1 //===-- Single-precision tanh 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/tanhf.h" 10 #include "src/__support/FPUtil/FPBits.h" 11 #include "src/__support/FPUtil/PolyEval.h" 12 #include "src/__support/FPUtil/multiply_add.h" 13 #include "src/__support/FPUtil/nearest_integer.h" 14 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY 15 #include "src/__support/macros/properties/cpu_features.h" 16 #include "src/math/generic/explogxf.h" 17 18 namespace LIBC_NAMESPACE { 19 20 // 2^6 * log2(e) 21 constexpr double LOG2_E_EXP2_6 = ExpBase::LOG2_B * 2.0; 22 23 LLVM_LIBC_FUNCTION(float, tanhf, (float x)) { 24 using FPBits = typename fputil::FPBits<float>; 25 FPBits xbits(x); 26 uint32_t x_abs = xbits.abs().uintval(); 27 28 const int sign_index = xbits.is_neg() ? 1 : 0; 29 30 // When |x| >= 15, or x is inf or nan, or |x| <= 0.078125 31 if (LIBC_UNLIKELY((x_abs >= 0x4170'0000U) || (x_abs <= 0x3da0'0000U))) { 32 if (x_abs <= 0x3da0'0000U) { 33 // |x| <= 0.078125 34 if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) { 35 // |x| <= 2^-26 36 return (x_abs != 0) 37 ? static_cast<float>(x - 0x1.5555555555555p-2 * x * x * x) 38 : x; 39 } 40 41 const double TAYLOR[] = {-0x1.5555555555555p-2, 0x1.1111111111111p-3, 42 -0x1.ba1ba1ba1ba1cp-5, 0x1.664f4882c10fap-6, 43 -0x1.226e355e6c23dp-7}; 44 double xdbl = x; 45 double x2 = xdbl * xdbl; 46 // Taylor polynomial. 47 double x4 = x2 * x2; 48 double c0 = x2 * TAYLOR[0]; 49 double c1 = fputil::multiply_add(x2, TAYLOR[2], TAYLOR[1]); 50 double c2 = fputil::multiply_add(x2, TAYLOR[4], TAYLOR[3]); 51 double pe = fputil::polyeval(x4, c0, c1, c2); 52 53 return static_cast<float>(fputil::multiply_add(xdbl, pe, xdbl)); 54 } 55 56 // |x| >= 15 57 if (LIBC_UNLIKELY(xbits.is_nan())) 58 return x + 1.0f; // sNaN to qNaN + signal 59 60 constexpr float SIGNS[2][2] = {{1.0f, -0x1.0p-25f}, {-1.0f, 0x1.0p-25f}}; 61 62 if (LIBC_UNLIKELY(xbits.is_inf())) 63 return SIGNS[sign_index][0]; 64 65 return SIGNS[sign_index][0] + SIGNS[sign_index][1]; 66 } 67 68 // Range reduction: e^(2x) = 2^(hi + mid) * e^lo 69 // Let k = round( x * 2^6 * log2(e)), 70 // So k = (hi + mid) * 2^5 71 // Then lo = 2x - (hi + mid) * log(2) = 2x - k * 2^-5 * log(2). 72 73 double xd = static_cast<double>(x); 74 // k = round( x* 2^6 * log2(e) ) 75 double k; 76 // mk = -k 77 int mk; 78 #ifdef LIBC_TARGET_CPU_HAS_NEAREST_INT 79 k = fputil::nearest_integer(xd * LOG2_E_EXP2_6); 80 mk = -static_cast<int>(k); 81 #else 82 constexpr double HALF_WAY[2] = {-0.5, 0.5}; 83 84 mk = static_cast<int>( 85 fputil::multiply_add(xd, -LOG2_E_EXP2_6, HALF_WAY[sign_index])); 86 k = static_cast<double>(-mk); 87 #endif // LIBC_TARGET_CPU_HAS_NEAREST_INT 88 // -hi = floor(-k * 2^(-MID_BITS)) 89 // exp_mhi = shift -hi to the exponent field of double precision. 90 int64_t exp_mhi = static_cast<int64_t>(mk >> ExpBase::MID_BITS) 91 << fputil::FPBits<double>::FRACTION_LEN; 92 // mh = 2^(-hi - mid) 93 int64_t mh_bits = ExpBase::EXP_2_MID[mk & ExpBase::MID_MASK] + exp_mhi; 94 double mh = fputil::FPBits<double>(uint64_t(mh_bits)).get_val(); 95 // dx = lo/2 = x - (hi + mid) * log(2)/2 = x - k * 2^-6 * log(2) 96 double dx = fputil::multiply_add( 97 k, ExpBase::M_LOGB_2_LO * 0.5, 98 fputil::multiply_add(k, ExpBase::M_LOGB_2_HI * 0.5, xd)); 99 100 // > P = fpminimax(expm1(2*x)/x, 4, [|D...|], [-log(2)/128, log(2)/128]); 101 constexpr double COEFFS[] = {0x1.ffffffffe5bc8p0, 0x1.555555555cd67p0, 102 0x1.5555c2a9b48b4p-1, 0x1.11112a0e34bdbp-2}; 103 104 double dx2 = dx * dx; 105 double c0 = fputil::multiply_add(dx, 2.0, 1.0); 106 double c1 = fputil::multiply_add(dx, COEFFS[1], COEFFS[0]); 107 double c2 = fputil::multiply_add(dx, COEFFS[3], COEFFS[2]); 108 double r = fputil::polyeval(dx2, c0, c1, c2); 109 110 // 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^lo - 1) / (2^(hi + mid) * e^lo + 1) 114 // = (e^lo - 2^(-hi - mid)) / (e^lo + 2^(-hi - mid)) 115 // = (r - mh) / (r + mh) 116 return static_cast<float>((r - mh) / (r + mh)); 117 } 118 119 } // namespace LIBC_NAMESPACE 120