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