From: Herbert Xu <herbert@gondor.apana.org.au>
To: Linus Torvalds <torvalds@linux-foundation.org>,
"David S. Miller" <davem@davemloft.net>,
"Jason A. Donenfeld" <Jason@zx2c4.com>,
Eric Biggers <ebiggers@kernel.org>,
Ard Biesheuvel <ard.biesheuvel@linaro.org>,
Linux Crypto Mailing List <linux-crypto@vger.kernel.org>,
linux-fscrypt@vger.kernel.org,
linux-arm-kernel@lists.infradead.org,
LKML <linux-kernel@vger.kernel.org>,
Paul Crowley <paulcrowley@google.com>,
Greg Kaiser <gkaiser@google.com>,
Samuel Neves <samuel.c.p.neves@gmail.com>,
Tomer Ashur <tomer.ashur@esat.kuleuven.be>,
Martin Willi <martin@strongswan.org>
Subject: [PATCH 14/17] zinc: Curve25519 x86_64 implementation
Date: Fri, 22 Mar 2019 14:29:54 +0800 [thread overview]
Message-ID: <E1h7Dgg-0001JW-LX@gondobar> (raw)
In-Reply-To: 20190322062740.nrwfx2rvmt7lzotj@gondor.apana.org.au
[-- Warning: decoded text below may be mangled, UTF-8 assumed --]
[-- Attachment #1: Type: text/plain, Size: 83780 bytes --]
From: Jason A. Donenfeld <Jason@zx2c4.com>
This implementation is the fastest available x86_64 implementation, and
unlike Sandy2x, it doesn't requie use of the floating point registers at
all. Instead it makes use of BMI2 and ADX, available on recent
microarchitectures. The implementation was written by Armando
Faz-Hernández with contributions (upstream) from Samuel Neves and me,
in addition to further changes in the kernel implementation from us.
Signed-off-by: Jason A. Donenfeld <Jason@zx2c4.com>
Signed-off-by: Samuel Neves <sneves@dei.uc.pt>
Cc: Armando Faz-Hernández <armfazh@gmail.com>
Cc: Thomas Gleixner <tglx@linutronix.de>
Cc: Ingo Molnar <mingo@redhat.com>
Cc: x86@kernel.org
Cc: Samuel Neves <sneves@dei.uc.pt>
Cc: Jean-Philippe Aumasson <jeanphilippe.aumasson@gmail.com>
Cc: Andy Lutomirski <luto@kernel.org>
Cc: Greg KH <gregkh@linuxfoundation.org>
Cc: Andrew Morton <akpm@linux-foundation.org>
Cc: Linus Torvalds <torvalds@linux-foundation.org>
Cc: kernel-hardening@lists.openwall.com
Cc: linux-crypto@vger.kernel.org
Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>
---
lib/zinc/curve25519/curve25519-x86_64-glue.c | 48
lib/zinc/curve25519/curve25519-x86_64.c | 2333 +++++++++++++++++++++++++++
lib/zinc/curve25519/curve25519.c | 4
3 files changed, 2385 insertions(+)
diff --git a/lib/zinc/curve25519/curve25519-x86_64-glue.c b/lib/zinc/curve25519/curve25519-x86_64-glue.c
new file mode 100644
index 000000000000..f79c1422a106
--- /dev/null
+++ b/lib/zinc/curve25519/curve25519-x86_64-glue.c
@@ -0,0 +1,48 @@
+// SPDX-License-Identifier: GPL-2.0 OR MIT
+/*
+ * Copyright (C) 2015-2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ */
+
+#include <asm/cpufeature.h>
+#include <asm/processor.h>
+
+#include "curve25519-x86_64.c"
+
+static bool curve25519_use_bmi2 __ro_after_init;
+static bool curve25519_use_adx __ro_after_init;
+static bool *const curve25519_nobs[] __initconst = {
+ &curve25519_use_bmi2, &curve25519_use_adx };
+
+static void __init curve25519_fpu_init(void)
+{
+ curve25519_use_bmi2 = boot_cpu_has(X86_FEATURE_BMI2);
+ curve25519_use_adx = boot_cpu_has(X86_FEATURE_BMI2) &&
+ boot_cpu_has(X86_FEATURE_ADX);
+}
+
+static inline bool curve25519_arch(u8 mypublic[CURVE25519_KEY_SIZE],
+ const u8 secret[CURVE25519_KEY_SIZE],
+ const u8 basepoint[CURVE25519_KEY_SIZE])
+{
+ if (curve25519_use_adx) {
+ curve25519_adx(mypublic, secret, basepoint);
+ return true;
+ } else if (curve25519_use_bmi2) {
+ curve25519_bmi2(mypublic, secret, basepoint);
+ return true;
+ }
+ return false;
+}
+
+static inline bool curve25519_base_arch(u8 pub[CURVE25519_KEY_SIZE],
+ const u8 secret[CURVE25519_KEY_SIZE])
+{
+ if (curve25519_use_adx) {
+ curve25519_adx_base(pub, secret);
+ return true;
+ } else if (curve25519_use_bmi2) {
+ curve25519_bmi2_base(pub, secret);
+ return true;
+ }
+ return false;
+}
diff --git a/lib/zinc/curve25519/curve25519-x86_64.c b/lib/zinc/curve25519/curve25519-x86_64.c
new file mode 100644
index 000000000000..db5e2e619e64
--- /dev/null
+++ b/lib/zinc/curve25519/curve25519-x86_64.c
@@ -0,0 +1,2333 @@
+// SPDX-License-Identifier: GPL-2.0 OR LGPL-2.1
+/*
+ * Copyright (c) 2017 Armando Faz <armfazh@ic.unicamp.br>. All Rights Reserved.
+ * Copyright (C) 2018 Jason A. Donenfeld <Jason@zx2c4.com>. All Rights Reserved.
+ * Copyright (C) 2018 Samuel Neves <sneves@dei.uc.pt>. All Rights Reserved.
+ */
+
+enum { NUM_WORDS_ELTFP25519 = 4 };
+typedef __aligned(32) u64 eltfp25519_1w[NUM_WORDS_ELTFP25519];
+typedef __aligned(32) u64 eltfp25519_1w_buffer[2 * NUM_WORDS_ELTFP25519];
+
+#define mul_eltfp25519_1w_adx(c, a, b) do { \
+ mul_256x256_integer_adx(m.buffer, a, b); \
+ red_eltfp25519_1w_adx(c, m.buffer); \
+} while (0)
+
+#define mul_eltfp25519_1w_bmi2(c, a, b) do { \
+ mul_256x256_integer_bmi2(m.buffer, a, b); \
+ red_eltfp25519_1w_bmi2(c, m.buffer); \
+} while (0)
+
+#define sqr_eltfp25519_1w_adx(a) do { \
+ sqr_256x256_integer_adx(m.buffer, a); \
+ red_eltfp25519_1w_adx(a, m.buffer); \
+} while (0)
+
+#define sqr_eltfp25519_1w_bmi2(a) do { \
+ sqr_256x256_integer_bmi2(m.buffer, a); \
+ red_eltfp25519_1w_bmi2(a, m.buffer); \
+} while (0)
+
+#define mul_eltfp25519_2w_adx(c, a, b) do { \
+ mul2_256x256_integer_adx(m.buffer, a, b); \
+ red_eltfp25519_2w_adx(c, m.buffer); \
+} while (0)
+
+#define mul_eltfp25519_2w_bmi2(c, a, b) do { \
+ mul2_256x256_integer_bmi2(m.buffer, a, b); \
+ red_eltfp25519_2w_bmi2(c, m.buffer); \
+} while (0)
+
+#define sqr_eltfp25519_2w_adx(a) do { \
+ sqr2_256x256_integer_adx(m.buffer, a); \
+ red_eltfp25519_2w_adx(a, m.buffer); \
+} while (0)
+
+#define sqr_eltfp25519_2w_bmi2(a) do { \
+ sqr2_256x256_integer_bmi2(m.buffer, a); \
+ red_eltfp25519_2w_bmi2(a, m.buffer); \
+} while (0)
+
+#define sqrn_eltfp25519_1w_adx(a, times) do { \
+ int ____counter = (times); \
+ while (____counter-- > 0) \
+ sqr_eltfp25519_1w_adx(a); \
+} while (0)
+
+#define sqrn_eltfp25519_1w_bmi2(a, times) do { \
+ int ____counter = (times); \
+ while (____counter-- > 0) \
+ sqr_eltfp25519_1w_bmi2(a); \
+} while (0)
+
+#define copy_eltfp25519_1w(C, A) do { \
+ (C)[0] = (A)[0]; \
+ (C)[1] = (A)[1]; \
+ (C)[2] = (A)[2]; \
+ (C)[3] = (A)[3]; \
+} while (0)
+
+#define setzero_eltfp25519_1w(C) do { \
+ (C)[0] = 0; \
+ (C)[1] = 0; \
+ (C)[2] = 0; \
+ (C)[3] = 0; \
+} while (0)
+
+__aligned(32) static const u64 table_ladder_8k[252 * NUM_WORDS_ELTFP25519] = {
+ /* 1 */ 0xfffffffffffffff3UL, 0xffffffffffffffffUL,
+ 0xffffffffffffffffUL, 0x5fffffffffffffffUL,
+ /* 2 */ 0x6b8220f416aafe96UL, 0x82ebeb2b4f566a34UL,
+ 0xd5a9a5b075a5950fUL, 0x5142b2cf4b2488f4UL,
+ /* 3 */ 0x6aaebc750069680cUL, 0x89cf7820a0f99c41UL,
+ 0x2a58d9183b56d0f4UL, 0x4b5aca80e36011a4UL,
+ /* 4 */ 0x329132348c29745dUL, 0xf4a2e616e1642fd7UL,
+ 0x1e45bb03ff67bc34UL, 0x306912d0f42a9b4aUL,
+ /* 5 */ 0xff886507e6af7154UL, 0x04f50e13dfeec82fUL,
+ 0xaa512fe82abab5ceUL, 0x174e251a68d5f222UL,
+ /* 6 */ 0xcf96700d82028898UL, 0x1743e3370a2c02c5UL,
+ 0x379eec98b4e86eaaUL, 0x0c59888a51e0482eUL,
+ /* 7 */ 0xfbcbf1d699b5d189UL, 0xacaef0d58e9fdc84UL,
+ 0xc1c20d06231f7614UL, 0x2938218da274f972UL,
+ /* 8 */ 0xf6af49beff1d7f18UL, 0xcc541c22387ac9c2UL,
+ 0x96fcc9ef4015c56bUL, 0x69c1627c690913a9UL,
+ /* 9 */ 0x7a86fd2f4733db0eUL, 0xfdb8c4f29e087de9UL,
+ 0x095e4b1a8ea2a229UL, 0x1ad7a7c829b37a79UL,
+ /* 10 */ 0x342d89cad17ea0c0UL, 0x67bedda6cced2051UL,
+ 0x19ca31bf2bb42f74UL, 0x3df7b4c84980acbbUL,
+ /* 11 */ 0xa8c6444dc80ad883UL, 0xb91e440366e3ab85UL,
+ 0xc215cda00164f6d8UL, 0x3d867c6ef247e668UL,
+ /* 12 */ 0xc7dd582bcc3e658cUL, 0xfd2c4748ee0e5528UL,
+ 0xa0fd9b95cc9f4f71UL, 0x7529d871b0675ddfUL,
+ /* 13 */ 0xb8f568b42d3cbd78UL, 0x1233011b91f3da82UL,
+ 0x2dce6ccd4a7c3b62UL, 0x75e7fc8e9e498603UL,
+ /* 14 */ 0x2f4f13f1fcd0b6ecUL, 0xf1a8ca1f29ff7a45UL,
+ 0xc249c1a72981e29bUL, 0x6ebe0dbb8c83b56aUL,
+ /* 15 */ 0x7114fa8d170bb222UL, 0x65a2dcd5bf93935fUL,
+ 0xbdc41f68b59c979aUL, 0x2f0eef79a2ce9289UL,
+ /* 16 */ 0x42ecbf0c083c37ceUL, 0x2930bc09ec496322UL,
+ 0xf294b0c19cfeac0dUL, 0x3780aa4bedfabb80UL,
+ /* 17 */ 0x56c17d3e7cead929UL, 0xe7cb4beb2e5722c5UL,
+ 0x0ce931732dbfe15aUL, 0x41b883c7621052f8UL,
+ /* 18 */ 0xdbf75ca0c3d25350UL, 0x2936be086eb1e351UL,
+ 0xc936e03cb4a9b212UL, 0x1d45bf82322225aaUL,
+ /* 19 */ 0xe81ab1036a024cc5UL, 0xe212201c304c9a72UL,
+ 0xc5d73fba6832b1fcUL, 0x20ffdb5a4d839581UL,
+ /* 20 */ 0xa283d367be5d0fadUL, 0x6c2b25ca8b164475UL,
+ 0x9d4935467caaf22eUL, 0x5166408eee85ff49UL,
+ /* 21 */ 0x3c67baa2fab4e361UL, 0xb3e433c67ef35cefUL,
+ 0x5259729241159b1cUL, 0x6a621892d5b0ab33UL,
+ /* 22 */ 0x20b74a387555cdcbUL, 0x532aa10e1208923fUL,
+ 0xeaa17b7762281dd1UL, 0x61ab3443f05c44bfUL,
+ /* 23 */ 0x257a6c422324def8UL, 0x131c6c1017e3cf7fUL,
+ 0x23758739f630a257UL, 0x295a407a01a78580UL,
+ /* 24 */ 0xf8c443246d5da8d9UL, 0x19d775450c52fa5dUL,
+ 0x2afcfc92731bf83dUL, 0x7d10c8e81b2b4700UL,
+ /* 25 */ 0xc8e0271f70baa20bUL, 0x993748867ca63957UL,
+ 0x5412efb3cb7ed4bbUL, 0x3196d36173e62975UL,
+ /* 26 */ 0xde5bcad141c7dffcUL, 0x47cc8cd2b395c848UL,
+ 0xa34cd942e11af3cbUL, 0x0256dbf2d04ecec2UL,
+ /* 27 */ 0x875ab7e94b0e667fUL, 0xcad4dd83c0850d10UL,
+ 0x47f12e8f4e72c79fUL, 0x5f1a87bb8c85b19bUL,
+ /* 28 */ 0x7ae9d0b6437f51b8UL, 0x12c7ce5518879065UL,
+ 0x2ade09fe5cf77aeeUL, 0x23a05a2f7d2c5627UL,
+ /* 29 */ 0x5908e128f17c169aUL, 0xf77498dd8ad0852dUL,
+ 0x74b4c4ceab102f64UL, 0x183abadd10139845UL,
+ /* 30 */ 0xb165ba8daa92aaacUL, 0xd5c5ef9599386705UL,
+ 0xbe2f8f0cf8fc40d1UL, 0x2701e635ee204514UL,
+ /* 31 */ 0x629fa80020156514UL, 0xf223868764a8c1ceUL,
+ 0x5b894fff0b3f060eUL, 0x60d9944cf708a3faUL,
+ /* 32 */ 0xaeea001a1c7a201fUL, 0xebf16a633ee2ce63UL,
+ 0x6f7709594c7a07e1UL, 0x79b958150d0208cbUL,
+ /* 33 */ 0x24b55e5301d410e7UL, 0xe3a34edff3fdc84dUL,
+ 0xd88768e4904032d8UL, 0x131384427b3aaeecUL,
+ /* 34 */ 0x8405e51286234f14UL, 0x14dc4739adb4c529UL,
+ 0xb8a2b5b250634ffdUL, 0x2fe2a94ad8a7ff93UL,
+ /* 35 */ 0xec5c57efe843faddUL, 0x2843ce40f0bb9918UL,
+ 0xa4b561d6cf3d6305UL, 0x743629bde8fb777eUL,
+ /* 36 */ 0x343edd46bbaf738fUL, 0xed981828b101a651UL,
+ 0xa401760b882c797aUL, 0x1fc223e28dc88730UL,
+ /* 37 */ 0x48604e91fc0fba0eUL, 0xb637f78f052c6fa4UL,
+ 0x91ccac3d09e9239cUL, 0x23f7eed4437a687cUL,
+ /* 38 */ 0x5173b1118d9bd800UL, 0x29d641b63189d4a7UL,
+ 0xfdbf177988bbc586UL, 0x2959894fcad81df5UL,
+ /* 39 */ 0xaebc8ef3b4bbc899UL, 0x4148995ab26992b9UL,
+ 0x24e20b0134f92cfbUL, 0x40d158894a05dee8UL,
+ /* 40 */ 0x46b00b1185af76f6UL, 0x26bac77873187a79UL,
+ 0x3dc0bf95ab8fff5fUL, 0x2a608bd8945524d7UL,
+ /* 41 */ 0x26449588bd446302UL, 0x7c4bc21c0388439cUL,
+ 0x8e98a4f383bd11b2UL, 0x26218d7bc9d876b9UL,
+ /* 42 */ 0xe3081542997c178aUL, 0x3c2d29a86fb6606fUL,
+ 0x5c217736fa279374UL, 0x7dde05734afeb1faUL,
+ /* 43 */ 0x3bf10e3906d42babUL, 0xe4f7803e1980649cUL,
+ 0xe6053bf89595bf7aUL, 0x394faf38da245530UL,
+ /* 44 */ 0x7a8efb58896928f4UL, 0xfbc778e9cc6a113cUL,
+ 0x72670ce330af596fUL, 0x48f222a81d3d6cf7UL,
+ /* 45 */ 0xf01fce410d72caa7UL, 0x5a20ecc7213b5595UL,
+ 0x7bc21165c1fa1483UL, 0x07f89ae31da8a741UL,
+ /* 46 */ 0x05d2c2b4c6830ff9UL, 0xd43e330fc6316293UL,
+ 0xa5a5590a96d3a904UL, 0x705edb91a65333b6UL,
+ /* 47 */ 0x048ee15e0bb9a5f7UL, 0x3240cfca9e0aaf5dUL,
+ 0x8f4b71ceedc4a40bUL, 0x621c0da3de544a6dUL,
+ /* 48 */ 0x92872836a08c4091UL, 0xce8375b010c91445UL,
+ 0x8a72eb524f276394UL, 0x2667fcfa7ec83635UL,
+ /* 49 */ 0x7f4c173345e8752aUL, 0x061b47feee7079a5UL,
+ 0x25dd9afa9f86ff34UL, 0x3780cef5425dc89cUL,
+ /* 50 */ 0x1a46035a513bb4e9UL, 0x3e1ef379ac575adaUL,
+ 0xc78c5f1c5fa24b50UL, 0x321a967634fd9f22UL,
+ /* 51 */ 0x946707b8826e27faUL, 0x3dca84d64c506fd0UL,
+ 0xc189218075e91436UL, 0x6d9284169b3b8484UL,
+ /* 52 */ 0x3a67e840383f2ddfUL, 0x33eec9a30c4f9b75UL,
+ 0x3ec7c86fa783ef47UL, 0x26ec449fbac9fbc4UL,
+ /* 53 */ 0x5c0f38cba09b9e7dUL, 0x81168cc762a3478cUL,
+ 0x3e23b0d306fc121cUL, 0x5a238aa0a5efdcddUL,
+ /* 54 */ 0x1ba26121c4ea43ffUL, 0x36f8c77f7c8832b5UL,
+ 0x88fbea0b0adcf99aUL, 0x5ca9938ec25bebf9UL,
+ /* 55 */ 0xd5436a5e51fccda0UL, 0x1dbc4797c2cd893bUL,
+ 0x19346a65d3224a08UL, 0x0f5034e49b9af466UL,
+ /* 56 */ 0xf23c3967a1e0b96eUL, 0xe58b08fa867a4d88UL,
+ 0xfb2fabc6a7341679UL, 0x2a75381eb6026946UL,
+ /* 57 */ 0xc80a3be4c19420acUL, 0x66b1f6c681f2b6dcUL,
+ 0x7cf7036761e93388UL, 0x25abbbd8a660a4c4UL,
+ /* 58 */ 0x91ea12ba14fd5198UL, 0x684950fc4a3cffa9UL,
+ 0xf826842130f5ad28UL, 0x3ea988f75301a441UL,
+ /* 59 */ 0xc978109a695f8c6fUL, 0x1746eb4a0530c3f3UL,
+ 0x444d6d77b4459995UL, 0x75952b8c054e5cc7UL,
+ /* 60 */ 0xa3703f7915f4d6aaUL, 0x66c346202f2647d8UL,
+ 0xd01469df811d644bUL, 0x77fea47d81a5d71fUL,
+ /* 61 */ 0xc5e9529ef57ca381UL, 0x6eeeb4b9ce2f881aUL,
+ 0xb6e91a28e8009bd6UL, 0x4b80be3e9afc3fecUL,
+ /* 62 */ 0x7e3773c526aed2c5UL, 0x1b4afcb453c9a49dUL,
+ 0xa920bdd7baffb24dUL, 0x7c54699f122d400eUL,
+ /* 63 */ 0xef46c8e14fa94bc8UL, 0xe0b074ce2952ed5eUL,
+ 0xbea450e1dbd885d5UL, 0x61b68649320f712cUL,
+ /* 64 */ 0x8a485f7309ccbdd1UL, 0xbd06320d7d4d1a2dUL,
+ 0x25232973322dbef4UL, 0x445dc4758c17f770UL,
+ /* 65 */ 0xdb0434177cc8933cUL, 0xed6fe82175ea059fUL,
+ 0x1efebefdc053db34UL, 0x4adbe867c65daf99UL,
+ /* 66 */ 0x3acd71a2a90609dfUL, 0xe5e991856dd04050UL,
+ 0x1ec69b688157c23cUL, 0x697427f6885cfe4dUL,
+ /* 67 */ 0xd7be7b9b65e1a851UL, 0xa03d28d522c536ddUL,
+ 0x28399d658fd2b645UL, 0x49e5b7e17c2641e1UL,
+ /* 68 */ 0x6f8c3a98700457a4UL, 0x5078f0a25ebb6778UL,
+ 0xd13c3ccbc382960fUL, 0x2e003258a7df84b1UL,
+ /* 69 */ 0x8ad1f39be6296a1cUL, 0xc1eeaa652a5fbfb2UL,
+ 0x33ee0673fd26f3cbUL, 0x59256173a69d2cccUL,
+ /* 70 */ 0x41ea07aa4e18fc41UL, 0xd9fc19527c87a51eUL,
+ 0xbdaacb805831ca6fUL, 0x445b652dc916694fUL,
+ /* 71 */ 0xce92a3a7f2172315UL, 0x1edc282de11b9964UL,
+ 0xa1823aafe04c314aUL, 0x790a2d94437cf586UL,
+ /* 72 */ 0x71c447fb93f6e009UL, 0x8922a56722845276UL,
+ 0xbf70903b204f5169UL, 0x2f7a89891ba319feUL,
+ /* 73 */ 0x02a08eb577e2140cUL, 0xed9a4ed4427bdcf4UL,
+ 0x5253ec44e4323cd1UL, 0x3e88363c14e9355bUL,
+ /* 74 */ 0xaa66c14277110b8cUL, 0x1ae0391610a23390UL,
+ 0x2030bd12c93fc2a2UL, 0x3ee141579555c7abUL,
+ /* 75 */ 0x9214de3a6d6e7d41UL, 0x3ccdd88607f17efeUL,
+ 0x674f1288f8e11217UL, 0x5682250f329f93d0UL,
+ /* 76 */ 0x6cf00b136d2e396eUL, 0x6e4cf86f1014debfUL,
+ 0x5930b1b5bfcc4e83UL, 0x047069b48aba16b6UL,
+ /* 77 */ 0x0d4ce4ab69b20793UL, 0xb24db91a97d0fb9eUL,
+ 0xcdfa50f54e00d01dUL, 0x221b1085368bddb5UL,
+ /* 78 */ 0xe7e59468b1e3d8d2UL, 0x53c56563bd122f93UL,
+ 0xeee8a903e0663f09UL, 0x61efa662cbbe3d42UL,
+ /* 79 */ 0x2cf8ddddde6eab2aUL, 0x9bf80ad51435f231UL,
+ 0x5deadacec9f04973UL, 0x29275b5d41d29b27UL,
+ /* 80 */ 0xcfde0f0895ebf14fUL, 0xb9aab96b054905a7UL,
+ 0xcae80dd9a1c420fdUL, 0x0a63bf2f1673bbc7UL,
+ /* 81 */ 0x092f6e11958fbc8cUL, 0x672a81e804822fadUL,
+ 0xcac8351560d52517UL, 0x6f3f7722c8f192f8UL,
+ /* 82 */ 0xf8ba90ccc2e894b7UL, 0x2c7557a438ff9f0dUL,
+ 0x894d1d855ae52359UL, 0x68e122157b743d69UL,
+ /* 83 */ 0xd87e5570cfb919f3UL, 0x3f2cdecd95798db9UL,
+ 0x2121154710c0a2ceUL, 0x3c66a115246dc5b2UL,
+ /* 84 */ 0xcbedc562294ecb72UL, 0xba7143c36a280b16UL,
+ 0x9610c2efd4078b67UL, 0x6144735d946a4b1eUL,
+ /* 85 */ 0x536f111ed75b3350UL, 0x0211db8c2041d81bUL,
+ 0xf93cb1000e10413cUL, 0x149dfd3c039e8876UL,
+ /* 86 */ 0xd479dde46b63155bUL, 0xb66e15e93c837976UL,
+ 0xdafde43b1f13e038UL, 0x5fafda1a2e4b0b35UL,
+ /* 87 */ 0x3600bbdf17197581UL, 0x3972050bbe3cd2c2UL,
+ 0x5938906dbdd5be86UL, 0x34fce5e43f9b860fUL,
+ /* 88 */ 0x75a8a4cd42d14d02UL, 0x828dabc53441df65UL,
+ 0x33dcabedd2e131d3UL, 0x3ebad76fb814d25fUL,
+ /* 89 */ 0xd4906f566f70e10fUL, 0x5d12f7aa51690f5aUL,
+ 0x45adb16e76cefcf2UL, 0x01f768aead232999UL,
+ /* 90 */ 0x2b6cc77b6248febdUL, 0x3cd30628ec3aaffdUL,
+ 0xce1c0b80d4ef486aUL, 0x4c3bff2ea6f66c23UL,
+ /* 91 */ 0x3f2ec4094aeaeb5fUL, 0x61b19b286e372ca7UL,
+ 0x5eefa966de2a701dUL, 0x23b20565de55e3efUL,
+ /* 92 */ 0xe301ca5279d58557UL, 0x07b2d4ce27c2874fUL,
+ 0xa532cd8a9dcf1d67UL, 0x2a52fee23f2bff56UL,
+ /* 93 */ 0x8624efb37cd8663dUL, 0xbbc7ac20ffbd7594UL,
+ 0x57b85e9c82d37445UL, 0x7b3052cb86a6ec66UL,
+ /* 94 */ 0x3482f0ad2525e91eUL, 0x2cb68043d28edca0UL,
+ 0xaf4f6d052e1b003aUL, 0x185f8c2529781b0aUL,
+ /* 95 */ 0xaa41de5bd80ce0d6UL, 0x9407b2416853e9d6UL,
+ 0x563ec36e357f4c3aUL, 0x4cc4b8dd0e297bceUL,
+ /* 96 */ 0xa2fc1a52ffb8730eUL, 0x1811f16e67058e37UL,
+ 0x10f9a366cddf4ee1UL, 0x72f4a0c4a0b9f099UL,
+ /* 97 */ 0x8c16c06f663f4ea7UL, 0x693b3af74e970fbaUL,
+ 0x2102e7f1d69ec345UL, 0x0ba53cbc968a8089UL,
+ /* 98 */ 0xca3d9dc7fea15537UL, 0x4c6824bb51536493UL,
+ 0xb9886314844006b1UL, 0x40d2a72ab454cc60UL,
+ /* 99 */ 0x5936a1b712570975UL, 0x91b9d648debda657UL,
+ 0x3344094bb64330eaUL, 0x006ba10d12ee51d0UL,
+ /* 100 */ 0x19228468f5de5d58UL, 0x0eb12f4c38cc05b0UL,
+ 0xa1039f9dd5601990UL, 0x4502d4ce4fff0e0bUL,
+ /* 101 */ 0xeb2054106837c189UL, 0xd0f6544c6dd3b93cUL,
+ 0x40727064c416d74fUL, 0x6e15c6114b502ef0UL,
+ /* 102 */ 0x4df2a398cfb1a76bUL, 0x11256c7419f2f6b1UL,
+ 0x4a497962066e6043UL, 0x705b3aab41355b44UL,
+ /* 103 */ 0x365ef536d797b1d8UL, 0x00076bd622ddf0dbUL,
+ 0x3bbf33b0e0575a88UL, 0x3777aa05c8e4ca4dUL,
+ /* 104 */ 0x392745c85578db5fUL, 0x6fda4149dbae5ae2UL,
+ 0xb1f0b00b8adc9867UL, 0x09963437d36f1da3UL,
+ /* 105 */ 0x7e824e90a5dc3853UL, 0xccb5f6641f135cbdUL,
+ 0x6736d86c87ce8fccUL, 0x625f3ce26604249fUL,
+ /* 106 */ 0xaf8ac8059502f63fUL, 0x0c05e70a2e351469UL,
+ 0x35292e9c764b6305UL, 0x1a394360c7e23ac3UL,
+ /* 107 */ 0xd5c6d53251183264UL, 0x62065abd43c2b74fUL,
+ 0xb5fbf5d03b973f9bUL, 0x13a3da3661206e5eUL,
+ /* 108 */ 0xc6bd5837725d94e5UL, 0x18e30912205016c5UL,
+ 0x2088ce1570033c68UL, 0x7fba1f495c837987UL,
+ /* 109 */ 0x5a8c7423f2f9079dUL, 0x1735157b34023fc5UL,
+ 0xe4f9b49ad2fab351UL, 0x6691ff72c878e33cUL,
+ /* 110 */ 0x122c2adedc5eff3eUL, 0xf8dd4bf1d8956cf4UL,
+ 0xeb86205d9e9e5bdaUL, 0x049b92b9d975c743UL,
+ /* 111 */ 0xa5379730b0f6c05aUL, 0x72a0ffacc6f3a553UL,
+ 0xb0032c34b20dcd6dUL, 0x470e9dbc88d5164aUL,
+ /* 112 */ 0xb19cf10ca237c047UL, 0xb65466711f6c81a2UL,
+ 0xb3321bd16dd80b43UL, 0x48c14f600c5fbe8eUL,
+ /* 113 */ 0x66451c264aa6c803UL, 0xb66e3904a4fa7da6UL,
+ 0xd45f19b0b3128395UL, 0x31602627c3c9bc10UL,
+ /* 114 */ 0x3120dc4832e4e10dUL, 0xeb20c46756c717f7UL,
+ 0x00f52e3f67280294UL, 0x566d4fc14730c509UL,
+ /* 115 */ 0x7e3a5d40fd837206UL, 0xc1e926dc7159547aUL,
+ 0x216730fba68d6095UL, 0x22e8c3843f69cea7UL,
+ /* 116 */ 0x33d074e8930e4b2bUL, 0xb6e4350e84d15816UL,
+ 0x5534c26ad6ba2365UL, 0x7773c12f89f1f3f3UL,
+ /* 117 */ 0x8cba404da57962aaUL, 0x5b9897a81999ce56UL,
+ 0x508e862f121692fcUL, 0x3a81907fa093c291UL,
+ /* 118 */ 0x0dded0ff4725a510UL, 0x10d8cc10673fc503UL,
+ 0x5b9d151c9f1f4e89UL, 0x32a5c1d5cb09a44cUL,
+ /* 119 */ 0x1e0aa442b90541fbUL, 0x5f85eb7cc1b485dbUL,
+ 0xbee595ce8a9df2e5UL, 0x25e496c722422236UL,
+ /* 120 */ 0x5edf3c46cd0fe5b9UL, 0x34e75a7ed2a43388UL,
+ 0xe488de11d761e352UL, 0x0e878a01a085545cUL,
+ /* 121 */ 0xba493c77e021bb04UL, 0x2b4d1843c7df899aUL,
+ 0x9ea37a487ae80d67UL, 0x67a9958011e41794UL,
+ /* 122 */ 0x4b58051a6697b065UL, 0x47e33f7d8d6ba6d4UL,
+ 0xbb4da8d483ca46c1UL, 0x68becaa181c2db0dUL,
+ /* 123 */ 0x8d8980e90b989aa5UL, 0xf95eb14a2c93c99bUL,
+ 0x51c6c7c4796e73a2UL, 0x6e228363b5efb569UL,
+ /* 124 */ 0xc6bbc0b02dd624c8UL, 0x777eb47dec8170eeUL,
+ 0x3cde15a004cfafa9UL, 0x1dc6bc087160bf9bUL,
+ /* 125 */ 0x2e07e043eec34002UL, 0x18e9fc677a68dc7fUL,
+ 0xd8da03188bd15b9aUL, 0x48fbc3bb00568253UL,
+ /* 126 */ 0x57547d4cfb654ce1UL, 0xd3565b82a058e2adUL,
+ 0xf63eaf0bbf154478UL, 0x47531ef114dfbb18UL,
+ /* 127 */ 0xe1ec630a4278c587UL, 0x5507d546ca8e83f3UL,
+ 0x85e135c63adc0c2bUL, 0x0aa7efa85682844eUL,
+ /* 128 */ 0x72691ba8b3e1f615UL, 0x32b4e9701fbe3ffaUL,
+ 0x97b6d92e39bb7868UL, 0x2cfe53dea02e39e8UL,
+ /* 129 */ 0x687392cd85cd52b0UL, 0x27ff66c910e29831UL,
+ 0x97134556a9832d06UL, 0x269bb0360a84f8a0UL,
+ /* 130 */ 0x706e55457643f85cUL, 0x3734a48c9b597d1bUL,
+ 0x7aee91e8c6efa472UL, 0x5cd6abc198a9d9e0UL,
+ /* 131 */ 0x0e04de06cb3ce41aUL, 0xd8c6eb893402e138UL,
+ 0x904659bb686e3772UL, 0x7215c371746ba8c8UL,
+ /* 132 */ 0xfd12a97eeae4a2d9UL, 0x9514b7516394f2c5UL,
+ 0x266fd5809208f294UL, 0x5c847085619a26b9UL,
+ /* 133 */ 0x52985410fed694eaUL, 0x3c905b934a2ed254UL,
+ 0x10bb47692d3be467UL, 0x063b3d2d69e5e9e1UL,
+ /* 134 */ 0x472726eedda57debUL, 0xefb6c4ae10f41891UL,
+ 0x2b1641917b307614UL, 0x117c554fc4f45b7cUL,
+ /* 135 */ 0xc07cf3118f9d8812UL, 0x01dbd82050017939UL,
+ 0xd7e803f4171b2827UL, 0x1015e87487d225eaUL,
+ /* 136 */ 0xc58de3fed23acc4dUL, 0x50db91c294a7be2dUL,
+ 0x0b94d43d1c9cf457UL, 0x6b1640fa6e37524aUL,
+ /* 137 */ 0x692f346c5fda0d09UL, 0x200b1c59fa4d3151UL,
+ 0xb8c46f760777a296UL, 0x4b38395f3ffdfbcfUL,
+ /* 138 */ 0x18d25e00be54d671UL, 0x60d50582bec8aba6UL,
+ 0x87ad8f263b78b982UL, 0x50fdf64e9cda0432UL,
+ /* 139 */ 0x90f567aac578dcf0UL, 0xef1e9b0ef2a3133bUL,
+ 0x0eebba9242d9de71UL, 0x15473c9bf03101c7UL,
+ /* 140 */ 0x7c77e8ae56b78095UL, 0xb678e7666e6f078eUL,
+ 0x2da0b9615348ba1fUL, 0x7cf931c1ff733f0bUL,
+ /* 141 */ 0x26b357f50a0a366cUL, 0xe9708cf42b87d732UL,
+ 0xc13aeea5f91cb2c0UL, 0x35d90c991143bb4cUL,
+ /* 142 */ 0x47c1c404a9a0d9dcUL, 0x659e58451972d251UL,
+ 0x3875a8c473b38c31UL, 0x1fbd9ed379561f24UL,
+ /* 143 */ 0x11fabc6fd41ec28dUL, 0x7ef8dfe3cd2a2dcaUL,
+ 0x72e73b5d8c404595UL, 0x6135fa4954b72f27UL,
+ /* 144 */ 0xccfc32a2de24b69cUL, 0x3f55698c1f095d88UL,
+ 0xbe3350ed5ac3f929UL, 0x5e9bf806ca477eebUL,
+ /* 145 */ 0xe9ce8fb63c309f68UL, 0x5376f63565e1f9f4UL,
+ 0xd1afcfb35a6393f1UL, 0x6632a1ede5623506UL,
+ /* 146 */ 0x0b7d6c390c2ded4cUL, 0x56cb3281df04cb1fUL,
+ 0x66305a1249ecc3c7UL, 0x5d588b60a38ca72aUL,
+ /* 147 */ 0xa6ecbf78e8e5f42dUL, 0x86eeb44b3c8a3eecUL,
+ 0xec219c48fbd21604UL, 0x1aaf1af517c36731UL,
+ /* 148 */ 0xc306a2836769bde7UL, 0x208280622b1e2adbUL,
+ 0x8027f51ffbff94a6UL, 0x76cfa1ce1124f26bUL,
+ /* 149 */ 0x18eb00562422abb6UL, 0xf377c4d58f8c29c3UL,
+ 0x4dbbc207f531561aUL, 0x0253b7f082128a27UL,
+ /* 150 */ 0x3d1f091cb62c17e0UL, 0x4860e1abd64628a9UL,
+ 0x52d17436309d4253UL, 0x356f97e13efae576UL,
+ /* 151 */ 0xd351e11aa150535bUL, 0x3e6b45bb1dd878ccUL,
+ 0x0c776128bed92c98UL, 0x1d34ae93032885b8UL,
+ /* 152 */ 0x4ba0488ca85ba4c3UL, 0x985348c33c9ce6ceUL,
+ 0x66124c6f97bda770UL, 0x0f81a0290654124aUL,
+ /* 153 */ 0x9ed09ca6569b86fdUL, 0x811009fd18af9a2dUL,
+ 0xff08d03f93d8c20aUL, 0x52a148199faef26bUL,
+ /* 154 */ 0x3e03f9dc2d8d1b73UL, 0x4205801873961a70UL,
+ 0xc0d987f041a35970UL, 0x07aa1f15a1c0d549UL,
+ /* 155 */ 0xdfd46ce08cd27224UL, 0x6d0a024f934e4239UL,
+ 0x808a7a6399897b59UL, 0x0a4556e9e13d95a2UL,
+ /* 156 */ 0xd21a991fe9c13045UL, 0x9b0e8548fe7751b8UL,
+ 0x5da643cb4bf30035UL, 0x77db28d63940f721UL,
+ /* 157 */ 0xfc5eeb614adc9011UL, 0x5229419ae8c411ebUL,
+ 0x9ec3e7787d1dcf74UL, 0x340d053e216e4cb5UL,
+ /* 158 */ 0xcac7af39b48df2b4UL, 0xc0faec2871a10a94UL,
+ 0x140a69245ca575edUL, 0x0cf1c37134273a4cUL,
+ /* 159 */ 0xc8ee306ac224b8a5UL, 0x57eaee7ccb4930b0UL,
+ 0xa1e806bdaacbe74fUL, 0x7d9a62742eeb657dUL,
+ /* 160 */ 0x9eb6b6ef546c4830UL, 0x885cca1fddb36e2eUL,
+ 0xe6b9f383ef0d7105UL, 0x58654fef9d2e0412UL,
+ /* 161 */ 0xa905c4ffbe0e8e26UL, 0x942de5df9b31816eUL,
+ 0x497d723f802e88e1UL, 0x30684dea602f408dUL,
+ /* 162 */ 0x21e5a278a3e6cb34UL, 0xaefb6e6f5b151dc4UL,
+ 0xb30b8e049d77ca15UL, 0x28c3c9cf53b98981UL,
+ /* 163 */ 0x287fb721556cdd2aUL, 0x0d317ca897022274UL,
+ 0x7468c7423a543258UL, 0x4a7f11464eb5642fUL,
+ /* 164 */ 0xa237a4774d193aa6UL, 0xd865986ea92129a1UL,
+ 0x24c515ecf87c1a88UL, 0x604003575f39f5ebUL,
+ /* 165 */ 0x47b9f189570a9b27UL, 0x2b98cede465e4b78UL,
+ 0x026df551dbb85c20UL, 0x74fcd91047e21901UL,
+ /* 166 */ 0x13e2a90a23c1bfa3UL, 0x0cb0074e478519f6UL,
+ 0x5ff1cbbe3af6cf44UL, 0x67fe5438be812dbeUL,
+ /* 167 */ 0xd13cf64fa40f05b0UL, 0x054dfb2f32283787UL,
+ 0x4173915b7f0d2aeaUL, 0x482f144f1f610d4eUL,
+ /* 168 */ 0xf6210201b47f8234UL, 0x5d0ae1929e70b990UL,
+ 0xdcd7f455b049567cUL, 0x7e93d0f1f0916f01UL,
+ /* 169 */ 0xdd79cbf18a7db4faUL, 0xbe8391bf6f74c62fUL,
+ 0x027145d14b8291bdUL, 0x585a73ea2cbf1705UL,
+ /* 170 */ 0x485ca03e928a0db2UL, 0x10fc01a5742857e7UL,
+ 0x2f482edbd6d551a7UL, 0x0f0433b5048fdb8aUL,
+ /* 171 */ 0x60da2e8dd7dc6247UL, 0x88b4c9d38cd4819aUL,
+ 0x13033ac001f66697UL, 0x273b24fe3b367d75UL,
+ /* 172 */ 0xc6e8f66a31b3b9d4UL, 0x281514a494df49d5UL,
+ 0xd1726fdfc8b23da7UL, 0x4b3ae7d103dee548UL,
+ /* 173 */ 0xc6256e19ce4b9d7eUL, 0xff5c5cf186e3c61cUL,
+ 0xacc63ca34b8ec145UL, 0x74621888fee66574UL,
+ /* 174 */ 0x956f409645290a1eUL, 0xef0bf8e3263a962eUL,
+ 0xed6a50eb5ec2647bUL, 0x0694283a9dca7502UL,
+ /* 175 */ 0x769b963643a2dcd1UL, 0x42b7c8ea09fc5353UL,
+ 0x4f002aee13397eabUL, 0x63005e2c19b7d63aUL,
+ /* 176 */ 0xca6736da63023beaUL, 0x966c7f6db12a99b7UL,
+ 0xace09390c537c5e1UL, 0x0b696063a1aa89eeUL,
+ /* 177 */ 0xebb03e97288c56e5UL, 0x432a9f9f938c8be8UL,
+ 0xa6a5a93d5b717f71UL, 0x1a5fb4c3e18f9d97UL,
+ /* 178 */ 0x1c94e7ad1c60cdceUL, 0xee202a43fc02c4a0UL,
+ 0x8dafe4d867c46a20UL, 0x0a10263c8ac27b58UL,
+ /* 179 */ 0xd0dea9dfe4432a4aUL, 0x856af87bbe9277c5UL,
+ 0xce8472acc212c71aUL, 0x6f151b6d9bbb1e91UL,
+ /* 180 */ 0x26776c527ceed56aUL, 0x7d211cb7fbf8faecUL,
+ 0x37ae66a6fd4609ccUL, 0x1f81b702d2770c42UL,
+ /* 181 */ 0x2fb0b057eac58392UL, 0xe1dd89fe29744e9dUL,
+ 0xc964f8eb17beb4f8UL, 0x29571073c9a2d41eUL,
+ /* 182 */ 0xa948a18981c0e254UL, 0x2df6369b65b22830UL,
+ 0xa33eb2d75fcfd3c6UL, 0x078cd6ec4199a01fUL,
+ /* 183 */ 0x4a584a41ad900d2fUL, 0x32142b78e2c74c52UL,
+ 0x68c4e8338431c978UL, 0x7f69ea9008689fc2UL,
+ /* 184 */ 0x52f2c81e46a38265UL, 0xfd78072d04a832fdUL,
+ 0x8cd7d5fa25359e94UL, 0x4de71b7454cc29d2UL,
+ /* 185 */ 0x42eb60ad1eda6ac9UL, 0x0aad37dfdbc09c3aUL,
+ 0x81004b71e33cc191UL, 0x44e6be345122803cUL,
+ /* 186 */ 0x03fe8388ba1920dbUL, 0xf5d57c32150db008UL,
+ 0x49c8c4281af60c29UL, 0x21edb518de701aeeUL,
+ /* 187 */ 0x7fb63e418f06dc99UL, 0xa4460d99c166d7b8UL,
+ 0x24dd5248ce520a83UL, 0x5ec3ad712b928358UL,
+ /* 188 */ 0x15022a5fbd17930fUL, 0xa4f64a77d82570e3UL,
+ 0x12bc8d6915783712UL, 0x498194c0fc620abbUL,
+ /* 189 */ 0x38a2d9d255686c82UL, 0x785c6bd9193e21f0UL,
+ 0xe4d5c81ab24a5484UL, 0x56307860b2e20989UL,
+ /* 190 */ 0x429d55f78b4d74c4UL, 0x22f1834643350131UL,
+ 0x1e60c24598c71fffUL, 0x59f2f014979983efUL,
+ /* 191 */ 0x46a47d56eb494a44UL, 0x3e22a854d636a18eUL,
+ 0xb346e15274491c3bUL, 0x2ceafd4e5390cde7UL,
+ /* 192 */ 0xba8a8538be0d6675UL, 0x4b9074bb50818e23UL,
+ 0xcbdab89085d304c3UL, 0x61a24fe0e56192c4UL,
+ /* 193 */ 0xcb7615e6db525bcbUL, 0xdd7d8c35a567e4caUL,
+ 0xe6b4153acafcdd69UL, 0x2d668e097f3c9766UL,
+ /* 194 */ 0xa57e7e265ce55ef0UL, 0x5d9f4e527cd4b967UL,
+ 0xfbc83606492fd1e5UL, 0x090d52beb7c3f7aeUL,
+ /* 195 */ 0x09b9515a1e7b4d7cUL, 0x1f266a2599da44c0UL,
+ 0xa1c49548e2c55504UL, 0x7ef04287126f15ccUL,
+ /* 196 */ 0xfed1659dbd30ef15UL, 0x8b4ab9eec4e0277bUL,
+ 0x884d6236a5df3291UL, 0x1fd96ea6bf5cf788UL,
+ /* 197 */ 0x42a161981f190d9aUL, 0x61d849507e6052c1UL,
+ 0x9fe113bf285a2cd5UL, 0x7c22d676dbad85d8UL,
+ /* 198 */ 0x82e770ed2bfbd27dUL, 0x4c05b2ece996f5a5UL,
+ 0xcd40a9c2b0900150UL, 0x5895319213d9bf64UL,
+ /* 199 */ 0xe7cc5d703fea2e08UL, 0xb50c491258e2188cUL,
+ 0xcce30baa48205bf0UL, 0x537c659ccfa32d62UL,
+ /* 200 */ 0x37b6623a98cfc088UL, 0xfe9bed1fa4d6aca4UL,
+ 0x04d29b8e56a8d1b0UL, 0x725f71c40b519575UL,
+ /* 201 */ 0x28c7f89cd0339ce6UL, 0x8367b14469ddc18bUL,
+ 0x883ada83a6a1652cUL, 0x585f1974034d6c17UL,
+ /* 202 */ 0x89cfb266f1b19188UL, 0xe63b4863e7c35217UL,
+ 0xd88c9da6b4c0526aUL, 0x3e035c9df0954635UL,
+ /* 203 */ 0xdd9d5412fb45de9dUL, 0xdd684532e4cff40dUL,
+ 0x4b5c999b151d671cUL, 0x2d8c2cc811e7f690UL,
+ /* 204 */ 0x7f54be1d90055d40UL, 0xa464c5df464aaf40UL,
+ 0x33979624f0e917beUL, 0x2c018dc527356b30UL,
+ /* 205 */ 0xa5415024e330b3d4UL, 0x73ff3d96691652d3UL,
+ 0x94ec42c4ef9b59f1UL, 0x0747201618d08e5aUL,
+ /* 206 */ 0x4d6ca48aca411c53UL, 0x66415f2fcfa66119UL,
+ 0x9c4dd40051e227ffUL, 0x59810bc09a02f7ebUL,
+ /* 207 */ 0x2a7eb171b3dc101dUL, 0x441c5ab99ffef68eUL,
+ 0x32025c9b93b359eaUL, 0x5e8ce0a71e9d112fUL,
+ /* 208 */ 0xbfcccb92429503fdUL, 0xd271ba752f095d55UL,
+ 0x345ead5e972d091eUL, 0x18c8df11a83103baUL,
+ /* 209 */ 0x90cd949a9aed0f4cUL, 0xc5d1f4cb6660e37eUL,
+ 0xb8cac52d56c52e0bUL, 0x6e42e400c5808e0dUL,
+ /* 210 */ 0xa3b46966eeaefd23UL, 0x0c4f1f0be39ecdcaUL,
+ 0x189dc8c9d683a51dUL, 0x51f27f054c09351bUL,
+ /* 211 */ 0x4c487ccd2a320682UL, 0x587ea95bb3df1c96UL,
+ 0xc8ccf79e555cb8e8UL, 0x547dc829a206d73dUL,
+ /* 212 */ 0xb822a6cd80c39b06UL, 0xe96d54732000d4c6UL,
+ 0x28535b6f91463b4dUL, 0x228f4660e2486e1dUL,
+ /* 213 */ 0x98799538de8d3abfUL, 0x8cd8330045ebca6eUL,
+ 0x79952a008221e738UL, 0x4322e1a7535cd2bbUL,
+ /* 214 */ 0xb114c11819d1801cUL, 0x2016e4d84f3f5ec7UL,
+ 0xdd0e2df409260f4cUL, 0x5ec362c0ae5f7266UL,
+ /* 215 */ 0xc0462b18b8b2b4eeUL, 0x7cc8d950274d1afbUL,
+ 0xf25f7105436b02d2UL, 0x43bbf8dcbff9ccd3UL,
+ /* 216 */ 0xb6ad1767a039e9dfUL, 0xb0714da8f69d3583UL,
+ 0x5e55fa18b42931f5UL, 0x4ed5558f33c60961UL,
+ /* 217 */ 0x1fe37901c647a5ddUL, 0x593ddf1f8081d357UL,
+ 0x0249a4fd813fd7a6UL, 0x69acca274e9caf61UL,
+ /* 218 */ 0x047ba3ea330721c9UL, 0x83423fc20e7e1ea0UL,
+ 0x1df4c0af01314a60UL, 0x09a62dab89289527UL,
+ /* 219 */ 0xa5b325a49cc6cb00UL, 0xe94b5dc654b56cb6UL,
+ 0x3be28779adc994a0UL, 0x4296e8f8ba3a4aadUL,
+ /* 220 */ 0x328689761e451eabUL, 0x2e4d598bff59594aUL,
+ 0x49b96853d7a7084aUL, 0x4980a319601420a8UL,
+ /* 221 */ 0x9565b9e12f552c42UL, 0x8a5318db7100fe96UL,
+ 0x05c90b4d43add0d7UL, 0x538b4cd66a5d4edaUL,
+ /* 222 */ 0xf4e94fc3e89f039fUL, 0x592c9af26f618045UL,
+ 0x08a36eb5fd4b9550UL, 0x25fffaf6c2ed1419UL,
+ /* 223 */ 0x34434459cc79d354UL, 0xeeecbfb4b1d5476bUL,
+ 0xddeb34a061615d99UL, 0x5129cecceb64b773UL,
+ /* 224 */ 0xee43215894993520UL, 0x772f9c7cf14c0b3bUL,
+ 0xd2e2fce306bedad5UL, 0x715f42b546f06a97UL,
+ /* 225 */ 0x434ecdceda5b5f1aUL, 0x0da17115a49741a9UL,
+ 0x680bd77c73edad2eUL, 0x487c02354edd9041UL,
+ /* 226 */ 0xb8efeff3a70ed9c4UL, 0x56a32aa3e857e302UL,
+ 0xdf3a68bd48a2a5a0UL, 0x07f650b73176c444UL,
+ /* 227 */ 0xe38b9b1626e0ccb1UL, 0x79e053c18b09fb36UL,
+ 0x56d90319c9f94964UL, 0x1ca941e7ac9ff5c4UL,
+ /* 228 */ 0x49c4df29162fa0bbUL, 0x8488cf3282b33305UL,
+ 0x95dfda14cabb437dUL, 0x3391f78264d5ad86UL,
+ /* 229 */ 0x729ae06ae2b5095dUL, 0xd58a58d73259a946UL,
+ 0xe9834262d13921edUL, 0x27fedafaa54bb592UL,
+ /* 230 */ 0xa99dc5b829ad48bbUL, 0x5f025742499ee260UL,
+ 0x802c8ecd5d7513fdUL, 0x78ceb3ef3f6dd938UL,
+ /* 231 */ 0xc342f44f8a135d94UL, 0x7b9edb44828cdda3UL,
+ 0x9436d11a0537cfe7UL, 0x5064b164ec1ab4c8UL,
+ /* 232 */ 0x7020eccfd37eb2fcUL, 0x1f31ea3ed90d25fcUL,
+ 0x1b930d7bdfa1bb34UL, 0x5344467a48113044UL,
+ /* 233 */ 0x70073170f25e6dfbUL, 0xe385dc1a50114cc8UL,
+ 0x2348698ac8fc4f00UL, 0x2a77a55284dd40d8UL,
+ /* 234 */ 0xfe06afe0c98c6ce4UL, 0xc235df96dddfd6e4UL,
+ 0x1428d01e33bf1ed3UL, 0x785768ec9300bdafUL,
+ /* 235 */ 0x9702e57a91deb63bUL, 0x61bdb8bfe5ce8b80UL,
+ 0x645b426f3d1d58acUL, 0x4804a82227a557bcUL,
+ /* 236 */ 0x8e57048ab44d2601UL, 0x68d6501a4b3a6935UL,
+ 0xc39c9ec3f9e1c293UL, 0x4172f257d4de63e2UL,
+ /* 237 */ 0xd368b450330c6401UL, 0x040d3017418f2391UL,
+ 0x2c34bb6090b7d90dUL, 0x16f649228fdfd51fUL,
+ /* 238 */ 0xbea6818e2b928ef5UL, 0xe28ccf91cdc11e72UL,
+ 0x594aaa68e77a36cdUL, 0x313034806c7ffd0fUL,
+ /* 239 */ 0x8a9d27ac2249bd65UL, 0x19a3b464018e9512UL,
+ 0xc26ccff352b37ec7UL, 0x056f68341d797b21UL,
+ /* 240 */ 0x5e79d6757efd2327UL, 0xfabdbcb6553afe15UL,
+ 0xd3e7222c6eaf5a60UL, 0x7046c76d4dae743bUL,
+ /* 241 */ 0x660be872b18d4a55UL, 0x19992518574e1496UL,
+ 0xc103053a302bdcbbUL, 0x3ed8e9800b218e8eUL,
+ /* 242 */ 0x7b0b9239fa75e03eUL, 0xefe9fb684633c083UL,
+ 0x98a35fbe391a7793UL, 0x6065510fe2d0fe34UL,
+ /* 243 */ 0x55cb668548abad0cUL, 0xb4584548da87e527UL,
+ 0x2c43ecea0107c1ddUL, 0x526028809372de35UL,
+ /* 244 */ 0x3415c56af9213b1fUL, 0x5bee1a4d017e98dbUL,
+ 0x13f6b105b5cf709bUL, 0x5ff20e3482b29ab6UL,
+ /* 245 */ 0x0aa29c75cc2e6c90UL, 0xfc7d73ca3a70e206UL,
+ 0x899fc38fc4b5c515UL, 0x250386b124ffc207UL,
+ /* 246 */ 0x54ea28d5ae3d2b56UL, 0x9913149dd6de60ceUL,
+ 0x16694fc58f06d6c1UL, 0x46b23975eb018fc7UL,
+ /* 247 */ 0x470a6a0fb4b7b4e2UL, 0x5d92475a8f7253deUL,
+ 0xabeee5b52fbd3adbUL, 0x7fa20801a0806968UL,
+ /* 248 */ 0x76f3faf19f7714d2UL, 0xb3e840c12f4660c3UL,
+ 0x0fb4cd8df212744eUL, 0x4b065a251d3a2dd2UL,
+ /* 249 */ 0x5cebde383d77cd4aUL, 0x6adf39df882c9cb1UL,
+ 0xa2dd242eb09af759UL, 0x3147c0e50e5f6422UL,
+ /* 250 */ 0x164ca5101d1350dbUL, 0xf8d13479c33fc962UL,
+ 0xe640ce4d13e5da08UL, 0x4bdee0c45061f8baUL,
+ /* 251 */ 0xd7c46dc1a4edb1c9UL, 0x5514d7b6437fd98aUL,
+ 0x58942f6bb2a1c00bUL, 0x2dffb2ab1d70710eUL,
+ /* 252 */ 0xccdfcf2fc18b6d68UL, 0xa8ebcba8b7806167UL,
+ 0x980697f95e2937e3UL, 0x02fbba1cd0126e8cUL
+};
+
+/* c is two 512-bit products: c0[0:7]=a0[0:3]*b0[0:3] and c1[8:15]=a1[4:7]*b1[4:7]
+ * a is two 256-bit integers: a0[0:3] and a1[4:7]
+ * b is two 256-bit integers: b0[0:3] and b1[4:7]
+ */
+static void mul2_256x256_integer_adx(u64 *const c, const u64 *const a,
+ const u64 *const b)
+{
+ asm volatile(
+ "xorl %%r14d, %%r14d ;"
+ "movq (%1), %%rdx; " /* A[0] */
+ "mulx (%2), %%r8, %%r15; " /* A[0]*B[0] */
+ "xorl %%r10d, %%r10d ;"
+ "movq %%r8, (%0) ;"
+ "mulx 8(%2), %%r10, %%rax; " /* A[0]*B[1] */
+ "adox %%r10, %%r15 ;"
+ "mulx 16(%2), %%r8, %%rbx; " /* A[0]*B[2] */
+ "adox %%r8, %%rax ;"
+ "mulx 24(%2), %%r10, %%rcx; " /* A[0]*B[3] */
+ "adox %%r10, %%rbx ;"
+ /******************************************/
+ "adox %%r14, %%rcx ;"
+
+ "movq 8(%1), %%rdx; " /* A[1] */
+ "mulx (%2), %%r8, %%r9; " /* A[1]*B[0] */
+ "adox %%r15, %%r8 ;"
+ "movq %%r8, 8(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[1]*B[1] */
+ "adox %%r10, %%r9 ;"
+ "adcx %%r9, %%rax ;"
+ "mulx 16(%2), %%r8, %%r13; " /* A[1]*B[2] */
+ "adox %%r8, %%r11 ;"
+ "adcx %%r11, %%rbx ;"
+ "mulx 24(%2), %%r10, %%r15; " /* A[1]*B[3] */
+ "adox %%r10, %%r13 ;"
+ "adcx %%r13, %%rcx ;"
+ /******************************************/
+ "adox %%r14, %%r15 ;"
+ "adcx %%r14, %%r15 ;"
+
+ "movq 16(%1), %%rdx; " /* A[2] */
+ "xorl %%r10d, %%r10d ;"
+ "mulx (%2), %%r8, %%r9; " /* A[2]*B[0] */
+ "adox %%rax, %%r8 ;"
+ "movq %%r8, 16(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[2]*B[1] */
+ "adox %%r10, %%r9 ;"
+ "adcx %%r9, %%rbx ;"
+ "mulx 16(%2), %%r8, %%r13; " /* A[2]*B[2] */
+ "adox %%r8, %%r11 ;"
+ "adcx %%r11, %%rcx ;"
+ "mulx 24(%2), %%r10, %%rax; " /* A[2]*B[3] */
+ "adox %%r10, %%r13 ;"
+ "adcx %%r13, %%r15 ;"
+ /******************************************/
+ "adox %%r14, %%rax ;"
+ "adcx %%r14, %%rax ;"
+
+ "movq 24(%1), %%rdx; " /* A[3] */
+ "xorl %%r10d, %%r10d ;"
+ "mulx (%2), %%r8, %%r9; " /* A[3]*B[0] */
+ "adox %%rbx, %%r8 ;"
+ "movq %%r8, 24(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[3]*B[1] */
+ "adox %%r10, %%r9 ;"
+ "adcx %%r9, %%rcx ;"
+ "movq %%rcx, 32(%0) ;"
+ "mulx 16(%2), %%r8, %%r13; " /* A[3]*B[2] */
+ "adox %%r8, %%r11 ;"
+ "adcx %%r11, %%r15 ;"
+ "movq %%r15, 40(%0) ;"
+ "mulx 24(%2), %%r10, %%rbx; " /* A[3]*B[3] */
+ "adox %%r10, %%r13 ;"
+ "adcx %%r13, %%rax ;"
+ "movq %%rax, 48(%0) ;"
+ /******************************************/
+ "adox %%r14, %%rbx ;"
+ "adcx %%r14, %%rbx ;"
+ "movq %%rbx, 56(%0) ;"
+
+ "movq 32(%1), %%rdx; " /* C[0] */
+ "mulx 32(%2), %%r8, %%r15; " /* C[0]*D[0] */
+ "xorl %%r10d, %%r10d ;"
+ "movq %%r8, 64(%0);"
+ "mulx 40(%2), %%r10, %%rax; " /* C[0]*D[1] */
+ "adox %%r10, %%r15 ;"
+ "mulx 48(%2), %%r8, %%rbx; " /* C[0]*D[2] */
+ "adox %%r8, %%rax ;"
+ "mulx 56(%2), %%r10, %%rcx; " /* C[0]*D[3] */
+ "adox %%r10, %%rbx ;"
+ /******************************************/
+ "adox %%r14, %%rcx ;"
+
+ "movq 40(%1), %%rdx; " /* C[1] */
+ "xorl %%r10d, %%r10d ;"
+ "mulx 32(%2), %%r8, %%r9; " /* C[1]*D[0] */
+ "adox %%r15, %%r8 ;"
+ "movq %%r8, 72(%0);"
+ "mulx 40(%2), %%r10, %%r11; " /* C[1]*D[1] */
+ "adox %%r10, %%r9 ;"
+ "adcx %%r9, %%rax ;"
+ "mulx 48(%2), %%r8, %%r13; " /* C[1]*D[2] */
+ "adox %%r8, %%r11 ;"
+ "adcx %%r11, %%rbx ;"
+ "mulx 56(%2), %%r10, %%r15; " /* C[1]*D[3] */
+ "adox %%r10, %%r13 ;"
+ "adcx %%r13, %%rcx ;"
+ /******************************************/
+ "adox %%r14, %%r15 ;"
+ "adcx %%r14, %%r15 ;"
+
+ "movq 48(%1), %%rdx; " /* C[2] */
+ "xorl %%r10d, %%r10d ;"
+ "mulx 32(%2), %%r8, %%r9; " /* C[2]*D[0] */
+ "adox %%rax, %%r8 ;"
+ "movq %%r8, 80(%0);"
+ "mulx 40(%2), %%r10, %%r11; " /* C[2]*D[1] */
+ "adox %%r10, %%r9 ;"
+ "adcx %%r9, %%rbx ;"
+ "mulx 48(%2), %%r8, %%r13; " /* C[2]*D[2] */
+ "adox %%r8, %%r11 ;"
+ "adcx %%r11, %%rcx ;"
+ "mulx 56(%2), %%r10, %%rax; " /* C[2]*D[3] */
+ "adox %%r10, %%r13 ;"
+ "adcx %%r13, %%r15 ;"
+ /******************************************/
+ "adox %%r14, %%rax ;"
+ "adcx %%r14, %%rax ;"
+
+ "movq 56(%1), %%rdx; " /* C[3] */
+ "xorl %%r10d, %%r10d ;"
+ "mulx 32(%2), %%r8, %%r9; " /* C[3]*D[0] */
+ "adox %%rbx, %%r8 ;"
+ "movq %%r8, 88(%0);"
+ "mulx 40(%2), %%r10, %%r11; " /* C[3]*D[1] */
+ "adox %%r10, %%r9 ;"
+ "adcx %%r9, %%rcx ;"
+ "movq %%rcx, 96(%0) ;"
+ "mulx 48(%2), %%r8, %%r13; " /* C[3]*D[2] */
+ "adox %%r8, %%r11 ;"
+ "adcx %%r11, %%r15 ;"
+ "movq %%r15, 104(%0) ;"
+ "mulx 56(%2), %%r10, %%rbx; " /* C[3]*D[3] */
+ "adox %%r10, %%r13 ;"
+ "adcx %%r13, %%rax ;"
+ "movq %%rax, 112(%0) ;"
+ /******************************************/
+ "adox %%r14, %%rbx ;"
+ "adcx %%r14, %%rbx ;"
+ "movq %%rbx, 120(%0) ;"
+ :
+ : "r"(c), "r"(a), "r"(b)
+ : "memory", "cc", "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9",
+ "%r10", "%r11", "%r13", "%r14", "%r15");
+}
+
+static void mul2_256x256_integer_bmi2(u64 *const c, const u64 *const a,
+ const u64 *const b)
+{
+ asm volatile(
+ "movq (%1), %%rdx; " /* A[0] */
+ "mulx (%2), %%r8, %%r15; " /* A[0]*B[0] */
+ "movq %%r8, (%0) ;"
+ "mulx 8(%2), %%r10, %%rax; " /* A[0]*B[1] */
+ "addq %%r10, %%r15 ;"
+ "mulx 16(%2), %%r8, %%rbx; " /* A[0]*B[2] */
+ "adcq %%r8, %%rax ;"
+ "mulx 24(%2), %%r10, %%rcx; " /* A[0]*B[3] */
+ "adcq %%r10, %%rbx ;"
+ /******************************************/
+ "adcq $0, %%rcx ;"
+
+ "movq 8(%1), %%rdx; " /* A[1] */
+ "mulx (%2), %%r8, %%r9; " /* A[1]*B[0] */
+ "addq %%r15, %%r8 ;"
+ "movq %%r8, 8(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[1]*B[1] */
+ "adcq %%r10, %%r9 ;"
+ "mulx 16(%2), %%r8, %%r13; " /* A[1]*B[2] */
+ "adcq %%r8, %%r11 ;"
+ "mulx 24(%2), %%r10, %%r15; " /* A[1]*B[3] */
+ "adcq %%r10, %%r13 ;"
+ /******************************************/
+ "adcq $0, %%r15 ;"
+
+ "addq %%r9, %%rax ;"
+ "adcq %%r11, %%rbx ;"
+ "adcq %%r13, %%rcx ;"
+ "adcq $0, %%r15 ;"
+
+ "movq 16(%1), %%rdx; " /* A[2] */
+ "mulx (%2), %%r8, %%r9; " /* A[2]*B[0] */
+ "addq %%rax, %%r8 ;"
+ "movq %%r8, 16(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[2]*B[1] */
+ "adcq %%r10, %%r9 ;"
+ "mulx 16(%2), %%r8, %%r13; " /* A[2]*B[2] */
+ "adcq %%r8, %%r11 ;"
+ "mulx 24(%2), %%r10, %%rax; " /* A[2]*B[3] */
+ "adcq %%r10, %%r13 ;"
+ /******************************************/
+ "adcq $0, %%rax ;"
+
+ "addq %%r9, %%rbx ;"
+ "adcq %%r11, %%rcx ;"
+ "adcq %%r13, %%r15 ;"
+ "adcq $0, %%rax ;"
+
+ "movq 24(%1), %%rdx; " /* A[3] */
+ "mulx (%2), %%r8, %%r9; " /* A[3]*B[0] */
+ "addq %%rbx, %%r8 ;"
+ "movq %%r8, 24(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[3]*B[1] */
+ "adcq %%r10, %%r9 ;"
+ "mulx 16(%2), %%r8, %%r13; " /* A[3]*B[2] */
+ "adcq %%r8, %%r11 ;"
+ "mulx 24(%2), %%r10, %%rbx; " /* A[3]*B[3] */
+ "adcq %%r10, %%r13 ;"
+ /******************************************/
+ "adcq $0, %%rbx ;"
+
+ "addq %%r9, %%rcx ;"
+ "movq %%rcx, 32(%0) ;"
+ "adcq %%r11, %%r15 ;"
+ "movq %%r15, 40(%0) ;"
+ "adcq %%r13, %%rax ;"
+ "movq %%rax, 48(%0) ;"
+ "adcq $0, %%rbx ;"
+ "movq %%rbx, 56(%0) ;"
+
+ "movq 32(%1), %%rdx; " /* C[0] */
+ "mulx 32(%2), %%r8, %%r15; " /* C[0]*D[0] */
+ "movq %%r8, 64(%0) ;"
+ "mulx 40(%2), %%r10, %%rax; " /* C[0]*D[1] */
+ "addq %%r10, %%r15 ;"
+ "mulx 48(%2), %%r8, %%rbx; " /* C[0]*D[2] */
+ "adcq %%r8, %%rax ;"
+ "mulx 56(%2), %%r10, %%rcx; " /* C[0]*D[3] */
+ "adcq %%r10, %%rbx ;"
+ /******************************************/
+ "adcq $0, %%rcx ;"
+
+ "movq 40(%1), %%rdx; " /* C[1] */
+ "mulx 32(%2), %%r8, %%r9; " /* C[1]*D[0] */
+ "addq %%r15, %%r8 ;"
+ "movq %%r8, 72(%0) ;"
+ "mulx 40(%2), %%r10, %%r11; " /* C[1]*D[1] */
+ "adcq %%r10, %%r9 ;"
+ "mulx 48(%2), %%r8, %%r13; " /* C[1]*D[2] */
+ "adcq %%r8, %%r11 ;"
+ "mulx 56(%2), %%r10, %%r15; " /* C[1]*D[3] */
+ "adcq %%r10, %%r13 ;"
+ /******************************************/
+ "adcq $0, %%r15 ;"
+
+ "addq %%r9, %%rax ;"
+ "adcq %%r11, %%rbx ;"
+ "adcq %%r13, %%rcx ;"
+ "adcq $0, %%r15 ;"
+
+ "movq 48(%1), %%rdx; " /* C[2] */
+ "mulx 32(%2), %%r8, %%r9; " /* C[2]*D[0] */
+ "addq %%rax, %%r8 ;"
+ "movq %%r8, 80(%0) ;"
+ "mulx 40(%2), %%r10, %%r11; " /* C[2]*D[1] */
+ "adcq %%r10, %%r9 ;"
+ "mulx 48(%2), %%r8, %%r13; " /* C[2]*D[2] */
+ "adcq %%r8, %%r11 ;"
+ "mulx 56(%2), %%r10, %%rax; " /* C[2]*D[3] */
+ "adcq %%r10, %%r13 ;"
+ /******************************************/
+ "adcq $0, %%rax ;"
+
+ "addq %%r9, %%rbx ;"
+ "adcq %%r11, %%rcx ;"
+ "adcq %%r13, %%r15 ;"
+ "adcq $0, %%rax ;"
+
+ "movq 56(%1), %%rdx; " /* C[3] */
+ "mulx 32(%2), %%r8, %%r9; " /* C[3]*D[0] */
+ "addq %%rbx, %%r8 ;"
+ "movq %%r8, 88(%0) ;"
+ "mulx 40(%2), %%r10, %%r11; " /* C[3]*D[1] */
+ "adcq %%r10, %%r9 ;"
+ "mulx 48(%2), %%r8, %%r13; " /* C[3]*D[2] */
+ "adcq %%r8, %%r11 ;"
+ "mulx 56(%2), %%r10, %%rbx; " /* C[3]*D[3] */
+ "adcq %%r10, %%r13 ;"
+ /******************************************/
+ "adcq $0, %%rbx ;"
+
+ "addq %%r9, %%rcx ;"
+ "movq %%rcx, 96(%0) ;"
+ "adcq %%r11, %%r15 ;"
+ "movq %%r15, 104(%0) ;"
+ "adcq %%r13, %%rax ;"
+ "movq %%rax, 112(%0) ;"
+ "adcq $0, %%rbx ;"
+ "movq %%rbx, 120(%0) ;"
+ :
+ : "r"(c), "r"(a), "r"(b)
+ : "memory", "cc", "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9",
+ "%r10", "%r11", "%r13", "%r15");
+}
+
+static void sqr2_256x256_integer_adx(u64 *const c, const u64 *const a)
+{
+ asm volatile(
+ "movq (%1), %%rdx ;" /* A[0] */
+ "mulx 8(%1), %%r8, %%r14 ;" /* A[1]*A[0] */
+ "xorl %%r15d, %%r15d;"
+ "mulx 16(%1), %%r9, %%r10 ;" /* A[2]*A[0] */
+ "adcx %%r14, %%r9 ;"
+ "mulx 24(%1), %%rax, %%rcx ;" /* A[3]*A[0] */
+ "adcx %%rax, %%r10 ;"
+ "movq 24(%1), %%rdx ;" /* A[3] */
+ "mulx 8(%1), %%r11, %%rbx ;" /* A[1]*A[3] */
+ "adcx %%rcx, %%r11 ;"
+ "mulx 16(%1), %%rax, %%r13 ;" /* A[2]*A[3] */
+ "adcx %%rax, %%rbx ;"
+ "movq 8(%1), %%rdx ;" /* A[1] */
+ "adcx %%r15, %%r13 ;"
+ "mulx 16(%1), %%rax, %%rcx ;" /* A[2]*A[1] */
+ "movq $0, %%r14 ;"
+ /******************************************/
+ "adcx %%r15, %%r14 ;"
+
+ "xorl %%r15d, %%r15d;"
+ "adox %%rax, %%r10 ;"
+ "adcx %%r8, %%r8 ;"
+ "adox %%rcx, %%r11 ;"
+ "adcx %%r9, %%r9 ;"
+ "adox %%r15, %%rbx ;"
+ "adcx %%r10, %%r10 ;"
+ "adox %%r15, %%r13 ;"
+ "adcx %%r11, %%r11 ;"
+ "adox %%r15, %%r14 ;"
+ "adcx %%rbx, %%rbx ;"
+ "adcx %%r13, %%r13 ;"
+ "adcx %%r14, %%r14 ;"
+
+ "movq (%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[0]^2 */
+ /*******************/
+ "movq %%rax, 0(%0) ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, 8(%0) ;"
+ "movq 8(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[1]^2 */
+ "adcq %%rax, %%r9 ;"
+ "movq %%r9, 16(%0) ;"
+ "adcq %%rcx, %%r10 ;"
+ "movq %%r10, 24(%0) ;"
+ "movq 16(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[2]^2 */
+ "adcq %%rax, %%r11 ;"
+ "movq %%r11, 32(%0) ;"
+ "adcq %%rcx, %%rbx ;"
+ "movq %%rbx, 40(%0) ;"
+ "movq 24(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[3]^2 */
+ "adcq %%rax, %%r13 ;"
+ "movq %%r13, 48(%0) ;"
+ "adcq %%rcx, %%r14 ;"
+ "movq %%r14, 56(%0) ;"
+
+
+ "movq 32(%1), %%rdx ;" /* B[0] */
+ "mulx 40(%1), %%r8, %%r14 ;" /* B[1]*B[0] */
+ "xorl %%r15d, %%r15d;"
+ "mulx 48(%1), %%r9, %%r10 ;" /* B[2]*B[0] */
+ "adcx %%r14, %%r9 ;"
+ "mulx 56(%1), %%rax, %%rcx ;" /* B[3]*B[0] */
+ "adcx %%rax, %%r10 ;"
+ "movq 56(%1), %%rdx ;" /* B[3] */
+ "mulx 40(%1), %%r11, %%rbx ;" /* B[1]*B[3] */
+ "adcx %%rcx, %%r11 ;"
+ "mulx 48(%1), %%rax, %%r13 ;" /* B[2]*B[3] */
+ "adcx %%rax, %%rbx ;"
+ "movq 40(%1), %%rdx ;" /* B[1] */
+ "adcx %%r15, %%r13 ;"
+ "mulx 48(%1), %%rax, %%rcx ;" /* B[2]*B[1] */
+ "movq $0, %%r14 ;"
+ /******************************************/
+ "adcx %%r15, %%r14 ;"
+
+ "xorl %%r15d, %%r15d;"
+ "adox %%rax, %%r10 ;"
+ "adcx %%r8, %%r8 ;"
+ "adox %%rcx, %%r11 ;"
+ "adcx %%r9, %%r9 ;"
+ "adox %%r15, %%rbx ;"
+ "adcx %%r10, %%r10 ;"
+ "adox %%r15, %%r13 ;"
+ "adcx %%r11, %%r11 ;"
+ "adox %%r15, %%r14 ;"
+ "adcx %%rbx, %%rbx ;"
+ "adcx %%r13, %%r13 ;"
+ "adcx %%r14, %%r14 ;"
+
+ "movq 32(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* B[0]^2 */
+ /*******************/
+ "movq %%rax, 64(%0) ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, 72(%0) ;"
+ "movq 40(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* B[1]^2 */
+ "adcq %%rax, %%r9 ;"
+ "movq %%r9, 80(%0) ;"
+ "adcq %%rcx, %%r10 ;"
+ "movq %%r10, 88(%0) ;"
+ "movq 48(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* B[2]^2 */
+ "adcq %%rax, %%r11 ;"
+ "movq %%r11, 96(%0) ;"
+ "adcq %%rcx, %%rbx ;"
+ "movq %%rbx, 104(%0) ;"
+ "movq 56(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* B[3]^2 */
+ "adcq %%rax, %%r13 ;"
+ "movq %%r13, 112(%0) ;"
+ "adcq %%rcx, %%r14 ;"
+ "movq %%r14, 120(%0) ;"
+ :
+ : "r"(c), "r"(a)
+ : "memory", "cc", "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9",
+ "%r10", "%r11", "%r13", "%r14", "%r15");
+}
+
+static void sqr2_256x256_integer_bmi2(u64 *const c, const u64 *const a)
+{
+ asm volatile(
+ "movq 8(%1), %%rdx ;" /* A[1] */
+ "mulx (%1), %%r8, %%r9 ;" /* A[0]*A[1] */
+ "mulx 16(%1), %%r10, %%r11 ;" /* A[2]*A[1] */
+ "mulx 24(%1), %%rcx, %%r14 ;" /* A[3]*A[1] */
+
+ "movq 16(%1), %%rdx ;" /* A[2] */
+ "mulx 24(%1), %%r15, %%r13 ;" /* A[3]*A[2] */
+ "mulx (%1), %%rax, %%rdx ;" /* A[0]*A[2] */
+
+ "addq %%rax, %%r9 ;"
+ "adcq %%rdx, %%r10 ;"
+ "adcq %%rcx, %%r11 ;"
+ "adcq %%r14, %%r15 ;"
+ "adcq $0, %%r13 ;"
+ "movq $0, %%r14 ;"
+ "adcq $0, %%r14 ;"
+
+ "movq (%1), %%rdx ;" /* A[0] */
+ "mulx 24(%1), %%rax, %%rcx ;" /* A[0]*A[3] */
+
+ "addq %%rax, %%r10 ;"
+ "adcq %%rcx, %%r11 ;"
+ "adcq $0, %%r15 ;"
+ "adcq $0, %%r13 ;"
+ "adcq $0, %%r14 ;"
+
+ "shldq $1, %%r13, %%r14 ;"
+ "shldq $1, %%r15, %%r13 ;"
+ "shldq $1, %%r11, %%r15 ;"
+ "shldq $1, %%r10, %%r11 ;"
+ "shldq $1, %%r9, %%r10 ;"
+ "shldq $1, %%r8, %%r9 ;"
+ "shlq $1, %%r8 ;"
+
+ /*******************/
+ "mulx %%rdx, %%rax, %%rcx ; " /* A[0]^2 */
+ /*******************/
+ "movq %%rax, 0(%0) ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, 8(%0) ;"
+ "movq 8(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ; " /* A[1]^2 */
+ "adcq %%rax, %%r9 ;"
+ "movq %%r9, 16(%0) ;"
+ "adcq %%rcx, %%r10 ;"
+ "movq %%r10, 24(%0) ;"
+ "movq 16(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ; " /* A[2]^2 */
+ "adcq %%rax, %%r11 ;"
+ "movq %%r11, 32(%0) ;"
+ "adcq %%rcx, %%r15 ;"
+ "movq %%r15, 40(%0) ;"
+ "movq 24(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ; " /* A[3]^2 */
+ "adcq %%rax, %%r13 ;"
+ "movq %%r13, 48(%0) ;"
+ "adcq %%rcx, %%r14 ;"
+ "movq %%r14, 56(%0) ;"
+
+ "movq 40(%1), %%rdx ;" /* B[1] */
+ "mulx 32(%1), %%r8, %%r9 ;" /* B[0]*B[1] */
+ "mulx 48(%1), %%r10, %%r11 ;" /* B[2]*B[1] */
+ "mulx 56(%1), %%rcx, %%r14 ;" /* B[3]*B[1] */
+
+ "movq 48(%1), %%rdx ;" /* B[2] */
+ "mulx 56(%1), %%r15, %%r13 ;" /* B[3]*B[2] */
+ "mulx 32(%1), %%rax, %%rdx ;" /* B[0]*B[2] */
+
+ "addq %%rax, %%r9 ;"
+ "adcq %%rdx, %%r10 ;"
+ "adcq %%rcx, %%r11 ;"
+ "adcq %%r14, %%r15 ;"
+ "adcq $0, %%r13 ;"
+ "movq $0, %%r14 ;"
+ "adcq $0, %%r14 ;"
+
+ "movq 32(%1), %%rdx ;" /* B[0] */
+ "mulx 56(%1), %%rax, %%rcx ;" /* B[0]*B[3] */
+
+ "addq %%rax, %%r10 ;"
+ "adcq %%rcx, %%r11 ;"
+ "adcq $0, %%r15 ;"
+ "adcq $0, %%r13 ;"
+ "adcq $0, %%r14 ;"
+
+ "shldq $1, %%r13, %%r14 ;"
+ "shldq $1, %%r15, %%r13 ;"
+ "shldq $1, %%r11, %%r15 ;"
+ "shldq $1, %%r10, %%r11 ;"
+ "shldq $1, %%r9, %%r10 ;"
+ "shldq $1, %%r8, %%r9 ;"
+ "shlq $1, %%r8 ;"
+
+ /*******************/
+ "mulx %%rdx, %%rax, %%rcx ; " /* B[0]^2 */
+ /*******************/
+ "movq %%rax, 64(%0) ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, 72(%0) ;"
+ "movq 40(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ; " /* B[1]^2 */
+ "adcq %%rax, %%r9 ;"
+ "movq %%r9, 80(%0) ;"
+ "adcq %%rcx, %%r10 ;"
+ "movq %%r10, 88(%0) ;"
+ "movq 48(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ; " /* B[2]^2 */
+ "adcq %%rax, %%r11 ;"
+ "movq %%r11, 96(%0) ;"
+ "adcq %%rcx, %%r15 ;"
+ "movq %%r15, 104(%0) ;"
+ "movq 56(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ; " /* B[3]^2 */
+ "adcq %%rax, %%r13 ;"
+ "movq %%r13, 112(%0) ;"
+ "adcq %%rcx, %%r14 ;"
+ "movq %%r14, 120(%0) ;"
+ :
+ : "r"(c), "r"(a)
+ : "memory", "cc", "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10",
+ "%r11", "%r13", "%r14", "%r15");
+}
+
+static void red_eltfp25519_2w_adx(u64 *const c, const u64 *const a)
+{
+ asm volatile(
+ "movl $38, %%edx; " /* 2*c = 38 = 2^256 */
+ "mulx 32(%1), %%r8, %%r10; " /* c*C[4] */
+ "xorl %%ebx, %%ebx ;"
+ "adox (%1), %%r8 ;"
+ "mulx 40(%1), %%r9, %%r11; " /* c*C[5] */
+ "adcx %%r10, %%r9 ;"
+ "adox 8(%1), %%r9 ;"
+ "mulx 48(%1), %%r10, %%rax; " /* c*C[6] */
+ "adcx %%r11, %%r10 ;"
+ "adox 16(%1), %%r10 ;"
+ "mulx 56(%1), %%r11, %%rcx; " /* c*C[7] */
+ "adcx %%rax, %%r11 ;"
+ "adox 24(%1), %%r11 ;"
+ /***************************************/
+ "adcx %%rbx, %%rcx ;"
+ "adox %%rbx, %%rcx ;"
+ "imul %%rdx, %%rcx ;" /* c*C[4], cf=0, of=0 */
+ "adcx %%rcx, %%r8 ;"
+ "adcx %%rbx, %%r9 ;"
+ "movq %%r9, 8(%0) ;"
+ "adcx %%rbx, %%r10 ;"
+ "movq %%r10, 16(%0) ;"
+ "adcx %%rbx, %%r11 ;"
+ "movq %%r11, 24(%0) ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%edx, %%ecx ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, (%0) ;"
+
+ "mulx 96(%1), %%r8, %%r10; " /* c*C[4] */
+ "xorl %%ebx, %%ebx ;"
+ "adox 64(%1), %%r8 ;"
+ "mulx 104(%1), %%r9, %%r11; " /* c*C[5] */
+ "adcx %%r10, %%r9 ;"
+ "adox 72(%1), %%r9 ;"
+ "mulx 112(%1), %%r10, %%rax; " /* c*C[6] */
+ "adcx %%r11, %%r10 ;"
+ "adox 80(%1), %%r10 ;"
+ "mulx 120(%1), %%r11, %%rcx; " /* c*C[7] */
+ "adcx %%rax, %%r11 ;"
+ "adox 88(%1), %%r11 ;"
+ /****************************************/
+ "adcx %%rbx, %%rcx ;"
+ "adox %%rbx, %%rcx ;"
+ "imul %%rdx, %%rcx ;" /* c*C[4], cf=0, of=0 */
+ "adcx %%rcx, %%r8 ;"
+ "adcx %%rbx, %%r9 ;"
+ "movq %%r9, 40(%0) ;"
+ "adcx %%rbx, %%r10 ;"
+ "movq %%r10, 48(%0) ;"
+ "adcx %%rbx, %%r11 ;"
+ "movq %%r11, 56(%0) ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%edx, %%ecx ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, 32(%0) ;"
+ :
+ : "r"(c), "r"(a)
+ : "memory", "cc", "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9",
+ "%r10", "%r11");
+}
+
+static void red_eltfp25519_2w_bmi2(u64 *const c, const u64 *const a)
+{
+ asm volatile(
+ "movl $38, %%edx ; " /* 2*c = 38 = 2^256 */
+ "mulx 32(%1), %%r8, %%r10 ;" /* c*C[4] */
+ "mulx 40(%1), %%r9, %%r11 ;" /* c*C[5] */
+ "addq %%r10, %%r9 ;"
+ "mulx 48(%1), %%r10, %%rax ;" /* c*C[6] */
+ "adcq %%r11, %%r10 ;"
+ "mulx 56(%1), %%r11, %%rcx ;" /* c*C[7] */
+ "adcq %%rax, %%r11 ;"
+ /***************************************/
+ "adcq $0, %%rcx ;"
+ "addq (%1), %%r8 ;"
+ "adcq 8(%1), %%r9 ;"
+ "adcq 16(%1), %%r10 ;"
+ "adcq 24(%1), %%r11 ;"
+ "adcq $0, %%rcx ;"
+ "imul %%rdx, %%rcx ;" /* c*C[4], cf=0 */
+ "addq %%rcx, %%r8 ;"
+ "adcq $0, %%r9 ;"
+ "movq %%r9, 8(%0) ;"
+ "adcq $0, %%r10 ;"
+ "movq %%r10, 16(%0) ;"
+ "adcq $0, %%r11 ;"
+ "movq %%r11, 24(%0) ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%edx, %%ecx ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, (%0) ;"
+
+ "mulx 96(%1), %%r8, %%r10 ;" /* c*C[4] */
+ "mulx 104(%1), %%r9, %%r11 ;" /* c*C[5] */
+ "addq %%r10, %%r9 ;"
+ "mulx 112(%1), %%r10, %%rax ;" /* c*C[6] */
+ "adcq %%r11, %%r10 ;"
+ "mulx 120(%1), %%r11, %%rcx ;" /* c*C[7] */
+ "adcq %%rax, %%r11 ;"
+ /****************************************/
+ "adcq $0, %%rcx ;"
+ "addq 64(%1), %%r8 ;"
+ "adcq 72(%1), %%r9 ;"
+ "adcq 80(%1), %%r10 ;"
+ "adcq 88(%1), %%r11 ;"
+ "adcq $0, %%rcx ;"
+ "imul %%rdx, %%rcx ;" /* c*C[4], cf=0 */
+ "addq %%rcx, %%r8 ;"
+ "adcq $0, %%r9 ;"
+ "movq %%r9, 40(%0) ;"
+ "adcq $0, %%r10 ;"
+ "movq %%r10, 48(%0) ;"
+ "adcq $0, %%r11 ;"
+ "movq %%r11, 56(%0) ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%edx, %%ecx ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, 32(%0) ;"
+ :
+ : "r"(c), "r"(a)
+ : "memory", "cc", "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10",
+ "%r11");
+}
+
+static void mul_256x256_integer_adx(u64 *const c, const u64 *const a,
+ const u64 *const b)
+{
+ asm volatile(
+ "movq (%1), %%rdx; " /* A[0] */
+ "mulx (%2), %%r8, %%r9; " /* A[0]*B[0] */
+ "xorl %%r10d, %%r10d ;"
+ "movq %%r8, (%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[0]*B[1] */
+ "adox %%r9, %%r10 ;"
+ "movq %%r10, 8(%0) ;"
+ "mulx 16(%2), %%r15, %%r13; " /* A[0]*B[2] */
+ "adox %%r11, %%r15 ;"
+ "mulx 24(%2), %%r14, %%rdx; " /* A[0]*B[3] */
+ "adox %%r13, %%r14 ;"
+ "movq $0, %%rax ;"
+ /******************************************/
+ "adox %%rdx, %%rax ;"
+
+ "movq 8(%1), %%rdx; " /* A[1] */
+ "mulx (%2), %%r8, %%r9; " /* A[1]*B[0] */
+ "xorl %%r10d, %%r10d ;"
+ "adcx 8(%0), %%r8 ;"
+ "movq %%r8, 8(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[1]*B[1] */
+ "adox %%r9, %%r10 ;"
+ "adcx %%r15, %%r10 ;"
+ "movq %%r10, 16(%0) ;"
+ "mulx 16(%2), %%r15, %%r13; " /* A[1]*B[2] */
+ "adox %%r11, %%r15 ;"
+ "adcx %%r14, %%r15 ;"
+ "movq $0, %%r8 ;"
+ "mulx 24(%2), %%r14, %%rdx; " /* A[1]*B[3] */
+ "adox %%r13, %%r14 ;"
+ "adcx %%rax, %%r14 ;"
+ "movq $0, %%rax ;"
+ /******************************************/
+ "adox %%rdx, %%rax ;"
+ "adcx %%r8, %%rax ;"
+
+ "movq 16(%1), %%rdx; " /* A[2] */
+ "mulx (%2), %%r8, %%r9; " /* A[2]*B[0] */
+ "xorl %%r10d, %%r10d ;"
+ "adcx 16(%0), %%r8 ;"
+ "movq %%r8, 16(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[2]*B[1] */
+ "adox %%r9, %%r10 ;"
+ "adcx %%r15, %%r10 ;"
+ "movq %%r10, 24(%0) ;"
+ "mulx 16(%2), %%r15, %%r13; " /* A[2]*B[2] */
+ "adox %%r11, %%r15 ;"
+ "adcx %%r14, %%r15 ;"
+ "movq $0, %%r8 ;"
+ "mulx 24(%2), %%r14, %%rdx; " /* A[2]*B[3] */
+ "adox %%r13, %%r14 ;"
+ "adcx %%rax, %%r14 ;"
+ "movq $0, %%rax ;"
+ /******************************************/
+ "adox %%rdx, %%rax ;"
+ "adcx %%r8, %%rax ;"
+
+ "movq 24(%1), %%rdx; " /* A[3] */
+ "mulx (%2), %%r8, %%r9; " /* A[3]*B[0] */
+ "xorl %%r10d, %%r10d ;"
+ "adcx 24(%0), %%r8 ;"
+ "movq %%r8, 24(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[3]*B[1] */
+ "adox %%r9, %%r10 ;"
+ "adcx %%r15, %%r10 ;"
+ "movq %%r10, 32(%0) ;"
+ "mulx 16(%2), %%r15, %%r13; " /* A[3]*B[2] */
+ "adox %%r11, %%r15 ;"
+ "adcx %%r14, %%r15 ;"
+ "movq %%r15, 40(%0) ;"
+ "movq $0, %%r8 ;"
+ "mulx 24(%2), %%r14, %%rdx; " /* A[3]*B[3] */
+ "adox %%r13, %%r14 ;"
+ "adcx %%rax, %%r14 ;"
+ "movq %%r14, 48(%0) ;"
+ "movq $0, %%rax ;"
+ /******************************************/
+ "adox %%rdx, %%rax ;"
+ "adcx %%r8, %%rax ;"
+ "movq %%rax, 56(%0) ;"
+ :
+ : "r"(c), "r"(a), "r"(b)
+ : "memory", "cc", "%rax", "%rdx", "%r8", "%r9", "%r10", "%r11",
+ "%r13", "%r14", "%r15");
+}
+
+static void mul_256x256_integer_bmi2(u64 *const c, const u64 *const a,
+ const u64 *const b)
+{
+ asm volatile(
+ "movq (%1), %%rdx; " /* A[0] */
+ "mulx (%2), %%r8, %%r15; " /* A[0]*B[0] */
+ "movq %%r8, (%0) ;"
+ "mulx 8(%2), %%r10, %%rax; " /* A[0]*B[1] */
+ "addq %%r10, %%r15 ;"
+ "mulx 16(%2), %%r8, %%rbx; " /* A[0]*B[2] */
+ "adcq %%r8, %%rax ;"
+ "mulx 24(%2), %%r10, %%rcx; " /* A[0]*B[3] */
+ "adcq %%r10, %%rbx ;"
+ /******************************************/
+ "adcq $0, %%rcx ;"
+
+ "movq 8(%1), %%rdx; " /* A[1] */
+ "mulx (%2), %%r8, %%r9; " /* A[1]*B[0] */
+ "addq %%r15, %%r8 ;"
+ "movq %%r8, 8(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[1]*B[1] */
+ "adcq %%r10, %%r9 ;"
+ "mulx 16(%2), %%r8, %%r13; " /* A[1]*B[2] */
+ "adcq %%r8, %%r11 ;"
+ "mulx 24(%2), %%r10, %%r15; " /* A[1]*B[3] */
+ "adcq %%r10, %%r13 ;"
+ /******************************************/
+ "adcq $0, %%r15 ;"
+
+ "addq %%r9, %%rax ;"
+ "adcq %%r11, %%rbx ;"
+ "adcq %%r13, %%rcx ;"
+ "adcq $0, %%r15 ;"
+
+ "movq 16(%1), %%rdx; " /* A[2] */
+ "mulx (%2), %%r8, %%r9; " /* A[2]*B[0] */
+ "addq %%rax, %%r8 ;"
+ "movq %%r8, 16(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[2]*B[1] */
+ "adcq %%r10, %%r9 ;"
+ "mulx 16(%2), %%r8, %%r13; " /* A[2]*B[2] */
+ "adcq %%r8, %%r11 ;"
+ "mulx 24(%2), %%r10, %%rax; " /* A[2]*B[3] */
+ "adcq %%r10, %%r13 ;"
+ /******************************************/
+ "adcq $0, %%rax ;"
+
+ "addq %%r9, %%rbx ;"
+ "adcq %%r11, %%rcx ;"
+ "adcq %%r13, %%r15 ;"
+ "adcq $0, %%rax ;"
+
+ "movq 24(%1), %%rdx; " /* A[3] */
+ "mulx (%2), %%r8, %%r9; " /* A[3]*B[0] */
+ "addq %%rbx, %%r8 ;"
+ "movq %%r8, 24(%0) ;"
+ "mulx 8(%2), %%r10, %%r11; " /* A[3]*B[1] */
+ "adcq %%r10, %%r9 ;"
+ "mulx 16(%2), %%r8, %%r13; " /* A[3]*B[2] */
+ "adcq %%r8, %%r11 ;"
+ "mulx 24(%2), %%r10, %%rbx; " /* A[3]*B[3] */
+ "adcq %%r10, %%r13 ;"
+ /******************************************/
+ "adcq $0, %%rbx ;"
+
+ "addq %%r9, %%rcx ;"
+ "movq %%rcx, 32(%0) ;"
+ "adcq %%r11, %%r15 ;"
+ "movq %%r15, 40(%0) ;"
+ "adcq %%r13, %%rax ;"
+ "movq %%rax, 48(%0) ;"
+ "adcq $0, %%rbx ;"
+ "movq %%rbx, 56(%0) ;"
+ :
+ : "r"(c), "r"(a), "r"(b)
+ : "memory", "cc", "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9",
+ "%r10", "%r11", "%r13", "%r15");
+}
+
+static void sqr_256x256_integer_adx(u64 *const c, const u64 *const a)
+{
+ asm volatile(
+ "movq (%1), %%rdx ;" /* A[0] */
+ "mulx 8(%1), %%r8, %%r14 ;" /* A[1]*A[0] */
+ "xorl %%r15d, %%r15d;"
+ "mulx 16(%1), %%r9, %%r10 ;" /* A[2]*A[0] */
+ "adcx %%r14, %%r9 ;"
+ "mulx 24(%1), %%rax, %%rcx ;" /* A[3]*A[0] */
+ "adcx %%rax, %%r10 ;"
+ "movq 24(%1), %%rdx ;" /* A[3] */
+ "mulx 8(%1), %%r11, %%rbx ;" /* A[1]*A[3] */
+ "adcx %%rcx, %%r11 ;"
+ "mulx 16(%1), %%rax, %%r13 ;" /* A[2]*A[3] */
+ "adcx %%rax, %%rbx ;"
+ "movq 8(%1), %%rdx ;" /* A[1] */
+ "adcx %%r15, %%r13 ;"
+ "mulx 16(%1), %%rax, %%rcx ;" /* A[2]*A[1] */
+ "movq $0, %%r14 ;"
+ /******************************************/
+ "adcx %%r15, %%r14 ;"
+
+ "xorl %%r15d, %%r15d;"
+ "adox %%rax, %%r10 ;"
+ "adcx %%r8, %%r8 ;"
+ "adox %%rcx, %%r11 ;"
+ "adcx %%r9, %%r9 ;"
+ "adox %%r15, %%rbx ;"
+ "adcx %%r10, %%r10 ;"
+ "adox %%r15, %%r13 ;"
+ "adcx %%r11, %%r11 ;"
+ "adox %%r15, %%r14 ;"
+ "adcx %%rbx, %%rbx ;"
+ "adcx %%r13, %%r13 ;"
+ "adcx %%r14, %%r14 ;"
+
+ "movq (%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[0]^2 */
+ /*******************/
+ "movq %%rax, 0(%0) ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, 8(%0) ;"
+ "movq 8(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[1]^2 */
+ "adcq %%rax, %%r9 ;"
+ "movq %%r9, 16(%0) ;"
+ "adcq %%rcx, %%r10 ;"
+ "movq %%r10, 24(%0) ;"
+ "movq 16(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[2]^2 */
+ "adcq %%rax, %%r11 ;"
+ "movq %%r11, 32(%0) ;"
+ "adcq %%rcx, %%rbx ;"
+ "movq %%rbx, 40(%0) ;"
+ "movq 24(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[3]^2 */
+ "adcq %%rax, %%r13 ;"
+ "movq %%r13, 48(%0) ;"
+ "adcq %%rcx, %%r14 ;"
+ "movq %%r14, 56(%0) ;"
+ :
+ : "r"(c), "r"(a)
+ : "memory", "cc", "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9",
+ "%r10", "%r11", "%r13", "%r14", "%r15");
+}
+
+static void sqr_256x256_integer_bmi2(u64 *const c, const u64 *const a)
+{
+ asm volatile(
+ "movq 8(%1), %%rdx ;" /* A[1] */
+ "mulx (%1), %%r8, %%r9 ;" /* A[0]*A[1] */
+ "mulx 16(%1), %%r10, %%r11 ;" /* A[2]*A[1] */
+ "mulx 24(%1), %%rcx, %%r14 ;" /* A[3]*A[1] */
+
+ "movq 16(%1), %%rdx ;" /* A[2] */
+ "mulx 24(%1), %%r15, %%r13 ;" /* A[3]*A[2] */
+ "mulx (%1), %%rax, %%rdx ;" /* A[0]*A[2] */
+
+ "addq %%rax, %%r9 ;"
+ "adcq %%rdx, %%r10 ;"
+ "adcq %%rcx, %%r11 ;"
+ "adcq %%r14, %%r15 ;"
+ "adcq $0, %%r13 ;"
+ "movq $0, %%r14 ;"
+ "adcq $0, %%r14 ;"
+
+ "movq (%1), %%rdx ;" /* A[0] */
+ "mulx 24(%1), %%rax, %%rcx ;" /* A[0]*A[3] */
+
+ "addq %%rax, %%r10 ;"
+ "adcq %%rcx, %%r11 ;"
+ "adcq $0, %%r15 ;"
+ "adcq $0, %%r13 ;"
+ "adcq $0, %%r14 ;"
+
+ "shldq $1, %%r13, %%r14 ;"
+ "shldq $1, %%r15, %%r13 ;"
+ "shldq $1, %%r11, %%r15 ;"
+ "shldq $1, %%r10, %%r11 ;"
+ "shldq $1, %%r9, %%r10 ;"
+ "shldq $1, %%r8, %%r9 ;"
+ "shlq $1, %%r8 ;"
+
+ /*******************/
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[0]^2 */
+ /*******************/
+ "movq %%rax, 0(%0) ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, 8(%0) ;"
+ "movq 8(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[1]^2 */
+ "adcq %%rax, %%r9 ;"
+ "movq %%r9, 16(%0) ;"
+ "adcq %%rcx, %%r10 ;"
+ "movq %%r10, 24(%0) ;"
+ "movq 16(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[2]^2 */
+ "adcq %%rax, %%r11 ;"
+ "movq %%r11, 32(%0) ;"
+ "adcq %%rcx, %%r15 ;"
+ "movq %%r15, 40(%0) ;"
+ "movq 24(%1), %%rdx ;"
+ "mulx %%rdx, %%rax, %%rcx ;" /* A[3]^2 */
+ "adcq %%rax, %%r13 ;"
+ "movq %%r13, 48(%0) ;"
+ "adcq %%rcx, %%r14 ;"
+ "movq %%r14, 56(%0) ;"
+ :
+ : "r"(c), "r"(a)
+ : "memory", "cc", "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10",
+ "%r11", "%r13", "%r14", "%r15");
+}
+
+static void red_eltfp25519_1w_adx(u64 *const c, const u64 *const a)
+{
+ asm volatile(
+ "movl $38, %%edx ;" /* 2*c = 38 = 2^256 */
+ "mulx 32(%1), %%r8, %%r10 ;" /* c*C[4] */
+ "xorl %%ebx, %%ebx ;"
+ "adox (%1), %%r8 ;"
+ "mulx 40(%1), %%r9, %%r11 ;" /* c*C[5] */
+ "adcx %%r10, %%r9 ;"
+ "adox 8(%1), %%r9 ;"
+ "mulx 48(%1), %%r10, %%rax ;" /* c*C[6] */
+ "adcx %%r11, %%r10 ;"
+ "adox 16(%1), %%r10 ;"
+ "mulx 56(%1), %%r11, %%rcx ;" /* c*C[7] */
+ "adcx %%rax, %%r11 ;"
+ "adox 24(%1), %%r11 ;"
+ /***************************************/
+ "adcx %%rbx, %%rcx ;"
+ "adox %%rbx, %%rcx ;"
+ "imul %%rdx, %%rcx ;" /* c*C[4], cf=0, of=0 */
+ "adcx %%rcx, %%r8 ;"
+ "adcx %%rbx, %%r9 ;"
+ "movq %%r9, 8(%0) ;"
+ "adcx %%rbx, %%r10 ;"
+ "movq %%r10, 16(%0) ;"
+ "adcx %%rbx, %%r11 ;"
+ "movq %%r11, 24(%0) ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%edx, %%ecx ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, (%0) ;"
+ :
+ : "r"(c), "r"(a)
+ : "memory", "cc", "%rax", "%rbx", "%rcx", "%rdx", "%r8", "%r9",
+ "%r10", "%r11");
+}
+
+static void red_eltfp25519_1w_bmi2(u64 *const c, const u64 *const a)
+{
+ asm volatile(
+ "movl $38, %%edx ;" /* 2*c = 38 = 2^256 */
+ "mulx 32(%1), %%r8, %%r10 ;" /* c*C[4] */
+ "mulx 40(%1), %%r9, %%r11 ;" /* c*C[5] */
+ "addq %%r10, %%r9 ;"
+ "mulx 48(%1), %%r10, %%rax ;" /* c*C[6] */
+ "adcq %%r11, %%r10 ;"
+ "mulx 56(%1), %%r11, %%rcx ;" /* c*C[7] */
+ "adcq %%rax, %%r11 ;"
+ /***************************************/
+ "adcq $0, %%rcx ;"
+ "addq (%1), %%r8 ;"
+ "adcq 8(%1), %%r9 ;"
+ "adcq 16(%1), %%r10 ;"
+ "adcq 24(%1), %%r11 ;"
+ "adcq $0, %%rcx ;"
+ "imul %%rdx, %%rcx ;" /* c*C[4], cf=0 */
+ "addq %%rcx, %%r8 ;"
+ "adcq $0, %%r9 ;"
+ "movq %%r9, 8(%0) ;"
+ "adcq $0, %%r10 ;"
+ "movq %%r10, 16(%0) ;"
+ "adcq $0, %%r11 ;"
+ "movq %%r11, 24(%0) ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%edx, %%ecx ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, (%0) ;"
+ :
+ : "r"(c), "r"(a)
+ : "memory", "cc", "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10",
+ "%r11");
+}
+
+static __always_inline void
+add_eltfp25519_1w_adx(u64 *const c, const u64 *const a, const u64 *const b)
+{
+ asm volatile(
+ "mov $38, %%eax ;"
+ "xorl %%ecx, %%ecx ;"
+ "movq (%2), %%r8 ;"
+ "adcx (%1), %%r8 ;"
+ "movq 8(%2), %%r9 ;"
+ "adcx 8(%1), %%r9 ;"
+ "movq 16(%2), %%r10 ;"
+ "adcx 16(%1), %%r10 ;"
+ "movq 24(%2), %%r11 ;"
+ "adcx 24(%1), %%r11 ;"
+ "cmovc %%eax, %%ecx ;"
+ "xorl %%eax, %%eax ;"
+ "adcx %%rcx, %%r8 ;"
+ "adcx %%rax, %%r9 ;"
+ "movq %%r9, 8(%0) ;"
+ "adcx %%rax, %%r10 ;"
+ "movq %%r10, 16(%0) ;"
+ "adcx %%rax, %%r11 ;"
+ "movq %%r11, 24(%0) ;"
+ "mov $38, %%ecx ;"
+ "cmovc %%ecx, %%eax ;"
+ "addq %%rax, %%r8 ;"
+ "movq %%r8, (%0) ;"
+ :
+ : "r"(c), "r"(a), "r"(b)
+ : "memory", "cc", "%rax", "%rcx", "%r8", "%r9", "%r10", "%r11");
+}
+
+static __always_inline void
+add_eltfp25519_1w_bmi2(u64 *const c, const u64 *const a, const u64 *const b)
+{
+ asm volatile(
+ "mov $38, %%eax ;"
+ "movq (%2), %%r8 ;"
+ "addq (%1), %%r8 ;"
+ "movq 8(%2), %%r9 ;"
+ "adcq 8(%1), %%r9 ;"
+ "movq 16(%2), %%r10 ;"
+ "adcq 16(%1), %%r10 ;"
+ "movq 24(%2), %%r11 ;"
+ "adcq 24(%1), %%r11 ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%eax, %%ecx ;"
+ "addq %%rcx, %%r8 ;"
+ "adcq $0, %%r9 ;"
+ "movq %%r9, 8(%0) ;"
+ "adcq $0, %%r10 ;"
+ "movq %%r10, 16(%0) ;"
+ "adcq $0, %%r11 ;"
+ "movq %%r11, 24(%0) ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%eax, %%ecx ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, (%0) ;"
+ :
+ : "r"(c), "r"(a), "r"(b)
+ : "memory", "cc", "%rax", "%rcx", "%r8", "%r9", "%r10", "%r11");
+}
+
+static __always_inline void
+sub_eltfp25519_1w(u64 *const c, const u64 *const a, const u64 *const b)
+{
+ asm volatile(
+ "mov $38, %%eax ;"
+ "movq (%1), %%r8 ;"
+ "subq (%2), %%r8 ;"
+ "movq 8(%1), %%r9 ;"
+ "sbbq 8(%2), %%r9 ;"
+ "movq 16(%1), %%r10 ;"
+ "sbbq 16(%2), %%r10 ;"
+ "movq 24(%1), %%r11 ;"
+ "sbbq 24(%2), %%r11 ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%eax, %%ecx ;"
+ "subq %%rcx, %%r8 ;"
+ "sbbq $0, %%r9 ;"
+ "movq %%r9, 8(%0) ;"
+ "sbbq $0, %%r10 ;"
+ "movq %%r10, 16(%0) ;"
+ "sbbq $0, %%r11 ;"
+ "movq %%r11, 24(%0) ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%eax, %%ecx ;"
+ "subq %%rcx, %%r8 ;"
+ "movq %%r8, (%0) ;"
+ :
+ : "r"(c), "r"(a), "r"(b)
+ : "memory", "cc", "%rax", "%rcx", "%r8", "%r9", "%r10", "%r11");
+}
+
+/* Multiplication by a24 = (A+2)/4 = (486662+2)/4 = 121666 */
+static __always_inline void
+mul_a24_eltfp25519_1w(u64 *const c, const u64 *const a)
+{
+ const u64 a24 = 121666;
+ asm volatile(
+ "movq %2, %%rdx ;"
+ "mulx (%1), %%r8, %%r10 ;"
+ "mulx 8(%1), %%r9, %%r11 ;"
+ "addq %%r10, %%r9 ;"
+ "mulx 16(%1), %%r10, %%rax ;"
+ "adcq %%r11, %%r10 ;"
+ "mulx 24(%1), %%r11, %%rcx ;"
+ "adcq %%rax, %%r11 ;"
+ /**************************/
+ "adcq $0, %%rcx ;"
+ "movl $38, %%edx ;" /* 2*c = 38 = 2^256 mod 2^255-19*/
+ "imul %%rdx, %%rcx ;"
+ "addq %%rcx, %%r8 ;"
+ "adcq $0, %%r9 ;"
+ "movq %%r9, 8(%0) ;"
+ "adcq $0, %%r10 ;"
+ "movq %%r10, 16(%0) ;"
+ "adcq $0, %%r11 ;"
+ "movq %%r11, 24(%0) ;"
+ "mov $0, %%ecx ;"
+ "cmovc %%edx, %%ecx ;"
+ "addq %%rcx, %%r8 ;"
+ "movq %%r8, (%0) ;"
+ :
+ : "r"(c), "r"(a), "r"(a24)
+ : "memory", "cc", "%rax", "%rcx", "%rdx", "%r8", "%r9", "%r10",
+ "%r11");
+}
+
+static void inv_eltfp25519_1w_adx(u64 *const c, const u64 *const a)
+{
+ struct {
+ eltfp25519_1w_buffer buffer;
+ eltfp25519_1w x0, x1, x2;
+ } __aligned(32) m;
+ u64 *T[4];
+
+ T[0] = m.x0;
+ T[1] = c; /* x^(-1) */
+ T[2] = m.x1;
+ T[3] = m.x2;
+
+ copy_eltfp25519_1w(T[1], a);
+ sqrn_eltfp25519_1w_adx(T[1], 1);
+ copy_eltfp25519_1w(T[2], T[1]);
+ sqrn_eltfp25519_1w_adx(T[2], 2);
+ mul_eltfp25519_1w_adx(T[0], a, T[2]);
+ mul_eltfp25519_1w_adx(T[1], T[1], T[0]);
+ copy_eltfp25519_1w(T[2], T[1]);
+ sqrn_eltfp25519_1w_adx(T[2], 1);
+ mul_eltfp25519_1w_adx(T[0], T[0], T[2]);
+ copy_eltfp25519_1w(T[2], T[0]);
+ sqrn_eltfp25519_1w_adx(T[2], 5);
+ mul_eltfp25519_1w_adx(T[0], T[0], T[2]);
+ copy_eltfp25519_1w(T[2], T[0]);
+ sqrn_eltfp25519_1w_adx(T[2], 10);
+ mul_eltfp25519_1w_adx(T[2], T[2], T[0]);
+ copy_eltfp25519_1w(T[3], T[2]);
+ sqrn_eltfp25519_1w_adx(T[3], 20);
+ mul_eltfp25519_1w_adx(T[3], T[3], T[2]);
+ sqrn_eltfp25519_1w_adx(T[3], 10);
+ mul_eltfp25519_1w_adx(T[3], T[3], T[0]);
+ copy_eltfp25519_1w(T[0], T[3]);
+ sqrn_eltfp25519_1w_adx(T[0], 50);
+ mul_eltfp25519_1w_adx(T[0], T[0], T[3]);
+ copy_eltfp25519_1w(T[2], T[0]);
+ sqrn_eltfp25519_1w_adx(T[2], 100);
+ mul_eltfp25519_1w_adx(T[2], T[2], T[0]);
+ sqrn_eltfp25519_1w_adx(T[2], 50);
+ mul_eltfp25519_1w_adx(T[2], T[2], T[3]);
+ sqrn_eltfp25519_1w_adx(T[2], 5);
+ mul_eltfp25519_1w_adx(T[1], T[1], T[2]);
+
+ memzero_explicit(&m, sizeof(m));
+}
+
+static void inv_eltfp25519_1w_bmi2(u64 *const c, const u64 *const a)
+{
+ struct {
+ eltfp25519_1w_buffer buffer;
+ eltfp25519_1w x0, x1, x2;
+ } __aligned(32) m;
+ u64 *T[5];
+
+ T[0] = m.x0;
+ T[1] = c; /* x^(-1) */
+ T[2] = m.x1;
+ T[3] = m.x2;
+
+ copy_eltfp25519_1w(T[1], a);
+ sqrn_eltfp25519_1w_bmi2(T[1], 1);
+ copy_eltfp25519_1w(T[2], T[1]);
+ sqrn_eltfp25519_1w_bmi2(T[2], 2);
+ mul_eltfp25519_1w_bmi2(T[0], a, T[2]);
+ mul_eltfp25519_1w_bmi2(T[1], T[1], T[0]);
+ copy_eltfp25519_1w(T[2], T[1]);
+ sqrn_eltfp25519_1w_bmi2(T[2], 1);
+ mul_eltfp25519_1w_bmi2(T[0], T[0], T[2]);
+ copy_eltfp25519_1w(T[2], T[0]);
+ sqrn_eltfp25519_1w_bmi2(T[2], 5);
+ mul_eltfp25519_1w_bmi2(T[0], T[0], T[2]);
+ copy_eltfp25519_1w(T[2], T[0]);
+ sqrn_eltfp25519_1w_bmi2(T[2], 10);
+ mul_eltfp25519_1w_bmi2(T[2], T[2], T[0]);
+ copy_eltfp25519_1w(T[3], T[2]);
+ sqrn_eltfp25519_1w_bmi2(T[3], 20);
+ mul_eltfp25519_1w_bmi2(T[3], T[3], T[2]);
+ sqrn_eltfp25519_1w_bmi2(T[3], 10);
+ mul_eltfp25519_1w_bmi2(T[3], T[3], T[0]);
+ copy_eltfp25519_1w(T[0], T[3]);
+ sqrn_eltfp25519_1w_bmi2(T[0], 50);
+ mul_eltfp25519_1w_bmi2(T[0], T[0], T[3]);
+ copy_eltfp25519_1w(T[2], T[0]);
+ sqrn_eltfp25519_1w_bmi2(T[2], 100);
+ mul_eltfp25519_1w_bmi2(T[2], T[2], T[0]);
+ sqrn_eltfp25519_1w_bmi2(T[2], 50);
+ mul_eltfp25519_1w_bmi2(T[2], T[2], T[3]);
+ sqrn_eltfp25519_1w_bmi2(T[2], 5);
+ mul_eltfp25519_1w_bmi2(T[1], T[1], T[2]);
+
+ memzero_explicit(&m, sizeof(m));
+}
+
+/* Given c, a 256-bit number, fred_eltfp25519_1w updates c
+ * with a number such that 0 <= C < 2**255-19.
+ */
+static __always_inline void fred_eltfp25519_1w(u64 *const c)
+{
+ u64 tmp0 = 38, tmp1 = 19;
+ asm volatile(
+ "btrq $63, %3 ;" /* Put bit 255 in carry flag and clear */
+ "cmovncl %k5, %k4 ;" /* c[255] ? 38 : 19 */
+
+ /* Add either 19 or 38 to c */
+ "addq %4, %0 ;"
+ "adcq $0, %1 ;"
+ "adcq $0, %2 ;"
+ "adcq $0, %3 ;"
+
+ /* Test for bit 255 again; only triggered on overflow modulo 2^255-19 */
+ "movl $0, %k4 ;"
+ "cmovnsl %k5, %k4 ;" /* c[255] ? 0 : 19 */
+ "btrq $63, %3 ;" /* Clear bit 255 */
+
+ /* Subtract 19 if necessary */
+ "subq %4, %0 ;"
+ "sbbq $0, %1 ;"
+ "sbbq $0, %2 ;"
+ "sbbq $0, %3 ;"
+
+ : "+r"(c[0]), "+r"(c[1]), "+r"(c[2]), "+r"(c[3]), "+r"(tmp0),
+ "+r"(tmp1)
+ :
+ : "memory", "cc");
+}
+
+static __always_inline void cswap(u8 bit, u64 *const px, u64 *const py)
+{
+ u64 temp;
+ asm volatile(
+ "test %9, %9 ;"
+ "movq %0, %8 ;"
+ "cmovnzq %4, %0 ;"
+ "cmovnzq %8, %4 ;"
+ "movq %1, %8 ;"
+ "cmovnzq %5, %1 ;"
+ "cmovnzq %8, %5 ;"
+ "movq %2, %8 ;"
+ "cmovnzq %6, %2 ;"
+ "cmovnzq %8, %6 ;"
+ "movq %3, %8 ;"
+ "cmovnzq %7, %3 ;"
+ "cmovnzq %8, %7 ;"
+ : "+r"(px[0]), "+r"(px[1]), "+r"(px[2]), "+r"(px[3]),
+ "+r"(py[0]), "+r"(py[1]), "+r"(py[2]), "+r"(py[3]),
+ "=r"(temp)
+ : "r"(bit)
+ : "cc"
+ );
+}
+
+static __always_inline void cselect(u8 bit, u64 *const px, const u64 *const py)
+{
+ asm volatile(
+ "test %4, %4 ;"
+ "cmovnzq %5, %0 ;"
+ "cmovnzq %6, %1 ;"
+ "cmovnzq %7, %2 ;"
+ "cmovnzq %8, %3 ;"
+ : "+r"(px[0]), "+r"(px[1]), "+r"(px[2]), "+r"(px[3])
+ : "r"(bit), "rm"(py[0]), "rm"(py[1]), "rm"(py[2]), "rm"(py[3])
+ : "cc"
+ );
+}
+
+static __always_inline void clamp_secret(u8 secret[CURVE25519_KEY_SIZE])
+{
+ secret[0] &= 248;
+ secret[31] &= 127;
+ secret[31] |= 64;
+}
+
+static void curve25519_adx(u8 shared[CURVE25519_KEY_SIZE],
+ const u8 private_key[CURVE25519_KEY_SIZE],
+ const u8 session_key[CURVE25519_KEY_SIZE])
+{
+ struct {
+ u64 buffer[4 * NUM_WORDS_ELTFP25519];
+ u64 coordinates[4 * NUM_WORDS_ELTFP25519];
+ u64 workspace[6 * NUM_WORDS_ELTFP25519];
+ u8 session[CURVE25519_KEY_SIZE];
+ u8 private[CURVE25519_KEY_SIZE];
+ } __aligned(32) m;
+
+ int i = 0, j = 0;
+ u64 prev = 0;
+ u64 *const X1 = (u64 *)m.session;
+ u64 *const key = (u64 *)m.private;
+ u64 *const Px = m.coordinates + 0;
+ u64 *const Pz = m.coordinates + 4;
+ u64 *const Qx = m.coordinates + 8;
+ u64 *const Qz = m.coordinates + 12;
+ u64 *const X2 = Qx;
+ u64 *const Z2 = Qz;
+ u64 *const X3 = Px;
+ u64 *const Z3 = Pz;
+ u64 *const X2Z2 = Qx;
+ u64 *const X3Z3 = Px;
+
+ u64 *const A = m.workspace + 0;
+ u64 *const B = m.workspace + 4;
+ u64 *const D = m.workspace + 8;
+ u64 *const C = m.workspace + 12;
+ u64 *const DA = m.workspace + 16;
+ u64 *const CB = m.workspace + 20;
+ u64 *const AB = A;
+ u64 *const DC = D;
+ u64 *const DACB = DA;
+
+ memcpy(m.private, private_key, sizeof(m.private));
+ memcpy(m.session, session_key, sizeof(m.session));
+
+ clamp_secret(m.private);
+
+ /* As in the draft:
+ * When receiving such an array, implementations of curve25519
+ * MUST mask the most-significant bit in the final byte. This
+ * is done to preserve compatibility with point formats which
+ * reserve the sign bit for use in other protocols and to
+ * increase resistance to implementation fingerprinting
+ */
+ m.session[CURVE25519_KEY_SIZE - 1] &= (1 << (255 % 8)) - 1;
+
+ copy_eltfp25519_1w(Px, X1);
+ setzero_eltfp25519_1w(Pz);
+ setzero_eltfp25519_1w(Qx);
+ setzero_eltfp25519_1w(Qz);
+
+ Pz[0] = 1;
+ Qx[0] = 1;
+
+ /* main-loop */
+ prev = 0;
+ j = 62;
+ for (i = 3; i >= 0; --i) {
+ while (j >= 0) {
+ u64 bit = (key[i] >> j) & 0x1;
+ u64 swap = bit ^ prev;
+ prev = bit;
+
+ add_eltfp25519_1w_adx(A, X2, Z2); /* A = (X2+Z2) */
+ sub_eltfp25519_1w(B, X2, Z2); /* B = (X2-Z2) */
+ add_eltfp25519_1w_adx(C, X3, Z3); /* C = (X3+Z3) */
+ sub_eltfp25519_1w(D, X3, Z3); /* D = (X3-Z3) */
+ mul_eltfp25519_2w_adx(DACB, AB, DC); /* [DA|CB] = [A|B]*[D|C] */
+
+ cselect(swap, A, C);
+ cselect(swap, B, D);
+
+ sqr_eltfp25519_2w_adx(AB); /* [AA|BB] = [A^2|B^2] */
+ add_eltfp25519_1w_adx(X3, DA, CB); /* X3 = (DA+CB) */
+ sub_eltfp25519_1w(Z3, DA, CB); /* Z3 = (DA-CB) */
+ sqr_eltfp25519_2w_adx(X3Z3); /* [X3|Z3] = [(DA+CB)|(DA+CB)]^2 */
+
+ copy_eltfp25519_1w(X2, B); /* X2 = B^2 */
+ sub_eltfp25519_1w(Z2, A, B); /* Z2 = E = AA-BB */
+
+ mul_a24_eltfp25519_1w(B, Z2); /* B = a24*E */
+ add_eltfp25519_1w_adx(B, B, X2); /* B = a24*E+B */
+ mul_eltfp25519_2w_adx(X2Z2, X2Z2, AB); /* [X2|Z2] = [B|E]*[A|a24*E+B] */
+ mul_eltfp25519_1w_adx(Z3, Z3, X1); /* Z3 = Z3*X1 */
+ --j;
+ }
+ j = 63;
+ }
+
+ inv_eltfp25519_1w_adx(A, Qz);
+ mul_eltfp25519_1w_adx((u64 *)shared, Qx, A);
+ fred_eltfp25519_1w((u64 *)shared);
+
+ memzero_explicit(&m, sizeof(m));
+}
+
+static void curve25519_adx_base(u8 session_key[CURVE25519_KEY_SIZE],
+ const u8 private_key[CURVE25519_KEY_SIZE])
+{
+ struct {
+ u64 buffer[4 * NUM_WORDS_ELTFP25519];
+ u64 coordinates[4 * NUM_WORDS_ELTFP25519];
+ u64 workspace[4 * NUM_WORDS_ELTFP25519];
+ u8 private[CURVE25519_KEY_SIZE];
+ } __aligned(32) m;
+
+ const int ite[4] = { 64, 64, 64, 63 };
+ const int q = 3;
+ u64 swap = 1;
+
+ int i = 0, j = 0, k = 0;
+ u64 *const key = (u64 *)m.private;
+ u64 *const Ur1 = m.coordinates + 0;
+ u64 *const Zr1 = m.coordinates + 4;
+ u64 *const Ur2 = m.coordinates + 8;
+ u64 *const Zr2 = m.coordinates + 12;
+
+ u64 *const UZr1 = m.coordinates + 0;
+ u64 *const ZUr2 = m.coordinates + 8;
+
+ u64 *const A = m.workspace + 0;
+ u64 *const B = m.workspace + 4;
+ u64 *const C = m.workspace + 8;
+ u64 *const D = m.workspace + 12;
+
+ u64 *const AB = m.workspace + 0;
+ u64 *const CD = m.workspace + 8;
+
+ const u64 *const P = table_ladder_8k;
+
+ memcpy(m.private, private_key, sizeof(m.private));
+
+ clamp_secret(m.private);
+
+ setzero_eltfp25519_1w(Ur1);
+ setzero_eltfp25519_1w(Zr1);
+ setzero_eltfp25519_1w(Zr2);
+ Ur1[0] = 1;
+ Zr1[0] = 1;
+ Zr2[0] = 1;
+
+ /* G-S */
+ Ur2[3] = 0x1eaecdeee27cab34UL;
+ Ur2[2] = 0xadc7a0b9235d48e2UL;
+ Ur2[1] = 0xbbf095ae14b2edf8UL;
+ Ur2[0] = 0x7e94e1fec82faabdUL;
+
+ /* main-loop */
+ j = q;
+ for (i = 0; i < NUM_WORDS_ELTFP25519; ++i) {
+ while (j < ite[i]) {
+ u64 bit = (key[i] >> j) & 0x1;
+ k = (64 * i + j - q);
+ swap = swap ^ bit;
+ cswap(swap, Ur1, Ur2);
+ cswap(swap, Zr1, Zr2);
+ swap = bit;
+ /* Addition */
+ sub_eltfp25519_1w(B, Ur1, Zr1); /* B = Ur1-Zr1 */
+ add_eltfp25519_1w_adx(A, Ur1, Zr1); /* A = Ur1+Zr1 */
+ mul_eltfp25519_1w_adx(C, &P[4 * k], B); /* C = M0-B */
+ sub_eltfp25519_1w(B, A, C); /* B = (Ur1+Zr1) - M*(Ur1-Zr1) */
+ add_eltfp25519_1w_adx(A, A, C); /* A = (Ur1+Zr1) + M*(Ur1-Zr1) */
+ sqr_eltfp25519_2w_adx(AB); /* A = A^2 | B = B^2 */
+ mul_eltfp25519_2w_adx(UZr1, ZUr2, AB); /* Ur1 = Zr2*A | Zr1 = Ur2*B */
+ ++j;
+ }
+ j = 0;
+ }
+
+ /* Doubling */
+ for (i = 0; i < q; ++i) {
+ add_eltfp25519_1w_adx(A, Ur1, Zr1); /* A = Ur1+Zr1 */
+ sub_eltfp25519_1w(B, Ur1, Zr1); /* B = Ur1-Zr1 */
+ sqr_eltfp25519_2w_adx(AB); /* A = A**2 B = B**2 */
+ copy_eltfp25519_1w(C, B); /* C = B */
+ sub_eltfp25519_1w(B, A, B); /* B = A-B */
+ mul_a24_eltfp25519_1w(D, B); /* D = my_a24*B */
+ add_eltfp25519_1w_adx(D, D, C); /* D = D+C */
+ mul_eltfp25519_2w_adx(UZr1, AB, CD); /* Ur1 = A*B Zr1 = Zr1*A */
+ }
+
+ /* Convert to affine coordinates */
+ inv_eltfp25519_1w_adx(A, Zr1);
+ mul_eltfp25519_1w_adx((u64 *)session_key, Ur1, A);
+ fred_eltfp25519_1w((u64 *)session_key);
+
+ memzero_explicit(&m, sizeof(m));
+}
+
+static void curve25519_bmi2(u8 shared[CURVE25519_KEY_SIZE],
+ const u8 private_key[CURVE25519_KEY_SIZE],
+ const u8 session_key[CURVE25519_KEY_SIZE])
+{
+ struct {
+ u64 buffer[4 * NUM_WORDS_ELTFP25519];
+ u64 coordinates[4 * NUM_WORDS_ELTFP25519];
+ u64 workspace[6 * NUM_WORDS_ELTFP25519];
+ u8 session[CURVE25519_KEY_SIZE];
+ u8 private[CURVE25519_KEY_SIZE];
+ } __aligned(32) m;
+
+ int i = 0, j = 0;
+ u64 prev = 0;
+ u64 *const X1 = (u64 *)m.session;
+ u64 *const key = (u64 *)m.private;
+ u64 *const Px = m.coordinates + 0;
+ u64 *const Pz = m.coordinates + 4;
+ u64 *const Qx = m.coordinates + 8;
+ u64 *const Qz = m.coordinates + 12;
+ u64 *const X2 = Qx;
+ u64 *const Z2 = Qz;
+ u64 *const X3 = Px;
+ u64 *const Z3 = Pz;
+ u64 *const X2Z2 = Qx;
+ u64 *const X3Z3 = Px;
+
+ u64 *const A = m.workspace + 0;
+ u64 *const B = m.workspace + 4;
+ u64 *const D = m.workspace + 8;
+ u64 *const C = m.workspace + 12;
+ u64 *const DA = m.workspace + 16;
+ u64 *const CB = m.workspace + 20;
+ u64 *const AB = A;
+ u64 *const DC = D;
+ u64 *const DACB = DA;
+
+ memcpy(m.private, private_key, sizeof(m.private));
+ memcpy(m.session, session_key, sizeof(m.session));
+
+ clamp_secret(m.private);
+
+ /* As in the draft:
+ * When receiving such an array, implementations of curve25519
+ * MUST mask the most-significant bit in the final byte. This
+ * is done to preserve compatibility with point formats which
+ * reserve the sign bit for use in other protocols and to
+ * increase resistance to implementation fingerprinting
+ */
+ m.session[CURVE25519_KEY_SIZE - 1] &= (1 << (255 % 8)) - 1;
+
+ copy_eltfp25519_1w(Px, X1);
+ setzero_eltfp25519_1w(Pz);
+ setzero_eltfp25519_1w(Qx);
+ setzero_eltfp25519_1w(Qz);
+
+ Pz[0] = 1;
+ Qx[0] = 1;
+
+ /* main-loop */
+ prev = 0;
+ j = 62;
+ for (i = 3; i >= 0; --i) {
+ while (j >= 0) {
+ u64 bit = (key[i] >> j) & 0x1;
+ u64 swap = bit ^ prev;
+ prev = bit;
+
+ add_eltfp25519_1w_bmi2(A, X2, Z2); /* A = (X2+Z2) */
+ sub_eltfp25519_1w(B, X2, Z2); /* B = (X2-Z2) */
+ add_eltfp25519_1w_bmi2(C, X3, Z3); /* C = (X3+Z3) */
+ sub_eltfp25519_1w(D, X3, Z3); /* D = (X3-Z3) */
+ mul_eltfp25519_2w_bmi2(DACB, AB, DC); /* [DA|CB] = [A|B]*[D|C] */
+
+ cselect(swap, A, C);
+ cselect(swap, B, D);
+
+ sqr_eltfp25519_2w_bmi2(AB); /* [AA|BB] = [A^2|B^2] */
+ add_eltfp25519_1w_bmi2(X3, DA, CB); /* X3 = (DA+CB) */
+ sub_eltfp25519_1w(Z3, DA, CB); /* Z3 = (DA-CB) */
+ sqr_eltfp25519_2w_bmi2(X3Z3); /* [X3|Z3] = [(DA+CB)|(DA+CB)]^2 */
+
+ copy_eltfp25519_1w(X2, B); /* X2 = B^2 */
+ sub_eltfp25519_1w(Z2, A, B); /* Z2 = E = AA-BB */
+
+ mul_a24_eltfp25519_1w(B, Z2); /* B = a24*E */
+ add_eltfp25519_1w_bmi2(B, B, X2); /* B = a24*E+B */
+ mul_eltfp25519_2w_bmi2(X2Z2, X2Z2, AB); /* [X2|Z2] = [B|E]*[A|a24*E+B] */
+ mul_eltfp25519_1w_bmi2(Z3, Z3, X1); /* Z3 = Z3*X1 */
+ --j;
+ }
+ j = 63;
+ }
+
+ inv_eltfp25519_1w_bmi2(A, Qz);
+ mul_eltfp25519_1w_bmi2((u64 *)shared, Qx, A);
+ fred_eltfp25519_1w((u64 *)shared);
+
+ memzero_explicit(&m, sizeof(m));
+}
+
+static void curve25519_bmi2_base(u8 session_key[CURVE25519_KEY_SIZE],
+ const u8 private_key[CURVE25519_KEY_SIZE])
+{
+ struct {
+ u64 buffer[4 * NUM_WORDS_ELTFP25519];
+ u64 coordinates[4 * NUM_WORDS_ELTFP25519];
+ u64 workspace[4 * NUM_WORDS_ELTFP25519];
+ u8 private[CURVE25519_KEY_SIZE];
+ } __aligned(32) m;
+
+ const int ite[4] = { 64, 64, 64, 63 };
+ const int q = 3;
+ u64 swap = 1;
+
+ int i = 0, j = 0, k = 0;
+ u64 *const key = (u64 *)m.private;
+ u64 *const Ur1 = m.coordinates + 0;
+ u64 *const Zr1 = m.coordinates + 4;
+ u64 *const Ur2 = m.coordinates + 8;
+ u64 *const Zr2 = m.coordinates + 12;
+
+ u64 *const UZr1 = m.coordinates + 0;
+ u64 *const ZUr2 = m.coordinates + 8;
+
+ u64 *const A = m.workspace + 0;
+ u64 *const B = m.workspace + 4;
+ u64 *const C = m.workspace + 8;
+ u64 *const D = m.workspace + 12;
+
+ u64 *const AB = m.workspace + 0;
+ u64 *const CD = m.workspace + 8;
+
+ const u64 *const P = table_ladder_8k;
+
+ memcpy(m.private, private_key, sizeof(m.private));
+
+ clamp_secret(m.private);
+
+ setzero_eltfp25519_1w(Ur1);
+ setzero_eltfp25519_1w(Zr1);
+ setzero_eltfp25519_1w(Zr2);
+ Ur1[0] = 1;
+ Zr1[0] = 1;
+ Zr2[0] = 1;
+
+ /* G-S */
+ Ur2[3] = 0x1eaecdeee27cab34UL;
+ Ur2[2] = 0xadc7a0b9235d48e2UL;
+ Ur2[1] = 0xbbf095ae14b2edf8UL;
+ Ur2[0] = 0x7e94e1fec82faabdUL;
+
+ /* main-loop */
+ j = q;
+ for (i = 0; i < NUM_WORDS_ELTFP25519; ++i) {
+ while (j < ite[i]) {
+ u64 bit = (key[i] >> j) & 0x1;
+ k = (64 * i + j - q);
+ swap = swap ^ bit;
+ cswap(swap, Ur1, Ur2);
+ cswap(swap, Zr1, Zr2);
+ swap = bit;
+ /* Addition */
+ sub_eltfp25519_1w(B, Ur1, Zr1); /* B = Ur1-Zr1 */
+ add_eltfp25519_1w_bmi2(A, Ur1, Zr1); /* A = Ur1+Zr1 */
+ mul_eltfp25519_1w_bmi2(C, &P[4 * k], B);/* C = M0-B */
+ sub_eltfp25519_1w(B, A, C); /* B = (Ur1+Zr1) - M*(Ur1-Zr1) */
+ add_eltfp25519_1w_bmi2(A, A, C); /* A = (Ur1+Zr1) + M*(Ur1-Zr1) */
+ sqr_eltfp25519_2w_bmi2(AB); /* A = A^2 | B = B^2 */
+ mul_eltfp25519_2w_bmi2(UZr1, ZUr2, AB); /* Ur1 = Zr2*A | Zr1 = Ur2*B */
+ ++j;
+ }
+ j = 0;
+ }
+
+ /* Doubling */
+ for (i = 0; i < q; ++i) {
+ add_eltfp25519_1w_bmi2(A, Ur1, Zr1); /* A = Ur1+Zr1 */
+ sub_eltfp25519_1w(B, Ur1, Zr1); /* B = Ur1-Zr1 */
+ sqr_eltfp25519_2w_bmi2(AB); /* A = A**2 B = B**2 */
+ copy_eltfp25519_1w(C, B); /* C = B */
+ sub_eltfp25519_1w(B, A, B); /* B = A-B */
+ mul_a24_eltfp25519_1w(D, B); /* D = my_a24*B */
+ add_eltfp25519_1w_bmi2(D, D, C); /* D = D+C */
+ mul_eltfp25519_2w_bmi2(UZr1, AB, CD); /* Ur1 = A*B Zr1 = Zr1*A */
+ }
+
+ /* Convert to affine coordinates */
+ inv_eltfp25519_1w_bmi2(A, Zr1);
+ mul_eltfp25519_1w_bmi2((u64 *)session_key, Ur1, A);
+ fred_eltfp25519_1w((u64 *)session_key);
+
+ memzero_explicit(&m, sizeof(m));
+}
diff --git a/lib/zinc/curve25519/curve25519.c b/lib/zinc/curve25519/curve25519.c
index 8d9d8fc0ca38..074fbb1c2149 100644
--- a/lib/zinc/curve25519/curve25519.c
+++ b/lib/zinc/curve25519/curve25519.c
@@ -20,6 +20,9 @@
#include <linux/init.h>
#include <crypto/algapi.h> // For crypto_memneq.
+#if defined(CONFIG_ZINC_ARCH_X86_64)
+#include "curve25519-x86_64-glue.c"
+#else
static bool *const curve25519_nobs[] __initconst = { };
static void __init curve25519_fpu_init(void)
{
@@ -35,6 +38,7 @@ static inline bool curve25519_base_arch(u8 pub[CURVE25519_KEY_SIZE],
{
return false;
}
+#endif
static __always_inline void normalize_secret(u8 secret[CURVE25519_KEY_SIZE])
{
next prev parent reply other threads:[~2019-03-22 6:38 UTC|newest]
Thread overview: 27+ messages / expand[flat|nested] mbox.gz Atom feed top
2019-03-22 6:27 [PATCH 0/17] Add zinc using existing algorithm implementations Herbert Xu
2019-03-22 6:29 ` [PATCH 1/17] asm: simd context helper API Herbert Xu
2019-03-22 6:29 ` [PATCH 2/17] crypto: chacha20 - Export chacha20 functions without crypto API Herbert Xu
2019-03-22 6:29 ` [PATCH 3/17] zinc: introduce minimal cryptography library Herbert Xu
2019-03-22 6:29 ` [PATCH 4/17] zinc: Add generic C implementation of chacha20 and self-test Herbert Xu
2019-03-22 6:29 ` [PATCH 5/17] zinc: Add x86 accelerated ChaCha20 Herbert Xu
2019-03-22 6:29 ` [PATCH 6/17] zinc: Add arm accelerated chacha20 Herbert Xu
2019-03-22 6:29 ` [PATCH 7/17] crypto: poly1305 - Export core functions without crypto API Herbert Xu
2019-03-22 6:29 ` [PATCH 8/17] zinc: Add generic C implementation of poly1305 and self-test Herbert Xu
2019-03-22 6:29 ` [PATCH 9/17] zinc: Add x86 accelerated poly1305 Herbert Xu
2019-03-22 6:29 ` [PATCH 10/17] zinc: ChaCha20Poly1305 construction and selftest Herbert Xu
2019-03-22 6:29 ` [PATCH 11/17] zinc: BLAKE2s generic C implementation " Herbert Xu
2019-03-22 6:29 ` [PATCH 12/17] zinc: BLAKE2s x86_64 implementation Herbert Xu
2019-03-22 6:29 ` [PATCH 13/17] zinc: Curve25519 generic C implementations and selftest Herbert Xu
2019-03-22 6:29 ` Herbert Xu [this message]
2019-03-22 6:29 ` [PATCH 15/17] zinc: import Bernstein and Schwabe's Curve25519 ARM implementation Herbert Xu
2019-03-22 6:29 ` [PATCH 16/17] zinc: " Herbert Xu
2019-03-22 6:29 ` [PATCH 17/17] security/keys: rewrite big_key crypto to use Zinc Herbert Xu
2019-03-22 6:41 ` [PATCH 0/17] Add zinc using existing algorithm implementations Jason A. Donenfeld
2019-03-22 7:56 ` Ard Biesheuvel
2019-03-22 8:10 ` Jason A. Donenfeld
2019-03-22 17:48 ` Linus Torvalds
2019-03-25 9:10 ` Pascal Van Leeuwen
2019-03-26 9:46 ` Riku Voipio
2019-04-09 16:14 ` Pascal Van Leeuwen
2019-03-25 10:43 ` Ard Biesheuvel
2019-03-25 10:45 ` Jason A. Donenfeld
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=E1h7Dgg-0001JW-LX@gondobar \
--to=herbert@gondor.apana.org.au \
--cc=Jason@zx2c4.com \
--cc=ard.biesheuvel@linaro.org \
--cc=davem@davemloft.net \
--cc=ebiggers@kernel.org \
--cc=gkaiser@google.com \
--cc=linux-arm-kernel@lists.infradead.org \
--cc=linux-crypto@vger.kernel.org \
--cc=linux-fscrypt@vger.kernel.org \
--cc=linux-kernel@vger.kernel.org \
--cc=martin@strongswan.org \
--cc=paulcrowley@google.com \
--cc=samuel.c.p.neves@gmail.com \
--cc=tomer.ashur@esat.kuleuven.be \
--cc=torvalds@linux-foundation.org \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).