diff options
Diffstat (limited to 'libc/src/math/generic')
| -rw-r--r-- | libc/src/math/generic/CMakeLists.txt | 22 | ||||
| -rw-r--r-- | libc/src/math/generic/exp2f16.cpp | 86 | ||||
| -rw-r--r-- | libc/src/math/generic/exp2m1f.cpp | 177 |
3 files changed, 6 insertions, 279 deletions
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt index 55f4aaf..6068c36 100644 --- a/libc/src/math/generic/CMakeLists.txt +++ b/libc/src/math/generic/CMakeLists.txt @@ -1478,15 +1478,7 @@ add_entrypoint_object( HDRS ../exp2f16.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.rounding_mode - libc.src.__support.macros.optimization - libc.src.__support.math.expxf16_utils + libc.src.__support.math.exp2f16 ) add_entrypoint_object( @@ -1496,17 +1488,7 @@ add_entrypoint_object( HDRS ../exp2m1f.h DEPENDS - libc.src.errno.errno - libc.src.__support.common - 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.rounding_mode - libc.src.__support.macros.optimization - libc.src.__support.macros.properties.cpu_features - libc.src.__support.math.exp10f_utils + libc.src.__support.math.exp2m1f ) add_entrypoint_object( diff --git a/libc/src/math/generic/exp2f16.cpp b/libc/src/math/generic/exp2f16.cpp index 5db0c3a..80799d4 100644 --- a/libc/src/math/generic/exp2f16.cpp +++ b/libc/src/math/generic/exp2f16.cpp @@ -7,92 +7,10 @@ //===----------------------------------------------------------------------===// #include "src/math/exp2f16.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/cast.h" -#include "src/__support/FPUtil/except_value_utils.h" -#include "src/__support/FPUtil/rounding_mode.h" -#include "src/__support/common.h" -#include "src/__support/macros/config.h" -#include "src/__support/macros/optimization.h" -#include "src/__support/math/expxf16_utils.h" +#include "src/__support/math/exp2f16.h" namespace LIBC_NAMESPACE_DECL { -#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS -static constexpr fputil::ExceptValues<float16, 3> EXP2F16_EXCEPTS = {{ - // (input, RZ output, RU offset, RD offset, RN offset) - // x = 0x1.714p-11, exp2f16(x) = 0x1p+0 (RZ) - {0x11c5U, 0x3c00U, 1U, 0U, 1U}, - // x = -0x1.558p-4, exp2f16(x) = 0x1.e34p-1 (RZ) - {0xad56U, 0x3b8dU, 1U, 0U, 0U}, - // x = -0x1.d5cp-4, exp2f16(x) = 0x1.d8cp-1 (RZ) - {0xaf57U, 0x3b63U, 1U, 0U, 0U}, -}}; -#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS - -LLVM_LIBC_FUNCTION(float16, exp2f16, (float16 x)) { - using namespace math::expxf16_internal; - using FPBits = fputil::FPBits<float16>; - FPBits x_bits(x); - - uint16_t x_u = x_bits.uintval(); - uint16_t x_abs = x_u & 0x7fffU; - - // When |x| >= 16, or x is NaN. - if (LIBC_UNLIKELY(x_abs >= 0x4c00U)) { - // exp2(NaN) = NaN - if (x_bits.is_nan()) { - if (x_bits.is_signaling_nan()) { - fputil::raise_except_if_required(FE_INVALID); - return FPBits::quiet_nan().get_val(); - } - - return x; - } - - // When x >= 16. - if (x_bits.is_pos()) { - // exp2(+inf) = +inf - if (x_bits.is_inf()) - return FPBits::inf().get_val(); - - switch (fputil::quick_get_round()) { - case FE_TONEAREST: - case FE_UPWARD: - fputil::set_errno_if_required(ERANGE); - fputil::raise_except_if_required(FE_OVERFLOW); - return FPBits::inf().get_val(); - default: - return FPBits::max_normal().get_val(); - } - } - - // When x <= -25. - if (x_u >= 0xce40U) { - // exp2(-inf) = +0 - if (x_bits.is_inf()) - return FPBits::zero().get_val(); - - fputil::set_errno_if_required(ERANGE); - fputil::raise_except_if_required(FE_UNDERFLOW | FE_INEXACT); - - if (fputil::fenv_is_round_up()) - return FPBits::min_subnormal().get_val(); - return FPBits::zero().get_val(); - } - } - -#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS - if (auto r = EXP2F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) - return r.value(); -#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS - - // exp2(x) = exp2(hi + mid) * exp2(lo) - auto [exp2_hi_mid, exp2_lo] = exp2_range_reduction(x); - return fputil::cast<float16>(exp2_hi_mid * exp2_lo); -} +LLVM_LIBC_FUNCTION(float16, exp2f16, (float16 x)) { return math::exp2f16(x); } } // namespace LIBC_NAMESPACE_DECL diff --git a/libc/src/math/generic/exp2m1f.cpp b/libc/src/math/generic/exp2m1f.cpp index 16244ed..14d026f 100644 --- a/libc/src/math/generic/exp2m1f.cpp +++ b/libc/src/math/generic/exp2m1f.cpp @@ -7,183 +7,10 @@ //===----------------------------------------------------------------------===// #include "src/math/exp2m1f.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/rounding_mode.h" -#include "src/__support/common.h" -#include "src/__support/libc_errno.h" -#include "src/__support/macros/config.h" -#include "src/__support/macros/optimization.h" -#include "src/__support/macros/properties/cpu_features.h" -#include "src/__support/math/exp10f_utils.h" +#include "src/__support/math/exp2m1f.h" namespace LIBC_NAMESPACE_DECL { -#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS -static constexpr size_t N_EXCEPTS_LO = 8; - -static constexpr fputil::ExceptValues<float, N_EXCEPTS_LO> EXP2M1F_EXCEPTS_LO = - {{ - // (input, RZ output, RU offset, RD offset, RN offset) - // x = 0x1.36dc8ep-36, exp2m1f(x) = 0x1.aef212p-37 (RZ) - {0x2d9b'6e47U, 0x2d57'7909U, 1U, 0U, 0U}, - // x = 0x1.224936p-19, exp2m1f(x) = 0x1.926c0ep-20 (RZ) - {0x3611'249bU, 0x35c9'3607U, 1U, 0U, 1U}, - // x = 0x1.d16d2p-20, exp2m1f(x) = 0x1.429becp-20 (RZ) - {0x35e8'b690U, 0x35a1'4df6U, 1U, 0U, 1U}, - // x = 0x1.17949ep-14, exp2m1f(x) = 0x1.8397p-15 (RZ) - {0x388b'ca4fU, 0x3841'cb80U, 1U, 0U, 1U}, - // x = -0x1.9c3e1ep-38, exp2m1f(x) = -0x1.1dbeacp-38 (RZ) - {0xacce'1f0fU, 0xac8e'df56U, 0U, 1U, 0U}, - // x = -0x1.4d89b4p-32, exp2m1f(x) = -0x1.ce61b6p-33 (RZ) - {0xafa6'c4daU, 0xaf67'30dbU, 0U, 1U, 1U}, - // x = -0x1.a6eac4p-10, exp2m1f(x) = -0x1.24fadap-10 (RZ) - {0xbad3'7562U, 0xba92'7d6dU, 0U, 1U, 1U}, - // x = -0x1.e7526ep-6, exp2m1f(x) = -0x1.4e53dep-6 (RZ) - {0xbcf3'a937U, 0xbca7'29efU, 0U, 1U, 1U}, - }}; - -static constexpr size_t N_EXCEPTS_HI = 3; - -static constexpr fputil::ExceptValues<float, N_EXCEPTS_HI> EXP2M1F_EXCEPTS_HI = - {{ - // (input, RZ output, RU offset, RD offset, RN offset) - // x = 0x1.16a972p-1, exp2m1f(x) = 0x1.d545b2p-2 (RZ) - {0x3f0b'54b9U, 0x3eea'a2d9U, 1U, 0U, 0U}, - // x = -0x1.9f12acp-5, exp2m1f(x) = -0x1.1ab68cp-5 (RZ) - {0xbd4f'8956U, 0xbd0d'5b46U, 0U, 1U, 0U}, - // x = -0x1.de7b9cp-5, exp2m1f(x) = -0x1.4508f4p-5 (RZ) - {0xbd6f'3dceU, 0xbd22'847aU, 0U, 1U, 1U}, - }}; -#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS - -LLVM_LIBC_FUNCTION(float, exp2m1f, (float x)) { - using FPBits = fputil::FPBits<float>; - FPBits xbits(x); - - uint32_t x_u = xbits.uintval(); - uint32_t x_abs = x_u & 0x7fff'ffffU; - - // When |x| >= 128, or x is nan, or |x| <= 2^-5 - if (LIBC_UNLIKELY(x_abs >= 0x4300'0000U || x_abs <= 0x3d00'0000U)) { - // |x| <= 2^-5 - if (x_abs <= 0x3d00'0000U) { -#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS - if (auto r = EXP2M1F_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value())) - return r.value(); -#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS - - // Minimax polynomial generated by Sollya with: - // > display = hexadecimal; - // > fpminimax((2^x - 1)/x, 5, [|D...|], [-2^-5, 2^-5]); - constexpr double COEFFS[] = { - 0x1.62e42fefa39f3p-1, 0x1.ebfbdff82c57bp-3, 0x1.c6b08d6f2d7aap-5, - 0x1.3b2ab6fc92f5dp-7, 0x1.5d897cfe27125p-10, 0x1.43090e61e6af1p-13}; - double xd = x; - double xsq = xd * xd; - double c0 = fputil::multiply_add(xd, COEFFS[1], COEFFS[0]); - double c1 = fputil::multiply_add(xd, COEFFS[3], COEFFS[2]); - double c2 = fputil::multiply_add(xd, COEFFS[5], COEFFS[4]); - double p = fputil::polyeval(xsq, c0, c1, c2); - return static_cast<float>(p * xd); - } - - // x >= 128, or x is nan - if (xbits.is_pos()) { - if (xbits.is_finite()) { - int rounding = fputil::quick_get_round(); - if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO) - return FPBits::max_normal().get_val(); - - fputil::set_errno_if_required(ERANGE); - fputil::raise_except_if_required(FE_OVERFLOW); - } - - // x >= 128 and 2^x - 1 rounds to +inf, or x is +inf or nan - return x + FPBits::inf().get_val(); - } - } - - if (LIBC_UNLIKELY(x <= -25.0f)) { - // 2^(-inf) - 1 = -1 - if (xbits.is_inf()) - return -1.0f; - // 2^nan - 1 = nan - if (xbits.is_nan()) - return x; - - int rounding = fputil::quick_get_round(); - if (rounding == FE_UPWARD || rounding == FE_TOWARDZERO) - return -0x1.ffff'fep-1f; // -1.0f + 0x1.0p-24f - - fputil::set_errno_if_required(ERANGE); - fputil::raise_except_if_required(FE_UNDERFLOW); - return -1.0f; - } - -#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS - if (auto r = EXP2M1F_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) - return r.value(); -#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS - - // For -25 < x < 128, to compute 2^x, we perform the following range - // reduction: find hi, mid, lo such that: - // x = hi + mid + lo, in which: - // hi is an integer, - // 0 <= mid * 2^5 < 32 is an integer, - // -2^(-6) <= lo <= 2^(-6). - // In particular, - // hi + mid = round(x * 2^5) * 2^(-5). - // Then, - // 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo. - // 2^mid is stored in the lookup table of 32 elements. - // 2^lo is computed using a degree-4 minimax polynomial generated by Sollya. - // We perform 2^hi * 2^mid by simply add hi to the exponent field of 2^mid. - - // kf = (hi + mid) * 2^5 = round(x * 2^5) - float kf; - int k; -#ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT - kf = fputil::nearest_integer(x * 32.0f); - k = static_cast<int>(kf); -#else - constexpr float HALF[2] = {0.5f, -0.5f}; - k = static_cast<int>(fputil::multiply_add(x, 32.0f, HALF[x < 0.0f])); - kf = static_cast<float>(k); -#endif // LIBC_TARGET_CPU_HAS_NEAREST_INT - - // lo = x - (hi + mid) = x - kf * 2^(-5) - double lo = fputil::multiply_add(-0x1.0p-5f, kf, x); - - // hi = floor(kf * 2^(-4)) - // exp2_hi = shift hi to the exponent field of double precision. - int64_t exp2_hi = - static_cast<int64_t>(static_cast<uint64_t>(k >> ExpBase::MID_BITS) - << fputil::FPBits<double>::FRACTION_LEN); - // mh = 2^hi * 2^mid - // mh_bits = bit field of mh - int64_t mh_bits = ExpBase::EXP_2_MID[k & ExpBase::MID_MASK] + exp2_hi; - double mh = fputil::FPBits<double>(static_cast<uint64_t>(mh_bits)).get_val(); - - // Degree-4 polynomial approximating (2^x - 1)/x generated by Sollya with: - // > display = hexadecimal; - // > fpminimax((2^x - 1)/x, 4, [|D...|], [-2^-6, 2^-6]); - constexpr double COEFFS[5] = {0x1.62e42fefa39efp-1, 0x1.ebfbdff8131c4p-3, - 0x1.c6b08d7061695p-5, 0x1.3b2b1bee74b2ap-7, - 0x1.5d88091198529p-10}; - double lo_sq = lo * lo; - double c1 = fputil::multiply_add(lo, COEFFS[0], 1.0); - double c2 = fputil::multiply_add(lo, COEFFS[2], COEFFS[1]); - double c3 = fputil::multiply_add(lo, COEFFS[4], COEFFS[3]); - double exp2_lo = fputil::polyeval(lo_sq, c1, c2, c3); - // 2^x - 1 = 2^(hi + mid + lo) - 1 - // = 2^(hi + mid) * 2^lo - 1 - // ~ mh * (1 + lo * P(lo)) - 1 - // = mh * exp2_lo - 1 - return static_cast<float>(fputil::multiply_add(exp2_lo, mh, -1.0)); -} +LLVM_LIBC_FUNCTION(float, exp2m1f, (float x)) { return math::exp2m1f(x); } } // namespace LIBC_NAMESPACE_DECL |