ref: b9656ec7e120d1fced20ea5ca826c57f2de4fc84
dir: /lib/math/atan-impl.myr/
use std
use "fpmath"
use "sin-impl"
use "util"
/*
As with other trig functions, we follow [GB91] here. This is a
relatively straight-forward "tabulate and approximate by local
polynomials" approach. The (relative) lack of sophistication can
be seen by the huge number of constants required. The only fancy
trick is that
atan(x) + atan(1/x) = pi/2
which allows quick reduction to the range [-1, 1].
The Highly Accurate Table approach of [GB91] then appears in the
constants for the polynomial approximations. This acts as a few
bits of insurance against subtractive cancellation of the first
few terms of the polynomial approximations.
See files generate-atan-tuples-for-GB91.c, and
generate-minimax-by-Remez.gp for where the constants come from.
*/
pkg math =
pkglocal const atan32 : (x : flt32 -> flt32)
pkglocal const atan64 : (x : flt64 -> flt64)
pkglocal const atan232 : (y : flt32, x : flt32 -> flt32)
pkglocal const atan264 : (y : flt64, x : flt64 -> flt64)
;;
/*
Coefficients for p(x), where arctan(x) is approximated in degree
13 by x*p(x^2).
*/
const atan_coeffs : uint64[7] = [
0x3ff0000000000000,
0xbfd5555555555555,
0x3fc9999999999128,
0xbfc2492493302077,
0x3fbc71bd4ec2b9ae,
0xbfb750eefa902315,
0x3fb226324f0122e0,
]
/*
Coefficients for degree 5 polynomial approximations of arctan(x)
on intervals of width 1/256, roughly filling the [0, 1] space.
Because of the slight shifting of the pivot xi variables by up
to 2^26 ulps, there are tiny gaps, of up to size 2*2^(-53 + 26)
= 2^-26, on which the minimax guarantees do not apply. This is
not expected to be a significant issue.
Note that the first few entries aren't actually used.
*/
const C : (uint64, uint64, uint64, uint64, uint64, uint64, uint64)[257] = [
(0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000),
(0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000),
(0x3f80000001f83362, 0x3f7fffd559ac119a, 0x3fefff8001ffd883, 0xbf7fff0009e129ba, 0xbfd55355689e3241, 0x3f7ffdcf9a784a0c, 0x3fc995f4bed14247),
(0x3f87ffffff37811c, 0x3f87ffb800bc4b32, 0x3feffee00a1fb7b6, 0xbf87fe5015f2c284, 0xbfd550d5b96bfd9c, 0x3f87fc076a4fd120, 0x3fc98fc8b892a7b2),
(0x3f8fffffffc1eade, 0x3f8fff555b7d615a, 0x3feffe001ffe07ed, 0xbf8ffc005fa9b585, 0xbfd54d5693a075a5, 0x3f8ff657f61b9dd7, 0x3fc9869ee5cadbbd),
(0x3f93fffffe0e9f70, 0x3f93ff595d2776fd, 0x3feffce04e18fad7, 0xbf93fc18907a7f60, 0xbfd548d85eda9a6c, 0x3f93f61bf2de1558, 0x3fc97abe5d2bf700),
(0x3f97ffffffec7ecd, 0x3f97fee01836ddc0, 0x3feffb80a1e94266, 0xbf97f9416c2a7c14, 0xbfd5435ba3ccdd9c, 0x3f97eefc49b67b90, 0x3fc96b9f97155700),
(0x3f9c000002043a2b, 0x3f9bfe36e12cee80, 0x3feff9e12be5b739, 0xbf9bf54b150fb215, 0xbfd53ce105d2bb59, 0x3f9be5104edd8ee0, 0x3fc9598af87d1c00),
(0x3fa00000022e99a5, 0x3f9ffd55c0059267, 0x3feff801ff7df250, 0xbf9ff006025a63b6, 0xbfd5356946bb4ad9, 0x3f9fd7e22b0f4cc0, 0x3fc94484728b9380),
(0x3fa200000058e037, 0x3fa1fe1a5c8788b8, 0x3feff5e3331c6ffa, 0xbfa1f4a166090962, 0xbfd52cf545c2c2d0, 0x3fa1e37e5b434560, 0x3fc92c909999c980),
(0x3fa3fffffe4fe9f8, 0x3fa3fd65efba5c58, 0x3feff384e01a9106, 0xbfa3f0692146d108, 0xbfd5238601c8043d, 0x3fa3d95263db398f, 0x3fc9116fa0344708),
(0x3fa5fffffd7d0899, 0x3fa5fc89a378731e, 0x3feff0e722c403ee, 0xbfa5eb42b2d510f3, 0xbfd5191c8f45f7ad, 0x3fa5cc83e91b1137, 0x3fc8f3b166e52899),
(0x3fa7fffffff47d57, 0x3fa7fb8184255df7, 0x3fefee0a1a5143a8, 0xbfa7e516b6ddd4cd, 0xbfd50dba2684300b, 0x3fa7bd2cb777bd9a, 0x3fc8d317587dd676),
(0x3fa9fffffc2c23a9, 0x3fa9fa4994982dbb, 0x3fefeaede8f76900, 0xbfa9ddcddc883e9e, 0xbfd501601a419c50, 0x3fa9ab141ce95d64, 0x3fc8afa883cd8ab3),
(0x3fabfffffd0f0cbd, 0x3fabf8ddee4b0fc3, 0x3fefe792b3b38c6e, 0xbfabd5510839a77b, 0xbfd4f40fd8f0a91b, 0x3fab9602138cdbe9, 0x3fc8896c8f290450),
(0x3fae000000ffdc11, 0x3fadf73aa09e1477, 0x3fefe3f8a27756be, 0xbfadcb8935b8415f, 0xbfd4e5cae94695f1, 0x3fad7d32cd68db68, 0x3fc860b09a86ff00),
(0x3fb0000002ad31a4, 0x3faff55bbc820c23, 0x3fefe01fe0154058, 0xbfafc05f85dd78f3, 0xbfd4d692f8f482ea, 0x3faf617ebeb00bd8, 0x3fc834f3a9931b00),
(0x3fb100000188824f, 0x3fb0f99ea8a41bcd, 0x3fefdc089a435d4f, 0xbfb0d9de9f1c8568, 0xbfd4c669ca505107, 0x3fb0a166428a466f, 0x3fc8063f36448e35),
(0x3fb20000009bc757, 0x3fb1f86dbfa33080, 0x3fefd7b3016f7596, 0xbfb1d2c5eedc6080, 0xbfd4b55130ac22d8, 0x3fb18fd8c2bb0ee4, 0x3fc7d526db38f039),
(0x3fb3000024c171ae, 0x3fb2f7195618302f, 0x3fefd31f48358ab4, 0xbfb2cadaa8a559c1, 0xbfd4a34b240cff5f, 0x3fb27c47c2ad49a6, 0x3fc7a1702e4d8d69),
(0x3fb4000000068d16, 0x3fb3f59f0e82d887, 0x3fefce4da6ab73c7, 0xbfb3c2114d1e9dc2, 0xbfd49059bce708bf, 0x3fb36699156cde19, 0x3fc76b264479966d),
(0x3fb4ffffffdaf503, 0x3fb4f3fd674dc761, 0x3fefc93e53a2ae2c, 0xbfb4b85f4a8c15c6, 0xbfd47c7f1d6673be, 0x3fb44eb3ca7ef180, 0x3fc7325487c15892),
(0x3fb60000005453f7, 0x3fb5f23250268d66, 0x3fefc3f18b52cb50, 0xbfb5adb99d22e5c3, 0xbfd467bd8b4de796, 0x3fb5347ee36faada, 0x3fc6f706fed2d6e1),
(0x3fb7000000057dfc, 0x3fb6f03bdcefbdc7, 0x3fefbe678c078564, 0xbfb6a2157e35172d, 0xbfd452176286cdb9, 0x3fb617e1fe0c1388, 0x3fc6b94a23d2539a),
(0x3fb7fffffe7c548b, 0x3fb7ee182482a642, 0x3fefb8a096b5e8ba, 0xbfb7956844e7782f, 0xbfd43b8f17095f3f, 0x3fb6f8c53a2a94dc, 0x3fc6792ae7109ee3),
(0x3fb9000000399ffa, 0x3fb8ebc544b20fc7, 0x3fefb29ceedb75bc, 0xbfb887a76b0a59ee, 0xbfd4242733f64aa6, 0x3fb7d7114183708e, 0x3fc636b6a9a36669),
(0x3fba000000503ea3, 0x3fb9e941541f49d9, 0x3fefac5cdacc38c0, 0xbfb978c880930264, 0xbfd40be25c5cc9fc, 0x3fb8b2af3f76ad1f, 0x3fc5f1fb3caa1a83),
(0x3fbafffffefd604e, 0x3fbae68a70c75b65, 0x3fefa5e0a3559ff9, 0xbfba68c13a88c726, 0xbfd3f2c349624f3b, 0x3fb98b88f1f263f7, 0x3fc5ab06d90ee046),
(0x3fbc0000027ada67, 0x3fbbe39ec0e260e9, 0x3fef9f2893aa9d84, 0xbfbb578774c87524, 0xbfd3d8ccc2282c36, 0x3fba6104a32547f8, 0x3fc5622c6b5cdc00),
(0x3fbcfffffe2aae0e, 0x3fbce07c5a6d6a81, 0x3fef9834fa03c879, 0xbfbc45111ba09bf8, 0xbfd3be01baf8bc7a, 0x3fbb3410872e3840, 0x3fc516f2437f8a00),
(0x3fbe000001dab907, 0x3fbddd2171f3051f, 0x3fef910626538a70, 0xbfbd3154591dc7f9, 0xbfd3a2652c4d0b90, 0x3fbc04a65d78b257, 0x3fc4c967e0fd9461),
(0x3fbeffffffa53a79, 0x3fbed98c21368e87, 0x3fef899c6bd1f677, 0xbfbe1c47601d7e8f, 0xbfd385fa159fbfca, 0x3fbcd19beca90b8c, 0x3fc47a256b36705a),
(0x3fc000000f142d5a, 0x3fbfd5bab85dc3d0, 0x3fef81f81e981366, 0xbfbf05e0b86e7006, 0xbfd368c39b4690e4, 0x3fbd9b66d4a9b7f8, 0x3fc428f6923eacde),
(0x3fc07ffffcdf1951, 0x3fc068d5810d5bd4, 0x3fef7a19994da3f1, 0xbfbfee169210a60e, 0xbfd34ac4fcd8967e, 0x3fbe61f4253945ff, 0x3fc3d5ebc0588a79),
(0x3fc1000002aa39f4, 0x3fc0e6adcf926f2e, 0x3fef7201326bccc1, 0xbfc06a70037899d2, 0xbfd32c01735432c2, 0x3fbf25323b0051d6, 0x3fc38115615f521e),
(0x3fc18000001fea3b, 0x3fc1646541255ca1, 0x3fef69af483d2f52, 0xbfc0dd19dadefc1f, 0xbfd30c7c5e62ba59, 0x3fbfe50f8f51460e, 0x3fc32a845cd3502a),
(0x3fc1fffffe8823bc, 0x3fc1e1faf993a4c8, 0x3fef612438bab95f, 0xbfc14f04587e458a, 0xbfd2ec3924d36b33, 0x3fc050bdc309e406, 0x3fc2d249bb3c927d),
(0x3fc27ffffc9337b0, 0x3fc25f6e13bf7bd7, 0x3fef586064c338f8, 0xbfc1c02b10b43292, 0xbfd2cb3b4055087c, 0x3fc0ad330fd21a61, 0x3fc27876c32ba8fe),
(0x3fc2fffffdc6bf7b, 0x3fc2dcbdb0cea731, 0x3fef4f642f0fe16c, 0xbfc23089b1286391, 0xbfd2a98638fb0d98, 0x3fc107e008ee7ac7, 0x3fc21d1ce9880c12),
(0x3fc3800000c2fb33, 0x3fc359e8eeaa28a7, 0x3fef462ffcd452fe, 0xbfc2a01bf88e9498, 0xbfd2871da71092b5, 0x3fc160bd5de46b03, 0x3fc1c04dd31f291d),
(0x3fc4000000d8f876, 0x3fc3d6eee99a2f23, 0x3fef3cc435a04a95, 0xbfc30eddb88397f1, 0xbfd26405321912f4, 0x3fc1b7c415010900, 0x3fc1621b4e780103),
(0x3fc48000000de728, 0x3fc453cec616b8c4, 0x3fef332142989e5d, 0xbfc37ccade8e0ca6, 0xbfd240408d609878, 0x3fc20ced92d9e381, 0x3fc1029747314f3d),
(0x3fc4ffffff0e7ab0, 0x3fc4d087a8ef1e63, 0x3fef29478efdfd42, 0xbfc3e9df6d60cba2, 0xbfd21bd3796a9ce3, 0x3fc26033953388f3, 0x3fc0a1d3c688050b),
(0x3fc57ffffc7377dc, 0x3fc54d18b69dbcdb, 0x3fef1f3788337a10, 0xbfc456177c933fea, 0xbfd1f6c1c37d2372, 0x3fc2b190331b73b1, 0x3fc03fe2eebeac95),
(0x3fc5ffffff069c34, 0x3fc5c9811d4c8683, 0x3fef14f19ce2618f, 0xbfc4c16f418df8ce, 0xbfd1d10f41eb9d16, 0x3fc300fde3b8367f, 0x3fbfb9addc08f782),
(0x3fc67ffffe3dace2, 0x3fc645bffdfed6b5, 0x3fef0a763ecf8d44, 0xbfc52be2fc09f17c, 0xbfd1aabfda46e407, 0x3fc34e776fde19e4, 0x3fbef18416e713f0),
(0x3fc6fffffe88eb88, 0x3fc6c1d4881ddaae, 0x3feeffc5e08c9b3d, 0xbfc5956f0e16385c, 0xbfd183d77857c309, 0x3fc399f803dfed36, 0x3fbe276d18332ee6),
(0x3fc77fffffbe804c, 0x3fc73dbde868750f, 0x3feef4e0f6d3f675, 0xbfc5fe0fed8db872, 0xbfd15c5a1291701e, 0x3fc3e37b24a92e8d, 0x3fbd5b8d76fa3afe),
(0x3fc7fffffc35d1d7, 0x3fc7b97b48251fed, 0x3feee9c7f89a7009, 0xbfc665c223be9680, 0xbfd1344ba9bdc601, 0x3fc42afcaf9262f8, 0x3fbc8e09cf02b355),
(0x3fc8800000a239dc, 0x3fc8350be43569e9, 0x3feede7b5cee6e27, 0xbfc6cc8260df5e45, 0xbfd10bb040c61a32, 0x3fc47078e771a1fe, 0x3fbbbf06908b1814),
(0x3fc90000027df7fa, 0x3fc8b06ee4ee22e7, 0x3feed2fb9e8bb11b, 0xbfc7324d5aa33c81, 0xbfd0e28be90da705, 0x3fc4b3ec5d56fe5c, 0x3fbaeea83980b70d),
(0x3fc9800002d31c2a, 0x3fc92ba37fbc8427, 0x3feec74938c8c904, 0xbfc7971fe886b4de, 0xbfd0b8e2b6d26476, 0x3fc4f55403930d95, 0x3fba1d131409b3ab),
(0x3fc9fffffcddfcfd, 0x3fc9a6a8e66a4ab7, 0x3feebb64a91453c7, 0xbfc7faf6f60a4367, 0xbfd08eb8c5fc4160, 0x3fc534ad23ed705c, 0x3fb94a6b493e7c18),
(0x3fca7fffff8b55ee, 0x3fca217e5fa0a315, 0x3feeaf4e6c86c253, 0xbfc85dcf96a2bb00, 0xbfd0641230fa59ed, 0x3fc571f56b9c5c8a, 0x3fb876d4adfc5ac3),
(0x3fcafffffd414cf5, 0x3fca9c23189f6ea5, 0x3feea30704596a99, 0xbfc8bfa6e0659b60, 0xbfd038f3200791fd, 0x3fc5ad2ad32c8d7a, 0x3fb7a273097623dd),
(0x3fcb7ffffe765c40, 0x3fcb169655d5327a, 0x3fee968ef1197db7, 0xbfc9207a13521ece, 0xbfd00d5fb7ad7b56, 0x3fc5e64bb64ff60a, 0x3fb6cd69b8f6e504),
(0x3fcc000000abc4ff, 0x3fcb90d753364d8b, 0x3fee89e6b5bbd593, 0xbfc980467fefa357, 0xbfcfc2b8463315e8, 0x3fc61d56c362a69c, 0x3fb5f7dbddfa3d81),
(0x3fcc7fffffda3e36, 0x3fcc0ae54d528b2b, 0x3fee7d0ed6b1420d, 0xbfc9df098ebe3358, 0xbfcf69d920a9cf8c, 0x3fc6524aff4b3332, 0x3fb521ec46597687),
(0x3fccfffffff895a3, 0x3fcc84bf8a6d20c0, 0x3fee7007d8e2c735, 0xbfca3cc0c754ee99, 0xbfcf102a3a0ed514, 0x3fc6849fe6a47028, 0x3fb44c40e5060800),
(0x3fcd800002e87b67, 0x3fccfe6550e0425b, 0x3fee62d242a27514, 0xbfca9969c88af14c, 0xbfceb5b42bd588bd, 0x3fc6b562a8259298, 0x3fb375f45f6e7800),
(0x3fce0000007c3fa1, 0x3fcd77d5df961e94, 0x3fee556e9c79c2d5, 0xbfcaf502433f724e, 0xbfce5a7f5c4a951a, 0x3fc6e49a1c28bf4d, 0x3fb29f2902804d52),
(0x3fce8000018c9844, 0x3fcdf11087c3e708, 0x3fee47dd6e4b27d1, 0xbfcb4f880dd31913, 0xbfcdfe93e4e6b22c, 0x3fc71130057e8a97, 0x3fb1c906570f0d02),
(0x3fcf0000011971a7, 0x3fce6a148fa0c60b, 0x3fee3a1f427d6bd1, 0xbfcba8f90d9b0ad8, 0xbfcda1fa4468eaa4, 0x3fc73baf35ad6fbc, 0x3fb0f329b1d71c3b),
(0x3fcf7fffffae07f0, 0x3fcee2e144d04e42, 0x3fee2c34a3e84e63, 0xbfcc015345086350, 0xbfcd44bad359c3db, 0x3fc76418a7b6f7b9, 0x3fb01db333c0e897),
(0x3fd0000003c8cfe7, 0x3fcf5b76004c2654, 0x3fee1e1e1d47929d, 0xbfcc5894d623e3cd, 0xbfcce6ddde8c38ac, 0x3fc78a6da87d134e, 0x3fae9184c911f786),
(0x3fd0400003e0f35b, 0x3fcfd3d2038a7c77, 0x3fee0fdc3d4407ce, 0xbfccaebbe9509c5a, 0xbfcc886bc113543a, 0x3fc7aeafca638093, 0x3face8ecd45e8a40),
(0x3fd08000032761cb, 0x3fd025fa53fb759e, 0x3fee016f90dfb3ea, 0xbfcd03c6cfa46b13, 0xbfcc296cbe2c693a, 0x3fc7d0e0f31c6cc9, 0x3fab41db5e90e29b),
(0x3fd0bffffd1bbae5, 0x3fd061ee9d889212, 0x3fedf2d8a7a1ddae, 0xbfcd57b3e8faad27, 0xbfcbc9e91c1a6c4e, 0x3fc7f1034f0598ee, 0x3fa99c8c39820b78),
(0x3fd0fffffda7b6b5, 0x3fd09dc595a7aa29, 0x3fede4180e167b90, 0xbfcdaa81c348841c, 0xbfcb69e8ff46f764, 0x3fc80f195bae93a5, 0x3fa7f9398b9c2669),
(0x3fd1400002df4b88, 0x3fd0d97ee7b72b9e, 0x3fedd52e54a32e74, 0xbfcdfc2ef2b6e464, 0xbfcb0974963c35fd, 0x3fc82b25d6d98068, 0x3fa6581c8d5f3f91),
(0x3fd18000007fef6f, 0x3fd1151a369b3ad0, 0x3fedc61c0ed3a8b3, 0xbfce4cba17180e39, 0xbfcaa89413bba312, 0x3fc8452bc0669ca5, 0x3fa4b96d672b82b0),
(0x3fd1bffffd750e56, 0x3fd1509738407215, 0x3fedb6e1cc5e56bc, 0xbfce9c22010b8ec2, 0xbfca474f8102a8b8, 0x3fc85d2e64dd2c0a, 0x3fa31d6268e4aace),
(0x3fd2000003ca0de4, 0x3fd18bf5a68ee3b3, 0x3feda7801cbd34e3, 0xbfceea659ca4de3f, 0xbfc9e5aed4b250a4, 0x3fc87331536725ba, 0x3fa184306c2c9ae3),
(0x3fd2400002036234, 0x3fd1c735230a790e, 0x3fed97f79692b2ec, 0xbfcf3783cc4f0a97, 0xbfc983ba20bb093a, 0x3fc887385275eb6c, 0x3f9fdc171f589263),
(0x3fd27fffffdfc6c4, 0x3fd2025567c6bf7b, 0x3fed8848caf35b89, 0xbfcf837ba93cd7cf, 0xbfc9217940ea8bf9, 0x3fc89947704663ae, 0x3f9cb64bbd3e6b8a),
(0x3fd2bffffed8628c, 0x3fd23d562a27d0d0, 0x3fed78744ce26842, 0xbfcfce4c5c6a3c83, 0xbfc8bef409ec6215, 0x3fc8a962f5b80e45, 0x3f999760297b6b81),
(0x3fd2fffffd9ac75c, 0x3fd278371e2461ca, 0x3fed687ab0799710, 0xbfd00bfa9178bb91, 0xbfc85c32431fb914, 0x3fc8b78f661ebb08, 0x3f967fb3033009f6),
(0x3fd33ffffe5a26b1, 0x3fd2b2f7fc188619, 0x3fed585c894c7f41, 0xbfd0303aaa9777f1, 0xbfc7f93b9bf3c072, 0x3fc8c3d17ee8c3ea, 0x3f936f9fb86fef86),
(0x3fd37ffffec1b143, 0x3fd2ed98795ef86b, 0x3fed481a6c610cdd, 0xbfd053e62ea7a861, 0xbfc79617b7755508, 0x3fc8ce2e3400f439, 0x3f90677ee0a18b9f),
(0x3fd3c000003531d6, 0x3fd328184fe61b16, 0x3fed37b4ee113238, 0xbfd076fce03b5660, 0xbfc732ce1eb44786, 0x3fc8d6aaaf852261, 0x3f8acf4b9ec59d46),
(0x3fd40000014b4f1a, 0x3fd362773835c112, 0x3fed272ca3a66d1e, 0xbfd0997e8b99570c, 0xbfc6cf664a09a01d, 0x3fc8dd4c4eb42bdc, 0x3f84e0cdba8b378e),
(0x3fd44000002a76ab, 0x3fd39cb4eb9caee5, 0x3fed168222b7fc82, 0xbfd0bb6b07fba0fc, 0xbfc66be79ca66f40, 0x3fc8e218a084b591, 0x3f7e0845137e79a8),
(0x3fd4800002f0ac40, 0x3fd3d6d12bd1b3a2, 0x3fed05b5fee9e15f, 0xbfd0dcc23bca443d, 0xbfc6085956bc3e59, 0x3fc8e5156401dd74, 0x3f7273c2f54049f0),
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(0x3fe500000148f840, 0x3fe2958e5a167f56, 0x3fe65e032465797a, 0xbfd485142f44c956, 0x3fa10498ca140c07, 0x3fb6d1eedb71be40, 0xbfb45fa94fe02000),
(0x3fe52000018790be, 0x3fe2abe21bef8766, 0x3fe649814c4855c7, 0xbfd47e9069f4e9e3, 0x3fa1b9a9349c106a, 0x3fb66c95866404c0, 0xbfb44234ea994000),
(0x3fe540000064c499, 0x3fe2c2215e483288, 0x3fe635061a93197b, 0xbfd477c956655f3a, 0x3fa26b9005b791fd, 0x3fb60aa234b1e8ae, 0xbfb4241dc5417ce3),
(0x3fe5600002c99e32, 0x3fe2d84c2b4f57a0, 0x3fe62091ced9107e, 0xbfd470c021eda05c, 0x3fa31a54b048ef02, 0x3fb5a6812d9df714, 0xbfb404ad3b9865e5),
(0x3fe5800000512c22, 0x3fe2ee62843eb8ef, 0x3fe60c24b0014185, 0xbfd46975facafcfc, 0x3fa3c5fc054af685, 0x3fb5402d421a8b40, 0xbfb3e3ee1a090000),
(0x3fe5a0000334351e, 0x3fe30464776e19ff, 0x3fe5f7bef7e40401, 0xbfd461ec08f203ca, 0x3fa46e88d0626c5c, 0x3fb4dd50a5475c80, 0xbfb3c2a9098b8000),
(0x3fe5bffffe315006, 0x3fe31a52034bf998, 0x3fe5e360ee28562d, 0xbfd45a23782bc020, 0x3fa51401526e2908, 0x3fb47b1e8f091a80, 0xbfb3a087d2364000),
(0x3fe5e00000a1545d, 0x3fe3302b3a257b83, 0x3fe5cf0ac716d488, 0xbfd4521d6b4842ab, 0x3fa5b66b3eb3bc3a, 0x3fb4199af14bd180, 0xbfb37d93b34fe000),
(0x3fe5ffffff69b013, 0x3fe345f01c682620, 0x3fe5babcc6a742c0, 0xbfd449db09841112, 0x3fa655cbe07609ee, 0x3fb3b8c9e12c1d00, 0xbfb359d5e3704000),
(0x3fe61fffffac056a, 0x3fe35ba0b5d5fb7f, 0x3fe5a677255bb094, 0xbfd4415d73f9ab8d, 0x3fa6f228f4a18aac, 0x3fb358af15142d80, 0xbfb3355762050000),
(0x3fe63ffffff36e95, 0x3fe3713d0dee4c27, 0x3fe5923a1ec404b6, 0xbfd438a5cb4c88be, 0x3fa78b88346f22ca, 0x3fb2f94e2b0e0300, 0xbfb310210f69a000),
(0x3fe6600002e268dc, 0x3fe386c52f2da1f4, 0x3fe57e05eabaaeda, 0xbfd42fb52cd4f99a, 0x3fa821ef88cc1c46, 0x3fb29aaa894e96c0, 0xbfb2ea3ba114c000),
(0x3fe67ffffca43b52, 0x3fe39c391a94c1f4, 0x3fe569dac91c1aae, 0xbfd4268cb7b7c4c8, 0x3fa8b56360fbfb90, 0x3fb23fb635b482a9, 0xbfb2c40c5aced0ef),
(0x3fe6a0000087414b, 0x3fe3b198e63c8377, 0x3fe555b8e509d4d9, 0xbfd41d2d803d48ce, 0x3fa945ecc8324226, 0x3fb1e29a04de9b6e, 0xbfb29ce1f03b462c),
(0x3fe6bffffca9ca2a, 0x3fe3c6e48f902296, 0x3fe541a07ff88a58, 0xbfd41398a2ef107f, 0x3fa9d3919aace755, 0x3fb1834f7d89ce40, 0xbfb274c5bef82000),
(0x3fe6e00003fa3010, 0x3fe3dc1c2cba5e80, 0x3fe52d91c323fcee, 0xbfd409cf2ee4f9e8, 0x3faa5e55c45b939a, 0x3fb127c00d4bf6c0, 0xbfb24c780da48000),
(0x3fe6fffffff5c5b2, 0x3fe3f13fb897d886, 0x3fe5198cf0b1cf1f, 0xbfd3ffd23dbec556, 0x3faae6408c051ffe, 0x3fb0ccfcbf6e6a40, 0xbfb223a49e696000),
(0x3fe71fffffa86b8e, 0x3fe4064f471d169e, 0x3fe50592322d092f, 0xbfd3f5a2db1bb316, 0x3fab6b589c6aa3fa, 0x3fb07307e1378480, 0xbfb1fa5329170000),
(0x3fe7400001ee24e8, 0x3fe41b4ae1b35499, 0x3fe4f1a1ba383080, 0xbfd3eb42151dc89b, 0x3fabeda46cf6c88a, 0x3fb019e3c81c74c0, 0xbfb1d08b51ab4000),
(0x3fe76000004807ad, 0x3fe430328e7a1ebd, 0x3fe4ddbbbdbb66b6, 0xbfd3e0b0f944ff81, 0x3fac6d2a725bb64f, 0x3faf832565793f00, 0xbfb1a6549afec000),
(0x3fe7800000c376a9, 0x3fe445065bf8569b, 0x3fe4c9e068c4d1e4, 0xbfd3d5f08e7e91ba, 0x3face9f164bddc9a, 0x3faed42d30818400, 0xbfb17bb64ef82000),
(0x3fe7a00000bb278d, 0x3fe459c65333fe05, 0x3fe4b60febc4560b, 0xbfd3cb01dc145c05, 0x3fad63ffe9117670, 0x3fae26e2c80dc580, 0xbfb150b79aec4000),
(0x3fe7bffffdb2e507, 0x3fe46e727d826a87, 0x3fe4a24a7607bef5, 0xbfd3bfe5e6b19c89, 0x3faddb5b54b3040c, 0x3fad816604197de2, 0xbfb125b8c8b0881c),
(0x3fe7e0000252f58a, 0x3fe4830aecddb00e, 0x3fe48e902dbec701, 0xbfd3b49dac459984, 0x3fae500eb957d5e6, 0x3facd1650ee54e80, 0xbfb0f9b4d2d88000),
(0x3fe7fffffc963c19, 0x3fe4978fa0f7692e, 0x3fe47ae149c6e6d9, 0xbfd3a92a31ac4439, 0x3faec21c8e9fe30c, 0x3fac29381cb8a880, 0xbfb0cdbe52f5c000),
(0x3fe81ffffd933f52, 0x3fe4ac00b03b4c38, 0x3fe4673dea60cfe4, 0xbfd39d8c6d24080f, 0x3faf318d54f3de26, 0x3fab82c543a90280, 0xbfb0a1827562e000),
(0x3fe8400002a90411, 0x3fe4c05e248f2ba3, 0x3fe453a63af9e7a4, 0xbfd391c5592e5cad, 0x3faf9e67efa37f40, 0x3faade0f0b5e4c00, 0xbfb075079e842000),
(0x3fe85ffffeda28ed, 0x3fe4d4a8017a21db, 0x3fe4401a6c55b7ff, 0xbfd385d5f1a3c88b, 0x3fb0045995221920, 0x3faa3b17f114e780, 0xbfb048541a0ac000),
(0x3fe87ffffcb5e629, 0x3fe4e8de59a40615, 0x3fe42c9a9fd97bd7, 0xbfd379bf270aa8eb, 0x3fb0383b14344703, 0x3fa999e1bc66d880, 0xbfb01b6deb596000),
(0x3fe8a0000170c515, 0x3fe4fd013c656e86, 0x3fe41926f94766d6, 0xbfd36d81e923c791, 0x3fb06adc00899d63, 0x3fa8fa6e1683e780, 0xbfafdcb5ebc98000),
(0x3fe8c0000013189d, 0x3fe51110add1e051, 0x3fe405bfa67ab9da, 0xbfd3611f2c074f8a, 0x3fb09c3fcc701a50, 0x3fa85cbec910c700, 0xbfaf82421fc08000),
(0x3fe8dffffea5a4e4, 0x3fe5250cbe1a044e, 0x3fe3f264c8d246d0, 0xbfd35497d9e7b6f1, 0x3fb0cc6a0b4acaae, 0x3fa7c0d506895100, 0xbfaf278b9c710000),
(0x3fe8fffffff532e7, 0x3fe538f57b82510b, 0x3fe3df1682be020a, 0xbfd347ecdb613f48, 0x3fb0fb5d96a0b379, 0x3fa72d0add537aa4, 0xbfaecd493ac67089),
(0x3fe9200000e0371d, 0x3fe54ccaf0c0e17a, 0x3fe3cbd4f95a3d43, 0xbfd33b1f192ca5ae, 0x3fb129201bd9bcf5, 0x3fa68e563bf5ca00, 0xbfae7181cd9f0000),
(0x3fe93ffffed17bb8, 0x3fe5608d290c9c45, 0x3fe3b8a0508476b6, 0xbfd32e2f7884690d, 0x3fb155b3032aa8fb, 0x3fa5f7c2e4e4cd80, 0xbfae16438ba38000),
(0x3fe95fffffb19d46, 0x3fe5743c34fb13c6, 0x3fe3a578a61f34cc, 0xbfd3211ed8f518b9, 0x3fb1811a9c607ce3, 0x3fa562f8391c6200, 0xbfadbaec7dd30000),
(0x3fe9800001fbd6cc, 0x3fe587d820a9ca1d, 0x3fe3925e1ba3c385, 0xbfd313ee1a3ddcff, 0x3fb1ab5a76e24f11, 0x3fa4cff68dc4ae00, 0xbfad5f866b46c000),
(0x3fe9a000028625b6, 0x3fe59b60f7595cc7, 0x3fe37f50d2a59cb4, 0xbfd3069e1a26c510, 0x3fb1d47620a6ae76, 0x3fa43ebe0fa40580, 0xbfad041ad7158000),
(0x3fe9c0000013e88f, 0x3fe5aed6c59caa8f, 0x3fe36c50eab346d4, 0xbfd2f92fb30656ff, 0x3fb1fc712a84e7c4, 0x3fa3af4eb4269c00, 0xbfaca8b2f6dac000),
(0x3fe9e00000c59ba9, 0x3fe5c2399c9bbead, 0x3fe3595e7e2616dd, 0xbfd2eba3b9686805, 0x3fb2234f2e03dca7, 0x3fa321a82363d200, 0xbfac4d57a3e34000),
(0x3fe9ffffff9af828, 0x3fe5d58986d9bfee, 0x3fe34679ad1b9f34, 0xbfd2ddfb03da55d4, 0x3fb24913b63c63f4, 0x3fa295ca0bd98800, 0xbfabf211910ac000),
(0x3fea1ffffe6f5c7c, 0x3fe5e8c6931fdc41, 0x3fe333a292cda05f, 0xbfd2d036635848cf, 0x3fb26dc255bbabd0, 0x3fa20bb3d390e000, 0xbfab96e9186cc000),
(0x3fea3ffffddba306, 0x3fe5fbf0cf8e022d, 0x3fe320d94a65b14d, 0xbfd2c256a69b9f29, 0x3fb2915ddee0c8a5, 0x3fa189f836ccd898, 0xbfab3c8bd862fbc5),
(0x3fea5ffffe550ddd, 0x3fe60f084a48a440, 0x3fe30e1dee5569d2, 0xbfd2b45c9a3476c6, 0x3fb2b3ec17359215, 0x3fa0fcdbe6e84800, 0xbfaae111172ec000),
(0x3fea800000e4f98f, 0x3fe6220d11e54f19, 0x3fe2fb7097ede8aa, 0xbfd2a64907194c54, 0x3fb2d56e5363f0a3, 0x3fa07818437a3900, 0xbfaa8670f6f14000),
(0x3fea9ffffda78430, 0x3fe634ff2fca48bb, 0x3fe2e8d164e983b8, 0xbfd2981cb8011622, 0x3fb2f5e8d1d6530f, 0x3f9fea318f2ad100, 0xbfaa2c0d5c400000),
(0x3feac00000a7650e, 0x3fe647deb944952c, 0x3fe2d64066a2b0d9, 0xbfd289d86c0d2d1b, 0x3fb3155f2583e8e6, 0x3f9ee7b7e4800000, 0xbfa9d1ed38234000),
(0x3feadffffedf751c, 0x3fe65aabb61747e5, 0x3fe2c3bdbb183012, 0xbfd27b7ce9f8bb53, 0x3fb333d4c786c2ea, 0x3f9de8c0fc5ad200, 0xbfa978177dbb8000),
(0x3feafffffd65ea17, 0x3fe66d66379ec9f1, 0x3fe2b149762e2d21, 0xbfd26d0aeeb178ab, 0x3fb3514d3de8eaea, 0x3f9ced4987a4d100, 0xbfa91e92b3a98000),
(0x3feb200000caf460, 0x3fe6800e4ef44188, 0x3fe29ee3ab610acd, 0xbfd25e8334b45cff, 0x3fb36dcc0a58c590, 0x3f9bf54dfdf31300, 0xbfa8c56525bc0000),
(0x3feb4000000e26ac, 0x3fe692a4055f2f52, 0x3fe28c8c753d776e, 0xbfd24fe67a0bb733, 0x3fb389549efd4d08, 0x3f9b00cb02862100, 0xbfa86c9508b40000),
(0x3feb6000018849cd, 0x3fe6a5276d2d89d2, 0x3fe27a43e4c58f7d, 0xbfd24135732df900, 0x3fb3a3ea77d68263, 0x3f9a0fbc87055500, 0xbfa814282ba74000),
(0x3feb8000010d9519, 0x3fe6b79892a64df0, 0x3fe2680a104c3459, 0xbfd23270d6aa460d, 0x3fb3bd90404e0eb5, 0x3f992fb610f8b7a1, 0xbfa7bcc387688703),
(0x3feb9ffffe599af5, 0x3fe6c9f7846a2b45, 0x3fe255df0b3288ee, 0xbfd22399572c6060, 0x3fb3d64bb1660697, 0x3f9837ece0652d00, 0xbfa7648eb5fe0000),
(0x3febc00000284356, 0x3fe6dc44552c4ed1, 0x3fe243c2e433adbd, 0xbfd214afa0d6b3b1, 0x3fb3ee1def591e9a, 0x3f975122b84b5a00, 0xbfa70d6caea6c000),
(0x3febdffffe085993, 0x3fe6ee7f0f01eeef, 0x3fe231b5b1f500b7, 0xbfd205b464c5bfb6, 0x3fb4050b1cb5f2a6, 0x3f966dbba68c0400, 0xbfa6b6c3404c0000),
(0x3fec0000034fb3e6, 0x3fe700a7c7586398, 0x3fe21fb77f46182c, 0xbfd1f6a8482e18b6, 0x3fb41b16a1f46d60, 0x3f958db278506e00, 0xbfa66097156f0000),
(0x3fec1ffffdfe62e8, 0x3fe712be83078c02, 0x3fe20dc866cc799f, 0xbfd1e78bfb883685, 0x3fb43043ce52cf56, 0x3f94b1029a5ec700, 0xbfa60aecf2b30000),
(0x3fec3fffff94c963, 0x3fe724c35b136d78, 0x3fe1fbe86e98a7b2, 0xbfd1d8601c0fd209, 0x3fb4449603e9797b, 0x3f93d7a656cf6400, 0xbfa5b5c9094d0000),
(0x3fec60000082bdf4, 0x3fe736b65a605f56, 0x3fe1ea17aa267316, 0xbfd1c92550541ec4, 0x3fb458108eb64abd, 0x3f9301987b6f8700, 0xbfa5612f9c3b8000),
(0x3fec800000df6764, 0x3fe748979037234f, 0x3fe1d85628043564, 0xbfd1b9dc38ce0a23, 0x3fb46ab6ba64e101, 0x3f922ed378f00200, 0xbfa50d24a7678000),
(0x3fec9fffff08b5c1, 0x3fe75a670af97a58, 0x3fe1c6a3f714bf96, 0xbfd1aa8574538e0f, 0x3fb47c8bcc0c4e1c, 0x3f915f51a50a7500, 0xbfa4b9abfb4dc000),
(0x3fecbfffff264192, 0x3fe76c24dc4e49f1, 0x3fe1b501226bbf38, 0xbfd19b219c625478, 0x3fb48d923c79c7f8, 0x3f90a110cf52e4ae, 0xbfa4676263f4c032),
(0x3fece00000316893, 0x3fe77dd113055eab, 0x3fe1a36db76194ae, 0xbfd18bb14affb17d, 0x3fb49dcfa250598d, 0x3f8f93ff72a6f600, 0xbfa4147fa51d0000),
(0x3fed0000028a12de, 0x3fe78f6bbec21f96, 0x3fe191e9c1f0e9ca, 0xbfd17c351662872d, 0x3fb4ad44d4d39570, 0x3f8e08471e932a00, 0xbfa3c2d2ad154000),
(0x3fed200003373601, 0x3fe7a0f4ed5e56f4, 0x3fe180754f521d39, 0xbfd16cad947835ea, 0x3fb4bbf5ca4e213b, 0x3f8c82e4ca8e1c00, 0xbfa371c55ec44000),
(0x3fed400000e2fa29, 0x3fe7b26cada9f9ab, 0x3fe16f106b412869, 0xbfd15d1b57e6e3de, 0x3fb4c9e5aa0c4652, 0x3f8b03cbd541a800, 0xbfa3215aa7d68000),
(0x3fed5ffffc647157, 0x3fe7c3d30fb0d432, 0x3fe15dbb1fb975b9, 0xbfd14d7eefeac143, 0x3fb4d71795f22c94, 0x3f898aef4bb08a00, 0xbfa2d19546608000),
(0x3fed8000030878d4, 0x3fe7d5282a436004, 0x3fe14c756f72ef0b, 0xbfd13dd8e34e747c, 0x3fb4e38eae04b3a6, 0x3f881841786e0000, 0xbfa28277b07e0000),
(0x3feda0000038b7ba, 0x3fe7e66c01df9f9b, 0x3fe13b3f6ee50309, 0xbfd12e29c71cae76, 0x3fb4ef4dfe6e2bfe, 0x3f86abb5fe255e00, 0xbfa2340488c34000),
(0x3fedc000024cc650, 0x3fe7f79eadf54885, 0x3fe12a191f2548cb, 0xbfd11e721cfd633f, 0x3fb4fa589a26b592, 0x3f85453ebe0b9e00, 0xbfa1e63df3f04000),
(0x3fede000009d89d2, 0x3fe808c0399495a2, 0x3fe119028d1fda26, 0xbfd10eb26f95f279, 0x3fb504b184ed26c3, 0x3f83e4ce746a9e00, 0xbfa1992629544000),
(0x3fee00000039743a, 0x3fe819d0b7341e61, 0x3fe107fbbde28c9e, 0xbfd0feeb406dd82e, 0x3fb50e5af0d5593e, 0x3f82a72ef1e0c167, 0xbfa14d527b168f8a),
(0x3fee1ffffe5cc00a, 0x3fe82ad03521bbb6, 0x3fe0f704ba259f97, 0xbfd0ef1d13273fc2, 0x3fb5175a44a65f21, 0x3f8135cae0939400, 0xbfa1010aa6568000),
(0x3fee4000019b115b, 0x3fe83bbec6a702d7, 0x3fe0e61d852e5196, 0xbfd0df4863d03473, 0x3fb51fb00570e1c7, 0x3f7fce36d18fd400, 0xbfa0b60a74c20000),
(0x3fee5ffffdf4f7e1, 0x3fe84c9c7540d5f2, 0x3fe0d5462b922e3d, 0xbfd0cf6db5f37b20, 0x3fb5275fea93680c, 0x3f7d3c75fad99000, 0xbfa06bc035858000),
(0x3fee80000323ee64, 0x3fe85d6959120279, 0x3fe0c47eaad03167, 0xbfd0bf8d7d13d57e, 0x3fb52e6cdb8a684c, 0x3f7ab635583b0400, 0xbfa0222d3764c000),
(0x3feea000027f9467, 0x3fe86e257a464e49, 0x3fe0b3c70fe40a0e, 0xbfd0afa8399b9a17, 0x3fb534d9b198efb2, 0x3f783b593b7d2000, 0xbf9fb2a5de1a8000),
(0x3feec000016d28f0, 0x3fe87ed0eb9a3410, 0x3fe0a31f5cc9486a, 0xbfd09fbe5fe0dff2, 0x3fb53aa9435bdcf3, 0x3f75cbc42e130c00, 0xbf9f226507280000),
(0x3feee0000186b339, 0x3fe88f6bbdcc87be, 0x3fe092879506eb54, 0xbfd08fd063fd06b3, 0x3fb53fde5f2950c0, 0x3f736758dd6aac00, 0xbf9e939a0cb08000),
(0x3feeffffffce4723, 0x3fe89ff5ff3e4b8a, 0x3fe081ffbe119e2e, 0xbfd07fdeba3b0de8, 0x3fb5447bcb488540, 0x3f710dfa27bda400, 0xbf9e0646ebfc0000),
(0x3fef20000017d916, 0x3fe8b06fc1db7f25, 0x3fe07187d965874a, 0xbfd06fe9d16dfdc9, 0x3fb5488447a9ed9c, 0x3f6d7f1490008000, 0xbf9d7a6d4a5b0000),
(0x3fef3ffffe33911c, 0x3fe8c0d9137147b0, 0x3fe0611fec30af7f, 0xbfd05ff21a3a42d4, 0x3fb54bf9b699774b, 0x3f696e589b06ec6f, 0xbf9cf12a32a34060),
(0x3fef5ffffe084599, 0x3fe8d13205f7eff9, 0x3fe050c7f70b73f8, 0xbfd04ff7ffb69502, 0x3fb54ee148abcb5e, 0x3f648602474d4800, 0xbf9c672c6e7a8000),
(0x3fef7ffffdfbe7bb, 0x3fe8e17aa896a3fa, 0x3fe0407ffcf5ee0b, 0xbfd03ffbecf3660f, 0x3fb5513b2748a2d9, 0x3f6029586a500800, 0xbf9bdfc7884c0000),
(0x3fef9fffff0fa180, 0x3fe8f1b30bcb577c, 0x3fe03047ff31c004, 0xbfd02ffe4a3a5b50, 0x3fb5530ac95cb722, 0x3f57c33cda611000, 0xbf9b59e0e3a28000),
(0x3fefc00001a24bf4, 0x3fe901db3fc1bb6f, 0x3fe0201ffeecb132, 0xbfd01fff7e0f13c7, 0x3fb55452c9166f13, 0x3f4eba61be0c4000, 0xbf9ad57931778000),
(0x3fefdfffffe38639, 0x3fe911f3518b3813, 0x3fe01008000a410c, 0xbfd00ffff01bf387, 0x3fb55515b9099fdd, 0x3f3c805a37250000, 0xbf9a52910b908000),
(0x3feff0000008727f, 0x3fe919f953f31326, 0x3fe00801fffb8473, 0xbfd007fffdfb4766, 0x3fb555453ecbbd3f, 0x3f30045a21318845, 0xbf9a12c2520fd1de),
]
const atan32 = {x
/*
Irritating special rounding cases that would require
more extra accuracy than they're worth to correctly round
back from 64 to 32 bits.
*/
var xb = std.flt32bits(x)
if xb == 0x3d8d6b23
-> std.flt32frombits(0x3d8d31c3)
elif xb == 0xbd8d6b23
-> std.flt32frombits(0xbd8d31c3)
;;
var r = atan264((x : flt64), 1.0)
-> (r : flt32)
}
const atan64 = {x
-> atan264(x, 1.0)
}
const atan232 = {y, x
/* Handle the special cases of atan32 for consistency */
if x == 1.0
var yb = std.flt32bits(y)
if yb == 0x3d8d6b23
-> std.flt32frombits(0x3d8d31c3)
elif yb == 0xbd8d6b23
-> std.flt32frombits(0xbd8d31c3)
;;
;;
var r = atan264((y : flt64), (x : flt64))
-> (r : flt32)
}
const atan264 = {y, x
if std.isnan(y) || std.isnan(x)
-> std.flt64nan()
;;
var xb = std.flt64bits(x)
var yb = std.flt64bits(y)
var xpos, xe, ypos, ye
(xpos, xe, _) = std.flt64explode(x)
(ypos, ye, _) = std.flt64explode(y)
xpos = !xpos
ypos = !ypos
/* All the special cases */
if yb == 0x0000000000000000
if xpos
-> 0.0
else
-> std.flt64frombits(0x400921fb54442d18)
;;
elif yb == 0x8000000000000000
if xpos
-> std.flt64frombits(0x8000000000000000)
else
-> std.flt64frombits(0xc00921fb54442d18)
;;
elif xb == 0x0000000000000000 || xb == 0x8000000000000000
if ypos
-> std.flt64frombits(0x3ff921fb54442d18)
else
-> std.flt64frombits(0xbff921fb54442d18)
;;
;;
var xinf = (xe == 1024)
var yinf = (ye == 1024)
match (yinf, ypos, xinf, xpos)
| (true, true, true, false): -> std.flt64frombits(0x4002d97c7f3321d2)
| (true, false, true, false): -> std.flt64frombits(0xc002d97c7f3321d2)
| (true, true, true, true ): -> std.flt64frombits(0x3fe921fb54442d18)
| (true, false, true, true ): -> std.flt64frombits(0xbfe921fb54442d18)
| (true, true, false, _ ): -> std.flt64frombits(0x3ff921fb54442d18)
| (true, false, false, _ ): -> std.flt64frombits(0xbff921fb54442d18)
| (false, true, true, false): -> std.flt64frombits(0x400921fb54442d18)
| (false, false, true, false): -> std.flt64frombits(0xc00921fb54442d18)
| (false, true, true, true ): -> std.flt64frombits(0x0000000000000000)
| (false, false, true, true ): -> std.flt64frombits(0x8000000000000000)
| _:
;;
/* Normal case. Here we just reduce y/x to [0, 1] */
var xabs = std.flt64frombits(std.flt64bits(x) & (~(0 : uint64)) >> 1)
var yabs = std.flt64frombits(std.flt64bits(y) & (~(0 : uint64)) >> 1)
var then_negate = !ypos
var then_subtract_from_pi = !xpos
x = xabs
y = yabs
var then_reverse = false
if y > x
then_reverse = true
std.swap(&x, &y)
;;
/* Compute y/x = u + du */
var u = y / x
var du
if u * x == y
du = 0.0
else
var t1, t2
(t1, t2) = two_by_two(u, x)
du = ((y - t1) - t2)/x
;;
var ret = atan_reduced(u, du)
if then_reverse
/* Compute pi/2 - ret; pi_over_2 is in sin-impl.myr */
var po2_hi = std.flt64frombits(pi_over_2[0])
var po2_lo = std.flt64frombits(pi_over_2[1])
ret = (po2_hi - ret) + po2_lo
;;
if then_subtract_from_pi
/* Compute pi - ret, or maybe -pi - ret */
var pi_hi = scale2(std.flt64frombits(pi_over_2[0]), 1)
var pi_lo = scale2(std.flt64frombits(pi_over_2[1]), 1)
ret = (pi_hi - ret) + pi_lo
;;
if then_negate
ret = -1.0 * ret
;;
-> ret
}
/* Handle arctan(z) with z in [0, 1] */
const atan_reduced = {u : flt64, du : flt64
var ret : flt64
/*
If u is less than 1/16, [GB91] uses a single polynomial
approximation. I am not quite sure why they don't employ
tables in this case: the speed appears to be about the
same. Perhaps to save a few bits for the first entries
of the table?
*/
if u < 0.0625
var s = u * u
var p = horner_polyu(s, atan_coeffs[:])
-> u*p + u*du
;;
/*
Extract a polynomial from the table.
*/
var j = rn(scale2(u, 8))
if j < 0
j = 0
elif j > 256
j = 256
;;
var xi_u : uint64, c : uint64[6]
(xi_u, c[0], c[1], c[2], c[3], c[4], c[5]) = C[j]
var xi : flt64 = std.flt64frombits(xi_u)
-> horner_polyu((u - xi) + du, c[:])
}