_out, y_out;
+    largefelem tmp;
+
+    if (EC_POINT_is_at_infinity(group, point)) {
+        ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES,
+              EC_R_POINT_AT_INFINITY);
+        return 0;
+    }
+    if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) ||
+        (!BN_to_felem(z1, point->Z)))
+        return 0;
+    felem_inv(z2, z1);
+    felem_square(tmp, z2);
+    felem_reduce(z1, tmp);
+    felem_mul(tmp, x_in, z1);
+    felem_reduce(x_in, tmp);
+    felem_contract(x_out, x_in);
+    if (x != NULL) {
+        if (!felem_to_BN(x, x_out)) {
+            ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES,
+                  ERR_R_BN_LIB);
+            return 0;
+        }
+    }
+    felem_mul(tmp, z1, z2);
+    felem_reduce(z1, tmp);
+    felem_mul(tmp, y_in, z1);
+    felem_reduce(y_in, tmp);
+    felem_contract(y_out, y_in);
+    if (y != NULL) {
+        if (!felem_to_BN(y, y_out)) {
+            ECerr(EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES,
+                  ERR_R_BN_LIB);
+            return 0;
+        }
+    }
+    return 1;
+}
+
+/* points below is of size |num|, and tmp_felems is of size |num+1/ */
+static void make_points_affine(size_t num, felem points[][3],
+                               felem tmp_felems[])
+{
+    /*
+     * Runs in constant time, unless an input is the point at infinity (which
+     * normally shouldn't happen).
+     */
+    ec_GFp_nistp_points_make_affine_internal(num,
+                                             points,
+                                             sizeof(felem),
+                                             tmp_felems,
+                                             (void (*)(void *))felem_one,
+                                             (int (*)(const void *))
+                                             felem_is_zero_int,
+                                             (void (*)(void *, const void *))
+                                             felem_assign,
+                                             (void (*)(void *, const void *))
+                                             felem_square_reduce, (void (*)
+                                                                   (void *,
+                                                                    const void
+                                                                    *,
+                                                                    const void
+                                                                    *))
+                                             felem_mul_reduce,
+                                             (void (*)(void *, const void *))
+                                             felem_inv,
+                                             (void (*)(void *, const void *))
+                                             felem_contract);
+}
+
+/*
+ * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL
+ * values Result is stored in r (r can equal one of the inputs).
+ */
 int ec_GFp_nistp521_points_mul(const EC_GROUP *group, EC_POINT *r,
-       const BIGNUM *scalar, size_t num, const EC_POINT *points[],
-       const BIGNUM *scalars[], BN_CTX *ctx)
-       {
-       int ret = 0;
-       int j;
-       int mixed = 0;
-       BN_CTX *new_ctx = NULL;
-       BIGNUM *x, *y, *z, *tmp_scalar;
-       felem_bytearray g_secret;
-       felem_bytearray *secrets = NULL;
-       felem (*pre_comp)[17][3] = NULL;
-       felem *tmp_felems = NULL;
-       felem_bytearray tmp;
-       unsigned i, num_bytes;
-       int have_pre_comp = 0;
-       size_t num_points = num;
-       felem x_in, y_in, z_in, x_out, y_out, z_out;
-       NISTP521_PRE_COMP *pre = NULL;
-       felem (*g_pre_comp)[3] = NULL;
-       EC_POINT *generator = NULL;
-       const EC_POINT *p = NULL;
-       const BIGNUM *p_scalar = NULL;
-
-       if (ctx == NULL)
-               if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
-       BN_CTX_start(ctx);
-       if (((x = BN_CTX_get(ctx)) == NULL) ||
-               ((y = BN_CTX_get(ctx)) == NULL) ||
-               ((z = BN_CTX_get(ctx)) == NULL) ||
-               ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
-               goto err;
-
-       if (scalar != NULL)
-               {
-               pre = EC_EX_DATA_get_data(group->extra_data,
-                       nistp521_pre_comp_dup, nistp521_pre_comp_free,
-                       nistp521_pre_comp_clear_free);
-               if (pre)
-                       /* we have precomputation, try to use it */
-                       g_pre_comp = &pre->g_pre_comp[0];
-               else
-                       /* try to use the standard precomputation */
-                       g_pre_comp = (felem (*)[3]) gmul;
-               generator = EC_POINT_new(group);
-               if (generator == NULL)
-                       goto err;
-               /* get the generator from precomputation */
-               if (!felem_to_BN(x, g_pre_comp[1][0]) ||
-                       !felem_to_BN(y, g_pre_comp[1][1]) ||
-                       !felem_to_BN(z, g_pre_comp[1][2]))
-                       {
-                       ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
-                       goto err;
-                       }
-               if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
-                               generator, x, y, z, ctx))
-                       goto err;
-               if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
-                       /* precomputation matches generator */
-                       have_pre_comp = 1;
-               else
-                       /* we don't have valid precomputation:
-                        * treat the generator as a random point */
-                       num_points++;
-               }
-
-       if (num_points > 0)
-               {
-               if (num_points >= 2)
-                       {
-                       /* unless we precompute multiples for just one point,
-                        * converting those into affine form is time well spent  */
-                       mixed = 1;
-                       }
-               secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray));
-               pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem));
-               if (mixed)
-                       tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem));
-               if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL)))
-                       {
-                       ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_MALLOC_FAILURE);
-                       goto err;
-                       }
-
-               /* we treat NULL scalars as 0, and NULL points as points at infinity,
-                * i.e., they contribute nothing to the linear combination */
-               memset(secrets, 0, num_points * sizeof(felem_bytearray));
-               memset(pre_comp, 0, num_points * 17 * 3 * sizeof(felem));
-               for (i = 0; i < num_points; ++i)
-                       {
-                       if (i == num)
-                               /* we didn't have a valid precomputation, so we pick
-                                * the generator */
-                               {
-                               p = EC_GROUP_get0_generator(group);
-                               p_scalar = scalar;
-                               }
-                       else
-                               /* the i^th point */
-                               {
-                               p = points[i];
-                               p_scalar = scalars[i];
-                               }
-                       if ((p_scalar != NULL) && (p != NULL))
-                               {
-                               /* reduce scalar to 0 <= scalar < 2^521 */
-                               if ((BN_num_bits(p_scalar) > 521) || (BN_is_negative(p_scalar)))
-                                       {
-                                       /* this is an unusual input, and we don't guarantee
-                                        * constant-timeness */
-                                       if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx))
-                                               {
-                                               ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
-                                               goto err;
-                                               }
-                                       num_bytes = BN_bn2bin(tmp_scalar, tmp);
-                                       }
-                               else
-                                       num_bytes = BN_bn2bin(p_scalar, tmp);
-                               flip_endian(secrets[i], tmp, num_bytes);
-                               /* precompute multiples */
-                               if ((!BN_to_felem(x_out, &p->X)) ||
-                                       (!BN_to_felem(y_out, &p->Y)) ||
-                                       (!BN_to_felem(z_out, &p->Z))) goto err;
-                               memcpy(pre_comp[i][1][0], x_out, sizeof(felem));
-                               memcpy(pre_comp[i][1][1], y_out, sizeof(felem));
-                               memcpy(pre_comp[i][1][2], z_out, sizeof(felem));
-                               for (j = 2; j <= 16; ++j)
-                                       {
-                                       if (j & 1)
-                                               {
-                                               point_add(
-                                                       pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
-                                                       pre_comp[i][1][0], pre_comp[i][1][1], pre_comp[i][1][2],
-                                                       0, pre_comp[i][j-1][0], pre_comp[i][j-1][1], pre_comp[i][j-1][2]);
-                                               }
-                                       else
-                                               {
-                                               point_double(
-                                                       pre_comp[i][j][0], pre_comp[i][j][1], pre_comp[i][j][2],
-                                                       pre_comp[i][j/2][0], pre_comp[i][j/2][1], pre_comp[i][j/2][2]);
-                                               }
-                                       }
-                               }
-                       }
-               if (mixed)
-                       make_points_affine(num_points * 17, pre_comp[0], tmp_felems);
-               }
-
-       /* the scalar for the generator */
-       if ((scalar != NULL) && (have_pre_comp))
-               {
-               memset(g_secret, 0, sizeof(g_secret));
-               /* reduce scalar to 0 <= scalar < 2^521 */
-               if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar)))
-                       {
-                       /* this is an unusual input, and we don't guarantee
-                        * constant-timeness */
-                       if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx))
-                               {
-                               ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
-                               goto err;
-                               }
-                       num_bytes = BN_bn2bin(tmp_scalar, tmp);
-                       }
-               else
-                       num_bytes = BN_bn2bin(scalar, tmp);
-               flip_endian(g_secret, tmp, num_bytes);
-               /* do the multiplication with generator precomputation*/
-               batch_mul(x_out, y_out, z_out,
-                       (const felem_bytearray (*)) secrets, num_points,
-                       g_secret,
-                       mixed, (const felem (*)[17][3]) pre_comp,
-                       (const felem (*)[3]) g_pre_comp);
-               }
-       else
-               /* do the multiplication without generator precomputation */
-               batch_mul(x_out, y_out, z_out,
-                       (const felem_bytearray (*)) secrets, num_points,
-                       NULL, mixed, (const felem (*)[17][3]) pre_comp, NULL);
-       /* reduce the output to its unique minimal representation */
-       felem_contract(x_in, x_out);
-       felem_contract(y_in, y_out);
-       felem_contract(z_in, z_out);
-       if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
-               (!felem_to_BN(z, z_in)))
-               {
-               ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
-               goto err;
-               }
-       ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
-
-err:
-       BN_CTX_end(ctx);
-       if (generator != NULL)
-               EC_POINT_free(generator);
-       if (new_ctx != NULL)
-               BN_CTX_free(new_ctx);
-       if (secrets != NULL)
-               OPENSSL_free(secrets);
-       if (pre_comp != NULL)
-               OPENSSL_free(pre_comp);
-       if (tmp_felems != NULL)
-               OPENSSL_free(tmp_felems);
-       return ret;
-       }
+                               const BIGNUM *scalar, size_t num,
+                               const EC_POINT *points[],
+                               const BIGNUM *scalars[], BN_CTX *ctx)
+{
+    int ret = 0;
+    int j;
+    int mixed = 0;
+    BN_CTX *new_ctx = NULL;
+    BIGNUM *x, *y, *z, *tmp_scalar;
+    felem_bytearray g_secret;
+    felem_bytearray *secrets = NULL;
+    felem (*pre_comp)[17][3] = NULL;
+    felem *tmp_felems = NULL;
+    felem_bytearray tmp;
+    unsigned i, num_bytes;
+    int have_pre_comp = 0;
+    size_t num_points = num;
+    felem x_in, y_in, z_in, x_out, y_out, z_out;
+    NISTP521_PRE_COMP *pre = NULL;
+    felem(*g_pre_comp)[3] = NULL;
+    EC_POINT *generator = NULL;
+    const EC_POINT *p = NULL;
+    const BIGNUM *p_scalar = NULL;
+
+    if (ctx == NULL)
+        if ((ctx = new_ctx = BN_CTX_new()) == NULL)
+            return 0;
+    BN_CTX_start(ctx);
+    if (((x = BN_CTX_get(ctx)) == NULL) ||
+        ((y = BN_CTX_get(ctx)) == NULL) ||
+        ((z = BN_CTX_get(ctx)) == NULL) ||
+        ((tmp_scalar = BN_CTX_get(ctx)) == NULL))
+        goto err;
+
+    if (scalar != NULL) {
+        pre = EC_EX_DATA_get_data(group->extra_data,
+                                  nistp521_pre_comp_dup,
+                                  nistp521_pre_comp_free,
+                                  nistp521_pre_comp_clear_free);
+        if (pre)
+            /* we have precomputation, try to use it */
+            g_pre_comp = &pre->g_pre_comp[0];
+        else
+            /* try to use the standard precomputation */
+            g_pre_comp = (felem(*)[3]) gmul;
+        generator = EC_POINT_new(group);
+        if (generator == NULL)
+            goto err;
+        /* get the generator from precomputation */
+        if (!felem_to_BN(x, g_pre_comp[1][0]) ||
+            !felem_to_BN(y, g_pre_comp[1][1]) ||
+            !felem_to_BN(z, g_pre_comp[1][2])) {
+            ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
+            goto err;
+        }
+        if (!EC_POINT_set_Jprojective_coordinates_GFp(group,
+                                                      generator, x, y, z,
+                                                      ctx))
+            goto err;
+        if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
+            /* precomputation matches generator */
+            have_pre_comp = 1;
+        else
+            /*
+             * we don't have valid precomputation: treat the generator as a
+             * random point
+             */
+            num_points++;
+    }
+
+    if (num_points > 0) {
+        if (num_points >= 2) {
+            /*
+             * unless we precompute multiples for just one point, converting
+             * those into affine form is time well spent
+             */
+            mixed = 1;
+        }
+        secrets = OPENSSL_malloc(sizeof(*secrets) * num_points);
+        pre_comp = OPENSSL_malloc(sizeof(*pre_comp) * num_points);
+        if (mixed)
+            tmp_felems =
+                OPENSSL_malloc(sizeof(*tmp_felemts) * (num_points * 17 + 1));
+        if ((secrets == NULL) || (pre_comp == NULL)
+            || (mixed && (tmp_felems == NULL))) {
+            ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_MALLOC_FAILURE);
+            goto err;
+        }
+
+        /*
+         * we treat NULL scalars as 0, and NULL points as points at infinity,
+         * i.e., they contribute nothing to the linear combination
+         */
+        memset(secrets, 0, sizeof(*secrets) * num_points);
+        memset(pre_comp, 0, sizseof(*pre_comp) * num_points);
+        for (i = 0; i < num_points; ++i) {
+            if (i == num)
+                /*
+                 * we didn't have a valid precomputation, so we pick the
+                 * generator
+                 */
+            {
+                p = EC_GROUP_get0_generator(group);
+                p_scalar = scalar;
+            } else
+                /* the i^th point */
+            {
+                p = points[i];
+                p_scalar = scalars[i];
+            }
+            if ((p_scalar != NULL) && (p != NULL)) {
+                /* reduce scalar to 0 <= scalar < 2^521 */
+                if ((BN_num_bits(p_scalar) > 521)
+                    || (BN_is_negative(p_scalar))) {
+                    /*
+                     * this is an unusual input, and we don't guarantee
+                     * constant-timeness
+                     */
+                    if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) {
+                        ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
+                        goto err;
+                    }
+                    num_bytes = BN_bn2bin(tmp_scalar, tmp);
+                } else
+                    num_bytes = BN_bn2bin(p_scalar, tmp);
+                flip_endian(secrets[i], tmp, num_bytes);
+                /* precompute multiples */
+                if ((!BN_to_felem(x_out, p->X)) ||
+                    (!BN_to_felem(y_out, p->Y)) ||
+                    (!BN_to_felem(z_out, p->Z)))
+                    goto err;
+                memcpy(pre_comp[i][1][0], x_out, sizeof(felem));
+                memcpy(pre_comp[i][1][1], y_out, sizeof(felem));
+                memcpy(pre_comp[i][1][2], z_out, sizeof(felem));
+                for (j = 2; j <= 16; ++j) {
+                    if (j & 1) {
+                        point_add(pre_comp[i][j][0], pre_comp[i][j][1],
+                                  pre_comp[i][j][2], pre_comp[i][1][0],
+                                  pre_comp[i][1][1], pre_comp[i][1][2], 0,
+                                  pre_comp[i][j - 1][0],
+                                  pre_comp[i][j - 1][1],
+                                  pre_comp[i][j - 1][2]);
+                    } else {
+                        point_double(pre_comp[i][j][0], pre_comp[i][j][1],
+                                     pre_comp[i][j][2], pre_comp[i][j / 2][0],
+                                     pre_comp[i][j / 2][1],
+                                     pre_comp[i][j / 2][2]);
+                    }
+                }
+            }
+        }
+        if (mixed)
+            make_points_affine(num_points * 17, pre_comp[0], tmp_felems);
+    }
+
+    /* the scalar for the generator */
+    if ((scalar != NULL) && (have_pre_comp)) {
+        memset(g_secret, 0, sizeof(g_secret));
+        /* reduce scalar to 0 <= scalar < 2^521 */
+        if ((BN_num_bits(scalar) > 521) || (BN_is_negative(scalar))) {
+            /*
+             * this is an unusual input, and we don't guarantee
+             * constant-timeness
+             */
+            if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
+                ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
+                goto err;
+            }
+            num_bytes = BN_bn2bin(tmp_scalar, tmp);
+        } else
+            num_bytes = BN_bn2bin(scalar, tmp);
+        flip_endian(g_secret, tmp, num_bytes);
+        /* do the multiplication with generator precomputation */
+        batch_mul(x_out, y_out, z_out,
+                  (const felem_bytearray(*))secrets, num_points,
+                  g_secret,
+                  mixed, (const felem(*)[17][3])pre_comp,
+                  (const felem(*)[3])g_pre_comp);
+    } else
+        /* do the multiplication without generator precomputation */
+        batch_mul(x_out, y_out, z_out,
+                  (const felem_bytearray(*))secrets, num_points,
+                  NULL, mixed, (const felem(*)[17][3])pre_comp, NULL);
+    /* reduce the output to its unique minimal representation */
+    felem_contract(x_in, x_out);
+    felem_contract(y_in, y_out);
+    felem_contract(z_in, z_out);
+    if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) ||
+        (!felem_to_BN(z, z_in))) {
+        ECerr(EC_F_EC_GFP_NISTP521_POINTS_MUL, ERR_R_BN_LIB);
+        goto err;
+    }
+    ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx);
+
+ err:
+    BN_CTX_end(ctx);
+    EC_POINT_free(generator);
+    BN_CTX_free(new_ctx);
+    OPENSSL_free(secrets);
+    OPENSSL_free(pre_comp);
+    OPENSSL_free(tmp_felems);
+    return ret;
+}
 
 int ec_GFp_nistp521_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
-       {
-       int ret = 0;
-       NISTP521_PRE_COMP *pre = NULL;
-       int i, j;
-       BN_CTX *new_ctx = NULL;
-       BIGNUM *x, *y;
-       EC_POINT *generator = NULL;
-       felem tmp_felems[16];
-
-       /* throw away old precomputation */
-       EC_EX_DATA_free_data(&group->extra_data, nistp521_pre_comp_dup,
-               nistp521_pre_comp_free, nistp521_pre_comp_clear_free);
-       if (ctx == NULL)
-               if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0;
-       BN_CTX_start(ctx);
-       if (((x = BN_CTX_get(ctx)) == NULL) ||
-               ((y = BN_CTX_get(ctx)) == NULL))
-               goto err;
-       /* get the generator */
-       if (group->generator == NULL) goto err;
-       generator = EC_POINT_new(group);
-       if (generator == NULL)
-               goto err;
-       BN_bin2bn(nistp521_curve_params[3], sizeof (felem_bytearray), x);
-       BN_bin2bn(nistp521_curve_params[4], sizeof (felem_bytearray), y);
-       if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
-               goto err;
-       if ((pre = nistp521_pre_comp_new()) == NULL)
-               goto err;
-       /* if the generator is the standard one, use built-in precomputation */
-       if (0 == EC_POINT_cmp(group, generator, group->generator, ctx))
-               {
-               memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
-               ret = 1;
-               goto err;
-               }
-       if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) ||
-               (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) ||
-               (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z)))
-               goto err;
-       /* compute 2^130*G, 2^260*G, 2^390*G */
-       for (i = 1; i <= 4; i <<= 1)
-               {
-               point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1],
-                       pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0],
-                       pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]);
-               for (j = 0; j < 129; ++j)
-                       {
-                       point_double(pre->g_pre_comp[2*i][0],
-                               pre->g_pre_comp[2*i][1],
-                               pre->g_pre_comp[2*i][2],
-                               pre->g_pre_comp[2*i][0],
-                               pre->g_pre_comp[2*i][1],
-                               pre->g_pre_comp[2*i][2]);
-                       }
-               }
-       /* g_pre_comp[0] is the point at infinity */
-       memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0]));
-       /* the remaining multiples */
-       /* 2^130*G + 2^260*G */
-       point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1],
-               pre->g_pre_comp[6][2], pre->g_pre_comp[4][0],
-               pre->g_pre_comp[4][1], pre->g_pre_comp[4][2],
-               0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
-               pre->g_pre_comp[2][2]);
-       /* 2^130*G + 2^390*G */
-       point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1],
-               pre->g_pre_comp[10][2], pre->g_pre_comp[8][0],
-               pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
-               0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
-               pre->g_pre_comp[2][2]);
-       /* 2^260*G + 2^390*G */
-       point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1],
-               pre->g_pre_comp[12][2], pre->g_pre_comp[8][0],
-               pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
-               0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1],
-               pre->g_pre_comp[4][2]);
-       /* 2^130*G + 2^260*G + 2^390*G */
-       point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1],
-               pre->g_pre_comp[14][2], pre->g_pre_comp[12][0],
-               pre->g_pre_comp[12][1], pre->g_pre_comp[12][2],
-               0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
-               pre->g_pre_comp[2][2]);
-       for (i = 1; i < 8; ++i)
-               {
-               /* odd multiples: add G */
-               point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1],
-                       pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0],
-                       pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2],
-                       0, pre->g_pre_comp[1][0], pre->g_pre_comp[1][1],
-                       pre->g_pre_comp[1][2]);
-               }
-       make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems);
-
-       if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp521_pre_comp_dup,
-                       nistp521_pre_comp_free, nistp521_pre_comp_clear_free))
-               goto err;
-       ret = 1;
-       pre = NULL;
+{
+    int ret = 0;
+    NISTP521_PRE_COMP *pre = NULL;
+    int i, j;
+    BN_CTX *new_ctx = NULL;
+    BIGNUM *x, *y;
+    EC_POINT *generator = NULL;
+    felem tmp_felems[16];
+
+    /* throw away old precomputation */
+    EC_EX_DATA_free_data(&group->extra_data, nistp521_pre_comp_dup,
+                         nistp521_pre_comp_free,
+                         nistp521_pre_comp_clear_free);
+    if (ctx == NULL)
+        if ((ctx = new_ctx = BN_CTX_new()) == NULL)
+            return 0;
+    BN_CTX_start(ctx);
+    if (((x = BN_CTX_get(ctx)) == NULL) || ((y = BN_CTX_get(ctx)) == NULL))
+        goto err;
+    /* get the generator */
+    if (group->generator == NULL)
+        goto err;
+    generator = EC_POINT_new(group);
+    if (generator == NULL)
+        goto err;
+    BN_bin2bn(nistp521_curve_params[3], sizeof(felem_bytearray), x);
+    BN_bin2bn(nistp521_curve_params[4], sizeof(felem_bytearray), y);
+    if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx))
+        goto err;
+    if ((pre = nistp521_pre_comp_new()) == NULL)
+        goto err;
+    /*
+     * if the generator is the standard one, use built-in precomputation
+     */
+    if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) {
+        memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp));
+        ret = 1;
+        goto err;
+    }
+    if ((!BN_to_felem(pre->g_pre_comp[1][0], group->generator->X)) ||
+        (!BN_to_felem(pre->g_pre_comp[1][1], group->generator->Y)) ||
+        (!BN_to_felem(pre->g_pre_comp[1][2], group->generator->Z)))
+        goto err;
+    /* compute 2^130*G, 2^260*G, 2^390*G */
+    for (i = 1; i <= 4; i <<= 1) {
+        point_double(pre->g_pre_comp[2 * i][0], pre->g_pre_comp[2 * i][1],
+                     pre->g_pre_comp[2 * i][2], pre->g_pre_comp[i][0],
+                     pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]);
+        for (j = 0; j < 129; ++j) {
+            point_double(pre->g_pre_comp[2 * i][0],
+                         pre->g_pre_comp[2 * i][1],
+                         pre->g_pre_comp[2 * i][2],
+                         pre->g_pre_comp[2 * i][0],
+                         pre->g_pre_comp[2 * i][1],
+                         pre->g_pre_comp[2 * i][2]);
+        }
+    }
+    /* g_pre_comp[0] is the point at infinity */
+    memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0]));
+    /* the remaining multiples */
+    /* 2^130*G + 2^260*G */
+    point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1],
+              pre->g_pre_comp[6][2], pre->g_pre_comp[4][0],
+              pre->g_pre_comp[4][1], pre->g_pre_comp[4][2],
+              0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
+              pre->g_pre_comp[2][2]);
+    /* 2^130*G + 2^390*G */
+    point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1],
+              pre->g_pre_comp[10][2], pre->g_pre_comp[8][0],
+              pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
+              0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
+              pre->g_pre_comp[2][2]);
+    /* 2^260*G + 2^390*G */
+    point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1],
+              pre->g_pre_comp[12][2], pre->g_pre_comp[8][0],
+              pre->g_pre_comp[8][1], pre->g_pre_comp[8][2],
+              0, pre->g_pre_comp[4][0], pre->g_pre_comp[4][1],
+              pre->g_pre_comp[4][2]);
+    /* 2^130*G + 2^260*G + 2^390*G */
+    point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1],
+              pre->g_pre_comp[14][2], pre->g_pre_comp[12][0],
+              pre->g_pre_comp[12][1], pre->g_pre_comp[12][2],
+              0, pre->g_pre_comp[2][0], pre->g_pre_comp[2][1],
+              pre->g_pre_comp[2][2]);
+    for (i = 1; i < 8; ++i) {
+        /* odd multiples: add G */
+        point_add(pre->g_pre_comp[2 * i + 1][0],
+                  pre->g_pre_comp[2 * i + 1][1],
+                  pre->g_pre_comp[2 * i + 1][2], pre->g_pre_comp[2 * i][0],
+                  pre->g_pre_comp[2 * i][1], pre->g_pre_comp[2 * i][2], 0,
+                  pre->g_pre_comp[1][0], pre->g_pre_comp[1][1],
+                  pre->g_pre_comp[1][2]);
+    }
+    make_points_affine(15, &(pre->g_pre_comp[1]), tmp_felems);
+
+    if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp521_pre_comp_dup,
+                             nistp521_pre_comp_free,
+                             nistp521_pre_comp_clear_free))
+        goto err;
+    ret = 1;
+    pre = NULL;
  err:
-       BN_CTX_end(ctx);
-       if (generator != NULL)
-               EC_POINT_free(generator);
-       if (new_ctx != NULL)
-               BN_CTX_free(new_ctx);
-       if (pre)
-               nistp521_pre_comp_free(pre);
-       return ret;
-       }
+    BN_CTX_end(ctx);
+    EC_POINT_free(generator);
+    BN_CTX_free(new_ctx);
+    nistp521_pre_comp_free(pre);
+    return ret;
+}
 
 int ec_GFp_nistp521_have_precompute_mult(const EC_GROUP *group)
-       {
-       if (EC_EX_DATA_get_data(group->extra_data, nistp521_pre_comp_dup,
-                       nistp521_pre_comp_free, nistp521_pre_comp_clear_free)
-               != NULL)
-               return 1;
-       else
-               return 0;
-       }
+{
+    if (EC_EX_DATA_get_data(group->extra_data, nistp521_pre_comp_dup,
+                            nistp521_pre_comp_free,
+                            nistp521_pre_comp_clear_free)
+        != NULL)
+        return 1;
+    else
+        return 0;
+}
 
 #else
-static void *dummy=&dummy;
+static void *dummy = &dummy;
 #endif