diff options
| author | Florian Mayer <fmayer@google.com> | 2024-08-07 14:00:51 -0700 |
|---|---|---|
| committer | Florian Mayer <fmayer@google.com> | 2024-08-07 14:00:51 -0700 |
| commit | 10fbc246b146dbdf6b7cd9083bf392505c534fbc (patch) | |
| tree | 898a2504a8bc941166603c77021937fd995e79ce /libc/src/math/generic/exp2f16.cpp | |
| parent | 191d02015fba3458bdf6381ee93c32e485daf25e (diff) | |
| parent | a05fa131db58f2d66a1f9e68fea74068f9218c2b (diff) | |
Created using spr 1.3.4
Diffstat (limited to 'libc/src/math/generic/exp2f16.cpp')
| -rw-r--r-- | libc/src/math/generic/exp2f16.cpp | 127 |
1 files changed, 127 insertions, 0 deletions
diff --git a/libc/src/math/generic/exp2f16.cpp b/libc/src/math/generic/exp2f16.cpp new file mode 100644 index 000000000000..66b795670400 --- /dev/null +++ b/libc/src/math/generic/exp2f16.cpp @@ -0,0 +1,127 @@ +//===-- Half-precision 2^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/exp2f16.h" +#include "expxf16.h" +#include "hdr/errno_macros.h" +#include "hdr/fenv_macros.h" +#include "src/__support/CPP/array.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/nearest_integer.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" + +namespace LIBC_NAMESPACE_DECL { + +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}, +}}; + +LLVM_LIBC_FUNCTION(float16, exp2f16, (float16 x)) { + 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(); + } + } + + if (auto r = EXP2F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) + return r.value(); + + // For -25 < x < 16, 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, + // mid * 2^3 is an integer, + // -2^(-4) <= lo < 2^(-4). + // In particular, + // hi + mid = round(x * 2^3) * 2^(-3). + // Then, + // 2^x = 2^(hi + mid + lo) = 2^hi * 2^mid * 2^lo. + // We store 2^mid in the lookup table EXP2_MID_BITS, and compute 2^hi * 2^mid + // by adding hi to the exponent field of 2^mid. 2^lo is computed using a + // degree-3 minimax polynomial generated by Sollya. + + float xf = x; + float kf = fputil::nearest_integer(xf * 0x1.0p+3f); + int x_hi_mid = static_cast<int>(kf); + int x_hi = x_hi_mid >> 3; + int x_mid = x_hi_mid & 0x7; + // lo = x - (hi + mid) = round(x * 2^3) * (-2^(-3)) + x + float lo = fputil::multiply_add(kf, -0x1.0p-3f, xf); + + uint32_t exp2_hi_mid_bits = + EXP2_MID_BITS[x_mid] + + static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN); + float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val(); + // Degree-3 minimax polynomial generated by Sollya with the following + // commands: + // > display = hexadecimal; + // > P = fpminimax((2^x - 1)/x, 2, [|SG...|], [-2^-4, 2^-4]); + // > 1 + x * P; + float exp2_lo = fputil::polyeval(lo, 0x1p+0f, 0x1.62e43p-1f, 0x1.ec0aa6p-3f, + 0x1.c6b4a6p-5f); + return static_cast<float16>(exp2_hi_mid * exp2_lo); +} + +} // namespace LIBC_NAMESPACE_DECL |
