diff options
Diffstat (limited to 'libc/src')
27 files changed, 41 insertions, 206 deletions
diff --git a/libc/src/__support/math/acos.h b/libc/src/__support/math/acos.h index a52ead7..0e1e413 100644 --- a/libc/src/__support/math/acos.h +++ b/libc/src/__support/math/acos.h @@ -24,7 +24,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr double acos(double x) { +LIBC_INLINE static constexpr double acos(double x) { using DoubleDouble = fputil::DoubleDouble; using namespace asin_internal; using FPBits = fputil::FPBits<double>; diff --git a/libc/src/__support/math/acosf.h b/libc/src/__support/math/acosf.h index 153087e..7a0c0e5 100644 --- a/libc/src/__support/math/acosf.h +++ b/libc/src/__support/math/acosf.h @@ -45,7 +45,7 @@ static constexpr fputil::ExceptValues<float, N_EXCEPTS> ACOSF_EXCEPTS = {{ } // namespace acosf_internal -static constexpr float acosf(float x) { +LIBC_INLINE static constexpr float acosf(float x) { using namespace acosf_internal; using namespace inv_trigf_utils_internal; using FPBits = typename fputil::FPBits<float>; diff --git a/libc/src/__support/math/acosf16.h b/libc/src/__support/math/acosf16.h index 58d3761..3f0e002 100644 --- a/libc/src/__support/math/acosf16.h +++ b/libc/src/__support/math/acosf16.h @@ -26,7 +26,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float16 acosf16(float16 x) { +LIBC_INLINE static constexpr float16 acosf16(float16 x) { // Generated by Sollya using the following command: // > round(pi/2, SG, RN); diff --git a/libc/src/__support/math/acoshf.h b/libc/src/__support/math/acoshf.h index f18f169..4e00311 100644 --- a/libc/src/__support/math/acoshf.h +++ b/libc/src/__support/math/acoshf.h @@ -21,7 +21,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float acoshf(float x) { +LIBC_INLINE static constexpr float acoshf(float x) { using namespace acoshf_internal; using FPBits_t = typename fputil::FPBits<float>; FPBits_t xbits(x); diff --git a/libc/src/__support/math/acoshf16.h b/libc/src/__support/math/acoshf16.h index a02b7b6..e5be2a8 100644 --- a/libc/src/__support/math/acoshf16.h +++ b/libc/src/__support/math/acoshf16.h @@ -28,7 +28,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float16 acoshf16(float16 x) { +LIBC_INLINE static constexpr float16 acoshf16(float16 x) { using namespace acoshf_internal; constexpr size_t N_EXCEPTS = 2; diff --git a/libc/src/__support/math/acospif16.h b/libc/src/__support/math/acospif16.h index 5829aed..cf29c76 100644 --- a/libc/src/__support/math/acospif16.h +++ b/libc/src/__support/math/acospif16.h @@ -25,7 +25,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float16 acospif16(float16 x) { +LIBC_INLINE static constexpr float16 acospif16(float16 x) { using FPBits = fputil::FPBits<float16>; FPBits xbits(x); diff --git a/libc/src/__support/math/asin.h b/libc/src/__support/math/asin.h index 84fc1cf..5e06d04 100644 --- a/libc/src/__support/math/asin.h +++ b/libc/src/__support/math/asin.h @@ -25,7 +25,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr double asin(double x) { +LIBC_INLINE static constexpr double asin(double x) { using namespace asin_internal; using FPBits = fputil::FPBits<double>; diff --git a/libc/src/__support/math/erff.h b/libc/src/__support/math/erff.h index e54ec77..b81be30 100644 --- a/libc/src/__support/math/erff.h +++ b/libc/src/__support/math/erff.h @@ -19,7 +19,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float erff(float x) { +LIBC_INLINE static constexpr float erff(float x) { // Polynomials approximating erf(x)/x on ( k/8, (k + 1)/8 ) generated by // Sollya with: > P = fpminimax(erf(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14|], diff --git a/libc/src/__support/math/exp.h b/libc/src/__support/math/exp.h index 14f0592..83638e8 100644 --- a/libc/src/__support/math/exp.h +++ b/libc/src/__support/math/exp.h @@ -67,7 +67,7 @@ namespace { // Return expm1(dx) / x ~ 1 + dx / 2 + dx^2 / 6 + dx^3 / 24. // For |dx| < 2^-13 + 2^-30: // | output - expm1(dx) / dx | < 2^-51. -static double poly_approx_d(double dx) { +LIBC_INLINE static double poly_approx_d(double dx) { // dx^2 double dx2 = dx * dx; // c0 = 1 + dx / 2 @@ -85,7 +85,7 @@ static double poly_approx_d(double dx) { // Return exp(dx) ~ 1 + dx + dx^2 / 2 + ... + dx^6 / 720 // For |dx| < 2^-13 + 2^-30: // | output - exp(dx) | < 2^-101 -static DoubleDouble poly_approx_dd(const DoubleDouble &dx) { +LIBC_INLINE static DoubleDouble poly_approx_dd(const DoubleDouble &dx) { // Taylor polynomial. constexpr DoubleDouble COEFFS[] = { {0, 0x1p0}, // 1 @@ -106,7 +106,7 @@ static DoubleDouble poly_approx_dd(const DoubleDouble &dx) { // Return exp(dx) ~ 1 + dx + dx^2 / 2 + ... + dx^7 / 5040 // For |dx| < 2^-13 + 2^-30: // | output - exp(dx) | < 2^-126. -static Float128 poly_approx_f128(const Float128 &dx) { +LIBC_INLINE static Float128 poly_approx_f128(const Float128 &dx) { constexpr Float128 COEFFS_128[]{ {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0 {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0 @@ -127,7 +127,7 @@ static Float128 poly_approx_f128(const Float128 &dx) { // Compute exp(x) using 128-bit precision. // TODO(lntue): investigate triple-double precision implementation for this // step. -static Float128 exp_f128(double x, double kd, int idx1, int idx2) { +LIBC_INLINE static Float128 exp_f128(double x, double kd, int idx1, int idx2) { // Recalculate dx: double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact @@ -160,8 +160,8 @@ static Float128 exp_f128(double x, double kd, int idx1, int idx2) { } // Compute exp(x) with double-double precision. -static DoubleDouble exp_double_double(double x, double kd, - const DoubleDouble &exp_mid) { +LIBC_INLINE static DoubleDouble exp_double_double(double x, double kd, + const DoubleDouble &exp_mid) { // Recalculate dx: // dx = x - k * 2^-12 * log(2) double t1 = fputil::multiply_add(kd, MLOG_2_EXP2_M12_HI, x); // exact @@ -184,7 +184,7 @@ static DoubleDouble exp_double_double(double x, double kd, // Check for exceptional cases when // |x| <= 2^-53 or x < log(2^-1075) or x >= 0x1.6232bdd7abcd3p+9 -static double set_exceptional(double x) { +LIBC_INLINE static double set_exceptional(double x) { using FPBits = typename fputil::FPBits<double>; FPBits xbits(x); diff --git a/libc/src/__support/math/exp10.h b/libc/src/__support/math/exp10.h index fa60e40c..12a09d7 100644 --- a/libc/src/__support/math/exp10.h +++ b/libc/src/__support/math/exp10.h @@ -83,7 +83,8 @@ LIBC_INLINE static double exp10_poly_approx_d(double dx) { // > P = fpminimax((10^x - 1)/x, 5, [|DD...|], [-2^-14, 2^-14]); // Error bounds: // | output - 10^(dx) | < 2^-101 -static constexpr DoubleDouble exp10_poly_approx_dd(const DoubleDouble &dx) { +LIBC_INLINE static constexpr DoubleDouble +exp10_poly_approx_dd(const DoubleDouble &dx) { // Taylor polynomial. constexpr DoubleDouble COEFFS[] = { {0, 0x1p0}, @@ -105,7 +106,8 @@ static constexpr DoubleDouble exp10_poly_approx_dd(const DoubleDouble &dx) { // Return exp(dx) ~ 1 + a0 * dx + a1 * dx^2 + ... + a6 * dx^7 // For |dx| < 2^-14: // | output - 10^dx | < 1.5 * 2^-124. -static constexpr Float128 exp10_poly_approx_f128(const Float128 &dx) { +LIBC_INLINE static constexpr Float128 +exp10_poly_approx_f128(const Float128 &dx) { constexpr Float128 COEFFS_128[]{ {Sign::POS, -127, 0x80000000'00000000'00000000'00000000_u128}, // 1.0 {Sign::POS, -126, 0x935d8ddd'aaa8ac16'ea56d62b'82d30a2d_u128}, @@ -126,7 +128,8 @@ static constexpr Float128 exp10_poly_approx_f128(const Float128 &dx) { // Compute 10^(x) using 128-bit precision. // TODO(lntue): investigate triple-double precision implementation for this // step. -static Float128 exp10_f128(double x, double kd, int idx1, int idx2) { +LIBC_INLINE static Float128 exp10_f128(double x, double kd, int idx1, + int idx2) { double t1 = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact double t2 = kd * MLOG10_2_EXP2_M12_MID_32; // exact double t3 = kd * MLOG10_2_EXP2_M12_LO; // Error < 2^-144 @@ -157,8 +160,8 @@ static Float128 exp10_f128(double x, double kd, int idx1, int idx2) { } // Compute 10^x with double-double precision. -static DoubleDouble exp10_double_double(double x, double kd, - const DoubleDouble &exp_mid) { +LIBC_INLINE static DoubleDouble +exp10_double_double(double x, double kd, const DoubleDouble &exp_mid) { // Recalculate dx: // dx = x - k * 2^-12 * log10(2) double t1 = fputil::multiply_add(kd, MLOG10_2_EXP2_M12_HI, x); // exact @@ -180,7 +183,7 @@ static DoubleDouble exp10_double_double(double x, double kd, #endif // LIBC_MATH_HAS_SKIP_ACCURATE_PASS // When output is denormal. -static double exp10_denorm(double x) { +LIBC_INLINE static double exp10_denorm(double x) { // Range reduction. double tmp = fputil::multiply_add(x, LOG2_10, 0x1.8000'0000'4p21); int k = static_cast<int>(cpp::bit_cast<uint64_t>(tmp) >> 19); @@ -234,7 +237,7 @@ static double exp10_denorm(double x) { // * x >= log10(2^1024) // * x <= log10(2^-1022) // * x is inf or nan -static constexpr double exp10_set_exceptional(double x) { +LIBC_INLINE static constexpr double exp10_set_exceptional(double x) { using FPBits = typename fputil::FPBits<double>; FPBits xbits(x); @@ -285,7 +288,7 @@ static constexpr double exp10_set_exceptional(double x) { namespace math { -static constexpr double exp10(double x) { +LIBC_INLINE static constexpr double exp10(double x) { using FPBits = typename fputil::FPBits<double>; FPBits xbits(x); diff --git a/libc/src/__support/math/exp10f.h b/libc/src/__support/math/exp10f.h index 807b4f0..76ae197 100644 --- a/libc/src/__support/math/exp10f.h +++ b/libc/src/__support/math/exp10f.h @@ -20,7 +20,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float exp10f(float x) { +LIBC_INLINE static constexpr float exp10f(float x) { using FPBits = typename fputil::FPBits<float>; FPBits xbits(x); diff --git a/libc/src/__support/math/exp10f16.h b/libc/src/__support/math/exp10f16.h index 0d8b125..3eca867 100644 --- a/libc/src/__support/math/exp10f16.h +++ b/libc/src/__support/math/exp10f16.h @@ -57,7 +57,7 @@ static constexpr fputil::ExceptValues<float16, N_EXP10F16_EXCEPTS> }}; #endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS -static constexpr float16 exp10f16(float16 x) { +LIBC_INLINE static constexpr float16 exp10f16(float16 x) { using FPBits = fputil::FPBits<float16>; FPBits x_bits(x); diff --git a/libc/src/__support/math/exp10f_utils.h b/libc/src/__support/math/exp10f_utils.h index c30def9..010a2f1 100644 --- a/libc/src/__support/math/exp10f_utils.h +++ b/libc/src/__support/math/exp10f_utils.h @@ -89,7 +89,7 @@ struct Exp10Base : public ExpBase { 0x1.0470591dff149p1, 0x1.2bd7c0a9fbc4dp0, 0x1.1429e74a98f43p-1}; - static double powb_lo(double dx) { + LIBC_INLINE static double powb_lo(double dx) { using fputil::multiply_add; double dx2 = dx * dx; // c0 = 1 + COEFFS[0] * dx diff --git a/libc/src/__support/math/exp_utils.h b/libc/src/__support/math/exp_utils.h index fc9ab10..ef408ed 100644 --- a/libc/src/__support/math/exp_utils.h +++ b/libc/src/__support/math/exp_utils.h @@ -22,8 +22,8 @@ namespace LIBC_NAMESPACE_DECL { // So if we scale x up by 2^1022, we can use // double(1.0 + 2^1022 * x) - 1.0 to test how x is rounded in denormal range. template <bool SKIP_ZIV_TEST = false> -static constexpr cpp::optional<double> ziv_test_denorm(int hi, double mid, - double lo, double err) { +LIBC_INLINE static constexpr cpp::optional<double> +ziv_test_denorm(int hi, double mid, double lo, double err) { using FPBits = typename fputil::FPBits<double>; // Scaling factor = 1/(min normal number) = 2^1022 diff --git a/libc/src/__support/math/expf.h b/libc/src/__support/math/expf.h index 88c1514..f7e11be 100644 --- a/libc/src/__support/math/expf.h +++ b/libc/src/__support/math/expf.h @@ -24,7 +24,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float expf(float x) { +LIBC_INLINE static constexpr float expf(float x) { using FPBits = typename fputil::FPBits<float>; FPBits xbits(x); diff --git a/libc/src/__support/math/expf16.h b/libc/src/__support/math/expf16.h index ded28c7..14302a7 100644 --- a/libc/src/__support/math/expf16.h +++ b/libc/src/__support/math/expf16.h @@ -31,7 +31,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float16 expf16(float16 x) { +LIBC_INLINE static constexpr float16 expf16(float16 x) { #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS constexpr fputil::ExceptValues<float16, 2> EXPF16_EXCEPTS_LO = {{ // (input, RZ output, RU offset, RD offset, RN offset) diff --git a/libc/src/__support/math/expf16_utils.h b/libc/src/__support/math/expf16_utils.h index 8a2fc94..4204dab7 100644 --- a/libc/src/__support/math/expf16_utils.h +++ b/libc/src/__support/math/expf16_utils.h @@ -47,7 +47,8 @@ struct ExpRangeReduction { float exp_lo; }; -[[maybe_unused]] static ExpRangeReduction exp_range_reduction(float16 x) { +[[maybe_unused]] LIBC_INLINE static ExpRangeReduction +exp_range_reduction(float16 x) { // For -18 < x < 12, to compute exp(x), we perform the following range // reduction: find hi, mid, lo, such that: // x = hi + mid + lo, in which diff --git a/libc/src/__support/math/frexpf.h b/libc/src/__support/math/frexpf.h index 4d2f494..7834a12 100644 --- a/libc/src/__support/math/frexpf.h +++ b/libc/src/__support/math/frexpf.h @@ -17,7 +17,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float frexpf(float x, int *exp) { +LIBC_INLINE static constexpr float frexpf(float x, int *exp) { return fputil::frexp(x, *exp); } diff --git a/libc/src/__support/math/frexpf128.h b/libc/src/__support/math/frexpf128.h index 2fd5bc4..5218b26 100644 --- a/libc/src/__support/math/frexpf128.h +++ b/libc/src/__support/math/frexpf128.h @@ -21,7 +21,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float128 frexpf128(float128 x, int *exp) { +LIBC_INLINE static constexpr float128 frexpf128(float128 x, int *exp) { return fputil::frexp(x, *exp); } diff --git a/libc/src/__support/math/frexpf16.h b/libc/src/__support/math/frexpf16.h index 8deeba0..530b61a 100644 --- a/libc/src/__support/math/frexpf16.h +++ b/libc/src/__support/math/frexpf16.h @@ -21,7 +21,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float16 frexpf16(float16 x, int *exp) { +LIBC_INLINE static constexpr float16 frexpf16(float16 x, int *exp) { return fputil::frexp(x, *exp); } diff --git a/libc/src/__support/math/ldexpf.h b/libc/src/__support/math/ldexpf.h index 3a5ec1d..9ef5d96 100644 --- a/libc/src/__support/math/ldexpf.h +++ b/libc/src/__support/math/ldexpf.h @@ -17,7 +17,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float ldexpf(float x, int exp) { +LIBC_INLINE static constexpr float ldexpf(float x, int exp) { return fputil::ldexp(x, exp); } diff --git a/libc/src/__support/math/ldexpf128.h b/libc/src/__support/math/ldexpf128.h index 3625830..4fba20c 100644 --- a/libc/src/__support/math/ldexpf128.h +++ b/libc/src/__support/math/ldexpf128.h @@ -21,7 +21,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float128 ldexpf128(float128 x, int exp) { +LIBC_INLINE static constexpr float128 ldexpf128(float128 x, int exp) { return fputil::ldexp(x, exp); } diff --git a/libc/src/__support/math/ldexpf16.h b/libc/src/__support/math/ldexpf16.h index fbead87..d978d22 100644 --- a/libc/src/__support/math/ldexpf16.h +++ b/libc/src/__support/math/ldexpf16.h @@ -21,7 +21,7 @@ namespace LIBC_NAMESPACE_DECL { namespace math { -static constexpr float16 ldexpf16(float16 x, int exp) { +LIBC_INLINE static constexpr float16 ldexpf16(float16 x, int exp) { return fputil::ldexp(x, exp); } diff --git a/libc/src/math/CMakeLists.txt b/libc/src/math/CMakeLists.txt index fc064ab..455ad34 100644 --- a/libc/src/math/CMakeLists.txt +++ b/libc/src/math/CMakeLists.txt @@ -58,8 +58,6 @@ add_math_entrypoint_object(asinh) add_math_entrypoint_object(asinhf) add_math_entrypoint_object(asinhf16) -add_math_entrypoint_object(asinpif16) - add_math_entrypoint_object(atan) add_math_entrypoint_object(atanf) add_math_entrypoint_object(atanf16) diff --git a/libc/src/math/asinpif16.h b/libc/src/math/asinpif16.h deleted file mode 100644 index b97166a..0000000 --- a/libc/src/math/asinpif16.h +++ /dev/null @@ -1,21 +0,0 @@ -//===-- Implementation header for asinpif16 ---------------------*- 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_MATH_ASINPIF16_H -#define LLVM_LIBC_SRC_MATH_ASINPIF16_H - -#include "src/__support/macros/config.h" -#include "src/__support/macros/properties/types.h" - -namespace LIBC_NAMESPACE_DECL { - -float16 asinpif16(float16 x); - -} // namespace LIBC_NAMESPACE_DECL - -#endif // LLVM_LIBC_SRC_MATH_ASINPIF16_H diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt index 8116ee2..ecf0967 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -3919,25 +3919,6 @@ add_entrypoint_object( ) add_entrypoint_object( - asinpif16 - SRCS - asinpif16.cpp - HDRS - ../asinpif16.h - DEPENDS - libc.hdr.errno_macros - libc.hdr.fenv_macros - libc.src.__support.FPUtil.cast - libc.src.__support.FPUtil.except_value_utils - 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 -) - -add_entrypoint_object( atanhf SRCS atanhf.cpp diff --git a/libc/src/math/generic/asinpif16.cpp b/libc/src/math/generic/asinpif16.cpp deleted file mode 100644 index aabc086..0000000 --- a/libc/src/math/generic/asinpif16.cpp +++ /dev/null @@ -1,127 +0,0 @@ -//===-- Half-precision asinpif16(x) 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/asinpif16.h" -#include "hdr/errno_macros.h" -#include "hdr/fenv_macros.h" -#include "src/__support/FPUtil/FEnvImpl.h" -#include "src/__support/FPUtil/FPBits.h" -#include "src/__support/FPUtil/PolyEval.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/FPUtil/sqrt.h" -#include "src/__support/macros/optimization.h" - -namespace LIBC_NAMESPACE_DECL { - -LLVM_LIBC_FUNCTION(float16, asinpif16, (float16 x)) { - using FPBits = fputil::FPBits<float16>; - - FPBits xbits(x); - bool is_neg = xbits.is_neg(); - double x_abs = fputil::cast<double>(xbits.abs().get_val()); - - auto signed_result = [is_neg](auto r) -> auto { return is_neg ? -r : r; }; - - if (LIBC_UNLIKELY(x_abs > 1.0)) { - // aspinf16(NaN) = NaN - if (xbits.is_nan()) { - if (xbits.is_signaling_nan()) { - fputil::raise_except_if_required(FE_INVALID); - return FPBits::quiet_nan().get_val(); - } - return x; - } - - // 1 < |x| <= +/-inf - fputil::raise_except_if_required(FE_INVALID); - fputil::set_errno_if_required(EDOM); - - return FPBits::quiet_nan().get_val(); - } - - // the coefficients for the polynomial approximation of asin(x)/pi in the - // range [0, 0.5] extracted using python-sympy - // - // Python code to generate the coefficients: - // > from sympy import * - // > import math - // > x = symbols('x') - // > print(series(asin(x)/math.pi, x, 0, 21)) - // - // OUTPUT: - // - // 0.318309886183791*x + 0.0530516476972984*x**3 + 0.0238732414637843*x**5 + - // 0.0142102627760621*x**7 + 0.00967087327815336*x**9 + - // 0.00712127941391293*x**11 + 0.00552355646848375*x**13 + - // 0.00444514782463692*x**15 + 0.00367705242846804*x**17 + - // 0.00310721681820837*x**19 + O(x**21) - // - // it's very accurate in the range [0, 0.5] and has a maximum error of - // 0.0000000000000001 in the range [0, 0.5]. - constexpr double POLY_COEFFS[] = { - 0x1.45f306dc9c889p-2, // x^1 - 0x1.b2995e7b7b5fdp-5, // x^3 - 0x1.8723a1d588a36p-6, // x^5 - 0x1.d1a452f20430dp-7, // x^7 - 0x1.3ce52a3a09f61p-7, // x^9 - 0x1.d2b33e303d375p-8, // x^11 - 0x1.69fde663c674fp-8, // x^13 - 0x1.235134885f19bp-8, // x^15 - }; - // polynomial evaluation using horner's method - // work only for |x| in [0, 0.5] - auto asinpi_polyeval = [](double x) -> double { - return x * fputil::polyeval(x * x, POLY_COEFFS[0], POLY_COEFFS[1], - POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4], - POLY_COEFFS[5], POLY_COEFFS[6], POLY_COEFFS[7]); - }; - - // if |x| <= 0.5: - if (LIBC_UNLIKELY(x_abs <= 0.5)) { - // Use polynomial approximation of asin(x)/pi in the range [0, 0.5] - double result = asinpi_polyeval(fputil::cast<double>(x)); - return fputil::cast<float16>(result); - } - - // If |x| > 0.5, we need to use the range reduction method: - // y = asin(x) => x = sin(y) - // because: sin(a) = cos(pi/2 - a) - // therefore: - // x = cos(pi/2 - y) - // let z = pi/2 - y, - // x = cos(z) - // because: cos(2a) = 1 - 2 * sin^2(a), z = 2a, a = z/2 - // therefore: - // cos(z) = 1 - 2 * sin^2(z/2) - // sin(z/2) = sqrt((1 - cos(z))/2) - // sin(z/2) = sqrt((1 - x)/2) - // let u = (1 - x)/2 - // then: - // sin(z/2) = sqrt(u) - // z/2 = asin(sqrt(u)) - // z = 2 * asin(sqrt(u)) - // pi/2 - y = 2 * asin(sqrt(u)) - // y = pi/2 - 2 * asin(sqrt(u)) - // y/pi = 1/2 - 2 * asin(sqrt(u))/pi - // - // Finally, we can write: - // asinpi(x) = 1/2 - 2 * asinpi(sqrt(u)) - // where u = (1 - x) /2 - // = 0.5 - 0.5 * x - // = multiply_add(-0.5, x, 0.5) - - double u = fputil::multiply_add(-0.5, x_abs, 0.5); - double asinpi_sqrt_u = asinpi_polyeval(fputil::sqrt<double>(u)); - double result = fputil::multiply_add(-2.0, asinpi_sqrt_u, 0.5); - - return fputil::cast<float16>(signed_result(result)); -} - -} // namespace LIBC_NAMESPACE_DECL |