diff options
Diffstat (limited to 'libc/src/math')
| -rw-r--r-- | libc/src/math/generic/CMakeLists.txt | 42 | ||||
| -rw-r--r-- | libc/src/math/generic/acospif16.cpp | 122 | ||||
| -rw-r--r-- | libc/src/math/generic/asin.cpp | 15 | ||||
| -rw-r--r-- | libc/src/math/generic/asinf.cpp | 155 | ||||
| -rw-r--r-- | libc/src/math/generic/asinf16.cpp | 121 | ||||
| -rw-r--r-- | libc/src/math/generic/range_reduction_double_common.h | 2 |
6 files changed, 14 insertions, 443 deletions
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt index a001d99..d4d268c 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -3958,13 +3958,7 @@ add_entrypoint_object( HDRS ../asinf.h DEPENDS - libc.src.__support.FPUtil.except_value_utils - 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.math.inv_trigf_utils + libc.src.__support.math.asinf ) add_entrypoint_object( @@ -3974,16 +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( @@ -3993,16 +3978,7 @@ add_entrypoint_object( HDRS ../asin.h DEPENDS - libc.src.__support.math.asin_utils - libc.src.__support.FPUtil.double_double - libc.src.__support.FPUtil.dyadic_float - 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.cpu_features + libc.src.__support.math.asin ) add_entrypoint_object( @@ -4043,16 +4019,8 @@ add_entrypoint_object( HDRS ../acospif16.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.acospif16 + libc.src.errno.errno ) add_header_library( diff --git a/libc/src/math/generic/acospif16.cpp b/libc/src/math/generic/acospif16.cpp index bfdf169..09cbd99 100644 --- a/libc/src/math/generic/acospif16.cpp +++ b/libc/src/math/generic/acospif16.cpp @@ -7,128 +7,12 @@ //===----------------------------------------------------------------------===// #include "src/math/acospif16.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/acospif16.h" namespace LIBC_NAMESPACE_DECL { LLVM_LIBC_FUNCTION(float16, acospif16, (float16 x)) { - using FPBits = fputil::FPBits<float16>; - FPBits xbits(x); - - uint16_t x_u = xbits.uintval(); - uint16_t x_abs = x_u & 0x7fff; - uint16_t x_sign = x_u >> 15; - - // |x| > 0x1p0, |x| > 1, or x is NaN. - if (LIBC_UNLIKELY(x_abs > 0x3c00)) { - // acospif16(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(); - } - - // |x| == 0x1p0, x is 1 or -1 - // if x is (-)1, return 1 - // if x is (+)1, return 0 - if (LIBC_UNLIKELY(x_abs == 0x3c00)) - return fputil::cast<float16>(x_sign ? 1.0f : 0.0f); - - float xf = x; - float xsq = xf * xf; - - // Degree-6 minimax polynomial coefficients of asin(x) generated by Sollya - // with: > P = fpminimax(asin(x)/(pi * x), [|0, 2, 4, 6, 8|], [|SG...|], [0, - // 0.5]); - constexpr float POLY_COEFFS[5] = {0x1.45f308p-2f, 0x1.b2900cp-5f, - 0x1.897e36p-6f, 0x1.9efafcp-7f, - 0x1.06d884p-6f}; - // |x| <= 0x1p-1, |x| <= 0.5 - if (x_abs <= 0x3800) { - // if x is 0, return 0.5 - if (LIBC_UNLIKELY(x_abs == 0)) - return fputil::cast<float16>(0.5f); - - // Note that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x), then - // acospi(x) = 0.5 - asin(x)/pi - float interm = - fputil::polyeval(xsq, POLY_COEFFS[0], POLY_COEFFS[1], POLY_COEFFS[2], - POLY_COEFFS[3], POLY_COEFFS[4]); - - return fputil::cast<float16>(fputil::multiply_add(-xf, interm, 0.5f)); - } - - // 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 - 2 * 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)) - // 11: Recall that: acos(x) = pi/2 + asin(-x) = pi/2 - asin(x) - // Therefore: - // acos(x) = pi/2 - (pi/2 - 2 * asin(sqrt(u))) - // acos(x) = 2 * asin(sqrt(u)) - // acospi(x) = 2 * (asin(sqrt(u)) / pi) - // - // THE RANGE REDUCTION, HOW? - // 12: Recall [7], u = (1 - x)/2 - // 13: 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 [11] as `sqrt(u)` is in range. - // When -1 < x <= -0.5, the identity: - // acos(x) = pi - acos(-x) - // acospi(x) = 1 - acos(-x)/pi - // allows us to compute for the negative x value (lhs) - // with a positive x value instead (rhs). - - float xf_abs = (xf < 0 ? -xf : xf); - float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f); - float sqrt_u = fputil::sqrt<float>(u); - - float asin_sqrt_u = - sqrt_u * fputil::polyeval(u, POLY_COEFFS[0], POLY_COEFFS[1], - POLY_COEFFS[2], POLY_COEFFS[3], POLY_COEFFS[4]); - - // Same as acos(x), but devided the expression with pi - return fputil::cast<float16>( - x_sign ? fputil::multiply_add(-2.0f, asin_sqrt_u, 1.0f) - : 2.0f * asin_sqrt_u); + return math::acospif16(x); } + } // namespace LIBC_NAMESPACE_DECL diff --git a/libc/src/math/generic/asin.cpp b/libc/src/math/generic/asin.cpp index d286fce..b5ba9ea 100644 --- a/libc/src/math/generic/asin.cpp +++ b/libc/src/math/generic/asin.cpp @@ -7,23 +7,10 @@ //===----------------------------------------------------------------------===// #include "src/math/asin.h" -#include "src/__support/FPUtil/FEnvImpl.h" -#include "src/__support/FPUtil/FPBits.h" -#include "src/__support/FPUtil/PolyEval.h" -#include "src/__support/FPUtil/double_double.h" -#include "src/__support/FPUtil/dyadic_float.h" -#include "src/__support/FPUtil/multiply_add.h" -#include "src/__support/FPUtil/sqrt.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 -#include "src/__support/math/asin_utils.h" +#include "src/__support/math/asin.h" namespace LIBC_NAMESPACE_DECL { -using DoubleDouble = fputil::DoubleDouble; -using Float128 = fputil::DyadicFloat<128>; - LLVM_LIBC_FUNCTION(double, asin, (double x)) { using namespace asin_internal; using FPBits = fputil::FPBits<double>; diff --git a/libc/src/math/generic/asinf.cpp b/libc/src/math/generic/asinf.cpp index 77d6de9..9c6766f 100644 --- a/libc/src/math/generic/asinf.cpp +++ b/libc/src/math/generic/asinf.cpp @@ -7,161 +7,10 @@ //===----------------------------------------------------------------------===// #include "src/math/asinf.h" -#include "src/__support/FPUtil/FEnvImpl.h" -#include "src/__support/FPUtil/FPBits.h" -#include "src/__support/FPUtil/PolyEval.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/config.h" -#include "src/__support/macros/optimization.h" // LIBC_UNLIKELY -#include "src/__support/macros/properties/cpu_features.h" // LIBC_TARGET_CPU_HAS_FMA - -#include "src/__support/math/inv_trigf_utils.h" +#include "src/__support/math/asinf.h" namespace LIBC_NAMESPACE_DECL { -#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS -static constexpr size_t N_EXCEPTS = 2; - -// Exceptional values when |x| <= 0.5 -static constexpr fputil::ExceptValues<float, N_EXCEPTS> ASINF_EXCEPTS_LO = {{ - // (inputs, RZ output, RU offset, RD offset, RN offset) - // x = 0x1.137f0cp-5, asinf(x) = 0x1.138c58p-5 (RZ) - {0x3d09bf86, 0x3d09c62c, 1, 0, 1}, - // x = 0x1.cbf43cp-4, asinf(x) = 0x1.cced1cp-4 (RZ) - {0x3de5fa1e, 0x3de6768e, 1, 0, 0}, -}}; - -// Exceptional values when 0.5 < |x| <= 1 -static constexpr fputil::ExceptValues<float, N_EXCEPTS> ASINF_EXCEPTS_HI = {{ - // (inputs, RZ output, RU offset, RD offset, RN offset) - // x = 0x1.107434p-1, asinf(x) = 0x1.1f4b64p-1 (RZ) - {0x3f083a1a, 0x3f0fa5b2, 1, 0, 0}, - // x = 0x1.ee836cp-1, asinf(x) = 0x1.4f0654p0 (RZ) - {0x3f7741b6, 0x3fa7832a, 1, 0, 0}, -}}; -#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS - -LLVM_LIBC_FUNCTION(float, asinf, (float x)) { - using namespace inv_trigf_utils_internal; - using FPBits = typename fputil::FPBits<float>; - - FPBits xbits(x); - uint32_t x_uint = xbits.uintval(); - uint32_t x_abs = xbits.uintval() & 0x7fff'ffffU; - constexpr double SIGN[2] = {1.0, -1.0}; - uint32_t x_sign = x_uint >> 31; - - // |x| <= 0.5-ish - if (x_abs < 0x3f04'471dU) { - // |x| < 0x1.d12edp-12 - if (LIBC_UNLIKELY(x_abs < 0x39e8'9768U)) { - // When |x| < 2^-12, the relative error of the approximation asin(x) ~ x - // is: - // |asin(x) - x| / |asin(x)| < |x^3| / (6|x|) - // = x^2 / 6 - // < 2^-25 - // < epsilon(1)/2. - // So the correctly rounded values of asin(x) are: - // = x + sign(x)*eps(x) if rounding mode = FE_TOWARDZERO, - // or (rounding mode = FE_UPWARD and x is - // negative), - // = x otherwise. - // To simplify the rounding decision and make it more efficient, we use - // fma(x, 2^-25, x) instead. - // An exhaustive test shows that this formula work correctly for all - // rounding modes up to |x| < 0x1.d12edp-12. - // Note: to use the formula x + 2^-25*x to decide the correct rounding, we - // do need fma(x, 2^-25, x) to prevent underflow caused by 2^-25*x when - // |x| < 2^-125. For targets without FMA instructions, we simply use - // double for intermediate results as it is more efficient than using an - // emulated version of FMA. -#if defined(LIBC_TARGET_CPU_HAS_FMA_FLOAT) - return fputil::multiply_add(x, 0x1.0p-25f, x); -#else - double xd = static_cast<double>(x); - return static_cast<float>(fputil::multiply_add(xd, 0x1.0p-25, xd)); -#endif // LIBC_TARGET_CPU_HAS_FMA_FLOAT - } - -#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS - // Check for exceptional values - if (auto r = ASINF_EXCEPTS_LO.lookup_odd(x_abs, x_sign); - LIBC_UNLIKELY(r.has_value())) - return r.value(); -#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS - - // For |x| <= 0.5, we approximate asinf(x) by: - // asin(x) = x * P(x^2) - // Where P(X^2) = Q(X) is a degree-20 minimax even polynomial approximating - // asin(x)/x on [0, 0.5] generated by Sollya with: - // > Q = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20|], - // [|1, D...|], [0, 0.5]); - // An exhaustive test shows that this approximation works well up to a - // little more than 0.5. - double xd = static_cast<double>(x); - double xsq = xd * xd; - double x3 = xd * xsq; - double r = asin_eval(xsq); - return static_cast<float>(fputil::multiply_add(x3, r, xd)); - } - - // |x| > 1, return NaNs. - if (LIBC_UNLIKELY(x_abs > 0x3f80'0000U)) { - 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 FPBits::quiet_nan().get_val(); - } - -#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS - // Check for exceptional values - if (auto r = ASINF_EXCEPTS_HI.lookup_odd(x_abs, x_sign); - LIBC_UNLIKELY(r.has_value())) - return r.value(); -#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS - - // When |x| > 0.5, we perform range reduction as follow: - // - // Assume further that 0.5 < x <= 1, and let: - // y = asin(x) - // We will use the double angle formula: - // cos(2y) = 1 - 2 sin^2(y) - // and the complement angle identity: - // x = sin(y) = cos(pi/2 - y) - // = 1 - 2 sin^2 (pi/4 - y/2) - // So: - // sin(pi/4 - y/2) = sqrt( (1 - x)/2 ) - // And hence: - // pi/4 - y/2 = asin( sqrt( (1 - x)/2 ) ) - // Equivalently: - // asin(x) = y = pi/2 - 2 * asin( sqrt( (1 - x)/2 ) ) - // Let u = (1 - x)/2, then: - // asin(x) = pi/2 - 2 * asin( sqrt(u) ) - // Moreover, since 0.5 < x <= 1: - // 0 <= u < 1/4, and 0 <= sqrt(u) < 0.5, - // And hence we can reuse the same polynomial approximation of asin(x) when - // |x| <= 0.5: - // asin(x) ~ pi/2 - 2 * sqrt(u) * P(u), - - xbits.set_sign(Sign::POS); - double sign = SIGN[x_sign]; - double xd = static_cast<double>(xbits.get_val()); - double u = fputil::multiply_add(-0.5, xd, 0.5); - double c1 = sign * (-2 * fputil::sqrt<double>(u)); - double c2 = fputil::multiply_add(sign, M_MATH_PI_2, c1); - double c3 = c1 * u; - - double r = asin_eval(u); - return static_cast<float>(fputil::multiply_add(c3, r, c2)); -} +LLVM_LIBC_FUNCTION(float, asinf, (float x)) { return math::asinf(x); } } // namespace LIBC_NAMESPACE_DECL 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 diff --git a/libc/src/math/generic/range_reduction_double_common.h b/libc/src/math/generic/range_reduction_double_common.h index f3dcdb9..a93ee25 100644 --- a/libc/src/math/generic/range_reduction_double_common.h +++ b/libc/src/math/generic/range_reduction_double_common.h @@ -278,7 +278,7 @@ private: }; #ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS -static Float128 range_reduction_small_f128(double x) { +LIBC_INLINE static Float128 range_reduction_small_f128(double x) { constexpr Float128 PI_OVER_128_F128 = { Sign::POS, -133, 0xc90f'daa2'2168'c234'c4c6'628b'80dc'1cd1_u128}; constexpr double ONE_TWENTY_EIGHT_OVER_PI_D = 0x1.45f306dc9c883p5; |