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Diffstat (limited to 'libc/src/math/generic/exp2m1f.cpp')
-rw-r--r-- | libc/src/math/generic/exp2m1f.cpp | 183 |
1 files changed, 183 insertions, 0 deletions
diff --git a/libc/src/math/generic/exp2m1f.cpp b/libc/src/math/generic/exp2m1f.cpp new file mode 100644 index 000000000000..c60930dd782e --- /dev/null +++ b/libc/src/math/generic/exp2m1f.cpp @@ -0,0 +1,183 @@ +//===-- Implementation of exp2m1f 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/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/macros/optimization.h" +#include "src/__support/macros/properties/cpu_features.h" +#include "src/errno/libc_errno.h" + +#include "explogxf.h" + +namespace LIBC_NAMESPACE { + +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}, + }}; + +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) { + if (auto r = EXP2M1F_EXCEPTS_LO.lookup(x_u); LIBC_UNLIKELY(r.has_value())) + return r.value(); + + // 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; + } + + if (auto r = EXP2M1F_EXCEPTS_HI.lookup(x_u); LIBC_UNLIKELY(r.has_value())) + return r.value(); + + // 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)); +} + +} // namespace LIBC_NAMESPACE |