From 4a81e0c3469dd25916d99705b1d1f43b019064b6 Mon Sep 17 00:00:00 2001 From: seiko2plus Date: Sat, 6 Sep 2025 03:12:39 +0300 Subject: [PATCH] Generate trigonometric constants and lookup tables using Sollya Added precomputed constants and lookup tables for sine/cosine functions generated with Sollya. These tables include: - Pi constants with different precision levels for float and double types - Sine approximation tables for fast trigonometric calculations - Angle reduction constants - KPi/16 inline constants for range reduction The data was generated using the 'spin sollya' tool and separated into multiple header files to reduce code size and improve organization. Files added: - npsr/trig/data/approx.h: Sine approximation tables - npsr/trig/data/constants.h: Pi and other trigonometric constants - npsr/trig/data/data.h: Main data header - npsr/trig/data/kpi16-inl.h: KPi/16 inline constants - npsr/trig/data/reduction.h: Angle reduction constants --- npsr/trig/data/approx.h | 1563 ++++++++++++++++++++++++ npsr/trig/data/constants.h | 50 + npsr/trig/data/data.h | 5 + npsr/trig/data/kpi16-inl.h | 41 + npsr/trig/data/reduction.h | 2320 ++++++++++++++++++++++++++++++++++++ 5 files changed, 3979 insertions(+) create mode 100644 npsr/trig/data/approx.h create mode 100644 npsr/trig/data/constants.h create mode 100644 npsr/trig/data/data.h create mode 100644 npsr/trig/data/kpi16-inl.h create mode 100644 npsr/trig/data/reduction.h diff --git a/npsr/trig/data/approx.h b/npsr/trig/data/approx.h new file mode 100644 index 0000000..43a1d01 --- /dev/null +++ b/npsr/trig/data/approx.h @@ -0,0 +1,1563 @@ +// Auto-generated by npsr/trig/data/approx.h.sol +// Use `spin sollya -f` to force regeneration +#ifndef NPSR_TRIG_DATA_APPROX_H +#define NPSR_TRIG_DATA_APPROX_H + +namespace npsr::trig::data { +template inline constexpr char kSinApproxTable[] = {}; +template <> inline constexpr float kSinApproxTable[] = +{ +0.0f, 0x1p0f, 0.0f, 0.0f, +-0x1.3bcfbep-12f, 0x1p0f, 0x1.92156p-6f, -0x1.0b933p-31f, +-0x1.3bc39p-10f, 0x1p0f, 0x1.91f66p-5f, -0x1.de44fep-30f, +-0x1.63253p-9f, 0x1p0f, 0x1.2d520ap-4f, -0x1.a63cc2p-29f, +-0x1.3b92e2p-8f, 0x1p0f, 0x1.917a6cp-4f, -0x1.eb25eap-31f, +-0x1.ecdc78p-8f, 0x1p0f, 0x1.f564e6p-4f, -0x1.2ad19ep-29f, +-0x1.62aa04p-7f, 0x1p0f, 0x1.2c8106p-3f, 0x1.d1cc28p-28f, +-0x1.e26c16p-7f, 0x1p0f, 0x1.5e2144p-3f, 0x1.22cff2p-29f, +-0x1.3ad06p-6f, 0x1p0f, 0x1.8f8b84p-3f, -0x1.cb2cfap-30f, +-0x1.8e18a8p-6f, 0x1p0f, 0x1.c0b826p-3f, 0x1.4fc9ecp-28f, +-0x1.eb0208p-6f, 0x1p0f, 0x1.f19f98p-3f, -0x1.37a83ap-29f, +-0x1.28bf18p-5f, 0x1p0f, 0x1.111d26p-2f, 0x1.58fb3cp-29f, +-0x1.60beaap-5f, 0x1p0f, 0x1.294062p-2f, 0x1.dab3ep-27f, +-0x1.9d7714p-5f, 0x1p0f, 0x1.4135cap-2f, -0x1.7d134p-27f, +-0x1.dedefcp-5f, 0x1p0f, 0x1.58f9a8p-2f, -0x1.4a9c04p-27f, +-0x1.127624p-4f, 0x1p0f, 0x1.708854p-2f, -0x1.e0b74cp-27f, +-0x1.37ca18p-4f, 0x1p0f, 0x1.87de2ap-2f, 0x1.abaa58p-28f, +-0x1.5f6598p-4f, 0x1p0f, 0x1.9ef794p-2f, 0x1.d476c6p-29f, +-0x1.894286p-4f, 0x1p0f, 0x1.b5d1p-2f, 0x1.3c2b98p-27f, +-0x1.b55a7p-4f, 0x1p0f, 0x1.cc66eap-2f, -0x1.b38ee8p-28f, +-0x1.e3a688p-4f, 0x1p0f, 0x1.e2b5d4p-2f, -0x1.fe4272p-28f, +-0x1.0a0fd4p-3f, 0x1p0f, 0x1.f8ba4ep-2f, -0x1.01d952p-28f, +-0x1.235f2ep-3f, 0x1p0f, 0x1.07387ap-1f, -0x1.b74004p-27f, +-0x1.3dbd6ap-3f, 0x1p0f, 0x1.11eb36p-1f, -0x1.7c969cp-26f, +-0x1.592676p-3f, 0x1p0f, 0x1.1c73b4p-1f, -0x1.9465cep-27f, +-0x1.759618p-3f, 0x1p0f, 0x1.26d054p-1f, 0x1.9ba25cp-26f, +-0x1.9307eep-3f, 0x1p0f, 0x1.30ff8p-1f, -0x1.8f47e6p-28f, +-0x1.b1776ep-3f, 0x1p0f, 0x1.3affa2p-1f, 0x1.240a18p-26f, +-0x1.d0dfe6p-3f, 0x1p0f, 0x1.44cf32p-1f, 0x1.424776p-27f, +-0x1.f13c7ep-3f, 0x1p0f, 0x1.4e6cacp-1f, -0x1.070686p-27f, +-0x1.09441cp-2f, 0x1p0f, 0x1.57d694p-1f, -0x1.6e626cp-26f, +-0x1.1a5efap-2f, 0x1p0f, 0x1.610b76p-1f, -0x1.5c5a64p-26f, +-0x1.2bec34p-2f, 0x1p0f, 0x1.6a09e6p-1f, 0x1.9fcef4p-27f, +-0x1.3de916p-2f, 0x1p0f, 0x1.72d084p-1f, -0x1.02000ep-26f, +-0x1.5052dap-2f, 0x1p0f, 0x1.7b5df2p-1f, 0x1.3557d8p-28f, +-0x1.6326a8p-2f, 0x1p0f, 0x1.83b0ep-1f, 0x1.7ff2eep-26f, +-0x1.76619cp-2f, 0x1p0f, 0x1.8bc806p-1f, 0x1.62a2e8p-26f, +-0x1.8a00bap-2f, 0x1p0f, 0x1.93a224p-1f, 0x1.324c8p-26f, +-0x1.9e01p-2f, 0x1p0f, 0x1.9b3e04p-1f, 0x1.fce1dp-27f, +-0x1.b25f56p-2f, 0x1p0f, 0x1.a29a7ap-1f, 0x1.189e08p-31f, +-0x1.c71898p-2f, 0x1p0f, 0x1.a9b662p-1f, 0x1.21d434p-26f, +-0x1.dc2996p-2f, 0x1p0f, 0x1.b090a6p-1f, -0x1.fabf8p-27f, +-0x1.f18f0cp-2f, 0x1p0f, 0x1.b72834p-1f, 0x1.465b9p-27f, +-0x1.d16c9p-8f, 0x1p-1f, 0x1.bd7c0ap-1f, 0x1.8df2a6p-26f, +-0x1.d4a2c8p-6f, 0x1p-1f, 0x1.c38b3p-1f, -0x1.cfe84ap-26f, +-0x1.9cc8b4p-5f, 0x1p-1f, 0x1.c954b2p-1f, 0x1.3411f4p-29f, +-0x1.28bbfep-4f, 0x1p-1f, 0x1.ced7bp-1f, -0x1.786712p-26f, +-0x1.8421bp-4f, 0x1p-1f, 0x1.d4134ep-1f, -0x1.d646d8p-26f, +-0x1.e08756p-4f, 0x1p-1f, 0x1.d906bcp-1f, 0x1.e651a8p-26f, +-0x1.1eef5ap-3f, 0x1p-1f, 0x1.ddb13cp-1f, -0x1.2667b8p-26f, +-0x1.4e0cb2p-3f, 0x1p-1f, 0x1.e2121p-1f, 0x1.3da1bap-27f, +-0x1.7d946ep-3f, 0x1p-1f, 0x1.e6288ep-1f, 0x1.891c22p-26f, +-0x1.ad7f3ap-3f, 0x1p-1f, 0x1.e9f416p-1f, -0x1.273a44p-26f, +-0x1.ddc5b4p-3f, 0x1p-1f, 0x1.ed740ep-1f, 0x1.da1258p-27f, +-0x1.cc0d0ap-8f, 0x1p-2f, 0x1.f0a7fp-1f, -0x1.1b73cap-27f, +-0x1.fa3ecap-6f, 0x1p-2f, 0x1.f38f3ap-1f, 0x1.8c9cb2p-26f, +-0x1.c1d1fp-5f, 0x1p-2f, 0x1.f6297cp-1f, 0x1.feeb96p-26f, +-0x1.43bd78p-4f, 0x1p-2f, 0x1.f8765p-1f, -0x1.63ad16p-27f, +-0x1.a6fdf2p-4f, 0x1p-2f, 0x1.fa7558p-1f, -0x1.eeb5d2p-30f, +-0x1.536352p-9f, 0x1p-3f, 0x1.fc2648p-1f, -0x1.e3cc06p-26f, +-0x1.ba165p-6f, 0x1p-3f, 0x1.fd88dap-1f, 0x1.e89292p-28f, +-0x1.a55beep-5f, 0x1p-3f, 0x1.fe9cdap-1f, 0x1.a03108p-26f, +-0x1.b82684p-7f, 0x1p-4f, 0x1.ff621ep-1f, 0x1.bcb6bep-28f, +-0x1.b7aa82p-8f, 0x1p-5f, 0x1.ffd886p-1f, 0x1.099a1ap-30f, +0.0f, 0.0f, 0x1p0f, 0.0f, +-0x1.003242p5f, 0x1p5f, 0x1.ffd886p-1f, 0x1.099a1ap-30f, +-0x1.00c8fcp4f, 0x1p4f, 0x1.ff621ep-1f, 0x1.bcb6bep-28f, +-0x1.025aa4p3f, 0x1p3f, 0x1.fe9cdap-1f, 0x1.a03108p-26f, +-0x1.0322f4p3f, 0x1p3f, 0x1.fd88dap-1f, 0x1.e89292p-28f, +-0x1.03eacap3f, 0x1p3f, 0x1.fc2648p-1f, -0x1.e3cc06p-26f, +-0x1.096408p2f, 0x1p2f, 0x1.fa7558p-1f, -0x1.eeb5d2p-30f, +-0x1.0af10ap2f, 0x1p2f, 0x1.f8765p-1f, -0x1.63ad16p-27f, +-0x1.0c7c5cp2f, 0x1p2f, 0x1.f6297cp-1f, 0x1.feeb96p-26f, +-0x1.0e05c2p2f, 0x1p2f, 0x1.f38f3ap-1f, 0x1.8c9cb2p-26f, +-0x1.0f8cfcp2f, 0x1p2f, 0x1.f0a7fp-1f, -0x1.1b73cap-27f, +-0x1.2223a4p1f, 0x1p1f, 0x1.ed740ep-1f, 0x1.da1258p-27f, +-0x1.25280cp1f, 0x1p1f, 0x1.e9f416p-1f, -0x1.273a44p-26f, +-0x1.2826bap1f, 0x1p1f, 0x1.e6288ep-1f, 0x1.891c22p-26f, +-0x1.2b1f34p1f, 0x1p1f, 0x1.e2121p-1f, 0x1.3da1bap-27f, +-0x1.2e110ap1f, 0x1p1f, 0x1.ddb13cp-1f, -0x1.2667b8p-26f, +-0x1.30fbc6p1f, 0x1p1f, 0x1.d906bcp-1f, 0x1.e651a8p-26f, +-0x1.33def2p1f, 0x1p1f, 0x1.d4134ep-1f, -0x1.d646d8p-26f, +-0x1.36ba2p1f, 0x1p1f, 0x1.ced7bp-1f, -0x1.786712p-26f, +-0x1.398cdep1f, 0x1p1f, 0x1.c954b2p-1f, 0x1.3411f4p-29f, +-0x1.3c56bap1f, 0x1p1f, 0x1.c38b3p-1f, -0x1.cfe84ap-26f, +-0x1.3f174ap1f, 0x1p1f, 0x1.bd7c0ap-1f, 0x1.8df2a6p-26f, +-0x1.839c3cp0f, 0x1p0f, 0x1.b72834p-1f, 0x1.465b9p-27f, +-0x1.88f59ap0f, 0x1p0f, 0x1.b090a6p-1f, -0x1.fabf8p-27f, +-0x1.8e39dap0f, 0x1p0f, 0x1.a9b662p-1f, 0x1.21d434p-26f, +-0x1.93682ap0f, 0x1p0f, 0x1.a29a7ap-1f, 0x1.189e08p-31f, +-0x1.987fcp0f, 0x1p0f, 0x1.9b3e04p-1f, 0x1.fce1dp-27f, +-0x1.9d7fd2p0f, 0x1p0f, 0x1.93a224p-1f, 0x1.324c8p-26f, +-0x1.a2679ap0f, 0x1p0f, 0x1.8bc806p-1f, 0x1.62a2e8p-26f, +-0x1.a73656p0f, 0x1p0f, 0x1.83b0ep-1f, 0x1.7ff2eep-26f, +-0x1.abeb4ap0f, 0x1p0f, 0x1.7b5df2p-1f, 0x1.3557d8p-28f, +-0x1.b085bap0f, 0x1p0f, 0x1.72d084p-1f, -0x1.02000ep-26f, +-0x1.b504f4p0f, 0x1p0f, 0x1.6a09e6p-1f, 0x1.9fcef4p-27f, +-0x1.b96842p0f, 0x1p0f, 0x1.610b76p-1f, -0x1.5c5a64p-26f, +-0x1.bdaefap0f, 0x1p0f, 0x1.57d694p-1f, -0x1.6e626cp-26f, +-0x1.c1d87p0f, 0x1p0f, 0x1.4e6cacp-1f, -0x1.070686p-27f, +-0x1.c5e404p0f, 0x1p0f, 0x1.44cf32p-1f, 0x1.424776p-27f, +-0x1.c9d112p0f, 0x1p0f, 0x1.3affa2p-1f, 0x1.240a18p-26f, +-0x1.cd9f02p0f, 0x1p0f, 0x1.30ff8p-1f, -0x1.8f47e6p-28f, +-0x1.d14d3ep0f, 0x1p0f, 0x1.26d054p-1f, 0x1.9ba25cp-26f, +-0x1.d4db32p0f, 0x1p0f, 0x1.1c73b4p-1f, -0x1.9465cep-27f, +-0x1.d84852p0f, 0x1p0f, 0x1.11eb36p-1f, -0x1.7c969cp-26f, +-0x1.db941ap0f, 0x1p0f, 0x1.07387ap-1f, -0x1.b74004p-27f, +-0x1.debe06p0f, 0x1p0f, 0x1.f8ba4ep-2f, -0x1.01d952p-28f, +-0x1.e1c598p0f, 0x1p0f, 0x1.e2b5d4p-2f, -0x1.fe4272p-28f, +-0x1.e4aa5ap0f, 0x1p0f, 0x1.cc66eap-2f, -0x1.b38ee8p-28f, +-0x1.e76bd8p0f, 0x1p0f, 0x1.b5d1p-2f, 0x1.3c2b98p-27f, +-0x1.ea09a6p0f, 0x1p0f, 0x1.9ef794p-2f, 0x1.d476c6p-29f, +-0x1.ec835ep0f, 0x1p0f, 0x1.87de2ap-2f, 0x1.abaa58p-28f, +-0x1.eed89ep0f, 0x1p0f, 0x1.708854p-2f, -0x1.e0b74cp-27f, +-0x1.f10908p0f, 0x1p0f, 0x1.58f9a8p-2f, -0x1.4a9c04p-27f, +-0x1.f31448p0f, 0x1p0f, 0x1.4135cap-2f, -0x1.7d134p-27f, +-0x1.f4fa0ap0f, 0x1p0f, 0x1.294062p-2f, 0x1.dab3ep-27f, +-0x1.f6ba08p0f, 0x1p0f, 0x1.111d26p-2f, 0x1.58fb3cp-29f, +-0x1.f853f8p0f, 0x1p0f, 0x1.f19f98p-3f, -0x1.37a83ap-29f, +-0x1.f9c79ep0f, 0x1p0f, 0x1.c0b826p-3f, 0x1.4fc9ecp-28f, +-0x1.fb14bep0f, 0x1p0f, 0x1.8f8b84p-3f, -0x1.cb2cfap-30f, +-0x1.fc3b28p0f, 0x1p0f, 0x1.5e2144p-3f, 0x1.22cff2p-29f, +-0x1.fd3aacp0f, 0x1p0f, 0x1.2c8106p-3f, 0x1.d1cc28p-28f, +-0x1.fe1324p0f, 0x1p0f, 0x1.f564e6p-4f, -0x1.2ad19ep-29f, +-0x1.fec46ep0f, 0x1p0f, 0x1.917a6cp-4f, -0x1.eb25eap-31f, +-0x1.ff4e6ep0f, 0x1p0f, 0x1.2d520ap-4f, -0x1.a63cc2p-29f, +-0x1.ffb11p0f, 0x1p0f, 0x1.91f66p-5f, -0x1.de44fep-30f, +-0x1.ffec44p0f, 0x1p0f, 0x1.92156p-6f, -0x1.0b933p-31f, +-0x1p1f, 0x1p0f, 0.0f, 0.0f, +-0x1.ffec44p0f, 0x1p0f, -0x1.92156p-6f, 0x1.0b933p-31f, +-0x1.ffb11p0f, 0x1p0f, -0x1.91f66p-5f, 0x1.de44fep-30f, +-0x1.ff4e6ep0f, 0x1p0f, -0x1.2d520ap-4f, 0x1.a63cc2p-29f, +-0x1.fec46ep0f, 0x1p0f, -0x1.917a6cp-4f, 0x1.eb25eap-31f, +-0x1.fe1324p0f, 0x1p0f, -0x1.f564e6p-4f, 0x1.2ad19ep-29f, +-0x1.fd3aacp0f, 0x1p0f, -0x1.2c8106p-3f, -0x1.d1cc28p-28f, +-0x1.fc3b28p0f, 0x1p0f, -0x1.5e2144p-3f, -0x1.22cff2p-29f, +-0x1.fb14bep0f, 0x1p0f, -0x1.8f8b84p-3f, 0x1.cb2cfap-30f, +-0x1.f9c79ep0f, 0x1p0f, -0x1.c0b826p-3f, -0x1.4fc9ecp-28f, +-0x1.f853f8p0f, 0x1p0f, -0x1.f19f98p-3f, 0x1.37a83ap-29f, +-0x1.f6ba08p0f, 0x1p0f, -0x1.111d26p-2f, -0x1.58fb3cp-29f, +-0x1.f4fa0ap0f, 0x1p0f, -0x1.294062p-2f, -0x1.dab3ep-27f, +-0x1.f31448p0f, 0x1p0f, -0x1.4135cap-2f, 0x1.7d134p-27f, +-0x1.f10908p0f, 0x1p0f, -0x1.58f9a8p-2f, 0x1.4a9c04p-27f, +-0x1.eed89ep0f, 0x1p0f, -0x1.708854p-2f, 0x1.e0b74cp-27f, +-0x1.ec835ep0f, 0x1p0f, -0x1.87de2ap-2f, -0x1.abaa58p-28f, +-0x1.ea09a6p0f, 0x1p0f, -0x1.9ef794p-2f, -0x1.d476c6p-29f, +-0x1.e76bd8p0f, 0x1p0f, -0x1.b5d1p-2f, -0x1.3c2b98p-27f, +-0x1.e4aa5ap0f, 0x1p0f, -0x1.cc66eap-2f, 0x1.b38ee8p-28f, +-0x1.e1c598p0f, 0x1p0f, -0x1.e2b5d4p-2f, 0x1.fe4272p-28f, +-0x1.debe06p0f, 0x1p0f, -0x1.f8ba4ep-2f, 0x1.01d952p-28f, +-0x1.db941ap0f, 0x1p0f, -0x1.07387ap-1f, 0x1.b74004p-27f, +-0x1.d84852p0f, 0x1p0f, -0x1.11eb36p-1f, 0x1.7c969cp-26f, +-0x1.d4db32p0f, 0x1p0f, -0x1.1c73b4p-1f, 0x1.9465cep-27f, +-0x1.d14d3ep0f, 0x1p0f, -0x1.26d054p-1f, -0x1.9ba25cp-26f, +-0x1.cd9f02p0f, 0x1p0f, -0x1.30ff8p-1f, 0x1.8f47e6p-28f, +-0x1.c9d112p0f, 0x1p0f, -0x1.3affa2p-1f, -0x1.240a18p-26f, +-0x1.c5e404p0f, 0x1p0f, -0x1.44cf32p-1f, -0x1.424776p-27f, +-0x1.c1d87p0f, 0x1p0f, -0x1.4e6cacp-1f, 0x1.070686p-27f, +-0x1.bdaefap0f, 0x1p0f, -0x1.57d694p-1f, 0x1.6e626cp-26f, +-0x1.b96842p0f, 0x1p0f, -0x1.610b76p-1f, 0x1.5c5a64p-26f, +-0x1.b504f4p0f, 0x1p0f, -0x1.6a09e6p-1f, -0x1.9fcef4p-27f, +-0x1.b085bap0f, 0x1p0f, -0x1.72d084p-1f, 0x1.02000ep-26f, +-0x1.abeb4ap0f, 0x1p0f, -0x1.7b5df2p-1f, -0x1.3557d8p-28f, +-0x1.a73656p0f, 0x1p0f, -0x1.83b0ep-1f, -0x1.7ff2eep-26f, +-0x1.a2679ap0f, 0x1p0f, -0x1.8bc806p-1f, -0x1.62a2e8p-26f, +-0x1.9d7fd2p0f, 0x1p0f, -0x1.93a224p-1f, -0x1.324c8p-26f, +-0x1.987fcp0f, 0x1p0f, -0x1.9b3e04p-1f, -0x1.fce1dp-27f, +-0x1.93682ap0f, 0x1p0f, -0x1.a29a7ap-1f, -0x1.189e08p-31f, +-0x1.8e39dap0f, 0x1p0f, -0x1.a9b662p-1f, -0x1.21d434p-26f, +-0x1.88f59ap0f, 0x1p0f, -0x1.b090a6p-1f, 0x1.fabf8p-27f, +-0x1.839c3cp0f, 0x1p0f, -0x1.b72834p-1f, -0x1.465b9p-27f, +-0x1.3f174ap1f, 0x1p1f, -0x1.bd7c0ap-1f, -0x1.8df2a6p-26f, +-0x1.3c56bap1f, 0x1p1f, -0x1.c38b3p-1f, 0x1.cfe84ap-26f, +-0x1.398cdep1f, 0x1p1f, -0x1.c954b2p-1f, -0x1.3411f4p-29f, +-0x1.36ba2p1f, 0x1p1f, -0x1.ced7bp-1f, 0x1.786712p-26f, +-0x1.33def2p1f, 0x1p1f, -0x1.d4134ep-1f, 0x1.d646d8p-26f, +-0x1.30fbc6p1f, 0x1p1f, -0x1.d906bcp-1f, -0x1.e651a8p-26f, +-0x1.2e110ap1f, 0x1p1f, -0x1.ddb13cp-1f, 0x1.2667b8p-26f, +-0x1.2b1f34p1f, 0x1p1f, -0x1.e2121p-1f, -0x1.3da1bap-27f, +-0x1.2826bap1f, 0x1p1f, -0x1.e6288ep-1f, -0x1.891c22p-26f, +-0x1.25280cp1f, 0x1p1f, -0x1.e9f416p-1f, 0x1.273a44p-26f, +-0x1.2223a4p1f, 0x1p1f, -0x1.ed740ep-1f, -0x1.da1258p-27f, +-0x1.0f8cfcp2f, 0x1p2f, -0x1.f0a7fp-1f, 0x1.1b73cap-27f, +-0x1.0e05c2p2f, 0x1p2f, -0x1.f38f3ap-1f, -0x1.8c9cb2p-26f, +-0x1.0c7c5cp2f, 0x1p2f, -0x1.f6297cp-1f, -0x1.feeb96p-26f, +-0x1.0af10ap2f, 0x1p2f, -0x1.f8765p-1f, 0x1.63ad16p-27f, +-0x1.096408p2f, 0x1p2f, -0x1.fa7558p-1f, 0x1.eeb5d2p-30f, +-0x1.03eacap3f, 0x1p3f, -0x1.fc2648p-1f, 0x1.e3cc06p-26f, +-0x1.0322f4p3f, 0x1p3f, -0x1.fd88dap-1f, -0x1.e89292p-28f, +-0x1.025aa4p3f, 0x1p3f, -0x1.fe9cdap-1f, -0x1.a03108p-26f, +-0x1.00c8fcp4f, 0x1p4f, -0x1.ff621ep-1f, -0x1.bcb6bep-28f, +-0x1.003242p5f, 0x1p5f, -0x1.ffd886p-1f, -0x1.099a1ap-30f, +0.0f, 0.0f, -0x1p0f, 0.0f, +-0x1.b7aa82p-8f, 0x1p-5f, -0x1.ffd886p-1f, -0x1.099a1ap-30f, +-0x1.b82684p-7f, 0x1p-4f, -0x1.ff621ep-1f, -0x1.bcb6bep-28f, +-0x1.a55beep-5f, 0x1p-3f, -0x1.fe9cdap-1f, -0x1.a03108p-26f, +-0x1.ba165p-6f, 0x1p-3f, -0x1.fd88dap-1f, -0x1.e89292p-28f, +-0x1.536352p-9f, 0x1p-3f, -0x1.fc2648p-1f, 0x1.e3cc06p-26f, +-0x1.a6fdf2p-4f, 0x1p-2f, -0x1.fa7558p-1f, 0x1.eeb5d2p-30f, +-0x1.43bd78p-4f, 0x1p-2f, -0x1.f8765p-1f, 0x1.63ad16p-27f, +-0x1.c1d1fp-5f, 0x1p-2f, -0x1.f6297cp-1f, -0x1.feeb96p-26f, +-0x1.fa3ecap-6f, 0x1p-2f, -0x1.f38f3ap-1f, -0x1.8c9cb2p-26f, +-0x1.cc0d0ap-8f, 0x1p-2f, -0x1.f0a7fp-1f, 0x1.1b73cap-27f, +-0x1.ddc5b4p-3f, 0x1p-1f, -0x1.ed740ep-1f, -0x1.da1258p-27f, +-0x1.ad7f3ap-3f, 0x1p-1f, -0x1.e9f416p-1f, 0x1.273a44p-26f, +-0x1.7d946ep-3f, 0x1p-1f, -0x1.e6288ep-1f, -0x1.891c22p-26f, +-0x1.4e0cb2p-3f, 0x1p-1f, -0x1.e2121p-1f, -0x1.3da1bap-27f, +-0x1.1eef5ap-3f, 0x1p-1f, -0x1.ddb13cp-1f, 0x1.2667b8p-26f, +-0x1.e08756p-4f, 0x1p-1f, -0x1.d906bcp-1f, -0x1.e651a8p-26f, +-0x1.8421bp-4f, 0x1p-1f, -0x1.d4134ep-1f, 0x1.d646d8p-26f, +-0x1.28bbfep-4f, 0x1p-1f, -0x1.ced7bp-1f, 0x1.786712p-26f, +-0x1.9cc8b4p-5f, 0x1p-1f, -0x1.c954b2p-1f, -0x1.3411f4p-29f, +-0x1.d4a2c8p-6f, 0x1p-1f, -0x1.c38b3p-1f, 0x1.cfe84ap-26f, +-0x1.d16c9p-8f, 0x1p-1f, -0x1.bd7c0ap-1f, -0x1.8df2a6p-26f, +-0x1.f18f0cp-2f, 0x1p0f, -0x1.b72834p-1f, -0x1.465b9p-27f, +-0x1.dc2996p-2f, 0x1p0f, -0x1.b090a6p-1f, 0x1.fabf8p-27f, +-0x1.c71898p-2f, 0x1p0f, -0x1.a9b662p-1f, -0x1.21d434p-26f, +-0x1.b25f56p-2f, 0x1p0f, -0x1.a29a7ap-1f, -0x1.189e08p-31f, +-0x1.9e01p-2f, 0x1p0f, -0x1.9b3e04p-1f, -0x1.fce1dp-27f, +-0x1.8a00bap-2f, 0x1p0f, -0x1.93a224p-1f, -0x1.324c8p-26f, +-0x1.76619cp-2f, 0x1p0f, -0x1.8bc806p-1f, -0x1.62a2e8p-26f, +-0x1.6326a8p-2f, 0x1p0f, -0x1.83b0ep-1f, -0x1.7ff2eep-26f, +-0x1.5052dap-2f, 0x1p0f, -0x1.7b5df2p-1f, -0x1.3557d8p-28f, +-0x1.3de916p-2f, 0x1p0f, -0x1.72d084p-1f, 0x1.02000ep-26f, +-0x1.2bec34p-2f, 0x1p0f, -0x1.6a09e6p-1f, -0x1.9fcef4p-27f, +-0x1.1a5efap-2f, 0x1p0f, -0x1.610b76p-1f, 0x1.5c5a64p-26f, +-0x1.09441cp-2f, 0x1p0f, -0x1.57d694p-1f, 0x1.6e626cp-26f, +-0x1.f13c7ep-3f, 0x1p0f, -0x1.4e6cacp-1f, 0x1.070686p-27f, +-0x1.d0dfe6p-3f, 0x1p0f, -0x1.44cf32p-1f, -0x1.424776p-27f, +-0x1.b1776ep-3f, 0x1p0f, -0x1.3affa2p-1f, -0x1.240a18p-26f, +-0x1.9307eep-3f, 0x1p0f, -0x1.30ff8p-1f, 0x1.8f47e6p-28f, +-0x1.759618p-3f, 0x1p0f, -0x1.26d054p-1f, -0x1.9ba25cp-26f, +-0x1.592676p-3f, 0x1p0f, -0x1.1c73b4p-1f, 0x1.9465cep-27f, +-0x1.3dbd6ap-3f, 0x1p0f, -0x1.11eb36p-1f, 0x1.7c969cp-26f, +-0x1.235f2ep-3f, 0x1p0f, -0x1.07387ap-1f, 0x1.b74004p-27f, +-0x1.0a0fd4p-3f, 0x1p0f, -0x1.f8ba4ep-2f, 0x1.01d952p-28f, +-0x1.e3a688p-4f, 0x1p0f, -0x1.e2b5d4p-2f, 0x1.fe4272p-28f, +-0x1.b55a7p-4f, 0x1p0f, -0x1.cc66eap-2f, 0x1.b38ee8p-28f, +-0x1.894286p-4f, 0x1p0f, -0x1.b5d1p-2f, -0x1.3c2b98p-27f, +-0x1.5f6598p-4f, 0x1p0f, -0x1.9ef794p-2f, -0x1.d476c6p-29f, +-0x1.37ca18p-4f, 0x1p0f, -0x1.87de2ap-2f, -0x1.abaa58p-28f, +-0x1.127624p-4f, 0x1p0f, -0x1.708854p-2f, 0x1.e0b74cp-27f, +-0x1.dedefcp-5f, 0x1p0f, -0x1.58f9a8p-2f, 0x1.4a9c04p-27f, +-0x1.9d7714p-5f, 0x1p0f, -0x1.4135cap-2f, 0x1.7d134p-27f, +-0x1.60beaap-5f, 0x1p0f, -0x1.294062p-2f, -0x1.dab3ep-27f, +-0x1.28bf18p-5f, 0x1p0f, -0x1.111d26p-2f, -0x1.58fb3cp-29f, +-0x1.eb0208p-6f, 0x1p0f, -0x1.f19f98p-3f, 0x1.37a83ap-29f, +-0x1.8e18a8p-6f, 0x1p0f, -0x1.c0b826p-3f, -0x1.4fc9ecp-28f, +-0x1.3ad06p-6f, 0x1p0f, -0x1.8f8b84p-3f, 0x1.cb2cfap-30f, +-0x1.e26c16p-7f, 0x1p0f, -0x1.5e2144p-3f, -0x1.22cff2p-29f, +-0x1.62aa04p-7f, 0x1p0f, -0x1.2c8106p-3f, -0x1.d1cc28p-28f, +-0x1.ecdc78p-8f, 0x1p0f, -0x1.f564e6p-4f, 0x1.2ad19ep-29f, +-0x1.3b92e2p-8f, 0x1p0f, -0x1.917a6cp-4f, 0x1.eb25eap-31f, +-0x1.63253p-9f, 0x1p0f, -0x1.2d520ap-4f, 0x1.a63cc2p-29f, +-0x1.3bc39p-10f, 0x1p0f, -0x1.91f66p-5f, 0x1.de44fep-30f, +-0x1.3bcfbep-12f, 0x1p0f, -0x1.92156p-6f, 0x1.0b933p-31f, +}; + +template <> inline constexpr double kSinApproxTable[] = +{ +0.0, 0x1p0, 0.0, 0.0, +-0x1.3bd2c8da49511p-14, 0x1p0, 0x1.921d1fcdec784p-7, 0x1.9878eap-61, +-0x1.3bcfbd9979a27p-12, 0x1p0, 0x1.92155f7a3667ep-6, -0x1.b1d63p-64, +-0x1.6344004228d8bp-11, 0x1p0, 0x1.2d865759455cdp-5, 0x1.686f64p-61, +-0x1.3bc390d250439p-10, 0x1p0, 0x1.91f65f10dd814p-5, -0x1.912bdp-61, +-0x1.ed534e31ca57fp-10, 0x1p0, 0x1.f656e79f820ep-5, -0x1.2e1ebep-61, +-0x1.63252fe77c5ebp-9, 0x1p0, 0x1.2d52092ce19f6p-4, -0x1.9a088ap-59, +-0x1.e350342a4f6e6p-9, 0x1p0, 0x1.5f6d00a9aa419p-4, -0x1.f4022cp-59, +-0x1.3b92e176d6d31p-8, 0x1p0, 0x1.917a6bc29b42cp-4, -0x1.e2718cp-60, +-0x1.8f501492cc296p-8, 0x1p0, 0x1.c3785c79ec2d5p-4, -0x1.4f39dep-61, +-0x1.ecdc78f30165cp-8, 0x1p0, 0x1.f564e56a9730ep-4, 0x1.a27046p-59, +-0x1.2a1a39a8a2fb7p-7, 0x1p0, 0x1.139f0cedaf577p-3, -0x1.523434p-57, +-0x1.62aa03dd6ba58p-7, 0x1p0, 0x1.2c8106e8e613ap-3, 0x1.13000ap-58, +-0x1.a01b6cdbd995ep-7, 0x1p0, 0x1.45576b1293e5ap-3, -0x1.285a24p-58, +-0x1.e26c163ad15b3p-7, 0x1p0, 0x1.5e214448b3fc6p-3, 0x1.531ff6p-57, +-0x1.14ccb8bdbf114p-6, 0x1p0, 0x1.76dd9de50bf31p-3, 0x1.1d5eeep-57, +-0x1.3ad06011469fbp-6, 0x1p0, 0x1.8f8b83c69a60bp-3, -0x1.26d19ap-57, +-0x1.633f89e9a1a66p-6, 0x1p0, 0x1.a82a025b00451p-3, -0x1.87905ep-57, +-0x1.8e18a73634ee7p-6, 0x1p0, 0x1.c0b826a7e4f63p-3, -0x1.af1438p-62, +-0x1.bb5a11138a4c9p-6, 0x1p0, 0x1.d934fe5454311p-3, 0x1.75b922p-57, +-0x1.eb0208db9e51bp-6, 0x1p0, 0x1.f19f97b215f1bp-3, -0x1.42deeep-57, +-0x1.0e875c1b8c3dap-5, 0x1p0, 0x1.04fb80e37fdaep-2, -0x1.412cdap-63, +-0x1.28bf1897b69ccp-5, 0x1p0, 0x1.111d262b1f677p-2, 0x1.824c2p-56, +-0x1.44273720f48bcp-5, 0x1p0, 0x1.1d3443f4cdb3ep-2, -0x1.720d4p-57, +-0x1.60bea939d225ap-5, 0x1p0, 0x1.294062ed59f06p-2, -0x1.5d28dap-56, +-0x1.7e8454b32ef34p-5, 0x1p0, 0x1.35410c2e18152p-2, -0x1.3cb002p-56, +-0x1.9d7713b71eee1p-5, 0x1p0, 0x1.4135c94176601p-2, 0x1.0c97c4p-56, +-0x1.bd95b4d43e819p-5, 0x1p0, 0x1.4d1e24278e76ap-2, 0x1.24172p-57, +-0x1.dedefb09791b4p-5, 0x1p0, 0x1.58f9a75ab1fddp-2, -0x1.efdc0cp-62, +-0x1.00a8cee920eabp-4, 0x1p0, 0x1.64c7ddd3f27c6p-2, 0x1.10d2b4p-58, +-0x1.127624999ee1dp-4, 0x1p0, 0x1.7088530fa459fp-2, -0x1.44b19ep-56, +-0x1.24d6cee3afb2ap-4, 0x1p0, 0x1.7c3a9311dcce7p-2, 0x1.9a3f2p-62, +-0x1.37ca1866b95cfp-4, 0x1p0, 0x1.87de2a6aea963p-2, -0x1.72cedcp-57, +-0x1.4b4f461b0cbaap-4, 0x1p0, 0x1.9372a63bc93d7p-2, 0x1.684318p-57, +-0x1.5f6597591b633p-4, 0x1p0, 0x1.9ef7943a8ed8ap-2, 0x1.6da812p-57, +-0x1.740c45e0e512p-4, 0x1p0, 0x1.aa6c82b6d3fcap-2, -0x1.d5f106p-56, +-0x1.894285e19c468p-4, 0x1p0, 0x1.b5d1009e15ccp-2, 0x1.5b362cp-57, +-0x1.9f07860181d1ep-4, 0x1p0, 0x1.c1249d8011ee7p-2, -0x1.813aaap-56, +-0x1.b55a6f65f7058p-4, 0x1p0, 0x1.cc66e9931c45ep-2, 0x1.6850e4p-58, +-0x1.cc3a65bbc6327p-4, 0x1p0, 0x1.d79775b86e389p-2, 0x1.550ec8p-56, +-0x1.e3a6873fa1279p-4, 0x1p0, 0x1.e2b5d3806f63bp-2, 0x1.e0d89p-58, +-0x1.fb9decc6d55b8p-4, 0x1p0, 0x1.edc1952ef78d6p-2, -0x1.dd0f7cp-56, +-0x1.0a0fd4e41ab5ap-3, 0x1p0, 0x1.f8ba4dbf89abap-2, -0x1.2ec1fcp-60, +-0x1.169566329bcb7p-3, 0x1p0, 0x1.01cfc874c3eb7p-1, -0x1.34a35ep-56, +-0x1.235f2eb9a470ap-3, 0x1p0, 0x1.073879922ffeep-1, -0x1.a5a014p-55, +-0x1.306cb042aa3bap-3, 0x1p0, 0x1.0c9704d5d898fp-1, -0x1.8d3d7cp-55, +-0x1.3dbd69fabf802p-3, 0x1p0, 0x1.11eb3541b4b23p-1, -0x1.ef23b6p-55, +-0x1.4b50d8778abbdp-3, 0x1p0, 0x1.1734d63dedb49p-1, -0x1.7eef2cp-55, +-0x1.592675bc57974p-3, 0x1p0, 0x1.1c73b39ae68c8p-1, 0x1.b25dd2p-55, +-0x1.673db93f41479p-3, 0x1p0, 0x1.21a799933eb59p-1, -0x1.3a7b16p-55, +-0x1.759617ee761f9p-3, 0x1p0, 0x1.26d054cdd12dfp-1, -0x1.5da742p-55, +-0x1.842f0435941afp-3, 0x1p0, 0x1.2bedb25faf3eap-1, -0x1.14981cp-58, +-0x1.9307ee031e2fdp-3, 0x1p0, 0x1.30ff7fce17035p-1, -0x1.efcc62p-57, +-0x1.a22042ce0a2f9p-3, 0x1p0, 0x1.36058b10659f3p-1, -0x1.1fcb3ap-55, +-0x1.b1776d9b67013p-3, 0x1p0, 0x1.3affa292050b9p-1, 0x1.e3e25ep-56, +-0x1.c10cd7041afccp-3, 0x1p0, 0x1.3fed9534556d4p-1, 0x1.369166p-55, +-0x1.d0dfe53aba2fdp-3, 0x1p0, 0x1.44cf325091dd6p-1, 0x1.8076a2p-57, +-0x1.e0effc1174505p-3, 0x1p0, 0x1.49a449b9b0939p-1, -0x1.27ee16p-55, +-0x1.f13c7d001a249p-3, 0x1p0, 0x1.4e6cabbe3e5e9p-1, 0x1.3c293ep-57, +-0x1.00e263951d11fp-2, 0x1p0, 0x1.5328292a35596p-1, -0x1.a12eb8p-56, +-0x1.09441bb2aa0a2p-2, 0x1p0, 0x1.57d69348cecap-1, -0x1.757208p-55, +-0x1.11c3141f91b3ep-2, 0x1p0, 0x1.5c77bbe65018cp-1, 0x1.069ea8p-55, +-0x1.1a5ef902000d3p-2, 0x1p0, 0x1.610b7551d2cdfp-1, -0x1.251b34p-56, +-0x1.23177562aaea3p-2, 0x1p0, 0x1.6591925f0783dp-1, 0x1.c3d64ep-55, +-0x1.2bec333018867p-2, 0x1p0, 0x1.6a09e667f3bcdp-1, -0x1.bdd34p-55, +-0x1.34dcdb41f0f85p-2, 0x1p0, 0x1.6e74454eaa8afp-1, -0x1.dbc03cp-55, +-0x1.3de9155c5a642p-2, 0x1p0, 0x1.72d0837efff96p-1, 0x1.0d4efp-55, +-0x1.471088335fce7p-2, 0x1p0, 0x1.771e75f037261p-1, 0x1.5cfce8p-56, +-0x1.5052d96e626c1p-2, 0x1p0, 0x1.7b5df226aafafp-1, -0x1.0f537ap-56, +-0x1.59afadab954d4p-2, 0x1p0, 0x1.7f8ece3571771p-1, -0x1.9c8d8cp-55, +-0x1.6326a8838342ep-2, 0x1p0, 0x1.83b0e0bff976ep-1, -0x1.6f420ep-56, +-0x1.6cb76c8c9ed8fp-2, 0x1p0, 0x1.87c400fba2ebfp-1, -0x1.2dabcp-55, +-0x1.76619b5edc454p-2, 0x1p0, 0x1.8bc806b151741p-1, -0x1.2c5e12p-55, +-0x1.8024d59755257p-2, 0x1p0, 0x1.8fbcca3ef940dp-1, -0x1.6dfa98p-57, +-0x1.8a00badbf5e8ep-2, 0x1p0, 0x1.93a22499263fbp-1, 0x1.3d419ap-55, +-0x1.93f4e9df34c1bp-2, 0x1p0, 0x1.9777ef4c7d742p-1, -0x1.15479ap-55, +-0x1.9e010063d1f96p-2, 0x1p0, 0x1.9b3e047f38741p-1, -0x1.30ee28p-55, +-0x1.a8249b40a182cp-2, 0x1p0, 0x1.9ef43ef29af94p-1, 0x1.b1dfcap-56, +-0x1.b25f56645da43p-2, 0x1p0, 0x1.a29a7a0462782p-1, -0x1.128bbp-56, +-0x1.bcb0ccd98294fp-2, 0x1p0, 0x1.a63091b02fae2p-1, -0x1.e91114p-56, +-0x1.c71898ca32e6fp-2, 0x1p0, 0x1.a9b66290ea1a3p-1, 0x1.9f630ep-60, +-0x1.d19653842496fp-2, 0x1p0, 0x1.ad2bc9e21d511p-1, -0x1.47fbep-55, +-0x1.dc29957c969bbp-2, 0x1p0, 0x1.b090a581502p-1, -0x1.926da2p-55, +-0x1.e6d1f6544ece3p-2, 0x1p0, 0x1.b3e4d3ef55712p-1, -0x1.eb6b8ap-55, +-0x1.f18f0cdba0025p-2, 0x1p0, 0x1.b728345196e3ep-1, -0x1.bc69f2p-55, +-0x1.fc606f1678292p-2, 0x1p0, 0x1.ba5aa673590d2p-1, 0x1.7ea4e2p-55, +-0x1.d16c901d95181p-8, 0x1p-1, 0x1.bd7c0ac6f952ap-1, -0x1.825a72p-55, +-0x1.23e6ad10872a7p-6, 0x1p-1, 0x1.c08c426725549p-1, 0x1.b157fcp-58, +-0x1.d4a2c7f909c4ep-6, 0x1p-1, 0x1.c38b2f180bdb1p-1, -0x1.6e0b16p-56, +-0x1.4344523c8e3b5p-5, 0x1p-1, 0x1.c678b3488739bp-1, 0x1.d86cacp-57, +-0x1.9cc8b3671dd0fp-5, 0x1p-1, 0x1.c954b213411f5p-1, -0x1.2fb76p-58, +-0x1.f6db13ff708cbp-5, 0x1p-1, 0x1.cc1f0f3fcfc5cp-1, 0x1.e57612p-56, +-0x1.28bbfd87a8cffp-4, 0x1p-1, 0x1.ced7af43cc773p-1, -0x1.e7b6bap-58, +-0x1.564df524b00dap-4, 0x1p-1, 0x1.d17e7743e35dcp-1, -0x1.101da2p-58, +-0x1.8421af15c49d7p-4, 0x1p-1, 0x1.d4134d14dc93ap-1, -0x1.4ef528p-55, +-0x1.b2356710db0a3p-4, 0x1p-1, 0x1.d696173c9e68bp-1, -0x1.e8c61cp-56, +-0x1.e087565455a75p-4, 0x1p-1, 0x1.d906bcf328d46p-1, 0x1.457e6p-56, +-0x1.078ad9dc46632p-3, 0x1p-1, 0x1.db6526238a09bp-1, -0x1.adee7ep-56, +-0x1.1eef59e0b74c3p-3, 0x1p-1, 0x1.ddb13b6ccc23cp-1, 0x1.83c37cp-55, +-0x1.367044581b074p-3, 0x1p-1, 0x1.dfeae622dbe2bp-1, -0x1.514ea8p-55, +-0x1.4e0cb14a9c046p-3, 0x1p-1, 0x1.e212104f686e5p-1, -0x1.014c76p-55, +-0x1.65c3b7b0e312cp-3, 0x1p-1, 0x1.e426a4b2bc17ep-1, 0x1.a87388p-55, +-0x1.7d946d7d133fdp-3, 0x1p-1, 0x1.e6288ec48e112p-1, -0x1.16b56ep-57, +-0x1.957de7a3cfd5dp-3, 0x1p-1, 0x1.e817bab4cd10dp-1, -0x1.d0afe6p-56, +-0x1.ad7f3a254c1f5p-3, 0x1p-1, 0x1.e9f4156c62ddap-1, 0x1.760b1ep-55, +-0x1.c597781664984p-3, 0x1p-1, 0x1.ebbd8c8df0b74p-1, 0x1.c6c8c6p-56, +-0x1.ddc5b3a9c1311p-3, 0x1p-1, 0x1.ed740e7684963p-1, 0x1.e82c78p-56, +-0x1.f608fe39004a4p-3, 0x1p-1, 0x1.ef178a3e473c2p-1, 0x1.6310a6p-55, +-0x1.cc0d09bd41caap-8, 0x1p-2, 0x1.f0a7efb9230d7p-1, 0x1.52c7acp-56, +-0x1.36580d5d5e775p-6, 0x1p-2, 0x1.f2252f7763adap-1, -0x1.20cb8p-55, +-0x1.fa3ecac0d84e8p-6, 0x1p-2, 0x1.f38f3ac64e589p-1, -0x1.d7bafap-56, +-0x1.5f57f693feebep-5, 0x1p-2, 0x1.f4e603b0b2f2dp-1, -0x1.8ee01ep-56, +-0x1.c1d1f0e5967d5p-5, 0x1p-2, 0x1.f6297cff75cbp-1, 0x1.562172p-56, +-0x1.1244c435e819dp-4, 0x1p-2, 0x1.f7599a3a12077p-1, 0x1.84f31cp-55, +-0x1.43bd776e98073p-4, 0x1p-2, 0x1.f8764fa714ba9p-1, 0x1.ab2566p-56, +-0x1.755129dad834cp-4, 0x1p-2, 0x1.f97f924c9099bp-1, -0x1.e2ae0ep-55, +-0x1.a6fdf22e33d8cp-4, 0x1p-2, 0x1.fa7557f08a517p-1, -0x1.7a0a8cp-55, +-0x1.d8c1e624a1513p-4, 0x1p-2, 0x1.fb5797195d741p-1, 0x1.1bfac6p-56, +-0x1.536352ad19e39p-9, 0x1p-3, 0x1.fc26470e19fd3p-1, 0x1.1ec866p-55, +-0x1.e43d1c309e958p-7, 0x1p-3, 0x1.fce15fd6da67bp-1, -0x1.5dd6f8p-56, +-0x1.ba1650f592f5p-6, 0x1p-3, 0x1.fd88da3d12526p-1, -0x1.87df62p-55, +-0x1.4125feacab7cep-5, 0x1p-3, 0x1.fe1cafcbd5b09p-1, 0x1.a23e32p-57, 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-0x1.e426a4b2bc17ep-1, -0x1.a87388p-55, +-0x1.4e0cb14a9c046p-3, 0x1p-1, -0x1.e212104f686e5p-1, 0x1.014c76p-55, +-0x1.367044581b074p-3, 0x1p-1, -0x1.dfeae622dbe2bp-1, 0x1.514ea8p-55, +-0x1.1eef59e0b74c3p-3, 0x1p-1, -0x1.ddb13b6ccc23cp-1, -0x1.83c37cp-55, +-0x1.078ad9dc46632p-3, 0x1p-1, -0x1.db6526238a09bp-1, 0x1.adee7ep-56, +-0x1.e087565455a75p-4, 0x1p-1, -0x1.d906bcf328d46p-1, -0x1.457e6p-56, +-0x1.b2356710db0a3p-4, 0x1p-1, -0x1.d696173c9e68bp-1, 0x1.e8c61cp-56, +-0x1.8421af15c49d7p-4, 0x1p-1, -0x1.d4134d14dc93ap-1, 0x1.4ef528p-55, +-0x1.564df524b00dap-4, 0x1p-1, -0x1.d17e7743e35dcp-1, 0x1.101da2p-58, +-0x1.28bbfd87a8cffp-4, 0x1p-1, -0x1.ced7af43cc773p-1, 0x1.e7b6bap-58, +-0x1.f6db13ff708cbp-5, 0x1p-1, -0x1.cc1f0f3fcfc5cp-1, -0x1.e57612p-56, +-0x1.9cc8b3671dd0fp-5, 0x1p-1, -0x1.c954b213411f5p-1, 0x1.2fb76p-58, +-0x1.4344523c8e3b5p-5, 0x1p-1, -0x1.c678b3488739bp-1, -0x1.d86cacp-57, +-0x1.d4a2c7f909c4ep-6, 0x1p-1, -0x1.c38b2f180bdb1p-1, 0x1.6e0b16p-56, +-0x1.23e6ad10872a7p-6, 0x1p-1, -0x1.c08c426725549p-1, -0x1.b157fcp-58, +-0x1.d16c901d95181p-8, 0x1p-1, -0x1.bd7c0ac6f952ap-1, 0x1.825a72p-55, +-0x1.fc606f1678292p-2, 0x1p0, -0x1.ba5aa673590d2p-1, -0x1.7ea4e2p-55, +-0x1.f18f0cdba0025p-2, 0x1p0, -0x1.b728345196e3ep-1, 0x1.bc69f2p-55, +-0x1.e6d1f6544ece3p-2, 0x1p0, -0x1.b3e4d3ef55712p-1, 0x1.eb6b8ap-55, +-0x1.dc29957c969bbp-2, 0x1p0, -0x1.b090a581502p-1, 0x1.926da2p-55, +-0x1.d19653842496fp-2, 0x1p0, -0x1.ad2bc9e21d511p-1, 0x1.47fbep-55, +-0x1.c71898ca32e6fp-2, 0x1p0, -0x1.a9b66290ea1a3p-1, -0x1.9f630ep-60, +-0x1.bcb0ccd98294fp-2, 0x1p0, -0x1.a63091b02fae2p-1, 0x1.e91114p-56, +-0x1.b25f56645da43p-2, 0x1p0, -0x1.a29a7a0462782p-1, 0x1.128bbp-56, +-0x1.a8249b40a182cp-2, 0x1p0, -0x1.9ef43ef29af94p-1, -0x1.b1dfcap-56, +-0x1.9e010063d1f96p-2, 0x1p0, -0x1.9b3e047f38741p-1, 0x1.30ee28p-55, +-0x1.93f4e9df34c1bp-2, 0x1p0, -0x1.9777ef4c7d742p-1, 0x1.15479ap-55, +-0x1.8a00badbf5e8ep-2, 0x1p0, -0x1.93a22499263fbp-1, -0x1.3d419ap-55, +-0x1.8024d59755257p-2, 0x1p0, -0x1.8fbcca3ef940dp-1, 0x1.6dfa98p-57, +-0x1.76619b5edc454p-2, 0x1p0, -0x1.8bc806b151741p-1, 0x1.2c5e12p-55, +-0x1.6cb76c8c9ed8fp-2, 0x1p0, -0x1.87c400fba2ebfp-1, 0x1.2dabcp-55, +-0x1.6326a8838342ep-2, 0x1p0, -0x1.83b0e0bff976ep-1, 0x1.6f420ep-56, +-0x1.59afadab954d4p-2, 0x1p0, -0x1.7f8ece3571771p-1, 0x1.9c8d8cp-55, +-0x1.5052d96e626c1p-2, 0x1p0, -0x1.7b5df226aafafp-1, 0x1.0f537ap-56, +-0x1.471088335fce7p-2, 0x1p0, -0x1.771e75f037261p-1, -0x1.5cfce8p-56, +-0x1.3de9155c5a642p-2, 0x1p0, -0x1.72d0837efff96p-1, -0x1.0d4efp-55, +-0x1.34dcdb41f0f85p-2, 0x1p0, -0x1.6e74454eaa8afp-1, 0x1.dbc03cp-55, +-0x1.2bec333018867p-2, 0x1p0, -0x1.6a09e667f3bcdp-1, 0x1.bdd34p-55, +-0x1.23177562aaea3p-2, 0x1p0, -0x1.6591925f0783dp-1, -0x1.c3d64ep-55, +-0x1.1a5ef902000d3p-2, 0x1p0, -0x1.610b7551d2cdfp-1, 0x1.251b34p-56, +-0x1.11c3141f91b3ep-2, 0x1p0, -0x1.5c77bbe65018cp-1, -0x1.069ea8p-55, +-0x1.09441bb2aa0a2p-2, 0x1p0, -0x1.57d69348cecap-1, 0x1.757208p-55, +-0x1.00e263951d11fp-2, 0x1p0, -0x1.5328292a35596p-1, 0x1.a12eb8p-56, +-0x1.f13c7d001a249p-3, 0x1p0, -0x1.4e6cabbe3e5e9p-1, -0x1.3c293ep-57, +-0x1.e0effc1174505p-3, 0x1p0, -0x1.49a449b9b0939p-1, 0x1.27ee16p-55, +-0x1.d0dfe53aba2fdp-3, 0x1p0, -0x1.44cf325091dd6p-1, -0x1.8076a2p-57, +-0x1.c10cd7041afccp-3, 0x1p0, -0x1.3fed9534556d4p-1, -0x1.369166p-55, +-0x1.b1776d9b67013p-3, 0x1p0, -0x1.3affa292050b9p-1, -0x1.e3e25ep-56, +-0x1.a22042ce0a2f9p-3, 0x1p0, -0x1.36058b10659f3p-1, 0x1.1fcb3ap-55, +-0x1.9307ee031e2fdp-3, 0x1p0, -0x1.30ff7fce17035p-1, 0x1.efcc62p-57, +-0x1.842f0435941afp-3, 0x1p0, -0x1.2bedb25faf3eap-1, 0x1.14981cp-58, +-0x1.759617ee761f9p-3, 0x1p0, -0x1.26d054cdd12dfp-1, 0x1.5da742p-55, +-0x1.673db93f41479p-3, 0x1p0, -0x1.21a799933eb59p-1, 0x1.3a7b16p-55, +-0x1.592675bc57974p-3, 0x1p0, -0x1.1c73b39ae68c8p-1, -0x1.b25dd2p-55, +-0x1.4b50d8778abbdp-3, 0x1p0, -0x1.1734d63dedb49p-1, 0x1.7eef2cp-55, +-0x1.3dbd69fabf802p-3, 0x1p0, -0x1.11eb3541b4b23p-1, 0x1.ef23b6p-55, +-0x1.306cb042aa3bap-3, 0x1p0, -0x1.0c9704d5d898fp-1, 0x1.8d3d7cp-55, +-0x1.235f2eb9a470ap-3, 0x1p0, -0x1.073879922ffeep-1, 0x1.a5a014p-55, +-0x1.169566329bcb7p-3, 0x1p0, -0x1.01cfc874c3eb7p-1, 0x1.34a35ep-56, +-0x1.0a0fd4e41ab5ap-3, 0x1p0, -0x1.f8ba4dbf89abap-2, 0x1.2ec1fcp-60, +-0x1.fb9decc6d55b8p-4, 0x1p0, -0x1.edc1952ef78d6p-2, 0x1.dd0f7cp-56, +-0x1.e3a6873fa1279p-4, 0x1p0, -0x1.e2b5d3806f63bp-2, -0x1.e0d89p-58, +-0x1.cc3a65bbc6327p-4, 0x1p0, -0x1.d79775b86e389p-2, -0x1.550ec8p-56, +-0x1.b55a6f65f7058p-4, 0x1p0, -0x1.cc66e9931c45ep-2, -0x1.6850e4p-58, +-0x1.9f07860181d1ep-4, 0x1p0, -0x1.c1249d8011ee7p-2, 0x1.813aaap-56, +-0x1.894285e19c468p-4, 0x1p0, -0x1.b5d1009e15ccp-2, -0x1.5b362cp-57, +-0x1.740c45e0e512p-4, 0x1p0, -0x1.aa6c82b6d3fcap-2, 0x1.d5f106p-56, +-0x1.5f6597591b633p-4, 0x1p0, -0x1.9ef7943a8ed8ap-2, -0x1.6da812p-57, +-0x1.4b4f461b0cbaap-4, 0x1p0, -0x1.9372a63bc93d7p-2, -0x1.684318p-57, +-0x1.37ca1866b95cfp-4, 0x1p0, -0x1.87de2a6aea963p-2, 0x1.72cedcp-57, +-0x1.24d6cee3afb2ap-4, 0x1p0, -0x1.7c3a9311dcce7p-2, -0x1.9a3f2p-62, +-0x1.127624999ee1dp-4, 0x1p0, -0x1.7088530fa459fp-2, 0x1.44b19ep-56, +-0x1.00a8cee920eabp-4, 0x1p0, -0x1.64c7ddd3f27c6p-2, -0x1.10d2b4p-58, +-0x1.dedefb09791b4p-5, 0x1p0, -0x1.58f9a75ab1fddp-2, 0x1.efdc0cp-62, +-0x1.bd95b4d43e819p-5, 0x1p0, -0x1.4d1e24278e76ap-2, -0x1.24172p-57, +-0x1.9d7713b71eee1p-5, 0x1p0, -0x1.4135c94176601p-2, -0x1.0c97c4p-56, +-0x1.7e8454b32ef34p-5, 0x1p0, -0x1.35410c2e18152p-2, 0x1.3cb002p-56, +-0x1.60bea939d225ap-5, 0x1p0, -0x1.294062ed59f06p-2, 0x1.5d28dap-56, +-0x1.44273720f48bcp-5, 0x1p0, -0x1.1d3443f4cdb3ep-2, 0x1.720d4p-57, +-0x1.28bf1897b69ccp-5, 0x1p0, -0x1.111d262b1f677p-2, -0x1.824c2p-56, +-0x1.0e875c1b8c3dap-5, 0x1p0, -0x1.04fb80e37fdaep-2, 0x1.412cdap-63, +-0x1.eb0208db9e51bp-6, 0x1p0, -0x1.f19f97b215f1bp-3, 0x1.42deeep-57, +-0x1.bb5a11138a4c9p-6, 0x1p0, -0x1.d934fe5454311p-3, -0x1.75b922p-57, +-0x1.8e18a73634ee7p-6, 0x1p0, -0x1.c0b826a7e4f63p-3, 0x1.af1438p-62, +-0x1.633f89e9a1a66p-6, 0x1p0, -0x1.a82a025b00451p-3, 0x1.87905ep-57, +-0x1.3ad06011469fbp-6, 0x1p0, -0x1.8f8b83c69a60bp-3, 0x1.26d19ap-57, +-0x1.14ccb8bdbf114p-6, 0x1p0, -0x1.76dd9de50bf31p-3, -0x1.1d5eeep-57, +-0x1.e26c163ad15b3p-7, 0x1p0, -0x1.5e214448b3fc6p-3, -0x1.531ff6p-57, +-0x1.a01b6cdbd995ep-7, 0x1p0, -0x1.45576b1293e5ap-3, 0x1.285a24p-58, +-0x1.62aa03dd6ba58p-7, 0x1p0, -0x1.2c8106e8e613ap-3, -0x1.13000ap-58, +-0x1.2a1a39a8a2fb7p-7, 0x1p0, -0x1.139f0cedaf577p-3, 0x1.523434p-57, +-0x1.ecdc78f30165cp-8, 0x1p0, -0x1.f564e56a9730ep-4, -0x1.a27046p-59, +-0x1.8f501492cc296p-8, 0x1p0, -0x1.c3785c79ec2d5p-4, 0x1.4f39dep-61, +-0x1.3b92e176d6d31p-8, 0x1p0, -0x1.917a6bc29b42cp-4, 0x1.e2718cp-60, +-0x1.e350342a4f6e6p-9, 0x1p0, -0x1.5f6d00a9aa419p-4, 0x1.f4022cp-59, +-0x1.63252fe77c5ebp-9, 0x1p0, -0x1.2d52092ce19f6p-4, 0x1.9a088ap-59, +-0x1.ed534e31ca57fp-10, 0x1p0, -0x1.f656e79f820ep-5, 0x1.2e1ebep-61, +-0x1.3bc390d250439p-10, 0x1p0, -0x1.91f65f10dd814p-5, 0x1.912bdp-61, +-0x1.6344004228d8bp-11, 0x1p0, -0x1.2d865759455cdp-5, -0x1.686f64p-61, +-0x1.3bcfbd9979a27p-12, 0x1p0, -0x1.92155f7a3667ep-6, 0x1.b1d63p-64, +-0x1.3bd2c8da49511p-14, 0x1p0, -0x1.921d1fcdec784p-7, -0x1.9878eap-61, +}; + +template inline constexpr char kCosApproxTable[] = {}; +template <> inline constexpr float kCosApproxTable[] = +{ +0.0f, 0.0f, 0x1p0f, 0.0f, +-0x1.003242p5f, 0x1p5f, 0x1.ffd886p-1f, 0x1.099a1ap-30f, +-0x1.00c8fcp4f, 0x1p4f, 0x1.ff621ep-1f, 0x1.bcb6bep-28f, +-0x1.025aa4p3f, 0x1p3f, 0x1.fe9cdap-1f, 0x1.a03108p-26f, +-0x1.0322f4p3f, 0x1p3f, 0x1.fd88dap-1f, 0x1.e89292p-28f, +-0x1.03eacap3f, 0x1p3f, 0x1.fc2648p-1f, -0x1.e3cc06p-26f, +-0x1.096408p2f, 0x1p2f, 0x1.fa7558p-1f, -0x1.eeb5d2p-30f, +-0x1.0af10ap2f, 0x1p2f, 0x1.f8765p-1f, -0x1.63ad16p-27f, +-0x1.0c7c5cp2f, 0x1p2f, 0x1.f6297cp-1f, 0x1.feeb96p-26f, +-0x1.0e05c2p2f, 0x1p2f, 0x1.f38f3ap-1f, 0x1.8c9cb2p-26f, +-0x1.0f8cfcp2f, 0x1p2f, 0x1.f0a7fp-1f, -0x1.1b73cap-27f, +-0x1.2223a4p1f, 0x1p1f, 0x1.ed740ep-1f, 0x1.da1258p-27f, +-0x1.25280cp1f, 0x1p1f, 0x1.e9f416p-1f, -0x1.273a44p-26f, +-0x1.2826bap1f, 0x1p1f, 0x1.e6288ep-1f, 0x1.891c22p-26f, +-0x1.2b1f34p1f, 0x1p1f, 0x1.e2121p-1f, 0x1.3da1bap-27f, +-0x1.2e110ap1f, 0x1p1f, 0x1.ddb13cp-1f, -0x1.2667b8p-26f, +-0x1.30fbc6p1f, 0x1p1f, 0x1.d906bcp-1f, 0x1.e651a8p-26f, +-0x1.33def2p1f, 0x1p1f, 0x1.d4134ep-1f, -0x1.d646d8p-26f, +-0x1.36ba2p1f, 0x1p1f, 0x1.ced7bp-1f, -0x1.786712p-26f, +-0x1.398cdep1f, 0x1p1f, 0x1.c954b2p-1f, 0x1.3411f4p-29f, +-0x1.3c56bap1f, 0x1p1f, 0x1.c38b3p-1f, -0x1.cfe84ap-26f, +-0x1.3f174ap1f, 0x1p1f, 0x1.bd7c0ap-1f, 0x1.8df2a6p-26f, +-0x1.839c3cp0f, 0x1p0f, 0x1.b72834p-1f, 0x1.465b9p-27f, +-0x1.88f59ap0f, 0x1p0f, 0x1.b090a6p-1f, -0x1.fabf8p-27f, +-0x1.8e39dap0f, 0x1p0f, 0x1.a9b662p-1f, 0x1.21d434p-26f, +-0x1.93682ap0f, 0x1p0f, 0x1.a29a7ap-1f, 0x1.189e08p-31f, +-0x1.987fcp0f, 0x1p0f, 0x1.9b3e04p-1f, 0x1.fce1dp-27f, +-0x1.9d7fd2p0f, 0x1p0f, 0x1.93a224p-1f, 0x1.324c8p-26f, +-0x1.a2679ap0f, 0x1p0f, 0x1.8bc806p-1f, 0x1.62a2e8p-26f, +-0x1.a73656p0f, 0x1p0f, 0x1.83b0ep-1f, 0x1.7ff2eep-26f, +-0x1.abeb4ap0f, 0x1p0f, 0x1.7b5df2p-1f, 0x1.3557d8p-28f, +-0x1.b085bap0f, 0x1p0f, 0x1.72d084p-1f, -0x1.02000ep-26f, +-0x1.b504f4p0f, 0x1p0f, 0x1.6a09e6p-1f, 0x1.9fcef4p-27f, +-0x1.b96842p0f, 0x1p0f, 0x1.610b76p-1f, -0x1.5c5a64p-26f, +-0x1.bdaefap0f, 0x1p0f, 0x1.57d694p-1f, -0x1.6e626cp-26f, +-0x1.c1d87p0f, 0x1p0f, 0x1.4e6cacp-1f, -0x1.070686p-27f, +-0x1.c5e404p0f, 0x1p0f, 0x1.44cf32p-1f, 0x1.424776p-27f, +-0x1.c9d112p0f, 0x1p0f, 0x1.3affa2p-1f, 0x1.240a18p-26f, +-0x1.cd9f02p0f, 0x1p0f, 0x1.30ff8p-1f, -0x1.8f47e6p-28f, +-0x1.d14d3ep0f, 0x1p0f, 0x1.26d054p-1f, 0x1.9ba25cp-26f, +-0x1.d4db32p0f, 0x1p0f, 0x1.1c73b4p-1f, -0x1.9465cep-27f, +-0x1.d84852p0f, 0x1p0f, 0x1.11eb36p-1f, -0x1.7c969cp-26f, +-0x1.db941ap0f, 0x1p0f, 0x1.07387ap-1f, -0x1.b74004p-27f, +-0x1.debe06p0f, 0x1p0f, 0x1.f8ba4ep-2f, -0x1.01d952p-28f, +-0x1.e1c598p0f, 0x1p0f, 0x1.e2b5d4p-2f, -0x1.fe4272p-28f, +-0x1.e4aa5ap0f, 0x1p0f, 0x1.cc66eap-2f, -0x1.b38ee8p-28f, +-0x1.e76bd8p0f, 0x1p0f, 0x1.b5d1p-2f, 0x1.3c2b98p-27f, +-0x1.ea09a6p0f, 0x1p0f, 0x1.9ef794p-2f, 0x1.d476c6p-29f, +-0x1.ec835ep0f, 0x1p0f, 0x1.87de2ap-2f, 0x1.abaa58p-28f, +-0x1.eed89ep0f, 0x1p0f, 0x1.708854p-2f, -0x1.e0b74cp-27f, +-0x1.f10908p0f, 0x1p0f, 0x1.58f9a8p-2f, -0x1.4a9c04p-27f, +-0x1.f31448p0f, 0x1p0f, 0x1.4135cap-2f, -0x1.7d134p-27f, +-0x1.f4fa0ap0f, 0x1p0f, 0x1.294062p-2f, 0x1.dab3ep-27f, +-0x1.f6ba08p0f, 0x1p0f, 0x1.111d26p-2f, 0x1.58fb3cp-29f, +-0x1.f853f8p0f, 0x1p0f, 0x1.f19f98p-3f, -0x1.37a83ap-29f, +-0x1.f9c79ep0f, 0x1p0f, 0x1.c0b826p-3f, 0x1.4fc9ecp-28f, +-0x1.fb14bep0f, 0x1p0f, 0x1.8f8b84p-3f, -0x1.cb2cfap-30f, +-0x1.fc3b28p0f, 0x1p0f, 0x1.5e2144p-3f, 0x1.22cff2p-29f, +-0x1.fd3aacp0f, 0x1p0f, 0x1.2c8106p-3f, 0x1.d1cc28p-28f, +-0x1.fe1324p0f, 0x1p0f, 0x1.f564e6p-4f, -0x1.2ad19ep-29f, +-0x1.fec46ep0f, 0x1p0f, 0x1.917a6cp-4f, -0x1.eb25eap-31f, +-0x1.ff4e6ep0f, 0x1p0f, 0x1.2d520ap-4f, -0x1.a63cc2p-29f, +-0x1.ffb11p0f, 0x1p0f, 0x1.91f66p-5f, -0x1.de44fep-30f, +-0x1.ffec44p0f, 0x1p0f, 0x1.92156p-6f, -0x1.0b933p-31f, +-0x1p1f, 0x1p0f, 0.0f, 0.0f, +-0x1.ffec44p0f, 0x1p0f, -0x1.92156p-6f, 0x1.0b933p-31f, +-0x1.ffb11p0f, 0x1p0f, -0x1.91f66p-5f, 0x1.de44fep-30f, +-0x1.ff4e6ep0f, 0x1p0f, -0x1.2d520ap-4f, 0x1.a63cc2p-29f, +-0x1.fec46ep0f, 0x1p0f, -0x1.917a6cp-4f, 0x1.eb25eap-31f, +-0x1.fe1324p0f, 0x1p0f, -0x1.f564e6p-4f, 0x1.2ad19ep-29f, +-0x1.fd3aacp0f, 0x1p0f, -0x1.2c8106p-3f, -0x1.d1cc28p-28f, +-0x1.fc3b28p0f, 0x1p0f, -0x1.5e2144p-3f, -0x1.22cff2p-29f, +-0x1.fb14bep0f, 0x1p0f, -0x1.8f8b84p-3f, 0x1.cb2cfap-30f, +-0x1.f9c79ep0f, 0x1p0f, -0x1.c0b826p-3f, -0x1.4fc9ecp-28f, +-0x1.f853f8p0f, 0x1p0f, -0x1.f19f98p-3f, 0x1.37a83ap-29f, +-0x1.f6ba08p0f, 0x1p0f, -0x1.111d26p-2f, -0x1.58fb3cp-29f, +-0x1.f4fa0ap0f, 0x1p0f, -0x1.294062p-2f, -0x1.dab3ep-27f, +-0x1.f31448p0f, 0x1p0f, -0x1.4135cap-2f, 0x1.7d134p-27f, +-0x1.f10908p0f, 0x1p0f, -0x1.58f9a8p-2f, 0x1.4a9c04p-27f, +-0x1.eed89ep0f, 0x1p0f, -0x1.708854p-2f, 0x1.e0b74cp-27f, +-0x1.ec835ep0f, 0x1p0f, -0x1.87de2ap-2f, -0x1.abaa58p-28f, +-0x1.ea09a6p0f, 0x1p0f, -0x1.9ef794p-2f, -0x1.d476c6p-29f, +-0x1.e76bd8p0f, 0x1p0f, -0x1.b5d1p-2f, -0x1.3c2b98p-27f, +-0x1.e4aa5ap0f, 0x1p0f, -0x1.cc66eap-2f, 0x1.b38ee8p-28f, +-0x1.e1c598p0f, 0x1p0f, -0x1.e2b5d4p-2f, 0x1.fe4272p-28f, +-0x1.debe06p0f, 0x1p0f, -0x1.f8ba4ep-2f, 0x1.01d952p-28f, +-0x1.db941ap0f, 0x1p0f, -0x1.07387ap-1f, 0x1.b74004p-27f, +-0x1.d84852p0f, 0x1p0f, -0x1.11eb36p-1f, 0x1.7c969cp-26f, +-0x1.d4db32p0f, 0x1p0f, -0x1.1c73b4p-1f, 0x1.9465cep-27f, +-0x1.d14d3ep0f, 0x1p0f, -0x1.26d054p-1f, -0x1.9ba25cp-26f, +-0x1.cd9f02p0f, 0x1p0f, -0x1.30ff8p-1f, 0x1.8f47e6p-28f, +-0x1.c9d112p0f, 0x1p0f, -0x1.3affa2p-1f, -0x1.240a18p-26f, +-0x1.c5e404p0f, 0x1p0f, -0x1.44cf32p-1f, -0x1.424776p-27f, +-0x1.c1d87p0f, 0x1p0f, -0x1.4e6cacp-1f, 0x1.070686p-27f, +-0x1.bdaefap0f, 0x1p0f, -0x1.57d694p-1f, 0x1.6e626cp-26f, +-0x1.b96842p0f, 0x1p0f, -0x1.610b76p-1f, 0x1.5c5a64p-26f, +-0x1.b504f4p0f, 0x1p0f, -0x1.6a09e6p-1f, -0x1.9fcef4p-27f, +-0x1.b085bap0f, 0x1p0f, -0x1.72d084p-1f, 0x1.02000ep-26f, +-0x1.abeb4ap0f, 0x1p0f, -0x1.7b5df2p-1f, -0x1.3557d8p-28f, +-0x1.a73656p0f, 0x1p0f, -0x1.83b0ep-1f, -0x1.7ff2eep-26f, +-0x1.a2679ap0f, 0x1p0f, -0x1.8bc806p-1f, -0x1.62a2e8p-26f, +-0x1.9d7fd2p0f, 0x1p0f, -0x1.93a224p-1f, -0x1.324c8p-26f, +-0x1.987fcp0f, 0x1p0f, -0x1.9b3e04p-1f, -0x1.fce1dp-27f, +-0x1.93682ap0f, 0x1p0f, -0x1.a29a7ap-1f, -0x1.189e08p-31f, +-0x1.8e39dap0f, 0x1p0f, -0x1.a9b662p-1f, -0x1.21d434p-26f, +-0x1.88f59ap0f, 0x1p0f, -0x1.b090a6p-1f, 0x1.fabf8p-27f, +-0x1.839c3cp0f, 0x1p0f, -0x1.b72834p-1f, -0x1.465b9p-27f, +-0x1.3f174ap1f, 0x1p1f, -0x1.bd7c0ap-1f, -0x1.8df2a6p-26f, +-0x1.3c56bap1f, 0x1p1f, -0x1.c38b3p-1f, 0x1.cfe84ap-26f, +-0x1.398cdep1f, 0x1p1f, -0x1.c954b2p-1f, -0x1.3411f4p-29f, +-0x1.36ba2p1f, 0x1p1f, -0x1.ced7bp-1f, 0x1.786712p-26f, +-0x1.33def2p1f, 0x1p1f, -0x1.d4134ep-1f, 0x1.d646d8p-26f, +-0x1.30fbc6p1f, 0x1p1f, -0x1.d906bcp-1f, -0x1.e651a8p-26f, +-0x1.2e110ap1f, 0x1p1f, -0x1.ddb13cp-1f, 0x1.2667b8p-26f, +-0x1.2b1f34p1f, 0x1p1f, -0x1.e2121p-1f, -0x1.3da1bap-27f, +-0x1.2826bap1f, 0x1p1f, -0x1.e6288ep-1f, -0x1.891c22p-26f, +-0x1.25280cp1f, 0x1p1f, -0x1.e9f416p-1f, 0x1.273a44p-26f, +-0x1.2223a4p1f, 0x1p1f, -0x1.ed740ep-1f, -0x1.da1258p-27f, +-0x1.0f8cfcp2f, 0x1p2f, -0x1.f0a7fp-1f, 0x1.1b73cap-27f, +-0x1.0e05c2p2f, 0x1p2f, -0x1.f38f3ap-1f, -0x1.8c9cb2p-26f, +-0x1.0c7c5cp2f, 0x1p2f, -0x1.f6297cp-1f, -0x1.feeb96p-26f, +-0x1.0af10ap2f, 0x1p2f, -0x1.f8765p-1f, 0x1.63ad16p-27f, +-0x1.096408p2f, 0x1p2f, -0x1.fa7558p-1f, 0x1.eeb5d2p-30f, +-0x1.03eacap3f, 0x1p3f, -0x1.fc2648p-1f, 0x1.e3cc06p-26f, +-0x1.0322f4p3f, 0x1p3f, -0x1.fd88dap-1f, -0x1.e89292p-28f, +-0x1.025aa4p3f, 0x1p3f, -0x1.fe9cdap-1f, -0x1.a03108p-26f, +-0x1.00c8fcp4f, 0x1p4f, -0x1.ff621ep-1f, -0x1.bcb6bep-28f, +-0x1.003242p5f, 0x1p5f, -0x1.ffd886p-1f, -0x1.099a1ap-30f, +0.0f, 0.0f, -0x1p0f, 0.0f, +-0x1.b7aa82p-8f, 0x1p-5f, -0x1.ffd886p-1f, -0x1.099a1ap-30f, +-0x1.b82684p-7f, 0x1p-4f, -0x1.ff621ep-1f, -0x1.bcb6bep-28f, +-0x1.a55beep-5f, 0x1p-3f, -0x1.fe9cdap-1f, -0x1.a03108p-26f, +-0x1.ba165p-6f, 0x1p-3f, -0x1.fd88dap-1f, -0x1.e89292p-28f, +-0x1.536352p-9f, 0x1p-3f, -0x1.fc2648p-1f, 0x1.e3cc06p-26f, +-0x1.a6fdf2p-4f, 0x1p-2f, -0x1.fa7558p-1f, 0x1.eeb5d2p-30f, +-0x1.43bd78p-4f, 0x1p-2f, -0x1.f8765p-1f, 0x1.63ad16p-27f, +-0x1.c1d1fp-5f, 0x1p-2f, -0x1.f6297cp-1f, -0x1.feeb96p-26f, +-0x1.fa3ecap-6f, 0x1p-2f, -0x1.f38f3ap-1f, -0x1.8c9cb2p-26f, +-0x1.cc0d0ap-8f, 0x1p-2f, -0x1.f0a7fp-1f, 0x1.1b73cap-27f, +-0x1.ddc5b4p-3f, 0x1p-1f, -0x1.ed740ep-1f, -0x1.da1258p-27f, +-0x1.ad7f3ap-3f, 0x1p-1f, -0x1.e9f416p-1f, 0x1.273a44p-26f, +-0x1.7d946ep-3f, 0x1p-1f, -0x1.e6288ep-1f, -0x1.891c22p-26f, +-0x1.4e0cb2p-3f, 0x1p-1f, -0x1.e2121p-1f, -0x1.3da1bap-27f, +-0x1.1eef5ap-3f, 0x1p-1f, -0x1.ddb13cp-1f, 0x1.2667b8p-26f, +-0x1.e08756p-4f, 0x1p-1f, -0x1.d906bcp-1f, -0x1.e651a8p-26f, +-0x1.8421bp-4f, 0x1p-1f, -0x1.d4134ep-1f, 0x1.d646d8p-26f, +-0x1.28bbfep-4f, 0x1p-1f, -0x1.ced7bp-1f, 0x1.786712p-26f, +-0x1.9cc8b4p-5f, 0x1p-1f, -0x1.c954b2p-1f, -0x1.3411f4p-29f, +-0x1.d4a2c8p-6f, 0x1p-1f, -0x1.c38b3p-1f, 0x1.cfe84ap-26f, +-0x1.d16c9p-8f, 0x1p-1f, -0x1.bd7c0ap-1f, -0x1.8df2a6p-26f, +-0x1.f18f0cp-2f, 0x1p0f, -0x1.b72834p-1f, -0x1.465b9p-27f, +-0x1.dc2996p-2f, 0x1p0f, -0x1.b090a6p-1f, 0x1.fabf8p-27f, +-0x1.c71898p-2f, 0x1p0f, -0x1.a9b662p-1f, -0x1.21d434p-26f, +-0x1.b25f56p-2f, 0x1p0f, -0x1.a29a7ap-1f, -0x1.189e08p-31f, +-0x1.9e01p-2f, 0x1p0f, -0x1.9b3e04p-1f, -0x1.fce1dp-27f, +-0x1.8a00bap-2f, 0x1p0f, -0x1.93a224p-1f, -0x1.324c8p-26f, +-0x1.76619cp-2f, 0x1p0f, -0x1.8bc806p-1f, -0x1.62a2e8p-26f, +-0x1.6326a8p-2f, 0x1p0f, -0x1.83b0ep-1f, -0x1.7ff2eep-26f, +-0x1.5052dap-2f, 0x1p0f, -0x1.7b5df2p-1f, -0x1.3557d8p-28f, +-0x1.3de916p-2f, 0x1p0f, -0x1.72d084p-1f, 0x1.02000ep-26f, +-0x1.2bec34p-2f, 0x1p0f, -0x1.6a09e6p-1f, -0x1.9fcef4p-27f, +-0x1.1a5efap-2f, 0x1p0f, -0x1.610b76p-1f, 0x1.5c5a64p-26f, +-0x1.09441cp-2f, 0x1p0f, -0x1.57d694p-1f, 0x1.6e626cp-26f, +-0x1.f13c7ep-3f, 0x1p0f, -0x1.4e6cacp-1f, 0x1.070686p-27f, +-0x1.d0dfe6p-3f, 0x1p0f, -0x1.44cf32p-1f, -0x1.424776p-27f, +-0x1.b1776ep-3f, 0x1p0f, -0x1.3affa2p-1f, -0x1.240a18p-26f, +-0x1.9307eep-3f, 0x1p0f, -0x1.30ff8p-1f, 0x1.8f47e6p-28f, +-0x1.759618p-3f, 0x1p0f, -0x1.26d054p-1f, -0x1.9ba25cp-26f, +-0x1.592676p-3f, 0x1p0f, -0x1.1c73b4p-1f, 0x1.9465cep-27f, +-0x1.3dbd6ap-3f, 0x1p0f, -0x1.11eb36p-1f, 0x1.7c969cp-26f, +-0x1.235f2ep-3f, 0x1p0f, -0x1.07387ap-1f, 0x1.b74004p-27f, +-0x1.0a0fd4p-3f, 0x1p0f, -0x1.f8ba4ep-2f, 0x1.01d952p-28f, +-0x1.e3a688p-4f, 0x1p0f, -0x1.e2b5d4p-2f, 0x1.fe4272p-28f, +-0x1.b55a7p-4f, 0x1p0f, -0x1.cc66eap-2f, 0x1.b38ee8p-28f, +-0x1.894286p-4f, 0x1p0f, -0x1.b5d1p-2f, -0x1.3c2b98p-27f, +-0x1.5f6598p-4f, 0x1p0f, -0x1.9ef794p-2f, -0x1.d476c6p-29f, +-0x1.37ca18p-4f, 0x1p0f, -0x1.87de2ap-2f, -0x1.abaa58p-28f, +-0x1.127624p-4f, 0x1p0f, -0x1.708854p-2f, 0x1.e0b74cp-27f, +-0x1.dedefcp-5f, 0x1p0f, -0x1.58f9a8p-2f, 0x1.4a9c04p-27f, +-0x1.9d7714p-5f, 0x1p0f, -0x1.4135cap-2f, 0x1.7d134p-27f, +-0x1.60beaap-5f, 0x1p0f, -0x1.294062p-2f, -0x1.dab3ep-27f, +-0x1.28bf18p-5f, 0x1p0f, -0x1.111d26p-2f, -0x1.58fb3cp-29f, +-0x1.eb0208p-6f, 0x1p0f, -0x1.f19f98p-3f, 0x1.37a83ap-29f, +-0x1.8e18a8p-6f, 0x1p0f, -0x1.c0b826p-3f, -0x1.4fc9ecp-28f, +-0x1.3ad06p-6f, 0x1p0f, -0x1.8f8b84p-3f, 0x1.cb2cfap-30f, +-0x1.e26c16p-7f, 0x1p0f, -0x1.5e2144p-3f, -0x1.22cff2p-29f, +-0x1.62aa04p-7f, 0x1p0f, -0x1.2c8106p-3f, -0x1.d1cc28p-28f, +-0x1.ecdc78p-8f, 0x1p0f, -0x1.f564e6p-4f, 0x1.2ad19ep-29f, +-0x1.3b92e2p-8f, 0x1p0f, -0x1.917a6cp-4f, 0x1.eb25eap-31f, +-0x1.63253p-9f, 0x1p0f, -0x1.2d520ap-4f, 0x1.a63cc2p-29f, +-0x1.3bc39p-10f, 0x1p0f, -0x1.91f66p-5f, 0x1.de44fep-30f, +-0x1.3bcfbep-12f, 0x1p0f, -0x1.92156p-6f, 0x1.0b933p-31f, +0.0f, 0x1p0f, 0.0f, 0.0f, +-0x1.3bcfbep-12f, 0x1p0f, 0x1.92156p-6f, -0x1.0b933p-31f, +-0x1.3bc39p-10f, 0x1p0f, 0x1.91f66p-5f, -0x1.de44fep-30f, +-0x1.63253p-9f, 0x1p0f, 0x1.2d520ap-4f, -0x1.a63cc2p-29f, +-0x1.3b92e2p-8f, 0x1p0f, 0x1.917a6cp-4f, -0x1.eb25eap-31f, +-0x1.ecdc78p-8f, 0x1p0f, 0x1.f564e6p-4f, -0x1.2ad19ep-29f, +-0x1.62aa04p-7f, 0x1p0f, 0x1.2c8106p-3f, 0x1.d1cc28p-28f, +-0x1.e26c16p-7f, 0x1p0f, 0x1.5e2144p-3f, 0x1.22cff2p-29f, +-0x1.3ad06p-6f, 0x1p0f, 0x1.8f8b84p-3f, -0x1.cb2cfap-30f, +-0x1.8e18a8p-6f, 0x1p0f, 0x1.c0b826p-3f, 0x1.4fc9ecp-28f, +-0x1.eb0208p-6f, 0x1p0f, 0x1.f19f98p-3f, -0x1.37a83ap-29f, +-0x1.28bf18p-5f, 0x1p0f, 0x1.111d26p-2f, 0x1.58fb3cp-29f, +-0x1.60beaap-5f, 0x1p0f, 0x1.294062p-2f, 0x1.dab3ep-27f, +-0x1.9d7714p-5f, 0x1p0f, 0x1.4135cap-2f, -0x1.7d134p-27f, +-0x1.dedefcp-5f, 0x1p0f, 0x1.58f9a8p-2f, -0x1.4a9c04p-27f, +-0x1.127624p-4f, 0x1p0f, 0x1.708854p-2f, -0x1.e0b74cp-27f, +-0x1.37ca18p-4f, 0x1p0f, 0x1.87de2ap-2f, 0x1.abaa58p-28f, +-0x1.5f6598p-4f, 0x1p0f, 0x1.9ef794p-2f, 0x1.d476c6p-29f, +-0x1.894286p-4f, 0x1p0f, 0x1.b5d1p-2f, 0x1.3c2b98p-27f, +-0x1.b55a7p-4f, 0x1p0f, 0x1.cc66eap-2f, -0x1.b38ee8p-28f, +-0x1.e3a688p-4f, 0x1p0f, 0x1.e2b5d4p-2f, -0x1.fe4272p-28f, +-0x1.0a0fd4p-3f, 0x1p0f, 0x1.f8ba4ep-2f, -0x1.01d952p-28f, +-0x1.235f2ep-3f, 0x1p0f, 0x1.07387ap-1f, -0x1.b74004p-27f, +-0x1.3dbd6ap-3f, 0x1p0f, 0x1.11eb36p-1f, -0x1.7c969cp-26f, +-0x1.592676p-3f, 0x1p0f, 0x1.1c73b4p-1f, -0x1.9465cep-27f, +-0x1.759618p-3f, 0x1p0f, 0x1.26d054p-1f, 0x1.9ba25cp-26f, +-0x1.9307eep-3f, 0x1p0f, 0x1.30ff8p-1f, -0x1.8f47e6p-28f, +-0x1.b1776ep-3f, 0x1p0f, 0x1.3affa2p-1f, 0x1.240a18p-26f, +-0x1.d0dfe6p-3f, 0x1p0f, 0x1.44cf32p-1f, 0x1.424776p-27f, +-0x1.f13c7ep-3f, 0x1p0f, 0x1.4e6cacp-1f, -0x1.070686p-27f, +-0x1.09441cp-2f, 0x1p0f, 0x1.57d694p-1f, -0x1.6e626cp-26f, +-0x1.1a5efap-2f, 0x1p0f, 0x1.610b76p-1f, -0x1.5c5a64p-26f, +-0x1.2bec34p-2f, 0x1p0f, 0x1.6a09e6p-1f, 0x1.9fcef4p-27f, +-0x1.3de916p-2f, 0x1p0f, 0x1.72d084p-1f, -0x1.02000ep-26f, +-0x1.5052dap-2f, 0x1p0f, 0x1.7b5df2p-1f, 0x1.3557d8p-28f, +-0x1.6326a8p-2f, 0x1p0f, 0x1.83b0ep-1f, 0x1.7ff2eep-26f, +-0x1.76619cp-2f, 0x1p0f, 0x1.8bc806p-1f, 0x1.62a2e8p-26f, +-0x1.8a00bap-2f, 0x1p0f, 0x1.93a224p-1f, 0x1.324c8p-26f, +-0x1.9e01p-2f, 0x1p0f, 0x1.9b3e04p-1f, 0x1.fce1dp-27f, +-0x1.b25f56p-2f, 0x1p0f, 0x1.a29a7ap-1f, 0x1.189e08p-31f, +-0x1.c71898p-2f, 0x1p0f, 0x1.a9b662p-1f, 0x1.21d434p-26f, +-0x1.dc2996p-2f, 0x1p0f, 0x1.b090a6p-1f, -0x1.fabf8p-27f, +-0x1.f18f0cp-2f, 0x1p0f, 0x1.b72834p-1f, 0x1.465b9p-27f, +-0x1.d16c9p-8f, 0x1p-1f, 0x1.bd7c0ap-1f, 0x1.8df2a6p-26f, +-0x1.d4a2c8p-6f, 0x1p-1f, 0x1.c38b3p-1f, -0x1.cfe84ap-26f, +-0x1.9cc8b4p-5f, 0x1p-1f, 0x1.c954b2p-1f, 0x1.3411f4p-29f, +-0x1.28bbfep-4f, 0x1p-1f, 0x1.ced7bp-1f, -0x1.786712p-26f, +-0x1.8421bp-4f, 0x1p-1f, 0x1.d4134ep-1f, -0x1.d646d8p-26f, +-0x1.e08756p-4f, 0x1p-1f, 0x1.d906bcp-1f, 0x1.e651a8p-26f, +-0x1.1eef5ap-3f, 0x1p-1f, 0x1.ddb13cp-1f, -0x1.2667b8p-26f, +-0x1.4e0cb2p-3f, 0x1p-1f, 0x1.e2121p-1f, 0x1.3da1bap-27f, +-0x1.7d946ep-3f, 0x1p-1f, 0x1.e6288ep-1f, 0x1.891c22p-26f, +-0x1.ad7f3ap-3f, 0x1p-1f, 0x1.e9f416p-1f, -0x1.273a44p-26f, +-0x1.ddc5b4p-3f, 0x1p-1f, 0x1.ed740ep-1f, 0x1.da1258p-27f, +-0x1.cc0d0ap-8f, 0x1p-2f, 0x1.f0a7fp-1f, -0x1.1b73cap-27f, +-0x1.fa3ecap-6f, 0x1p-2f, 0x1.f38f3ap-1f, 0x1.8c9cb2p-26f, +-0x1.c1d1fp-5f, 0x1p-2f, 0x1.f6297cp-1f, 0x1.feeb96p-26f, +-0x1.43bd78p-4f, 0x1p-2f, 0x1.f8765p-1f, -0x1.63ad16p-27f, +-0x1.a6fdf2p-4f, 0x1p-2f, 0x1.fa7558p-1f, -0x1.eeb5d2p-30f, +-0x1.536352p-9f, 0x1p-3f, 0x1.fc2648p-1f, -0x1.e3cc06p-26f, +-0x1.ba165p-6f, 0x1p-3f, 0x1.fd88dap-1f, 0x1.e89292p-28f, +-0x1.a55beep-5f, 0x1p-3f, 0x1.fe9cdap-1f, 0x1.a03108p-26f, +-0x1.b82684p-7f, 0x1p-4f, 0x1.ff621ep-1f, 0x1.bcb6bep-28f, +-0x1.b7aa82p-8f, 0x1p-5f, 0x1.ffd886p-1f, 0x1.099a1ap-30f, +}; + +template <> inline constexpr double kCosApproxTable[] = +{ +0.0, 0.0, 0x1p0, 0.0, +-0x1.000c90e8fe6f6p6, 0x1p6, 0x1.fff62169b92dbp-1, 0x1.5dda3cp-55, +-0x1.003242abef46dp5, 0x1p5, 0x1.ffd886084cd0dp-1, -0x1.1354d4p-55, +-0x1.0096c32baca2bp4, 0x1p4, 0x1.ffa72effef75dp-1, -0x1.8b4cdcp-55, +-0x1.00c8fb2f886ecp4, 0x1p4, 0x1.ff621e3796d7ep-1, -0x1.c57bc2p-57, +-0x1.00fb2b73cfc1p4, 0x1p4, 0x1.ff095658e71adp-1, 0x1.01a8cep-55, +-0x1.025aa41259c34p3, 0x1p3, 0x1.fe9cdad01883ap-1, 0x1.521eccp-57, 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+-0x1.cc3a65bbc6327p-4, 0x1p0, 0x1.d79775b86e389p-2, 0x1.550ec8p-56, +-0x1.e3a6873fa1279p-4, 0x1p0, 0x1.e2b5d3806f63bp-2, 0x1.e0d89p-58, +-0x1.fb9decc6d55b8p-4, 0x1p0, 0x1.edc1952ef78d6p-2, -0x1.dd0f7cp-56, +-0x1.0a0fd4e41ab5ap-3, 0x1p0, 0x1.f8ba4dbf89abap-2, -0x1.2ec1fcp-60, +-0x1.169566329bcb7p-3, 0x1p0, 0x1.01cfc874c3eb7p-1, -0x1.34a35ep-56, +-0x1.235f2eb9a470ap-3, 0x1p0, 0x1.073879922ffeep-1, -0x1.a5a014p-55, +-0x1.306cb042aa3bap-3, 0x1p0, 0x1.0c9704d5d898fp-1, -0x1.8d3d7cp-55, +-0x1.3dbd69fabf802p-3, 0x1p0, 0x1.11eb3541b4b23p-1, -0x1.ef23b6p-55, +-0x1.4b50d8778abbdp-3, 0x1p0, 0x1.1734d63dedb49p-1, -0x1.7eef2cp-55, +-0x1.592675bc57974p-3, 0x1p0, 0x1.1c73b39ae68c8p-1, 0x1.b25dd2p-55, +-0x1.673db93f41479p-3, 0x1p0, 0x1.21a799933eb59p-1, -0x1.3a7b16p-55, +-0x1.759617ee761f9p-3, 0x1p0, 0x1.26d054cdd12dfp-1, -0x1.5da742p-55, +-0x1.842f0435941afp-3, 0x1p0, 0x1.2bedb25faf3eap-1, -0x1.14981cp-58, +-0x1.9307ee031e2fdp-3, 0x1p0, 0x1.30ff7fce17035p-1, -0x1.efcc62p-57, +-0x1.a22042ce0a2f9p-3, 0x1p0, 0x1.36058b10659f3p-1, -0x1.1fcb3ap-55, +-0x1.b1776d9b67013p-3, 0x1p0, 0x1.3affa292050b9p-1, 0x1.e3e25ep-56, +-0x1.c10cd7041afccp-3, 0x1p0, 0x1.3fed9534556d4p-1, 0x1.369166p-55, +-0x1.d0dfe53aba2fdp-3, 0x1p0, 0x1.44cf325091dd6p-1, 0x1.8076a2p-57, +-0x1.e0effc1174505p-3, 0x1p0, 0x1.49a449b9b0939p-1, -0x1.27ee16p-55, +-0x1.f13c7d001a249p-3, 0x1p0, 0x1.4e6cabbe3e5e9p-1, 0x1.3c293ep-57, +-0x1.00e263951d11fp-2, 0x1p0, 0x1.5328292a35596p-1, -0x1.a12eb8p-56, +-0x1.09441bb2aa0a2p-2, 0x1p0, 0x1.57d69348cecap-1, -0x1.757208p-55, +-0x1.11c3141f91b3ep-2, 0x1p0, 0x1.5c77bbe65018cp-1, 0x1.069ea8p-55, +-0x1.1a5ef902000d3p-2, 0x1p0, 0x1.610b7551d2cdfp-1, -0x1.251b34p-56, +-0x1.23177562aaea3p-2, 0x1p0, 0x1.6591925f0783dp-1, 0x1.c3d64ep-55, +-0x1.2bec333018867p-2, 0x1p0, 0x1.6a09e667f3bcdp-1, -0x1.bdd34p-55, +-0x1.34dcdb41f0f85p-2, 0x1p0, 0x1.6e74454eaa8afp-1, -0x1.dbc03cp-55, +-0x1.3de9155c5a642p-2, 0x1p0, 0x1.72d0837efff96p-1, 0x1.0d4efp-55, +-0x1.471088335fce7p-2, 0x1p0, 0x1.771e75f037261p-1, 0x1.5cfce8p-56, +-0x1.5052d96e626c1p-2, 0x1p0, 0x1.7b5df226aafafp-1, -0x1.0f537ap-56, +-0x1.59afadab954d4p-2, 0x1p0, 0x1.7f8ece3571771p-1, -0x1.9c8d8cp-55, +-0x1.6326a8838342ep-2, 0x1p0, 0x1.83b0e0bff976ep-1, -0x1.6f420ep-56, +-0x1.6cb76c8c9ed8fp-2, 0x1p0, 0x1.87c400fba2ebfp-1, -0x1.2dabcp-55, +-0x1.76619b5edc454p-2, 0x1p0, 0x1.8bc806b151741p-1, -0x1.2c5e12p-55, +-0x1.8024d59755257p-2, 0x1p0, 0x1.8fbcca3ef940dp-1, -0x1.6dfa98p-57, +-0x1.8a00badbf5e8ep-2, 0x1p0, 0x1.93a22499263fbp-1, 0x1.3d419ap-55, +-0x1.93f4e9df34c1bp-2, 0x1p0, 0x1.9777ef4c7d742p-1, -0x1.15479ap-55, +-0x1.9e010063d1f96p-2, 0x1p0, 0x1.9b3e047f38741p-1, -0x1.30ee28p-55, +-0x1.a8249b40a182cp-2, 0x1p0, 0x1.9ef43ef29af94p-1, 0x1.b1dfcap-56, +-0x1.b25f56645da43p-2, 0x1p0, 0x1.a29a7a0462782p-1, -0x1.128bbp-56, +-0x1.bcb0ccd98294fp-2, 0x1p0, 0x1.a63091b02fae2p-1, -0x1.e91114p-56, +-0x1.c71898ca32e6fp-2, 0x1p0, 0x1.a9b66290ea1a3p-1, 0x1.9f630ep-60, +-0x1.d19653842496fp-2, 0x1p0, 0x1.ad2bc9e21d511p-1, -0x1.47fbep-55, +-0x1.dc29957c969bbp-2, 0x1p0, 0x1.b090a581502p-1, -0x1.926da2p-55, +-0x1.e6d1f6544ece3p-2, 0x1p0, 0x1.b3e4d3ef55712p-1, -0x1.eb6b8ap-55, +-0x1.f18f0cdba0025p-2, 0x1p0, 0x1.b728345196e3ep-1, -0x1.bc69f2p-55, +-0x1.fc606f1678292p-2, 0x1p0, 0x1.ba5aa673590d2p-1, 0x1.7ea4e2p-55, +-0x1.d16c901d95181p-8, 0x1p-1, 0x1.bd7c0ac6f952ap-1, -0x1.825a72p-55, +-0x1.23e6ad10872a7p-6, 0x1p-1, 0x1.c08c426725549p-1, 0x1.b157fcp-58, +-0x1.d4a2c7f909c4ep-6, 0x1p-1, 0x1.c38b2f180bdb1p-1, -0x1.6e0b16p-56, +-0x1.4344523c8e3b5p-5, 0x1p-1, 0x1.c678b3488739bp-1, 0x1.d86cacp-57, +-0x1.9cc8b3671dd0fp-5, 0x1p-1, 0x1.c954b213411f5p-1, -0x1.2fb76p-58, +-0x1.f6db13ff708cbp-5, 0x1p-1, 0x1.cc1f0f3fcfc5cp-1, 0x1.e57612p-56, +-0x1.28bbfd87a8cffp-4, 0x1p-1, 0x1.ced7af43cc773p-1, -0x1.e7b6bap-58, +-0x1.564df524b00dap-4, 0x1p-1, 0x1.d17e7743e35dcp-1, -0x1.101da2p-58, +-0x1.8421af15c49d7p-4, 0x1p-1, 0x1.d4134d14dc93ap-1, -0x1.4ef528p-55, +-0x1.b2356710db0a3p-4, 0x1p-1, 0x1.d696173c9e68bp-1, -0x1.e8c61cp-56, +-0x1.e087565455a75p-4, 0x1p-1, 0x1.d906bcf328d46p-1, 0x1.457e6p-56, +-0x1.078ad9dc46632p-3, 0x1p-1, 0x1.db6526238a09bp-1, -0x1.adee7ep-56, +-0x1.1eef59e0b74c3p-3, 0x1p-1, 0x1.ddb13b6ccc23cp-1, 0x1.83c37cp-55, +-0x1.367044581b074p-3, 0x1p-1, 0x1.dfeae622dbe2bp-1, -0x1.514ea8p-55, +-0x1.4e0cb14a9c046p-3, 0x1p-1, 0x1.e212104f686e5p-1, -0x1.014c76p-55, +-0x1.65c3b7b0e312cp-3, 0x1p-1, 0x1.e426a4b2bc17ep-1, 0x1.a87388p-55, +-0x1.7d946d7d133fdp-3, 0x1p-1, 0x1.e6288ec48e112p-1, -0x1.16b56ep-57, +-0x1.957de7a3cfd5dp-3, 0x1p-1, 0x1.e817bab4cd10dp-1, -0x1.d0afe6p-56, +-0x1.ad7f3a254c1f5p-3, 0x1p-1, 0x1.e9f4156c62ddap-1, 0x1.760b1ep-55, +-0x1.c597781664984p-3, 0x1p-1, 0x1.ebbd8c8df0b74p-1, 0x1.c6c8c6p-56, +-0x1.ddc5b3a9c1311p-3, 0x1p-1, 0x1.ed740e7684963p-1, 0x1.e82c78p-56, +-0x1.f608fe39004a4p-3, 0x1p-1, 0x1.ef178a3e473c2p-1, 0x1.6310a6p-55, +-0x1.cc0d09bd41caap-8, 0x1p-2, 0x1.f0a7efb9230d7p-1, 0x1.52c7acp-56, +-0x1.36580d5d5e775p-6, 0x1p-2, 0x1.f2252f7763adap-1, -0x1.20cb8p-55, +-0x1.fa3ecac0d84e8p-6, 0x1p-2, 0x1.f38f3ac64e589p-1, -0x1.d7bafap-56, +-0x1.5f57f693feebep-5, 0x1p-2, 0x1.f4e603b0b2f2dp-1, -0x1.8ee01ep-56, +-0x1.c1d1f0e5967d5p-5, 0x1p-2, 0x1.f6297cff75cbp-1, 0x1.562172p-56, +-0x1.1244c435e819dp-4, 0x1p-2, 0x1.f7599a3a12077p-1, 0x1.84f31cp-55, +-0x1.43bd776e98073p-4, 0x1p-2, 0x1.f8764fa714ba9p-1, 0x1.ab2566p-56, +-0x1.755129dad834cp-4, 0x1p-2, 0x1.f97f924c9099bp-1, -0x1.e2ae0ep-55, +-0x1.a6fdf22e33d8cp-4, 0x1p-2, 0x1.fa7557f08a517p-1, -0x1.7a0a8cp-55, +-0x1.d8c1e624a1513p-4, 0x1p-2, 0x1.fb5797195d741p-1, 0x1.1bfac6p-56, +-0x1.536352ad19e39p-9, 0x1p-3, 0x1.fc26470e19fd3p-1, 0x1.1ec866p-55, +-0x1.e43d1c309e958p-7, 0x1p-3, 0x1.fce15fd6da67bp-1, -0x1.5dd6f8p-56, +-0x1.ba1650f592f5p-6, 0x1p-3, 0x1.fd88da3d12526p-1, -0x1.87df62p-55, +-0x1.4125feacab7cep-5, 0x1p-3, 0x1.fe1cafcbd5b09p-1, 0x1.a23e32p-57, +-0x1.a55beda63cc14p-5, 0x1p-3, 0x1.fe9cdad01883ap-1, 0x1.521eccp-57, +-0x1.35230c0fbe402p-10, 0x1p-4, 0x1.ff095658e71adp-1, 0x1.01a8cep-55, +-0x1.b82683bc89fbp-7, 0x1p-4, 0x1.ff621e3796d7ep-1, -0x1.c57bc2p-57, +-0x1.a4f3514d75466p-6, 0x1p-4, 0x1.ffa72effef75dp-1, -0x1.8b4cdcp-55, +-0x1.b7aa821726608p-8, 0x1p-5, 0x1.ffd886084cd0dp-1, -0x1.1354d4p-55, +-0x1.b78b80c84e1eep-9, 0x1p-6, 0x1.fff62169b92dbp-1, 0x1.5dda3cp-55, +}; + +} // namespace npsr::trig::data + +#endif // NPSR_TRIG_DATA_APPROX_H diff --git a/npsr/trig/data/constants.h b/npsr/trig/data/constants.h new file mode 100644 index 0000000..358290f --- /dev/null +++ b/npsr/trig/data/constants.h @@ -0,0 +1,50 @@ +// Auto-generated by npsr/trig/data/constants.h.sol +// Use `spin sollya -f` to force regeneration +#ifndef NPSR_TRIG_DATA_CONSTANTS_H +#define NPSR_TRIG_DATA_CONSTANTS_H + +namespace npsr::trig::data { +template inline constexpr char kPi[] = {}; +template <> inline constexpr float kPi[] = { +0x1.921fb6p1f, -0x1.777a5cp-24f, -0x1.ee59dap-49f, }; +template <> inline constexpr float kPi[] = { +0x1.92p1f, 0x1.fb4p-11f, 0x1.444p-23f, 0x1.68c234p-38f, +}; +template <> inline constexpr double kPi[] = { +0x1.921fb54442d18p1, 0x1.1a62633145c06p-53, 0x1.c1cd129024e09p-106, }; +template <> inline constexpr double kPi[] = { +0x1.921fb6p1, -0x1.777a5cp-24, -0x1.ee59dap-49, 0x1.98a2e03707345p-76, +}; + +template inline constexpr double kPiPrec35[] = { +0x1.921fb5444p1, 0x1.68c234c4c6628p-38, }; +template <> inline constexpr double kPiPrec35[] = { +0x1.921fb6p1, -0x1.777a5cp-24, -0x1.ee59dap-49, }; + +template inline constexpr char kPiMul2[] = {}; +template <> inline constexpr float kPiMul2[] = { +0x1.921fb6p2f, -0x1.777a5cp-23f, }; +template <> inline constexpr double kPiMul2[] = { +0x1.921fb54442d18p2, 0x1.1a62633145c07p-52, }; + +template inline constexpr double kPiDiv16Prec29[] = { +0x1.921fb54442d18p-3, 0x1.1a62633p-57, 0x1.45c06e0e68948p-89, }; +template <> inline constexpr double kPiDiv16Prec29[] = { +0x1.921fb54p-3, 0x1.a626331p-61, 0x1.1701b839a252p-91, 0x1.10b461p-33, +}; + +template inline constexpr char kInvPi = '_'; +template <> inline constexpr float kInvPi = 0x1.45f306p-2f; +template <> inline constexpr double kInvPi = 0x1.45f306dc9c883p-2; + +template inline constexpr char kHalfPi = '_'; +template <> inline constexpr float kHalfPi = 0x1.921fb6p0f; +template <> inline constexpr double kHalfPi = 0x1.921fb54442d18p0; + +template inline constexpr char k16DivPi = '_'; +template <> inline constexpr float k16DivPi = 0x1.45f306p2f; +template <> inline constexpr double k16DivPi = 0x1.45f306dc9c883p2; + +} // namespace npsr::trig::data + +#endif // NPSR_TRIG_DATA_CONSTANTS_H diff --git a/npsr/trig/data/data.h b/npsr/trig/data/data.h new file mode 100644 index 0000000..b5dbc01 --- /dev/null +++ b/npsr/trig/data/data.h @@ -0,0 +1,5 @@ +#include "npsr/lut-inl.h" +#include "npsr/trig/data/constants.h" +#include "npsr/trig/data/kpi16-inl.h" +#include "npsr/trig/data/approx.h" +#include "npsr/trig/data/reduction.h" diff --git a/npsr/trig/data/kpi16-inl.h b/npsr/trig/data/kpi16-inl.h new file mode 100644 index 0000000..81beafb --- /dev/null +++ b/npsr/trig/data/kpi16-inl.h @@ -0,0 +1,41 @@ +// Auto-generated by npsr/trig/data/kpi16-inl.h.sol +// Use `spin sollya -f` to force regeneration +#if defined(NPSR_TRIG_DATA_KPI16_INL_H) == defined(HWY_TARGET_TOGGLE) // NOLINT +#ifdef NPSR_TRIG_DATA_KPI16_INL_H +#undef NPSR_TRIG_DATA_KPI16_INL_H +#else +#define NPSR_TRIG_DATA_KPI16_INL_H +#endif + +HWY_BEFORE_NAMESPACE(); +namespace npsr::HWY_NAMESPACE::trig { +inline constexpr auto kKPi16Table = MakeLut( +// High parts of sin(k·π/16) where k = 0, 1, ..., 15 +{ +0.0, 0x1.8f8b83c69a60bp-3, 0x1.87de2a6aea963p-2, 0x1.1c73b39ae68c8p-1, +0x1.6a09e667f3bcdp-1, 0x1.a9b66290ea1a3p-1, 0x1.d906bcf328d46p-1, 0x1.f6297cff75cbp-1, +0x1p0, 0x1.f6297cff75cbp-1, 0x1.d906bcf328d46p-1, 0x1.a9b66290ea1a3p-1, +0x1.6a09e667f3bcdp-1, 0x1.1c73b39ae68c8p-1, 0x1.87de2a6aea963p-2, 0x1.8f8b83c69a60bp-3, +}, +// High parts of cos(k·π/16) where k = 0, 1, ..., 15 +{ +0x1p0, 0x1.f6297cff75cbp-1, 0x1.d906bcf328d46p-1, 0x1.a9b66290ea1a3p-1, +0x1.6a09e667f3bcdp-1, 0x1.1c73b39ae68c8p-1, 0x1.87de2a6aea963p-2, 0x1.8f8b83c69a60bp-3, +0.0, -0x1.8f8b83c69a60bp-3, -0x1.87de2a6aea963p-2, -0x1.1c73b39ae68c8p-1, +-0x1.6a09e667f3bcdp-1, -0x1.a9b66290ea1a3p-1, -0x1.d906bcf328d46p-1, -0x1.f6297cff75cbp-1, +}, +// Lower parts of sin(k·π/16) and cos(k·π/16) packed together +// Format: bits [63:32] = cos_low, bits [31:0] = sin_low +// This packing saves 16×8 = 128 bytes of memory +{ +0.0, 0x1.56217bc626d19p-56, 0x1.457e6bc672cedp-56, 0x1.9f6303c8b25ddp-60, +-0x1.bdd34bc8bdd34p-55, 0x1.b25dd3c39f63p-55, -0x1.72ced3c7457e6p-57, -0x1.26d193c756217p-57, +0.0, 0x1.26d193c756217p-57, 0x1.72ced3c7457e6p-57, -0x1.b25dd3c39f63p-55, +0x1.bdd34bc8bdd34p-55, -0x1.9f6303c8b25ddp-60, -0x1.457e6bc672cedp-56, -0x1.56217bc626d19p-56, +} + +); +inline HWY_ATTR void _dummy_supress_unused_target(){} +} // namespace npsr::HWY_NAMESPACE::trig +HWY_AFTER_NAMESPACE(); +#endif // NPSR_TRIG_DATA_KPI16_INL_H diff --git a/npsr/trig/data/reduction.h b/npsr/trig/data/reduction.h new file mode 100644 index 0000000..fedc8b4 --- /dev/null +++ b/npsr/trig/data/reduction.h @@ -0,0 +1,2320 @@ +// Auto-generated by npsr/trig/data/reduction.h.sol +// Use `spin sollya -f` to force regeneration +#ifndef NPSR_TRIG_DATA_REDUCTION_H +#define NPSR_TRIG_DATA_REDUCTION_H + +namespace npsr::trig::data { +template inline constexpr T kLargeReductionTable[] = {}; +template <> inline constexpr uint32_t kLargeReductionTable[] = { +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 0u, +0u, 0u, 1u, +0u, 0u, 2u, +0u, 0u, 5u, +0u, 0u, 10u, +0u, 0u, 20u, +0u, 0u, 40u, +0u, 0u, 81u, +0u, 0u, 162u, +0u, 0u, 325u, +0u, 0u, 651u, +0u, 0u, 1303u, +0u, 0u, 2607u, +0u, 0u, 5215u, +0u, 0u, 10430u, +0u, 0u, 20860u, +0u, 0u, 41721u, +0u, 0u, 83443u, +0u, 0u, 166886u, +0u, 0u, 333772u, +0u, 0u, 667544u, +0u, 0u, 1335088u, +0u, 0u, 2670176u, +0u, 0u, 5340353u, +0u, 0u, 10680707u, +0u, 0u, 21361414u, +0u, 0u, 42722829u, +0u, 0u, 85445659u, +0u, 0u, 170891318u, +0u, 0u, 341782637u, +0u, 0u, 683565275u, +0u, 0u, 1367130551u, +0u, 0u, 2734261102u, +0u, 1u, 1173554908u, +0u, 2u, 2347109817u, +0u, 5u, 399252338u, +0u, 10u, 798504676u, +0u, 20u, 1597009353u, +0u, 40u, 3194018707u, +0u, 81u, 2093070119u, +0u, 162u, 4186140238u, +0u, 325u, 4077313180u, +0u, 651u, 3859659065u, +0u, 1303u, 3424350834u, +0u, 2607u, 2553734372u, +0u, 5215u, 812501448u, +0u, 10430u, 1625002897u, +0u, 20860u, 3250005794u, +0u, 41721u, 2205044292u, +0u, 83443u, 115121288u, +0u, 166886u, 230242576u, +0u, 333772u, 460485152u, +0u, 667544u, 920970305u, +0u, 1335088u, 1841940610u, +0u, 2670176u, 3683881221u, +0u, 5340353u, 3072795146u, +0u, 10680707u, 1850622997u, +0u, 21361414u, 3701245994u, +0u, 42722829u, 3107524692u, +0u, 85445659u, 1920082089u, +0u, 170891318u, 3840164178u, +0u, 341782637u, 3385361061u, +0u, 683565275u, 2475754826u, +0u, 1367130551u, 656542356u, +0u, 2734261102u, 1313084713u, +1u, 1173554908u, 2626169427u, +2u, 2347109817u, 957371559u, +5u, 399252338u, 1914743119u, +10u, 798504676u, 3829486239u, +20u, 1597009353u, 3364005183u, +40u, 3194018707u, 2433043071u, +81u, 2093070119u, 571118846u, +162u, 4186140238u, 1142237692u, +325u, 4077313180u, 2284475384u, +651u, 3859659065u, 273983472u, +1303u, 3424350834u, 547966945u, +2607u, 2553734372u, 1095933890u, +5215u, 812501448u, 2191867780u, +10430u, 1625002897u, 88768265u, +20860u, 3250005794u, 177536531u, +41721u, 2205044292u, 355073063u, +83443u, 115121288u, 710146126u, +166886u, 230242576u, 1420292253u, +333772u, 460485152u, 2840584506u, +667544u, 920970305u, 1386201717u, +1335088u, 1841940610u, 2772403434u, +2670176u, 3683881221u, 1249839573u, +5340353u, 3072795146u, 2499679147u, +10680707u, 1850622997u, 704390999u, +21361414u, 3701245994u, 1408781999u, +42722829u, 3107524692u, 2817563999u, +85445659u, 1920082089u, 1340160702u, +170891318u, 3840164178u, 2680321405u, +341782637u, 3385361061u, 1065675514u, +683565275u, 2475754826u, 2131351028u, +1367130551u, 656542356u, 4262702056u, +2734261102u, 1313084713u, 4230436817u, +1173554908u, 2626169427u, 4165906339u, +2347109817u, 957371559u, 4036845383u, +399252338u, 1914743119u, 3778723471u, +798504676u, 3829486239u, 3262479647u, +1597009353u, 3364005183u, 2229991998u, +3194018707u, 2433043071u, 165016701u, +2093070119u, 571118846u, 330033402u, +4186140238u, 1142237692u, 660066805u, +4077313180u, 2284475384u, 1320133610u, +3859659065u, 273983472u, 2640267220u, +3424350834u, 547966945u, 985567145u, +2553734372u, 1095933890u, 1971134291u, +812501448u, 2191867780u, 3942268582u, +1625002897u, 88768265u, 3589569869u, +3250005794u, 177536531u, 2884172442u, +2205044292u, 355073063u, 1473377588u, +115121288u, 710146126u, 2946755177u, +230242576u, 1420292253u, 1598543059u, +460485152u, 2840584506u, 3197086118u, +920970305u, 1386201717u, 2099204941u, +1841940610u, 2772403434u, 4198409883u, +3683881221u, 1249839573u, 4101852471u, +3072795146u, 2499679147u, 3908737646u, +1850622997u, 704390999u, 3522507997u, +3701245994u, 1408781999u, 2750048699u, +3107524692u, 2817563999u, 1205130103u, +1920082089u, 1340160702u, 2410260206u, +3840164178u, 2680321405u, 525553116u, +3385361061u, 1065675514u, 1051106232u, +2475754826u, 2131351028u, 2102212464u, +656542356u, 4262702056u, 4204424928u, +1313084713u, 4230436817u, 4113882560u, +2626169427u, 4165906339u, 3932797825u, +957371559u, 4036845383u, 3570628355u, +1914743119u, 3778723471u, 2846289414u, +3829486239u, 3262479647u, 1397611533u, +3364005183u, 2229991998u, 2795223067u, +2433043071u, 165016701u, 1295478838u, +571118846u, 330033402u, 2590957677u, +1142237692u, 660066805u, 886948059u, +2284475384u, 1320133610u, 1773896118u, +273983472u, 2640267220u, 3547792237u, +547966945u, 985567145u, 2800617179u, +1095933890u, 1971134291u, 1306267062u, +2191867780u, 3942268582u, 2612534124u, +88768265u, 3589569869u, 930100952u, +177536531u, 2884172442u, 1860201905u, +355073063u, 1473377588u, 3720403810u, +710146126u, 2946755177u, 3145840325u, +1420292253u, 1598543059u, 1996713354u, +2840584506u, 3197086118u, 3993426708u, +1386201717u, 2099204941u, 3691886121u, +2772403434u, 4198409883u, 3088804946u, +1249839573u, 4101852471u, 1882642597u, +2499679147u, 3908737646u, 3765285194u, +704390999u, 3522507997u, 3235603093u, +1408781999u, 2750048699u, 2176238891u, +2817563999u, 1205130103u, 57510486u, +1340160702u, 2410260206u, 115020972u, +2680321405u, 525553116u, 230041945u, +1065675514u, 1051106232u, 460083891u, +2131351028u, 2102212464u, 920167782u, +4262702056u, 4204424928u, 1840335564u, +4230436817u, 4113882560u, 3680671129u, +4165906339u, 3932797825u, 3066374962u, +4036845383u, 3570628355u, 1837782628u, +3778723471u, 2846289414u, 3675565257u, +3262479647u, 1397611533u, 3056163219u, +2229991998u, 2795223067u, 1817359143u, +165016701u, 1295478838u, 3634718287u, +330033402u, 2590957677u, 2974469278u, +660066805u, 886948059u, 1653971260u, +1320133610u, 1773896118u, 3307942520u, +2640267220u, 3547792237u, 2320917745u, +985567145u, 2800617179u, 346868194u, +1971134291u, 1306267062u, 693736388u, +3942268582u, 2612534124u, 1387472776u, +3589569869u, 930100952u, 2774945552u, +2884172442u, 1860201905u, 1254923809u, +1473377588u, 3720403810u, 2509847619u, +2946755177u, 3145840325u, 724727943u, +1598543059u, 1996713354u, 1449455886u, +3197086118u, 3993426708u, 2898911772u, +2099204941u, 3691886121u, 1502856249u, +4198409883u, 3088804946u, 3005712498u, +4101852471u, 1882642597u, 1716457700u, +3908737646u, 3765285194u, 3432915400u, +3522507997u, 3235603093u, 2570863504u, +2750048699u, 2176238891u, 846759712u, +1205130103u, 57510486u, 1693519425u, +2410260206u, 115020972u, 3387038850u, +525553116u, 230041945u, 2479110404u, +1051106232u, 460083891u, 663253512u, +2102212464u, 920167782u, 1326507024u, +4204424928u, 1840335564u, 2653014048u, +4113882560u, 3680671129u, 1011060801u, +3932797825u, 3066374962u, 2022121603u, +3570628355u, 1837782628u, 4044243207u, +2846289414u, 3675565257u, 3793519119u, +1397611533u, 3056163219u, 3292070943u, +2795223067u, 1817359143u, 2289174591u, +1295478838u, 3634718287u, 283381887u, +2590957677u, 2974469278u, 566763775u, +};; + +template <> inline constexpr uint64_t kLargeReductionTable[] = { +0ull, 0ull, 0ull, +0ull, 0ull, 0ull, +0ull, 0ull, 0ull, +0ull, 0ull, 0ull, +0ull, 0ull, 0ull, +0ull, 0ull, 0ull, +0ull, 0ull, 0ull, 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