[libc-commits] [libc] [libc][math] Implement double precision sin correctly rounded to all rounding modes. (PR #95736)
via libc-commits
libc-commits at lists.llvm.org
Wed Jun 19 05:15:48 PDT 2024
================
@@ -0,0 +1,570 @@
+//===-- Double-precision sin function -------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/sin.h"
+#include "hdr/errno_macros.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/double_double.h"
+#include "src/__support/FPUtil/dyadic_float.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/nearest_integer.h"
+#include "src/__support/FPUtil/rounding_mode.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
+#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA
+
+#include "range_reduction_double_fma.h"
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+using LIBC_NAMESPACE::fma::range_reduction_small;
+#else
+#include "range_reduction_double.h"
+using LIBC_NAMESPACE::generic::range_reduction_small;
+#endif // LIBC_TARGET_CPU_HAS_FMA
+
+// TODO: Implement generic's range_reduction_large correctly rounded for all
+// rounding modes. The current fma's range_reduction_large only works for
+// round-to-nearest without FMA instruction.
+using LIBC_NAMESPACE::fma::range_reduction_large;
+using LIBC_NAMESPACE::fma::range_reduction_large_f128;
+using LIBC_NAMESPACE::fma::range_reduction_small_f128;
+
+#include "sincos_eval.h"
+
+#if ((LIBC_MATH & LIBC_MATH_SKIP_ACCURATE_PASS) != 0)
+#define LIBC_MATH_SIN_SKIP_ACCURATE_PASS
+#endif
+
+namespace LIBC_NAMESPACE {
+
+using DoubleDouble = fputil::DoubleDouble;
+using Float128 = typename fputil::DyadicFloat<128>;
+
+namespace {
+
+// Lookup table for sin(k * pi / 128) with k = 0, ..., 255.
+// Table is generated with Sollya as follow:
+// > display = hexadecimal;
+// > for k from 0 to 255 do {
+// a = D(sin(k * pi/128)); };
+// b = D(sin(k * pi/128) - a);
+// print("{", b, ",", a, "},");
+// };
+LIBC_INLINE constexpr DoubleDouble SIN_K_PI_OVER_128[256] = {
+ {0, 0},
+ {-0x1.b1d63091a013p-64, 0x1.92155f7a3667ep-6},
+ {-0x1.912bd0d569a9p-61, 0x1.91f65f10dd814p-5},
+ {-0x1.9a088a8bf6b2cp-59, 0x1.2d52092ce19f6p-4},
+ {-0x1.e2718d26ed688p-60, 0x1.917a6bc29b42cp-4},
+ {0x1.a2704729ae56dp-59, 0x1.f564e56a9730ep-4},
+ {0x1.13000a89a11ep-58, 0x1.2c8106e8e613ap-3},
+ {0x1.531ff779ddac6p-57, 0x1.5e214448b3fc6p-3},
+ {-0x1.26d19b9ff8d82p-57, 0x1.8f8b83c69a60bp-3},
+ {-0x1.af1439e521935p-62, 0x1.c0b826a7e4f63p-3},
+ {-0x1.42deef11da2c4p-57, 0x1.f19f97b215f1bp-3},
+ {0x1.824c20ab7aa9ap-56, 0x1.111d262b1f677p-2},
+ {-0x1.5d28da2c4612dp-56, 0x1.294062ed59f06p-2},
+ {0x1.0c97c4afa2518p-56, 0x1.4135c94176601p-2},
+ {-0x1.efdc0d58cf62p-62, 0x1.58f9a75ab1fddp-2},
+ {-0x1.44b19e0864c5dp-56, 0x1.7088530fa459fp-2},
+ {-0x1.72cedd3d5a61p-57, 0x1.87de2a6aea963p-2},
+ {0x1.6da81290bdbabp-57, 0x1.9ef7943a8ed8ap-2},
+ {0x1.5b362cb974183p-57, 0x1.b5d1009e15ccp-2},
+ {0x1.6850e59c37f8fp-58, 0x1.cc66e9931c45ep-2},
+ {0x1.e0d891d3c6841p-58, 0x1.e2b5d3806f63bp-2},
+ {-0x1.2ec1fc1b776b8p-60, 0x1.f8ba4dbf89abap-2},
+ {-0x1.a5a014347406cp-55, 0x1.073879922ffeep-1},
+ {-0x1.ef23b69abe4f1p-55, 0x1.11eb3541b4b23p-1},
+ {0x1.b25dd267f66p-55, 0x1.1c73b39ae68c8p-1},
+ {-0x1.5da743ef3770cp-55, 0x1.26d054cdd12dfp-1},
+ {-0x1.efcc626f74a6fp-57, 0x1.30ff7fce17035p-1},
+ {0x1.e3e25e3954964p-56, 0x1.3affa292050b9p-1},
+ {0x1.8076a2cfdc6b3p-57, 0x1.44cf325091dd6p-1},
+ {0x1.3c293edceb327p-57, 0x1.4e6cabbe3e5e9p-1},
+ {-0x1.75720992bfbb2p-55, 0x1.57d69348cecap-1},
+ {-0x1.251b352ff2a37p-56, 0x1.610b7551d2cdfp-1},
+ {-0x1.bdd3413b26456p-55, 0x1.6a09e667f3bcdp-1},
+ {0x1.0d4ef0f1d915cp-55, 0x1.72d0837efff96p-1},
+ {-0x1.0f537acdf0ad7p-56, 0x1.7b5df226aafafp-1},
+ {-0x1.6f420f8ea3475p-56, 0x1.83b0e0bff976ep-1},
+ {-0x1.2c5e12ed1336dp-55, 0x1.8bc806b151741p-1},
+ {0x1.3d419a920df0bp-55, 0x1.93a22499263fbp-1},
+ {-0x1.30ee286712474p-55, 0x1.9b3e047f38741p-1},
+ {-0x1.128bb015df175p-56, 0x1.a29a7a0462782p-1},
+ {0x1.9f630e8b6dac8p-60, 0x1.a9b66290ea1a3p-1},
+ {-0x1.926da300ffccep-55, 0x1.b090a581502p-1},
+ {-0x1.bc69f324e6d61p-55, 0x1.b728345196e3ep-1},
+ {-0x1.825a732ac700ap-55, 0x1.bd7c0ac6f952ap-1},
+ {-0x1.6e0b1757c8d07p-56, 0x1.c38b2f180bdb1p-1},
+ {-0x1.2fb761e946603p-58, 0x1.c954b213411f5p-1},
+ {-0x1.e7b6bb5ab58aep-58, 0x1.ced7af43cc773p-1},
+ {-0x1.4ef5295d25af2p-55, 0x1.d4134d14dc93ap-1},
+ {0x1.457e610231ac2p-56, 0x1.d906bcf328d46p-1},
+ {0x1.83c37c6107db3p-55, 0x1.ddb13b6ccc23cp-1},
+ {-0x1.014c76c126527p-55, 0x1.e212104f686e5p-1},
+ {-0x1.16b56f2847754p-57, 0x1.e6288ec48e112p-1},
+ {0x1.760b1e2e3f81ep-55, 0x1.e9f4156c62ddap-1},
+ {0x1.e82c791f59cc2p-56, 0x1.ed740e7684963p-1},
+ {0x1.52c7adc6b4989p-56, 0x1.f0a7efb9230d7p-1},
+ {-0x1.d7bafb51f72e6p-56, 0x1.f38f3ac64e589p-1},
+ {0x1.562172a361fd3p-56, 0x1.f6297cff75cbp-1},
+ {0x1.ab256778ffcb6p-56, 0x1.f8764fa714ba9p-1},
+ {-0x1.7a0a8ca13571fp-55, 0x1.fa7557f08a517p-1},
+ {0x1.1ec8668ecaceep-55, 0x1.fc26470e19fd3p-1},
+ {-0x1.87df6378811c7p-55, 0x1.fd88da3d12526p-1},
+ {0x1.521ecd0c67e35p-57, 0x1.fe9cdad01883ap-1},
+ {-0x1.c57bc2e24aa15p-57, 0x1.ff621e3796d7ep-1},
+ {-0x1.1354d4556e4cbp-55, 0x1.ffd886084cd0dp-1},
+ {0, 1},
+ {-0x1.1354d4556e4cbp-55, 0x1.ffd886084cd0dp-1},
+ {-0x1.c57bc2e24aa15p-57, 0x1.ff621e3796d7ep-1},
+ {0x1.521ecd0c67e35p-57, 0x1.fe9cdad01883ap-1},
+ {-0x1.87df6378811c7p-55, 0x1.fd88da3d12526p-1},
+ {0x1.1ec8668ecaceep-55, 0x1.fc26470e19fd3p-1},
+ {-0x1.7a0a8ca13571fp-55, 0x1.fa7557f08a517p-1},
+ {0x1.ab256778ffcb6p-56, 0x1.f8764fa714ba9p-1},
+ {0x1.562172a361fd3p-56, 0x1.f6297cff75cbp-1},
+ {-0x1.d7bafb51f72e6p-56, 0x1.f38f3ac64e589p-1},
+ {0x1.52c7adc6b4989p-56, 0x1.f0a7efb9230d7p-1},
+ {0x1.e82c791f59cc2p-56, 0x1.ed740e7684963p-1},
+ {0x1.760b1e2e3f81ep-55, 0x1.e9f4156c62ddap-1},
+ {-0x1.16b56f2847754p-57, 0x1.e6288ec48e112p-1},
+ {-0x1.014c76c126527p-55, 0x1.e212104f686e5p-1},
+ {0x1.83c37c6107db3p-55, 0x1.ddb13b6ccc23cp-1},
+ {0x1.457e610231ac2p-56, 0x1.d906bcf328d46p-1},
+ {-0x1.4ef5295d25af2p-55, 0x1.d4134d14dc93ap-1},
+ {-0x1.e7b6bb5ab58aep-58, 0x1.ced7af43cc773p-1},
+ {-0x1.2fb761e946603p-58, 0x1.c954b213411f5p-1},
+ {-0x1.6e0b1757c8d07p-56, 0x1.c38b2f180bdb1p-1},
+ {-0x1.825a732ac700ap-55, 0x1.bd7c0ac6f952ap-1},
+ {-0x1.bc69f324e6d61p-55, 0x1.b728345196e3ep-1},
+ {-0x1.926da300ffccep-55, 0x1.b090a581502p-1},
+ {0x1.9f630e8b6dac8p-60, 0x1.a9b66290ea1a3p-1},
+ {-0x1.128bb015df175p-56, 0x1.a29a7a0462782p-1},
+ {-0x1.30ee286712474p-55, 0x1.9b3e047f38741p-1},
+ {0x1.3d419a920df0bp-55, 0x1.93a22499263fbp-1},
+ {-0x1.2c5e12ed1336dp-55, 0x1.8bc806b151741p-1},
+ {-0x1.6f420f8ea3475p-56, 0x1.83b0e0bff976ep-1},
+ {-0x1.0f537acdf0ad7p-56, 0x1.7b5df226aafafp-1},
+ {0x1.0d4ef0f1d915cp-55, 0x1.72d0837efff96p-1},
+ {-0x1.bdd3413b26456p-55, 0x1.6a09e667f3bcdp-1},
+ {-0x1.251b352ff2a37p-56, 0x1.610b7551d2cdfp-1},
+ {-0x1.75720992bfbb2p-55, 0x1.57d69348cecap-1},
+ {0x1.3c293edceb327p-57, 0x1.4e6cabbe3e5e9p-1},
+ {0x1.8076a2cfdc6b3p-57, 0x1.44cf325091dd6p-1},
+ {0x1.e3e25e3954964p-56, 0x1.3affa292050b9p-1},
+ {-0x1.efcc626f74a6fp-57, 0x1.30ff7fce17035p-1},
+ {-0x1.5da743ef3770cp-55, 0x1.26d054cdd12dfp-1},
+ {0x1.b25dd267f66p-55, 0x1.1c73b39ae68c8p-1},
+ {-0x1.ef23b69abe4f1p-55, 0x1.11eb3541b4b23p-1},
+ {-0x1.a5a014347406cp-55, 0x1.073879922ffeep-1},
+ {-0x1.2ec1fc1b776b8p-60, 0x1.f8ba4dbf89abap-2},
+ {0x1.e0d891d3c6841p-58, 0x1.e2b5d3806f63bp-2},
+ {0x1.6850e59c37f8fp-58, 0x1.cc66e9931c45ep-2},
+ {0x1.5b362cb974183p-57, 0x1.b5d1009e15ccp-2},
+ {0x1.6da81290bdbabp-57, 0x1.9ef7943a8ed8ap-2},
+ {-0x1.72cedd3d5a61p-57, 0x1.87de2a6aea963p-2},
+ {-0x1.44b19e0864c5dp-56, 0x1.7088530fa459fp-2},
+ {-0x1.efdc0d58cf62p-62, 0x1.58f9a75ab1fddp-2},
+ {0x1.0c97c4afa2518p-56, 0x1.4135c94176601p-2},
+ {-0x1.5d28da2c4612dp-56, 0x1.294062ed59f06p-2},
+ {0x1.824c20ab7aa9ap-56, 0x1.111d262b1f677p-2},
+ {-0x1.42deef11da2c4p-57, 0x1.f19f97b215f1bp-3},
+ {-0x1.af1439e521935p-62, 0x1.c0b826a7e4f63p-3},
+ {-0x1.26d19b9ff8d82p-57, 0x1.8f8b83c69a60bp-3},
+ {0x1.531ff779ddac6p-57, 0x1.5e214448b3fc6p-3},
+ {0x1.13000a89a11ep-58, 0x1.2c8106e8e613ap-3},
+ {0x1.a2704729ae56dp-59, 0x1.f564e56a9730ep-4},
+ {-0x1.e2718d26ed688p-60, 0x1.917a6bc29b42cp-4},
+ {-0x1.9a088a8bf6b2cp-59, 0x1.2d52092ce19f6p-4},
+ {-0x1.912bd0d569a9p-61, 0x1.91f65f10dd814p-5},
+ {-0x1.b1d63091a013p-64, 0x1.92155f7a3667ep-6},
+ {0, 0},
+ {0x1.b1d63091a013p-64, -0x1.92155f7a3667ep-6},
+ {0x1.912bd0d569a9p-61, -0x1.91f65f10dd814p-5},
+ {0x1.9a088a8bf6b2cp-59, -0x1.2d52092ce19f6p-4},
+ {0x1.e2718d26ed688p-60, -0x1.917a6bc29b42cp-4},
+ {-0x1.a2704729ae56dp-59, -0x1.f564e56a9730ep-4},
+ {-0x1.13000a89a11ep-58, -0x1.2c8106e8e613ap-3},
+ {-0x1.531ff779ddac6p-57, -0x1.5e214448b3fc6p-3},
+ {0x1.26d19b9ff8d82p-57, -0x1.8f8b83c69a60bp-3},
+ {0x1.af1439e521935p-62, -0x1.c0b826a7e4f63p-3},
+ {0x1.42deef11da2c4p-57, -0x1.f19f97b215f1bp-3},
+ {-0x1.824c20ab7aa9ap-56, -0x1.111d262b1f677p-2},
+ {0x1.5d28da2c4612dp-56, -0x1.294062ed59f06p-2},
+ {-0x1.0c97c4afa2518p-56, -0x1.4135c94176601p-2},
+ {0x1.efdc0d58cf62p-62, -0x1.58f9a75ab1fddp-2},
+ {0x1.44b19e0864c5dp-56, -0x1.7088530fa459fp-2},
+ {0x1.72cedd3d5a61p-57, -0x1.87de2a6aea963p-2},
+ {-0x1.6da81290bdbabp-57, -0x1.9ef7943a8ed8ap-2},
+ {-0x1.5b362cb974183p-57, -0x1.b5d1009e15ccp-2},
+ {-0x1.6850e59c37f8fp-58, -0x1.cc66e9931c45ep-2},
+ {-0x1.e0d891d3c6841p-58, -0x1.e2b5d3806f63bp-2},
+ {0x1.2ec1fc1b776b8p-60, -0x1.f8ba4dbf89abap-2},
+ {0x1.a5a014347406cp-55, -0x1.073879922ffeep-1},
+ {0x1.ef23b69abe4f1p-55, -0x1.11eb3541b4b23p-1},
+ {-0x1.b25dd267f66p-55, -0x1.1c73b39ae68c8p-1},
+ {0x1.5da743ef3770cp-55, -0x1.26d054cdd12dfp-1},
+ {0x1.efcc626f74a6fp-57, -0x1.30ff7fce17035p-1},
+ {-0x1.e3e25e3954964p-56, -0x1.3affa292050b9p-1},
+ {-0x1.8076a2cfdc6b3p-57, -0x1.44cf325091dd6p-1},
+ {-0x1.3c293edceb327p-57, -0x1.4e6cabbe3e5e9p-1},
+ {0x1.75720992bfbb2p-55, -0x1.57d69348cecap-1},
+ {0x1.251b352ff2a37p-56, -0x1.610b7551d2cdfp-1},
+ {0x1.bdd3413b26456p-55, -0x1.6a09e667f3bcdp-1},
+ {-0x1.0d4ef0f1d915cp-55, -0x1.72d0837efff96p-1},
+ {0x1.0f537acdf0ad7p-56, -0x1.7b5df226aafafp-1},
+ {0x1.6f420f8ea3475p-56, -0x1.83b0e0bff976ep-1},
+ {0x1.2c5e12ed1336dp-55, -0x1.8bc806b151741p-1},
+ {-0x1.3d419a920df0bp-55, -0x1.93a22499263fbp-1},
+ {0x1.30ee286712474p-55, -0x1.9b3e047f38741p-1},
+ {0x1.128bb015df175p-56, -0x1.a29a7a0462782p-1},
+ {-0x1.9f630e8b6dac8p-60, -0x1.a9b66290ea1a3p-1},
+ {0x1.926da300ffccep-55, -0x1.b090a581502p-1},
+ {0x1.bc69f324e6d61p-55, -0x1.b728345196e3ep-1},
+ {0x1.825a732ac700ap-55, -0x1.bd7c0ac6f952ap-1},
+ {0x1.6e0b1757c8d07p-56, -0x1.c38b2f180bdb1p-1},
+ {0x1.2fb761e946603p-58, -0x1.c954b213411f5p-1},
+ {0x1.e7b6bb5ab58aep-58, -0x1.ced7af43cc773p-1},
+ {0x1.4ef5295d25af2p-55, -0x1.d4134d14dc93ap-1},
+ {-0x1.457e610231ac2p-56, -0x1.d906bcf328d46p-1},
+ {-0x1.83c37c6107db3p-55, -0x1.ddb13b6ccc23cp-1},
+ {0x1.014c76c126527p-55, -0x1.e212104f686e5p-1},
+ {0x1.16b56f2847754p-57, -0x1.e6288ec48e112p-1},
+ {-0x1.760b1e2e3f81ep-55, -0x1.e9f4156c62ddap-1},
+ {-0x1.e82c791f59cc2p-56, -0x1.ed740e7684963p-1},
+ {-0x1.52c7adc6b4989p-56, -0x1.f0a7efb9230d7p-1},
+ {0x1.d7bafb51f72e6p-56, -0x1.f38f3ac64e589p-1},
+ {-0x1.562172a361fd3p-56, -0x1.f6297cff75cbp-1},
+ {-0x1.ab256778ffcb6p-56, -0x1.f8764fa714ba9p-1},
+ {0x1.7a0a8ca13571fp-55, -0x1.fa7557f08a517p-1},
+ {-0x1.1ec8668ecaceep-55, -0x1.fc26470e19fd3p-1},
+ {0x1.87df6378811c7p-55, -0x1.fd88da3d12526p-1},
+ {-0x1.521ecd0c67e35p-57, -0x1.fe9cdad01883ap-1},
+ {0x1.c57bc2e24aa15p-57, -0x1.ff621e3796d7ep-1},
+ {0x1.1354d4556e4cbp-55, -0x1.ffd886084cd0dp-1},
+ {0, -1},
+ {0x1.1354d4556e4cbp-55, -0x1.ffd886084cd0dp-1},
+ {0x1.c57bc2e24aa15p-57, -0x1.ff621e3796d7ep-1},
+ {-0x1.521ecd0c67e35p-57, -0x1.fe9cdad01883ap-1},
+ {0x1.87df6378811c7p-55, -0x1.fd88da3d12526p-1},
+ {-0x1.1ec8668ecaceep-55, -0x1.fc26470e19fd3p-1},
+ {0x1.7a0a8ca13571fp-55, -0x1.fa7557f08a517p-1},
+ {-0x1.ab256778ffcb6p-56, -0x1.f8764fa714ba9p-1},
+ {-0x1.562172a361fd3p-56, -0x1.f6297cff75cbp-1},
+ {0x1.d7bafb51f72e6p-56, -0x1.f38f3ac64e589p-1},
+ {-0x1.52c7adc6b4989p-56, -0x1.f0a7efb9230d7p-1},
+ {-0x1.e82c791f59cc2p-56, -0x1.ed740e7684963p-1},
+ {-0x1.760b1e2e3f81ep-55, -0x1.e9f4156c62ddap-1},
+ {0x1.16b56f2847754p-57, -0x1.e6288ec48e112p-1},
+ {0x1.014c76c126527p-55, -0x1.e212104f686e5p-1},
+ {-0x1.83c37c6107db3p-55, -0x1.ddb13b6ccc23cp-1},
+ {-0x1.457e610231ac2p-56, -0x1.d906bcf328d46p-1},
+ {0x1.4ef5295d25af2p-55, -0x1.d4134d14dc93ap-1},
+ {0x1.e7b6bb5ab58aep-58, -0x1.ced7af43cc773p-1},
+ {0x1.2fb761e946603p-58, -0x1.c954b213411f5p-1},
+ {0x1.6e0b1757c8d07p-56, -0x1.c38b2f180bdb1p-1},
+ {0x1.825a732ac700ap-55, -0x1.bd7c0ac6f952ap-1},
+ {0x1.bc69f324e6d61p-55, -0x1.b728345196e3ep-1},
+ {0x1.926da300ffccep-55, -0x1.b090a581502p-1},
+ {-0x1.9f630e8b6dac8p-60, -0x1.a9b66290ea1a3p-1},
+ {0x1.128bb015df175p-56, -0x1.a29a7a0462782p-1},
+ {0x1.30ee286712474p-55, -0x1.9b3e047f38741p-1},
+ {-0x1.3d419a920df0bp-55, -0x1.93a22499263fbp-1},
+ {0x1.2c5e12ed1336dp-55, -0x1.8bc806b151741p-1},
+ {0x1.6f420f8ea3475p-56, -0x1.83b0e0bff976ep-1},
+ {0x1.0f537acdf0ad7p-56, -0x1.7b5df226aafafp-1},
+ {-0x1.0d4ef0f1d915cp-55, -0x1.72d0837efff96p-1},
+ {0x1.bdd3413b26456p-55, -0x1.6a09e667f3bcdp-1},
+ {0x1.251b352ff2a37p-56, -0x1.610b7551d2cdfp-1},
+ {0x1.75720992bfbb2p-55, -0x1.57d69348cecap-1},
+ {-0x1.3c293edceb327p-57, -0x1.4e6cabbe3e5e9p-1},
+ {-0x1.8076a2cfdc6b3p-57, -0x1.44cf325091dd6p-1},
+ {-0x1.e3e25e3954964p-56, -0x1.3affa292050b9p-1},
+ {0x1.efcc626f74a6fp-57, -0x1.30ff7fce17035p-1},
+ {0x1.5da743ef3770cp-55, -0x1.26d054cdd12dfp-1},
+ {-0x1.b25dd267f66p-55, -0x1.1c73b39ae68c8p-1},
+ {0x1.ef23b69abe4f1p-55, -0x1.11eb3541b4b23p-1},
+ {0x1.a5a014347406cp-55, -0x1.073879922ffeep-1},
+ {0x1.2ec1fc1b776b8p-60, -0x1.f8ba4dbf89abap-2},
+ {-0x1.e0d891d3c6841p-58, -0x1.e2b5d3806f63bp-2},
+ {-0x1.6850e59c37f8fp-58, -0x1.cc66e9931c45ep-2},
+ {-0x1.5b362cb974183p-57, -0x1.b5d1009e15ccp-2},
+ {-0x1.6da81290bdbabp-57, -0x1.9ef7943a8ed8ap-2},
+ {0x1.72cedd3d5a61p-57, -0x1.87de2a6aea963p-2},
+ {0x1.44b19e0864c5dp-56, -0x1.7088530fa459fp-2},
+ {0x1.efdc0d58cf62p-62, -0x1.58f9a75ab1fddp-2},
+ {-0x1.0c97c4afa2518p-56, -0x1.4135c94176601p-2},
+ {0x1.5d28da2c4612dp-56, -0x1.294062ed59f06p-2},
+ {-0x1.824c20ab7aa9ap-56, -0x1.111d262b1f677p-2},
+ {0x1.42deef11da2c4p-57, -0x1.f19f97b215f1bp-3},
+ {0x1.af1439e521935p-62, -0x1.c0b826a7e4f63p-3},
+ {0x1.26d19b9ff8d82p-57, -0x1.8f8b83c69a60bp-3},
+ {-0x1.531ff779ddac6p-57, -0x1.5e214448b3fc6p-3},
+ {-0x1.13000a89a11ep-58, -0x1.2c8106e8e613ap-3},
+ {-0x1.a2704729ae56dp-59, -0x1.f564e56a9730ep-4},
+ {0x1.e2718d26ed688p-60, -0x1.917a6bc29b42cp-4},
+ {0x1.9a088a8bf6b2cp-59, -0x1.2d52092ce19f6p-4},
+ {0x1.912bd0d569a9p-61, -0x1.91f65f10dd814p-5},
+ {0x1.b1d63091a013p-64, -0x1.92155f7a3667ep-6},
+};
+
+#ifndef LIBC_MATH_SIN_SKIP_ACCURATE_PASS
+LIBC_INLINE constexpr Float128 SIN_K_PI_OVER_128_F128[65] = {
+ {Sign::POS, 0, 0},
+ {Sign::POS, -133, 0xc90a'afbd'1b33'efc9'c539'edcb'fda0'cf2c_u128},
+ {Sign::POS, -132, 0xc8fb'2f88'6ec0'9f37'6a17'954b'2b7c'5171_u128},
+ {Sign::POS, -131, 0x96a9'0496'70cf'ae65'f775'7409'4d3c'35c4_u128},
+ {Sign::POS, -131, 0xc8bd'35e1'4da1'5f0e'c739'6c89'4bbf'7389_u128},
+ {Sign::POS, -131, 0xfab2'72b5'4b98'71a2'7047'29ae'56d7'8a37_u128},
+ {Sign::POS, -130, 0x9640'8374'7309'd113'000a'89a1'1e07'c1fe_u128},
+ {Sign::POS, -130, 0xaf10'a224'59fe'32a6'3fee'f3bb'58b1'f10d_u128},
+ {Sign::POS, -130, 0xc7c5'c1e3'4d30'55b2'5cc8'c00e'4fcc'd850_u128},
+ {Sign::POS, -130, 0xe05c'1353'f27b'17e5'0ebc'61ad'e6ca'83cd_u128},
+ {Sign::POS, -130, 0xf8cf'cbd9'0af8'd57a'4221'dc4b'a772'598d_u128},
+ {Sign::POS, -129, 0x888e'9315'8fb3'bb04'9841'56f5'5334'4306_u128},
+ {Sign::POS, -129, 0x94a0'3176'acf8'2d45'ae4b'a773'da6b'f754_u128},
+ {Sign::POS, -129, 0xa09a'e4a0'bb30'0a19'2f89'5f44'a303'cc0b_u128},
+ {Sign::POS, -129, 0xac7c'd3ad'58fe'e7f0'811f'9539'84ef'f83e_u128},
+ {Sign::POS, -129, 0xb844'2987'd22c'f576'9cc3'ef36'746d'e3b8_u128},
+ {Sign::POS, -129, 0xc3ef'1535'754b'168d'3122'c2a5'9efd'dc37_u128},
+ {Sign::POS, -129, 0xcf7b'ca1d'476c'516d'a812'90bd'baad'62e4_u128},
+ {Sign::POS, -129, 0xdae8'804f'0ae6'015b'362c'b974'182e'3030_u128},
+ {Sign::POS, -129, 0xe633'74c9'8e22'f0b4'2872'ce1b'fc7a'd1cd_u128},
+ {Sign::POS, -129, 0xf15a'e9c0'37b1'd8f0'6c48'e9e3'420b'0f1e_u128},
+ {Sign::POS, -129, 0xfc5d'26df'c4d5'cfda'27c0'7c91'1290'b8d1_u128},
+ {Sign::POS, -128, 0x839c'3cc9'17ff'6cb4'bfd7'9717'f288'0abf_u128},
+ {Sign::POS, -128, 0x88f5'9aa0'da59'1421'b892'ca83'61d8'c84c_u128},
+ {Sign::POS, -128, 0x8e39'd9cd'7346'4364'bba4'cfec'bff5'4867_u128},
+ {Sign::POS, -128, 0x9368'2a66'e896'f544'b178'2191'1e71'c16e_u128},
+ {Sign::POS, -128, 0x987f'bfe7'0b81'a708'19ce'c845'ac87'a5c6_u128},
+ {Sign::POS, -128, 0x9d7f'd149'0285'c9e3'e25e'3954'9638'ae68_u128},
+ {Sign::POS, -128, 0xa267'9928'48ee'b0c0'3b51'67ee'359a'234e_u128},
+ {Sign::POS, -128, 0xa736'55df'1f2f'489e'149f'6e75'9934'68a3_u128},
+ {Sign::POS, -128, 0xabeb'49a4'6764'fd15'1bec'da80'89c1'a94c_u128},
+ {Sign::POS, -128, 0xb085'baa8'e966'f6da'e4ca'd00d'5c94'bcd2_u128},
+ {Sign::POS, -128, 0xb504'f333'f9de'6484'597d'89b3'754a'be9f_u128},
+ {Sign::POS, -128, 0xb968'41bf'7ffc'b21a'9de1'e3b2'2b8b'f4db_u128},
+ {Sign::POS, -128, 0xbdae'f913'557d'76f0'ac85'320f'528d'6d5d_u128},
+ {Sign::POS, -128, 0xc1d8'705f'fcbb'6e90'bdf0'715c'b8b2'0bd7_u128},
+ {Sign::POS, -128, 0xc5e4'0358'a8ba'05a7'43da'25d9'9267'326b_u128},
+ {Sign::POS, -128, 0xc9d1'124c'931f'da7a'8335'241b'e169'3225_u128},
+ {Sign::POS, -128, 0xcd9f'023f'9c3a'059e'23af'31db'7179'a4aa_u128},
+ {Sign::POS, -128, 0xd14d'3d02'313c'0eed'744f'ea20'e8ab'ef92_u128},
+ {Sign::POS, -128, 0xd4db'3148'750d'1819'f630'e8b6'dac8'3e69_u128},
+ {Sign::POS, -128, 0xd848'52c0'a80f'fcdb'24b9'fe00'6635'74a4_u128},
+ {Sign::POS, -128, 0xdb94'1a28'cb71'ec87'2c19'b632'53da'43fc_u128},
+ {Sign::POS, -128, 0xdebe'0563'7ca9'4cfb'4b19'aa71'fec3'ae6d_u128},
+ {Sign::POS, -128, 0xe1c5'978c'05ed'8691'f4e8'a837'2f8c'5810_u128},
+ {Sign::POS, -128, 0xe4aa'5909'a08f'a7b4'1227'85ae'67f5'515d_u128},
+ {Sign::POS, -128, 0xe76b'd7a1'e63b'9786'1251'2952'9d48'a92f_u128},
+ {Sign::POS, -128, 0xea09'a68a'6e49'cd62'15ad'45b4'a1b5'e823_u128},
+ {Sign::POS, -128, 0xec83'5e79'946a'3145'7e61'0231'ac1d'6181_u128},
+ {Sign::POS, -128, 0xeed8'9db6'6611'e307'86f8'c20f'b664'b01b_u128},
+ {Sign::POS, -128, 0xf109'0827'b437'25fd'6712'7db3'5b28'7316_u128},
+ {Sign::POS, -128, 0xf314'4762'4708'8f74'a548'6bdc'455d'56a2_u128},
+ {Sign::POS, -128, 0xf4fa'0ab6'316e'd2ec'163c'5c7f'03b7'18c5_u128},
+ {Sign::POS, -128, 0xf6ba'073b'424b'19e8'2c79'1f59'cc1f'fc23_u128},
+ {Sign::POS, -128, 0xf853'f7dc'9186'b952'c7ad'c6b4'9888'91bb_u128},
+ {Sign::POS, -128, 0xf9c7'9d63'272c'4628'4504'ae08'd19b'2980_u128},
+ {Sign::POS, -128, 0xfb14'be7f'bae5'8156'2172'a361'fd2a'722f_u128},
+ {Sign::POS, -128, 0xfc3b'27d3'8a5d'49ab'2567'78ff'cb5c'1769_u128},
+ {Sign::POS, -128, 0xfd3a'abf8'4528'b50b'eae6'bd95'1c1d'abbe_u128},
+ {Sign::POS, -128, 0xfe13'2387'0cfe'9a3d'90cd'1d95'9db6'74ef_u128},
+ {Sign::POS, -128, 0xfec4'6d1e'8929'2cf0'4139'0efd'c726'e9ef_u128},
+ {Sign::POS, -128, 0xff4e'6d68'0c41'd0a9'0f66'8633'f1ab'858a_u128},
+ {Sign::POS, -128, 0xffb1'0f1b'cb6b'ef1d'421e'8eda'af59'453e_u128},
+ {Sign::POS, -128, 0xffec'4304'2668'65d9'5657'5523'6696'1732_u128},
+ {Sign::POS, 0, 1},
+};
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+constexpr double ERR = 0x1.0p-70;
+#else
+constexpr double ERR = 0x1.0p-67;
+#endif // LIBC_TARGET_CPU_HAS_FMA
+#endif // !LIBC_MATH_SIN_SKIP_ACCURATE_PASS
+
+} // anonymous namespace
+
+LLVM_LIBC_FUNCTION(double, sin, (double x)) {
+ using FPBits = typename fputil::FPBits<double>;
+ FPBits xbits(x);
+
+ uint16_t x_e = xbits.get_biased_exponent();
+
+ DoubleDouble y;
+ int k;
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+ constexpr int SMALL_EXPONENT = 32;
+#else
+ constexpr int SMALL_EXPONENT = 23;
+#endif
+
+ if (LIBC_LIKELY(x_e < FPBits::EXP_BIAS + SMALL_EXPONENT)) {
+ // |x| < 2^32
+ if (LIBC_UNLIKELY(x_e < FPBits::EXP_BIAS - 26)) {
+ // Signed zeros.
+ if (LIBC_UNLIKELY(x == 0.0))
+ return x;
+
+ // For |x| < 2^-26, |sin(x) - x| < ulp(x)/2.
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+ return fputil::multiply_add(x, -0x1.0p-54, x);
+#else
+ if (LIBC_UNLIKELY(x_e < 4)) {
+ int rounding_mode = fputil::quick_get_round();
+ if (rounding_mode == FE_TOWARDZERO ||
+ (xbits.sign() == Sign::POS && rounding_mode == FE_DOWNWARD) ||
+ (xbits.sign() == Sign::NEG && rounding_mode == FE_UPWARD))
+ return FPBits(xbits.uintval() - 1).get_val();
+ }
+ return fputil::multiply_add(x, -0x1.0p-54, x);
+#endif // LIBC_TARGET_CPU_HAS_FMA
+ }
+
+ // // Small range reduction.
+ k = range_reduction_small(x, y);
+ } else {
+ if (LIBC_UNLIKELY(x_e > 2 * FPBits::EXP_BIAS)) {
+ // Inf or NaN
+ if (xbits.get_mantissa() == 0) {
----------------
lntue wrote:
Updated the comments, `Inf or NaN` is for the above `if` statement, this one is actually `is_inf()`, but under all the checks above, `get_mantissa() == 0` will generate the less codes than `is_inf()`.
https://github.com/llvm/llvm-project/pull/95736
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