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371 lines
12 KiB
371 lines
12 KiB
4 months ago
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/*
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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 "config.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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// compute pow using log and exp
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// x^y = exp(y * log(x))
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//
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// we take care not to lose precision in the intermediate steps
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//
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// When computing log, calculate it in splits,
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//
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// r = f * (p_invead + p_inv_tail)
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// r = rh + rt
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//
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// calculate log polynomial using r, in end addition, do
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// poly = poly + ((rh-r) + rt)
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//
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// lth = -r
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// ltt = ((xexp * log2_t) - poly) + logT
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// lt = lth + ltt
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//
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// lh = (xexp * log2_h) + logH
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// l = lh + lt
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//
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// Calculate final log answer as gh and gt,
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// gh = l & higher-half bits
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// gt = (((ltt - (lt - lth)) + ((lh - l) + lt)) + (l - gh))
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//
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// yh = y & higher-half bits
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// yt = y - yh
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//
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// Before entering computation of exp,
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// vs = ((yt*gt + yt*gh) + yh*gt)
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// v = vs + yh*gh
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// vt = ((yh*gh - v) + vs)
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//
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// In calculation of exp, add vt to r that is used for poly
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// At the end of exp, do
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// ((((expT * poly) + expT) + expH*poly) + expH)
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_CLC_DEF _CLC_OVERLOAD float __clc_pown(float x, int ny)
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{
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float y = (float)ny;
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int ix = as_int(x);
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int ax = ix & EXSIGNBIT_SP32;
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int xpos = ix == ax;
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int iy = as_int(y);
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int ay = iy & EXSIGNBIT_SP32;
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int ypos = iy == ay;
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// Extra precise log calculation
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// First handle case that x is close to 1
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float r = 1.0f - as_float(ax);
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int near1 = fabs(r) < 0x1.0p-4f;
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float r2 = r*r;
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// Coefficients are just 1/3, 1/4, 1/5 and 1/6
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float poly = mad(r,
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mad(r,
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mad(r,
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mad(r, 0x1.24924ap-3f, 0x1.555556p-3f),
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0x1.99999ap-3f),
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0x1.000000p-2f),
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0x1.555556p-2f);
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poly *= r2*r;
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float lth_near1 = -r2 * 0.5f;
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float ltt_near1 = -poly;
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float lt_near1 = lth_near1 + ltt_near1;
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float lh_near1 = -r;
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float l_near1 = lh_near1 + lt_near1;
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// Computations for x not near 1
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int m = (int)(ax >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
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float mf = (float)m;
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int ixs = as_int(as_float(ax | 0x3f800000) - 1.0f);
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float mfs = (float)((ixs >> EXPSHIFTBITS_SP32) - 253);
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int c = m == -127;
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int ixn = c ? ixs : ax;
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float mfn = c ? mfs : mf;
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int indx = (ixn & 0x007f0000) + ((ixn & 0x00008000) << 1);
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// F - Y
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float f = as_float(0x3f000000 | indx) - as_float(0x3f000000 | (ixn & MANTBITS_SP32));
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indx = indx >> 16;
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float2 tv = USE_TABLE(log_inv_tbl_ep, indx);
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float rh = f * tv.s0;
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float rt = f * tv.s1;
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r = rh + rt;
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poly = mad(r, mad(r, 0x1.0p-2f, 0x1.555556p-2f), 0x1.0p-1f) * (r*r);
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poly += (rh - r) + rt;
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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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tv = USE_TABLE(loge_tbl, indx);
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float lth = -r;
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float ltt = mad(mfn, LOG2_TAIL, -poly) + tv.s1;
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float lt = lth + ltt;
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float lh = mad(mfn, LOG2_HEAD, tv.s0);
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float l = lh + lt;
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// Select near 1 or not
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lth = near1 ? lth_near1 : lth;
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ltt = near1 ? ltt_near1 : ltt;
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lt = near1 ? lt_near1 : lt;
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lh = near1 ? lh_near1 : lh;
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l = near1 ? l_near1 : l;
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float gh = as_float(as_int(l) & 0xfffff000);
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float gt = ((ltt - (lt - lth)) + ((lh - l) + lt)) + (l - gh);
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float yh = as_float(iy & 0xfffff000);
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float yt = (float)(ny - (int)yh);
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float ylogx_s = mad(gt, yh, mad(gh, yt, yt*gt));
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float ylogx = mad(yh, gh, ylogx_s);
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float ylogx_t = mad(yh, gh, -ylogx) + ylogx_s;
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// Extra precise exp of ylogx
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const float R_64_BY_LOG2 = 0x1.715476p+6f; // 64/log2 : 92.332482616893657
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int n = convert_int(ylogx * R_64_BY_LOG2);
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float nf = (float) n;
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int j = n & 0x3f;
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m = n >> 6;
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int m2 = m << EXPSHIFTBITS_SP32;
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const float R_LOG2_BY_64_LD = 0x1.620000p-7f; // log2/64 lead: 0.0108032227
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const float R_LOG2_BY_64_TL = 0x1.c85fdep-16f; // log2/64 tail: 0.0000272020388
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r = mad(nf, -R_LOG2_BY_64_TL, mad(nf, -R_LOG2_BY_64_LD, ylogx)) + ylogx_t;
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// Truncated Taylor series for e^r
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poly = mad(mad(mad(r, 0x1.555556p-5f, 0x1.555556p-3f), r, 0x1.000000p-1f), r*r, r);
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tv = USE_TABLE(exp_tbl_ep, j);
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float expylogx = mad(tv.s0, poly, mad(tv.s1, poly, tv.s1)) + tv.s0;
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float sexpylogx = expylogx * as_float(0x1 << (m + 149));
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float texpylogx = as_float(as_int(expylogx) + m2);
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expylogx = m < -125 ? sexpylogx : texpylogx;
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// Result is +-Inf if (ylogx + ylogx_t) > 128*log2
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expylogx = ((ylogx > 0x1.62e430p+6f) | (ylogx == 0x1.62e430p+6f & ylogx_t > -0x1.05c610p-22f)) ? as_float(PINFBITPATT_SP32) : expylogx;
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// Result is 0 if ylogx < -149*log2
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expylogx = ylogx < -0x1.9d1da0p+6f ? 0.0f : expylogx;
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// Classify y:
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// inty = 0 means not an integer.
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// inty = 1 means odd integer.
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// inty = 2 means even integer.
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int inty = 2 - (ny & 1);
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float signval = as_float((as_uint(expylogx) ^ SIGNBIT_SP32));
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expylogx = ((inty == 1) & !xpos) ? signval : expylogx;
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int ret = as_int(expylogx);
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// Corner case handling
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int xinf = xpos ? PINFBITPATT_SP32 : NINFBITPATT_SP32;
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ret = ((ax == 0) & !ypos & (inty == 1)) ? xinf : ret;
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ret = ((ax == 0) & !ypos & (inty == 2)) ? PINFBITPATT_SP32 : ret;
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ret = ((ax == 0) & ypos & (inty == 2)) ? 0 : ret;
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int xzero = !xpos ? 0x80000000 : 0L;
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ret = ((ax == 0) & ypos & (inty == 1)) ? xzero : ret;
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ret = ((ix == NINFBITPATT_SP32) & !ypos & (inty == 1)) ? 0x80000000 : ret;
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ret = ((ix == NINFBITPATT_SP32) & !ypos & (inty != 1)) ? 0 : ret;
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ret = ((ix == NINFBITPATT_SP32) & ypos & (inty == 1)) ? NINFBITPATT_SP32 : ret;
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ret = ((ix == NINFBITPATT_SP32) & ypos & (inty != 1)) ? PINFBITPATT_SP32 : ret;
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ret = ((ix == PINFBITPATT_SP32) & !ypos) ? 0 : ret;
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ret = ((ix == PINFBITPATT_SP32) & ypos) ? PINFBITPATT_SP32 : ret;
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ret = ax > PINFBITPATT_SP32 ? ix : ret;
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ret = ny == 0 ? 0x3f800000 : ret;
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return as_float(ret);
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}
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_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_pown, float, int)
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#ifdef cl_khr_fp64
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_CLC_DEF _CLC_OVERLOAD double __clc_pown(double x, int ny)
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{
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const double real_log2_tail = 5.76999904754328540596e-08;
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const double real_log2_lead = 6.93147122859954833984e-01;
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double y = (double) ny;
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long ux = as_long(x);
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long ax = ux & (~SIGNBIT_DP64);
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int xpos = ax == ux;
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long uy = as_long(y);
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long ay = uy & (~SIGNBIT_DP64);
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int ypos = ay == uy;
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// Extended precision log
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double v, vt;
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{
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int exp = (int)(ax >> 52) - 1023;
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int mask_exp_1023 = exp == -1023;
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double xexp = (double) exp;
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long mantissa = ax & 0x000FFFFFFFFFFFFFL;
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long temp_ux = as_long(as_double(0x3ff0000000000000L | mantissa) - 1.0);
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exp = ((temp_ux & 0x7FF0000000000000L) >> 52) - 2045;
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double xexp1 = (double) exp;
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long mantissa1 = temp_ux & 0x000FFFFFFFFFFFFFL;
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xexp = mask_exp_1023 ? xexp1 : xexp;
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mantissa = mask_exp_1023 ? mantissa1 : mantissa;
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long rax = (mantissa & 0x000ff00000000000) + ((mantissa & 0x0000080000000000) << 1);
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int index = rax >> 44;
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double F = as_double(rax | 0x3FE0000000000000L);
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double Y = as_double(mantissa | 0x3FE0000000000000L);
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double f = F - Y;
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double2 tv = USE_TABLE(log_f_inv_tbl, index);
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double log_h = tv.s0;
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double log_t = tv.s1;
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double f_inv = (log_h + log_t) * f;
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double r1 = as_double(as_long(f_inv) & 0xfffffffff8000000L);
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double r2 = fma(-F, r1, f) * (log_h + log_t);
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double r = r1 + r2;
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double poly = fma(r,
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fma(r,
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fma(r,
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fma(r, 1.0/7.0, 1.0/6.0),
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1.0/5.0),
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1.0/4.0),
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1.0/3.0);
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poly = poly * r * r * r;
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double hr1r1 = 0.5*r1*r1;
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double poly0h = r1 + hr1r1;
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double poly0t = r1 - poly0h + hr1r1;
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poly = fma(r1, r2, fma(0.5*r2, r2, poly)) + r2 + poly0t;
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tv = USE_TABLE(powlog_tbl, index);
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log_h = tv.s0;
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log_t = tv.s1;
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double resT_t = fma(xexp, real_log2_tail, + log_t) - poly;
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double resT = resT_t - poly0h;
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double resH = fma(xexp, real_log2_lead, log_h);
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double resT_h = poly0h;
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double H = resT + resH;
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double H_h = as_double(as_long(H) & 0xfffffffff8000000L);
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double T = (resH - H + resT) + (resT_t - (resT + resT_h)) + (H - H_h);
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H = H_h;
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double y_head = as_double(uy & 0xfffffffff8000000L);
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double y_tail = y - y_head;
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int mask_2_24 = ay > 0x4170000000000000; // 2^24
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int nyh = convert_int(y_head);
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int nyt = ny - nyh;
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double y_tail1 = (double)nyt;
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y_tail = mask_2_24 ? y_tail1 : y_tail;
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double temp = fma(y_tail, H, fma(y_head, T, y_tail*T));
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v = fma(y_head, H, temp);
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vt = fma(y_head, H, -v) + temp;
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}
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// Now calculate exp of (v,vt)
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double expv;
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{
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const double max_exp_arg = 709.782712893384;
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const double min_exp_arg = -745.1332191019411;
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const double sixtyfour_by_lnof2 = 92.33248261689366;
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const double lnof2_by_64_head = 0.010830424260348081;
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const double lnof2_by_64_tail = -4.359010638708991e-10;
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double temp = v * sixtyfour_by_lnof2;
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int n = (int)temp;
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double dn = (double)n;
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int j = n & 0x0000003f;
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int m = n >> 6;
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double2 tv = USE_TABLE(two_to_jby64_ep_tbl, j);
|
||
|
|
double f1 = tv.s0;
|
||
|
|
double f2 = tv.s1;
|
||
|
|
double f = f1 + f2;
|
||
|
|
|
||
|
|
double r1 = fma(dn, -lnof2_by_64_head, v);
|
||
|
|
double r2 = dn * lnof2_by_64_tail;
|
||
|
|
double r = (r1 + r2) + vt;
|
||
|
|
|
||
|
|
double q = fma(r,
|
||
|
|
fma(r,
|
||
|
|
fma(r,
|
||
|
|
fma(r, 1.38889490863777199667e-03, 8.33336798434219616221e-03),
|
||
|
|
4.16666666662260795726e-02),
|
||
|
|
1.66666666665260878863e-01),
|
||
|
|
5.00000000000000008883e-01);
|
||
|
|
q = fma(r*r, q, r);
|
||
|
|
|
||
|
|
expv = fma(f, q, f2) + f1;
|
||
|
|
expv = ldexp(expv, m);
|
||
|
|
|
||
|
|
expv = v > max_exp_arg ? as_double(0x7FF0000000000000L) : expv;
|
||
|
|
expv = v < min_exp_arg ? 0.0 : expv;
|
||
|
|
}
|
||
|
|
|
||
|
|
// See whether y is an integer.
|
||
|
|
// inty = 0 means not an integer.
|
||
|
|
// inty = 1 means odd integer.
|
||
|
|
// inty = 2 means even integer.
|
||
|
|
|
||
|
|
int inty = 2 - (ny & 1);
|
||
|
|
|
||
|
|
expv *= ((inty == 1) & !xpos) ? -1.0 : 1.0;
|
||
|
|
|
||
|
|
long ret = as_long(expv);
|
||
|
|
|
||
|
|
// Now all the edge cases
|
||
|
|
long xinf = xpos ? PINFBITPATT_DP64 : NINFBITPATT_DP64;
|
||
|
|
ret = ((ax == 0L) & !ypos & (inty == 1)) ? xinf : ret;
|
||
|
|
ret = ((ax == 0L) & !ypos & (inty == 2)) ? PINFBITPATT_DP64 : ret;
|
||
|
|
ret = ((ax == 0L) & ypos & (inty == 2)) ? 0L : ret;
|
||
|
|
long xzero = !xpos ? 0x8000000000000000L : 0L;
|
||
|
|
ret = ((ax == 0L) & ypos & (inty == 1)) ? xzero : ret;
|
||
|
|
ret = ((ux == NINFBITPATT_DP64) & !ypos & (inty == 1)) ? 0x8000000000000000L : ret;
|
||
|
|
ret = ((ux == NINFBITPATT_DP64) & !ypos & (inty != 1)) ? 0L : ret;
|
||
|
|
ret = ((ux == NINFBITPATT_DP64) & ypos & (inty == 1)) ? NINFBITPATT_DP64 : ret;
|
||
|
|
ret = ((ux == NINFBITPATT_DP64) & ypos & (inty != 1)) ? PINFBITPATT_DP64 : ret;
|
||
|
|
ret = ((ux == PINFBITPATT_DP64) & !ypos) ? 0L : ret;
|
||
|
|
ret = ((ux == PINFBITPATT_DP64) & ypos) ? PINFBITPATT_DP64 : ret;
|
||
|
|
ret = ax > PINFBITPATT_DP64 ? ux : ret;
|
||
|
|
ret = ny == 0 ? 0x3ff0000000000000L : ret;
|
||
|
|
|
||
|
|
return as_double(ret);
|
||
|
|
}
|
||
|
|
_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_pown, double, int)
|
||
|
|
#endif
|