//===-- Single-precision tanpi 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/tanpif.h" #include "sincosf_utils.h" #include "src/__support/FPUtil/FEnvImpl.h" #include "src/__support/FPUtil/FPBits.h" #include "src/__support/FPUtil/cast.h" #include "src/__support/FPUtil/except_value_utils.h" #include "src/__support/FPUtil/multiply_add.h" #include "src/__support/common.h" #include "src/__support/macros/config.h" #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY namespace LIBC_NAMESPACE_DECL { #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS constexpr size_t N_EXCEPTS = 3; constexpr fputil::ExceptValues TANPIF_EXCEPTS{{ // (input, RZ output, RU offset, RD offset, RN offset) {0x38F26685, 0x39BE6182, 1, 0, 0}, {0x3E933802, 0x3FA267DD, 1, 0, 0}, {0x3F3663FF, 0xBFA267DD, 0, 1, 0}, }}; #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS LLVM_LIBC_FUNCTION(float, tanpif, (float x)) { using FPBits = typename fputil::FPBits; FPBits xbits(x); uint32_t x_u = xbits.uintval(); uint32_t x_abs = x_u & 0x7fff'ffffU; double xd = static_cast(xbits.get_val()); // Handle exceptional values if (LIBC_UNLIKELY(x_abs <= 0x3F3663FF)) { if (LIBC_UNLIKELY(x_abs == 0U)) return x; #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS bool x_sign = x_u >> 31; if (auto r = TANPIF_EXCEPTS.lookup_odd(x_abs, x_sign); LIBC_UNLIKELY(r.has_value())) return r.value(); #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS } // Numbers greater or equal to 2^23 are always integers, or infinity, or NaN if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) { // x is inf or NaN. if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) { if (xbits.is_signaling_nan()) { fputil::raise_except_if_required(FE_INVALID); return FPBits::quiet_nan().get_val(); } if (x_abs == 0x7f80'0000U) { fputil::set_errno_if_required(EDOM); fputil::raise_except_if_required(FE_INVALID); } return x + FPBits::quiet_nan().get_val(); } return FPBits::zero(xbits.sign()).get_val(); } // Range reduction: // For |x| > 1/32, we perform range reduction as follows: // Find k and y such that: // x = (k + y) * 1/32 // k is an integer // |y| < 0.5 // // This is done by performing: // k = round(x * 32) // y = x * 32 - k // // Once k and y are computed, we then deduce the answer by the formula: // tan(x) = sin(x) / cos(x) // = (sin_y * cos_k + cos_y * sin_k) / (cos_y * cos_k - sin_y * sin_k) double sin_k, cos_k, sin_y, cosm1_y; sincospif_eval(xd, sin_k, cos_k, sin_y, cosm1_y); if (LIBC_UNLIKELY(sin_y == 0 && cos_k == 0)) { fputil::set_errno_if_required(EDOM); fputil::raise_except_if_required(FE_DIVBYZERO); int32_t x_mp5_i = static_cast(xd - 0.5); return FPBits::inf((x_mp5_i & 0x1) ? Sign::NEG : Sign::POS).get_val(); } using fputil::multiply_add; return fputil::cast( multiply_add(sin_y, cos_k, multiply_add(cosm1_y, sin_k, sin_k)) / multiply_add(sin_y, -sin_k, multiply_add(cosm1_y, cos_k, cos_k))); } } // namespace LIBC_NAMESPACE_DECL