[libc][math] Refactored atanpif16 to header only (#184316)
Fixes #178105
This commit is contained in:
Abhijeet
GitHub
parent
f00145aa52
commit
cf979d5a96
@ -34,6 +34,7 @@
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#include "math/atanf16.h"
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#include "math/atanhf.h"
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#include "math/atanhf16.h"
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#include "math/atanpif16.h"
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#include "math/bf16add.h"
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#include "math/bf16addf.h"
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#include "math/bf16addf128.h"
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29
libc/shared/math/atanpif16.h
Normal file
29
libc/shared/math/atanpif16.h
Normal file
@ -0,0 +1,29 @@
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//===-- Shared atanpif16 function -------------------------------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef LLVM_LIBC_SHARED_MATH_ATANPIF16_H
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#define LLVM_LIBC_SHARED_MATH_ATANPIF16_H
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#include "include/llvm-libc-macros/float16-macros.h"
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#ifdef LIBC_TYPES_HAS_FLOAT16
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#include "shared/libc_common.h"
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#include "src/__support/math/atanpif16.h"
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namespace LIBC_NAMESPACE_DECL {
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namespace shared {
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using math::atanpif16;
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} // namespace shared
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LIBC_TYPES_HAS_FLOAT16
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#endif // LLVM_LIBC_SHARED_MATH_ATANPIF16_H
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@ -346,6 +346,23 @@ add_header_library(
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libc.src.__support.macros.optimization
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)
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add_header_library(
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atanpif16
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HDRS
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atanpif16.h
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DEPENDS
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libc.hdr.fenv_macros
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libc.include.llvm-libc-macros.float16_macros
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libc.src.__support.FPUtil.cast
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libc.src.__support.FPUtil.fenv_impl
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libc.src.__support.FPUtil.fp_bits
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libc.src.__support.FPUtil.multiply_add
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libc.src.__support.FPUtil.polyeval
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libc.src.__support.FPUtil.sqrt
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libc.src.__support.macros.config
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libc.src.__support.macros.optimization
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)
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add_header_library(
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asinf
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HDRS
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168
libc/src/__support/math/atanpif16.h
Normal file
168
libc/src/__support/math/atanpif16.h
Normal file
@ -0,0 +1,168 @@
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//===-- Implementation header for atanpif16 ---------------------*- C++ -*-===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ATANPIF16_H
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#define LLVM_LIBC_SRC___SUPPORT_MATH_ATANPIF16_H
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#include "include/llvm-libc-macros/float16-macros.h"
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#ifdef LIBC_TYPES_HAS_FLOAT16
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#include "hdr/fenv_macros.h"
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#include "src/__support/FPUtil/FEnvImpl.h"
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#include "src/__support/FPUtil/FPBits.h"
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#include "src/__support/FPUtil/PolyEval.h"
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#include "src/__support/FPUtil/cast.h"
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#include "src/__support/FPUtil/multiply_add.h"
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#include "src/__support/FPUtil/sqrt.h"
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#include "src/__support/macros/optimization.h"
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namespace LIBC_NAMESPACE_DECL {
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namespace math {
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// Using Python's SymPy library, we can obtain the polynomial approximation of
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// arctan(x)/pi. The steps are as follows:
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// >>> from sympy import *
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// >>> import math
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// >>> x = symbols('x')
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// >>> print(series(atan(x)/math.pi, x, 0, 17))
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//
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// Output:
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// 0.318309886183791*x - 0.106103295394597*x**3 + 0.0636619772367581*x**5 -
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// 0.0454728408833987*x**7 + 0.0353677651315323*x**9 - 0.0289372623803446*x**11
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// + 0.0244853758602916*x**13 - 0.0212206590789194*x**15 + O(x**17)
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//
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// We will assign this degree-15 Taylor polynomial as g(x). This polynomial
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// approximation is accurate for arctan(x)/pi when |x| is in the range [0, 0.5].
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//
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//
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// To compute arctan(x) for all real x, we divide the domain into the following
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// cases:
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//
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// * Case 1: |x| <= 0.5
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// In this range, the direct polynomial approximation is used:
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// arctan(x)/pi = sign(x) * g(|x|)
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// or equivalently, arctan(x) = sign(x) * pi * g(|x|).
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//
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// * Case 2: 0.5 < |x| <= 1
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// We use the double-angle identity for the tangent function, specifically:
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// arctan(x) = 2 * arctan(x / (1 + sqrt(1 + x^2))).
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// Applying this, we have:
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// arctan(x)/pi = sign(x) * 2 * arctan(x')/pi,
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// where x' = |x| / (1 + sqrt(1 + x^2)).
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// Thus, arctan(x)/pi = sign(x) * 2 * g(x')
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//
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// When |x| is in (0.5, 1], the value of x' will always fall within the
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// interval [0.207, 0.414], which is within the accurate range of g(x).
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//
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// * Case 3: |x| > 1
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// For values of |x| greater than 1, we use the reciprocal transformation
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// identity:
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// arctan(x) = pi/2 - arctan(1/x) for x > 0.
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// For any x (real number), this generalizes to:
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// arctan(x)/pi = sign(x) * (1/2 - arctan(1/|x|)/pi).
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// Then, using g(x) for arctan(1/|x|)/pi:
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// arctan(x)/pi = sign(x) * (1/2 - g(1/|x|)).
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//
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// Note that if 1/|x| still falls outside the
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// g(x)'s primary range of accuracy (i.e., if 0.5 < 1/|x| <= 1), the rule
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// from Case 2 must be applied recursively to 1/|x|.
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LIBC_INLINE float16 atanpif16(float16 x) {
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using FPBits = fputil::FPBits<float16>;
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FPBits xbits(x);
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bool is_neg = xbits.is_neg();
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auto signed_result = [is_neg](double r) -> float16 {
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return fputil::cast<float16>(is_neg ? -r : r);
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};
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if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) {
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if (xbits.is_nan()) {
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if (xbits.is_signaling_nan()) {
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fputil::raise_except_if_required(FE_INVALID);
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return FPBits::quiet_nan().get_val();
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}
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return x;
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}
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// atanpi(+-inf) = +-0.5
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return signed_result(0.5);
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}
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if (LIBC_UNLIKELY(xbits.is_zero()))
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return x;
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double x_abs = fputil::cast<double>(xbits.abs().get_val());
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if (LIBC_UNLIKELY(x_abs == 1.0))
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return signed_result(0.25);
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// evaluate atan(x)/pi using polynomial approximation, valid for |x| <= 0.5
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constexpr auto atanpi_eval = [](double x) -> double {
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// polynomial coefficients for atan(x)/pi taylor series
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// generated using sympy: series(atan(x)/pi, x, 0, 17)
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constexpr static double POLY_COEFFS[] = {
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0x1.45f306dc9c889p-2, // x^1: 1/pi
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-0x1.b2995e7b7b60bp-4, // x^3: -1/(3*pi)
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0x1.04c26be3b06ccp-4, // x^5: 1/(5*pi)
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-0x1.7483758e69c08p-5, // x^7: -1/(7*pi)
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0x1.21bb945252403p-5, // x^9: 1/(9*pi)
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-0x1.da1bace3cc68ep-6, // x^11: -1/(11*pi)
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0x1.912b1c2336cf2p-6, // x^13: 1/(13*pi)
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-0x1.5bade52f95e7p-6, // x^15: -1/(15*pi)
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};
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double x_sq = x * x;
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return x * fputil::polyeval(x_sq, POLY_COEFFS[0], POLY_COEFFS[1],
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POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4],
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POLY_COEFFS[5], POLY_COEFFS[6], POLY_COEFFS[7]);
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};
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// case 1: |x| <= 0.5 - direct polynomial evaluation
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if (LIBC_LIKELY(x_abs <= 0.5)) {
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double result = atanpi_eval(x_abs);
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return signed_result(result);
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}
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// case 2: 0.5 < |x| <= 1 - use double-angle reduction
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// atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))
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// so atanpi(x) = 2 * atanpi(x') where x' = x / (1 + sqrt(1 + x^2))
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if (x_abs <= 1.0) {
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double x_abs_sq = x_abs * x_abs;
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double sqrt_term = fputil::sqrt<double>(1.0 + x_abs_sq);
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double x_prime = x_abs / (1.0 + sqrt_term);
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double result = 2.0 * atanpi_eval(x_prime);
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return signed_result(result);
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}
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// case 3: |x| > 1 - use reciprocal transformation
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// atan(x) = pi/2 - atan(1/x) for x > 0
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// so atanpi(x) = 1/2 - atanpi(1/x)
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double x_recip = 1.0 / x_abs;
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double result = 0.0;
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// if 1/|x| > 0.5, we need to apply Case 2 transformation to 1/|x|
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if (x_recip > 0.5) {
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double x_recip_sq = x_recip * x_recip;
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double sqrt_term = fputil::sqrt<double>(1.0 + x_recip_sq);
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double x_prime = x_recip / (1.0 + sqrt_term);
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result = fputil::multiply_add(-2.0, atanpi_eval(x_prime), 0.5);
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} else {
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// direct evaluation since 1/|x| <= 0.5
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result = 0.5 - atanpi_eval(x_recip);
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}
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return signed_result(result);
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}
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} // namespace math
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} // namespace LIBC_NAMESPACE_DECL
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#endif // LIBC_TYPES_HAS_FLOAT16
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#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ATANPIF16_H
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@ -4076,16 +4076,7 @@ add_entrypoint_object(
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HDRS
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../atanpif16.h
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DEPENDS
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libc.hdr.errno_macros
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libc.hdr.fenv_macros
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libc.src.__support.FPUtil.cast
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libc.src.__support.FPUtil.fenv_impl
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libc.src.__support.FPUtil.fp_bits
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libc.src.__support.FPUtil.multiply_add
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libc.src.__support.FPUtil.polyeval
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libc.src.__support.FPUtil.sqrt
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libc.src.__support.macros.optimization
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libc.src.__support.macros.properties.types
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libc.src.__support.math.atanpif16
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)
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add_entrypoint_object(
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@ -7,151 +7,12 @@
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//===----------------------------------------------------------------------===//
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#include "src/math/atanpif16.h"
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#include "hdr/errno_macros.h"
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#include "hdr/fenv_macros.h"
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#include "src/__support/FPUtil/FEnvImpl.h"
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#include "src/__support/FPUtil/FPBits.h"
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#include "src/__support/FPUtil/PolyEval.h"
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#include "src/__support/FPUtil/cast.h"
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#include "src/__support/FPUtil/multiply_add.h"
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#include "src/__support/FPUtil/sqrt.h"
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#include "src/__support/macros/optimization.h"
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#include "src/__support/math/atanpif16.h"
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namespace LIBC_NAMESPACE_DECL {
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// Using Python's SymPy library, we can obtain the polynomial approximation of
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// arctan(x)/pi. The steps are as follows:
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// >>> from sympy import *
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// >>> import math
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// >>> x = symbols('x')
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// >>> print(series(atan(x)/math.pi, x, 0, 17))
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//
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// Output:
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// 0.318309886183791*x - 0.106103295394597*x**3 + 0.0636619772367581*x**5 -
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// 0.0454728408833987*x**7 + 0.0353677651315323*x**9 - 0.0289372623803446*x**11
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// + 0.0244853758602916*x**13 - 0.0212206590789194*x**15 + O(x**17)
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//
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// We will assign this degree-15 Taylor polynomial as g(x). This polynomial
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// approximation is accurate for arctan(x)/pi when |x| is in the range [0, 0.5].
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//
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//
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// To compute arctan(x) for all real x, we divide the domain into the following
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// cases:
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//
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// * Case 1: |x| <= 0.5
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// In this range, the direct polynomial approximation is used:
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// arctan(x)/pi = sign(x) * g(|x|)
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// or equivalently, arctan(x) = sign(x) * pi * g(|x|).
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//
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// * Case 2: 0.5 < |x| <= 1
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// We use the double-angle identity for the tangent function, specifically:
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// arctan(x) = 2 * arctan(x / (1 + sqrt(1 + x^2))).
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// Applying this, we have:
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// arctan(x)/pi = sign(x) * 2 * arctan(x')/pi,
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// where x' = |x| / (1 + sqrt(1 + x^2)).
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// Thus, arctan(x)/pi = sign(x) * 2 * g(x')
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//
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// When |x| is in (0.5, 1], the value of x' will always fall within the
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// interval [0.207, 0.414], which is within the accurate range of g(x).
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//
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// * Case 3: |x| > 1
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// For values of |x| greater than 1, we use the reciprocal transformation
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// identity:
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// arctan(x) = pi/2 - arctan(1/x) for x > 0.
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// For any x (real number), this generalizes to:
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// arctan(x)/pi = sign(x) * (1/2 - arctan(1/|x|)/pi).
|
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// Then, using g(x) for arctan(1/|x|)/pi:
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// arctan(x)/pi = sign(x) * (1/2 - g(1/|x|)).
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//
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// Note that if 1/|x| still falls outside the
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// g(x)'s primary range of accuracy (i.e., if 0.5 < 1/|x| <= 1), the rule
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// from Case 2 must be applied recursively to 1/|x|.
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LLVM_LIBC_FUNCTION(float16, atanpif16, (float16 x)) {
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using FPBits = fputil::FPBits<float16>;
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FPBits xbits(x);
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bool is_neg = xbits.is_neg();
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auto signed_result = [is_neg](double r) -> float16 {
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return fputil::cast<float16>(is_neg ? -r : r);
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};
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if (LIBC_UNLIKELY(xbits.is_inf_or_nan())) {
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if (xbits.is_nan()) {
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if (xbits.is_signaling_nan()) {
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fputil::raise_except_if_required(FE_INVALID);
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return FPBits::quiet_nan().get_val();
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}
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return x;
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}
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// atanpi(±∞) = ±0.5
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return signed_result(0.5);
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}
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if (LIBC_UNLIKELY(xbits.is_zero()))
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return x;
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double x_abs = fputil::cast<double>(xbits.abs().get_val());
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if (LIBC_UNLIKELY(x_abs == 1.0))
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return signed_result(0.25);
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// evaluate atan(x)/pi using polynomial approximation, valid for |x| <= 0.5
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constexpr auto atanpi_eval = [](double x) -> double {
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// polynomial coefficients for atan(x)/pi taylor series
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// generated using sympy: series(atan(x)/pi, x, 0, 17)
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constexpr static double POLY_COEFFS[] = {
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0x1.45f306dc9c889p-2, // x^1: 1/pi
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-0x1.b2995e7b7b60bp-4, // x^3: -1/(3*pi)
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0x1.04c26be3b06ccp-4, // x^5: 1/(5*pi)
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-0x1.7483758e69c08p-5, // x^7: -1/(7*pi)
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0x1.21bb945252403p-5, // x^9: 1/(9*pi)
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-0x1.da1bace3cc68ep-6, // x^11: -1/(11*pi)
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0x1.912b1c2336cf2p-6, // x^13: 1/(13*pi)
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-0x1.5bade52f95e7p-6, // x^15: -1/(15*pi)
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};
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double x_sq = x * x;
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return x * fputil::polyeval(x_sq, POLY_COEFFS[0], POLY_COEFFS[1],
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POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4],
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POLY_COEFFS[5], POLY_COEFFS[6], POLY_COEFFS[7]);
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};
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// Case 1: |x| <= 0.5 - Direct polynomial evaluation
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if (LIBC_LIKELY(x_abs <= 0.5)) {
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double result = atanpi_eval(x_abs);
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return signed_result(result);
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}
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// case 2: 0.5 < |x| <= 1 - use double-angle reduction
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// atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2)))
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// so atanpi(x) = 2 * atanpi(x') where x' = x / (1 + sqrt(1 + x^2))
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if (x_abs <= 1.0) {
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double x_abs_sq = x_abs * x_abs;
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double sqrt_term = fputil::sqrt<double>(1.0 + x_abs_sq);
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double x_prime = x_abs / (1.0 + sqrt_term);
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double result = 2.0 * atanpi_eval(x_prime);
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||||
return signed_result(result);
|
||||
}
|
||||
|
||||
// case 3: |x| > 1 - use reciprocal transformation
|
||||
// atan(x) = pi/2 - atan(1/x) for x > 0
|
||||
// so atanpi(x) = 1/2 - atanpi(1/x)
|
||||
double x_recip = 1.0 / x_abs;
|
||||
double result;
|
||||
|
||||
// if 1/|x| > 0.5, we need to apply Case 2 transformation to 1/|x|
|
||||
if (x_recip > 0.5) {
|
||||
double x_recip_sq = x_recip * x_recip;
|
||||
double sqrt_term = fputil::sqrt<double>(1.0 + x_recip_sq);
|
||||
double x_prime = x_recip / (1.0 + sqrt_term);
|
||||
result = fputil::multiply_add(-2.0, atanpi_eval(x_prime), 0.5);
|
||||
} else {
|
||||
// direct evaluation since 1/|x| <= 0.5
|
||||
result = 0.5 - atanpi_eval(x_recip);
|
||||
}
|
||||
|
||||
return signed_result(result);
|
||||
return math::atanpif16(x);
|
||||
}
|
||||
|
||||
} // namespace LIBC_NAMESPACE_DECL
|
||||
|
||||
@ -31,6 +31,7 @@ add_fp_unittest(
|
||||
libc.src.__support.math.atanf16
|
||||
libc.src.__support.math.atanhf
|
||||
libc.src.__support.math.atanhf16
|
||||
libc.src.__support.math.atanpif16
|
||||
libc.src.__support.math.bf16add
|
||||
libc.src.__support.math.bf16addf
|
||||
libc.src.__support.math.bf16addl
|
||||
|
||||
@ -27,6 +27,7 @@ TEST(LlvmLibcSharedMathTest, AllFloat16) {
|
||||
EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::atan2f16(0.0f16, 0.0f16));
|
||||
EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::atanf16(0.0f16));
|
||||
EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::atanhf16(0.0f16));
|
||||
EXPECT_FP_EQ(0x0p+0f16, LIBC_NAMESPACE::shared::atanpif16(0.0f16));
|
||||
EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::cosf16(0.0f16));
|
||||
EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::coshf16(0.0f16));
|
||||
EXPECT_FP_EQ(0x1p+0f16, LIBC_NAMESPACE::shared::cospif16(0.0f16));
|
||||
|
||||
@ -3107,6 +3107,23 @@ libc_support_library(
|
||||
],
|
||||
)
|
||||
|
||||
libc_support_library(
|
||||
name = "__support_math_atanpif16",
|
||||
hdrs = ["src/__support/math/atanpif16.h"],
|
||||
deps = [
|
||||
":__support_fputil_cast",
|
||||
":__support_fputil_fenv_impl",
|
||||
":__support_fputil_fp_bits",
|
||||
":__support_fputil_multiply_add",
|
||||
":__support_fputil_polyeval",
|
||||
":__support_fputil_sqrt",
|
||||
":__support_macros_config",
|
||||
":__support_macros_optimization",
|
||||
":hdr_fenv_macros",
|
||||
":llvm_libc_macros_float16_macros",
|
||||
],
|
||||
)
|
||||
|
||||
libc_support_library(
|
||||
name = "__support_math_bf16add",
|
||||
hdrs = ["src/__support/math/bf16add.h"],
|
||||
@ -6198,6 +6215,11 @@ libc_math_function(
|
||||
],
|
||||
)
|
||||
|
||||
libc_math_function(
|
||||
name = "atanpif16",
|
||||
additional_deps = [":__support_math_atanpif16"],
|
||||
)
|
||||
|
||||
libc_math_function(
|
||||
name = "bf16add",
|
||||
additional_deps = [":__support_math_bf16add"],
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user