diff options
Diffstat (limited to 'libc/src')
27 files changed, 204 insertions, 166 deletions
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt index b096c61..1050938 100644 --- a/libc/src/__support/math/CMakeLists.txt +++ b/libc/src/__support/math/CMakeLists.txt @@ -157,6 +157,20 @@ add_header_library( ) add_header_library( + asinf16 + HDRS + asinf16.h + DEPENDS + libc.src.__support.FPUtil.fenv_impl + libc.src.__support.FPUtil.fp_bits + libc.src.__support.FPUtil.polyeval + libc.src.__support.FPUtil.cast + libc.src.__support.FPUtil.multiply_add + libc.src.__support.FPUtil.sqrt + libc.src.__support.macros.optimization +) + +add_header_library( erff HDRS erff.h 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/asinf16.h b/libc/src/__support/math/asinf16.h new file mode 100644 index 0000000..3d032a4 --- /dev/null +++ b/libc/src/__support/math/asinf16.h @@ -0,0 +1,146 @@ +//===-- Implementation header for asinf16 -----------------------*- 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_ASINF16_H +#define LLVM_LIBC_SRC___SUPPORT_MATH_ASINF16_H + +#include "include/llvm-libc-macros/float16-macros.h" + +#ifdef LIBC_TYPES_HAS_FLOAT16 + +#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/multiply_add.h" +#include "src/__support/FPUtil/sqrt.h" +#include "src/__support/macros/optimization.h" + +namespace LIBC_NAMESPACE_DECL { + +namespace math { + +LIBC_INLINE static constexpr float16 asinf16(float16 x) { + + // Generated by Sollya using the following command: + // > round(pi/2, D, RN); + constexpr float PI_2 = 0x1.921fb54442d18p0f; + + using FPBits = fputil::FPBits<float16>; + FPBits xbits(x); + + uint16_t x_u = xbits.uintval(); + uint16_t x_abs = x_u & 0x7fff; + float xf = x; + + // |x| > 0x1p0, |x| > 1, or x is NaN. + if (LIBC_UNLIKELY(x_abs > 0x3c00)) { + // asinf16(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(); + } + + float xsq = xf * xf; + + // |x| <= 0x1p-1, |x| <= 0.5 + if (x_abs <= 0x3800) { + // asinf16(+/-0) = +/-0 + if (LIBC_UNLIKELY(x_abs == 0)) + return x; + + // Exhaustive tests show that, + // for |x| <= 0x1.878p-9, when: + // x > 0, and rounding upward, or + // x < 0, and rounding downward, then, + // asin(x) = x * 2^-11 + x + // else, in other rounding modes, + // asin(x) = x + if (LIBC_UNLIKELY(x_abs <= 0x1a1e)) { + int rounding = fputil::quick_get_round(); + + if ((xbits.is_pos() && rounding == FE_UPWARD) || + (xbits.is_neg() && rounding == FE_DOWNWARD)) + return fputil::cast<float16>(fputil::multiply_add(xf, 0x1.0p-11f, xf)); + return x; + } + + // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with: + // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]); + float result = + fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f, + 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); + return fputil::cast<float16>(xf * result); + } + + // When |x| > 0.5, assume that 0.5 < |x| <= 1, + // + // Step-by-step range-reduction proof: + // 1: Let y = asin(x), such that, x = sin(y) + // 2: From complimentary angle identity: + // x = sin(y) = cos(pi/2 - y) + // 3: Let z = pi/2 - y, such that x = cos(z) + // 4: From double angle formula; cos(2A) = 1 - sin^2(A): + // z = 2A, z/2 = A + // cos(z) = 1 - 2 * sin^2(z/2) + // 5: Make sin(z/2) subject of the formula: + // sin(z/2) = sqrt((1 - cos(z))/2) + // 6: Recall [3]; x = cos(z). Therefore: + // sin(z/2) = sqrt((1 - x)/2) + // 7: Let u = (1 - x)/2 + // 8: Therefore: + // asin(sqrt(u)) = z/2 + // 2 * asin(sqrt(u)) = z + // 9: Recall [3], z = pi/2 - y. Therefore: + // y = pi/2 - z + // y = pi/2 - 2 * asin(sqrt(u)) + // 10: Recall [1], y = asin(x). Therefore: + // asin(x) = pi/2 - 2 * asin(sqrt(u)) + // + // WHY? + // 11: Recall [7], u = (1 - x)/2 + // 12: Since 0.5 < x <= 1, therefore: + // 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5 + // + // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for + // Step [10] as `sqrt(u)` is in range. + + // 0x1p-1 < |x| <= 0x1p0, 0.5 < |x| <= 1.0 + float xf_abs = (xf < 0 ? -xf : xf); + float sign = (xbits.uintval() >> 15 == 1 ? -1.0 : 1.0); + float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f); + float u_sqrt = fputil::sqrt<float>(u); + + // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with: + // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]); + float asin_sqrt_u = + u_sqrt * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f, + 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); + + return fputil::cast<float16>(sign * + fputil::multiply_add(-2.0f, asin_sqrt_u, PI_2)); +} + +} // namespace math + +} // namespace LIBC_NAMESPACE_DECL + +#endif // LIBC_TYPES_HAS_FLOAT16 + +#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ASINF16_H 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/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt index ecf0967..d4d268c 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -3968,16 +3968,7 @@ add_entrypoint_object( HDRS ../asinf16.h DEPENDS - libc.hdr.errno_macros - libc.hdr.fenv_macros - libc.src.__support.FPUtil.cast - 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.macros.properties.types + libc.src.__support.math.asinf16 ) add_entrypoint_object( diff --git a/libc/src/math/generic/asinf16.cpp b/libc/src/math/generic/asinf16.cpp index 518c384..af8dbfe 100644 --- a/libc/src/math/generic/asinf16.cpp +++ b/libc/src/math/generic/asinf16.cpp @@ -7,127 +7,10 @@ //===----------------------------------------------------------------------===// #include "src/math/asinf16.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/multiply_add.h" -#include "src/__support/FPUtil/sqrt.h" -#include "src/__support/macros/optimization.h" +#include "src/__support/math/asinf16.h" namespace LIBC_NAMESPACE_DECL { -// Generated by Sollya using the following command: -// > round(pi/2, D, RN); -static constexpr float PI_2 = 0x1.921fb54442d18p0f; - -LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { - using FPBits = fputil::FPBits<float16>; - FPBits xbits(x); - - uint16_t x_u = xbits.uintval(); - uint16_t x_abs = x_u & 0x7fff; - float xf = x; - - // |x| > 0x1p0, |x| > 1, or x is NaN. - if (LIBC_UNLIKELY(x_abs > 0x3c00)) { - // asinf16(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(); - } - - float xsq = xf * xf; - - // |x| <= 0x1p-1, |x| <= 0.5 - if (x_abs <= 0x3800) { - // asinf16(+/-0) = +/-0 - if (LIBC_UNLIKELY(x_abs == 0)) - return x; - - // Exhaustive tests show that, - // for |x| <= 0x1.878p-9, when: - // x > 0, and rounding upward, or - // x < 0, and rounding downward, then, - // asin(x) = x * 2^-11 + x - // else, in other rounding modes, - // asin(x) = x - if (LIBC_UNLIKELY(x_abs <= 0x1a1e)) { - int rounding = fputil::quick_get_round(); - - if ((xbits.is_pos() && rounding == FE_UPWARD) || - (xbits.is_neg() && rounding == FE_DOWNWARD)) - return fputil::cast<float16>(fputil::multiply_add(xf, 0x1.0p-11f, xf)); - return x; - } - - // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with: - // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]); - float result = - fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f, - 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); - return fputil::cast<float16>(xf * result); - } - - // When |x| > 0.5, assume that 0.5 < |x| <= 1, - // - // Step-by-step range-reduction proof: - // 1: Let y = asin(x), such that, x = sin(y) - // 2: From complimentary angle identity: - // x = sin(y) = cos(pi/2 - y) - // 3: Let z = pi/2 - y, such that x = cos(z) - // 4: From double angle formula; cos(2A) = 1 - sin^2(A): - // z = 2A, z/2 = A - // cos(z) = 1 - 2 * sin^2(z/2) - // 5: Make sin(z/2) subject of the formula: - // sin(z/2) = sqrt((1 - cos(z))/2) - // 6: Recall [3]; x = cos(z). Therefore: - // sin(z/2) = sqrt((1 - x)/2) - // 7: Let u = (1 - x)/2 - // 8: Therefore: - // asin(sqrt(u)) = z/2 - // 2 * asin(sqrt(u)) = z - // 9: Recall [3], z = pi/2 - y. Therefore: - // y = pi/2 - z - // y = pi/2 - 2 * asin(sqrt(u)) - // 10: Recall [1], y = asin(x). Therefore: - // asin(x) = pi/2 - 2 * asin(sqrt(u)) - // - // WHY? - // 11: Recall [7], u = (1 - x)/2 - // 12: Since 0.5 < x <= 1, therefore: - // 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5 - // - // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for - // Step [10] as `sqrt(u)` is in range. - - // 0x1p-1 < |x| <= 0x1p0, 0.5 < |x| <= 1.0 - float xf_abs = (xf < 0 ? -xf : xf); - float sign = (xbits.uintval() >> 15 == 1 ? -1.0 : 1.0); - float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f); - float u_sqrt = fputil::sqrt<float>(u); - - // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with: - // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]); - float asin_sqrt_u = - u_sqrt * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f, - 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f); - - return fputil::cast<float16>(sign * - fputil::multiply_add(-2.0f, asin_sqrt_u, PI_2)); -} +LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { return math::asinf16(x); } } // namespace LIBC_NAMESPACE_DECL |