diff --git a/libc/shared/math.h b/libc/shared/math.h index f2ad0b09a392c..33fe235c51824 100644 --- a/libc/shared/math.h +++ b/libc/shared/math.h @@ -14,6 +14,7 @@ #include "math/acos.h" #include "math/acosf.h" #include "math/acosf16.h" +#include "math/acoshf.h" #include "math/erff.h" #include "math/exp.h" #include "math/exp10.h" diff --git a/libc/shared/math/acoshf.h b/libc/shared/math/acoshf.h new file mode 100644 index 0000000000000..86bdbce3d905c --- /dev/null +++ b/libc/shared/math/acoshf.h @@ -0,0 +1,23 @@ +//===-- Shared acoshf function ----------------------------------*- C++ -*-===// +// +// 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 +// +//===----------------------------------------------------------------------===// + +#ifndef LLVM_LIBC_SHARED_MATH_ACOSHF_H +#define LLVM_LIBC_SHARED_MATH_ACOSHF_H + +#include "shared/libc_common.h" +#include "src/__support/math/acoshf.h" + +namespace LIBC_NAMESPACE_DECL { +namespace shared { + +using math::acoshf; + +} // namespace shared +} // namespace LIBC_NAMESPACE_DECL + +#endif // LLVM_LIBC_SHARED_MATH_ACOSHF_H diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt index 91cbf379ba5fc..b0e562fb20d0d 100644 --- a/libc/src/__support/math/CMakeLists.txt +++ b/libc/src/__support/math/CMakeLists.txt @@ -47,6 +47,38 @@ add_header_library( libc.src.__support.macros.properties.types ) +add_header_library( + acosh_float_constants + HDRS + acosh_float_constants.h + DEPENDS + libc.src.__support.macros.config +) + +add_header_library( + acoshf_utils + HDRS + acoshf_utils.h + DEPENDS + .acosh_float_constants + libc.src.__support.FPUtil.fp_bits + libc.src.__support.FPUtil.multiply_add + libc.src.__support.FPUtil.polyeval +) + +add_header_library( + acoshf + HDRS + acoshf.h + DEPENDS + .acoshf_utils + libc.src.__support.FPUtil.fenv_impl + libc.src.__support.FPUtil.fp_bits + libc.src.__support.FPUtil.multiply_add + libc.src.__support.FPUtil.sqrt + libc.src.__support.macros.optimization +) + add_header_library( asin_utils HDRS diff --git a/libc/src/__support/math/acosh_float_constants.h b/libc/src/__support/math/acosh_float_constants.h new file mode 100644 index 0000000000000..2eb245d8265e0 --- /dev/null +++ b/libc/src/__support/math/acosh_float_constants.h @@ -0,0 +1,114 @@ +//===-- Common constants for acoshf function --------------------*- C++ -*-===// +// +// 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 +// +//===----------------------------------------------------------------------===// + +#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOSH_FLOAT_CONSTANTS_H +#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSH_FLOAT_CONSTANTS_H + +#include "src/__support/macros/config.h" + +namespace LIBC_NAMESPACE_DECL { + +namespace acoshf_internal { + +// Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127. +static constexpr double ONE_OVER_F[128] = { + 0x1.0000000000000p+0, 0x1.fc07f01fc07f0p-1, 0x1.f81f81f81f820p-1, + 0x1.f44659e4a4271p-1, 0x1.f07c1f07c1f08p-1, 0x1.ecc07b301ecc0p-1, + 0x1.e9131abf0b767p-1, 0x1.e573ac901e574p-1, 0x1.e1e1e1e1e1e1ep-1, + 0x1.de5d6e3f8868ap-1, 0x1.dae6076b981dbp-1, 0x1.d77b654b82c34p-1, + 0x1.d41d41d41d41dp-1, 0x1.d0cb58f6ec074p-1, 0x1.cd85689039b0bp-1, + 0x1.ca4b3055ee191p-1, 0x1.c71c71c71c71cp-1, 0x1.c3f8f01c3f8f0p-1, + 0x1.c0e070381c0e0p-1, 0x1.bdd2b899406f7p-1, 0x1.bacf914c1bad0p-1, + 0x1.b7d6c3dda338bp-1, 0x1.b4e81b4e81b4fp-1, 0x1.b2036406c80d9p-1, + 0x1.af286bca1af28p-1, 0x1.ac5701ac5701bp-1, 0x1.a98ef606a63bep-1, + 0x1.a6d01a6d01a6dp-1, 0x1.a41a41a41a41ap-1, 0x1.a16d3f97a4b02p-1, + 0x1.9ec8e951033d9p-1, 0x1.9c2d14ee4a102p-1, 0x1.999999999999ap-1, + 0x1.970e4f80cb872p-1, 0x1.948b0fcd6e9e0p-1, 0x1.920fb49d0e229p-1, + 0x1.8f9c18f9c18fap-1, 0x1.8d3018d3018d3p-1, 0x1.8acb90f6bf3aap-1, + 0x1.886e5f0abb04ap-1, 0x1.8618618618618p-1, 0x1.83c977ab2beddp-1, + 0x1.8181818181818p-1, 0x1.7f405fd017f40p-1, 0x1.7d05f417d05f4p-1, + 0x1.7ad2208e0ecc3p-1, 0x1.78a4c8178a4c8p-1, 0x1.767dce434a9b1p-1, + 0x1.745d1745d1746p-1, 0x1.724287f46debcp-1, 0x1.702e05c0b8170p-1, + 0x1.6e1f76b4337c7p-1, 0x1.6c16c16c16c17p-1, 0x1.6a13cd1537290p-1, + 0x1.6816816816817p-1, 0x1.661ec6a5122f9p-1, 0x1.642c8590b2164p-1, + 0x1.623fa77016240p-1, 0x1.6058160581606p-1, 0x1.5e75bb8d015e7p-1, + 0x1.5c9882b931057p-1, 0x1.5ac056b015ac0p-1, 0x1.58ed2308158edp-1, + 0x1.571ed3c506b3ap-1, 0x1.5555555555555p-1, 0x1.5390948f40febp-1, + 0x1.51d07eae2f815p-1, 0x1.5015015015015p-1, 0x1.4e5e0a72f0539p-1, + 0x1.4cab88725af6ep-1, 0x1.4afd6a052bf5bp-1, 0x1.49539e3b2d067p-1, + 0x1.47ae147ae147bp-1, 0x1.460cbc7f5cf9ap-1, 0x1.446f86562d9fbp-1, + 0x1.42d6625d51f87p-1, 0x1.4141414141414p-1, 0x1.3fb013fb013fbp-1, + 0x1.3e22cbce4a902p-1, 0x1.3c995a47babe7p-1, 0x1.3b13b13b13b14p-1, + 0x1.3991c2c187f63p-1, 0x1.3813813813814p-1, 0x1.3698df3de0748p-1, + 0x1.3521cfb2b78c1p-1, 0x1.33ae45b57bcb2p-1, 0x1.323e34a2b10bfp-1, + 0x1.30d190130d190p-1, 0x1.2f684bda12f68p-1, 0x1.2e025c04b8097p-1, + 0x1.2c9fb4d812ca0p-1, 0x1.2b404ad012b40p-1, 0x1.29e4129e4129ep-1, + 0x1.288b01288b013p-1, 0x1.27350b8812735p-1, 0x1.25e22708092f1p-1, + 0x1.2492492492492p-1, 0x1.23456789abcdfp-1, 0x1.21fb78121fb78p-1, + 0x1.20b470c67c0d9p-1, 0x1.1f7047dc11f70p-1, 0x1.1e2ef3b3fb874p-1, + 0x1.1cf06ada2811dp-1, 0x1.1bb4a4046ed29p-1, 0x1.1a7b9611a7b96p-1, + 0x1.19453808ca29cp-1, 0x1.1811811811812p-1, 0x1.16e0689427379p-1, + 0x1.15b1e5f75270dp-1, 0x1.1485f0e0acd3bp-1, 0x1.135c81135c811p-1, + 0x1.12358e75d3033p-1, 0x1.1111111111111p-1, 0x1.0fef010fef011p-1, + 0x1.0ecf56be69c90p-1, 0x1.0db20a88f4696p-1, 0x1.0c9714fbcda3bp-1, + 0x1.0b7e6ec259dc8p-1, 0x1.0a6810a6810a7p-1, 0x1.0953f39010954p-1, + 0x1.0842108421084p-1, 0x1.073260a47f7c6p-1, 0x1.0624dd2f1a9fcp-1, + 0x1.05197f7d73404p-1, 0x1.0410410410410p-1, 0x1.03091b51f5e1ap-1, + 0x1.0204081020408p-1, 0x1.0101010101010p-1}; + +// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127. +static constexpr double LOG_F[128] = { + 0x0.0000000000000p+0, 0x1.fe02a6b106788p-8, 0x1.fc0a8b0fc03e3p-7, + 0x1.7b91b07d5b11ap-6, 0x1.f829b0e783300p-6, 0x1.39e87b9febd5fp-5, + 0x1.77458f632dcfcp-5, 0x1.b42dd711971bep-5, 0x1.f0a30c01162a6p-5, + 0x1.16536eea37ae0p-4, 0x1.341d7961bd1d0p-4, 0x1.51b073f06183fp-4, + 0x1.6f0d28ae56b4bp-4, 0x1.8c345d6319b20p-4, 0x1.a926d3a4ad563p-4, + 0x1.c5e548f5bc743p-4, 0x1.e27076e2af2e5p-4, 0x1.fec9131dbeabap-4, + 0x1.0d77e7cd08e59p-3, 0x1.1b72ad52f67a0p-3, 0x1.29552f81ff523p-3, + 0x1.371fc201e8f74p-3, 0x1.44d2b6ccb7d1ep-3, 0x1.526e5e3a1b437p-3, + 0x1.5ff3070a793d3p-3, 0x1.6d60fe719d21cp-3, 0x1.7ab890210d909p-3, + 0x1.87fa06520c910p-3, 0x1.9525a9cf456b4p-3, 0x1.a23bc1fe2b563p-3, + 0x1.af3c94e80bff2p-3, 0x1.bc286742d8cd6p-3, 0x1.c8ff7c79a9a21p-3, + 0x1.d5c216b4fbb91p-3, 0x1.e27076e2af2e5p-3, 0x1.ef0adcbdc5936p-3, + 0x1.fb9186d5e3e2ap-3, 0x1.0402594b4d040p-2, 0x1.0a324e27390e3p-2, + 0x1.1058bf9ae4ad5p-2, 0x1.1675cababa60ep-2, 0x1.1c898c16999fap-2, + 0x1.22941fbcf7965p-2, 0x1.2895a13de86a3p-2, 0x1.2e8e2bae11d30p-2, + 0x1.347dd9a987d54p-2, 0x1.3a64c556945e9p-2, 0x1.404308686a7e3p-2, + 0x1.4618bc21c5ec2p-2, 0x1.4be5f957778a0p-2, 0x1.51aad872df82dp-2, + 0x1.5767717455a6cp-2, 0x1.5d1bdbf5809cap-2, 0x1.62c82f2b9c795p-2, + 0x1.686c81e9b14aep-2, 0x1.6e08eaa2ba1e3p-2, 0x1.739d7f6bbd006p-2, + 0x1.792a55fdd47a2p-2, 0x1.7eaf83b82afc3p-2, 0x1.842d1da1e8b17p-2, + 0x1.89a3386c1425ap-2, 0x1.8f11e873662c7p-2, 0x1.947941c2116fap-2, + 0x1.99d958117e08ap-2, 0x1.9f323ecbf984bp-2, 0x1.a484090e5bb0ap-2, + 0x1.a9cec9a9a0849p-2, 0x1.af1293247786bp-2, 0x1.b44f77bcc8f62p-2, + 0x1.b9858969310fbp-2, 0x1.beb4d9da71b7bp-2, 0x1.c3dd7a7cdad4dp-2, + 0x1.c8ff7c79a9a21p-2, 0x1.ce1af0b85f3ebp-2, 0x1.d32fe7e00ebd5p-2, + 0x1.d83e7258a2f3ep-2, 0x1.dd46a04c1c4a0p-2, 0x1.e24881a7c6c26p-2, + 0x1.e744261d68787p-2, 0x1.ec399d2468cc0p-2, 0x1.f128f5faf06ecp-2, + 0x1.f6123fa7028acp-2, 0x1.faf588f78f31ep-2, 0x1.ffd2e0857f498p-2, + 0x1.02552a5a5d0fep-1, 0x1.04bdf9da926d2p-1, 0x1.0723e5c1cdf40p-1, + 0x1.0986f4f573520p-1, 0x1.0be72e4252a82p-1, 0x1.0e44985d1cc8bp-1, + 0x1.109f39e2d4c96p-1, 0x1.12f719593efbcp-1, 0x1.154c3d2f4d5e9p-1, + 0x1.179eabbd899a0p-1, 0x1.19ee6b467c96ep-1, 0x1.1c3b81f713c24p-1, + 0x1.1e85f5e7040d0p-1, 0x1.20cdcd192ab6dp-1, 0x1.23130d7bebf42p-1, + 0x1.2555bce98f7cbp-1, 0x1.2795e1289b11ap-1, 0x1.29d37fec2b08ap-1, + 0x1.2c0e9ed448e8bp-1, 0x1.2e47436e40268p-1, 0x1.307d7334f10bep-1, + 0x1.32b1339121d71p-1, 0x1.34e289d9ce1d3p-1, 0x1.37117b54747b5p-1, + 0x1.393e0d3562a19p-1, 0x1.3b68449fffc22p-1, 0x1.3d9026a7156fap-1, + 0x1.3fb5b84d16f42p-1, 0x1.41d8fe84672aep-1, 0x1.43f9fe2f9ce67p-1, + 0x1.4618bc21c5ec2p-1, 0x1.48353d1ea88dfp-1, 0x1.4a4f85db03ebbp-1, + 0x1.4c679afccee39p-1, 0x1.4e7d811b75bb0p-1, 0x1.50913cc01686bp-1, + 0x1.52a2d265bc5aap-1, 0x1.54b2467999497p-1, 0x1.56bf9d5b3f399p-1, + 0x1.58cadb5cd7989p-1, 0x1.5ad404c359f2cp-1, 0x1.5cdb1dc6c1764p-1, + 0x1.5ee02a9241675p-1, 0x1.60e32f44788d8p-1}; + +} // namespace acoshf_internal + +} // namespace LIBC_NAMESPACE_DECL + +#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOSH_FLOAT_CONSTANTS_H diff --git a/libc/src/__support/math/acoshf.h b/libc/src/__support/math/acoshf.h new file mode 100644 index 0000000000000..f18f169f49bb8 --- /dev/null +++ b/libc/src/__support/math/acoshf.h @@ -0,0 +1,86 @@ +//===-- Implementation header for acoshf ------------------------*- C++ -*-===// +// +// 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 +// +//===----------------------------------------------------------------------===// + +#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_H +#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_H + +#include "acoshf_utils.h" +#include "src/__support/FPUtil/FEnvImpl.h" +#include "src/__support/FPUtil/FPBits.h" +#include "src/__support/FPUtil/multiply_add.h" +#include "src/__support/FPUtil/sqrt.h" +#include "src/__support/macros/config.h" +#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY + +namespace LIBC_NAMESPACE_DECL { + +namespace math { + +static constexpr float acoshf(float x) { + using namespace acoshf_internal; + using FPBits_t = typename fputil::FPBits; + FPBits_t xbits(x); + + if (LIBC_UNLIKELY(x <= 1.0f)) { + if (x == 1.0f) + return 0.0f; + // x < 1. + fputil::set_errno_if_required(EDOM); + fputil::raise_except_if_required(FE_INVALID); + return FPBits_t::quiet_nan().get_val(); + } + +#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS + uint32_t x_u = xbits.uintval(); + if (LIBC_UNLIKELY(x_u >= 0x4f8ffb03)) { + if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) + return x; + + // Helper functions to set results for exceptional cases. + auto round_result_slightly_down = [](float r) -> float { + volatile float tmp = r; + tmp = tmp - 0x1.0p-25f; + return tmp; + }; + auto round_result_slightly_up = [](float r) -> float { + volatile float tmp = r; + tmp = tmp + 0x1.0p-25f; + return tmp; + }; + + switch (x_u) { + case 0x4f8ffb03: // x = 0x1.1ff606p32f + return round_result_slightly_up(0x1.6fdd34p4f); + case 0x5c569e88: // x = 0x1.ad3d1p57f + return round_result_slightly_up(0x1.45c146p5f); + case 0x5e68984e: // x = 0x1.d1309cp61f + return round_result_slightly_up(0x1.5c9442p5f); + case 0x655890d3: // x = 0x1.b121a6p75f + return round_result_slightly_down(0x1.a9a3f2p5f); + case 0x6eb1a8ec: // x = 0x1.6351d8p94f + return round_result_slightly_down(0x1.08b512p6f); + case 0x7997f30a: // x = 0x1.2fe614p116f + return round_result_slightly_up(0x1.451436p6f); + } + } +#else + if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) + return x; +#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS + + double x_d = static_cast(x); + // acosh(x) = log(x + sqrt(x^2 - 1)) + return static_cast(log_eval( + x_d + fputil::sqrt(fputil::multiply_add(x_d, x_d, -1.0)))); +} + +} // namespace math + +} // namespace LIBC_NAMESPACE_DECL + +#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_H diff --git a/libc/src/__support/math/acoshf_utils.h b/libc/src/__support/math/acoshf_utils.h new file mode 100644 index 0000000000000..808c3dd41cfe4 --- /dev/null +++ b/libc/src/__support/math/acoshf_utils.h @@ -0,0 +1,60 @@ +//===-- Collection of utils for acoshf --------------------------*- C++ -*-===// +// +// 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 +// +//===----------------------------------------------------------------------===// + +#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_UTILS_H +#define LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_UTILS_H + +#include "acosh_float_constants.h" +#include "src/__support/FPUtil/FPBits.h" +#include "src/__support/FPUtil/PolyEval.h" +#include "src/__support/FPUtil/multiply_add.h" + +namespace LIBC_NAMESPACE_DECL { + +namespace acoshf_internal { + +// x should be positive, normal finite value +LIBC_INLINE static double log_eval(double x) { + // For x = 2^ex * (1 + mx) + // log(x) = ex * log(2) + log(1 + mx) + using FPB = fputil::FPBits; + FPB bs(x); + + double ex = static_cast(bs.get_exponent()); + + // p1 is the leading 7 bits of mx, i.e. + // p1 * 2^(-7) <= m_x < (p1 + 1) * 2^(-7). + int p1 = static_cast(bs.get_mantissa() >> (FPB::FRACTION_LEN - 7)); + + // Set bs to (1 + (mx - p1*2^(-7)) + bs.set_uintval(bs.uintval() & (FPB::FRACTION_MASK >> 7)); + bs.set_biased_exponent(FPB::EXP_BIAS); + // dx = (mx - p1*2^(-7)) / (1 + p1*2^(-7)). + double dx = (bs.get_val() - 1.0) * ONE_OVER_F[p1]; + + // Minimax polynomial of log(1 + dx) generated by Sollya with: + // > P = fpminimax(log(1 + x)/x, 6, [|D...|], [0, 2^-7]); + const double COEFFS[6] = {-0x1.ffffffffffffcp-2, 0x1.5555555552ddep-2, + -0x1.ffffffefe562dp-3, 0x1.9999817d3a50fp-3, + -0x1.554317b3f67a5p-3, 0x1.1dc5c45e09c18p-3}; + double dx2 = dx * dx; + double c1 = fputil::multiply_add(dx, COEFFS[1], COEFFS[0]); + double c2 = fputil::multiply_add(dx, COEFFS[3], COEFFS[2]); + double c3 = fputil::multiply_add(dx, COEFFS[5], COEFFS[4]); + + double p = fputil::polyeval(dx2, dx, c1, c2, c3); + double result = + fputil::multiply_add(ex, /*log(2)*/ 0x1.62e42fefa39efp-1, LOG_F[p1] + p); + return result; +} + +} // namespace acoshf_internal + +} // namespace LIBC_NAMESPACE_DECL + +#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ACOSHF_UTILS_H diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt index 6f16e8d95d29e..86baf2b981bb2 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -1894,6 +1894,7 @@ add_object_library( common_constants.cpp DEPENDS libc.src.__support.math.exp_constants + libc.src.__support.math.acosh_float_constants libc.src.__support.number_pair ) @@ -3757,7 +3758,7 @@ add_header_library( DEPENDS .common_constants libc.src.__support.math.exp_utils - libc.src.__support.math.exp10f_utils + libc.src.__support.math.acoshf_utils libc.src.__support.macros.properties.cpu_features libc.src.errno.errno ) @@ -3867,12 +3868,7 @@ add_entrypoint_object( ../acoshf.h DEPENDS .explogxf - libc.src.__support.FPUtil.fenv_impl - libc.src.__support.FPUtil.fp_bits - libc.src.__support.FPUtil.multiply_add - libc.src.__support.FPUtil.polyeval - libc.src.__support.FPUtil.sqrt - libc.src.__support.macros.optimization + libc.src.__support.math.acoshf ) add_entrypoint_object( diff --git a/libc/src/math/generic/acoshf.cpp b/libc/src/math/generic/acoshf.cpp index c4927fa27a84b..5c04583650e62 100644 --- a/libc/src/math/generic/acoshf.cpp +++ b/libc/src/math/generic/acoshf.cpp @@ -7,73 +7,11 @@ //===----------------------------------------------------------------------===// #include "src/math/acoshf.h" -#include "src/__support/FPUtil/FEnvImpl.h" -#include "src/__support/FPUtil/FPBits.h" -#include "src/__support/FPUtil/PolyEval.h" -#include "src/__support/FPUtil/multiply_add.h" -#include "src/__support/FPUtil/sqrt.h" -#include "src/__support/macros/config.h" -#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY -#include "src/math/generic/common_constants.h" -#include "src/math/generic/explogxf.h" -namespace LIBC_NAMESPACE_DECL { - -LLVM_LIBC_FUNCTION(float, acoshf, (float x)) { - using FPBits_t = typename fputil::FPBits; - FPBits_t xbits(x); - - if (LIBC_UNLIKELY(x <= 1.0f)) { - if (x == 1.0f) - return 0.0f; - // x < 1. - fputil::set_errno_if_required(EDOM); - fputil::raise_except_if_required(FE_INVALID); - return FPBits_t::quiet_nan().get_val(); - } +#include "src/__support/math/acoshf.h" -#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS - uint32_t x_u = xbits.uintval(); - if (LIBC_UNLIKELY(x_u >= 0x4f8ffb03)) { - if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) - return x; - - // Helper functions to set results for exceptional cases. - auto round_result_slightly_down = [](float r) -> float { - volatile float tmp = r; - tmp = tmp - 0x1.0p-25f; - return tmp; - }; - auto round_result_slightly_up = [](float r) -> float { - volatile float tmp = r; - tmp = tmp + 0x1.0p-25f; - return tmp; - }; - - switch (x_u) { - case 0x4f8ffb03: // x = 0x1.1ff606p32f - return round_result_slightly_up(0x1.6fdd34p4f); - case 0x5c569e88: // x = 0x1.ad3d1p57f - return round_result_slightly_up(0x1.45c146p5f); - case 0x5e68984e: // x = 0x1.d1309cp61f - return round_result_slightly_up(0x1.5c9442p5f); - case 0x655890d3: // x = 0x1.b121a6p75f - return round_result_slightly_down(0x1.a9a3f2p5f); - case 0x6eb1a8ec: // x = 0x1.6351d8p94f - return round_result_slightly_down(0x1.08b512p6f); - case 0x7997f30a: // x = 0x1.2fe614p116f - return round_result_slightly_up(0x1.451436p6f); - } - } -#else - if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) - return x; -#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS +namespace LIBC_NAMESPACE_DECL { - double x_d = static_cast(x); - // acosh(x) = log(x + sqrt(x^2 - 1)) - return static_cast(log_eval( - x_d + fputil::sqrt(fputil::multiply_add(x_d, x_d, -1.0)))); -} +LLVM_LIBC_FUNCTION(float, acoshf, (float x)) { return math::acoshf(x); } } // namespace LIBC_NAMESPACE_DECL diff --git a/libc/src/math/generic/acoshf16.cpp b/libc/src/math/generic/acoshf16.cpp index 44783a8749ac2..96ca956c82147 100644 --- a/libc/src/math/generic/acoshf16.cpp +++ b/libc/src/math/generic/acoshf16.cpp @@ -33,6 +33,7 @@ static constexpr fputil::ExceptValues ACOSHF16_EXCEPTS{{ }}; LLVM_LIBC_FUNCTION(float16, acoshf16, (float16 x)) { + using namespace acoshf_internal; using FPBits = fputil::FPBits; FPBits xbits(x); uint16_t x_u = xbits.uintval(); diff --git a/libc/src/math/generic/asinhf.cpp b/libc/src/math/generic/asinhf.cpp index 0bb7065eb1cfe..3aed3bc2c9cde 100644 --- a/libc/src/math/generic/asinhf.cpp +++ b/libc/src/math/generic/asinhf.cpp @@ -19,6 +19,7 @@ namespace LIBC_NAMESPACE_DECL { LLVM_LIBC_FUNCTION(float, asinhf, (float x)) { + using namespace acoshf_internal; using FPBits_t = typename fputil::FPBits; FPBits_t xbits(x); uint32_t x_u = xbits.uintval(); diff --git a/libc/src/math/generic/asinhf16.cpp b/libc/src/math/generic/asinhf16.cpp index 78786320b5f71..0a0b471d87ecc 100644 --- a/libc/src/math/generic/asinhf16.cpp +++ b/libc/src/math/generic/asinhf16.cpp @@ -49,6 +49,7 @@ static constexpr fputil::ExceptValues ASINHF16_EXCEPTS{{ #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS LLVM_LIBC_FUNCTION(float16, asinhf16, (float16 x)) { + using namespace acoshf_internal; using FPBits = fputil::FPBits; FPBits xbits(x); diff --git a/libc/src/math/generic/atanhf.cpp b/libc/src/math/generic/atanhf.cpp index f6fde766ef785..602a8f042f783 100644 --- a/libc/src/math/generic/atanhf.cpp +++ b/libc/src/math/generic/atanhf.cpp @@ -16,6 +16,7 @@ namespace LIBC_NAMESPACE_DECL { LLVM_LIBC_FUNCTION(float, atanhf, (float x)) { + using namespace acoshf_internal; using FPBits = typename fputil::FPBits; FPBits xbits(x); diff --git a/libc/src/math/generic/common_constants.cpp b/libc/src/math/generic/common_constants.cpp index 4dcf84d00ad50..42e3ff0deb348 100644 --- a/libc/src/math/generic/common_constants.cpp +++ b/libc/src/math/generic/common_constants.cpp @@ -51,52 +51,6 @@ const float ONE_OVER_F_FLOAT[128] = { 0x1.08421p-1f, 0x1.07326p-1f, 0x1.0624dep-1f, 0x1.05198p-1f, 0x1.041042p-1f, 0x1.03091cp-1f, 0x1.020408p-1f, 0x1.010102p-1f}; -// Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127. -const double ONE_OVER_F[128] = { - 0x1.0000000000000p+0, 0x1.fc07f01fc07f0p-1, 0x1.f81f81f81f820p-1, - 0x1.f44659e4a4271p-1, 0x1.f07c1f07c1f08p-1, 0x1.ecc07b301ecc0p-1, - 0x1.e9131abf0b767p-1, 0x1.e573ac901e574p-1, 0x1.e1e1e1e1e1e1ep-1, - 0x1.de5d6e3f8868ap-1, 0x1.dae6076b981dbp-1, 0x1.d77b654b82c34p-1, - 0x1.d41d41d41d41dp-1, 0x1.d0cb58f6ec074p-1, 0x1.cd85689039b0bp-1, - 0x1.ca4b3055ee191p-1, 0x1.c71c71c71c71cp-1, 0x1.c3f8f01c3f8f0p-1, - 0x1.c0e070381c0e0p-1, 0x1.bdd2b899406f7p-1, 0x1.bacf914c1bad0p-1, - 0x1.b7d6c3dda338bp-1, 0x1.b4e81b4e81b4fp-1, 0x1.b2036406c80d9p-1, - 0x1.af286bca1af28p-1, 0x1.ac5701ac5701bp-1, 0x1.a98ef606a63bep-1, - 0x1.a6d01a6d01a6dp-1, 0x1.a41a41a41a41ap-1, 0x1.a16d3f97a4b02p-1, - 0x1.9ec8e951033d9p-1, 0x1.9c2d14ee4a102p-1, 0x1.999999999999ap-1, - 0x1.970e4f80cb872p-1, 0x1.948b0fcd6e9e0p-1, 0x1.920fb49d0e229p-1, - 0x1.8f9c18f9c18fap-1, 0x1.8d3018d3018d3p-1, 0x1.8acb90f6bf3aap-1, - 0x1.886e5f0abb04ap-1, 0x1.8618618618618p-1, 0x1.83c977ab2beddp-1, - 0x1.8181818181818p-1, 0x1.7f405fd017f40p-1, 0x1.7d05f417d05f4p-1, - 0x1.7ad2208e0ecc3p-1, 0x1.78a4c8178a4c8p-1, 0x1.767dce434a9b1p-1, - 0x1.745d1745d1746p-1, 0x1.724287f46debcp-1, 0x1.702e05c0b8170p-1, - 0x1.6e1f76b4337c7p-1, 0x1.6c16c16c16c17p-1, 0x1.6a13cd1537290p-1, - 0x1.6816816816817p-1, 0x1.661ec6a5122f9p-1, 0x1.642c8590b2164p-1, - 0x1.623fa77016240p-1, 0x1.6058160581606p-1, 0x1.5e75bb8d015e7p-1, - 0x1.5c9882b931057p-1, 0x1.5ac056b015ac0p-1, 0x1.58ed2308158edp-1, - 0x1.571ed3c506b3ap-1, 0x1.5555555555555p-1, 0x1.5390948f40febp-1, - 0x1.51d07eae2f815p-1, 0x1.5015015015015p-1, 0x1.4e5e0a72f0539p-1, - 0x1.4cab88725af6ep-1, 0x1.4afd6a052bf5bp-1, 0x1.49539e3b2d067p-1, - 0x1.47ae147ae147bp-1, 0x1.460cbc7f5cf9ap-1, 0x1.446f86562d9fbp-1, - 0x1.42d6625d51f87p-1, 0x1.4141414141414p-1, 0x1.3fb013fb013fbp-1, - 0x1.3e22cbce4a902p-1, 0x1.3c995a47babe7p-1, 0x1.3b13b13b13b14p-1, - 0x1.3991c2c187f63p-1, 0x1.3813813813814p-1, 0x1.3698df3de0748p-1, - 0x1.3521cfb2b78c1p-1, 0x1.33ae45b57bcb2p-1, 0x1.323e34a2b10bfp-1, - 0x1.30d190130d190p-1, 0x1.2f684bda12f68p-1, 0x1.2e025c04b8097p-1, - 0x1.2c9fb4d812ca0p-1, 0x1.2b404ad012b40p-1, 0x1.29e4129e4129ep-1, - 0x1.288b01288b013p-1, 0x1.27350b8812735p-1, 0x1.25e22708092f1p-1, - 0x1.2492492492492p-1, 0x1.23456789abcdfp-1, 0x1.21fb78121fb78p-1, - 0x1.20b470c67c0d9p-1, 0x1.1f7047dc11f70p-1, 0x1.1e2ef3b3fb874p-1, - 0x1.1cf06ada2811dp-1, 0x1.1bb4a4046ed29p-1, 0x1.1a7b9611a7b96p-1, - 0x1.19453808ca29cp-1, 0x1.1811811811812p-1, 0x1.16e0689427379p-1, - 0x1.15b1e5f75270dp-1, 0x1.1485f0e0acd3bp-1, 0x1.135c81135c811p-1, - 0x1.12358e75d3033p-1, 0x1.1111111111111p-1, 0x1.0fef010fef011p-1, - 0x1.0ecf56be69c90p-1, 0x1.0db20a88f4696p-1, 0x1.0c9714fbcda3bp-1, - 0x1.0b7e6ec259dc8p-1, 0x1.0a6810a6810a7p-1, 0x1.0953f39010954p-1, - 0x1.0842108421084p-1, 0x1.073260a47f7c6p-1, 0x1.0624dd2f1a9fcp-1, - 0x1.05197f7d73404p-1, 0x1.0410410410410p-1, 0x1.03091b51f5e1ap-1, - 0x1.0204081020408p-1, 0x1.0101010101010p-1}; - // Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127, // computed and stored as float precision constants. // Generated by Sollya with the following commands: @@ -136,52 +90,6 @@ const float LOG_F_FLOAT[128] = { 0x1.52a2d2p-1f, 0x1.54b246p-1f, 0x1.56bf9ep-1f, 0x1.58cadcp-1f, 0x1.5ad404p-1f, 0x1.5cdb1ep-1f, 0x1.5ee02ap-1f, 0x1.60e33p-1f}; -// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127. -const double LOG_F[128] = { - 0x0.0000000000000p+0, 0x1.fe02a6b106788p-8, 0x1.fc0a8b0fc03e3p-7, - 0x1.7b91b07d5b11ap-6, 0x1.f829b0e783300p-6, 0x1.39e87b9febd5fp-5, - 0x1.77458f632dcfcp-5, 0x1.b42dd711971bep-5, 0x1.f0a30c01162a6p-5, - 0x1.16536eea37ae0p-4, 0x1.341d7961bd1d0p-4, 0x1.51b073f06183fp-4, - 0x1.6f0d28ae56b4bp-4, 0x1.8c345d6319b20p-4, 0x1.a926d3a4ad563p-4, - 0x1.c5e548f5bc743p-4, 0x1.e27076e2af2e5p-4, 0x1.fec9131dbeabap-4, - 0x1.0d77e7cd08e59p-3, 0x1.1b72ad52f67a0p-3, 0x1.29552f81ff523p-3, - 0x1.371fc201e8f74p-3, 0x1.44d2b6ccb7d1ep-3, 0x1.526e5e3a1b437p-3, - 0x1.5ff3070a793d3p-3, 0x1.6d60fe719d21cp-3, 0x1.7ab890210d909p-3, - 0x1.87fa06520c910p-3, 0x1.9525a9cf456b4p-3, 0x1.a23bc1fe2b563p-3, - 0x1.af3c94e80bff2p-3, 0x1.bc286742d8cd6p-3, 0x1.c8ff7c79a9a21p-3, - 0x1.d5c216b4fbb91p-3, 0x1.e27076e2af2e5p-3, 0x1.ef0adcbdc5936p-3, - 0x1.fb9186d5e3e2ap-3, 0x1.0402594b4d040p-2, 0x1.0a324e27390e3p-2, - 0x1.1058bf9ae4ad5p-2, 0x1.1675cababa60ep-2, 0x1.1c898c16999fap-2, - 0x1.22941fbcf7965p-2, 0x1.2895a13de86a3p-2, 0x1.2e8e2bae11d30p-2, - 0x1.347dd9a987d54p-2, 0x1.3a64c556945e9p-2, 0x1.404308686a7e3p-2, - 0x1.4618bc21c5ec2p-2, 0x1.4be5f957778a0p-2, 0x1.51aad872df82dp-2, - 0x1.5767717455a6cp-2, 0x1.5d1bdbf5809cap-2, 0x1.62c82f2b9c795p-2, - 0x1.686c81e9b14aep-2, 0x1.6e08eaa2ba1e3p-2, 0x1.739d7f6bbd006p-2, - 0x1.792a55fdd47a2p-2, 0x1.7eaf83b82afc3p-2, 0x1.842d1da1e8b17p-2, - 0x1.89a3386c1425ap-2, 0x1.8f11e873662c7p-2, 0x1.947941c2116fap-2, - 0x1.99d958117e08ap-2, 0x1.9f323ecbf984bp-2, 0x1.a484090e5bb0ap-2, - 0x1.a9cec9a9a0849p-2, 0x1.af1293247786bp-2, 0x1.b44f77bcc8f62p-2, - 0x1.b9858969310fbp-2, 0x1.beb4d9da71b7bp-2, 0x1.c3dd7a7cdad4dp-2, - 0x1.c8ff7c79a9a21p-2, 0x1.ce1af0b85f3ebp-2, 0x1.d32fe7e00ebd5p-2, - 0x1.d83e7258a2f3ep-2, 0x1.dd46a04c1c4a0p-2, 0x1.e24881a7c6c26p-2, - 0x1.e744261d68787p-2, 0x1.ec399d2468cc0p-2, 0x1.f128f5faf06ecp-2, - 0x1.f6123fa7028acp-2, 0x1.faf588f78f31ep-2, 0x1.ffd2e0857f498p-2, - 0x1.02552a5a5d0fep-1, 0x1.04bdf9da926d2p-1, 0x1.0723e5c1cdf40p-1, - 0x1.0986f4f573520p-1, 0x1.0be72e4252a82p-1, 0x1.0e44985d1cc8bp-1, - 0x1.109f39e2d4c96p-1, 0x1.12f719593efbcp-1, 0x1.154c3d2f4d5e9p-1, - 0x1.179eabbd899a0p-1, 0x1.19ee6b467c96ep-1, 0x1.1c3b81f713c24p-1, - 0x1.1e85f5e7040d0p-1, 0x1.20cdcd192ab6dp-1, 0x1.23130d7bebf42p-1, - 0x1.2555bce98f7cbp-1, 0x1.2795e1289b11ap-1, 0x1.29d37fec2b08ap-1, - 0x1.2c0e9ed448e8bp-1, 0x1.2e47436e40268p-1, 0x1.307d7334f10bep-1, - 0x1.32b1339121d71p-1, 0x1.34e289d9ce1d3p-1, 0x1.37117b54747b5p-1, - 0x1.393e0d3562a19p-1, 0x1.3b68449fffc22p-1, 0x1.3d9026a7156fap-1, - 0x1.3fb5b84d16f42p-1, 0x1.41d8fe84672aep-1, 0x1.43f9fe2f9ce67p-1, - 0x1.4618bc21c5ec2p-1, 0x1.48353d1ea88dfp-1, 0x1.4a4f85db03ebbp-1, - 0x1.4c679afccee39p-1, 0x1.4e7d811b75bb0p-1, 0x1.50913cc01686bp-1, - 0x1.52a2d265bc5aap-1, 0x1.54b2467999497p-1, 0x1.56bf9d5b3f399p-1, - 0x1.58cadb5cd7989p-1, 0x1.5ad404c359f2cp-1, 0x1.5cdb1dc6c1764p-1, - 0x1.5ee02a9241675p-1, 0x1.60e32f44788d8p-1}; - // Range reduction constants for logarithms. // r(0) = 1, r(127) = 0.5 // r(k) = 2^-8 * ceil(2^8 * (1 - 2^-8) / (1 + k*2^-7)) diff --git a/libc/src/math/generic/common_constants.h b/libc/src/math/generic/common_constants.h index 291816a7889ad..72b1d564ca472 100644 --- a/libc/src/math/generic/common_constants.h +++ b/libc/src/math/generic/common_constants.h @@ -11,6 +11,7 @@ #include "src/__support/FPUtil/triple_double.h" #include "src/__support/macros/config.h" +#include "src/__support/math/acosh_float_constants.h" #include "src/__support/math/exp_constants.h" #include "src/__support/number_pair.h" @@ -20,16 +21,10 @@ namespace LIBC_NAMESPACE_DECL { // computed and stored as float precision constants. extern const float ONE_OVER_F_FLOAT[128]; -// Lookup table for (1/f) where f = 1 + n*2^(-7), n = 0..127. -extern const double ONE_OVER_F[128]; - // Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127, // computed and stored as float precision constants. extern const float LOG_F_FLOAT[128]; -// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127. -extern const double LOG_F[128]; - // Lookup table for range reduction constants r for logarithms. extern const float R[128]; diff --git a/libc/src/math/generic/explogxf.h b/libc/src/math/generic/explogxf.h index be4328a4f48b5..a2a6d60f41f76 100644 --- a/libc/src/math/generic/explogxf.h +++ b/libc/src/math/generic/explogxf.h @@ -13,6 +13,7 @@ #include "src/__support/common.h" #include "src/__support/macros/properties/cpu_features.h" +#include "src/__support/math/acoshf_utils.h" #include "src/__support/math/exp10f_utils.h" #include "src/__support/math/exp_utils.h" @@ -163,41 +164,6 @@ LIBC_INLINE static float log_eval_f(float x) { return result; } -// x should be positive, normal finite value -LIBC_INLINE static double log_eval(double x) { - // For x = 2^ex * (1 + mx) - // log(x) = ex * log(2) + log(1 + mx) - using FPB = fputil::FPBits; - FPB bs(x); - - double ex = static_cast(bs.get_exponent()); - - // p1 is the leading 7 bits of mx, i.e. - // p1 * 2^(-7) <= m_x < (p1 + 1) * 2^(-7). - int p1 = static_cast(bs.get_mantissa() >> (FPB::FRACTION_LEN - 7)); - - // Set bs to (1 + (mx - p1*2^(-7)) - bs.set_uintval(bs.uintval() & (FPB::FRACTION_MASK >> 7)); - bs.set_biased_exponent(FPB::EXP_BIAS); - // dx = (mx - p1*2^(-7)) / (1 + p1*2^(-7)). - double dx = (bs.get_val() - 1.0) * ONE_OVER_F[p1]; - - // Minimax polynomial of log(1 + dx) generated by Sollya with: - // > P = fpminimax(log(1 + x)/x, 6, [|D...|], [0, 2^-7]); - const double COEFFS[6] = {-0x1.ffffffffffffcp-2, 0x1.5555555552ddep-2, - -0x1.ffffffefe562dp-3, 0x1.9999817d3a50fp-3, - -0x1.554317b3f67a5p-3, 0x1.1dc5c45e09c18p-3}; - double dx2 = dx * dx; - double c1 = fputil::multiply_add(dx, COEFFS[1], COEFFS[0]); - double c2 = fputil::multiply_add(dx, COEFFS[3], COEFFS[2]); - double c3 = fputil::multiply_add(dx, COEFFS[5], COEFFS[4]); - - double p = fputil::polyeval(dx2, dx, c1, c2, c3); - double result = - fputil::multiply_add(ex, /*log(2)*/ 0x1.62e42fefa39efp-1, LOG_F[p1] + p); - return result; -} - } // namespace LIBC_NAMESPACE_DECL #endif // LLVM_LIBC_SRC_MATH_GENERIC_EXPLOGXF_H diff --git a/libc/src/math/generic/log1pf.cpp b/libc/src/math/generic/log1pf.cpp index 7f614293029de..16b1b34a6c944 100644 --- a/libc/src/math/generic/log1pf.cpp +++ b/libc/src/math/generic/log1pf.cpp @@ -37,6 +37,7 @@ namespace internal { // We don't need to treat denormal and 0 LIBC_INLINE float log(double x) { + using namespace acoshf_internal; constexpr double LOG_2 = 0x1.62e42fefa39efp-1; using FPBits = typename fputil::FPBits; diff --git a/libc/test/shared/CMakeLists.txt b/libc/test/shared/CMakeLists.txt index bf050065cfca6..a402d6e39fa0b 100644 --- a/libc/test/shared/CMakeLists.txt +++ b/libc/test/shared/CMakeLists.txt @@ -10,6 +10,7 @@ add_fp_unittest( libc.src.__support.math.acos libc.src.__support.math.acosf libc.src.__support.math.acosf16 + libc.src.__support.math.acoshf libc.src.__support.math.erff libc.src.__support.math.exp libc.src.__support.math.exp10 diff --git a/libc/test/shared/shared_math_test.cpp b/libc/test/shared/shared_math_test.cpp index 05960de550a12..25555b8caf534 100644 --- a/libc/test/shared/shared_math_test.cpp +++ b/libc/test/shared/shared_math_test.cpp @@ -38,6 +38,7 @@ TEST(LlvmLibcSharedMathTest, AllFloat) { EXPECT_FP_EQ(0x1p+0f, LIBC_NAMESPACE::shared::exp10f(0.0f)); EXPECT_FP_EQ(0x1p+0f, LIBC_NAMESPACE::shared::expf(0.0f)); EXPECT_FP_EQ(0x0p+0f, LIBC_NAMESPACE::shared::erff(0.0f)); + EXPECT_FP_EQ(0x0p+0f, LIBC_NAMESPACE::shared::acoshf(1.0f)); EXPECT_FP_EQ_ALL_ROUNDING(0.75f, LIBC_NAMESPACE::shared::frexpf(24.0f, &exponent)); diff --git a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel index e4a6d9862f37b..34b84c5229f98 100644 --- a/utils/bazel/llvm-project-overlay/libc/BUILD.bazel +++ b/utils/bazel/llvm-project-overlay/libc/BUILD.bazel @@ -1920,6 +1920,7 @@ libc_support_library( hdrs = ["src/math/generic/common_constants.h"], deps = [ ":__support_math_exp_constants", + ":__support_math_acosh_float_constants", ":__support_number_pair", ], ) @@ -2004,6 +2005,7 @@ libc_support_library( ":__support_fputil_nearest_integer", ":__support_math_exp_utils", ":__support_math_exp10f_utils", + ":__support_math_acoshf_utils", ":__support_macros_properties_cpu_features", ":common_constants", ], @@ -2107,6 +2109,38 @@ libc_support_library( ], ) +libc_support_library( + name = "__support_math_acosh_float_constants", + hdrs = ["src/__support/math/acosh_float_constants.h"], + deps = [ + ":__support_macros_config", + ], +) + +libc_support_library( + name = "__support_math_acoshf_utils", + hdrs = ["src/__support/math/acoshf_utils.h"], + deps = [ + ":__support_math_acosh_float_constants", + ":__support_fputil_fp_bits", + ":__support_fputil_multiply_add", + ":__support_fputil_polyeval", + ], +) + +libc_support_library( + name = "__support_math_acoshf", + hdrs = ["src/__support/math/acoshf.h"], + deps = [ + ":__support_math_acoshf_utils", + ":__support_fputil_fenv_impl", + ":__support_fputil_fp_bits", + ":__support_fputil_multiply_add", + ":__support_fputil_sqrt", + ":__support_macros_optimization", + ], +) + libc_support_library( name = "__support_math_asin_utils", hdrs = ["src/__support/math/asin_utils.h"], @@ -2643,13 +2677,7 @@ libc_math_function( libc_math_function( name = "acoshf", additional_deps = [ - ":__support_fputil_fma", - ":__support_fputil_multiply_add", - ":__support_fputil_nearest_integer", - ":__support_fputil_polyeval", - ":__support_fputil_sqrt", - ":__support_macros_optimization", - ":common_constants", + ":__support_math_acoshf", ":explogxf", ], )