| //===-- Single-precision cospi 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/cospif.h" |
| #include "sincosf_utils.h" |
| #include "src/__support/FPUtil/FEnvImpl.h" |
| #include "src/__support/FPUtil/FPBits.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 |
| #include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA |
| |
| namespace LIBC_NAMESPACE_DECL { |
| |
| LLVM_LIBC_FUNCTION(float, cospif, (float x)) { |
| using FPBits = typename fputil::FPBits<float>; |
| |
| FPBits xbits(x); |
| xbits.set_sign(Sign::POS); |
| |
| uint32_t x_abs = xbits.uintval(); |
| double xd = static_cast<double>(xbits.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 cosine of sum |
| // formula: |
| // cospi(x) = cos((k + y)*pi/32) |
| // = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32) |
| // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..63 are precomputed |
| // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are |
| // computed using degree-7 and degree-6 minimax polynomials generated by |
| // Sollya respectively. |
| |
| // The exhautive test passes for smaller values |
| if (LIBC_UNLIKELY(x_abs < 0x38A2'F984U)) { |
| |
| #if defined(LIBC_TARGET_CPU_HAS_FMA_FLOAT) |
| return fputil::multiply_add(xbits.get_val(), -0x1.0p-25f, 1.0f); |
| #else |
| return static_cast<float>(fputil::multiply_add(xd, -0x1.0p-25, 1.0)); |
| #endif // LIBC_TARGET_CPU_HAS_FMA_FLOAT |
| } |
| |
| // Numbers greater or equal to 2^23 are always integers or NaN |
| if (LIBC_UNLIKELY(x_abs >= 0x4B00'0000)) { |
| |
| if (LIBC_UNLIKELY(x_abs < 0x4B80'0000)) { |
| return (x_abs & 0x1) ? -1.0f : 1.0f; |
| } |
| |
| // x is inf or nan. |
| if (LIBC_UNLIKELY(x_abs >= 0x7f80'0000U)) { |
| 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 1.0f; |
| } |
| |
| // Combine the results with the sine of sum formula: |
| // cos(pi * x) = cos((k + y)*pi/32) |
| // = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32) |
| // = (cosm1_y + 1) * cos_k - sin_y * sin_k |
| // = (cosm1_y * cos_k + 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)) { |
| return 0.0f; |
| } |
| |
| return static_cast<float>(fputil::multiply_add( |
| sin_y, -sin_k, fputil::multiply_add(cosm1_y, cos_k, cos_k))); |
| } |
| |
| } // namespace LIBC_NAMESPACE_DECL |