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| 1 | +//===-- Half-precision tanh(x) function -----------------------------------===// |
| 2 | +// |
| 3 | +// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
| 4 | +// See https://llvm.org/LICENSE.txt for license information. |
| 5 | +// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
| 6 | +// |
| 7 | +//===----------------------------------------------------------------------===// |
| 8 | + |
| 9 | +#include "src/math/tanhf16.h" |
| 10 | +#include "expxf16.h" |
| 11 | +#include "hdr/fenv_macros.h" |
| 12 | +#include "src/__support/CPP/array.h" |
| 13 | +#include "src/__support/FPUtil/FEnvImpl.h" |
| 14 | +#include "src/__support/FPUtil/FPBits.h" |
| 15 | +#include "src/__support/FPUtil/PolyEval.h" |
| 16 | +#include "src/__support/FPUtil/except_value_utils.h" |
| 17 | +#include "src/__support/FPUtil/multiply_add.h" |
| 18 | +#include "src/__support/FPUtil/nearest_integer.h" |
| 19 | +#include "src/__support/FPUtil/rounding_mode.h" |
| 20 | +#include "src/__support/common.h" |
| 21 | +#include "src/__support/macros/config.h" |
| 22 | +#include "src/__support/macros/optimization.h" |
| 23 | + |
| 24 | +namespace LIBC_NAMESPACE_DECL { |
| 25 | + |
| 26 | +static constexpr fputil::ExceptValues<float16, 2> TANHF16_EXCEPTS = {{ |
| 27 | + // x = 0x1.f54p+0, tanhf16(x) = 0x1.ecp-1 (RZ) |
| 28 | + {0x3fd5U, 0x3bb0U, 1U, 0U, 0U}, |
| 29 | + // x = -0x1.f54p+0, tanhf16(x) = -0x1.ecp-1 (RZ) |
| 30 | + {0xbfd5U, 0xbbb0U, 0U, 1U, 0U}, |
| 31 | +}}; |
| 32 | + |
| 33 | +LLVM_LIBC_FUNCTION(float16, tanhf16, (float16 x)) { |
| 34 | + using FPBits = fputil::FPBits<float16>; |
| 35 | + FPBits x_bits(x); |
| 36 | + |
| 37 | + uint16_t x_u = x_bits.uintval(); |
| 38 | + uint16_t x_abs = x_u & 0x7fffU; |
| 39 | + |
| 40 | + // When -2^(-14) <= x <= -2^(-9), or |x| <= 0x1.d2p-4, |
| 41 | + // or |x| >= atanh(1 - 2^(-11)), or x is NaN. |
| 42 | + if (LIBC_UNLIKELY((x_u >= 0x8400U && x_u <= 0x9800U) || x_abs <= 0x2f48U || |
| 43 | + x_abs >= 0x4429U)) { |
| 44 | + // tanh(NaN) = NaN |
| 45 | + if (x_bits.is_nan()) { |
| 46 | + if (x_bits.is_signaling_nan()) { |
| 47 | + fputil::raise_except_if_required(FE_INVALID); |
| 48 | + return FPBits::quiet_nan().get_val(); |
| 49 | + } |
| 50 | + |
| 51 | + return x; |
| 52 | + } |
| 53 | + |
| 54 | + // When -2^(-14) <= x <= -2^(-9). |
| 55 | + if (x_u >= 0x8400U && x_u <= 0x9800U) { |
| 56 | + switch (fputil::quick_get_round()) { |
| 57 | + case FE_TONEAREST: |
| 58 | + case FE_DOWNWARD: |
| 59 | + return x; |
| 60 | + default: |
| 61 | + return FPBits(static_cast<uint16_t>(x_u - 1U)).get_val(); |
| 62 | + } |
| 63 | + } |
| 64 | + |
| 65 | + // When |x| <= 0x1.d2p-4. |
| 66 | + if (x_abs <= 0x2f48U) { |
| 67 | + float xf = x; |
| 68 | + float xf_sq = xf * xf; |
| 69 | + // Degree-7 Taylor expansion generated by Sollya with the following |
| 70 | + // commands: |
| 71 | + // > taylor(tanh(x), 7, 0); |
| 72 | + // > display = hexadecimal; |
| 73 | + // > // For each coefficient: |
| 74 | + // > round(/* put coefficient here */, SG, RN); |
| 75 | + return static_cast<float16>( |
| 76 | + xf * fputil::polyeval(xf_sq, 0x1p+0f, -0x1.555556p-2f, 0x1.111112p-3f, |
| 77 | + -0x1.ba1ba2p-5f)); |
| 78 | + } |
| 79 | + |
| 80 | + // tanh(+/-inf) = +/-1 |
| 81 | + if (x_bits.is_inf()) |
| 82 | + return FPBits::one(x_bits.sign()).get_val(); |
| 83 | + |
| 84 | + // When |x| >= atanh(1 - 2^(-11)). |
| 85 | + fputil::raise_except_if_required(FE_INEXACT); |
| 86 | + |
| 87 | + int rounding_mode = fputil::quick_get_round(); |
| 88 | + if ((rounding_mode == FE_TONEAREST && x_abs >= 0x4482U) || |
| 89 | + (rounding_mode == FE_UPWARD && x_bits.is_pos()) || |
| 90 | + (rounding_mode == FE_DOWNWARD && x_bits.is_neg())) { |
| 91 | + return FPBits::one(x_bits.sign()).get_val(); |
| 92 | + } |
| 93 | + if (x_bits.is_pos()) |
| 94 | + return static_cast<float16>(0x1.ffcp-1); |
| 95 | + return static_cast<float16>(-0x1.ffcp-1); |
| 96 | + } |
| 97 | + |
| 98 | + if (auto r = TANHF16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value())) |
| 99 | + return r.value(); |
| 100 | + |
| 101 | + // For atanh(-1 + 2^(-11)) < x < atanh(1 - 2^(-11)), to compute tanh(x), we |
| 102 | + // perform the following range reduction: find hi, mid, lo, such that: |
| 103 | + // x = (hi + mid) * log(2) * 0.5 + lo, in which |
| 104 | + // hi is an integer, |
| 105 | + // mid * 2^5 is an integer, |
| 106 | + // -2^(-5) <= lo < 2^(-5). |
| 107 | + // In particular, |
| 108 | + // hi + mid = round(x * log2(e) * 2 * 2^5) * 2^(-5). |
| 109 | + // Then, |
| 110 | + // tanh(x) = sinh(x)/cosh(x) |
| 111 | + // = (e^x - e^(-x)) / (e^x + e^(-x)) |
| 112 | + // = (e^(2x) - 1) / (e^(2x) + 1) |
| 113 | + // = (2^(hi + mid) * e^(2*lo) - 1) / (2^(hi + mid) * e^(2*lo) + 1) |
| 114 | + // = (e^(2*lo) - 2^(-hi - mid)) / (e^(2*lo) + 2^(-hi - mid)) |
| 115 | + // We store 2^(-mid) in the lookup table EXP2_MID_5_BITS, and compute |
| 116 | + // 2^(-hi - mid) by adding -hi to the exponent field of 2^(-mid). |
| 117 | + // e^lo is computed using a degree-3 minimax polynomial generated by Sollya. |
| 118 | + |
| 119 | + float xf = x; |
| 120 | + float kf = fputil::nearest_integer(xf * (LOG2F_E * 2.0f * 0x1.0p+5f)); |
| 121 | + int x_hi_mid = -static_cast<int>(kf); |
| 122 | + int x_hi = x_hi_mid >> 5; |
| 123 | + int x_mid = x_hi_mid & 0x1f; |
| 124 | + // lo = x - (hi + mid) |
| 125 | + // = round(x * log2(e) * 2 * 2^5) * log(2) * 0.5 * (-2^(-5)) + x |
| 126 | + float lo = fputil::multiply_add(kf, LOGF_2 * 0.5f * -0x1.0p-5f, xf); |
| 127 | + |
| 128 | + uint32_t exp2_hi_mid_bits = |
| 129 | + EXP2_MID_5_BITS[x_mid] + |
| 130 | + static_cast<uint32_t>(x_hi << fputil::FPBits<float>::FRACTION_LEN); |
| 131 | + // exp2_hi_mid = 2^(-hi - mid) |
| 132 | + float exp2_hi_mid = fputil::FPBits<float>(exp2_hi_mid_bits).get_val(); |
| 133 | + // Degree-3 minimax polynomial generated by Sollya with the following |
| 134 | + // commands: |
| 135 | + // > display = hexadecimal; |
| 136 | + // > P = fpminimax(expm1(2*x)/x, 2, [|SG...|], [-2^-5, 2^-5]); |
| 137 | + // > 1 + x * P; |
| 138 | + float exp_2lo = |
| 139 | + fputil::polyeval(lo, 0x1p+0f, 0x1p+1f, 0x1.001p+1f, 0x1.555ddep+0f); |
| 140 | + return static_cast<float16>((exp_2lo - exp2_hi_mid) / |
| 141 | + (exp_2lo + exp2_hi_mid)); |
| 142 | +} |
| 143 | + |
| 144 | +} // namespace LIBC_NAMESPACE_DECL |
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