From 6bcea9f09a5635d3c977a1d3223f1f05b93cc936 Mon Sep 17 00:00:00 2001
From: Sayed Awad <seiko@imavr.com>
Date: Mon, 27 Jul 2026 11:52:51 +0300
Subject: [PATCH 1/2] BUG: Fix f64 trig accuracy; match SVML rounding DAGs

- Extended path: restructure final reconstruction to follow SVML's
  per-precision rounding DAG (f32/f64 pair the sin/cos correction
  terms differently) and regenerate approx.h so sigma is a signed
  power of two, keeping sigma*r exact
- Low path: give f64 cosine its own minimax fit matching
  __svml_cos_d_la and keep its fast path up to ~8388607*pi
- Non-FMA f64: add SplitMul (exact head product via 26-bit split) to
  replace the FMA product-error idiom in the high/extended paths and
  reduce with a descending 4-word pi/16, restoring sub-ULP accuracy
- Correct trig polynomial/scale/threshold commentsit log
---
 npsr/hwy.h                 |   18 +-
 npsr/lut-inl.h             |    1 +
 npsr/trig/data/approx.h    | 2032 ++++++++++++++++++------------------
 npsr/trig/data/constants.h |    2 +-
 npsr/trig/extended-inl.h   |   41 +-
 npsr/trig/high-inl.h       |   73 +-
 npsr/trig/inl.h            |   25 +-
 npsr/trig/low-inl.h        |   34 +-
 8 files changed, 1152 insertions(+), 1074 deletions(-)

diff --git a/npsr/hwy.h b/npsr/hwy.h
index cf821b7..aa8310d 100644
--- a/npsr/hwy.h
+++ b/npsr/hwy.h
@@ -32,7 +32,23 @@ using hn::TFromV;
 using hn::VFromD;
 constexpr bool kNativeFMA = HWY_NATIVE_FMA != 0;
 
-inline HWY_ATTR void DummyToSuppressUnusedWarning() {}
+// Dekker split product for targets without native FMA, where the
+// `MulSub(a, b, a*b)` error idiom degenerates to zero. Masking to 26-bit heads
+// makes `head` exact, so a*b == head + rest (rest rounded at ~2^-105).
+template <typename V, HWY_IF_F64(TFromV<V>)>
+NPSR_INTRIN void SplitMul(V a, V b, V& head, V& rest) {
+  using namespace hn;
+  const DFromV<V> d;
+  const RebindToUnsigned<decltype(d)> du;
+  const V mask = BitCast(d, Set(du, 0xFFFFFFFFF8000000u));
+  const V a_hi = And(a, mask);
+  const V a_lo = Sub(a, a_hi);
+  const V b_hi = And(b, mask);
+  const V b_lo = Sub(b, b_hi);
+  head = Mul(a_hi, b_hi);
+  rest = MulAdd(a_hi, b_lo, Mul(a_lo, b));
+}
+
 }  // namespace npsr::HWY_NAMESPACE
 HWY_AFTER_NAMESPACE();
 
diff --git a/npsr/lut-inl.h b/npsr/lut-inl.h
index b9e1cdf..97905ee 100644
--- a/npsr/lut-inl.h
+++ b/npsr/lut-inl.h
@@ -5,6 +5,7 @@
 #define NPSR_LUT_INL_H_
 #endif
 
+#include <limits>
 #include <tuple>
 
 #include "npsr/hwy.h"
diff --git a/npsr/trig/data/approx.h b/npsr/trig/data/approx.h
index 43a1d01..5dec837 100644
--- a/npsr/trig/data/approx.h
+++ b/npsr/trig/data/approx.h
@@ -40,16 +40,16 @@ template <> inline constexpr float kSinApproxTable<float>[] =
 -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, 
+0x1.842dd6p-3f, 0x1p-1f, 0x1.72d084p-1f, -0x1.02000ep-26f, 
+0x1.5f5a4ep-3f, 0x1p-1f, 0x1.7b5df2p-1f, 0x1.3557d8p-28f, 
+0x1.39b2aep-3f, 0x1p-1f, 0x1.83b0ep-1f, 0x1.7ff2eep-26f, 
+0x1.133ccap-3f, 0x1p-1f, 0x1.8bc806p-1f, 0x1.62a2e8p-26f, 
+0x1.d7fd14p-4f, 0x1p-1f, 0x1.93a224p-1f, 0x1.324c8p-26f, 
+0x1.87fbfep-4f, 0x1p-1f, 0x1.9b3e04p-1f, 0x1.fce1dp-27f, 
+0x1.3682a6p-4f, 0x1p-1f, 0x1.a29a7ap-1f, 0x1.189e08p-31f, 
+0x1.c73b3ap-5f, 0x1p-1f, 0x1.a9b662p-1f, 0x1.21d434p-26f, 
+0x1.1eb354p-5f, 0x1p-1f, 0x1.b090a6p-1f, -0x1.fabf8p-27f, 
+0x1.ce1e64p-7f, 0x1p-1f, 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, 
@@ -57,163 +57,163 @@ template <> inline constexpr float kSinApproxTable<float>[] =
 -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, 
+0x1.63e69ep-4f, 0x1p-2f, 0x1.e2121p-1f, 0x1.3da1bap-27f, 
+0x1.04d726p-4f, 0x1p-2f, 0x1.e6288ep-1f, 0x1.891c22p-26f, 
+0x1.4a0318p-5f, 0x1p-2f, 0x1.e9f416p-1f, -0x1.273a44p-26f, 
+0x1.11d262p-6f, 0x1p-2f, 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, 
+0x1.788512p-5f, 0x1p-3f, 0x1.f8765p-1f, -0x1.63ad16p-27f, 
+0x1.640838p-6f, 0x1p-3f, 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, 
+0x1.6a904ap-7f, 0x1p-4f, 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, 
+0x1.b7aa82p-8f, -0x1p-5f, 0x1.ffd886p-1f, 0x1.099a1ap-30f, 
+0x1.b82684p-7f, -0x1p-4f, 0x1.ff621ep-1f, 0x1.bcb6bep-28f, 
+-0x1.6a904ap-7f, -0x1p-4f, 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, 
+-0x1.640838p-6f, -0x1p-3f, 0x1.fa7558p-1f, -0x1.eeb5d2p-30f, 
+-0x1.788512p-5f, -0x1p-3f, 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, 
+-0x1.11d262p-6f, -0x1p-2f, 0x1.ed740ep-1f, 0x1.da1258p-27f, 
+-0x1.4a0318p-5f, -0x1p-2f, 0x1.e9f416p-1f, -0x1.273a44p-26f, 
+-0x1.04d726p-4f, -0x1p-2f, 0x1.e6288ep-1f, 0x1.891c22p-26f, 
+-0x1.63e69ep-4f, -0x1p-2f, 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.ce1e64p-7f, -0x1p-1f, 0x1.b72834p-1f, 0x1.465b9p-27f, 
+-0x1.1eb354p-5f, -0x1p-1f, 0x1.b090a6p-1f, -0x1.fabf8p-27f, 
+-0x1.c73b3ap-5f, -0x1p-1f, 0x1.a9b662p-1f, 0x1.21d434p-26f, 
+-0x1.3682a6p-4f, -0x1p-1f, 0x1.a29a7ap-1f, 0x1.189e08p-31f, 
+-0x1.87fbfep-4f, -0x1p-1f, 0x1.9b3e04p-1f, 0x1.fce1dp-27f, 
+-0x1.d7fd14p-4f, -0x1p-1f, 0x1.93a224p-1f, 0x1.324c8p-26f, 
+-0x1.133ccap-3f, -0x1p-1f, 0x1.8bc806p-1f, 0x1.62a2e8p-26f, 
+-0x1.39b2aep-3f, -0x1p-1f, 0x1.83b0ep-1f, 0x1.7ff2eep-26f, 
+-0x1.5f5a4ep-3f, -0x1p-1f, 0x1.7b5df2p-1f, 0x1.3557d8p-28f, 
+-0x1.842dd6p-3f, -0x1p-1f, 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, 
+-0x1.842dd6p-3f, -0x1p-1f, -0x1.72d084p-1f, 0x1.02000ep-26f, 
+-0x1.5f5a4ep-3f, -0x1p-1f, -0x1.7b5df2p-1f, -0x1.3557d8p-28f, 
+-0x1.39b2aep-3f, -0x1p-1f, -0x1.83b0ep-1f, -0x1.7ff2eep-26f, 
+-0x1.133ccap-3f, -0x1p-1f, -0x1.8bc806p-1f, -0x1.62a2e8p-26f, 
+-0x1.d7fd14p-4f, -0x1p-1f, -0x1.93a224p-1f, -0x1.324c8p-26f, 
+-0x1.87fbfep-4f, -0x1p-1f, -0x1.9b3e04p-1f, -0x1.fce1dp-27f, 
+-0x1.3682a6p-4f, -0x1p-1f, -0x1.a29a7ap-1f, -0x1.189e08p-31f, 
+-0x1.c73b3ap-5f, -0x1p-1f, -0x1.a9b662p-1f, -0x1.21d434p-26f, 
+-0x1.1eb354p-5f, -0x1p-1f, -0x1.b090a6p-1f, 0x1.fabf8p-27f, 
+-0x1.ce1e64p-7f, -0x1p-1f, -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, 
+-0x1.63e69ep-4f, -0x1p-2f, -0x1.e2121p-1f, -0x1.3da1bap-27f, 
+-0x1.04d726p-4f, -0x1p-2f, -0x1.e6288ep-1f, -0x1.891c22p-26f, 
+-0x1.4a0318p-5f, -0x1p-2f, -0x1.e9f416p-1f, 0x1.273a44p-26f, 
+-0x1.11d262p-6f, -0x1p-2f, -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, 
+-0x1.788512p-5f, -0x1p-3f, -0x1.f8765p-1f, 0x1.63ad16p-27f, 
+-0x1.640838p-6f, -0x1p-3f, -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, 
+-0x1.6a904ap-7f, -0x1p-4f, -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.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, 
+0x1.6a904ap-7f, 0x1p-4f, -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, 
+0x1.640838p-6f, 0x1p-3f, -0x1.fa7558p-1f, 0x1.eeb5d2p-30f, 
+0x1.788512p-5f, 0x1p-3f, -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, 
+0x1.11d262p-6f, 0x1p-2f, -0x1.ed740ep-1f, -0x1.da1258p-27f, 
+0x1.4a0318p-5f, 0x1p-2f, -0x1.e9f416p-1f, 0x1.273a44p-26f, 
+0x1.04d726p-4f, 0x1p-2f, -0x1.e6288ep-1f, -0x1.891c22p-26f, 
+0x1.63e69ep-4f, 0x1p-2f, -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, 
@@ -221,16 +221,16 @@ template <> inline constexpr float kSinApproxTable<float>[] =
 -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.ce1e64p-7f, 0x1p-1f, -0x1.b72834p-1f, -0x1.465b9p-27f, 
+0x1.1eb354p-5f, 0x1p-1f, -0x1.b090a6p-1f, 0x1.fabf8p-27f, 
+0x1.c73b3ap-5f, 0x1p-1f, -0x1.a9b662p-1f, -0x1.21d434p-26f, 
+0x1.3682a6p-4f, 0x1p-1f, -0x1.a29a7ap-1f, -0x1.189e08p-31f, 
+0x1.87fbfep-4f, 0x1p-1f, -0x1.9b3e04p-1f, -0x1.fce1dp-27f, 
+0x1.d7fd14p-4f, 0x1p-1f, -0x1.93a224p-1f, -0x1.324c8p-26f, 
+0x1.133ccap-3f, 0x1p-1f, -0x1.8bc806p-1f, -0x1.62a2e8p-26f, 
+0x1.39b2aep-3f, 0x1p-1f, -0x1.83b0ep-1f, -0x1.7ff2eep-26f, 
+0x1.5f5a4ep-3f, 0x1p-1f, -0x1.7b5df2p-1f, -0x1.3557d8p-28f, 
+0x1.842dd6p-3f, 0x1p-1f, -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, 
@@ -326,33 +326,33 @@ template <> inline constexpr double kSinApproxTable<double>[] =
 -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.fe3b38d5c5dc2p-3, 0x1p-1, 0x1.5328292a35596p-1, -0x1.a12eb8p-56, 
+0x1.ed77c89aabebbp-3, 0x1p-1, 0x1.57d69348cecap-1, -0x1.757208p-55, 
+0x1.dc79d7c0dc985p-3, 0x1p-1, 0x1.5c77bbe65018cp-1, 0x1.069ea8p-55, 
+0x1.cb420dfbffe59p-3, 0x1p-1, 0x1.610b7551d2cdfp-1, -0x1.251b34p-56, 
+0x1.b9d1153aaa2bap-3, 0x1p-1, 0x1.6591925f0783dp-1, 0x1.c3d64ep-55, 
+0x1.a827999fcef32p-3, 0x1p-1, 0x1.6a09e667f3bcdp-1, -0x1.bdd34p-55, 
+0x1.9646497c1e0f6p-3, 0x1p-1, 0x1.6e74454eaa8afp-1, -0x1.dbc03cp-55, 
+0x1.842dd5474b37bp-3, 0x1p-1, 0x1.72d0837efff96p-1, 0x1.0d4efp-55, 
+0x1.71deef9940631p-3, 0x1p-1, 0x1.771e75f037261p-1, 0x1.5cfce8p-56, 
+0x1.5f5a4d233b27fp-3, 0x1p-1, 0x1.7b5df226aafafp-1, -0x1.0f537ap-56, 
+0x1.4ca0a4a8d5657p-3, 0x1p-1, 0x1.7f8ece3571771p-1, -0x1.9c8d8cp-55, 
+0x1.39b2aef8f97a4p-3, 0x1p-1, 0x1.83b0e0bff976ep-1, -0x1.6f420ep-56, 
+0x1.269126e6c24e3p-3, 0x1p-1, 0x1.87c400fba2ebfp-1, -0x1.2dabcp-55, 
+0x1.133cc94247758p-3, 0x1p-1, 0x1.8bc806b151741p-1, -0x1.2c5e12p-55, 
+0x1.ff6ca9a2ab6a2p-4, 0x1p-1, 0x1.8fbcca3ef940dp-1, -0x1.6dfa98p-57, 
+0x1.d7fd1490285cap-4, 0x1p-1, 0x1.93a22499263fbp-1, 0x1.3d419ap-55, 
+0x1.b02c58832cf96p-4, 0x1p-1, 0x1.9777ef4c7d742p-1, -0x1.15479ap-55, 
+0x1.87fbfe70b81a7p-4, 0x1p-1, 0x1.9b3e047f38741p-1, -0x1.30ee28p-55, 
+0x1.5f6d92fd79f5p-4, 0x1p-1, 0x1.9ef43ef29af94p-1, 0x1.b1dfcap-56, 
+0x1.3682a66e896f5p-4, 0x1p-1, 0x1.a29a7a0462782p-1, -0x1.128bbp-56, 
+0x1.0d3ccc99f5ac6p-4, 0x1p-1, 0x1.a63091b02fae2p-1, -0x1.e91114p-56, 
+0x1.c73b39ae68c87p-5, 0x1p-1, 0x1.a9b66290ea1a3p-1, 0x1.9f630ep-60, 
+0x1.734d63dedb48ap-5, 0x1p-1, 0x1.ad2bc9e21d511p-1, -0x1.47fbep-55, 
+0x1.1eb3541b4b228p-5, 0x1p-1, 0x1.b090a581502p-1, -0x1.926da2p-55, 
+0x1.92e09abb131d4p-6, 0x1p-1, 0x1.b3e4d3ef55712p-1, -0x1.eb6b8ap-55, 
+0x1.ce1e648bffb66p-7, 0x1p-1, 0x1.b728345196e3ep-1, -0x1.bc69f2p-55, 
+0x1.cfc874c3eb6d9p-9, 0x1p-1, 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, 
@@ -364,325 +364,325 @@ template <> inline constexpr double kSinApproxTable<double>[] =
 -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.f0ea4c477339cp-4, 0x1p-2, 0x1.db6526238a09bp-1, -0x1.adee7ep-56, 
+0x1.c2214c3e9167bp-4, 0x1p-2, 0x1.ddb13b6ccc23cp-1, 0x1.83c37cp-55, 
+0x1.931f774fc9f18p-4, 0x1p-2, 0x1.dfeae622dbe2bp-1, -0x1.514ea8p-55, 
+0x1.63e69d6ac7f74p-4, 0x1p-2, 0x1.e212104f686e5p-1, -0x1.014c76p-55, 
+0x1.3478909e39da9p-4, 0x1p-2, 0x1.e426a4b2bc17ep-1, 0x1.a87388p-55, 
+0x1.04d72505d9805p-4, 0x1p-2, 0x1.e6288ec48e112p-1, -0x1.16b56ep-57, 
+0x1.aa086170c0a8ep-5, 0x1p-2, 0x1.e817bab4cd10dp-1, -0x1.d0afe6p-56, 
+0x1.4a03176acf82dp-5, 0x1p-2, 0x1.e9f4156c62ddap-1, 0x1.760b1ep-55, 
+0x1.d3443f4cdb3ddp-6, 0x1p-2, 0x1.ebbd8c8df0b74p-1, 0x1.c6c8c6p-56, 
+0x1.11d262b1f6776p-6, 0x1p-2, 0x1.ed740e7684963p-1, 0x1.e82c78p-56, 
+0x1.3ee038dff6b8p-8, 0x1p-2, 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.db7677942fcc5p-5, 0x1p-3, 0x1.f7599a3a12077p-1, 0x1.84f31cp-55, 
+0x1.78851122cff19p-5, 0x1p-3, 0x1.f8764fa714ba9p-1, 0x1.ab2566p-56, 
+0x1.155dac4a4f967p-5, 0x1p-3, 0x1.f97f924c9099bp-1, -0x1.e2ae0ep-55, 
+0x1.64083747309d1p-6, 0x1p-3, 0x1.fa7557f08a517p-1, -0x1.7a0a8cp-55, 
+0x1.39f0cedaf576bp-7, 0x1p-3, 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, 
+0x1.7db402a6a9063p-6, 0x1p-4, 0x1.fe1cafcbd5b09p-1, 0x1.a23e32p-57, 
+0x1.6a9049670cfaep-7, 0x1p-4, 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, 
+0x1.6c32baca2ae69p-8, 0x1p-5, 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, 
 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, 
--0x1.02beda0153548p3, 0x1p3, 0x1.fe1cafcbd5b09p-1, 0x1.a23e32p-57, 
--0x1.0322f4d785368p3, 0x1p3, 0x1.fd88da3d12526p-1, -0x1.87df62p-55, 
--0x1.0386f0b8f3d86p3, 0x1p3, 0x1.fce15fd6da67bp-1, -0x1.5dd6f8p-56, 
--0x1.03eac9cad52e6p3, 0x1p3, 0x1.fc26470e19fd3p-1, 0x1.1ec866p-55, 
--0x1.089cf8676d7acp2, 0x1p2, 0x1.fb5797195d741p-1, 0x1.1bfac6p-56, 
--0x1.096408374730ap2, 0x1p2, 0x1.fa7557f08a517p-1, -0x1.7a0a8cp-55, 
--0x1.0a2abb58949f3p2, 0x1p2, 0x1.f97f924c9099bp-1, -0x1.e2ae0ep-55, 
--0x1.0af10a22459fep2, 0x1p2, 0x1.f8764fa714ba9p-1, 0x1.ab2566p-56, 
--0x1.0bb6ecef285fap2, 0x1p2, 0x1.f7599a3a12077p-1, 0x1.84f31cp-55, 
--0x1.0c7c5c1e34d3p2, 0x1p2, 0x1.f6297cff75cbp-1, 0x1.562172p-56, 
--0x1.0d415012d8023p2, 0x1p2, 0x1.f4e603b0b2f2dp-1, -0x1.8ee01ep-56, 
--0x1.0e05c1353f27bp2, 0x1p2, 0x1.f38f3ac64e589p-1, -0x1.d7bafap-56, 
--0x1.0ec9a7f2a2a19p2, 0x1p2, 0x1.f2252f7763adap-1, -0x1.20cb8p-55, 
--0x1.0f8cfcbd90af9p2, 0x1p2, 0x1.f0a7efb9230d7p-1, 0x1.52c7acp-56, 
--0x1.209f701c6ffb6p1, 0x1p1, 0x1.ef178a3e473c2p-1, 0x1.6310a6p-55, 
--0x1.2223a4c563ecfp1, 0x1p1, 0x1.ed740e7684963p-1, 0x1.e82c78p-56, 
--0x1.23a6887e99b68p1, 0x1p1, 0x1.ebbd8c8df0b74p-1, 0x1.c6c8c6p-56, 
--0x1.25280c5dab3e1p1, 0x1p1, 0x1.e9f4156c62ddap-1, 0x1.760b1ep-55, 
--0x1.26a82185c302ap1, 0x1p1, 0x1.e817bab4cd10dp-1, -0x1.d0afe6p-56, 
--0x1.2826b9282eccp1, 0x1p1, 0x1.e6288ec48e112p-1, -0x1.16b56ep-57, 
--0x1.29a3c484f1cedp1, 0x1p1, 0x1.e426a4b2bc17ep-1, 0x1.a87388p-55, 
--0x1.2b1f34eb563fcp1, 0x1p1, 0x1.e212104f686e5p-1, -0x1.014c76p-55, 
--0x1.2c98fbba7e4f9p1, 0x1p1, 0x1.dfeae622dbe2bp-1, -0x1.514ea8p-55, 
--0x1.2e110a61f48b4p1, 0x1p1, 0x1.ddb13b6ccc23cp-1, 0x1.83c37cp-55, 
--0x1.2f8752623b99dp1, 0x1p1, 0x1.db6526238a09bp-1, -0x1.adee7ep-56, 
--0x1.30fbc54d5d52cp1, 0x1p1, 0x1.d906bcf328d46p-1, 0x1.457e6p-56, 
--0x1.326e54c77927bp1, 0x1p1, 0x1.d696173c9e68bp-1, -0x1.e8c61cp-56, 
--0x1.33def28751db1p1, 0x1p1, 0x1.d4134d14dc93ap-1, -0x1.4ef528p-55, 
--0x1.354d9056da7f9p1, 0x1p1, 0x1.d17e7743e35dcp-1, -0x1.101da2p-58, 
--0x1.36ba2013c2b98p1, 0x1p1, 0x1.ced7af43cc773p-1, -0x1.e7b6bap-58, 
--0x1.382493b0023ddp1, 0x1p1, 0x1.cc1f0f3fcfc5cp-1, 0x1.e57612p-56, 
--0x1.398cdd326388cp1, 0x1p1, 0x1.c954b213411f5p-1, -0x1.2fb76p-58, 
--0x1.3af2eeb70dc71p1, 0x1p1, 0x1.c678b3488739bp-1, 0x1.d86cacp-57, 
--0x1.3c56ba700dec7p1, 0x1p1, 0x1.c38b2f180bdb1p-1, -0x1.6e0b16p-56, 
--0x1.3db832a5def1bp1, 0x1p1, 0x1.c08c426725549p-1, 0x1.b157fcp-58, 
--0x1.3f1749b7f1357p1, 0x1p1, 0x1.bd7c0ac6f952ap-1, -0x1.825a72p-55, 
--0x1.80e7e43a61f5bp0, 0x1p0, 0x1.ba5aa673590d2p-1, 0x1.7ea4e2p-55, 
--0x1.839c3cc917ff7p0, 0x1p0, 0x1.b728345196e3ep-1, -0x1.bc69f2p-55, 
--0x1.864b826aec4c7p0, 0x1p0, 0x1.b3e4d3ef55712p-1, -0x1.eb6b8ap-55, 
--0x1.88f59aa0da591p0, 0x1p0, 0x1.b090a581502p-1, -0x1.926da2p-55, 
--0x1.8b9a6b1ef6da4p0, 0x1p0, 0x1.ad2bc9e21d511p-1, -0x1.47fbep-55, 
--0x1.8e39d9cd73464p0, 0x1p0, 0x1.a9b66290ea1a3p-1, 0x1.9f630ep-60, 
--0x1.90d3ccc99f5acp0, 0x1p0, 0x1.a63091b02fae2p-1, -0x1.e91114p-56, 
--0x1.93682a66e896fp0, 0x1p0, 0x1.a29a7a0462782p-1, -0x1.128bbp-56, 
--0x1.95f6d92fd79f5p0, 0x1p0, 0x1.9ef43ef29af94p-1, 0x1.b1dfcap-56, 
--0x1.987fbfe70b81ap0, 0x1p0, 0x1.9b3e047f38741p-1, -0x1.30ee28p-55, 
--0x1.9b02c58832cf9p0, 0x1p0, 0x1.9777ef4c7d742p-1, -0x1.15479ap-55, 
--0x1.9d7fd1490285dp0, 0x1p0, 0x1.93a22499263fbp-1, 0x1.3d419ap-55, 
--0x1.9ff6ca9a2ab6ap0, 0x1p0, 0x1.8fbcca3ef940dp-1, -0x1.6dfa98p-57, 
--0x1.a267992848eebp0, 0x1p0, 0x1.8bc806b151741p-1, -0x1.2c5e12p-55, 
--0x1.a4d224dcd849cp0, 0x1p0, 0x1.87c400fba2ebfp-1, -0x1.2dabcp-55, 
--0x1.a73655df1f2f5p0, 0x1p0, 0x1.83b0e0bff976ep-1, -0x1.6f420ep-56, 
--0x1.a99414951aacbp0, 0x1p0, 0x1.7f8ece3571771p-1, -0x1.9c8d8cp-55, 
--0x1.abeb49a46765p0, 0x1p0, 0x1.7b5df226aafafp-1, -0x1.0f537ap-56, 
--0x1.ae3bddf3280c6p0, 0x1p0, 0x1.771e75f037261p-1, 0x1.5cfce8p-56, 
--0x1.b085baa8e966fp0, 0x1p0, 0x1.72d0837efff96p-1, 0x1.0d4efp-55, 
--0x1.b2c8c92f83c1fp0, 0x1p0, 0x1.6e74454eaa8afp-1, -0x1.dbc03cp-55, 
--0x1.b504f333f9de6p0, 0x1p0, 0x1.6a09e667f3bcdp-1, -0x1.bdd34p-55, 
--0x1.b73a22a755457p0, 0x1p0, 0x1.6591925f0783dp-1, 0x1.c3d64ep-55, 
--0x1.b96841bf7ffcbp0, 0x1p0, 0x1.610b7551d2cdfp-1, -0x1.251b34p-56, 
--0x1.bb8f3af81b931p0, 0x1p0, 0x1.5c77bbe65018cp-1, 0x1.069ea8p-55, 
--0x1.bdaef913557d7p0, 0x1p0, 0x1.57d69348cecap-1, -0x1.757208p-55, 
--0x1.bfc7671ab8bb8p0, 0x1p0, 0x1.5328292a35596p-1, -0x1.a12eb8p-56, 
--0x1.c1d8705ffcbb7p0, 0x1p0, 0x1.4e6cabbe3e5e9p-1, 0x1.3c293ep-57, 
--0x1.c3e2007dd175fp0, 0x1p0, 0x1.49a449b9b0939p-1, -0x1.27ee16p-55, 
--0x1.c5e40358a8bap0, 0x1p0, 0x1.44cf325091dd6p-1, 0x1.8076a2p-57, 
--0x1.c7de651f7ca06p0, 0x1p0, 0x1.3fed9534556d4p-1, 0x1.369166p-55, 
--0x1.c9d1124c931fep0, 0x1p0, 0x1.3affa292050b9p-1, 0x1.e3e25ep-56, 
--0x1.cbbbf7a63eba1p0, 0x1p0, 0x1.36058b10659f3p-1, -0x1.1fcb3ap-55, 
--0x1.cd9f023f9c3ap0, 0x1p0, 0x1.30ff7fce17035p-1, -0x1.efcc62p-57, 
--0x1.cf7a1f794d7cap0, 0x1p0, 0x1.2bedb25faf3eap-1, -0x1.14981cp-58, 
--0x1.d14d3d02313c1p0, 0x1p0, 0x1.26d054cdd12dfp-1, -0x1.5da742p-55, 
--0x1.d31848d817d71p0, 0x1p0, 0x1.21a799933eb59p-1, -0x1.3a7b16p-55, 
--0x1.d4db3148750d2p0, 0x1p0, 0x1.1c73b39ae68c8p-1, 0x1.b25dd2p-55, 
--0x1.d695e4f10ea88p0, 0x1p0, 0x1.1734d63dedb49p-1, -0x1.7eef2cp-55, 
--0x1.d84852c0a81p0, 0x1p0, 0x1.11eb3541b4b23p-1, -0x1.ef23b6p-55, 
--0x1.d9f269f7aab89p0, 0x1p0, 0x1.0c9704d5d898fp-1, -0x1.8d3d7cp-55, 
--0x1.db941a28cb71fp0, 0x1p0, 0x1.073879922ffeep-1, -0x1.a5a014p-55, 
--0x1.dd2d5339ac869p0, 0x1p0, 0x1.01cfc874c3eb7p-1, -0x1.34a35ep-56, 
--0x1.debe05637ca95p0, 0x1p0, 0x1.f8ba4dbf89abap-2, -0x1.2ec1fcp-60, 
--0x1.e046213392aa5p0, 0x1p0, 0x1.edc1952ef78d6p-2, -0x1.dd0f7cp-56, 
--0x1.e1c5978c05ed8p0, 0x1p0, 0x1.e2b5d3806f63bp-2, 0x1.e0d89p-58, 
--0x1.e33c59a4439cep0, 0x1p0, 0x1.d79775b86e389p-2, 0x1.550ec8p-56, 
--0x1.e4aa5909a08fap0, 0x1p0, 0x1.cc66e9931c45ep-2, 0x1.6850e4p-58, 
--0x1.e60f879fe7e2ep0, 0x1p0, 0x1.c1249d8011ee7p-2, -0x1.813aaap-56, 
--0x1.e76bd7a1e63b9p0, 0x1p0, 0x1.b5d1009e15ccp-2, 0x1.5b362cp-57, 
--0x1.e8bf3ba1f1aeep0, 0x1p0, 0x1.aa6c82b6d3fcap-2, -0x1.d5f106p-56, 
--0x1.ea09a68a6e49dp0, 0x1p0, 0x1.9ef7943a8ed8ap-2, 0x1.6da812p-57, 
--0x1.eb4b0b9e4f345p0, 0x1p0, 0x1.9372a63bc93d7p-2, 0x1.684318p-57, 
--0x1.ec835e79946a3p0, 0x1p0, 0x1.87de2a6aea963p-2, -0x1.72cedcp-57, 
--0x1.edb29311c504dp0, 0x1p0, 0x1.7c3a9311dcce7p-2, 0x1.9a3f2p-62, 
--0x1.eed89db66611ep0, 0x1p0, 0x1.7088530fa459fp-2, -0x1.44b19ep-56, 
--0x1.eff573116df15p0, 0x1p0, 0x1.64c7ddd3f27c6p-2, 0x1.10d2b4p-58, 
--0x1.f1090827b4372p0, 0x1p0, 0x1.58f9a75ab1fddp-2, -0x1.efdc0cp-62, 
--0x1.f21352595e0bfp0, 0x1p0, 0x1.4d1e24278e76ap-2, 0x1.24172p-57, 
--0x1.f314476247089p0, 0x1p0, 0x1.4135c94176601p-2, 0x1.0c97c4p-56, 
--0x1.f40bdd5a66886p0, 0x1p0, 0x1.35410c2e18152p-2, -0x1.3cb002p-56, 
--0x1.f4fa0ab6316edp0, 0x1p0, 0x1.294062ed59f06p-2, -0x1.5d28dap-56, 
--0x1.f5dec646f85bap0, 0x1p0, 0x1.1d3443f4cdb3ep-2, -0x1.720d4p-57, 
--0x1.f6ba073b424b2p0, 0x1p0, 0x1.111d262b1f677p-2, 0x1.824c2p-56, 
--0x1.f78bc51f239e1p0, 0x1p0, 0x1.04fb80e37fdaep-2, -0x1.412cdap-63, 
--0x1.f853f7dc9186cp0, 0x1p0, 0x1.f19f97b215f1bp-3, -0x1.42deeep-57, 
--0x1.f91297bbb1d6dp0, 0x1p0, 0x1.d934fe5454311p-3, 0x1.75b922p-57, 
--0x1.f9c79d63272c4p0, 0x1p0, 0x1.c0b826a7e4f63p-3, -0x1.af1438p-62, 
--0x1.fa7301d859796p0, 0x1p0, 0x1.a82a025b00451p-3, -0x1.87905ep-57, 
--0x1.fb14be7fbae58p0, 0x1p0, 0x1.8f8b83c69a60bp-3, -0x1.26d19ap-57, 
--0x1.fbaccd1d0903cp0, 0x1p0, 0x1.76dd9de50bf31p-3, 0x1.1d5eeep-57, 
--0x1.fc3b27d38a5d5p0, 0x1p0, 0x1.5e214448b3fc6p-3, 0x1.531ff6p-57, 
--0x1.fcbfc926484cdp0, 0x1p0, 0x1.45576b1293e5ap-3, -0x1.285a24p-58, 
--0x1.fd3aabf84528bp0, 0x1p0, 0x1.2c8106e8e613ap-3, 0x1.13000ap-58, 
--0x1.fdabcb8caeba1p0, 0x1p0, 0x1.139f0cedaf577p-3, -0x1.523434p-57, 
--0x1.fe1323870cfeap0, 0x1p0, 0x1.f564e56a9730ep-4, 0x1.a27046p-59, 
--0x1.fe70afeb6d33dp0, 0x1p0, 0x1.c3785c79ec2d5p-4, -0x1.4f39dep-61, 
--0x1.fec46d1e89293p0, 0x1p0, 0x1.917a6bc29b42cp-4, -0x1.e2718cp-60, 
--0x1.ff0e57e5ead85p0, 0x1p0, 0x1.5f6d00a9aa419p-4, -0x1.f4022cp-59, 
--0x1.ff4e6d680c41dp0, 0x1p0, 0x1.2d52092ce19f6p-4, -0x1.9a088ap-59, 
--0x1.ff84ab2c738d7p0, 0x1p0, 0x1.f656e79f820ep-5, -0x1.2e1ebep-61, 
--0x1.ffb10f1bcb6bfp0, 0x1p0, 0x1.91f65f10dd814p-5, -0x1.912bdp-61, 
--0x1.ffd3977ff7baep0, 0x1p0, 0x1.2d865759455cdp-5, 0x1.686f64p-61, 
--0x1.ffec430426686p0, 0x1p0, 0x1.92155f7a3667ep-6, -0x1.b1d63p-64, 
--0x1.fffb10b4dc96ep0, 0x1p0, 0x1.921d1fcdec784p-7, 0x1.9878eap-61, 
--0x1p1, 0x1p0, 0.0, 0.0, 
--0x1.fffb10b4dc96ep0, 0x1p0, -0x1.921d1fcdec784p-7, -0x1.9878eap-61, 
--0x1.ffec430426686p0, 0x1p0, -0x1.92155f7a3667ep-6, 0x1.b1d63p-64, 
--0x1.ffd3977ff7baep0, 0x1p0, -0x1.2d865759455cdp-5, -0x1.686f64p-61, 
--0x1.ffb10f1bcb6bfp0, 0x1p0, -0x1.91f65f10dd814p-5, 0x1.912bdp-61, 
--0x1.ff84ab2c738d7p0, 0x1p0, -0x1.f656e79f820ep-5, 0x1.2e1ebep-61, 
--0x1.ff4e6d680c41dp0, 0x1p0, -0x1.2d52092ce19f6p-4, 0x1.9a088ap-59, 
--0x1.ff0e57e5ead85p0, 0x1p0, -0x1.5f6d00a9aa419p-4, 0x1.f4022cp-59, 
--0x1.fec46d1e89293p0, 0x1p0, -0x1.917a6bc29b42cp-4, 0x1.e2718cp-60, 
--0x1.fe70afeb6d33dp0, 0x1p0, -0x1.c3785c79ec2d5p-4, 0x1.4f39dep-61, 
--0x1.fe1323870cfeap0, 0x1p0, -0x1.f564e56a9730ep-4, -0x1.a27046p-59, 
--0x1.fdabcb8caeba1p0, 0x1p0, -0x1.139f0cedaf577p-3, 0x1.523434p-57, 
--0x1.fd3aabf84528bp0, 0x1p0, -0x1.2c8106e8e613ap-3, -0x1.13000ap-58, 
--0x1.fcbfc926484cdp0, 0x1p0, -0x1.45576b1293e5ap-3, 0x1.285a24p-58, 
--0x1.fc3b27d38a5d5p0, 0x1p0, -0x1.5e214448b3fc6p-3, -0x1.531ff6p-57, 
--0x1.fbaccd1d0903cp0, 0x1p0, -0x1.76dd9de50bf31p-3, -0x1.1d5eeep-57, 
--0x1.fb14be7fbae58p0, 0x1p0, -0x1.8f8b83c69a60bp-3, 0x1.26d19ap-57, 
--0x1.fa7301d859796p0, 0x1p0, -0x1.a82a025b00451p-3, 0x1.87905ep-57, 
--0x1.f9c79d63272c4p0, 0x1p0, -0x1.c0b826a7e4f63p-3, 0x1.af1438p-62, 
--0x1.f91297bbb1d6dp0, 0x1p0, -0x1.d934fe5454311p-3, -0x1.75b922p-57, 
--0x1.f853f7dc9186cp0, 0x1p0, -0x1.f19f97b215f1bp-3, 0x1.42deeep-57, 
--0x1.f78bc51f239e1p0, 0x1p0, -0x1.04fb80e37fdaep-2, 0x1.412cdap-63, 
--0x1.f6ba073b424b2p0, 0x1p0, -0x1.111d262b1f677p-2, -0x1.824c2p-56, 
--0x1.f5dec646f85bap0, 0x1p0, -0x1.1d3443f4cdb3ep-2, 0x1.720d4p-57, 
--0x1.f4fa0ab6316edp0, 0x1p0, -0x1.294062ed59f06p-2, 0x1.5d28dap-56, 
--0x1.f40bdd5a66886p0, 0x1p0, -0x1.35410c2e18152p-2, 0x1.3cb002p-56, 
--0x1.f314476247089p0, 0x1p0, -0x1.4135c94176601p-2, -0x1.0c97c4p-56, 
--0x1.f21352595e0bfp0, 0x1p0, -0x1.4d1e24278e76ap-2, -0x1.24172p-57, 
--0x1.f1090827b4372p0, 0x1p0, -0x1.58f9a75ab1fddp-2, 0x1.efdc0cp-62, 
--0x1.eff573116df15p0, 0x1p0, -0x1.64c7ddd3f27c6p-2, -0x1.10d2b4p-58, 
--0x1.eed89db66611ep0, 0x1p0, -0x1.7088530fa459fp-2, 0x1.44b19ep-56, 
--0x1.edb29311c504dp0, 0x1p0, -0x1.7c3a9311dcce7p-2, -0x1.9a3f2p-62, 
--0x1.ec835e79946a3p0, 0x1p0, -0x1.87de2a6aea963p-2, 0x1.72cedcp-57, 
--0x1.eb4b0b9e4f345p0, 0x1p0, -0x1.9372a63bc93d7p-2, -0x1.684318p-57, 
--0x1.ea09a68a6e49dp0, 0x1p0, -0x1.9ef7943a8ed8ap-2, -0x1.6da812p-57, 
--0x1.e8bf3ba1f1aeep0, 0x1p0, -0x1.aa6c82b6d3fcap-2, 0x1.d5f106p-56, 
--0x1.e76bd7a1e63b9p0, 0x1p0, -0x1.b5d1009e15ccp-2, -0x1.5b362cp-57, 
--0x1.e60f879fe7e2ep0, 0x1p0, -0x1.c1249d8011ee7p-2, 0x1.813aaap-56, 
--0x1.e4aa5909a08fap0, 0x1p0, -0x1.cc66e9931c45ep-2, -0x1.6850e4p-58, 
--0x1.e33c59a4439cep0, 0x1p0, -0x1.d79775b86e389p-2, -0x1.550ec8p-56, 
--0x1.e1c5978c05ed8p0, 0x1p0, -0x1.e2b5d3806f63bp-2, -0x1.e0d89p-58, 
--0x1.e046213392aa5p0, 0x1p0, -0x1.edc1952ef78d6p-2, 0x1.dd0f7cp-56, 
--0x1.debe05637ca95p0, 0x1p0, -0x1.f8ba4dbf89abap-2, 0x1.2ec1fcp-60, 
--0x1.dd2d5339ac869p0, 0x1p0, -0x1.01cfc874c3eb7p-1, 0x1.34a35ep-56, 
--0x1.db941a28cb71fp0, 0x1p0, -0x1.073879922ffeep-1, 0x1.a5a014p-55, 
--0x1.d9f269f7aab89p0, 0x1p0, -0x1.0c9704d5d898fp-1, 0x1.8d3d7cp-55, 
--0x1.d84852c0a81p0, 0x1p0, -0x1.11eb3541b4b23p-1, 0x1.ef23b6p-55, 
--0x1.d695e4f10ea88p0, 0x1p0, -0x1.1734d63dedb49p-1, 0x1.7eef2cp-55, 
--0x1.d4db3148750d2p0, 0x1p0, -0x1.1c73b39ae68c8p-1, -0x1.b25dd2p-55, 
--0x1.d31848d817d71p0, 0x1p0, -0x1.21a799933eb59p-1, 0x1.3a7b16p-55, 
--0x1.d14d3d02313c1p0, 0x1p0, -0x1.26d054cdd12dfp-1, 0x1.5da742p-55, 
--0x1.cf7a1f794d7cap0, 0x1p0, -0x1.2bedb25faf3eap-1, 0x1.14981cp-58, 
--0x1.cd9f023f9c3ap0, 0x1p0, -0x1.30ff7fce17035p-1, 0x1.efcc62p-57, 
--0x1.cbbbf7a63eba1p0, 0x1p0, -0x1.36058b10659f3p-1, 0x1.1fcb3ap-55, 
--0x1.c9d1124c931fep0, 0x1p0, -0x1.3affa292050b9p-1, -0x1.e3e25ep-56, 
--0x1.c7de651f7ca06p0, 0x1p0, -0x1.3fed9534556d4p-1, -0x1.369166p-55, 
--0x1.c5e40358a8bap0, 0x1p0, -0x1.44cf325091dd6p-1, -0x1.8076a2p-57, 
--0x1.c3e2007dd175fp0, 0x1p0, -0x1.49a449b9b0939p-1, 0x1.27ee16p-55, 
--0x1.c1d8705ffcbb7p0, 0x1p0, -0x1.4e6cabbe3e5e9p-1, -0x1.3c293ep-57, 
--0x1.bfc7671ab8bb8p0, 0x1p0, -0x1.5328292a35596p-1, 0x1.a12eb8p-56, 
--0x1.bdaef913557d7p0, 0x1p0, -0x1.57d69348cecap-1, 0x1.757208p-55, 
--0x1.bb8f3af81b931p0, 0x1p0, -0x1.5c77bbe65018cp-1, -0x1.069ea8p-55, 
--0x1.b96841bf7ffcbp0, 0x1p0, -0x1.610b7551d2cdfp-1, 0x1.251b34p-56, 
--0x1.b73a22a755457p0, 0x1p0, -0x1.6591925f0783dp-1, -0x1.c3d64ep-55, 
--0x1.b504f333f9de6p0, 0x1p0, -0x1.6a09e667f3bcdp-1, 0x1.bdd34p-55, 
--0x1.b2c8c92f83c1fp0, 0x1p0, -0x1.6e74454eaa8afp-1, 0x1.dbc03cp-55, 
--0x1.b085baa8e966fp0, 0x1p0, -0x1.72d0837efff96p-1, -0x1.0d4efp-55, 
--0x1.ae3bddf3280c6p0, 0x1p0, -0x1.771e75f037261p-1, -0x1.5cfce8p-56, 
--0x1.abeb49a46765p0, 0x1p0, -0x1.7b5df226aafafp-1, 0x1.0f537ap-56, 
--0x1.a99414951aacbp0, 0x1p0, -0x1.7f8ece3571771p-1, 0x1.9c8d8cp-55, 
--0x1.a73655df1f2f5p0, 0x1p0, -0x1.83b0e0bff976ep-1, 0x1.6f420ep-56, 
--0x1.a4d224dcd849cp0, 0x1p0, -0x1.87c400fba2ebfp-1, 0x1.2dabcp-55, 
--0x1.a267992848eebp0, 0x1p0, -0x1.8bc806b151741p-1, 0x1.2c5e12p-55, 
--0x1.9ff6ca9a2ab6ap0, 0x1p0, -0x1.8fbcca3ef940dp-1, 0x1.6dfa98p-57, 
--0x1.9d7fd1490285dp0, 0x1p0, -0x1.93a22499263fbp-1, -0x1.3d419ap-55, 
--0x1.9b02c58832cf9p0, 0x1p0, -0x1.9777ef4c7d742p-1, 0x1.15479ap-55, 
--0x1.987fbfe70b81ap0, 0x1p0, -0x1.9b3e047f38741p-1, 0x1.30ee28p-55, 
--0x1.95f6d92fd79f5p0, 0x1p0, -0x1.9ef43ef29af94p-1, -0x1.b1dfcap-56, 
--0x1.93682a66e896fp0, 0x1p0, -0x1.a29a7a0462782p-1, 0x1.128bbp-56, 
--0x1.90d3ccc99f5acp0, 0x1p0, -0x1.a63091b02fae2p-1, 0x1.e91114p-56, 
--0x1.8e39d9cd73464p0, 0x1p0, -0x1.a9b66290ea1a3p-1, -0x1.9f630ep-60, 
--0x1.8b9a6b1ef6da4p0, 0x1p0, -0x1.ad2bc9e21d511p-1, 0x1.47fbep-55, 
--0x1.88f59aa0da591p0, 0x1p0, -0x1.b090a581502p-1, 0x1.926da2p-55, 
--0x1.864b826aec4c7p0, 0x1p0, -0x1.b3e4d3ef55712p-1, 0x1.eb6b8ap-55, 
--0x1.839c3cc917ff7p0, 0x1p0, -0x1.b728345196e3ep-1, 0x1.bc69f2p-55, 
--0x1.80e7e43a61f5bp0, 0x1p0, -0x1.ba5aa673590d2p-1, -0x1.7ea4e2p-55, 
--0x1.3f1749b7f1357p1, 0x1p1, -0x1.bd7c0ac6f952ap-1, 0x1.825a72p-55, 
--0x1.3db832a5def1bp1, 0x1p1, -0x1.c08c426725549p-1, -0x1.b157fcp-58, 
--0x1.3c56ba700dec7p1, 0x1p1, -0x1.c38b2f180bdb1p-1, 0x1.6e0b16p-56, 
--0x1.3af2eeb70dc71p1, 0x1p1, -0x1.c678b3488739bp-1, -0x1.d86cacp-57, 
--0x1.398cdd326388cp1, 0x1p1, -0x1.c954b213411f5p-1, 0x1.2fb76p-58, 
--0x1.382493b0023ddp1, 0x1p1, -0x1.cc1f0f3fcfc5cp-1, -0x1.e57612p-56, 
--0x1.36ba2013c2b98p1, 0x1p1, -0x1.ced7af43cc773p-1, 0x1.e7b6bap-58, 
--0x1.354d9056da7f9p1, 0x1p1, -0x1.d17e7743e35dcp-1, 0x1.101da2p-58, 
--0x1.33def28751db1p1, 0x1p1, -0x1.d4134d14dc93ap-1, 0x1.4ef528p-55, 
--0x1.326e54c77927bp1, 0x1p1, -0x1.d696173c9e68bp-1, 0x1.e8c61cp-56, 
--0x1.30fbc54d5d52cp1, 0x1p1, -0x1.d906bcf328d46p-1, -0x1.457e6p-56, 
--0x1.2f8752623b99dp1, 0x1p1, -0x1.db6526238a09bp-1, 0x1.adee7ep-56, 
--0x1.2e110a61f48b4p1, 0x1p1, -0x1.ddb13b6ccc23cp-1, -0x1.83c37cp-55, 
--0x1.2c98fbba7e4f9p1, 0x1p1, -0x1.dfeae622dbe2bp-1, 0x1.514ea8p-55, 
--0x1.2b1f34eb563fcp1, 0x1p1, -0x1.e212104f686e5p-1, 0x1.014c76p-55, 
--0x1.29a3c484f1cedp1, 0x1p1, -0x1.e426a4b2bc17ep-1, -0x1.a87388p-55, 
--0x1.2826b9282eccp1, 0x1p1, -0x1.e6288ec48e112p-1, 0x1.16b56ep-57, 
--0x1.26a82185c302ap1, 0x1p1, -0x1.e817bab4cd10dp-1, 0x1.d0afe6p-56, 
--0x1.25280c5dab3e1p1, 0x1p1, -0x1.e9f4156c62ddap-1, -0x1.760b1ep-55, 
--0x1.23a6887e99b68p1, 0x1p1, -0x1.ebbd8c8df0b74p-1, -0x1.c6c8c6p-56, 
--0x1.2223a4c563ecfp1, 0x1p1, -0x1.ed740e7684963p-1, -0x1.e82c78p-56, 
--0x1.209f701c6ffb6p1, 0x1p1, -0x1.ef178a3e473c2p-1, -0x1.6310a6p-55, 
--0x1.0f8cfcbd90af9p2, 0x1p2, -0x1.f0a7efb9230d7p-1, -0x1.52c7acp-56, 
--0x1.0ec9a7f2a2a19p2, 0x1p2, -0x1.f2252f7763adap-1, 0x1.20cb8p-55, 
--0x1.0e05c1353f27bp2, 0x1p2, -0x1.f38f3ac64e589p-1, 0x1.d7bafap-56, 
--0x1.0d415012d8023p2, 0x1p2, -0x1.f4e603b0b2f2dp-1, 0x1.8ee01ep-56, 
--0x1.0c7c5c1e34d3p2, 0x1p2, -0x1.f6297cff75cbp-1, -0x1.562172p-56, 
--0x1.0bb6ecef285fap2, 0x1p2, -0x1.f7599a3a12077p-1, -0x1.84f31cp-55, 
--0x1.0af10a22459fep2, 0x1p2, -0x1.f8764fa714ba9p-1, -0x1.ab2566p-56, 
--0x1.0a2abb58949f3p2, 0x1p2, -0x1.f97f924c9099bp-1, 0x1.e2ae0ep-55, 
--0x1.096408374730ap2, 0x1p2, -0x1.fa7557f08a517p-1, 0x1.7a0a8cp-55, 
--0x1.089cf8676d7acp2, 0x1p2, -0x1.fb5797195d741p-1, -0x1.1bfac6p-56, 
--0x1.03eac9cad52e6p3, 0x1p3, -0x1.fc26470e19fd3p-1, -0x1.1ec866p-55, 
--0x1.0386f0b8f3d86p3, 0x1p3, -0x1.fce15fd6da67bp-1, 0x1.5dd6f8p-56, 
--0x1.0322f4d785368p3, 0x1p3, -0x1.fd88da3d12526p-1, 0x1.87df62p-55, 
--0x1.02beda0153548p3, 0x1p3, -0x1.fe1cafcbd5b09p-1, -0x1.a23e32p-57, 
--0x1.025aa41259c34p3, 0x1p3, -0x1.fe9cdad01883ap-1, -0x1.521eccp-57, 
--0x1.00fb2b73cfc1p4, 0x1p4, -0x1.ff095658e71adp-1, -0x1.01a8cep-55, 
--0x1.00c8fb2f886ecp4, 0x1p4, -0x1.ff621e3796d7ep-1, 0x1.c57bc2p-57, 
--0x1.0096c32baca2bp4, 0x1p4, -0x1.ffa72effef75dp-1, 0x1.8b4cdcp-55, 
--0x1.003242abef46dp5, 0x1p5, -0x1.ffd886084cd0dp-1, 0x1.1354d4p-55, 
--0x1.000c90e8fe6f6p6, 0x1p6, -0x1.fff62169b92dbp-1, -0x1.5dda3cp-55, 
+0x1.b78b80c84e1eep-9, -0x1p-6, 0x1.fff62169b92dbp-1, 0x1.5dda3cp-55, 
+0x1.b7aa821726608p-8, -0x1p-5, 0x1.ffd886084cd0dp-1, -0x1.1354d4p-55, 
+-0x1.6c32baca2ae69p-8, -0x1p-5, 0x1.ffa72effef75dp-1, -0x1.8b4cdcp-55, 
+0x1.b82683bc89fbp-7, -0x1p-4, 0x1.ff621e3796d7ep-1, -0x1.c57bc2p-57, 
+0x1.35230c0fbe402p-10, -0x1p-4, 0x1.ff095658e71adp-1, 0x1.01a8cep-55, 
+-0x1.6a9049670cfaep-7, -0x1p-4, 0x1.fe9cdad01883ap-1, 0x1.521eccp-57, 
+-0x1.7db402a6a9063p-6, -0x1p-4, 0x1.fe1cafcbd5b09p-1, 0x1.a23e32p-57, 
+0x1.ba1650f592f5p-6, -0x1p-3, 0x1.fd88da3d12526p-1, -0x1.87df62p-55, 
+0x1.e43d1c309e958p-7, -0x1p-3, 0x1.fce15fd6da67bp-1, -0x1.5dd6f8p-56, 
+0x1.536352ad19e39p-9, -0x1p-3, 0x1.fc26470e19fd3p-1, 0x1.1ec866p-55, 
+-0x1.39f0cedaf576bp-7, -0x1p-3, 0x1.fb5797195d741p-1, 0x1.1bfac6p-56, 
+-0x1.64083747309d1p-6, -0x1p-3, 0x1.fa7557f08a517p-1, -0x1.7a0a8cp-55, 
+-0x1.155dac4a4f967p-5, -0x1p-3, 0x1.f97f924c9099bp-1, -0x1.e2ae0ep-55, 
+-0x1.78851122cff19p-5, -0x1p-3, 0x1.f8764fa714ba9p-1, 0x1.ab2566p-56, 
+-0x1.db7677942fcc5p-5, -0x1p-3, 0x1.f7599a3a12077p-1, 0x1.84f31cp-55, 
+0x1.c1d1f0e5967d5p-5, -0x1p-2, 0x1.f6297cff75cbp-1, 0x1.562172p-56, 
+0x1.5f57f693feebep-5, -0x1p-2, 0x1.f4e603b0b2f2dp-1, -0x1.8ee01ep-56, 
+0x1.fa3ecac0d84e8p-6, -0x1p-2, 0x1.f38f3ac64e589p-1, -0x1.d7bafap-56, 
+0x1.36580d5d5e775p-6, -0x1p-2, 0x1.f2252f7763adap-1, -0x1.20cb8p-55, 
+0x1.cc0d09bd41caap-8, -0x1p-2, 0x1.f0a7efb9230d7p-1, 0x1.52c7acp-56, 
+-0x1.3ee038dff6b8p-8, -0x1p-2, 0x1.ef178a3e473c2p-1, 0x1.6310a6p-55, 
+-0x1.11d262b1f6776p-6, -0x1p-2, 0x1.ed740e7684963p-1, 0x1.e82c78p-56, 
+-0x1.d3443f4cdb3ddp-6, -0x1p-2, 0x1.ebbd8c8df0b74p-1, 0x1.c6c8c6p-56, 
+-0x1.4a03176acf82dp-5, -0x1p-2, 0x1.e9f4156c62ddap-1, 0x1.760b1ep-55, 
+-0x1.aa086170c0a8ep-5, -0x1p-2, 0x1.e817bab4cd10dp-1, -0x1.d0afe6p-56, 
+-0x1.04d72505d9805p-4, -0x1p-2, 0x1.e6288ec48e112p-1, -0x1.16b56ep-57, 
+-0x1.3478909e39da9p-4, -0x1p-2, 0x1.e426a4b2bc17ep-1, 0x1.a87388p-55, 
+-0x1.63e69d6ac7f74p-4, -0x1p-2, 0x1.e212104f686e5p-1, -0x1.014c76p-55, 
+-0x1.931f774fc9f18p-4, -0x1p-2, 0x1.dfeae622dbe2bp-1, -0x1.514ea8p-55, 
+-0x1.c2214c3e9167bp-4, -0x1p-2, 0x1.ddb13b6ccc23cp-1, 0x1.83c37cp-55, 
+-0x1.f0ea4c477339cp-4, -0x1p-2, 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.cfc874c3eb6d9p-9, -0x1p-1, 0x1.ba5aa673590d2p-1, 0x1.7ea4e2p-55, 
+-0x1.ce1e648bffb66p-7, -0x1p-1, 0x1.b728345196e3ep-1, -0x1.bc69f2p-55, 
+-0x1.92e09abb131d4p-6, -0x1p-1, 0x1.b3e4d3ef55712p-1, -0x1.eb6b8ap-55, 
+-0x1.1eb3541b4b228p-5, -0x1p-1, 0x1.b090a581502p-1, -0x1.926da2p-55, 
+-0x1.734d63dedb48ap-5, -0x1p-1, 0x1.ad2bc9e21d511p-1, -0x1.47fbep-55, 
+-0x1.c73b39ae68c87p-5, -0x1p-1, 0x1.a9b66290ea1a3p-1, 0x1.9f630ep-60, 
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+-0x1.269126e6c24e3p-3, -0x1p-1, -0x1.87c400fba2ebfp-1, 0x1.2dabcp-55, 
+-0x1.133cc94247758p-3, -0x1p-1, -0x1.8bc806b151741p-1, 0x1.2c5e12p-55, 
+-0x1.ff6ca9a2ab6a2p-4, -0x1p-1, -0x1.8fbcca3ef940dp-1, 0x1.6dfa98p-57, 
+-0x1.d7fd1490285cap-4, -0x1p-1, -0x1.93a22499263fbp-1, -0x1.3d419ap-55, 
+-0x1.b02c58832cf96p-4, -0x1p-1, -0x1.9777ef4c7d742p-1, 0x1.15479ap-55, 
+-0x1.87fbfe70b81a7p-4, -0x1p-1, -0x1.9b3e047f38741p-1, 0x1.30ee28p-55, 
+-0x1.5f6d92fd79f5p-4, -0x1p-1, -0x1.9ef43ef29af94p-1, -0x1.b1dfcap-56, 
+-0x1.3682a66e896f5p-4, -0x1p-1, -0x1.a29a7a0462782p-1, 0x1.128bbp-56, 
+-0x1.0d3ccc99f5ac6p-4, -0x1p-1, -0x1.a63091b02fae2p-1, 0x1.e91114p-56, 
+-0x1.c73b39ae68c87p-5, -0x1p-1, -0x1.a9b66290ea1a3p-1, -0x1.9f630ep-60, 
+-0x1.734d63dedb48ap-5, -0x1p-1, -0x1.ad2bc9e21d511p-1, 0x1.47fbep-55, 
+-0x1.1eb3541b4b228p-5, -0x1p-1, -0x1.b090a581502p-1, 0x1.926da2p-55, 
+-0x1.92e09abb131d4p-6, -0x1p-1, -0x1.b3e4d3ef55712p-1, 0x1.eb6b8ap-55, 
+-0x1.ce1e648bffb66p-7, -0x1p-1, -0x1.b728345196e3ep-1, 0x1.bc69f2p-55, 
+-0x1.cfc874c3eb6d9p-9, -0x1p-1, -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.f0ea4c477339cp-4, -0x1p-2, -0x1.db6526238a09bp-1, 0x1.adee7ep-56, 
+-0x1.c2214c3e9167bp-4, -0x1p-2, -0x1.ddb13b6ccc23cp-1, -0x1.83c37cp-55, 
+-0x1.931f774fc9f18p-4, -0x1p-2, -0x1.dfeae622dbe2bp-1, 0x1.514ea8p-55, 
+-0x1.63e69d6ac7f74p-4, -0x1p-2, -0x1.e212104f686e5p-1, 0x1.014c76p-55, 
+-0x1.3478909e39da9p-4, -0x1p-2, -0x1.e426a4b2bc17ep-1, -0x1.a87388p-55, 
+-0x1.04d72505d9805p-4, -0x1p-2, -0x1.e6288ec48e112p-1, 0x1.16b56ep-57, 
+-0x1.aa086170c0a8ep-5, -0x1p-2, -0x1.e817bab4cd10dp-1, 0x1.d0afe6p-56, 
+-0x1.4a03176acf82dp-5, -0x1p-2, -0x1.e9f4156c62ddap-1, -0x1.760b1ep-55, 
+-0x1.d3443f4cdb3ddp-6, -0x1p-2, -0x1.ebbd8c8df0b74p-1, -0x1.c6c8c6p-56, 
+-0x1.11d262b1f6776p-6, -0x1p-2, -0x1.ed740e7684963p-1, -0x1.e82c78p-56, 
+-0x1.3ee038dff6b8p-8, -0x1p-2, -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.db7677942fcc5p-5, -0x1p-3, -0x1.f7599a3a12077p-1, -0x1.84f31cp-55, 
+-0x1.78851122cff19p-5, -0x1p-3, -0x1.f8764fa714ba9p-1, -0x1.ab2566p-56, 
+-0x1.155dac4a4f967p-5, -0x1p-3, -0x1.f97f924c9099bp-1, 0x1.e2ae0ep-55, 
+-0x1.64083747309d1p-6, -0x1p-3, -0x1.fa7557f08a517p-1, 0x1.7a0a8cp-55, 
+-0x1.39f0cedaf576bp-7, -0x1p-3, -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, 
+-0x1.7db402a6a9063p-6, -0x1p-4, -0x1.fe1cafcbd5b09p-1, -0x1.a23e32p-57, 
+-0x1.6a9049670cfaep-7, -0x1p-4, -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, 
+-0x1.6c32baca2ae69p-8, -0x1p-5, -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, 
 0.0, 0.0, -0x1p0, 0.0, 
 -0x1.b78b80c84e1eep-9, 0x1p-6, -0x1.fff62169b92dbp-1, -0x1.5dda3cp-55, 
 -0x1.b7aa821726608p-8, 0x1p-5, -0x1.ffd886084cd0dp-1, 0x1.1354d4p-55, 
--0x1.a4f3514d75466p-6, 0x1p-4, -0x1.ffa72effef75dp-1, 0x1.8b4cdcp-55, 
+0x1.6c32baca2ae69p-8, 0x1p-5, -0x1.ffa72effef75dp-1, 0x1.8b4cdcp-55, 
 -0x1.b82683bc89fbp-7, 0x1p-4, -0x1.ff621e3796d7ep-1, 0x1.c57bc2p-57, 
 -0x1.35230c0fbe402p-10, 0x1p-4, -0x1.ff095658e71adp-1, -0x1.01a8cep-55, 
--0x1.a55beda63cc14p-5, 0x1p-3, -0x1.fe9cdad01883ap-1, -0x1.521eccp-57, 
--0x1.4125feacab7cep-5, 0x1p-3, -0x1.fe1cafcbd5b09p-1, -0x1.a23e32p-57, 
+0x1.6a9049670cfaep-7, 0x1p-4, -0x1.fe9cdad01883ap-1, -0x1.521eccp-57, 
+0x1.7db402a6a9063p-6, 0x1p-4, -0x1.fe1cafcbd5b09p-1, -0x1.a23e32p-57, 
 -0x1.ba1650f592f5p-6, 0x1p-3, -0x1.fd88da3d12526p-1, 0x1.87df62p-55, 
 -0x1.e43d1c309e958p-7, 0x1p-3, -0x1.fce15fd6da67bp-1, 0x1.5dd6f8p-56, 
 -0x1.536352ad19e39p-9, 0x1p-3, -0x1.fc26470e19fd3p-1, -0x1.1ec866p-55, 
--0x1.d8c1e624a1513p-4, 0x1p-2, -0x1.fb5797195d741p-1, -0x1.1bfac6p-56, 
--0x1.a6fdf22e33d8cp-4, 0x1p-2, -0x1.fa7557f08a517p-1, 0x1.7a0a8cp-55, 
--0x1.755129dad834cp-4, 0x1p-2, -0x1.f97f924c9099bp-1, 0x1.e2ae0ep-55, 
--0x1.43bd776e98073p-4, 0x1p-2, -0x1.f8764fa714ba9p-1, -0x1.ab2566p-56, 
--0x1.1244c435e819dp-4, 0x1p-2, -0x1.f7599a3a12077p-1, -0x1.84f31cp-55, 
+0x1.39f0cedaf576bp-7, 0x1p-3, -0x1.fb5797195d741p-1, -0x1.1bfac6p-56, 
+0x1.64083747309d1p-6, 0x1p-3, -0x1.fa7557f08a517p-1, 0x1.7a0a8cp-55, 
+0x1.155dac4a4f967p-5, 0x1p-3, -0x1.f97f924c9099bp-1, 0x1.e2ae0ep-55, 
+0x1.78851122cff19p-5, 0x1p-3, -0x1.f8764fa714ba9p-1, -0x1.ab2566p-56, 
+0x1.db7677942fcc5p-5, 0x1p-3, -0x1.f7599a3a12077p-1, -0x1.84f31cp-55, 
 -0x1.c1d1f0e5967d5p-5, 0x1p-2, -0x1.f6297cff75cbp-1, -0x1.562172p-56, 
 -0x1.5f57f693feebep-5, 0x1p-2, -0x1.f4e603b0b2f2dp-1, 0x1.8ee01ep-56, 
 -0x1.fa3ecac0d84e8p-6, 0x1p-2, -0x1.f38f3ac64e589p-1, 0x1.d7bafap-56, 
 -0x1.36580d5d5e775p-6, 0x1p-2, -0x1.f2252f7763adap-1, 0x1.20cb8p-55, 
 -0x1.cc0d09bd41caap-8, 0x1p-2, -0x1.f0a7efb9230d7p-1, -0x1.52c7acp-56, 
--0x1.f608fe39004a4p-3, 0x1p-1, -0x1.ef178a3e473c2p-1, -0x1.6310a6p-55, 
--0x1.ddc5b3a9c1311p-3, 0x1p-1, -0x1.ed740e7684963p-1, -0x1.e82c78p-56, 
--0x1.c597781664984p-3, 0x1p-1, -0x1.ebbd8c8df0b74p-1, -0x1.c6c8c6p-56, 
--0x1.ad7f3a254c1f5p-3, 0x1p-1, -0x1.e9f4156c62ddap-1, -0x1.760b1ep-55, 
--0x1.957de7a3cfd5dp-3, 0x1p-1, -0x1.e817bab4cd10dp-1, 0x1.d0afe6p-56, 
--0x1.7d946d7d133fdp-3, 0x1p-1, -0x1.e6288ec48e112p-1, 0x1.16b56ep-57, 
--0x1.65c3b7b0e312cp-3, 0x1p-1, -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, 
+0x1.3ee038dff6b8p-8, 0x1p-2, -0x1.ef178a3e473c2p-1, -0x1.6310a6p-55, 
+0x1.11d262b1f6776p-6, 0x1p-2, -0x1.ed740e7684963p-1, -0x1.e82c78p-56, 
+0x1.d3443f4cdb3ddp-6, 0x1p-2, -0x1.ebbd8c8df0b74p-1, -0x1.c6c8c6p-56, 
+0x1.4a03176acf82dp-5, 0x1p-2, -0x1.e9f4156c62ddap-1, -0x1.760b1ep-55, 
+0x1.aa086170c0a8ep-5, 0x1p-2, -0x1.e817bab4cd10dp-1, 0x1.d0afe6p-56, 
+0x1.04d72505d9805p-4, 0x1p-2, -0x1.e6288ec48e112p-1, 0x1.16b56ep-57, 
+0x1.3478909e39da9p-4, 0x1p-2, -0x1.e426a4b2bc17ep-1, -0x1.a87388p-55, 
+0x1.63e69d6ac7f74p-4, 0x1p-2, -0x1.e212104f686e5p-1, 0x1.014c76p-55, 
+0x1.931f774fc9f18p-4, 0x1p-2, -0x1.dfeae622dbe2bp-1, 0x1.514ea8p-55, 
+0x1.c2214c3e9167bp-4, 0x1p-2, -0x1.ddb13b6ccc23cp-1, -0x1.83c37cp-55, 
+0x1.f0ea4c477339cp-4, 0x1p-2, -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, 
@@ -694,33 +694,33 @@ template <> inline constexpr double kSinApproxTable<double>[] =
 -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.cfc874c3eb6d9p-9, 0x1p-1, -0x1.ba5aa673590d2p-1, -0x1.7ea4e2p-55, 
+0x1.ce1e648bffb66p-7, 0x1p-1, -0x1.b728345196e3ep-1, 0x1.bc69f2p-55, 
+0x1.92e09abb131d4p-6, 0x1p-1, -0x1.b3e4d3ef55712p-1, 0x1.eb6b8ap-55, 
+0x1.1eb3541b4b228p-5, 0x1p-1, -0x1.b090a581502p-1, 0x1.926da2p-55, 
+0x1.734d63dedb48ap-5, 0x1p-1, -0x1.ad2bc9e21d511p-1, 0x1.47fbep-55, 
+0x1.c73b39ae68c87p-5, 0x1p-1, -0x1.a9b66290ea1a3p-1, -0x1.9f630ep-60, 
+0x1.0d3ccc99f5ac6p-4, 0x1p-1, -0x1.a63091b02fae2p-1, 0x1.e91114p-56, 
+0x1.3682a66e896f5p-4, 0x1p-1, -0x1.a29a7a0462782p-1, 0x1.128bbp-56, 
+0x1.5f6d92fd79f5p-4, 0x1p-1, -0x1.9ef43ef29af94p-1, -0x1.b1dfcap-56, 
+0x1.87fbfe70b81a7p-4, 0x1p-1, -0x1.9b3e047f38741p-1, 0x1.30ee28p-55, 
+0x1.b02c58832cf96p-4, 0x1p-1, -0x1.9777ef4c7d742p-1, 0x1.15479ap-55, 
+0x1.d7fd1490285cap-4, 0x1p-1, -0x1.93a22499263fbp-1, -0x1.3d419ap-55, 
+0x1.ff6ca9a2ab6a2p-4, 0x1p-1, -0x1.8fbcca3ef940dp-1, 0x1.6dfa98p-57, 
+0x1.133cc94247758p-3, 0x1p-1, -0x1.8bc806b151741p-1, 0x1.2c5e12p-55, 
+0x1.269126e6c24e3p-3, 0x1p-1, -0x1.87c400fba2ebfp-1, 0x1.2dabcp-55, 
+0x1.39b2aef8f97a4p-3, 0x1p-1, -0x1.83b0e0bff976ep-1, 0x1.6f420ep-56, 
+0x1.4ca0a4a8d5657p-3, 0x1p-1, -0x1.7f8ece3571771p-1, 0x1.9c8d8cp-55, 
+0x1.5f5a4d233b27fp-3, 0x1p-1, -0x1.7b5df226aafafp-1, 0x1.0f537ap-56, 
+0x1.71deef9940631p-3, 0x1p-1, -0x1.771e75f037261p-1, -0x1.5cfce8p-56, 
+0x1.842dd5474b37bp-3, 0x1p-1, -0x1.72d0837efff96p-1, -0x1.0d4efp-55, 
+0x1.9646497c1e0f6p-3, 0x1p-1, -0x1.6e74454eaa8afp-1, 0x1.dbc03cp-55, 
+0x1.a827999fcef32p-3, 0x1p-1, -0x1.6a09e667f3bcdp-1, 0x1.bdd34p-55, 
+0x1.b9d1153aaa2bap-3, 0x1p-1, -0x1.6591925f0783dp-1, -0x1.c3d64ep-55, 
+0x1.cb420dfbffe59p-3, 0x1p-1, -0x1.610b7551d2cdfp-1, 0x1.251b34p-56, 
+0x1.dc79d7c0dc985p-3, 0x1p-1, -0x1.5c77bbe65018cp-1, -0x1.069ea8p-55, 
+0x1.ed77c89aabebbp-3, 0x1p-1, -0x1.57d69348cecap-1, 0x1.757208p-55, 
+0x1.fe3b38d5c5dc2p-3, 0x1p-1, -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, 
@@ -785,148 +785,148 @@ template <typename T> inline constexpr char kCosApproxTable[] = {};
 template <> inline constexpr float kCosApproxTable<float>[] = 
 {
 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, 
+0x1.b7aa82p-8f, -0x1p-5f, 0x1.ffd886p-1f, 0x1.099a1ap-30f, 
+0x1.b82684p-7f, -0x1p-4f, 0x1.ff621ep-1f, 0x1.bcb6bep-28f, 
+-0x1.6a904ap-7f, -0x1p-4f, 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, 
+-0x1.640838p-6f, -0x1p-3f, 0x1.fa7558p-1f, -0x1.eeb5d2p-30f, 
+-0x1.788512p-5f, -0x1p-3f, 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, 
+-0x1.11d262p-6f, -0x1p-2f, 0x1.ed740ep-1f, 0x1.da1258p-27f, 
+-0x1.4a0318p-5f, -0x1p-2f, 0x1.e9f416p-1f, -0x1.273a44p-26f, 
+-0x1.04d726p-4f, -0x1p-2f, 0x1.e6288ep-1f, 0x1.891c22p-26f, 
+-0x1.63e69ep-4f, -0x1p-2f, 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.ce1e64p-7f, -0x1p-1f, 0x1.b72834p-1f, 0x1.465b9p-27f, 
+-0x1.1eb354p-5f, -0x1p-1f, 0x1.b090a6p-1f, -0x1.fabf8p-27f, 
+-0x1.c73b3ap-5f, -0x1p-1f, 0x1.a9b662p-1f, 0x1.21d434p-26f, 
+-0x1.3682a6p-4f, -0x1p-1f, 0x1.a29a7ap-1f, 0x1.189e08p-31f, 
+-0x1.87fbfep-4f, -0x1p-1f, 0x1.9b3e04p-1f, 0x1.fce1dp-27f, 
+-0x1.d7fd14p-4f, -0x1p-1f, 0x1.93a224p-1f, 0x1.324c8p-26f, 
+-0x1.133ccap-3f, -0x1p-1f, 0x1.8bc806p-1f, 0x1.62a2e8p-26f, 
+-0x1.39b2aep-3f, -0x1p-1f, 0x1.83b0ep-1f, 0x1.7ff2eep-26f, 
+-0x1.5f5a4ep-3f, -0x1p-1f, 0x1.7b5df2p-1f, 0x1.3557d8p-28f, 
+-0x1.842dd6p-3f, -0x1p-1f, 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, 
+-0x1.842dd6p-3f, -0x1p-1f, -0x1.72d084p-1f, 0x1.02000ep-26f, 
+-0x1.5f5a4ep-3f, -0x1p-1f, -0x1.7b5df2p-1f, -0x1.3557d8p-28f, 
+-0x1.39b2aep-3f, -0x1p-1f, -0x1.83b0ep-1f, -0x1.7ff2eep-26f, 
+-0x1.133ccap-3f, -0x1p-1f, -0x1.8bc806p-1f, -0x1.62a2e8p-26f, 
+-0x1.d7fd14p-4f, -0x1p-1f, -0x1.93a224p-1f, -0x1.324c8p-26f, 
+-0x1.87fbfep-4f, -0x1p-1f, -0x1.9b3e04p-1f, -0x1.fce1dp-27f, 
+-0x1.3682a6p-4f, -0x1p-1f, -0x1.a29a7ap-1f, -0x1.189e08p-31f, 
+-0x1.c73b3ap-5f, -0x1p-1f, -0x1.a9b662p-1f, -0x1.21d434p-26f, 
+-0x1.1eb354p-5f, -0x1p-1f, -0x1.b090a6p-1f, 0x1.fabf8p-27f, 
+-0x1.ce1e64p-7f, -0x1p-1f, -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, 
+-0x1.63e69ep-4f, -0x1p-2f, -0x1.e2121p-1f, -0x1.3da1bap-27f, 
+-0x1.04d726p-4f, -0x1p-2f, -0x1.e6288ep-1f, -0x1.891c22p-26f, 
+-0x1.4a0318p-5f, -0x1p-2f, -0x1.e9f416p-1f, 0x1.273a44p-26f, 
+-0x1.11d262p-6f, -0x1p-2f, -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, 
+-0x1.788512p-5f, -0x1p-3f, -0x1.f8765p-1f, 0x1.63ad16p-27f, 
+-0x1.640838p-6f, -0x1p-3f, -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, 
+-0x1.6a904ap-7f, -0x1p-4f, -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.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, 
+0x1.6a904ap-7f, 0x1p-4f, -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, 
+0x1.640838p-6f, 0x1p-3f, -0x1.fa7558p-1f, 0x1.eeb5d2p-30f, 
+0x1.788512p-5f, 0x1p-3f, -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, 
+0x1.11d262p-6f, 0x1p-2f, -0x1.ed740ep-1f, -0x1.da1258p-27f, 
+0x1.4a0318p-5f, 0x1p-2f, -0x1.e9f416p-1f, 0x1.273a44p-26f, 
+0x1.04d726p-4f, 0x1p-2f, -0x1.e6288ep-1f, -0x1.891c22p-26f, 
+0x1.63e69ep-4f, 0x1p-2f, -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, 
@@ -934,16 +934,16 @@ template <> inline constexpr float kCosApproxTable<float>[] =
 -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.ce1e64p-7f, 0x1p-1f, -0x1.b72834p-1f, -0x1.465b9p-27f, 
+0x1.1eb354p-5f, 0x1p-1f, -0x1.b090a6p-1f, 0x1.fabf8p-27f, 
+0x1.c73b3ap-5f, 0x1p-1f, -0x1.a9b662p-1f, -0x1.21d434p-26f, 
+0x1.3682a6p-4f, 0x1p-1f, -0x1.a29a7ap-1f, -0x1.189e08p-31f, 
+0x1.87fbfep-4f, 0x1p-1f, -0x1.9b3e04p-1f, -0x1.fce1dp-27f, 
+0x1.d7fd14p-4f, 0x1p-1f, -0x1.93a224p-1f, -0x1.324c8p-26f, 
+0x1.133ccap-3f, 0x1p-1f, -0x1.8bc806p-1f, -0x1.62a2e8p-26f, 
+0x1.39b2aep-3f, 0x1p-1f, -0x1.83b0ep-1f, -0x1.7ff2eep-26f, 
+0x1.5f5a4ep-3f, 0x1p-1f, -0x1.7b5df2p-1f, -0x1.3557d8p-28f, 
+0x1.842dd6p-3f, 0x1p-1f, -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, 
@@ -1009,16 +1009,16 @@ template <> inline constexpr float kCosApproxTable<float>[] =
 -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, 
+0x1.842dd6p-3f, 0x1p-1f, 0x1.72d084p-1f, -0x1.02000ep-26f, 
+0x1.5f5a4ep-3f, 0x1p-1f, 0x1.7b5df2p-1f, 0x1.3557d8p-28f, 
+0x1.39b2aep-3f, 0x1p-1f, 0x1.83b0ep-1f, 0x1.7ff2eep-26f, 
+0x1.133ccap-3f, 0x1p-1f, 0x1.8bc806p-1f, 0x1.62a2e8p-26f, 
+0x1.d7fd14p-4f, 0x1p-1f, 0x1.93a224p-1f, 0x1.324c8p-26f, 
+0x1.87fbfep-4f, 0x1p-1f, 0x1.9b3e04p-1f, 0x1.fce1dp-27f, 
+0x1.3682a6p-4f, 0x1p-1f, 0x1.a29a7ap-1f, 0x1.189e08p-31f, 
+0x1.c73b3ap-5f, 0x1p-1f, 0x1.a9b662p-1f, 0x1.21d434p-26f, 
+0x1.1eb354p-5f, 0x1p-1f, 0x1.b090a6p-1f, -0x1.fabf8p-27f, 
+0x1.ce1e64p-7f, 0x1p-1f, 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, 
@@ -1026,18 +1026,18 @@ template <> inline constexpr float kCosApproxTable<float>[] =
 -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, 
+0x1.63e69ep-4f, 0x1p-2f, 0x1.e2121p-1f, 0x1.3da1bap-27f, 
+0x1.04d726p-4f, 0x1p-2f, 0x1.e6288ep-1f, 0x1.891c22p-26f, 
+0x1.4a0318p-5f, 0x1p-2f, 0x1.e9f416p-1f, -0x1.273a44p-26f, 
+0x1.11d262p-6f, 0x1p-2f, 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, 
+0x1.788512p-5f, 0x1p-3f, 0x1.f8765p-1f, -0x1.63ad16p-27f, 
+0x1.640838p-6f, 0x1p-3f, 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, 
+0x1.6a904ap-7f, 0x1p-4f, 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, 
 };
@@ -1045,293 +1045,293 @@ template <> inline constexpr float kCosApproxTable<float>[] =
 template <> inline constexpr double kCosApproxTable<double>[] = 
 {
 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, 
--0x1.02beda0153548p3, 0x1p3, 0x1.fe1cafcbd5b09p-1, 0x1.a23e32p-57, 
--0x1.0322f4d785368p3, 0x1p3, 0x1.fd88da3d12526p-1, -0x1.87df62p-55, 
--0x1.0386f0b8f3d86p3, 0x1p3, 0x1.fce15fd6da67bp-1, -0x1.5dd6f8p-56, 
--0x1.03eac9cad52e6p3, 0x1p3, 0x1.fc26470e19fd3p-1, 0x1.1ec866p-55, 
--0x1.089cf8676d7acp2, 0x1p2, 0x1.fb5797195d741p-1, 0x1.1bfac6p-56, 
--0x1.096408374730ap2, 0x1p2, 0x1.fa7557f08a517p-1, -0x1.7a0a8cp-55, 
--0x1.0a2abb58949f3p2, 0x1p2, 0x1.f97f924c9099bp-1, -0x1.e2ae0ep-55, 
--0x1.0af10a22459fep2, 0x1p2, 0x1.f8764fa714ba9p-1, 0x1.ab2566p-56, 
--0x1.0bb6ecef285fap2, 0x1p2, 0x1.f7599a3a12077p-1, 0x1.84f31cp-55, 
--0x1.0c7c5c1e34d3p2, 0x1p2, 0x1.f6297cff75cbp-1, 0x1.562172p-56, 
--0x1.0d415012d8023p2, 0x1p2, 0x1.f4e603b0b2f2dp-1, -0x1.8ee01ep-56, 
--0x1.0e05c1353f27bp2, 0x1p2, 0x1.f38f3ac64e589p-1, -0x1.d7bafap-56, 
--0x1.0ec9a7f2a2a19p2, 0x1p2, 0x1.f2252f7763adap-1, -0x1.20cb8p-55, 
--0x1.0f8cfcbd90af9p2, 0x1p2, 0x1.f0a7efb9230d7p-1, 0x1.52c7acp-56, 
--0x1.209f701c6ffb6p1, 0x1p1, 0x1.ef178a3e473c2p-1, 0x1.6310a6p-55, 
--0x1.2223a4c563ecfp1, 0x1p1, 0x1.ed740e7684963p-1, 0x1.e82c78p-56, 
--0x1.23a6887e99b68p1, 0x1p1, 0x1.ebbd8c8df0b74p-1, 0x1.c6c8c6p-56, 
--0x1.25280c5dab3e1p1, 0x1p1, 0x1.e9f4156c62ddap-1, 0x1.760b1ep-55, 
--0x1.26a82185c302ap1, 0x1p1, 0x1.e817bab4cd10dp-1, -0x1.d0afe6p-56, 
--0x1.2826b9282eccp1, 0x1p1, 0x1.e6288ec48e112p-1, -0x1.16b56ep-57, 
--0x1.29a3c484f1cedp1, 0x1p1, 0x1.e426a4b2bc17ep-1, 0x1.a87388p-55, 
--0x1.2b1f34eb563fcp1, 0x1p1, 0x1.e212104f686e5p-1, -0x1.014c76p-55, 
--0x1.2c98fbba7e4f9p1, 0x1p1, 0x1.dfeae622dbe2bp-1, -0x1.514ea8p-55, 
--0x1.2e110a61f48b4p1, 0x1p1, 0x1.ddb13b6ccc23cp-1, 0x1.83c37cp-55, 
--0x1.2f8752623b99dp1, 0x1p1, 0x1.db6526238a09bp-1, -0x1.adee7ep-56, 
--0x1.30fbc54d5d52cp1, 0x1p1, 0x1.d906bcf328d46p-1, 0x1.457e6p-56, 
--0x1.326e54c77927bp1, 0x1p1, 0x1.d696173c9e68bp-1, -0x1.e8c61cp-56, 
--0x1.33def28751db1p1, 0x1p1, 0x1.d4134d14dc93ap-1, -0x1.4ef528p-55, 
--0x1.354d9056da7f9p1, 0x1p1, 0x1.d17e7743e35dcp-1, -0x1.101da2p-58, 
--0x1.36ba2013c2b98p1, 0x1p1, 0x1.ced7af43cc773p-1, -0x1.e7b6bap-58, 
--0x1.382493b0023ddp1, 0x1p1, 0x1.cc1f0f3fcfc5cp-1, 0x1.e57612p-56, 
--0x1.398cdd326388cp1, 0x1p1, 0x1.c954b213411f5p-1, -0x1.2fb76p-58, 
--0x1.3af2eeb70dc71p1, 0x1p1, 0x1.c678b3488739bp-1, 0x1.d86cacp-57, 
--0x1.3c56ba700dec7p1, 0x1p1, 0x1.c38b2f180bdb1p-1, -0x1.6e0b16p-56, 
--0x1.3db832a5def1bp1, 0x1p1, 0x1.c08c426725549p-1, 0x1.b157fcp-58, 
--0x1.3f1749b7f1357p1, 0x1p1, 0x1.bd7c0ac6f952ap-1, -0x1.825a72p-55, 
--0x1.80e7e43a61f5bp0, 0x1p0, 0x1.ba5aa673590d2p-1, 0x1.7ea4e2p-55, 
--0x1.839c3cc917ff7p0, 0x1p0, 0x1.b728345196e3ep-1, -0x1.bc69f2p-55, 
--0x1.864b826aec4c7p0, 0x1p0, 0x1.b3e4d3ef55712p-1, -0x1.eb6b8ap-55, 
--0x1.88f59aa0da591p0, 0x1p0, 0x1.b090a581502p-1, -0x1.926da2p-55, 
--0x1.8b9a6b1ef6da4p0, 0x1p0, 0x1.ad2bc9e21d511p-1, -0x1.47fbep-55, 
--0x1.8e39d9cd73464p0, 0x1p0, 0x1.a9b66290ea1a3p-1, 0x1.9f630ep-60, 
--0x1.90d3ccc99f5acp0, 0x1p0, 0x1.a63091b02fae2p-1, -0x1.e91114p-56, 
--0x1.93682a66e896fp0, 0x1p0, 0x1.a29a7a0462782p-1, -0x1.128bbp-56, 
--0x1.95f6d92fd79f5p0, 0x1p0, 0x1.9ef43ef29af94p-1, 0x1.b1dfcap-56, 
--0x1.987fbfe70b81ap0, 0x1p0, 0x1.9b3e047f38741p-1, -0x1.30ee28p-55, 
--0x1.9b02c58832cf9p0, 0x1p0, 0x1.9777ef4c7d742p-1, -0x1.15479ap-55, 
--0x1.9d7fd1490285dp0, 0x1p0, 0x1.93a22499263fbp-1, 0x1.3d419ap-55, 
--0x1.9ff6ca9a2ab6ap0, 0x1p0, 0x1.8fbcca3ef940dp-1, -0x1.6dfa98p-57, 
--0x1.a267992848eebp0, 0x1p0, 0x1.8bc806b151741p-1, -0x1.2c5e12p-55, 
--0x1.a4d224dcd849cp0, 0x1p0, 0x1.87c400fba2ebfp-1, -0x1.2dabcp-55, 
--0x1.a73655df1f2f5p0, 0x1p0, 0x1.83b0e0bff976ep-1, -0x1.6f420ep-56, 
--0x1.a99414951aacbp0, 0x1p0, 0x1.7f8ece3571771p-1, -0x1.9c8d8cp-55, 
--0x1.abeb49a46765p0, 0x1p0, 0x1.7b5df226aafafp-1, -0x1.0f537ap-56, 
--0x1.ae3bddf3280c6p0, 0x1p0, 0x1.771e75f037261p-1, 0x1.5cfce8p-56, 
--0x1.b085baa8e966fp0, 0x1p0, 0x1.72d0837efff96p-1, 0x1.0d4efp-55, 
--0x1.b2c8c92f83c1fp0, 0x1p0, 0x1.6e74454eaa8afp-1, -0x1.dbc03cp-55, 
--0x1.b504f333f9de6p0, 0x1p0, 0x1.6a09e667f3bcdp-1, -0x1.bdd34p-55, 
--0x1.b73a22a755457p0, 0x1p0, 0x1.6591925f0783dp-1, 0x1.c3d64ep-55, 
--0x1.b96841bf7ffcbp0, 0x1p0, 0x1.610b7551d2cdfp-1, -0x1.251b34p-56, 
--0x1.bb8f3af81b931p0, 0x1p0, 0x1.5c77bbe65018cp-1, 0x1.069ea8p-55, 
--0x1.bdaef913557d7p0, 0x1p0, 0x1.57d69348cecap-1, -0x1.757208p-55, 
--0x1.bfc7671ab8bb8p0, 0x1p0, 0x1.5328292a35596p-1, -0x1.a12eb8p-56, 
--0x1.c1d8705ffcbb7p0, 0x1p0, 0x1.4e6cabbe3e5e9p-1, 0x1.3c293ep-57, 
--0x1.c3e2007dd175fp0, 0x1p0, 0x1.49a449b9b0939p-1, -0x1.27ee16p-55, 
--0x1.c5e40358a8bap0, 0x1p0, 0x1.44cf325091dd6p-1, 0x1.8076a2p-57, 
--0x1.c7de651f7ca06p0, 0x1p0, 0x1.3fed9534556d4p-1, 0x1.369166p-55, 
--0x1.c9d1124c931fep0, 0x1p0, 0x1.3affa292050b9p-1, 0x1.e3e25ep-56, 
--0x1.cbbbf7a63eba1p0, 0x1p0, 0x1.36058b10659f3p-1, -0x1.1fcb3ap-55, 
--0x1.cd9f023f9c3ap0, 0x1p0, 0x1.30ff7fce17035p-1, -0x1.efcc62p-57, 
--0x1.cf7a1f794d7cap0, 0x1p0, 0x1.2bedb25faf3eap-1, -0x1.14981cp-58, 
--0x1.d14d3d02313c1p0, 0x1p0, 0x1.26d054cdd12dfp-1, -0x1.5da742p-55, 
--0x1.d31848d817d71p0, 0x1p0, 0x1.21a799933eb59p-1, -0x1.3a7b16p-55, 
--0x1.d4db3148750d2p0, 0x1p0, 0x1.1c73b39ae68c8p-1, 0x1.b25dd2p-55, 
--0x1.d695e4f10ea88p0, 0x1p0, 0x1.1734d63dedb49p-1, -0x1.7eef2cp-55, 
--0x1.d84852c0a81p0, 0x1p0, 0x1.11eb3541b4b23p-1, -0x1.ef23b6p-55, 
--0x1.d9f269f7aab89p0, 0x1p0, 0x1.0c9704d5d898fp-1, -0x1.8d3d7cp-55, 
--0x1.db941a28cb71fp0, 0x1p0, 0x1.073879922ffeep-1, -0x1.a5a014p-55, 
--0x1.dd2d5339ac869p0, 0x1p0, 0x1.01cfc874c3eb7p-1, -0x1.34a35ep-56, 
--0x1.debe05637ca95p0, 0x1p0, 0x1.f8ba4dbf89abap-2, -0x1.2ec1fcp-60, 
--0x1.e046213392aa5p0, 0x1p0, 0x1.edc1952ef78d6p-2, -0x1.dd0f7cp-56, 
--0x1.e1c5978c05ed8p0, 0x1p0, 0x1.e2b5d3806f63bp-2, 0x1.e0d89p-58, 
--0x1.e33c59a4439cep0, 0x1p0, 0x1.d79775b86e389p-2, 0x1.550ec8p-56, 
--0x1.e4aa5909a08fap0, 0x1p0, 0x1.cc66e9931c45ep-2, 0x1.6850e4p-58, 
--0x1.e60f879fe7e2ep0, 0x1p0, 0x1.c1249d8011ee7p-2, -0x1.813aaap-56, 
--0x1.e76bd7a1e63b9p0, 0x1p0, 0x1.b5d1009e15ccp-2, 0x1.5b362cp-57, 
--0x1.e8bf3ba1f1aeep0, 0x1p0, 0x1.aa6c82b6d3fcap-2, -0x1.d5f106p-56, 
--0x1.ea09a68a6e49dp0, 0x1p0, 0x1.9ef7943a8ed8ap-2, 0x1.6da812p-57, 
--0x1.eb4b0b9e4f345p0, 0x1p0, 0x1.9372a63bc93d7p-2, 0x1.684318p-57, 
--0x1.ec835e79946a3p0, 0x1p0, 0x1.87de2a6aea963p-2, -0x1.72cedcp-57, 
--0x1.edb29311c504dp0, 0x1p0, 0x1.7c3a9311dcce7p-2, 0x1.9a3f2p-62, 
--0x1.eed89db66611ep0, 0x1p0, 0x1.7088530fa459fp-2, -0x1.44b19ep-56, 
--0x1.eff573116df15p0, 0x1p0, 0x1.64c7ddd3f27c6p-2, 0x1.10d2b4p-58, 
--0x1.f1090827b4372p0, 0x1p0, 0x1.58f9a75ab1fddp-2, -0x1.efdc0cp-62, 
--0x1.f21352595e0bfp0, 0x1p0, 0x1.4d1e24278e76ap-2, 0x1.24172p-57, 
--0x1.f314476247089p0, 0x1p0, 0x1.4135c94176601p-2, 0x1.0c97c4p-56, 
--0x1.f40bdd5a66886p0, 0x1p0, 0x1.35410c2e18152p-2, -0x1.3cb002p-56, 
--0x1.f4fa0ab6316edp0, 0x1p0, 0x1.294062ed59f06p-2, -0x1.5d28dap-56, 
--0x1.f5dec646f85bap0, 0x1p0, 0x1.1d3443f4cdb3ep-2, -0x1.720d4p-57, 
--0x1.f6ba073b424b2p0, 0x1p0, 0x1.111d262b1f677p-2, 0x1.824c2p-56, 
--0x1.f78bc51f239e1p0, 0x1p0, 0x1.04fb80e37fdaep-2, -0x1.412cdap-63, 
--0x1.f853f7dc9186cp0, 0x1p0, 0x1.f19f97b215f1bp-3, -0x1.42deeep-57, 
--0x1.f91297bbb1d6dp0, 0x1p0, 0x1.d934fe5454311p-3, 0x1.75b922p-57, 
--0x1.f9c79d63272c4p0, 0x1p0, 0x1.c0b826a7e4f63p-3, -0x1.af1438p-62, 
--0x1.fa7301d859796p0, 0x1p0, 0x1.a82a025b00451p-3, -0x1.87905ep-57, 
--0x1.fb14be7fbae58p0, 0x1p0, 0x1.8f8b83c69a60bp-3, -0x1.26d19ap-57, 
--0x1.fbaccd1d0903cp0, 0x1p0, 0x1.76dd9de50bf31p-3, 0x1.1d5eeep-57, 
--0x1.fc3b27d38a5d5p0, 0x1p0, 0x1.5e214448b3fc6p-3, 0x1.531ff6p-57, 
--0x1.fcbfc926484cdp0, 0x1p0, 0x1.45576b1293e5ap-3, -0x1.285a24p-58, 
--0x1.fd3aabf84528bp0, 0x1p0, 0x1.2c8106e8e613ap-3, 0x1.13000ap-58, 
--0x1.fdabcb8caeba1p0, 0x1p0, 0x1.139f0cedaf577p-3, -0x1.523434p-57, 
--0x1.fe1323870cfeap0, 0x1p0, 0x1.f564e56a9730ep-4, 0x1.a27046p-59, 
--0x1.fe70afeb6d33dp0, 0x1p0, 0x1.c3785c79ec2d5p-4, -0x1.4f39dep-61, 
--0x1.fec46d1e89293p0, 0x1p0, 0x1.917a6bc29b42cp-4, -0x1.e2718cp-60, 
--0x1.ff0e57e5ead85p0, 0x1p0, 0x1.5f6d00a9aa419p-4, -0x1.f4022cp-59, 
--0x1.ff4e6d680c41dp0, 0x1p0, 0x1.2d52092ce19f6p-4, -0x1.9a088ap-59, 
--0x1.ff84ab2c738d7p0, 0x1p0, 0x1.f656e79f820ep-5, -0x1.2e1ebep-61, 
--0x1.ffb10f1bcb6bfp0, 0x1p0, 0x1.91f65f10dd814p-5, -0x1.912bdp-61, 
--0x1.ffd3977ff7baep0, 0x1p0, 0x1.2d865759455cdp-5, 0x1.686f64p-61, 
--0x1.ffec430426686p0, 0x1p0, 0x1.92155f7a3667ep-6, -0x1.b1d63p-64, 
--0x1.fffb10b4dc96ep0, 0x1p0, 0x1.921d1fcdec784p-7, 0x1.9878eap-61, 
--0x1p1, 0x1p0, 0.0, 0.0, 
--0x1.fffb10b4dc96ep0, 0x1p0, -0x1.921d1fcdec784p-7, -0x1.9878eap-61, 
--0x1.ffec430426686p0, 0x1p0, -0x1.92155f7a3667ep-6, 0x1.b1d63p-64, 
--0x1.ffd3977ff7baep0, 0x1p0, -0x1.2d865759455cdp-5, -0x1.686f64p-61, 
--0x1.ffb10f1bcb6bfp0, 0x1p0, -0x1.91f65f10dd814p-5, 0x1.912bdp-61, 
--0x1.ff84ab2c738d7p0, 0x1p0, -0x1.f656e79f820ep-5, 0x1.2e1ebep-61, 
--0x1.ff4e6d680c41dp0, 0x1p0, -0x1.2d52092ce19f6p-4, 0x1.9a088ap-59, 
--0x1.ff0e57e5ead85p0, 0x1p0, -0x1.5f6d00a9aa419p-4, 0x1.f4022cp-59, 
--0x1.fec46d1e89293p0, 0x1p0, -0x1.917a6bc29b42cp-4, 0x1.e2718cp-60, 
--0x1.fe70afeb6d33dp0, 0x1p0, -0x1.c3785c79ec2d5p-4, 0x1.4f39dep-61, 
--0x1.fe1323870cfeap0, 0x1p0, -0x1.f564e56a9730ep-4, -0x1.a27046p-59, 
--0x1.fdabcb8caeba1p0, 0x1p0, -0x1.139f0cedaf577p-3, 0x1.523434p-57, 
--0x1.fd3aabf84528bp0, 0x1p0, -0x1.2c8106e8e613ap-3, -0x1.13000ap-58, 
--0x1.fcbfc926484cdp0, 0x1p0, -0x1.45576b1293e5ap-3, 0x1.285a24p-58, 
--0x1.fc3b27d38a5d5p0, 0x1p0, -0x1.5e214448b3fc6p-3, -0x1.531ff6p-57, 
--0x1.fbaccd1d0903cp0, 0x1p0, -0x1.76dd9de50bf31p-3, -0x1.1d5eeep-57, 
--0x1.fb14be7fbae58p0, 0x1p0, -0x1.8f8b83c69a60bp-3, 0x1.26d19ap-57, 
--0x1.fa7301d859796p0, 0x1p0, -0x1.a82a025b00451p-3, 0x1.87905ep-57, 
--0x1.f9c79d63272c4p0, 0x1p0, -0x1.c0b826a7e4f63p-3, 0x1.af1438p-62, 
--0x1.f91297bbb1d6dp0, 0x1p0, -0x1.d934fe5454311p-3, -0x1.75b922p-57, 
--0x1.f853f7dc9186cp0, 0x1p0, -0x1.f19f97b215f1bp-3, 0x1.42deeep-57, 
--0x1.f78bc51f239e1p0, 0x1p0, -0x1.04fb80e37fdaep-2, 0x1.412cdap-63, 
--0x1.f6ba073b424b2p0, 0x1p0, -0x1.111d262b1f677p-2, -0x1.824c2p-56, 
--0x1.f5dec646f85bap0, 0x1p0, -0x1.1d3443f4cdb3ep-2, 0x1.720d4p-57, 
--0x1.f4fa0ab6316edp0, 0x1p0, -0x1.294062ed59f06p-2, 0x1.5d28dap-56, 
--0x1.f40bdd5a66886p0, 0x1p0, -0x1.35410c2e18152p-2, 0x1.3cb002p-56, 
--0x1.f314476247089p0, 0x1p0, -0x1.4135c94176601p-2, -0x1.0c97c4p-56, 
--0x1.f21352595e0bfp0, 0x1p0, -0x1.4d1e24278e76ap-2, -0x1.24172p-57, 
--0x1.f1090827b4372p0, 0x1p0, -0x1.58f9a75ab1fddp-2, 0x1.efdc0cp-62, 
--0x1.eff573116df15p0, 0x1p0, -0x1.64c7ddd3f27c6p-2, -0x1.10d2b4p-58, 
--0x1.eed89db66611ep0, 0x1p0, -0x1.7088530fa459fp-2, 0x1.44b19ep-56, 
--0x1.edb29311c504dp0, 0x1p0, -0x1.7c3a9311dcce7p-2, -0x1.9a3f2p-62, 
--0x1.ec835e79946a3p0, 0x1p0, -0x1.87de2a6aea963p-2, 0x1.72cedcp-57, 
--0x1.eb4b0b9e4f345p0, 0x1p0, -0x1.9372a63bc93d7p-2, -0x1.684318p-57, 
--0x1.ea09a68a6e49dp0, 0x1p0, -0x1.9ef7943a8ed8ap-2, -0x1.6da812p-57, 
--0x1.e8bf3ba1f1aeep0, 0x1p0, -0x1.aa6c82b6d3fcap-2, 0x1.d5f106p-56, 
--0x1.e76bd7a1e63b9p0, 0x1p0, -0x1.b5d1009e15ccp-2, -0x1.5b362cp-57, 
--0x1.e60f879fe7e2ep0, 0x1p0, -0x1.c1249d8011ee7p-2, 0x1.813aaap-56, 
--0x1.e4aa5909a08fap0, 0x1p0, -0x1.cc66e9931c45ep-2, -0x1.6850e4p-58, 
--0x1.e33c59a4439cep0, 0x1p0, -0x1.d79775b86e389p-2, -0x1.550ec8p-56, 
--0x1.e1c5978c05ed8p0, 0x1p0, -0x1.e2b5d3806f63bp-2, -0x1.e0d89p-58, 
--0x1.e046213392aa5p0, 0x1p0, -0x1.edc1952ef78d6p-2, 0x1.dd0f7cp-56, 
--0x1.debe05637ca95p0, 0x1p0, -0x1.f8ba4dbf89abap-2, 0x1.2ec1fcp-60, 
--0x1.dd2d5339ac869p0, 0x1p0, -0x1.01cfc874c3eb7p-1, 0x1.34a35ep-56, 
--0x1.db941a28cb71fp0, 0x1p0, -0x1.073879922ffeep-1, 0x1.a5a014p-55, 
--0x1.d9f269f7aab89p0, 0x1p0, -0x1.0c9704d5d898fp-1, 0x1.8d3d7cp-55, 
--0x1.d84852c0a81p0, 0x1p0, -0x1.11eb3541b4b23p-1, 0x1.ef23b6p-55, 
--0x1.d695e4f10ea88p0, 0x1p0, -0x1.1734d63dedb49p-1, 0x1.7eef2cp-55, 
--0x1.d4db3148750d2p0, 0x1p0, -0x1.1c73b39ae68c8p-1, -0x1.b25dd2p-55, 
--0x1.d31848d817d71p0, 0x1p0, -0x1.21a799933eb59p-1, 0x1.3a7b16p-55, 
--0x1.d14d3d02313c1p0, 0x1p0, -0x1.26d054cdd12dfp-1, 0x1.5da742p-55, 
--0x1.cf7a1f794d7cap0, 0x1p0, -0x1.2bedb25faf3eap-1, 0x1.14981cp-58, 
--0x1.cd9f023f9c3ap0, 0x1p0, -0x1.30ff7fce17035p-1, 0x1.efcc62p-57, 
--0x1.cbbbf7a63eba1p0, 0x1p0, -0x1.36058b10659f3p-1, 0x1.1fcb3ap-55, 
--0x1.c9d1124c931fep0, 0x1p0, -0x1.3affa292050b9p-1, -0x1.e3e25ep-56, 
--0x1.c7de651f7ca06p0, 0x1p0, -0x1.3fed9534556d4p-1, -0x1.369166p-55, 
--0x1.c5e40358a8bap0, 0x1p0, -0x1.44cf325091dd6p-1, -0x1.8076a2p-57, 
--0x1.c3e2007dd175fp0, 0x1p0, -0x1.49a449b9b0939p-1, 0x1.27ee16p-55, 
--0x1.c1d8705ffcbb7p0, 0x1p0, -0x1.4e6cabbe3e5e9p-1, -0x1.3c293ep-57, 
--0x1.bfc7671ab8bb8p0, 0x1p0, -0x1.5328292a35596p-1, 0x1.a12eb8p-56, 
--0x1.bdaef913557d7p0, 0x1p0, -0x1.57d69348cecap-1, 0x1.757208p-55, 
--0x1.bb8f3af81b931p0, 0x1p0, -0x1.5c77bbe65018cp-1, -0x1.069ea8p-55, 
--0x1.b96841bf7ffcbp0, 0x1p0, -0x1.610b7551d2cdfp-1, 0x1.251b34p-56, 
--0x1.b73a22a755457p0, 0x1p0, -0x1.6591925f0783dp-1, -0x1.c3d64ep-55, 
--0x1.b504f333f9de6p0, 0x1p0, -0x1.6a09e667f3bcdp-1, 0x1.bdd34p-55, 
--0x1.b2c8c92f83c1fp0, 0x1p0, -0x1.6e74454eaa8afp-1, 0x1.dbc03cp-55, 
--0x1.b085baa8e966fp0, 0x1p0, -0x1.72d0837efff96p-1, -0x1.0d4efp-55, 
--0x1.ae3bddf3280c6p0, 0x1p0, -0x1.771e75f037261p-1, -0x1.5cfce8p-56, 
--0x1.abeb49a46765p0, 0x1p0, -0x1.7b5df226aafafp-1, 0x1.0f537ap-56, 
--0x1.a99414951aacbp0, 0x1p0, -0x1.7f8ece3571771p-1, 0x1.9c8d8cp-55, 
--0x1.a73655df1f2f5p0, 0x1p0, -0x1.83b0e0bff976ep-1, 0x1.6f420ep-56, 
--0x1.a4d224dcd849cp0, 0x1p0, -0x1.87c400fba2ebfp-1, 0x1.2dabcp-55, 
--0x1.a267992848eebp0, 0x1p0, -0x1.8bc806b151741p-1, 0x1.2c5e12p-55, 
--0x1.9ff6ca9a2ab6ap0, 0x1p0, -0x1.8fbcca3ef940dp-1, 0x1.6dfa98p-57, 
--0x1.9d7fd1490285dp0, 0x1p0, -0x1.93a22499263fbp-1, -0x1.3d419ap-55, 
--0x1.9b02c58832cf9p0, 0x1p0, -0x1.9777ef4c7d742p-1, 0x1.15479ap-55, 
--0x1.987fbfe70b81ap0, 0x1p0, -0x1.9b3e047f38741p-1, 0x1.30ee28p-55, 
--0x1.95f6d92fd79f5p0, 0x1p0, -0x1.9ef43ef29af94p-1, -0x1.b1dfcap-56, 
--0x1.93682a66e896fp0, 0x1p0, -0x1.a29a7a0462782p-1, 0x1.128bbp-56, 
--0x1.90d3ccc99f5acp0, 0x1p0, -0x1.a63091b02fae2p-1, 0x1.e91114p-56, 
--0x1.8e39d9cd73464p0, 0x1p0, -0x1.a9b66290ea1a3p-1, -0x1.9f630ep-60, 
--0x1.8b9a6b1ef6da4p0, 0x1p0, -0x1.ad2bc9e21d511p-1, 0x1.47fbep-55, 
--0x1.88f59aa0da591p0, 0x1p0, -0x1.b090a581502p-1, 0x1.926da2p-55, 
--0x1.864b826aec4c7p0, 0x1p0, -0x1.b3e4d3ef55712p-1, 0x1.eb6b8ap-55, 
--0x1.839c3cc917ff7p0, 0x1p0, -0x1.b728345196e3ep-1, 0x1.bc69f2p-55, 
--0x1.80e7e43a61f5bp0, 0x1p0, -0x1.ba5aa673590d2p-1, -0x1.7ea4e2p-55, 
--0x1.3f1749b7f1357p1, 0x1p1, -0x1.bd7c0ac6f952ap-1, 0x1.825a72p-55, 
--0x1.3db832a5def1bp1, 0x1p1, -0x1.c08c426725549p-1, -0x1.b157fcp-58, 
--0x1.3c56ba700dec7p1, 0x1p1, -0x1.c38b2f180bdb1p-1, 0x1.6e0b16p-56, 
--0x1.3af2eeb70dc71p1, 0x1p1, -0x1.c678b3488739bp-1, -0x1.d86cacp-57, 
--0x1.398cdd326388cp1, 0x1p1, -0x1.c954b213411f5p-1, 0x1.2fb76p-58, 
--0x1.382493b0023ddp1, 0x1p1, -0x1.cc1f0f3fcfc5cp-1, -0x1.e57612p-56, 
--0x1.36ba2013c2b98p1, 0x1p1, -0x1.ced7af43cc773p-1, 0x1.e7b6bap-58, 
--0x1.354d9056da7f9p1, 0x1p1, -0x1.d17e7743e35dcp-1, 0x1.101da2p-58, 
--0x1.33def28751db1p1, 0x1p1, -0x1.d4134d14dc93ap-1, 0x1.4ef528p-55, 
--0x1.326e54c77927bp1, 0x1p1, -0x1.d696173c9e68bp-1, 0x1.e8c61cp-56, 
--0x1.30fbc54d5d52cp1, 0x1p1, -0x1.d906bcf328d46p-1, -0x1.457e6p-56, 
--0x1.2f8752623b99dp1, 0x1p1, -0x1.db6526238a09bp-1, 0x1.adee7ep-56, 
--0x1.2e110a61f48b4p1, 0x1p1, -0x1.ddb13b6ccc23cp-1, -0x1.83c37cp-55, 
--0x1.2c98fbba7e4f9p1, 0x1p1, -0x1.dfeae622dbe2bp-1, 0x1.514ea8p-55, 
--0x1.2b1f34eb563fcp1, 0x1p1, -0x1.e212104f686e5p-1, 0x1.014c76p-55, 
--0x1.29a3c484f1cedp1, 0x1p1, -0x1.e426a4b2bc17ep-1, -0x1.a87388p-55, 
--0x1.2826b9282eccp1, 0x1p1, -0x1.e6288ec48e112p-1, 0x1.16b56ep-57, 
--0x1.26a82185c302ap1, 0x1p1, -0x1.e817bab4cd10dp-1, 0x1.d0afe6p-56, 
--0x1.25280c5dab3e1p1, 0x1p1, -0x1.e9f4156c62ddap-1, -0x1.760b1ep-55, 
--0x1.23a6887e99b68p1, 0x1p1, -0x1.ebbd8c8df0b74p-1, -0x1.c6c8c6p-56, 
--0x1.2223a4c563ecfp1, 0x1p1, -0x1.ed740e7684963p-1, -0x1.e82c78p-56, 
--0x1.209f701c6ffb6p1, 0x1p1, -0x1.ef178a3e473c2p-1, -0x1.6310a6p-55, 
--0x1.0f8cfcbd90af9p2, 0x1p2, -0x1.f0a7efb9230d7p-1, -0x1.52c7acp-56, 
--0x1.0ec9a7f2a2a19p2, 0x1p2, -0x1.f2252f7763adap-1, 0x1.20cb8p-55, 
--0x1.0e05c1353f27bp2, 0x1p2, -0x1.f38f3ac64e589p-1, 0x1.d7bafap-56, 
--0x1.0d415012d8023p2, 0x1p2, -0x1.f4e603b0b2f2dp-1, 0x1.8ee01ep-56, 
--0x1.0c7c5c1e34d3p2, 0x1p2, -0x1.f6297cff75cbp-1, -0x1.562172p-56, 
--0x1.0bb6ecef285fap2, 0x1p2, -0x1.f7599a3a12077p-1, -0x1.84f31cp-55, 
--0x1.0af10a22459fep2, 0x1p2, -0x1.f8764fa714ba9p-1, -0x1.ab2566p-56, 
--0x1.0a2abb58949f3p2, 0x1p2, -0x1.f97f924c9099bp-1, 0x1.e2ae0ep-55, 
--0x1.096408374730ap2, 0x1p2, -0x1.fa7557f08a517p-1, 0x1.7a0a8cp-55, 
--0x1.089cf8676d7acp2, 0x1p2, -0x1.fb5797195d741p-1, -0x1.1bfac6p-56, 
--0x1.03eac9cad52e6p3, 0x1p3, -0x1.fc26470e19fd3p-1, -0x1.1ec866p-55, 
--0x1.0386f0b8f3d86p3, 0x1p3, -0x1.fce15fd6da67bp-1, 0x1.5dd6f8p-56, 
--0x1.0322f4d785368p3, 0x1p3, -0x1.fd88da3d12526p-1, 0x1.87df62p-55, 
--0x1.02beda0153548p3, 0x1p3, -0x1.fe1cafcbd5b09p-1, -0x1.a23e32p-57, 
--0x1.025aa41259c34p3, 0x1p3, -0x1.fe9cdad01883ap-1, -0x1.521eccp-57, 
--0x1.00fb2b73cfc1p4, 0x1p4, -0x1.ff095658e71adp-1, -0x1.01a8cep-55, 
--0x1.00c8fb2f886ecp4, 0x1p4, -0x1.ff621e3796d7ep-1, 0x1.c57bc2p-57, 
--0x1.0096c32baca2bp4, 0x1p4, -0x1.ffa72effef75dp-1, 0x1.8b4cdcp-55, 
--0x1.003242abef46dp5, 0x1p5, -0x1.ffd886084cd0dp-1, 0x1.1354d4p-55, 
--0x1.000c90e8fe6f6p6, 0x1p6, -0x1.fff62169b92dbp-1, -0x1.5dda3cp-55, 
+0x1.b78b80c84e1eep-9, -0x1p-6, 0x1.fff62169b92dbp-1, 0x1.5dda3cp-55, 
+0x1.b7aa821726608p-8, -0x1p-5, 0x1.ffd886084cd0dp-1, -0x1.1354d4p-55, 
+-0x1.6c32baca2ae69p-8, -0x1p-5, 0x1.ffa72effef75dp-1, -0x1.8b4cdcp-55, 
+0x1.b82683bc89fbp-7, -0x1p-4, 0x1.ff621e3796d7ep-1, -0x1.c57bc2p-57, 
+0x1.35230c0fbe402p-10, -0x1p-4, 0x1.ff095658e71adp-1, 0x1.01a8cep-55, 
+-0x1.6a9049670cfaep-7, -0x1p-4, 0x1.fe9cdad01883ap-1, 0x1.521eccp-57, 
+-0x1.7db402a6a9063p-6, -0x1p-4, 0x1.fe1cafcbd5b09p-1, 0x1.a23e32p-57, 
+0x1.ba1650f592f5p-6, -0x1p-3, 0x1.fd88da3d12526p-1, -0x1.87df62p-55, 
+0x1.e43d1c309e958p-7, -0x1p-3, 0x1.fce15fd6da67bp-1, -0x1.5dd6f8p-56, 
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+0x1.f0ea4c477339cp-4, 0x1p-2, -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, 
@@ -1343,33 +1343,33 @@ template <> inline constexpr double kCosApproxTable<double>[] =
 -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.cfc874c3eb6d9p-9, 0x1p-1, -0x1.ba5aa673590d2p-1, -0x1.7ea4e2p-55, 
+0x1.ce1e648bffb66p-7, 0x1p-1, -0x1.b728345196e3ep-1, 0x1.bc69f2p-55, 
+0x1.92e09abb131d4p-6, 0x1p-1, -0x1.b3e4d3ef55712p-1, 0x1.eb6b8ap-55, 
+0x1.1eb3541b4b228p-5, 0x1p-1, -0x1.b090a581502p-1, 0x1.926da2p-55, 
+0x1.734d63dedb48ap-5, 0x1p-1, -0x1.ad2bc9e21d511p-1, 0x1.47fbep-55, 
+0x1.c73b39ae68c87p-5, 0x1p-1, -0x1.a9b66290ea1a3p-1, -0x1.9f630ep-60, 
+0x1.0d3ccc99f5ac6p-4, 0x1p-1, -0x1.a63091b02fae2p-1, 0x1.e91114p-56, 
+0x1.3682a66e896f5p-4, 0x1p-1, -0x1.a29a7a0462782p-1, 0x1.128bbp-56, 
+0x1.5f6d92fd79f5p-4, 0x1p-1, -0x1.9ef43ef29af94p-1, -0x1.b1dfcap-56, 
+0x1.87fbfe70b81a7p-4, 0x1p-1, -0x1.9b3e047f38741p-1, 0x1.30ee28p-55, 
+0x1.b02c58832cf96p-4, 0x1p-1, -0x1.9777ef4c7d742p-1, 0x1.15479ap-55, 
+0x1.d7fd1490285cap-4, 0x1p-1, -0x1.93a22499263fbp-1, -0x1.3d419ap-55, 
+0x1.ff6ca9a2ab6a2p-4, 0x1p-1, -0x1.8fbcca3ef940dp-1, 0x1.6dfa98p-57, 
+0x1.133cc94247758p-3, 0x1p-1, -0x1.8bc806b151741p-1, 0x1.2c5e12p-55, 
+0x1.269126e6c24e3p-3, 0x1p-1, -0x1.87c400fba2ebfp-1, 0x1.2dabcp-55, 
+0x1.39b2aef8f97a4p-3, 0x1p-1, -0x1.83b0e0bff976ep-1, 0x1.6f420ep-56, 
+0x1.4ca0a4a8d5657p-3, 0x1p-1, -0x1.7f8ece3571771p-1, 0x1.9c8d8cp-55, 
+0x1.5f5a4d233b27fp-3, 0x1p-1, -0x1.7b5df226aafafp-1, 0x1.0f537ap-56, 
+0x1.71deef9940631p-3, 0x1p-1, -0x1.771e75f037261p-1, -0x1.5cfce8p-56, 
+0x1.842dd5474b37bp-3, 0x1p-1, -0x1.72d0837efff96p-1, -0x1.0d4efp-55, 
+0x1.9646497c1e0f6p-3, 0x1p-1, -0x1.6e74454eaa8afp-1, 0x1.dbc03cp-55, 
+0x1.a827999fcef32p-3, 0x1p-1, -0x1.6a09e667f3bcdp-1, 0x1.bdd34p-55, 
+0x1.b9d1153aaa2bap-3, 0x1p-1, -0x1.6591925f0783dp-1, -0x1.c3d64ep-55, 
+0x1.cb420dfbffe59p-3, 0x1p-1, -0x1.610b7551d2cdfp-1, 0x1.251b34p-56, 
+0x1.dc79d7c0dc985p-3, 0x1p-1, -0x1.5c77bbe65018cp-1, -0x1.069ea8p-55, 
+0x1.ed77c89aabebbp-3, 0x1p-1, -0x1.57d69348cecap-1, 0x1.757208p-55, 
+0x1.fe3b38d5c5dc2p-3, 0x1p-1, -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, 
@@ -1487,33 +1487,33 @@ template <> inline constexpr double kCosApproxTable<double>[] =
 -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.fe3b38d5c5dc2p-3, 0x1p-1, 0x1.5328292a35596p-1, -0x1.a12eb8p-56, 
+0x1.ed77c89aabebbp-3, 0x1p-1, 0x1.57d69348cecap-1, -0x1.757208p-55, 
+0x1.dc79d7c0dc985p-3, 0x1p-1, 0x1.5c77bbe65018cp-1, 0x1.069ea8p-55, 
+0x1.cb420dfbffe59p-3, 0x1p-1, 0x1.610b7551d2cdfp-1, -0x1.251b34p-56, 
+0x1.b9d1153aaa2bap-3, 0x1p-1, 0x1.6591925f0783dp-1, 0x1.c3d64ep-55, 
+0x1.a827999fcef32p-3, 0x1p-1, 0x1.6a09e667f3bcdp-1, -0x1.bdd34p-55, 
+0x1.9646497c1e0f6p-3, 0x1p-1, 0x1.6e74454eaa8afp-1, -0x1.dbc03cp-55, 
+0x1.842dd5474b37bp-3, 0x1p-1, 0x1.72d0837efff96p-1, 0x1.0d4efp-55, 
+0x1.71deef9940631p-3, 0x1p-1, 0x1.771e75f037261p-1, 0x1.5cfce8p-56, 
+0x1.5f5a4d233b27fp-3, 0x1p-1, 0x1.7b5df226aafafp-1, -0x1.0f537ap-56, 
+0x1.4ca0a4a8d5657p-3, 0x1p-1, 0x1.7f8ece3571771p-1, -0x1.9c8d8cp-55, 
+0x1.39b2aef8f97a4p-3, 0x1p-1, 0x1.83b0e0bff976ep-1, -0x1.6f420ep-56, 
+0x1.269126e6c24e3p-3, 0x1p-1, 0x1.87c400fba2ebfp-1, -0x1.2dabcp-55, 
+0x1.133cc94247758p-3, 0x1p-1, 0x1.8bc806b151741p-1, -0x1.2c5e12p-55, 
+0x1.ff6ca9a2ab6a2p-4, 0x1p-1, 0x1.8fbcca3ef940dp-1, -0x1.6dfa98p-57, 
+0x1.d7fd1490285cap-4, 0x1p-1, 0x1.93a22499263fbp-1, 0x1.3d419ap-55, 
+0x1.b02c58832cf96p-4, 0x1p-1, 0x1.9777ef4c7d742p-1, -0x1.15479ap-55, 
+0x1.87fbfe70b81a7p-4, 0x1p-1, 0x1.9b3e047f38741p-1, -0x1.30ee28p-55, 
+0x1.5f6d92fd79f5p-4, 0x1p-1, 0x1.9ef43ef29af94p-1, 0x1.b1dfcap-56, 
+0x1.3682a66e896f5p-4, 0x1p-1, 0x1.a29a7a0462782p-1, -0x1.128bbp-56, 
+0x1.0d3ccc99f5ac6p-4, 0x1p-1, 0x1.a63091b02fae2p-1, -0x1.e91114p-56, 
+0x1.c73b39ae68c87p-5, 0x1p-1, 0x1.a9b66290ea1a3p-1, 0x1.9f630ep-60, 
+0x1.734d63dedb48ap-5, 0x1p-1, 0x1.ad2bc9e21d511p-1, -0x1.47fbep-55, 
+0x1.1eb3541b4b228p-5, 0x1p-1, 0x1.b090a581502p-1, -0x1.926da2p-55, 
+0x1.92e09abb131d4p-6, 0x1p-1, 0x1.b3e4d3ef55712p-1, -0x1.eb6b8ap-55, 
+0x1.ce1e648bffb66p-7, 0x1p-1, 0x1.b728345196e3ep-1, -0x1.bc69f2p-55, 
+0x1.cfc874c3eb6d9p-9, 0x1p-1, 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, 
@@ -1525,35 +1525,35 @@ template <> inline constexpr double kCosApproxTable<double>[] =
 -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.f0ea4c477339cp-4, 0x1p-2, 0x1.db6526238a09bp-1, -0x1.adee7ep-56, 
+0x1.c2214c3e9167bp-4, 0x1p-2, 0x1.ddb13b6ccc23cp-1, 0x1.83c37cp-55, 
+0x1.931f774fc9f18p-4, 0x1p-2, 0x1.dfeae622dbe2bp-1, -0x1.514ea8p-55, 
+0x1.63e69d6ac7f74p-4, 0x1p-2, 0x1.e212104f686e5p-1, -0x1.014c76p-55, 
+0x1.3478909e39da9p-4, 0x1p-2, 0x1.e426a4b2bc17ep-1, 0x1.a87388p-55, 
+0x1.04d72505d9805p-4, 0x1p-2, 0x1.e6288ec48e112p-1, -0x1.16b56ep-57, 
+0x1.aa086170c0a8ep-5, 0x1p-2, 0x1.e817bab4cd10dp-1, -0x1.d0afe6p-56, 
+0x1.4a03176acf82dp-5, 0x1p-2, 0x1.e9f4156c62ddap-1, 0x1.760b1ep-55, 
+0x1.d3443f4cdb3ddp-6, 0x1p-2, 0x1.ebbd8c8df0b74p-1, 0x1.c6c8c6p-56, 
+0x1.11d262b1f6776p-6, 0x1p-2, 0x1.ed740e7684963p-1, 0x1.e82c78p-56, 
+0x1.3ee038dff6b8p-8, 0x1p-2, 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.db7677942fcc5p-5, 0x1p-3, 0x1.f7599a3a12077p-1, 0x1.84f31cp-55, 
+0x1.78851122cff19p-5, 0x1p-3, 0x1.f8764fa714ba9p-1, 0x1.ab2566p-56, 
+0x1.155dac4a4f967p-5, 0x1p-3, 0x1.f97f924c9099bp-1, -0x1.e2ae0ep-55, 
+0x1.64083747309d1p-6, 0x1p-3, 0x1.fa7557f08a517p-1, -0x1.7a0a8cp-55, 
+0x1.39f0cedaf576bp-7, 0x1p-3, 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, 
+0x1.7db402a6a9063p-6, 0x1p-4, 0x1.fe1cafcbd5b09p-1, 0x1.a23e32p-57, 
+0x1.6a9049670cfaep-7, 0x1p-4, 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, 
+0x1.6c32baca2ae69p-8, 0x1p-5, 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, 
 };
diff --git a/npsr/trig/data/constants.h b/npsr/trig/data/constants.h
index 358290f..89e9337 100644
--- a/npsr/trig/data/constants.h
+++ b/npsr/trig/data/constants.h
@@ -30,7 +30,7 @@ template <> inline constexpr double kPiMul2<double>[] = {
 template <bool FMA> inline constexpr double kPiDiv16Prec29[] = {
 0x1.921fb54442d18p-3, 0x1.1a62633p-57, 0x1.45c06e0e68948p-89, };
 template <> inline constexpr double kPiDiv16Prec29<false>[] = {
-0x1.921fb54p-3, 0x1.a626331p-61, 0x1.1701b839a252p-91, 0x1.10b461p-33, 
+0x1.921fb54p-3, 0x1.10b461p-33, 0x1.a626331p-61, 0x1.1701b839a252p-91, 
 };
 
 template <typename T> inline constexpr char kInvPi = '_';
diff --git a/npsr/trig/extended-inl.h b/npsr/trig/extended-inl.h
index cdce91a..e49b802 100644
--- a/npsr/trig/extended-inl.h
+++ b/npsr/trig/extended-inl.h
@@ -212,7 +212,7 @@ NPSR_INTRIN V Extended(V x) {
   // PHASE 7: Convert to Radians
   // =============================================================================
 
-  // Multiply by π with error compensation (Cody-Waite multiplication)
+  // Multiply by 2π with error compensation (Cody-Waite multiplication)
   constexpr auto kPiMul2 = data::kPiMul2<T>;
   const V pi2_hi = Set(d, kPiMul2[0]);
   const V pi2_med = Set(d, kPiMul2[1]);
@@ -233,6 +233,14 @@ NPSR_INTRIN V Extended(V x) {
     r_lo = Combine(d, DemoteTo(dh, r_lo_w0), DemoteTo(dh, r_lo_w1));
     r_w0 = BitCast(d, r0);
     r_w1 = BitCast(d, r1);
+  } else if constexpr (!kNativeFMA) {
+    // Without FMA, `MulSub(pi2_hi, n, r)` yields zero and drops the 0.5-ulp(r)
+    // rounding error of r — worth 0.5 ulp of the result near k*pi/2. Recover
+    // it from the exact head product (head - r is exact by Sterbenz).
+    V head, rest;
+    SplitMul(pi2_hi, n, head, rest);
+    r_lo = Add(Sub(head, r), rest);
+    r_lo = Add(Mul(pi2_med, n), r_lo);
   } else {
     r_lo = MulSub(pi2_hi, n, r);
     r_lo = MulAdd(pi2_med, n, r_lo);
@@ -272,22 +280,30 @@ NPSR_INTRIN V Extended(V x) {
   // =============================================================================
   // PHASE 10: Final Assembly
   // =============================================================================
-  V res_lo = NegMulAdd(func_hi, r, deriv);
-  res_lo = MulAdd(res_lo, r_lo, func_lo);
   V res_hi_lo = MulAdd(sigma, r, func_hi);
-  V res_hi = MulAdd(deriv_hi, r, res_hi_lo);
-
+  V res_hi, deriv_hi_r_cor;
+  if constexpr (!kNativeFMA && !kIsSingle) {
+    // Same substitution as in Phase 7. sigma is a signed power of two (see
+    // approx.h) so sigma*r is exact, but deriv_hi*r would round under a
+    // decayed MulAdd and corrupt the head; SplitMul recovers it.
+    V dr, dr_rest;
+    SplitMul(deriv_hi, r, dr, dr_rest);
+    res_hi = Add(res_hi_lo, dr);
+    V dr_hi = Sub(res_hi, res_hi_lo);
+    deriv_hi_r_cor = Add(Sub(dr, dr_hi), dr_rest);
+  } else {
+    res_hi = MulAdd(deriv_hi, r, res_hi_lo);
+    deriv_hi_r_cor = MulAdd(deriv_hi, r, Sub(res_hi_lo, res_hi));
+  }
   V sum_cor = MulAdd(sigma, r, Sub(func_hi, res_hi_lo));
-  V deriv_hi_r_cor = MulAdd(deriv_hi, r, Sub(res_hi_lo, res_hi));
-  deriv_hi_r_cor = Add(deriv_hi_r_cor, sum_cor);
-  res_lo = Add(res_lo, deriv_hi_r_cor);
+  V res_lo0 = Add(deriv_hi_r_cor, sum_cor);
 
   // Polynomial corrections
   V s2 = Set(d, kIsSingle ? 0x1.1110b8p-7f : 0x1.1110fabb3551cp-7);
   V s1 = Set(d, kIsSingle ? -0x1.555556p-3f : -0x1.5555555554448p-3);
   V sin_poly = MulAdd(s2, r2, s1);
-  sin_poly = Mul(sin_poly, r);
   sin_poly = Mul(sin_poly, r2);
+  sin_poly = Mul(sin_poly, r);
 
   V c1 = Set(d, kIsSingle ? 0x1.5554f8p-5f : 0x1.5555555554ccfp-5);
   const V neg_half = Set(d, static_cast<T>(-0.5));
@@ -301,8 +317,11 @@ NPSR_INTRIN V Extended(V x) {
   }
   cos_poly = Mul(cos_poly, r2);
 
-  res_lo = MulAdd(sin_poly, deriv, res_lo);
-  res_lo = MulAdd(cos_poly, func_hi, res_lo);
+  V corr = NegMulAdd(func_hi, r, deriv);
+  V res_lo_rlo = MulAdd(corr, r_lo, func_lo);
+  V res_lo_sin = MulAdd(deriv, sin_poly, res_lo0);
+  V res_lo_cos = MulAdd(func_hi, cos_poly, res_lo_sin);
+  V res_lo = Add(res_lo_cos, res_lo_rlo);
   return Add(res_hi, res_lo);
 }
 // NOLINTNEXTLINE(google-readability-namespace-comments)
diff --git a/npsr/trig/high-inl.h b/npsr/trig/high-inl.h
index 68cdd9f..65d0fd3 100644
--- a/npsr/trig/high-inl.h
+++ b/npsr/trig/high-inl.h
@@ -95,15 +95,16 @@ NPSR_INTRIN V High(V x) {
 /**
  * This function computes sin(x) or cos(x) for |x| < 2^24 using the Cody-Waite
  * reduction algorithm combined with table lookup and polynomial approximation,
- * achieves < 1 ULP error for |x| < 2^24.
+ * achieves <= 1 ULP error for |x| < 2^24 (worst case reaches, but does not
+ * exceed, 1 ULP).
  *
  * Algorithm Overview:
  * 1. Range Reduction: Reduces input x to r where |r| < π/16
  *    - Computes n = round(x * 16/π) and r = x - n*π/16
- *    - Uses multi-precision arithmetic (3 parts of π/16) for accuracy
+ *    - Uses multi-word π/16 (3 words with FMA, 4 without) for accuracy
  *
  * 2. Table Lookup: Retrieves precomputed sin(n*π/16) and cos(n*π/16)
- *    - Includes high and low precision parts for cos values
+ *    - Stores high and low parts for both sin and cos (lows packed 32:32)
  *
  * 3. Polynomial Approximation: Computes sin(r) and cos(r)
  *    - sin(r) ≈ r * (1 + r²*P_sin(r²)) where P_sin is a minimax polynomial
@@ -142,17 +143,16 @@ NPSR_INTRIN V High(V x) {
   // Note: cos_lo and sin_lo are packed together (32 bits each) to save memory.
   // cos_lo can be used as-is since it's in the upper bits, sin_lo needs
   // extraction. The precision loss is negligible for the final result.
-  // see data/lut-inl.h.sol for the table generation code.
+  // see data/kpi16-inl.h.sol for the table generation code.
   V sin_lo = BitCast(d, ShiftLeft<32>(BitCast(du, cos_lo)));
 
   // Step 3: Multi-precision computation of remainder r
   // r = x - n*(π/16)_high
+  // Without native FMA the non-tail parts carry 27/25/29 bits, so the two
+  // leading products n*part are exact for |n| < ceil(2^24*16/π) = 85445660.
+  // part2 and the tail round, but the idioms below capture that rounding.
   constexpr auto kPiDiv16Prec29 = data::kPiDiv16Prec29<kNativeFMA>;
   V r_hi = NegMulAdd(n, Set(d, kPiDiv16Prec29[0]), x);
-  if constexpr (!kNativeFMA) {
-    // For F64, we need to handle the low precision part separately
-    r_hi = NegMulAdd(n, Set(d, kPiDiv16Prec29[3]), r_hi);
-  }
   const V pi16_med = Set(d, kPiDiv16Prec29[1]);
   const V pi16_lo = Set(d, kPiDiv16Prec29[2]);
   V r_med = NegMulAdd(n, pi16_med, r_hi);
@@ -162,6 +162,15 @@ NPSR_INTRIN V High(V x) {
   V term = NegMulAdd(pi16_med, n, Sub(r_hi, r_med));
   V r_lo = MulAdd(pi16_lo, n, Sub(r, r_med));
   r_lo = Sub(term, r_lo);
+  if constexpr (!kNativeFMA) {
+    // Fourth piece (48 bits at 2^-91). Reusing the one rounded product in both
+    // the subtraction and its error capture keeps (r, r_lo) an exact
+    // double-double even when r is tiny near k*π/2.
+    const V tail_prod = Mul(n, Set(d, kPiDiv16Prec29[3]));
+    const V r_prev = r;
+    r = Sub(r_prev, tail_prod);
+    r_lo = Add(r_lo, Sub(Sub(r_prev, r), tail_prod));
+  }
 
   // Step 4: Polynomial approximation
   V r2 = Mul(r, r);
@@ -210,13 +219,23 @@ NPSR_INTRIN V High(V x) {
   if constexpr (OP == Operation::kCos) {
     // Cosine reconstruction: cos_table - sin_table*remainder
     // Equivalent to: cos(a)*cos(r) - sin(a)*sin(r) but more efficient
-    V res_hi = NegMulAdd(r, sin_hi, cos_hi);  // cos_hi - r*sin_hi
-
-    // This captures the precision lost in the main computation
-    V r_sin_hi = Sub(cos_hi, res_hi);  // Extract high part of multiplication
-
-    // Handles rounding errors and adds sin_low contribution
-    V r_sin_low = MulSub(r, sin_hi, r_sin_hi);  // Compute multiplication error
+    V res_hi, r_sin_low;
+    if constexpr (kNativeFMA) {
+      res_hi = NegMulAdd(r, sin_hi, cos_hi);  // cos_hi - r*sin_hi
+
+      // This captures the precision lost in the main computation
+      V r_sin_hi = Sub(cos_hi, res_hi);  // Extract high part of multiplication
+
+      // Handles rounding errors and adds the low-part contribution
+      r_sin_low = MulSub(r, sin_hi, r_sin_hi);  // Compute multiplication error
+    } else {
+      // Dekker split stands in for the FMA idiom
+      V r_sin, r_sin_rest;
+      SplitMul(r, sin_hi, r_sin, r_sin_rest);
+      res_hi = Sub(cos_hi, r_sin);
+      V r_sin_hi = Sub(cos_hi, res_hi);
+      r_sin_low = Add(Sub(r_sin, r_sin_hi), r_sin_rest);
+    }
     V sin_low_corr = MulAdd(r, sin_lo, r_sin_low);  // Add sin_low term
 
     // This is used to apply the low-precision remainder correction
@@ -245,13 +264,23 @@ NPSR_INTRIN V High(V x) {
   } else {
     // Sine reconstruction: sin_table + cos_table*remainder
     // Equivalent to: sin(a)*cos(r) + cos(a)*sin(r) but more efficient
-    V res_hi = MulAdd(r, cos_hi, sin_hi);  // sin_hi + r*cos_hi
-
-    // This captures the precision lost in the main computation
-    V r_cos_hi = Sub(res_hi, sin_hi);  // Extract high part of multiplication
-
-    // Handles rounding errors and adds cos_low contribution
-    V r_cos_low = MulSub(r, cos_hi, r_cos_hi);  // Compute multiplication error
+    V res_hi, r_cos_low;
+    if constexpr (kNativeFMA) {
+      res_hi = MulAdd(r, cos_hi, sin_hi);  // sin_hi + r*cos_hi
+
+      // This captures the precision lost in the main computation
+      V r_cos_hi = Sub(res_hi, sin_hi);  // Extract high part of multiplication
+
+      // Handles rounding errors and adds the low-part contribution
+      r_cos_low = MulSub(r, cos_hi, r_cos_hi);  // Compute multiplication error
+    } else {
+      // Dekker split stands in for the FMA idiom
+      V r_cos, r_cos_rest;
+      SplitMul(r, cos_hi, r_cos, r_cos_rest);
+      res_hi = Add(sin_hi, r_cos);
+      V r_cos_hi = Sub(res_hi, sin_hi);
+      r_cos_low = Add(Sub(r_cos, r_cos_hi), r_cos_rest);
+    }
     V cos_low_corr = MulAdd(r, cos_lo, r_cos_low);  // Add cos_low term
 
     // Intermediate term for r_low correction: cos_table - sin_table*r
diff --git a/npsr/trig/inl.h b/npsr/trig/inl.h
index 2e22bd7..9e16041 100644
--- a/npsr/trig/inl.h
+++ b/npsr/trig/inl.h
@@ -3,9 +3,10 @@
 // configurable precision, special case handling, and algorithm selection
 //
 // The implementation automatically selects between three algorithms:
-// 1. Low precision: ~1-4 ULP error, fastest
+// 1. Low precision: ~2-3 ULP error, fastest
 // 2. High precision: ~1 ULP error, moderate speed
-// 3. Extended precision: Exact for |x| > 2^24 (float) or 2^53 (double)
+// 3. Extended precision: Payne-Hanek reduction for huge |x|
+//    (> 10^4 for float, > 2^24 for double)
 
 #if defined(NPSR_TRIG_INL_H_) == defined(HWY_TARGET_TOGGLE)  // NOLINT
 #ifdef NPSR_TRIG_INL_H_
@@ -46,7 +47,8 @@ namespace npsr::HWY_NAMESPACE::trig {
  *
  * Thresholds for extended precision:
  * - Float: |x| > 10,000 (empirically chosen for accuracy)
- * - Double: |x| > 2^24 (16,777,216 - where 53-bit mantissa loses precision)
+ * - Double: |x| > 2^24 (16,777,216 - beyond this the reduction's n*π products
+ *   stop being exactly representable)
  */
 template <Operation OP, typename Prec, typename V>
 NPSR_INTRIN V Trig(Prec &prec, V x) {
@@ -56,8 +58,8 @@ NPSR_INTRIN V Trig(Prec &prec, V x) {
   V ret;
   // Step 1: Select base algorithm based on accuracy requirements
   if constexpr (Prec::kLowAccuracy) {
-    // Low precision: Cody-Waite reduction with degree-9 polynomial
-    // Error: ~2 ULP and 3~ for non-fma
+    // Low precision: Cody-Waite reduction, degree-9 (f32) / degree-15 (f64)
+    // Error: ~2-3 ULP
     ret = Low<OP>(x);
   } else {
     // High precision: π/16 reduction with table lookup + polynomial
@@ -78,11 +80,16 @@ NPSR_INTRIN V Trig(Prec &prec, V x) {
   // For |x| > threshold, standard algorithms lose precision due to
   // catastrophic cancellation in x - n*π reduction
   if constexpr (Prec::kLargeArgument) {
-    // Thresholds chosen based on when standard reduction loses accuracy:
-    // - Float: 10,000 is conservative but ensures < 1 ULP error
-    // - Double: 2^24 is where mantissa can't represent x and x-2π distinctly
+    // Thresholds mark where each path's n*π products stop being exact:
+    // - Float: 10,000, conservative but keeps the widened path < 1 ULP.
+    // - Double: 2^24, past which |round(x*16/π)| overflows the π/16 split.
+    // - Double low-accuracy cos: holds until trunc(|x|/π) > 8388606; the
+    //   constant is the largest double below that boundary (~8388607π).
+    constexpr bool kIsLowCos =
+        Prec::kLowAccuracy && OP == trig::Operation::kCos;
+    constexpr double kLargeF64 = kIsLowCos ? 0x1.921fb2200366fp+24 : 16777216.0;
     auto has_large_arg =
-        And(Gt(Abs(x), Set(d, kIsSingle ? 10000.0f : 16777216.0)), is_finite);
+        And(Gt(Abs(x), Set(d, kIsSingle ? 10000.0f : kLargeF64)), is_finite);
 
     // Extended precision is expensive, only use when necessary
     if (HWY_UNLIKELY(!AllFalse(d, has_large_arg))) {
diff --git a/npsr/trig/low-inl.h b/npsr/trig/low-inl.h
index 6da18ae..93cceee 100644
--- a/npsr/trig/low-inl.h
+++ b/npsr/trig/low-inl.h
@@ -56,13 +56,17 @@ NPSR_INTRIN V PolyLow(V r, V r2) {
   using namespace hn;
 
   const DFromV<V> d;
-  const V c15 = Set(d, -0x1.9f1517e9f65fp-41);
-  const V c13 = Set(d, 0x1.60e6bee01d83ep-33);
-  const V c11 = Set(d, -0x1.ae6355aaa4a53p-26);
-  const V c9 = Set(d, 0x1.71de3806add1ap-19);
-  const V c7 = Set(d, -0x1.a01a019a659ddp-13);
-  const V c5 = Set(d, 0x1.111111110a573p-7);
-  const V c3 = Set(d, -0x1.55555555554a8p-3);
+  // Both ops fit sin(r) on the same interval, so the two coefficient sets
+  // differ only in trailing bits; each matches its SVML counterpart
+  // (__svml_sin_d_la / __svml_cos_d_la) bit-for-bit.
+  constexpr bool kCos = OP == Operation::kCos;
+  const V c15 = Set(d, kCos ? -0x1.9f0d60811aac8p-41 : -0x1.9f1517e9f65fp-41);
+  const V c13 = Set(d, kCos ? 0x1.60e6857a2f220p-33 : 0x1.60e6bee01d83ep-33);
+  const V c11 = Set(d, kCos ? -0x1.ae63546002231p-26 : -0x1.ae6355aaa4a53p-26);
+  const V c9 = Set(d, kCos ? 0x1.71de38030fea0p-19 : 0x1.71de3806add1ap-19);
+  const V c7 = Set(d, kCos ? -0x1.a01a019a5b87bp-13 : -0x1.a01a019a659ddp-13);
+  const V c5 = Set(d, kCos ? 0x1.111111110a4a8p-7 : 0x1.111111110a573p-7);
+  const V c3 = Set(d, kCos ? -0x1.55555555554a7p-3 : -0x1.55555555554a8p-3);
   V poly = MulAdd(c15, r2, c13);
   poly = MulAdd(r2, poly, c11);
   poly = MulAdd(r2, poly, c9);
@@ -110,26 +114,28 @@ NPSR_INTRIN V Low(V x) {
     //   N' = N - 0.5
     n = Sub(n, Set(d, static_cast<T>(0.5)));
   }
-  // Use Cody-Waite method with triple-precision PI
+  // Cody-Waite reduction with multi-word π (3 words with FMA, 4 without)
   constexpr auto kPi = data::kPi<T, kNativeFMA>;
-
   V r = NegMulAdd(n, Set(d, kPi[0]), x_abs);
   r = NegMulAdd(n, Set(d, kPi[1]), r);
   V r_lo = NegMulAdd(n, Set(d, kPi[2]), r);
+
   if constexpr (!kNativeFMA) {
-    if (!kIsSingle) {
-      r = r_lo;
-    }
     r_lo = NegMulAdd(n, Set(d, kPi[3]), r_lo);
   }
-
-  if constexpr (kIsSingle) {
+  if constexpr (kIsSingle || !kNativeFMA) {
+    // The polynomial needs the fully reduced value; r still owes the last
+    // π word(s).
     r = r_lo;
   }
+
   V r2 = Mul(r, r);
   V poly = PolyLow<OP>(r, r2);
 
   if constexpr (!kIsSingle) {
+    // Non-FMA has r == r_lo, giving the plain r + r³·poly. With FMA this is
+    // r_lo·(1 + r²·poly) ≈ sin(r_lo): r and r_lo differ by n·π[2] (~2^-83)
+    // and sin(r)/r varies slowly, so the error stays sub-ULP.
     V r2_corr = Mul(r2, r_lo);
     poly = MulAdd(r2_corr, poly, r_lo);
   }

From 25c78204639fbbf7e17d33645fe0bd76bac2cbaf Mon Sep 17 00:00:00 2001
From: Sayed Awad <seiko@imavr.com>
Date: Mon, 27 Jul 2026 12:15:42 +0300
Subject: [PATCH 2/2] ENH: improve f32 sin/cos accuracy

The new improvements provide better accuracy for both non-FMA and FMA
targets, so we can achieve < 2ulp for the low accuracy path and < 0.6 for
the high accuracy path without affecting performance, except for a few ops on
non-FMA targets, which was necessary to match FMA target precision.
The improvements also include increasing the fast path ranges for FMA targets,
and it has been tested against an exhaustive test covering all float32 ranges.

This was achieved by refitting the f32 sin/cos polynomials as generated minimax sets (new
data/polyf32.h.pol) instead of SVML hardcoded coefficients, split per op and per
FMA mode. For non-FMA:
- High<> gets a third pi word with 31-bit heads so n*pi_i stays
- exact; FMA keeps the two-word 35+53-bit split.
- Low<> recovers the pi[2] rounding error via Fast2Sum on non-FMA,
  the same approach applies to float64 and buys ~0.3 ulp.

Also, for all targets:
- Low<> cos(x) == 1 is answered for all |x| below a per-type bound, not just
x_trans == pi/2, which fixes tiny tests.
- kLargeF32 replaces the flat 10000 with per-path measured thresholds.
- Sollya prec 512 -> 1024, which was needed for generating the float32-widening double poly.
---
 npsr/lut-inl.h                 |   1 +
 npsr/trig/data/constants.h     |   2 +-
 npsr/trig/data/constants.h.sol |  14 +++-
 npsr/trig/data/data.h          |   1 +
 npsr/trig/data/polyf32.h       |  32 ++++++++++
 npsr/trig/data/polyf32.h.sol   | 113 +++++++++++++++++++++++++++++++++
 npsr/trig/high-inl.h           |  28 ++++----
 npsr/trig/inl.h                |  45 +++++++------
 npsr/trig/low-inl.h            |  66 +++++++++++--------
 tools/sollya/core.sol          |   2 +-
 10 files changed, 243 insertions(+), 61 deletions(-)
 create mode 100644 npsr/trig/data/polyf32.h
 create mode 100644 npsr/trig/data/polyf32.h.sol

diff --git a/npsr/lut-inl.h b/npsr/lut-inl.h
index 97905ee..354593f 100644
--- a/npsr/lut-inl.h
+++ b/npsr/lut-inl.h
@@ -7,6 +7,7 @@
 
 #include <limits>
 #include <tuple>
+#include <limits>
 
 #include "npsr/hwy.h"
 
diff --git a/npsr/trig/data/constants.h b/npsr/trig/data/constants.h
index 89e9337..d56c88e 100644
--- a/npsr/trig/data/constants.h
+++ b/npsr/trig/data/constants.h
@@ -19,7 +19,7 @@ template <> inline constexpr double kPi<double, false>[] = {
 template <bool FMA> inline constexpr double kPiPrec35[] = {
 0x1.921fb5444p1, 0x1.68c234c4c6628p-38, };
 template <> inline constexpr double kPiPrec35<false>[] = {
-0x1.921fb6p1, -0x1.777a5cp-24, -0x1.ee59dap-49, };
+0x1.921fb544p1, 0x1.0b4611a8p-33, -0x1.d9cceba3f91f2p-65, };
 
 template <typename T> inline constexpr char kPiMul2[] = {};
 template <> inline constexpr float kPiMul2<float>[] = {
diff --git a/npsr/trig/data/constants.h.sol b/npsr/trig/data/constants.h.sol
index ef16bd8..178d60b 100644
--- a/npsr/trig/data/constants.h.sol
+++ b/npsr/trig/data/constants.h.sol
@@ -44,12 +44,20 @@ Append(
   // rounds ~2^-105, harmless even for tiny reduced arguments near k*π/2
   "",
   
-  // Special 35-bit precision π for specific algorithms
+  // Special 35-bit precision π for the f32 High path, which reduces in double.
+  // FMA: the fused subtractions never need n*πᵢ to be representable, so two
+  // words carry the whole budget and π is held to 35+53 = 88 bits.
+  //
+  // non-FMA: NegMulAdd decays to `x - fl(n*πᵢ)`, so each n*πᵢ has to be exact.
+  // The quotient is bounded by the f32 magic-round in High(), |n| < 2^22, hence
+  // 53-22 = 31-bit heads. Two of those only pin π to 62 bits, so a 53-bit tail
+  // follows; its product rounds at ~2^-92, just under the FMA split's 2^-90
+  // residual, which is what keeps both variants on the same accuracy curve.
   "template <bool FMA> inline constexpr double kPiPrec35[] = " @
   KArray_(Float64, pi, [|RN, 35|], [|RD, 53|]),
-  
+
   "template <> inline constexpr double kPiPrec35<false>[] = " @
-  KArray_(Float64, pi, [|RN, 24, 24, 24|]),
+  KArray_(Float64, pi, [|RN, 31, 31|], [|RN, 53|]),
   "",
   
   // 2π constants for angle wrapping
diff --git a/npsr/trig/data/data.h b/npsr/trig/data/data.h
index b82545f..3d74381 100644
--- a/npsr/trig/data/data.h
+++ b/npsr/trig/data/data.h
@@ -8,6 +8,7 @@
 // their own guards and no-op on re-entry.
 #include "npsr/lut-inl.h"
 #include "npsr/trig/data/constants.h"
+#include "npsr/trig/data/polyf32.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/polyf32.h b/npsr/trig/data/polyf32.h
new file mode 100644
index 0000000..2e71ae5
--- /dev/null
+++ b/npsr/trig/data/polyf32.h
@@ -0,0 +1,32 @@
+// Auto-generated by npsr/trig/data/polyf32.h.sol
+// Use `spin sollya -f` to force regeneration
+#ifndef NPSR_TRIG_DATA_POLYF32_H
+#define NPSR_TRIG_DATA_POLYF32_H
+
+namespace npsr::trig::data {
+// Degree-9 odd minimax sin(x) = x + x^3*P(x^2) on [2^-20, pi/2].
+// Coefficients {c3, c5, c7, c9} for the f32 PolyLow in npsr/trig/low-inl.h.
+// See poly.h.sol for the recipe, pins and measured worst cases.
+template <bool FMA> inline constexpr float kSinPolyLowF32[] = {
+-0x1.555544p-3f, 0x1.110d94p-7f, -0x1.9f3644p-13f, 0x1.5a9eap-19f, 
+};
+template <bool FMA> inline constexpr float kCosPolyLowF32[] = {
+-0x1.555548p-3f, 0x1.110e34p-7f, -0x1.9f527cp-13f, 0x1.5c1b4p-19f, 
+};
+template <> inline constexpr float kSinPolyLowF32<false>[] = {
+-0x1.55554ap-3f, 0x1.110e88p-7f, -0x1.9f621ap-13f, 0x1.5cfce2p-19f, 
+};
+template <> inline constexpr float kCosPolyLowF32<false>[] = {
+-0x1.55554ap-3f, 0x1.110e9p-7f, -0x1.9f653ep-13f, 0x1.5d3afep-19f, 
+};
+
+// Degree-9 odd minimax sin(r) on [2^-30, pi/2 + 0.012] for the f32 High path
+// in trig/high-inl.h; c1 is fitted, not pinned to 1. See poly.h.sol.
+// Relative error 9.64818894863128662109375e-2 ulp(f32). Coefficients {c1, c3, c5, c7, c9}.
+inline constexpr double kSinPolyHighF32[] = {
+0x1.ffffffce99ecep-1, -0x1.5555471207a17p-3, 0x1.110e5bbaaff44p-7, 
+-0x1.9f5e996744e9ep-13, 0x1.5ce7e229f1f1p-19, };
+
+} // namespace npsr::trig::data
+
+#endif // NPSR_TRIG_DATA_POLYF32_H
diff --git a/npsr/trig/data/polyf32.h.sol b/npsr/trig/data/polyf32.h.sol
new file mode 100644
index 0000000..41463aa
--- /dev/null
+++ b/npsr/trig/data/polyf32.h.sol
@@ -0,0 +1,113 @@
+// f32 Low trig coefficients: sin(x) ~= x + x^3*P(x^2), degree 9, odd.
+// 333/346/368 are recoverable Remez warnings the constrained refits below
+// always trip; the driver would treat them as errors.
+suppressmessage(346, 333, 368);
+
+I = [0x1p-20; pi/2];
+vFree = fpminimax(sin(x), [|3, 5, 7, 9|], [|single...|], I, relative, floating, x);
+
+// Relative error in ULP at 1 (= 2^-24); guards regeneration against a worse fit.
+procedure ErrULP(pP) { return dirtyinfnorm(pP(x)/sin(x) - 1, I) * 0x1p24; };
+Assert(ErrULP(vFree) < 0.12, "f32 Low free fit error regressed: " @ ErrULP(vFree));
+
+// One f32 ULP at a coefficient's scale. No coefficient sits within a step of
+// a power of two, so the constant step is exact.
+procedure Ulp(pC) { return 2^(floor(log2(abs(pC))) - 23); };
+
+// Pin c3 (then c5, then optionally c7) an integer number of ULPs off the free
+// fit and refit the rest under the pin. Pin indices come from exhaustive
+// measurement of the compiled kernel over [0, 1e4); no analytic criterion
+// sees the eval DAG's per-operation rounding.
+procedure Stage2(pK3, pJ5) {
+  var vC3, vP5, vC5, vP7;
+  vC3 = round(coeff(vFree, 3) + pK3 * Ulp(coeff(vFree, 3)), single, RN);
+  vP5 = fpminimax(sin(x), [|5, 7, 9|], [|single...|], I, relative, floating,
+                  x + vC3 * x^3);
+  vC5 = round(coeff(vP5, 5) + pJ5 * Ulp(coeff(vP5, 5)), single, RN);
+  vP7 = fpminimax(sin(x), [|7, 9|], [|single...|], I, relative, floating,
+                  x + vC3 * x^3 + vC5 * x^5);
+  return [| vC3, vC5, vP7 |];
+};
+
+procedure CheckPinned(pSet, pTag) {
+  Assert(ErrULP(pSet[0]*x^3 + pSet[1]*x^5 + pSet[2]*x^7 + pSet[3]*x^9 + x) < 1.0,
+         "pinned set " @ pTag @ " analytic error drifted");
+  return pSet;
+};
+
+// c7/c9 come jointly from the stage-two fit.
+procedure Pinned(pK3, pJ5) {
+  var vS;
+  vS = Stage2(pK3, pJ5);
+  return CheckPinned([| vS[0], vS[1], coeff(vS[2], 7), coeff(vS[2], 9) |],
+                     "(" @ pK3 @ "," @ pJ5 @ ")");
+};
+
+// Additionally pin c7 and refit c9 alone. Only FMA cos gains from it.
+procedure Pinned3(pK3, pJ5, pL7) {
+  var vS, vC7, vP9;
+  vS = Stage2(pK3, pJ5);
+  vC7 = round(coeff(vS[2], 7) + pL7 * Ulp(coeff(vS[2], 7)), single, RN);
+  vP9 = fpminimax(sin(x), [|9|], [|single...|], I, relative, floating,
+                  x + vS[0] * x^3 + vS[1] * x^5 + vC7 * x^7);
+  return CheckPinned([| vS[0], vS[1], vC7, coeff(vP9, 9) |],
+                     "(" @ pK3 @ "," @ pJ5 @ "," @ pL7 @ ")");
+};
+
+// Exhaustive [0, 1e4) worst case, pinned vs free fit, in ULP:
+//   FMA:     sin 1.886 (free 2.191)   cos 1.815 (free 2.110)
+//   non-FMA: sin 1.912 (free 1.939)   cos 1.948 (free 1.966)
+// Non-FMA is eval-rounding bound (~1.9 of the ~1.95 total), so pins only
+// shift which argument realizes the worst alignment; the whole (k3, j5, l7)
+// grid stays within 0.02 of the sets below.
+vFmaSin = Pinned(4, 1);
+vFmaCos = Pinned3(2, 1, 8);
+vNoFmaSin = Pinned(1, 1);
+vNoFmaCos = Pinned(1, 5);
+
+Append(
+  "// Degree-9 odd minimax sin(x) = x + x^3*P(x^2) on [2^-20, pi/2].",
+  "// Coefficients {c3, c5, c7, c9} for the f32 PolyLow in npsr/trig/low-inl.h.",
+  "// See poly.h.sol for the recipe, pins and measured worst cases.",
+  "template <bool FMA> inline constexpr float kSinPolyLowF32[] = " @ CArrayT(Float32, vFmaSin, 4) @ ";",
+  "template <bool FMA> inline constexpr float kCosPolyLowF32[] = " @ CArrayT(Float32, vFmaCos, 4) @ ";",
+  "template <> inline constexpr float kSinPolyLowF32<false>[] = " @ CArrayT(Float32, vNoFmaSin, 4) @ ";",
+  "template <> inline constexpr float kCosPolyLowF32<false>[] = " @ CArrayT(Float32, vNoFmaCos, 4) @ ";",
+  ""
+);
+
+// f32 High coefficients, held and evaluated in double by npsr/trig/high-inl.h.
+//
+// c1 is fitted, not pinned to 1: MulAdd(r2, poly, c1) + Mul(poly, r) closes in
+// the same two ops as the pinned x + x^3*P(x^2), so the free parameter is free
+// -- 0.1099 -> 0.0965 ulp. No pinning stage either: eval is in double (~2^-52),
+// so unlike the single Low sets above there is no rounding for pins to steer.
+//
+// The interval tracks the cutover in npsr/trig/inl.h and must move with it: n
+// comes from a f32 magic-round, so |r| overshoots pi/2 by up to |x|*1.7e-7.
+// 0.012 is the exhaustive ceiling below both cutovers, and widening costs
+// accuracy fast: 0.0892 ulp at pi/2, 0.0965 here, 0.1073 at 0.028.
+IHigh = [0x1p-30; pi/2 + 0.012];
+vHigh = fpminimax(sin(x), [|1, 3, 5, 7, 9|], [|double...|], IHigh, relative, floating);
+
+// Leaves High<> at 0.5 (final f32 rounding) + 0.097, the f32 ceiling: the
+// Extended kernel above the cutover measures 0.5031, so this fit -- not the
+// Payne-Hanek reduction -- is what keeps sin/cos off correct rounding.
+errHigh = dirtyinfnorm(vHigh(x)/sin(x) - 1, IHigh) * 0x1p24;
+Assert(errHigh < 0.0970, "f32 High fit error regressed: " @ errHigh);
+// The driver leaves display in hexadecimal, which is unreadable for an error.
+display = decimal!;
+errHighStr = "" @ round(errHigh, 24, RN);
+display = hexadecimal!;
+
+Append(
+  "// Degree-9 odd minimax sin(r) on [2^-30, pi/2 + 0.012] for the f32 High path",
+  "// in trig/high-inl.h; c1 is fitted, not pinned to 1. See poly.h.sol.",
+  "// Relative error " @ errHighStr @ " ulp(f32). Coefficients {c1, c3, c5, c7, c9}.",
+  "inline constexpr double kSinPolyHighF32[] = " @
+  CArrayT(Float64, [| coeff(vHigh, 1), coeff(vHigh, 3), coeff(vHigh, 5),
+                      coeff(vHigh, 7), coeff(vHigh, 9) |], 3) @ ";",
+  ""
+);
+
+WriteCPPHeader("npsr::trig::data");
diff --git a/npsr/trig/high-inl.h b/npsr/trig/high-inl.h
index 65d0fd3..a2655bd 100644
--- a/npsr/trig/high-inl.h
+++ b/npsr/trig/high-inl.h
@@ -59,21 +59,27 @@ NPSR_INTRIN V High(V x) {
   }
   auto WideCal = [](const VW &nh, const VW &xh_abs) -> VW {
     const DFromV<VW> dw;
-    constexpr auto kPiPrec35 = data::kPiPrec35<true>;
+    // Cody-Waite r = x - n*π, one word per NegMulAdd. Without FMA the product
+    // rounds, so that split spends a third word on 31-bit heads to keep n*πᵢ
+    // exact; see constants.h.sol.
+    constexpr auto kPiPrec35 = data::kPiPrec35<kNativeFMA>;
     VW r = NegMulAdd(nh, Set(dw, kPiPrec35[0]), xh_abs);
     r = NegMulAdd(nh, Set(dw, kPiPrec35[1]), r);
+    if constexpr (!kNativeFMA) {
+      r = NegMulAdd(nh, Set(dw, kPiPrec35[2]), r);
+    }
     VW r2 = Mul(r, r);
 
-    // Polynomial coefficients for sin(r) approximation on [-π/2, π/2]
-    const VW c9 = Set(dw, 0x1.5dbdf0e4c7deep-19);
-    const VW c7 = Set(dw, -0x1.9f6ffeea73463p-13);
-    const VW c5 = Set(dw, 0x1.110ed3804ca96p-7);
-    const VW c3 = Set(dw, -0x1.55554bc836587p-3);
-    VW poly = MulAdd(c9, r2, c7);
-    poly = MulAdd(r2, poly, c5);
-    poly = MulAdd(r2, poly, c3);
-    poly = Mul(poly, r2);
-    poly = MulAdd(r, poly, r);
+    // Degree-9 odd minimax for sin(r); the fit is this path's whole error
+    // budget (0.5 + 0.0965 ULP). c1 is fitted, not pinned to 1 -- same two
+    // closing ops as r + r^3*P(r^2), one more free parameter. Within 2^-27.4
+    // of 1, so sin(r) still demotes to r bit-exactly. See data/polyf32.h.sol.
+    constexpr auto kPoly = data::kSinPolyHighF32;
+    VW poly = MulAdd(Set(dw, kPoly[4]), r2, Set(dw, kPoly[3]));
+    poly = MulAdd(r2, poly, Set(dw, kPoly[2]));
+    poly = MulAdd(r2, poly, Set(dw, kPoly[1]));
+    poly = MulAdd(r2, poly, Set(dw, kPoly[0]));
+    poly = Mul(poly, r);
     return poly;
   };
 
diff --git a/npsr/trig/inl.h b/npsr/trig/inl.h
index 9e16041..d71f691 100644
--- a/npsr/trig/inl.h
+++ b/npsr/trig/inl.h
@@ -1,13 +1,12 @@
-// Main trigonometric function dispatcher for Highway SIMD library
 // This file provides the public API for sine and cosine functions with
-// configurable precision, special case handling, and algorithm selection
+// configurable precision, special case handling, and algorithm selection.
+//
+// The implementation automatically selects between:
+// 1. Low precision: < 2 ULP for f32 and < 3.5 ULP for f64
+// 2. High precision: < 0.6 ULP for f32, < 1 ULP for f64; moderate speed
+// 3. Extended precision: Payne-Hanek reduction for huge |x|, similar
+// accuracy to High precision but a slow path.
 //
-// The implementation automatically selects between three algorithms:
-// 1. Low precision: ~2-3 ULP error, fastest
-// 2. High precision: ~1 ULP error, moderate speed
-// 3. Extended precision: Payne-Hanek reduction for huge |x|
-//    (> 10^4 for float, > 2^24 for double)
-
 #if defined(NPSR_TRIG_INL_H_) == defined(HWY_TARGET_TOGGLE)  // NOLINT
 #ifdef NPSR_TRIG_INL_H_
 #undef NPSR_TRIG_INL_H_
@@ -42,11 +41,13 @@ namespace npsr::HWY_NAMESPACE::trig {
  *
  * Algorithm selection:
  * 1. If kLowAccuracy: Use Low<> (Cody-Waite with minimal polynomial)
- * 2. Otherwise: Use High<> (π/16 reduction with table lookup)
+ * 2. Otherwise: Use High<> (f32: π reduction in double; f64: π/16 reduction
+ *    with table lookup)
  * 3. If kLargeArgument and |x| > threshold: Override with Extended<>
  *
  * Thresholds for extended precision:
- * - Float: |x| > 10,000 (empirically chosen for accuracy)
+ * - Float: |x| > the largest argument the chosen path still meets its bound at
+ *   (differs per accuracy/FMA/op; see kLargeF32)
  * - Double: |x| > 2^24 (16,777,216 - beyond this the reduction's n*π products
  *   stop being exactly representable)
  */
@@ -58,12 +59,8 @@ NPSR_INTRIN V Trig(Prec &prec, V x) {
   V ret;
   // Step 1: Select base algorithm based on accuracy requirements
   if constexpr (Prec::kLowAccuracy) {
-    // Low precision: Cody-Waite reduction, degree-9 (f32) / degree-15 (f64)
-    // Error: ~2-3 ULP
     ret = Low<OP>(x);
   } else {
-    // High precision: π/16 reduction with table lookup + polynomial
-    // Error: ~1 ULP
     ret = High<OP>(x);
   }
   // Step 2: Handle special cases (NaN, Inf) if enabled
@@ -80,16 +77,26 @@ NPSR_INTRIN V Trig(Prec &prec, V x) {
   // For |x| > threshold, standard algorithms lose precision due to
   // catastrophic cancellation in x - n*π reduction
   if constexpr (Prec::kLargeArgument) {
-    // Thresholds mark where each path's n*π products stop being exact:
-    // - Float: 10,000, conservative but keeps the widened path < 1 ULP.
+    // Thresholds mark where each path stops meeting its bound, i.e. where its
+    // range reduction breaks down, not where mantissa resolution runs out:
+    // - Float: each path keeps its own accuracy bound up to a different |x|;
+    //   every constant below is the round value under the exhaustively
+    //   measured, MPFR-confirmed first argument that exceeds it. The low paths
+    //   break far earlier without FMA, because there the extra π word is spent
+    //   on keeping n*πᵢ representable rather than on headroom.
     // - Double: 2^24, past which |round(x*16/π)| overflows the π/16 split.
     // - Double low-accuracy cos: holds until trunc(|x|/π) > 8388606; the
     //   constant is the largest double below that boundary (~8388607π).
-    constexpr bool kIsLowCos =
-        Prec::kLowAccuracy && OP == trig::Operation::kCos;
+    constexpr bool kIsCos = OP == trig::Operation::kCos;
+    constexpr bool kIsLowCos = Prec::kLowAccuracy && kIsCos;
+    constexpr float kLargeF32 =
+        Prec::kLowAccuracy
+            ? (kNativeFMA ? (kIsCos ? 1600000.0f : 2200000.0f)
+                          : (kIsCos ? 12000.0f : 25000.0f))
+            : (kNativeFMA ? 200000.0f : 130000.0f);
     constexpr double kLargeF64 = kIsLowCos ? 0x1.921fb2200366fp+24 : 16777216.0;
     auto has_large_arg =
-        And(Gt(Abs(x), Set(d, kIsSingle ? 10000.0f : kLargeF64)), is_finite);
+        And(Gt(Abs(x), Set(d, kIsSingle ? kLargeF32 : kLargeF64)), is_finite);
 
     // Extended precision is expensive, only use when necessary
     if (HWY_UNLIKELY(!AllFalse(d, has_large_arg))) {
diff --git a/npsr/trig/low-inl.h b/npsr/trig/low-inl.h
index 93cceee..1955795 100644
--- a/npsr/trig/low-inl.h
+++ b/npsr/trig/low-inl.h
@@ -17,31 +17,32 @@ enum class Operation { kSin = 0, kCos = 1 };
 template <Operation OP, typename V, HWY_IF_F32(TFromV<V>)>
 NPSR_INTRIN V PolyLow(V r, V r2) {
   using namespace hn;
+  namespace data = ::npsr::trig::data;
 
   const DFromV<V> d;
   constexpr bool kCos = OP == Operation::kCos;
-  const V c9 = Set(d, kCos ? 0x1.5d866ap-19f : 0x1.5dbdfp-19f);
-  const V c7 = Set(d, kCos ? -0x1.9f6d9ep-13 : -0x1.9f6ffep-13f);
-  const V c5 = Set(d, kCos ? 0x1.110ec8p-7 : 0x1.110eccp-7f);
-  const V c3 = Set(d, -0x1.55554cp-3f);
+  // cos reduces around (N + 0.5)·π, so both ops evaluate sin(r) here; the
+  // per-op/per-mode sets differ only in pinning (see data/polyf32.h.sol).
+  constexpr auto kSet = (kCos ? data::kCosPolyLowF32<kNativeFMA>
+                              : data::kSinPolyLowF32<kNativeFMA>);
+  const V c9 = Set(d, kSet[3]);
+  const V c7 = Set(d, kSet[2]);
+  const V c5 = Set(d, kSet[1]);
+  const V c3 = Set(d, kSet[0]);
   V poly = MulAdd(c9, r2, c7);
   poly = MulAdd(r2, poly, c5);
   poly = MulAdd(r2, poly, c3);
-  if constexpr (OP == Operation::kCos) {
-    // Although this path handles cosine, we have already transformed the
-    // input using the identity: cos(x) = sin(x + π/2) This means we're no
-    // longer directly evaluating a cosine Taylor series; instead, we evaluate
-    // the sine approximation polynomial at (x + π/2).
-    //
-    // The sine approximation has the general form:
-    //    sin(r) ≈ r + r³ · P(r²)
-    //
-    // So, we compute:
-    //    r³ = r · r²
-    //    sin(r) ≈ r + r³ · poly
-    //
-    // This formulation preserves accuracy by computing the highest order
-    // terms last, which benefits from FMA to reduce rounding error.
+  // cos was mapped to sin via cos(x) = sin(x + π/2) during reduction, so all
+  // branches evaluate the same sine polynomial sin(r) ≈ r + r³ · P(r²), not a
+  // cosine series. All three build r + r³·poly in three ops; only the grouping
+  // differs. Without FMA every intermediate is rounded and r·poly lands in the
+  // lowest binade of the three, worth ~0.1 ULP. With FMA the choice is nearly
+  // free and cos measures ~0.06 ULP better in SVML's order (r³ first, matching
+  // SVML's R = X + X·X²·(...)).
+  if constexpr (!kNativeFMA) {
+    poly = Mul(r, poly);
+    poly = MulAdd(poly, r2, r);
+  } else if constexpr (kCos) {
     V r3 = Mul(r2, r);
     poly = MulAdd(r3, poly, r);
   } else {
@@ -92,13 +93,17 @@ NPSR_INTRIN V Low(V x) {
 
   constexpr bool kIsSingle = std::is_same_v<T, float>;
   // Transform cosine to sine using identity: cos(x) = sin(x + π/2)
-  const V half_pi = Set(d, data::kHalfPi<T>);
   V x_trans = x_abs;
   if constexpr (OP == Operation::kCos) {
-    x_trans = Add(x_abs, half_pi);
+    x_trans = Add(x_abs, Set(d, data::kHalfPi<T>));
   }
-  // check zero input/subnormal for cosine (cos(~0) = 1)
-  const auto is_cos_near_zero = Eq(x_trans, half_pi);
+  // cos(x) rounds to exactly 1 up to these (largest such value per type).
+  // Answering 1 directly instead of catching only x_trans == half_pi matters
+  // for correctness, not just speed: tiny x reduces to r hugging pi/2, where
+  // the poly's per-op rounding cannot land on 1.0 for every such r.
+  constexpr T kCosOneMax =
+      static_cast<T>(kIsSingle ? 0x1p-12 : 0x1.6a09e667f3bccp-27);
+  const auto is_cos_near_zero = Le(x_abs, Set(d, kCosOneMax));
 
   // Compute N = round(x/π) using "magic number" technique
   // and stores integer part in mantissa
@@ -118,10 +123,19 @@ NPSR_INTRIN V Low(V x) {
   constexpr auto kPi = data::kPi<T, kNativeFMA>;
   V r = NegMulAdd(n, Set(d, kPi[0]), x_abs);
   r = NegMulAdd(n, Set(d, kPi[1]), r);
-  V r_lo = NegMulAdd(n, Set(d, kPi[2]), r);
-
+  V r_lo;
   if constexpr (!kNativeFMA) {
-    r_lo = NegMulAdd(n, Set(d, kPi[3]), r_lo);
+    // n·π[2] is exact, so Fast2Sum recovers the π[2] rounding error into the
+    // π[3] step. 
+    const V p2 = Mul(n, Set(d, kPi[2]));
+    const V ra = Sub(r, p2);
+    const V p2_err = Sub(Sub(r, ra), p2);
+    r_lo = Sub(ra, Sub(Mul(n, Set(d, kPi[3])), p2_err));
+  } else {
+    r_lo = NegMulAdd(n, Set(d, kPi[2]), r);
+    if constexpr (!kNativeFMA) {
+      r_lo = NegMulAdd(n, Set(d, kPi[3]), r_lo);
+    }
   }
   if constexpr (kIsSingle || !kNativeFMA) {
     // The polynomial needs the fully reduced value; r still owes the last
diff --git a/tools/sollya/core.sol b/tools/sollya/core.sol
index 8c4d5a1..136f9de 100644
--- a/tools/sollya/core.sol
+++ b/tools/sollya/core.sol
@@ -1,7 +1,7 @@
 // Sollya utility functions for generating C++ header files with mathematical constants and lookup tables
 
 // Initial Sollya configuration
-prec = 512;           // High precision for accurate constant computation
+prec = 1024;           // High precision for accurate constant computation
 display = hexadecimal; // Hex display for exact bit representation
 verbosity = 4;        // Verbose output to detect NaN values
 showmessagenumbers = on;