/* * Copyright (c) 2014 Advanced Micro Devices, Inc. * * Permission is hereby granted, free of charge, to any person obtaining a copy * of this software and associated documentation files (the "Software"), to deal * in the Software without restriction, including without limitation the rights * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell * copies of the Software, and to permit persons to whom the Software is * furnished to do so, subject to the following conditions: * * The above copyright notice and this permission notice shall be included in * all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN * THE SOFTWARE. */ #include #include "math.h" #include "tables.h" #include "../clcmacro.h" _CLC_OVERLOAD _CLC_DEF float log1p(float x) { float w = x; uint ux = as_uint(x); uint ax = ux & EXSIGNBIT_SP32; // |x| < 2^-4 float u2 = MATH_DIVIDE(x, 2.0f + x); float u = u2 + u2; float v = u * u; // 2/(5 * 2^5), 2/(3 * 2^3) float zsmall = mad(-u2, x, mad(v, 0x1.99999ap-7f, 0x1.555556p-4f) * v * u) + x; // |x| >= 2^-4 ux = as_uint(x + 1.0f); int m = (int)((ux >> EXPSHIFTBITS_SP32) & 0xff) - EXPBIAS_SP32; float mf = (float)m; uint indx = (ux & 0x007f0000) + ((ux & 0x00008000) << 1); float F = as_float(indx | 0x3f000000); // x > 2^24 float fg24 = F - as_float(0x3f000000 | (ux & MANTBITS_SP32)); // x <= 2^24 uint xhi = ux & 0xffff8000; float xh = as_float(xhi); float xt = (1.0f - xh) + w; uint xnm = ((~(xhi & 0x7f800000)) - 0x00800000) & 0x7f800000; xt = xt * as_float(xnm) * 0.5f; float fl24 = F - as_float(0x3f000000 | (xhi & MANTBITS_SP32)) - xt; float f = mf > 24.0f ? fg24 : fl24; indx = indx >> 16; float r = f * USE_TABLE(log_inv_tbl, indx); // 1/3, 1/2 float poly = mad(mad(r, 0x1.555556p-2f, 0x1.0p-1f), r*r, r); const float LOG2_HEAD = 0x1.62e000p-1f; // 0.693115234 const float LOG2_TAIL = 0x1.0bfbe8p-15f; // 0.0000319461833 float2 tv = USE_TABLE(loge_tbl, indx); float z1 = mad(mf, LOG2_HEAD, tv.s0); float z2 = mad(mf, LOG2_TAIL, -poly) + tv.s1; float z = z1 + z2; z = ax < 0x3d800000U ? zsmall : z; // Edge cases z = ax >= PINFBITPATT_SP32 ? w : z; z = w < -1.0f ? as_float(QNANBITPATT_SP32) : z; z = w == -1.0f ? as_float(NINFBITPATT_SP32) : z; //fix subnormals z = ax < 0x33800000 ? x : z; return z; } _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, log1p, float); #ifdef cl_khr_fp64 #pragma OPENCL EXTENSION cl_khr_fp64 : enable _CLC_OVERLOAD _CLC_DEF double log1p(double x) { // Computes natural log(1+x). Algorithm based on: // Ping-Tak Peter Tang // "Table-driven implementation of the logarithm function in IEEE // floating-point arithmetic" // ACM Transactions on Mathematical Software (TOMS) // Volume 16, Issue 4 (December 1990) // Note that we use a lookup table of size 64 rather than 128, // and compensate by having extra terms in the minimax polynomial // for the kernel approximation. // Process Inside the threshold now ulong ux = as_ulong(1.0 + x); int xexp = ((as_int2(ux).hi >> 20) & 0x7ff) - EXPBIAS_DP64; double f = as_double(ONEEXPBITS_DP64 | (ux & MANTBITS_DP64)); int j = as_int2(ux).hi >> 13; j = ((0x80 | (j & 0x7e)) >> 1) + (j & 0x1); double f1 = (double)j * 0x1.0p-6; j -= 64; double f2temp = f - f1; double m2 = as_double(convert_ulong(0x3ff - xexp) << EXPSHIFTBITS_DP64); double f2l = fma(m2, x, m2 - f1); double f2g = fma(m2, x, -f1) + m2; double f2 = xexp <= MANTLENGTH_DP64-1 ? f2l : f2g; f2 = (xexp <= -2) | (xexp >= MANTLENGTH_DP64+8) ? f2temp : f2; double2 tv = USE_TABLE(ln_tbl, j); double z1 = tv.s0; double q = tv.s1; double u = MATH_DIVIDE(f2, fma(0.5, f2, f1)); double v = u * u; double poly = v * fma(v, fma(v, 2.23219810758559851206e-03, 1.24999999978138668903e-02), 8.33333333333333593622e-02); // log2_lead and log2_tail sum to an extra-precise version of log(2) const double log2_lead = 6.93147122859954833984e-01; /* 0x3fe62e42e0000000 */ const double log2_tail = 5.76999904754328540596e-08; /* 0x3e6efa39ef35793c */ double z2 = q + fma(u, poly, u); double dxexp = (double)xexp; double r1 = fma(dxexp, log2_lead, z1); double r2 = fma(dxexp, log2_tail, z2); double result1 = r1 + r2; // Process Outside the threshold now double r = x; u = r / (2.0 + r); double correction = r * u; u = u + u; v = u * u; r1 = r; poly = fma(v, fma(v, fma(v, 4.34887777707614552256e-04, 2.23213998791944806202e-03), 1.25000000037717509602e-02), 8.33333333333317923934e-02); r2 = fma(u*v, poly, -correction); // The values exp(-1/16)-1 and exp(1/16)-1 const double log1p_thresh1 = -0x1.f0540438fd5c3p-5; const double log1p_thresh2 = 0x1.082b577d34ed8p-4; double result2 = r1 + r2; result2 = x < log1p_thresh1 | x > log1p_thresh2 ? result1 : result2; result2 = isinf(x) ? x : result2; result2 = x < -1.0 ? as_double(QNANBITPATT_DP64) : result2; result2 = x == -1.0 ? as_double(NINFBITPATT_DP64) : result2; return result2; } _CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, log1p, double); #endif // cl_khr_fp64