Add better computation of carry chain

We port the computation of the carry chain from generate_parameters.py
to Coq, for unsaturated solinas.

Note that while we now bounds-check p448, we do not yet support
goldilocks nor karatsuba.

However, there is still an issue with the synthesized p448 code, which
is that on 64-bit, it tries to use 256-bit and 512-bit integers.  I'm
not sure what's up with that.

Partial progress towards #507

After    | File Name                                    | Before   || Change    | % Change
------------------------------------------------------------------------------------------
8m51.64s | Total                                        | 8m34.60s || +0m17.04s | +3.31%
------------------------------------------------------------------------------------------
0m15.16s | p448_solinas_64.c                            |   N/A    || +0m15.16s | ∞
3m09.12s | p384_32.c                                    | 3m09.36s || -0m00.24s | -0.12%
0m44.99s | ExtractionHaskell/word_by_word_montgomery    | 0m44.91s || +0m00.08s | +0.17%
0m39.58s | p521_32.c                                    | 0m39.22s || +0m00.35s | +0.91%
0m32.54s | p521_64.c                                    | 0m32.49s || +0m00.04s | +0.15%
0m30.87s | ExtractionHaskell/unsaturated_solinas        | 0m31.04s || -0m00.16s | -0.54%
0m24.31s | ExtractionHaskell/saturated_solinas          | 0m24.32s || -0m00.01s | -0.04%
0m18.62s | PushButtonSynthesis/UnsaturatedSolinas.vo    | 0m17.90s || +0m00.72s | +4.02%
0m17.53s | ExtractionOCaml/word_by_word_montgomery      | 0m17.44s || +0m00.08s | +0.51%
0m13.36s | secp256k1_32.c                               | 0m13.58s || -0m00.22s | -1.62%
0m13.21s | p256_32.c                                    | 0m13.15s || +0m00.06s | +0.45%
0m11.47s | p484_64.c                                    | 0m11.39s || +0m00.08s | +0.70%
0m11.27s | ExtractionOCaml/unsaturated_solinas          | 0m10.71s || +0m00.55s | +5.22%
0m10.48s | ExtractionOCaml/word_by_word_montgomery.ml   | 0m10.34s || +0m00.14s | +1.35%
0m07.97s | ExtractionOCaml/saturated_solinas            | 0m07.98s || -0m00.01s | -0.12%
0m07.05s | ExtractionOCaml/unsaturated_solinas.ml       | 0m06.98s || +0m00.06s | +1.00%
0m06.58s | ExtractionHaskell/word_by_word_montgomery.hs | 0m06.48s || +0m00.09s | +1.54%
0m06.09s | p224_32.c                                    | 0m06.04s || +0m00.04s | +0.82%
0m05.24s | p384_64.c                                    | 0m05.34s || -0m00.09s | -1.87%
0m05.13s | ExtractionOCaml/saturated_solinas.ml         | 0m05.19s || -0m00.06s | -1.15%
0m05.00s | ExtractionHaskell/unsaturated_solinas.hs     | 0m04.98s || +0m00.01s | +0.40%
0m04.14s | ExtractionHaskell/saturated_solinas.hs       | 0m04.04s || +0m00.09s | +2.47%
0m02.22s | curve25519_32.c                              | 0m02.22s || +0m00.00s | +0.00%
0m01.49s | curve25519_64.c                              | 0m01.53s || -0m00.04s | -2.61%
0m01.46s | CLI.vo                                       | 0m01.44s || +0m00.02s | +1.38%
0m01.29s | SlowPrimeSynthesisExamples.vo                | 0m01.24s || +0m00.05s | +4.03%
0m01.08s | p256_64.c                                    | 0m01.00s || +0m00.08s | +8.00%
0m01.06s | StandaloneOCamlMain.vo                       | 0m00.96s || +0m00.10s | +10.41%
0m01.06s | secp256k1_64.c                               | 0m01.17s || -0m00.10s | -9.40%
0m01.02s | p224_64.c                                    | 0m01.08s || -0m00.06s | -5.55%
0m00.99s | StandaloneHaskellMain.vo                     | 0m01.08s || -0m00.09s | -8.33%
0m00.27s | TAPSort.vo                                   |   N/A    || +0m00.27s | ∞

1 files changed, 813 insertions, 0 deletions

diff --git a/p448_solinas_64.c b/p448_solinas_64.c
new file mode 100644
index 000000000..af57a7611
--- /dev/null
+++ b/p448_solinas_64.c
@@ -0,0 +1,813 @@
+/* Autogenerated */
+/* curve description: p448 */
+/* requested operations: (all) */
+/* n = 8 (from "8") */
+/* s = 0x10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 (from "2^448") */
+/* c = [(26959946667150639794667015087019630673637144422540572481103610249216, 1), (1, 1)] (from "2^224,1;1,1") */
+/* machine_wordsize = 64 (from "64") */
+
+#include <stdint.h>
+typedef unsigned char fiat_p448_uint1;
+typedef signed char fiat_p448_int1;
+typedef signed __int128 fiat_p448_int128;
+typedef unsigned __int128 fiat_p448_uint128;
+
+
+/*
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0xffffffffffffff]
+ *   arg3: [0x0 ~> 0xffffffffffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0xffffffffffffff]
+ *   out2: [0x0 ~> 0x1]
+ */
+static void fiat_p448_addcarryx_u56(uint64_t* out1, fiat_p448_uint1* out2, fiat_p448_uint1 arg1, uint64_t arg2, uint64_t arg3) {
+  uint64_t x1 = ((arg1 + arg2) + arg3);
+  uint64_t x2 = (x1 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint1 x3 = (fiat_p448_uint1)(x1 >> 56);
+  *out1 = x2;
+  *out2 = x3;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0xffffffffffffff]
+ *   arg3: [0x0 ~> 0xffffffffffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0xffffffffffffff]
+ *   out2: [0x0 ~> 0x1]
+ */
+static void fiat_p448_subborrowx_u56(uint64_t* out1, fiat_p448_uint1* out2, fiat_p448_uint1 arg1, uint64_t arg2, uint64_t arg3) {
+  int64_t x1 = ((int64_t)(arg2 - (int64_t)arg1) - (int64_t)arg3);
+  fiat_p448_int1 x2 = (fiat_p448_int1)(x1 >> 56);
+  uint64_t x3 = (x1 & UINT64_C(0xffffffffffffff));
+  *out1 = x3;
+  *out2 = (fiat_p448_uint1)(0x0 - x2);
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [0x0 ~> 0xffffffffffffffff]
+ *   arg3: [0x0 ~> 0xffffffffffffffff]
+ * Output Bounds:
+ *   out1: [0x0 ~> 0xffffffffffffffff]
+ */
+static void fiat_p448_cmovznz_u64(uint64_t* out1, fiat_p448_uint1 arg1, uint64_t arg2, uint64_t arg3) {
+  fiat_p448_uint1 x1 = (!(!arg1));
+  uint64_t x2 = ((fiat_p448_int1)(0x0 - x1) & UINT64_C(0xffffffffffffffff));
+  uint64_t x3 = ((x2 & arg3) | ((~x2) & arg2));
+  *out1 = x3;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb]]
+ *   arg2: [[0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999]]
+ */
+static void fiat_p448_carry_mul(uint64_t out1[8], const uint64_t arg1[8], const uint64_t arg2[8]) {
+  fiat_p448_uint128 x1 = ((fiat_p448_uint128)(arg1[7]) * (arg2[7]));
+  fiat_p448_uint128 x2 = ((fiat_p448_uint128)(arg1[7]) * (arg2[6]));
+  fiat_p448_uint128 x3 = ((fiat_p448_uint128)(arg1[7]) * (arg2[5]));
+  fiat_p448_uint128 x4 = ((fiat_p448_uint128)(arg1[7]) * (arg2[4]));
+  fiat_p448_uint128 x5 = ((fiat_p448_uint128)(arg1[7]) * (arg2[3]));
+  fiat_p448_uint128 x6 = ((fiat_p448_uint128)(arg1[7]) * (arg2[2]));
+  fiat_p448_uint128 x7 = ((fiat_p448_uint128)(arg1[7]) * (arg2[1]));
+  fiat_p448_uint128 x8 = ((fiat_p448_uint128)(arg1[6]) * (arg2[7]));
+  fiat_p448_uint128 x9 = ((fiat_p448_uint128)(arg1[6]) * (arg2[6]));
+  fiat_p448_uint128 x10 = ((fiat_p448_uint128)(arg1[6]) * (arg2[5]));
+  fiat_p448_uint128 x11 = ((fiat_p448_uint128)(arg1[6]) * (arg2[4]));
+  fiat_p448_uint128 x12 = ((fiat_p448_uint128)(arg1[6]) * (arg2[3]));
+  fiat_p448_uint128 x13 = ((fiat_p448_uint128)(arg1[6]) * (arg2[2]));
+  fiat_p448_uint128 x14 = ((fiat_p448_uint128)(arg1[5]) * (arg2[7]));
+  fiat_p448_uint128 x15 = ((fiat_p448_uint128)(arg1[5]) * (arg2[6]));
+  fiat_p448_uint128 x16 = ((fiat_p448_uint128)(arg1[5]) * (arg2[5]));
+  fiat_p448_uint128 x17 = ((fiat_p448_uint128)(arg1[5]) * (arg2[4]));
+  fiat_p448_uint128 x18 = ((fiat_p448_uint128)(arg1[5]) * (arg2[3]));
+  fiat_p448_uint128 x19 = ((fiat_p448_uint128)(arg1[4]) * (arg2[7]));
+  fiat_p448_uint128 x20 = ((fiat_p448_uint128)(arg1[4]) * (arg2[6]));
+  fiat_p448_uint128 x21 = ((fiat_p448_uint128)(arg1[4]) * (arg2[5]));
+  fiat_p448_uint128 x22 = ((fiat_p448_uint128)(arg1[4]) * (arg2[4]));
+  fiat_p448_uint128 x23 = ((fiat_p448_uint128)(arg1[3]) * (arg2[7]));
+  fiat_p448_uint128 x24 = ((fiat_p448_uint128)(arg1[3]) * (arg2[6]));
+  fiat_p448_uint128 x25 = ((fiat_p448_uint128)(arg1[3]) * (arg2[5]));
+  fiat_p448_uint128 x26 = ((fiat_p448_uint128)(arg1[2]) * (arg2[7]));
+  fiat_p448_uint128 x27 = ((fiat_p448_uint128)(arg1[2]) * (arg2[6]));
+  fiat_p448_uint128 x28 = ((fiat_p448_uint128)(arg1[1]) * (arg2[7]));
+  fiat_p448_uint512 x29 = ((fiat_p448_uint512)((fiat_p448_uint128)(arg1[7]) * (arg2[7])) << 168);
+  fiat_p448_uint256 x30 = ((fiat_p448_uint256)((fiat_p448_uint128)(arg1[7]) * (arg2[6])) << 112);
+  fiat_p448_uint256 x31 = ((fiat_p448_uint256)((fiat_p448_uint128)(arg1[7]) * (arg2[5])) << 56);
+  fiat_p448_uint128 x32 = ((fiat_p448_uint128)(arg1[7]) * (arg2[4]));
+  fiat_p448_uint128 x33 = ((fiat_p448_uint128)(arg1[7]) * (arg2[3]));
+  fiat_p448_uint128 x34 = ((fiat_p448_uint128)(arg1[7]) * (arg2[2]));
+  fiat_p448_uint128 x35 = ((fiat_p448_uint128)(arg1[7]) * (arg2[1]));
+  fiat_p448_uint256 x36 = ((fiat_p448_uint256)((fiat_p448_uint128)(arg1[6]) * (arg2[7])) << 112);
+  fiat_p448_uint256 x37 = ((fiat_p448_uint256)((fiat_p448_uint128)(arg1[6]) * (arg2[6])) << 56);
+  fiat_p448_uint128 x38 = ((fiat_p448_uint128)(arg1[6]) * (arg2[5]));
+  fiat_p448_uint128 x39 = ((fiat_p448_uint128)(arg1[6]) * (arg2[4]));
+  fiat_p448_uint128 x40 = ((fiat_p448_uint128)(arg1[6]) * (arg2[3]));
+  fiat_p448_uint128 x41 = ((fiat_p448_uint128)(arg1[6]) * (arg2[2]));
+  fiat_p448_uint256 x42 = ((fiat_p448_uint256)((fiat_p448_uint128)(arg1[5]) * (arg2[7])) << 56);
+  fiat_p448_uint128 x43 = ((fiat_p448_uint128)(arg1[5]) * (arg2[6]));
+  fiat_p448_uint128 x44 = ((fiat_p448_uint128)(arg1[5]) * (arg2[5]));
+  fiat_p448_uint128 x45 = ((fiat_p448_uint128)(arg1[5]) * (arg2[4]));
+  fiat_p448_uint128 x46 = ((fiat_p448_uint128)(arg1[5]) * (arg2[3]));
+  fiat_p448_uint128 x47 = ((fiat_p448_uint128)(arg1[4]) * (arg2[7]));
+  fiat_p448_uint128 x48 = ((fiat_p448_uint128)(arg1[4]) * (arg2[6]));
+  fiat_p448_uint128 x49 = ((fiat_p448_uint128)(arg1[4]) * (arg2[5]));
+  fiat_p448_uint128 x50 = ((fiat_p448_uint128)(arg1[4]) * (arg2[4]));
+  fiat_p448_uint128 x51 = ((fiat_p448_uint128)(arg1[3]) * (arg2[7]));
+  fiat_p448_uint128 x52 = ((fiat_p448_uint128)(arg1[3]) * (arg2[6]));
+  fiat_p448_uint128 x53 = ((fiat_p448_uint128)(arg1[3]) * (arg2[5]));
+  fiat_p448_uint128 x54 = ((fiat_p448_uint128)(arg1[2]) * (arg2[7]));
+  fiat_p448_uint128 x55 = ((fiat_p448_uint128)(arg1[2]) * (arg2[6]));
+  fiat_p448_uint128 x56 = ((fiat_p448_uint128)(arg1[1]) * (arg2[7]));
+  fiat_p448_uint128 x57 = ((fiat_p448_uint128)(arg1[7]) * (arg2[0]));
+  fiat_p448_uint128 x58 = ((fiat_p448_uint128)(arg1[6]) * (arg2[1]));
+  fiat_p448_uint128 x59 = ((fiat_p448_uint128)(arg1[6]) * (arg2[0]));
+  fiat_p448_uint128 x60 = ((fiat_p448_uint128)(arg1[5]) * (arg2[2]));
+  fiat_p448_uint128 x61 = ((fiat_p448_uint128)(arg1[5]) * (arg2[1]));
+  fiat_p448_uint128 x62 = ((fiat_p448_uint128)(arg1[5]) * (arg2[0]));
+  fiat_p448_uint128 x63 = ((fiat_p448_uint128)(arg1[4]) * (arg2[3]));
+  fiat_p448_uint128 x64 = ((fiat_p448_uint128)(arg1[4]) * (arg2[2]));
+  fiat_p448_uint128 x65 = ((fiat_p448_uint128)(arg1[4]) * (arg2[1]));
+  fiat_p448_uint128 x66 = ((fiat_p448_uint128)(arg1[4]) * (arg2[0]));
+  fiat_p448_uint128 x67 = ((fiat_p448_uint128)(arg1[3]) * (arg2[4]));
+  fiat_p448_uint128 x68 = ((fiat_p448_uint128)(arg1[3]) * (arg2[3]));
+  fiat_p448_uint128 x69 = ((fiat_p448_uint128)(arg1[3]) * (arg2[2]));
+  fiat_p448_uint128 x70 = ((fiat_p448_uint128)(arg1[3]) * (arg2[1]));
+  fiat_p448_uint128 x71 = ((fiat_p448_uint128)(arg1[3]) * (arg2[0]));
+  fiat_p448_uint128 x72 = ((fiat_p448_uint128)(arg1[2]) * (arg2[5]));
+  fiat_p448_uint128 x73 = ((fiat_p448_uint128)(arg1[2]) * (arg2[4]));
+  fiat_p448_uint128 x74 = ((fiat_p448_uint128)(arg1[2]) * (arg2[3]));
+  fiat_p448_uint128 x75 = ((fiat_p448_uint128)(arg1[2]) * (arg2[2]));
+  fiat_p448_uint128 x76 = ((fiat_p448_uint128)(arg1[2]) * (arg2[1]));
+  fiat_p448_uint128 x77 = ((fiat_p448_uint128)(arg1[2]) * (arg2[0]));
+  fiat_p448_uint128 x78 = ((fiat_p448_uint128)(arg1[1]) * (arg2[6]));
+  fiat_p448_uint128 x79 = ((fiat_p448_uint128)(arg1[1]) * (arg2[5]));
+  fiat_p448_uint128 x80 = ((fiat_p448_uint128)(arg1[1]) * (arg2[4]));
+  fiat_p448_uint128 x81 = ((fiat_p448_uint128)(arg1[1]) * (arg2[3]));
+  fiat_p448_uint128 x82 = ((fiat_p448_uint128)(arg1[1]) * (arg2[2]));
+  fiat_p448_uint128 x83 = ((fiat_p448_uint128)(arg1[1]) * (arg2[1]));
+  fiat_p448_uint128 x84 = ((fiat_p448_uint128)(arg1[1]) * (arg2[0]));
+  fiat_p448_uint128 x85 = ((fiat_p448_uint128)(arg1[0]) * (arg2[7]));
+  fiat_p448_uint128 x86 = ((fiat_p448_uint128)(arg1[0]) * (arg2[6]));
+  fiat_p448_uint128 x87 = ((fiat_p448_uint128)(arg1[0]) * (arg2[5]));
+  fiat_p448_uint128 x88 = ((fiat_p448_uint128)(arg1[0]) * (arg2[4]));
+  fiat_p448_uint128 x89 = ((fiat_p448_uint128)(arg1[0]) * (arg2[3]));
+  fiat_p448_uint128 x90 = ((fiat_p448_uint128)(arg1[0]) * (arg2[2]));
+  fiat_p448_uint128 x91 = ((fiat_p448_uint128)(arg1[0]) * (arg2[1]));
+  fiat_p448_uint128 x92 = ((fiat_p448_uint128)(arg1[0]) * (arg2[0]));
+  fiat_p448_uint128 x93 = (x89 + (x82 + (x76 + (x71 + (x19 + (x15 + (x10 + x4)))))));
+  uint64_t x94 = (uint64_t)(x93 >> 56);
+  uint64_t x95 = (uint64_t)(x93 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint512 x96 = (x85 + (x78 + (x72 + (x67 + (x63 + (x60 + (x58 + (x57 + (x47 + (x43 + (x42 + (x38 + (x37 + (x36 + (x32 + (x31 + (x30 + x29)))))))))))))))));
+  fiat_p448_uint128 x97 = (x86 + (x79 + (x73 + (x68 + (x64 + (x61 + (x59 + (x51 + (x48 + (x44 + (x39 + (x33 + x1))))))))))));
+  fiat_p448_uint128 x98 = (x87 + (x80 + (x74 + (x69 + (x65 + (x62 + (x54 + (x52 + (x49 + (x45 + (x40 + (x34 + (x8 + x2)))))))))))));
+  fiat_p448_uint128 x99 = (x88 + (x81 + (x75 + (x70 + (x66 + (x56 + (x55 + (x53 + (x50 + (x46 + (x41 + (x35 + (x14 + (x9 + x3))))))))))))));
+  fiat_p448_uint128 x100 = (x90 + (x83 + (x77 + (x23 + (x20 + (x16 + (x11 + x5)))))));
+  fiat_p448_uint128 x101 = (x91 + (x84 + (x26 + (x24 + (x21 + (x17 + (x12 + x6)))))));
+  fiat_p448_uint128 x102 = (x92 + (x28 + (x27 + (x25 + (x22 + (x18 + (x13 + x7)))))));
+  fiat_p448_uint128 x103 = (x94 + x99);
+  fiat_p448_uint256 x104 = (fiat_p448_uint256)(x96 >> 56);
+  uint64_t x105 = (uint64_t)(x96 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint256 x106 = (x103 + x104);
+  fiat_p448_uint256 x107 = (x106 >> 56);
+  uint64_t x108 = (uint64_t)(x106 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint256 x109 = (x102 + x104);
+  fiat_p448_uint256 x110 = (x107 + x98);
+  fiat_p448_uint256 x111 = (x109 >> 56);
+  uint64_t x112 = (uint64_t)(x109 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint256 x113 = (x111 + x101);
+  fiat_p448_uint128 x114 = (fiat_p448_uint128)(x110 >> 56);
+  uint64_t x115 = (uint64_t)(x110 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint128 x116 = (x114 + x97);
+  fiat_p448_uint128 x117 = (fiat_p448_uint128)(x113 >> 56);
+  uint64_t x118 = (uint64_t)(x113 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint128 x119 = (x117 + x100);
+  uint64_t x120 = (uint64_t)(x116 >> 56);
+  uint64_t x121 = (uint64_t)(x116 & UINT64_C(0xffffffffffffff));
+  uint64_t x122 = (x120 + x105);
+  uint64_t x123 = (uint64_t)(x119 >> 56);
+  uint64_t x124 = (uint64_t)(x119 & UINT64_C(0xffffffffffffff));
+  uint64_t x125 = (x123 + x95);
+  uint64_t x126 = (x122 >> 56);
+  uint64_t x127 = (x122 & UINT64_C(0xffffffffffffff));
+  uint64_t x128 = (x125 >> 56);
+  uint64_t x129 = (x125 & UINT64_C(0xffffffffffffff));
+  uint64_t x130 = (x108 + x126);
+  uint64_t x131 = (x112 + x126);
+  uint64_t x132 = (x128 + x130);
+  uint64_t x133 = (x132 >> 56);
+  uint64_t x134 = (x132 & UINT64_C(0xffffffffffffff));
+  uint64_t x135 = (x133 + x115);
+  uint64_t x136 = (x131 >> 56);
+  uint64_t x137 = (x131 & UINT64_C(0xffffffffffffff));
+  uint64_t x138 = (x136 + x118);
+  out1[0] = x137;
+  out1[1] = x138;
+  out1[2] = x124;
+  out1[3] = x129;
+  out1[4] = x134;
+  out1[5] = x135;
+  out1[6] = x121;
+  out1[7] = x127;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999]]
+ */
+static void fiat_p448_carry_square(uint64_t out1[8], const uint64_t arg1[8]) {
+  uint64_t x1 = (arg1[7]);
+  uint64_t x2 = (arg1[7]);
+  uint64_t x3 = (x1 * (uint64_t)0x2);
+  uint64_t x4 = (x2 * (uint64_t)0x2);
+  uint64_t x5 = ((arg1[7]) * (uint64_t)0x2);
+  uint64_t x6 = (arg1[6]);
+  uint64_t x7 = (arg1[6]);
+  uint64_t x8 = (x6 * (uint64_t)0x2);
+  uint64_t x9 = (x7 * (uint64_t)0x2);
+  uint64_t x10 = ((arg1[6]) * (uint64_t)0x2);
+  uint64_t x11 = (arg1[5]);
+  uint64_t x12 = (arg1[5]);
+  uint64_t x13 = (x11 * (uint64_t)0x2);
+  uint64_t x14 = (x12 * (uint64_t)0x2);
+  uint64_t x15 = ((arg1[5]) * (uint64_t)0x2);
+  uint64_t x16 = (arg1[4]);
+  uint64_t x17 = (arg1[4]);
+  uint64_t x18 = ((arg1[4]) * (uint64_t)0x2);
+  uint64_t x19 = ((arg1[3]) * (uint64_t)0x2);
+  uint64_t x20 = ((arg1[2]) * (uint64_t)0x2);
+  uint64_t x21 = ((arg1[1]) * (uint64_t)0x2);
+  fiat_p448_uint128 x22 = ((fiat_p448_uint128)(arg1[7]) * x2);
+  fiat_p448_uint512 x23 = ((fiat_p448_uint512)((fiat_p448_uint128)(arg1[7]) * x1) << 168);
+  fiat_p448_uint128 x24 = ((fiat_p448_uint128)(arg1[6]) * x4);
+  fiat_p448_uint256 x25 = ((fiat_p448_uint256)((fiat_p448_uint128)(arg1[6]) * x3) << 112);
+  fiat_p448_uint128 x26 = ((fiat_p448_uint128)(arg1[6]) * x7);
+  fiat_p448_uint256 x27 = ((fiat_p448_uint256)((fiat_p448_uint128)(arg1[6]) * x6) << 56);
+  fiat_p448_uint128 x28 = ((fiat_p448_uint128)(arg1[5]) * x4);
+  fiat_p448_uint256 x29 = ((fiat_p448_uint256)((fiat_p448_uint128)(arg1[5]) * x3) << 56);
+  fiat_p448_uint128 x30 = ((fiat_p448_uint128)(arg1[5]) * x9);
+  fiat_p448_uint128 x31 = ((fiat_p448_uint128)(arg1[5]) * x8);
+  fiat_p448_uint128 x32 = ((fiat_p448_uint128)(arg1[5]) * x12);
+  fiat_p448_uint128 x33 = ((fiat_p448_uint128)(arg1[5]) * x11);
+  fiat_p448_uint128 x34 = ((fiat_p448_uint128)(arg1[4]) * x4);
+  fiat_p448_uint128 x35 = ((fiat_p448_uint128)(arg1[4]) * x3);
+  fiat_p448_uint128 x36 = ((fiat_p448_uint128)(arg1[4]) * x9);
+  fiat_p448_uint128 x37 = ((fiat_p448_uint128)(arg1[4]) * x8);
+  fiat_p448_uint128 x38 = ((fiat_p448_uint128)(arg1[4]) * x14);
+  fiat_p448_uint128 x39 = ((fiat_p448_uint128)(arg1[4]) * x13);
+  fiat_p448_uint128 x40 = ((fiat_p448_uint128)(arg1[4]) * x17);
+  fiat_p448_uint128 x41 = ((fiat_p448_uint128)(arg1[4]) * x16);
+  fiat_p448_uint128 x42 = ((fiat_p448_uint128)(arg1[3]) * x4);
+  fiat_p448_uint128 x43 = ((fiat_p448_uint128)(arg1[3]) * x3);
+  fiat_p448_uint128 x44 = ((fiat_p448_uint128)(arg1[3]) * x9);
+  fiat_p448_uint128 x45 = ((fiat_p448_uint128)(arg1[3]) * x8);
+  fiat_p448_uint128 x46 = ((fiat_p448_uint128)(arg1[3]) * x14);
+  fiat_p448_uint128 x47 = ((fiat_p448_uint128)(arg1[3]) * x13);
+  fiat_p448_uint128 x48 = ((fiat_p448_uint128)(arg1[3]) * x18);
+  fiat_p448_uint128 x49 = ((fiat_p448_uint128)(arg1[3]) * (arg1[3]));
+  fiat_p448_uint128 x50 = ((fiat_p448_uint128)(arg1[2]) * x4);
+  fiat_p448_uint128 x51 = ((fiat_p448_uint128)(arg1[2]) * x3);
+  fiat_p448_uint128 x52 = ((fiat_p448_uint128)(arg1[2]) * x9);
+  fiat_p448_uint128 x53 = ((fiat_p448_uint128)(arg1[2]) * x8);
+  fiat_p448_uint128 x54 = ((fiat_p448_uint128)(arg1[2]) * x15);
+  fiat_p448_uint128 x55 = ((fiat_p448_uint128)(arg1[2]) * x18);
+  fiat_p448_uint128 x56 = ((fiat_p448_uint128)(arg1[2]) * x19);
+  fiat_p448_uint128 x57 = ((fiat_p448_uint128)(arg1[2]) * (arg1[2]));
+  fiat_p448_uint128 x58 = ((fiat_p448_uint128)(arg1[1]) * x4);
+  fiat_p448_uint128 x59 = ((fiat_p448_uint128)(arg1[1]) * x3);
+  fiat_p448_uint128 x60 = ((fiat_p448_uint128)(arg1[1]) * x10);
+  fiat_p448_uint128 x61 = ((fiat_p448_uint128)(arg1[1]) * x15);
+  fiat_p448_uint128 x62 = ((fiat_p448_uint128)(arg1[1]) * x18);
+  fiat_p448_uint128 x63 = ((fiat_p448_uint128)(arg1[1]) * x19);
+  fiat_p448_uint128 x64 = ((fiat_p448_uint128)(arg1[1]) * x20);
+  fiat_p448_uint128 x65 = ((fiat_p448_uint128)(arg1[1]) * (arg1[1]));
+  fiat_p448_uint128 x66 = ((fiat_p448_uint128)(arg1[0]) * x5);
+  fiat_p448_uint128 x67 = ((fiat_p448_uint128)(arg1[0]) * x10);
+  fiat_p448_uint128 x68 = ((fiat_p448_uint128)(arg1[0]) * x15);
+  fiat_p448_uint128 x69 = ((fiat_p448_uint128)(arg1[0]) * x18);
+  fiat_p448_uint128 x70 = ((fiat_p448_uint128)(arg1[0]) * x19);
+  fiat_p448_uint128 x71 = ((fiat_p448_uint128)(arg1[0]) * x20);
+  fiat_p448_uint128 x72 = ((fiat_p448_uint128)(arg1[0]) * x21);
+  fiat_p448_uint128 x73 = ((fiat_p448_uint128)(arg1[0]) * (arg1[0]));
+  fiat_p448_uint128 x74 = (x70 + (x64 + (x34 + x30)));
+  uint64_t x75 = (uint64_t)(x74 >> 56);
+  uint64_t x76 = (uint64_t)(x74 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint512 x77 = (x66 + (x60 + (x54 + (x48 + (x35 + (x31 + (x29 + (x27 + (x25 + x23)))))))));
+  fiat_p448_uint128 x78 = (x67 + (x61 + (x55 + (x49 + (x43 + (x37 + (x33 + x22)))))));
+  fiat_p448_uint128 x79 = (x68 + (x62 + (x56 + (x51 + (x45 + (x39 + x24))))));
+  fiat_p448_uint128 x80 = (x69 + (x63 + (x59 + (x57 + (x53 + (x47 + (x41 + (x28 + x26))))))));
+  fiat_p448_uint128 x81 = (x71 + (x65 + (x42 + (x36 + x32))));
+  fiat_p448_uint128 x82 = (x72 + (x50 + (x44 + x38)));
+  fiat_p448_uint128 x83 = (x73 + (x58 + (x52 + (x46 + x40))));
+  fiat_p448_uint128 x84 = (x75 + x80);
+  fiat_p448_uint256 x85 = (fiat_p448_uint256)(x77 >> 56);
+  uint64_t x86 = (uint64_t)(x77 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint256 x87 = (x84 + x85);
+  fiat_p448_uint256 x88 = (x87 >> 56);
+  uint64_t x89 = (uint64_t)(x87 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint256 x90 = (x83 + x85);
+  fiat_p448_uint256 x91 = (x88 + x79);
+  fiat_p448_uint256 x92 = (x90 >> 56);
+  uint64_t x93 = (uint64_t)(x90 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint256 x94 = (x92 + x82);
+  fiat_p448_uint128 x95 = (fiat_p448_uint128)(x91 >> 56);
+  uint64_t x96 = (uint64_t)(x91 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint128 x97 = (x95 + x78);
+  fiat_p448_uint128 x98 = (fiat_p448_uint128)(x94 >> 56);
+  uint64_t x99 = (uint64_t)(x94 & UINT64_C(0xffffffffffffff));
+  fiat_p448_uint128 x100 = (x98 + x81);
+  uint64_t x101 = (uint64_t)(x97 >> 56);
+  uint64_t x102 = (uint64_t)(x97 & UINT64_C(0xffffffffffffff));
+  uint64_t x103 = (x101 + x86);
+  uint64_t x104 = (uint64_t)(x100 >> 56);
+  uint64_t x105 = (uint64_t)(x100 & UINT64_C(0xffffffffffffff));
+  uint64_t x106 = (x104 + x76);
+  uint64_t x107 = (x103 >> 56);
+  uint64_t x108 = (x103 & UINT64_C(0xffffffffffffff));
+  uint64_t x109 = (x106 >> 56);
+  uint64_t x110 = (x106 & UINT64_C(0xffffffffffffff));
+  uint64_t x111 = (x89 + x107);
+  uint64_t x112 = (x93 + x107);
+  uint64_t x113 = (x109 + x111);
+  uint64_t x114 = (x113 >> 56);
+  uint64_t x115 = (x113 & UINT64_C(0xffffffffffffff));
+  uint64_t x116 = (x114 + x96);
+  uint64_t x117 = (x112 >> 56);
+  uint64_t x118 = (x112 & UINT64_C(0xffffffffffffff));
+  uint64_t x119 = (x117 + x99);
+  out1[0] = x118;
+  out1[1] = x119;
+  out1[2] = x105;
+  out1[3] = x110;
+  out1[4] = x115;
+  out1[5] = x116;
+  out1[6] = x102;
+  out1[7] = x108;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999]]
+ */
+static void fiat_p448_carry(uint64_t out1[8], const uint64_t arg1[8]) {
+  uint64_t x1 = (arg1[3]);
+  uint64_t x2 = (arg1[7]);
+  uint64_t x3 = (x2 >> 56);
+  uint64_t x4 = (((x1 >> 56) + (arg1[4])) + x3);
+  uint64_t x5 = ((arg1[0]) + x3);
+  uint64_t x6 = ((x4 >> 56) + (arg1[5]));
+  uint64_t x7 = ((x5 >> 56) + (arg1[1]));
+  uint64_t x8 = ((x6 >> 56) + (arg1[6]));
+  uint64_t x9 = ((x7 >> 56) + (arg1[2]));
+  uint64_t x10 = ((x8 >> 56) + (x2 & UINT64_C(0xffffffffffffff)));
+  uint64_t x11 = ((x9 >> 56) + (x1 & UINT64_C(0xffffffffffffff)));
+  uint64_t x12 = (x10 >> 56);
+  uint64_t x13 = ((x5 & UINT64_C(0xffffffffffffff)) + x12);
+  uint64_t x14 = ((x11 >> 56) + ((x4 & UINT64_C(0xffffffffffffff)) + x12));
+  uint64_t x15 = (x13 & UINT64_C(0xffffffffffffff));
+  uint64_t x16 = ((x13 >> 56) + (x7 & UINT64_C(0xffffffffffffff)));
+  uint64_t x17 = (x9 & UINT64_C(0xffffffffffffff));
+  uint64_t x18 = (x11 & UINT64_C(0xffffffffffffff));
+  uint64_t x19 = (x14 & UINT64_C(0xffffffffffffff));
+  uint64_t x20 = ((x14 >> 56) + (x6 & UINT64_C(0xffffffffffffff)));
+  uint64_t x21 = (x8 & UINT64_C(0xffffffffffffff));
+  uint64_t x22 = (x10 & UINT64_C(0xffffffffffffff));
+  out1[0] = x15;
+  out1[1] = x16;
+  out1[2] = x17;
+  out1[3] = x18;
+  out1[4] = x19;
+  out1[5] = x20;
+  out1[6] = x21;
+  out1[7] = x22;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999]]
+ *   arg2: [[0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb]]
+ */
+static void fiat_p448_add(uint64_t out1[8], const uint64_t arg1[8], const uint64_t arg2[8]) {
+  uint64_t x1 = ((arg1[0]) + (arg2[0]));
+  uint64_t x2 = ((arg1[1]) + (arg2[1]));
+  uint64_t x3 = ((arg1[2]) + (arg2[2]));
+  uint64_t x4 = ((arg1[3]) + (arg2[3]));
+  uint64_t x5 = ((arg1[4]) + (arg2[4]));
+  uint64_t x6 = ((arg1[5]) + (arg2[5]));
+  uint64_t x7 = ((arg1[6]) + (arg2[6]));
+  uint64_t x8 = ((arg1[7]) + (arg2[7]));
+  out1[0] = x1;
+  out1[1] = x2;
+  out1[2] = x3;
+  out1[3] = x4;
+  out1[4] = x5;
+  out1[5] = x6;
+  out1[6] = x7;
+  out1[7] = x8;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999]]
+ *   arg2: [[0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb]]
+ */
+static void fiat_p448_sub(uint64_t out1[8], const uint64_t arg1[8], const uint64_t arg2[8]) {
+  uint64_t x1 = ((UINT64_C(0x1fffffffffffffe) + (arg1[0])) - (arg2[0]));
+  uint64_t x2 = ((UINT64_C(0x1fffffffffffffe) + (arg1[1])) - (arg2[1]));
+  uint64_t x3 = ((UINT64_C(0x1fffffffffffffe) + (arg1[2])) - (arg2[2]));
+  uint64_t x4 = ((UINT64_C(0x1fffffffffffffe) + (arg1[3])) - (arg2[3]));
+  uint64_t x5 = ((UINT64_C(0x1fffffffffffffc) + (arg1[4])) - (arg2[4]));
+  uint64_t x6 = ((UINT64_C(0x1fffffffffffffe) + (arg1[5])) - (arg2[5]));
+  uint64_t x7 = ((UINT64_C(0x1fffffffffffffe) + (arg1[6])) - (arg2[6]));
+  uint64_t x8 = ((UINT64_C(0x1fffffffffffffe) + (arg1[7])) - (arg2[7]));
+  out1[0] = x1;
+  out1[1] = x2;
+  out1[2] = x3;
+  out1[3] = x4;
+  out1[4] = x5;
+  out1[5] = x6;
+  out1[6] = x7;
+  out1[7] = x8;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb], [0x0 ~> 0x34ccccccccccccb]]
+ */
+static void fiat_p448_opp(uint64_t out1[8], const uint64_t arg1[8]) {
+  uint64_t x1 = (UINT64_C(0x1fffffffffffffe) - (arg1[0]));
+  uint64_t x2 = (UINT64_C(0x1fffffffffffffe) - (arg1[1]));
+  uint64_t x3 = (UINT64_C(0x1fffffffffffffe) - (arg1[2]));
+  uint64_t x4 = (UINT64_C(0x1fffffffffffffe) - (arg1[3]));
+  uint64_t x5 = (UINT64_C(0x1fffffffffffffc) - (arg1[4]));
+  uint64_t x6 = (UINT64_C(0x1fffffffffffffe) - (arg1[5]));
+  uint64_t x7 = (UINT64_C(0x1fffffffffffffe) - (arg1[6]));
+  uint64_t x8 = (UINT64_C(0x1fffffffffffffe) - (arg1[7]));
+  out1[0] = x1;
+  out1[1] = x2;
+  out1[2] = x3;
+  out1[3] = x4;
+  out1[4] = x5;
+  out1[5] = x6;
+  out1[6] = x7;
+  out1[7] = x8;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [0x0 ~> 0x1]
+ *   arg2: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+ *   arg3: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
+ */
+static void fiat_p448_selectznz(uint64_t out1[8], fiat_p448_uint1 arg1, const uint64_t arg2[8], const uint64_t arg3[8]) {
+  uint64_t x1;
+  fiat_p448_cmovznz_u64(&x1, arg1, (arg2[0]), (arg3[0]));
+  uint64_t x2;
+  fiat_p448_cmovznz_u64(&x2, arg1, (arg2[1]), (arg3[1]));
+  uint64_t x3;
+  fiat_p448_cmovznz_u64(&x3, arg1, (arg2[2]), (arg3[2]));
+  uint64_t x4;
+  fiat_p448_cmovznz_u64(&x4, arg1, (arg2[3]), (arg3[3]));
+  uint64_t x5;
+  fiat_p448_cmovznz_u64(&x5, arg1, (arg2[4]), (arg3[4]));
+  uint64_t x6;
+  fiat_p448_cmovznz_u64(&x6, arg1, (arg2[5]), (arg3[5]));
+  uint64_t x7;
+  fiat_p448_cmovznz_u64(&x7, arg1, (arg2[6]), (arg3[6]));
+  uint64_t x8;
+  fiat_p448_cmovznz_u64(&x8, arg1, (arg2[7]), (arg3[7]));
+  out1[0] = x1;
+  out1[1] = x2;
+  out1[2] = x3;
+  out1[3] = x4;
+  out1[4] = x5;
+  out1[5] = x6;
+  out1[6] = x7;
+  out1[7] = x8;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]]
+ */
+static void fiat_p448_to_bytes(uint8_t out1[56], const uint64_t arg1[8]) {
+  uint64_t x1;
+  fiat_p448_uint1 x2;
+  fiat_p448_subborrowx_u56(&x1, &x2, 0x0, (arg1[0]), UINT64_C(0xffffffffffffff));
+  uint64_t x3;
+  fiat_p448_uint1 x4;
+  fiat_p448_subborrowx_u56(&x3, &x4, x2, (arg1[1]), UINT64_C(0xffffffffffffff));
+  uint64_t x5;
+  fiat_p448_uint1 x6;
+  fiat_p448_subborrowx_u56(&x5, &x6, x4, (arg1[2]), UINT64_C(0xffffffffffffff));
+  uint64_t x7;
+  fiat_p448_uint1 x8;
+  fiat_p448_subborrowx_u56(&x7, &x8, x6, (arg1[3]), UINT64_C(0xffffffffffffff));
+  uint64_t x9;
+  fiat_p448_uint1 x10;
+  fiat_p448_subborrowx_u56(&x9, &x10, x8, (arg1[4]), UINT64_C(0xfffffffffffffe));
+  uint64_t x11;
+  fiat_p448_uint1 x12;
+  fiat_p448_subborrowx_u56(&x11, &x12, x10, (arg1[5]), UINT64_C(0xffffffffffffff));
+  uint64_t x13;
+  fiat_p448_uint1 x14;
+  fiat_p448_subborrowx_u56(&x13, &x14, x12, (arg1[6]), UINT64_C(0xffffffffffffff));
+  uint64_t x15;
+  fiat_p448_uint1 x16;
+  fiat_p448_subborrowx_u56(&x15, &x16, x14, (arg1[7]), UINT64_C(0xffffffffffffff));
+  uint64_t x17;
+  fiat_p448_cmovznz_u64(&x17, x16, 0x0, UINT64_C(0xffffffffffffffff));
+  uint64_t x18;
+  fiat_p448_uint1 x19;
+  fiat_p448_addcarryx_u56(&x18, &x19, 0x0, (x17 & UINT64_C(0xffffffffffffff)), x1);
+  uint64_t x20;
+  fiat_p448_uint1 x21;
+  fiat_p448_addcarryx_u56(&x20, &x21, x19, (x17 & UINT64_C(0xffffffffffffff)), x3);
+  uint64_t x22;
+  fiat_p448_uint1 x23;
+  fiat_p448_addcarryx_u56(&x22, &x23, x21, (x17 & UINT64_C(0xffffffffffffff)), x5);
+  uint64_t x24;
+  fiat_p448_uint1 x25;
+  fiat_p448_addcarryx_u56(&x24, &x25, x23, (x17 & UINT64_C(0xffffffffffffff)), x7);
+  uint64_t x26;
+  fiat_p448_uint1 x27;
+  fiat_p448_addcarryx_u56(&x26, &x27, x25, (x17 & UINT64_C(0xfffffffffffffe)), x9);
+  uint64_t x28;
+  fiat_p448_uint1 x29;
+  fiat_p448_addcarryx_u56(&x28, &x29, x27, (x17 & UINT64_C(0xffffffffffffff)), x11);
+  uint64_t x30;
+  fiat_p448_uint1 x31;
+  fiat_p448_addcarryx_u56(&x30, &x31, x29, (x17 & UINT64_C(0xffffffffffffff)), x13);
+  uint64_t x32;
+  fiat_p448_uint1 x33;
+  fiat_p448_addcarryx_u56(&x32, &x33, x31, (x17 & UINT64_C(0xffffffffffffff)), x15);
+  uint64_t x34 = (x18 >> 8);
+  uint8_t x35 = (uint8_t)(x18 & UINT8_C(0xff));
+  uint64_t x36 = (x34 >> 8);
+  uint8_t x37 = (uint8_t)(x34 & UINT8_C(0xff));
+  uint64_t x38 = (x36 >> 8);
+  uint8_t x39 = (uint8_t)(x36 & UINT8_C(0xff));
+  uint64_t x40 = (x38 >> 8);
+  uint8_t x41 = (uint8_t)(x38 & UINT8_C(0xff));
+  uint64_t x42 = (x40 >> 8);
+  uint8_t x43 = (uint8_t)(x40 & UINT8_C(0xff));
+  uint8_t x44 = (uint8_t)(x42 >> 8);
+  uint8_t x45 = (uint8_t)(x42 & UINT8_C(0xff));
+  uint8_t x46 = (uint8_t)(x44 & UINT8_C(0xff));
+  uint64_t x47 = (x20 >> 8);
+  uint8_t x48 = (uint8_t)(x20 & UINT8_C(0xff));
+  uint64_t x49 = (x47 >> 8);
+  uint8_t x50 = (uint8_t)(x47 & UINT8_C(0xff));
+  uint64_t x51 = (x49 >> 8);
+  uint8_t x52 = (uint8_t)(x49 & UINT8_C(0xff));
+  uint64_t x53 = (x51 >> 8);
+  uint8_t x54 = (uint8_t)(x51 & UINT8_C(0xff));
+  uint64_t x55 = (x53 >> 8);
+  uint8_t x56 = (uint8_t)(x53 & UINT8_C(0xff));
+  uint8_t x57 = (uint8_t)(x55 >> 8);
+  uint8_t x58 = (uint8_t)(x55 & UINT8_C(0xff));
+  uint8_t x59 = (uint8_t)(x57 & UINT8_C(0xff));
+  uint64_t x60 = (x22 >> 8);
+  uint8_t x61 = (uint8_t)(x22 & UINT8_C(0xff));
+  uint64_t x62 = (x60 >> 8);
+  uint8_t x63 = (uint8_t)(x60 & UINT8_C(0xff));
+  uint64_t x64 = (x62 >> 8);
+  uint8_t x65 = (uint8_t)(x62 & UINT8_C(0xff));
+  uint64_t x66 = (x64 >> 8);
+  uint8_t x67 = (uint8_t)(x64 & UINT8_C(0xff));
+  uint64_t x68 = (x66 >> 8);
+  uint8_t x69 = (uint8_t)(x66 & UINT8_C(0xff));
+  uint8_t x70 = (uint8_t)(x68 >> 8);
+  uint8_t x71 = (uint8_t)(x68 & UINT8_C(0xff));
+  uint8_t x72 = (uint8_t)(x70 & UINT8_C(0xff));
+  uint64_t x73 = (x24 >> 8);
+  uint8_t x74 = (uint8_t)(x24 & UINT8_C(0xff));
+  uint64_t x75 = (x73 >> 8);
+  uint8_t x76 = (uint8_t)(x73 & UINT8_C(0xff));
+  uint64_t x77 = (x75 >> 8);
+  uint8_t x78 = (uint8_t)(x75 & UINT8_C(0xff));
+  uint64_t x79 = (x77 >> 8);
+  uint8_t x80 = (uint8_t)(x77 & UINT8_C(0xff));
+  uint64_t x81 = (x79 >> 8);
+  uint8_t x82 = (uint8_t)(x79 & UINT8_C(0xff));
+  uint8_t x83 = (uint8_t)(x81 >> 8);
+  uint8_t x84 = (uint8_t)(x81 & UINT8_C(0xff));
+  uint8_t x85 = (uint8_t)(x83 & UINT8_C(0xff));
+  uint64_t x86 = (x26 >> 8);
+  uint8_t x87 = (uint8_t)(x26 & UINT8_C(0xff));
+  uint64_t x88 = (x86 >> 8);
+  uint8_t x89 = (uint8_t)(x86 & UINT8_C(0xff));
+  uint64_t x90 = (x88 >> 8);
+  uint8_t x91 = (uint8_t)(x88 & UINT8_C(0xff));
+  uint64_t x92 = (x90 >> 8);
+  uint8_t x93 = (uint8_t)(x90 & UINT8_C(0xff));
+  uint64_t x94 = (x92 >> 8);
+  uint8_t x95 = (uint8_t)(x92 & UINT8_C(0xff));
+  uint8_t x96 = (uint8_t)(x94 >> 8);
+  uint8_t x97 = (uint8_t)(x94 & UINT8_C(0xff));
+  uint8_t x98 = (uint8_t)(x96 & UINT8_C(0xff));
+  uint64_t x99 = (x28 >> 8);
+  uint8_t x100 = (uint8_t)(x28 & UINT8_C(0xff));
+  uint64_t x101 = (x99 >> 8);
+  uint8_t x102 = (uint8_t)(x99 & UINT8_C(0xff));
+  uint64_t x103 = (x101 >> 8);
+  uint8_t x104 = (uint8_t)(x101 & UINT8_C(0xff));
+  uint64_t x105 = (x103 >> 8);
+  uint8_t x106 = (uint8_t)(x103 & UINT8_C(0xff));
+  uint64_t x107 = (x105 >> 8);
+  uint8_t x108 = (uint8_t)(x105 & UINT8_C(0xff));
+  uint8_t x109 = (uint8_t)(x107 >> 8);
+  uint8_t x110 = (uint8_t)(x107 & UINT8_C(0xff));
+  uint8_t x111 = (uint8_t)(x109 & UINT8_C(0xff));
+  uint64_t x112 = (x30 >> 8);
+  uint8_t x113 = (uint8_t)(x30 & UINT8_C(0xff));
+  uint64_t x114 = (x112 >> 8);
+  uint8_t x115 = (uint8_t)(x112 & UINT8_C(0xff));
+  uint64_t x116 = (x114 >> 8);
+  uint8_t x117 = (uint8_t)(x114 & UINT8_C(0xff));
+  uint64_t x118 = (x116 >> 8);
+  uint8_t x119 = (uint8_t)(x116 & UINT8_C(0xff));
+  uint64_t x120 = (x118 >> 8);
+  uint8_t x121 = (uint8_t)(x118 & UINT8_C(0xff));
+  uint8_t x122 = (uint8_t)(x120 >> 8);
+  uint8_t x123 = (uint8_t)(x120 & UINT8_C(0xff));
+  uint8_t x124 = (uint8_t)(x122 & UINT8_C(0xff));
+  uint64_t x125 = (x32 >> 8);
+  uint8_t x126 = (uint8_t)(x32 & UINT8_C(0xff));
+  uint64_t x127 = (x125 >> 8);
+  uint8_t x128 = (uint8_t)(x125 & UINT8_C(0xff));
+  uint64_t x129 = (x127 >> 8);
+  uint8_t x130 = (uint8_t)(x127 & UINT8_C(0xff));
+  uint64_t x131 = (x129 >> 8);
+  uint8_t x132 = (uint8_t)(x129 & UINT8_C(0xff));
+  uint64_t x133 = (x131 >> 8);
+  uint8_t x134 = (uint8_t)(x131 & UINT8_C(0xff));
+  uint8_t x135 = (uint8_t)(x133 >> 8);
+  uint8_t x136 = (uint8_t)(x133 & UINT8_C(0xff));
+  out1[0] = x35;
+  out1[1] = x37;
+  out1[2] = x39;
+  out1[3] = x41;
+  out1[4] = x43;
+  out1[5] = x45;
+  out1[6] = x46;
+  out1[7] = x48;
+  out1[8] = x50;
+  out1[9] = x52;
+  out1[10] = x54;
+  out1[11] = x56;
+  out1[12] = x58;
+  out1[13] = x59;
+  out1[14] = x61;
+  out1[15] = x63;
+  out1[16] = x65;
+  out1[17] = x67;
+  out1[18] = x69;
+  out1[19] = x71;
+  out1[20] = x72;
+  out1[21] = x74;
+  out1[22] = x76;
+  out1[23] = x78;
+  out1[24] = x80;
+  out1[25] = x82;
+  out1[26] = x84;
+  out1[27] = x85;
+  out1[28] = x87;
+  out1[29] = x89;
+  out1[30] = x91;
+  out1[31] = x93;
+  out1[32] = x95;
+  out1[33] = x97;
+  out1[34] = x98;
+  out1[35] = x100;
+  out1[36] = x102;
+  out1[37] = x104;
+  out1[38] = x106;
+  out1[39] = x108;
+  out1[40] = x110;
+  out1[41] = x111;
+  out1[42] = x113;
+  out1[43] = x115;
+  out1[44] = x117;
+  out1[45] = x119;
+  out1[46] = x121;
+  out1[47] = x123;
+  out1[48] = x124;
+  out1[49] = x126;
+  out1[50] = x128;
+  out1[51] = x130;
+  out1[52] = x132;
+  out1[53] = x134;
+  out1[54] = x136;
+  out1[55] = x135;
+}
+
+/*
+ * Input Bounds:
+ *   arg1: [[0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff], [0x0 ~> 0xff]]
+ * Output Bounds:
+ *   out1: [[0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999], [0x0 ~> 0x119999999999999]]
+ */
+static void fiat_p448_from_bytes(uint64_t out1[8], const uint8_t arg1[56]) {
+  uint64_t x1 = ((uint64_t)(arg1[55]) << 48);
+  uint64_t x2 = ((uint64_t)(arg1[54]) << 40);
+  uint64_t x3 = ((uint64_t)(arg1[53]) << 32);
+  uint64_t x4 = ((uint64_t)(arg1[52]) << 24);
+  uint64_t x5 = ((uint64_t)(arg1[51]) << 16);
+  uint64_t x6 = ((uint64_t)(arg1[50]) << 8);
+  uint8_t x7 = (arg1[49]);
+  uint64_t x8 = ((uint64_t)(arg1[48]) << 48);
+  uint64_t x9 = ((uint64_t)(arg1[47]) << 40);
+  uint64_t x10 = ((uint64_t)(arg1[46]) << 32);
+  uint64_t x11 = ((uint64_t)(arg1[45]) << 24);
+  uint64_t x12 = ((uint64_t)(arg1[44]) << 16);
+  uint64_t x13 = ((uint64_t)(arg1[43]) << 8);
+  uint8_t x14 = (arg1[42]);
+  uint64_t x15 = ((uint64_t)(arg1[41]) << 48);
+  uint64_t x16 = ((uint64_t)(arg1[40]) << 40);
+  uint64_t x17 = ((uint64_t)(arg1[39]) << 32);
+  uint64_t x18 = ((uint64_t)(arg1[38]) << 24);
+  uint64_t x19 = ((uint64_t)(arg1[37]) << 16);
+  uint64_t x20 = ((uint64_t)(arg1[36]) << 8);
+  uint8_t x21 = (arg1[35]);
+  uint64_t x22 = ((uint64_t)(arg1[34]) << 48);
+  uint64_t x23 = ((uint64_t)(arg1[33]) << 40);
+  uint64_t x24 = ((uint64_t)(arg1[32]) << 32);
+  uint64_t x25 = ((uint64_t)(arg1[31]) << 24);
+  uint64_t x26 = ((uint64_t)(arg1[30]) << 16);
+  uint64_t x27 = ((uint64_t)(arg1[29]) << 8);
+  uint8_t x28 = (arg1[28]);
+  uint64_t x29 = ((uint64_t)(arg1[27]) << 48);
+  uint64_t x30 = ((uint64_t)(arg1[26]) << 40);
+  uint64_t x31 = ((uint64_t)(arg1[25]) << 32);
+  uint64_t x32 = ((uint64_t)(arg1[24]) << 24);
+  uint64_t x33 = ((uint64_t)(arg1[23]) << 16);
+  uint64_t x34 = ((uint64_t)(arg1[22]) << 8);
+  uint8_t x35 = (arg1[21]);
+  uint64_t x36 = ((uint64_t)(arg1[20]) << 48);
+  uint64_t x37 = ((uint64_t)(arg1[19]) << 40);
+  uint64_t x38 = ((uint64_t)(arg1[18]) << 32);
+  uint64_t x39 = ((uint64_t)(arg1[17]) << 24);
+  uint64_t x40 = ((uint64_t)(arg1[16]) << 16);
+  uint64_t x41 = ((uint64_t)(arg1[15]) << 8);
+  uint8_t x42 = (arg1[14]);
+  uint64_t x43 = ((uint64_t)(arg1[13]) << 48);
+  uint64_t x44 = ((uint64_t)(arg1[12]) << 40);
+  uint64_t x45 = ((uint64_t)(arg1[11]) << 32);
+  uint64_t x46 = ((uint64_t)(arg1[10]) << 24);
+  uint64_t x47 = ((uint64_t)(arg1[9]) << 16);
+  uint64_t x48 = ((uint64_t)(arg1[8]) << 8);
+  uint8_t x49 = (arg1[7]);
+  uint64_t x50 = ((uint64_t)(arg1[6]) << 48);
+  uint64_t x51 = ((uint64_t)(arg1[5]) << 40);
+  uint64_t x52 = ((uint64_t)(arg1[4]) << 32);
+  uint64_t x53 = ((uint64_t)(arg1[3]) << 24);
+  uint64_t x54 = ((uint64_t)(arg1[2]) << 16);
+  uint64_t x55 = ((uint64_t)(arg1[1]) << 8);
+  uint8_t x56 = (arg1[0]);
+  uint64_t x57 = (x56 + (x55 + (x54 + (x53 + (x52 + (x51 + x50))))));
+  uint64_t x58 = (x57 & UINT64_C(0xffffffffffffff));
+  uint64_t x59 = (x7 + (x6 + (x5 + (x4 + (x3 + (x2 + x1))))));
+  uint64_t x60 = (x14 + (x13 + (x12 + (x11 + (x10 + (x9 + x8))))));
+  uint64_t x61 = (x21 + (x20 + (x19 + (x18 + (x17 + (x16 + x15))))));
+  uint64_t x62 = (x28 + (x27 + (x26 + (x25 + (x24 + (x23 + x22))))));
+  uint64_t x63 = (x35 + (x34 + (x33 + (x32 + (x31 + (x30 + x29))))));
+  uint64_t x64 = (x42 + (x41 + (x40 + (x39 + (x38 + (x37 + x36))))));
+  uint64_t x65 = (x49 + (x48 + (x47 + (x46 + (x45 + (x44 + x43))))));
+  uint64_t x66 = (x65 & UINT64_C(0xffffffffffffff));
+  uint64_t x67 = (x64 & UINT64_C(0xffffffffffffff));
+  uint64_t x68 = (x63 & UINT64_C(0xffffffffffffff));
+  uint64_t x69 = (x62 & UINT64_C(0xffffffffffffff));
+  uint64_t x70 = (x61 & UINT64_C(0xffffffffffffff));
+  uint64_t x71 = (x60 & UINT64_C(0xffffffffffffff));
+  out1[0] = x58;
+  out1[1] = x66;
+  out1[2] = x67;
+  out1[3] = x68;
+  out1[4] = x69;
+  out1[5] = x70;
+  out1[6] = x71;
+  out1[7] = x59;
+}
+