# R = A % M where 0 <= A < M**2.

# A == 0
R = 00
A = 00
M = 813bc46ee19ffeab364073a89f96913f340d43ee72129ea9edac1beb4ebe1336450d2eabc7b26e51c400cec60d6ee459033b

# A == M
R = 00
A = 813bc46ee19ffeab364073a89f96913f340d43ee72129ea9edac1beb4ebe1336450d2eabc7b26e51c400cec60d6ee459033b
M = 813bc46ee19ffeab364073a89f96913f340d43ee72129ea9edac1beb4ebe1336450d2eabc7b26e51c400cec60d6ee459033b

# A == M - 1
R = 813bc46ee19ffeab364073a89f96913f340d43ee72129ea9edac1beb4ebe1336450d2eabc7b26e51c400cec60d6ee459033a
A = 813bc46ee19ffeab364073a89f96913f340d43ee72129ea9edac1beb4ebe1336450d2eabc7b26e51c400cec60d6ee459033a
M = 813bc46ee19ffeab364073a89f96913f340d43ee72129ea9edac1beb4ebe1336450d2eabc7b26e51c400cec60d6ee459033b

# A == M**2 - 1.
R = fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe
A = fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe0000000000000000000000000000000000000000000000000000000000000000
M = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff

# Test vector adapted from the regression test for CVE-2015-3193, A is the
# square of the original test vector's A.
R = 19324b647d967d644b3219
A = 19324b647d967d644b3219
M = 414141414141414141414127414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141414141800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001

# Test vector adapted from the regression test for CVE-2017-3732. A is the
# square of the original test vector's A.
R = fffffffdfffffd01000009000002f6fffdf403000312000402f3fff5f602fe080a0005fdfafffa00010001ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00000002000002fefffff7fffffd07000109fdfffef3fffdfd06000405ff00fdfbfffe00010001
A = fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe00000000000001fffffffe00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000fffffffffffffe00000002000000fffffffe00000200fffffffffffdfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffe00000000000003fffffffdfffffe00000002000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000fffffffffffffe000000000000010000000000000000
M = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff00000000000000ffffffff00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000ffffffffffffff


# These vectors were adapted from BoringSSL's "Quotient" BIGNUM tests in the
# following ways:
#
#   * The quotient in each vector was removed (*ring* only calculates
#     remainders, never quotients).
#   * B was renamed to M and Remainder was renamed to R.
#   * Only the test vectors with positive inputs were imported.
#   * Only the test vectors with odd moduli were imported.
#   * A < M**2; any larger values of A were split up into multiple reduction
#     steps. The first step uses the initial A and the smallest power of the
#     original M that makes A < M**2 true, the subsequent steps have smaller
#     powers of M using the result R from the previous step as A, and where the
#     last step has the initial value of M.
#   * Only test vectors with moduli that require at least 4 64-bit words to
#     represent are included (*ring*'s modular multiplication has this lower
#     bound, and modular multiplication is used as part of reduction).

# Step 1
R = 04
A = 0813bc46ee19ffeab364073a89f96913f340d43ee72129ea9edac1beb4ebe1336450d2eabc7b26e51c400cec60d6ee459033b4
M = 813bc46ee19ffeab364073a89f96913f340d43ee72129ea9edac1beb4ebe1336450d2eabc7b26e51c400cec60d6ee459033b

# Step 1
R = 18
A = 966df62c26acab2d3d1dbe729e48d0181c68e9f5eba45f6caefa38d60e34057d09fe620abb8640cec8cac755957aaad7c6fd000018
M = 966df62c26acab2d3d1dbe729e48d0181c68e9f5eba45f6caefa38d60e34057d09fe620abb8640cec8cac755957aaad7c6fd

# Step 1
R = 20
A = 89a2f1792afc54467955839eddc9ef2e37d391ce7a1a4a205291220c1f49f59ee31fc7a7a7f7706c199bf5c8c951a0d0743d00000020
M = 89a2f1792afc54467955839eddc9ef2e37d391ce7a1a4a205291220c1f49f59ee31fc7a7a7f7706c199bf5c8c951a0d0743d

# Step 1
R = 24
A = 0877f1caf75e7166ef18484d0718947893fd1ec016984387debc55c19e378a487a5ddbb03a80a88316f6fca16ae148933e719000000024
M = 877f1caf75e7166ef18484d0718947893fd1ec016984387debc55c19e378a487a5ddbb03a80a88316f6fca16ae148933e719

# Step 1
R = 2c
A = 087bd03a64d9c56fe340137065ba36bd07b556119546dd1fc3ae087ead32bc79ca7efb5c7230ea7bfb00ad419096d9279fbe10000000002c
M = 87bd03a64d9c56fe340137065ba36bd07b556119546dd1fc3ae087ead32bc79ca7efb5c7230ea7bfb00ad419096d9279fbe1

# Step 1
R = 30
A = d00fec043edadc093673e5f5abef0c6bacdf1f3faa49a831a645bf80db7539d657f69403b122a5c6f879eb8e63be54d35ed7000000000030
M = d00fec043edadc093673e5f5abef0c6bacdf1f3faa49a831a645bf80db7539d657f69403b122a5c6f879eb8e63be54d35ed7

# Step 1
R = 458f5c63c063b09790a28c6cbd9afc98ded6d6c1d12c8e4e081e4f6a5638a5319a548fe711b3142d6d32827f415a41d457048783c3
A = 01280d26263c574f655ea63006f2930666fbaa4de1b09a11ab0e47dbe0054711aab90a05b1185454dcf046745436391a673426000000000031
M = 4e5d7ec324e42afb2d8b381c6d07869985cd3b3de3cbc06853a387c076e6525fd93c3b6de887f31a7580bafb0546f45b785c4e5199

# Step 2
R = 029abc8898d5ef85f87323c2a6fa36ab6e1bdbcc0ca742b1a2347e
A = 458f5c63c063b09790a28c6cbd9afc98ded6d6c1d12c8e4e081e4f6a5638a5319a548fe711b3142d6d32827f415a41d457048783c3
M = 08da37bc9c7c9bdc62f49cadcd40e156e776b7f4c8f7ad543f463b

# Step 1
R = 2000f9c8569d20abce69ced0d66a44ae47a9516205732183408c6ab6c135cd172880f0c0d160862d49a0003656276f3884e88a3c9664d45f
A = 01280d26263c574f655ea63006f2930666fbaa4de1b09a11ab0e47dbe0054711aab90a05b1185454dcf046745436391a673426000000000031
M = 8406162ef2dd175cc81e309b0e1460dc5a007e3fd5937813e6ddb894a208a249c8448a782379e757d3533a0ef008d597579ebae1b4cd95e9

# Step 2
R = 6c9e547a77c98eaba1b021777dbd98ea88f7fd37c95a2b182f2b9067
A = 2000f9c8569d20abce69ced0d66a44ae47a9516205732183408c6ab6c135cd172880f0c0d160862d49a0003656276f3884e88a3c9664d45f
M = b7d7b1f95f4fe2f267af88b81af88fbdf603e54ab6de73ccd000c32d

# Step 1
R = 0bbfaf15a90e744dc4a1caceda3cb339e5491e4507a1118613c5e9739f976b
A = 01280d26263c574f655ea63006f2930666fbaa4de1b09a11ab0e47dbe0054711aab90a05b1185454dcf046745436391a673426000000000031
M = 82ae783b8a13e2e65d52dd3a6d6b057163347872f4d72245ff364dbf2421ff

# Step 1
R = 82e3fb3f7252dd87b5370d26d9e8b9e98c7d333701f0ce8a05c337054c7aeb343d04d7e342
A = 01280d26263c574f655ea63006f2930666fbaa4de1b09a11ab0e47dbe0054711aab90a05b1185454dcf046745436391a673426000000000031
M = 8faf8c0a3ef94ab1069394998e5412a7d84f44aff97edf63abc46d96f897172c38faa0b13f

# Step 1
R = 65bf2ef1c2f8e94d98060aa305f85e6cb869c74eabad99877010d30654aa2e578ef6aa3c5f1122e3
A = 01280d26263c574f655ea63006f2930666fbaa4de1b09a11ab0e47dbe0054711aab90a05b1185454dcf046745436391a673426000000000031
M = 83cfc25e90a61cf8686e3d5857b2f958674d478622c54cf8427275ca5e9312ed24e44ed4a1b5e413

# Step 1
R = 02c89373720b834d718ff3df985ae47c3a7cde0e0309f682f5fd48dc97a1ff3d69fa0dcaa1245e956445
A = 01280d26263c574f655ea63006f2930666fbaa4de1b09a11ab0e47dbe0054711aab90a05b1185454dcf046745436391a673426000000000031
M = 0d6721300e877a8145d05f4f3d8085697c2ca5f34a5357fed0bdb7169f83b6f8d855232eeea594846b79

# Step 1
R = 1b02a7b97f9ac1f6306aa00fff0e59f55fce463ffdc640364a950df29474e08b67cdfcec0628e973d42fa1e4f98e988ec4c47e4915651a1731b71d5e36a10a0d1b3420427dbb79ba7d52
A = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
M = 3f74cafe9ab0c1b307cd7571fd442665fa3205fb2f45b3811b92d1d38b096a2025b8170663a29c52ca84da102e62048e583fba96a594c0b23952fec587814857c25221ff2cd0533cba6d

# Step 1
R = 13849ef93cbc77460c3c496e8f31f7e01a98c21cdfcd6877547161f9601680665b394933d3a0824f0d32854508c89f0e4a0873280c779c7ca636cd89cf6ee5d42a917b4f382be3b9654039f623c11b43164827f870fa0f0781
A = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
M = 23ab6042240a7709d43de7ee17332a9710bd0d913c42b3591341527bf48d5bc30abb962482292d45a15cb03c9457cc8d78d1e00aaa63358427b000e59e4260bfe1e2cc603e175d7fcf02bd9f61fae3740cb8e10a510ea3d1d5

# Step 1
R = 0d8c77134a75584ecd5ab29e97a909ec139464901f9cfcb1d3d9e29a63d204615b6845d466c8710873980f107c40ab54eca9f8933ef6d726f9bd0f3e9e97eade5eb1a9bcaa7b01b6ad51ff3ecf67d6e4d345f128e990494a2db434fcd3ab
A = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
M = 3e7dd961be36c0c286eb9e78bf3b33e6f9bdf2c2137a0c660f1d21dea31ac9a044e526bf47ec8190e137a60f1f55e947046b9cd04a2485679e48cac80a1bb064a915208889289d63a6e338cf7069ad799861c31ec6eafe02a4ef2c2641c9

# Step 1
R = 0a1a70f674cb141a896c4adace0dc58cdcbe2503fd0ad36ce348dc5b8afc96d0f2f8c65bbbadabf2920012798b7ccaedbe8d896dd2674082ad3cc75b54c5c190ad56ff34e8cb5dd29c031656497d48571295d6da396d5f4cdb652732d874a79a674d06a1d7b979f5
A = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
M = 21917f48bb8e65646c618068fd9069c06e22ce8c679a845f9c4ec843849010abeee12e2d3c61fb963297abca30813c446f2ae82e909ca6ac7839fb58974fa65f3b5d91fb8b3f99d948519ed56653d50026d694060208cf48e3c757f64885b4ed4328c6f071e9f5d5

# Step 1
R = 252d055186ec896cb3142c9e4e49c441e2ddad365b86ad21ae4ef1c522d3306c2834d6993a5e1f8c64a1ed582bad8ab746f7e773fc004b1c47814f73560db72f7237ef6e2f671d3b19a8777be2e4c662a76db87ea64f32c48ea371b1ffb15df26726854a417e18afcf49054c6d2e0e337e71
A = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
M = 2b6eb2caa3ca650be02fa199e9ea6c48646a76434e268713753a547e49571f9817ad396f2cb7b16d307801fc8892f0af3e7f93ce08f7955a8acfbc0b56add4b4c7ef7351f60e402b9a8ef7fe02ccdcb4b00b7ffe78c7009268dbcf1d606c3a1b5307d9a8ee6121c6a635a742b8bf36b56cc7

# Step 1
R = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
A = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
M = 3a8682d0e5a4efa985dfa8bbddc2c0d72a4400b8b070a8cf7450aa8f831d8a91c9ae3542641b7a4ad793e232a0d301b82664fe2c7f20bd9bf8275828a2a20027d6056b211638b9b0220fa4252d058bb485dd3c4622b1eac97d54b9634b558ff1bd5bd11085d4f3d288f7965af52beaa922b23ac0207d5763c24c085076128e0ef7370eeaa19d

# Step 1
R = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
A = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
M = 33aeafda3cfc20710f0b4a3d9ace4817eed80ca57ce6c82dc2e7946058a40983c9204ac95a1399fa633bc96cb10af3ddeee3ad2337c64391a42dc7794fca629e3e1e4e03a2ae24a000e7113b91c1b6230cce9592e45b6ee7984680b45aa0aabd7f56cab1a64ec310cefe5211821a75deef2e0c8e43eb467dea79dc8c03d2d523734498d079d5493c904a2ebfd8a3a9bd

# Step 1
R = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
A = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
M = 3083421e375f0722b9397e156de47f77635d62ba1d51794469371b473b71c02e3722841bca2ca06b5d1cf1492bbacfa0abfe394dfdaa7bb8787550ddbd953540e9c97631d9a1efe0c8f8e14f395c82d20245cec6d8021f8564b4d66e7779c3245734c56fb74481172f4e349d9a113cd0ee5263c69ebf746c5285cd4c0fa91d9531f769fea3610c2972ccfe9a22c00aa62ebf52b3a4c6135f3069

# Step 1
R = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
A = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
M = 2f26e156b3b1117f7cec542b20fcc06ca66cec03a19b6f5eeebf22b4c0fc265df5ff06fc9dcac569735135bdc142b526b295225711efb71577b10aacda2fa446f5208487c725407c2188b3185237740c813e4455a6f1dde4f62916237f23164a3471aac0fcfe24ad1ce1dd81a6144f5861ad0cf22dc337abe10fc4a88b36116dc4929602ab48eb971fdd7a5ff747d6b9e0b2bff75c59621550991966a0a19f

# Step 1
R = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
A = ea87c57f6cdbfd4f836431be3e9950c90ee8ecc291eb4efb881617512fd62e2d86caefce713cfd8a20f4b4925bfc7dba1fcbe99c72932725b5d11eccefde4c5e505952754891e9ded499ec453a1c01a82152c8933f7db4f2b4b19e97baac322eb483cd661a43e458774ef27a29a19c3562ba466381056a3b92c35d9b8b71372b
M = 2a8f2c530342bb6ce683a760540e956a1155c0fe065476e400caec59861ca97ca71e51a11b3213b2baea1a41a29449998778e0f533fcc181698d293f05e28bff2750ef4095170de98a19a36ddcf59a65f3789a3808ead51680245070262c9544e446f23652eba47065a2bc4701c55378bd49733619ed2c213f8ed12a4a317c465f37efe07ff2df8e88fc33d3eb42cde9408dda28215702bfa607030839285a8bbf89b5e8842fa7d7f50d83fd4ab5