generic/lib/math/clc_powr.cl - llvm-project/libclc - Git at Google

 /*
  * 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 <clc/clc.h>

 #include "config.h"
 #include "math.h"
 #include "tables.h"
 #include "../clcmacro.h"

 // compute pow using log and exp
 // x^y = exp(y * log(x))
 //
 // we take care not to lose precision in the intermediate steps
 //
 // When computing log, calculate it in splits,
 //
 // r = f * (p_invead + p_inv_tail)
 // r = rh + rt
 //
 // calculate log polynomial using r, in end addition, do
 // poly = poly + ((rh-r) + rt)
 //
 // lth = -r
 // ltt = ((xexp * log2_t) - poly) + logT
 // lt = lth + ltt
 //
 // lh = (xexp * log2_h) + logH
 // l = lh + lt
 //
 // Calculate final log answer as gh and gt,
 // gh = l & higher-half bits
 // gt = (((ltt - (lt - lth)) + ((lh - l) + lt)) + (l - gh))
 //
 // yh = y & higher-half bits
 // yt = y - yh
 //
 // Before entering computation of exp,
 // vs = ((yt*gt + yt*gh) + yh*gt)
 // v = vs + yh*gh
 // vt = ((yh*gh - v) + vs)
 //
 // In calculation of exp, add vt to r that is used for poly
 // At the end of exp, do
 // ((((expT * poly) + expT) + expH*poly) + expH)

 _CLC_DEF _CLC_OVERLOAD float __clc_powr(float x, float y)
 {
     int ix = as_int(x);
     int ax = ix & EXSIGNBIT_SP32;
     int xpos = ix == ax;

     int iy = as_int(y);
     int ay = iy & EXSIGNBIT_SP32;
     int ypos = iy == ay;

     // Extra precise log calculation
     // First handle case that x is close to 1
     float r = 1.0f - as_float(ax);
     int near1 = fabs(r) < 0x1.0p-4f;
     float r2 = r*r;

     // Coefficients are just 1/3, 1/4, 1/5 and 1/6
     float poly = mad(r,
                      mad(r,
                          mad(r,
                              mad(r, 0x1.24924ap-3f, 0x1.555556p-3f),
                              0x1.99999ap-3f),
                          0x1.000000p-2f),
                      0x1.555556p-2f);

     poly *= r2*r;

     float lth_near1 = -r2 * 0.5f;
     float ltt_near1 = -poly;
     float lt_near1 = lth_near1 + ltt_near1;
     float lh_near1 = -r;
     float l_near1 = lh_near1 + lt_near1;

     // Computations for x not near 1
     int m = (int)(ax >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
     float mf = (float)m;
     int ixs = as_int(as_float(ax | 0x3f800000) - 1.0f);
     float mfs = (float)((ixs >> EXPSHIFTBITS_SP32) - 253);
     int c = m == -127;
     int ixn = c ? ixs : ax;
     float mfn = c ? mfs : mf;

     int indx = (ixn & 0x007f0000) + ((ixn & 0x00008000) << 1);

     // F - Y
     float f = as_float(0x3f000000 | indx) - as_float(0x3f000000 | (ixn & MANTBITS_SP32));

     indx = indx >> 16;
     float2 tv = USE_TABLE(log_inv_tbl_ep, indx);
     float rh = f * tv.s0;
     float rt = f * tv.s1;
     r = rh + rt;

     poly = mad(r, mad(r, 0x1.0p-2f, 0x1.555556p-2f), 0x1.0p-1f) * (r*r);
     poly += (rh - r) + rt;

     const float LOG2_HEAD = 0x1.62e000p-1f;  // 0.693115234
     const float LOG2_TAIL = 0x1.0bfbe8p-15f; // 0.0000319461833
     tv = USE_TABLE(loge_tbl, indx);
     float lth = -r;
     float ltt = mad(mfn, LOG2_TAIL, -poly) + tv.s1;
     float lt = lth + ltt;
     float lh = mad(mfn, LOG2_HEAD, tv.s0);
     float l = lh + lt;

     // Select near 1 or not
     lth = near1 ? lth_near1 : lth;
     ltt = near1 ? ltt_near1 : ltt;
     lt = near1 ? lt_near1 : lt;
     lh = near1 ? lh_near1 : lh;
     l = near1 ? l_near1 : l;

     float gh = as_float(as_int(l) & 0xfffff000);
     float gt = ((ltt - (lt - lth)) + ((lh - l) + lt)) + (l - gh);

     float yh = as_float(iy & 0xfffff000);

     float yt = y - yh;

     float ylogx_s = mad(gt, yh, mad(gh, yt, yt*gt));
     float ylogx = mad(yh, gh, ylogx_s);
     float ylogx_t = mad(yh, gh, -ylogx) + ylogx_s;

     // Extra precise exp of ylogx
     const float R_64_BY_LOG2 = 0x1.715476p+6f; // 64/log2 : 92.332482616893657
     int n = convert_int(ylogx * R_64_BY_LOG2);
     float nf = (float) n;

     int j = n & 0x3f;
     m = n >> 6;
     int m2 = m << EXPSHIFTBITS_SP32;

     const float R_LOG2_BY_64_LD = 0x1.620000p-7f;  // log2/64 lead: 0.0108032227
     const float R_LOG2_BY_64_TL = 0x1.c85fdep-16f; // log2/64 tail: 0.0000272020388
     r = mad(nf, -R_LOG2_BY_64_TL, mad(nf, -R_LOG2_BY_64_LD, ylogx)) + ylogx_t;

     // Truncated Taylor series for e^r
     poly = mad(mad(mad(r, 0x1.555556p-5f, 0x1.555556p-3f), r, 0x1.000000p-1f), r*r, r);

     tv = USE_TABLE(exp_tbl_ep, j);

     float expylogx = mad(tv.s0, poly, mad(tv.s1, poly, tv.s1)) + tv.s0;
     float sexpylogx = expylogx * as_float(0x1 << (m + 149));
     float texpylogx = as_float(as_int(expylogx) + m2);
     expylogx = m < -125 ? sexpylogx : texpylogx;

     // Result is +-Inf if (ylogx + ylogx_t) > 128*log2
     expylogx = ((ylogx > 0x1.62e430p+6f) | (ylogx == 0x1.62e430p+6f & ylogx_t > -0x1.05c610p-22f)) ? as_float(PINFBITPATT_SP32) : expylogx;

     // Result is 0 if ylogx < -149*log2
     expylogx = ylogx <  -0x1.9d1da0p+6f ? 0.0f : expylogx;

     // Classify y:
     //   inty = 0 means not an integer.
     //   inty = 1 means odd integer.
     //   inty = 2 means even integer.

     int yexp = (int)(ay >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32 + 1;
     int mask = (1 << (24 - yexp)) - 1;
     int yodd = ((iy >> (24 - yexp)) & 0x1) != 0;
     int inty = yodd ? 1 : 2;
     inty = (iy & mask) != 0 ? 0 : inty;
     inty = yexp < 1 ? 0 : inty;
     inty = yexp > 24 ? 2 : inty;

     float signval = as_float((as_uint(expylogx) ^ SIGNBIT_SP32));
     expylogx = ((inty == 1) & !xpos) ? signval : expylogx;
     int ret = as_int(expylogx);

     // Corner case handling
     ret = ax < 0x3f800000 & iy == NINFBITPATT_SP32 ? PINFBITPATT_SP32 : ret;
     ret = ax < 0x3f800000 & iy == PINFBITPATT_SP32 ? 0 : ret;
     ret = ax == 0x3f800000 & ay < PINFBITPATT_SP32 ? 0x3f800000 : ret;
     ret = ax == 0x3f800000 & ay == PINFBITPATT_SP32 ? QNANBITPATT_SP32 : ret;
     ret = ax > 0x3f800000 & iy == NINFBITPATT_SP32 ? 0 : ret;
     ret = ax > 0x3f800000 & iy == PINFBITPATT_SP32 ? PINFBITPATT_SP32 : ret;
     ret = ((ix < PINFBITPATT_SP32) & (ay == 0)) ? 0x3f800000 : ret;
     ret = ((ax == PINFBITPATT_SP32) & !ypos) ? 0 : ret;
     ret = ((ax == PINFBITPATT_SP32) & ypos) ? PINFBITPATT_SP32 : ret;
     ret = ((ax == PINFBITPATT_SP32) & (iy == PINFBITPATT_SP32)) ? PINFBITPATT_SP32 : ret;
     ret = ((ax == PINFBITPATT_SP32) & (ay == 0)) ? QNANBITPATT_SP32 : ret;
     ret = ((ax == 0) & !ypos) ? PINFBITPATT_SP32 : ret;
     ret = ((ax == 0) & ypos) ? 0 : ret;
     ret = ((ax == 0) & (ay == 0)) ? QNANBITPATT_SP32 : ret;
     ret = ((ax != 0) & !xpos) ? QNANBITPATT_SP32 : ret;
     ret = ax > PINFBITPATT_SP32 ? ix : ret;
     ret = ay > PINFBITPATT_SP32 ? iy : ret;

     return as_float(ret);
 }
 _CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_powr, float, float)

 #ifdef cl_khr_fp64
 _CLC_DEF _CLC_OVERLOAD double __clc_powr(double x, double y)
 {
     const double real_log2_tail = 5.76999904754328540596e-08;
     const double real_log2_lead = 6.93147122859954833984e-01;

     long ux = as_long(x);
     long ax = ux & (~SIGNBIT_DP64);
     int xpos = ax == ux;

     long uy = as_long(y);
     long ay = uy & (~SIGNBIT_DP64);
     int ypos = ay == uy;

     // Extended precision log
     double v, vt;
     {
         int exp = (int)(ax >> 52) - 1023;
         int mask_exp_1023 = exp == -1023;
         double xexp = (double) exp;
         long mantissa = ax & 0x000FFFFFFFFFFFFFL;

         long temp_ux = as_long(as_double(0x3ff0000000000000L | mantissa) - 1.0);
         exp = ((temp_ux & 0x7FF0000000000000L) >> 52) - 2045;
         double xexp1 = (double) exp;
         long mantissa1 = temp_ux & 0x000FFFFFFFFFFFFFL;

         xexp = mask_exp_1023 ? xexp1 : xexp;
         mantissa = mask_exp_1023 ? mantissa1 : mantissa;

         long rax = (mantissa & 0x000ff00000000000) + ((mantissa & 0x0000080000000000) << 1);
         int index = rax >> 44;

         double F = as_double(rax | 0x3FE0000000000000L);
         double Y = as_double(mantissa | 0x3FE0000000000000L);
         double f = F - Y;
         double2 tv = USE_TABLE(log_f_inv_tbl, index);
         double log_h = tv.s0;
         double log_t = tv.s1;
         double f_inv = (log_h + log_t) * f;
         double r1 = as_double(as_long(f_inv) & 0xfffffffff8000000L);
         double r2 = fma(-F, r1, f) * (log_h + log_t);
         double r = r1 + r2;

         double poly = fma(r,
                           fma(r,
                               fma(r,
                                   fma(r, 1.0/7.0, 1.0/6.0),
                                   1.0/5.0),
                               1.0/4.0),
                           1.0/3.0);
         poly = poly * r * r * r;

         double hr1r1 = 0.5*r1*r1;
         double poly0h = r1 + hr1r1;
         double poly0t = r1 - poly0h + hr1r1;
         poly = fma(r1, r2, fma(0.5*r2, r2, poly)) + r2 + poly0t;

         tv = USE_TABLE(powlog_tbl, index);
         log_h = tv.s0;
         log_t = tv.s1;

         double resT_t = fma(xexp, real_log2_tail, + log_t) - poly;
         double resT = resT_t - poly0h;
         double resH = fma(xexp, real_log2_lead, log_h);
         double resT_h = poly0h;

         double H = resT + resH;
         double H_h = as_double(as_long(H) & 0xfffffffff8000000L);
         double T = (resH - H + resT) + (resT_t - (resT + resT_h)) + (H - H_h);
         H = H_h;

         double y_head = as_double(uy & 0xfffffffff8000000L);
         double y_tail = y - y_head;

         double temp = fma(y_tail, H, fma(y_head, T, y_tail*T));
         v = fma(y_head, H, temp);
         vt = fma(y_head, H, -v) + temp;
     }

     // Now calculate exp of (v,vt)

     double expv;
     {
         const double max_exp_arg = 709.782712893384;
         const double min_exp_arg = -745.1332191019411;
         const double sixtyfour_by_lnof2 = 92.33248261689366;
         const double lnof2_by_64_head = 0.010830424260348081;
         const double lnof2_by_64_tail = -4.359010638708991e-10;

         double temp = v * sixtyfour_by_lnof2;
         int n = (int)temp;
         double dn = (double)n;
         int j = n & 0x0000003f;
         int m = n >> 6;

         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;
     {
         int yexp = (int)(ay >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64 + 1;
         inty = yexp < 1 ? 0 : 2;
         inty = yexp > 53 ? 2 : inty;
         long mask = (1L << (53 - yexp)) - 1L;
         int inty1 = (((ay & ~mask) >> (53 - yexp)) & 1L) == 1L ? 1 : 2;
         inty1 = (ay & mask) != 0 ? 0 : inty1;
         inty = !(yexp < 1) & !(yexp > 53) ? inty1 : inty;
     }

     expv *= ((inty == 1) & !xpos) ? -1.0 : 1.0;

     long ret = as_long(expv);

     // Now all the edge cases
     ret = ax < 0x3ff0000000000000L & uy == NINFBITPATT_DP64 ? PINFBITPATT_DP64 : ret;
     ret = ax < 0x3ff0000000000000L & uy == PINFBITPATT_DP64 ? 0L : ret;
     ret = ax == 0x3ff0000000000000L & ay < PINFBITPATT_DP64 ? 0x3ff0000000000000L : ret;
     ret = ax == 0x3ff0000000000000L & ay == PINFBITPATT_DP64 ? QNANBITPATT_DP64 : ret;
     ret = ax > 0x3ff0000000000000L & uy == NINFBITPATT_DP64 ? 0L : ret;
     ret = ax > 0x3ff0000000000000L & uy == PINFBITPATT_DP64 ? PINFBITPATT_DP64 : ret;
     ret = ux < PINFBITPATT_DP64 & ay == 0L ? 0x3ff0000000000000L : ret;
     ret = ((ax == PINFBITPATT_DP64) & !ypos) ? 0L : ret;
     ret = ((ax == PINFBITPATT_DP64) & ypos) ? PINFBITPATT_DP64 : ret;
     ret = ((ax == PINFBITPATT_DP64) & (uy == PINFBITPATT_DP64)) ? PINFBITPATT_DP64 : ret;
     ret = ((ax == PINFBITPATT_DP64) & (ay == 0L)) ? QNANBITPATT_DP64 : ret;
     ret = ((ax == 0L) & !ypos) ? PINFBITPATT_DP64 : ret;
     ret = ((ax == 0L) & ypos) ? 0L : ret;
     ret = ((ax == 0L) & (ay == 0L)) ? QNANBITPATT_DP64 : ret;
     ret = ((ax != 0L) & !xpos) ? QNANBITPATT_DP64 : ret;
     ret = ax > PINFBITPATT_DP64 ? ux : ret;
     ret = ay > PINFBITPATT_DP64 ? uy : ret;

     return as_double(ret);
 }
 _CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_powr, double, double)
 #endif
	/*
	* 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 <clc/clc.h>

	#include "config.h"
	#include "math.h"
	#include "tables.h"
	#include "../clcmacro.h"

	// compute pow using log and exp
	// x^y = exp(y * log(x))
	//
	// we take care not to lose precision in the intermediate steps
	//
	// When computing log, calculate it in splits,
	//
	// r = f * (p_invead + p_inv_tail)
	// r = rh + rt
	//
	// calculate log polynomial using r, in end addition, do
	// poly = poly + ((rh-r) + rt)
	//
	// lth = -r
	// ltt = ((xexp * log2_t) - poly) + logT
	// lt = lth + ltt
	//
	// lh = (xexp * log2_h) + logH
	// l = lh + lt
	//
	// Calculate final log answer as gh and gt,
	// gh = l & higher-half bits
	// gt = (((ltt - (lt - lth)) + ((lh - l) + lt)) + (l - gh))
	//
	// yh = y & higher-half bits
	// yt = y - yh
	//
	// Before entering computation of exp,
	// vs = ((ytgt + ytgh) + yh*gt)
	// v = vs + yh*gh
	// vt = ((yh*gh - v) + vs)
	//
	// In calculation of exp, add vt to r that is used for poly
	// At the end of exp, do
	// ((((expT * poly) + expT) + expH*poly) + expH)

	_CLC_DEF _CLC_OVERLOAD float __clc_powr(float x, float y)
	{
	int ix = as_int(x);
	int ax = ix & EXSIGNBIT_SP32;
	int xpos = ix == ax;

	int iy = as_int(y);
	int ay = iy & EXSIGNBIT_SP32;
	int ypos = iy == ay;

	// Extra precise log calculation
	// First handle case that x is close to 1
	float r = 1.0f - as_float(ax);
	int near1 = fabs(r) < 0x1.0p-4f;
	float r2 = r*r;

	// Coefficients are just 1/3, 1/4, 1/5 and 1/6
	float poly = mad(r,
	mad(r,
	mad(r,
	mad(r, 0x1.24924ap-3f, 0x1.555556p-3f),
	0x1.99999ap-3f),
	0x1.000000p-2f),
	0x1.555556p-2f);

	poly = r2r;

	float lth_near1 = -r2 * 0.5f;
	float ltt_near1 = -poly;
	float lt_near1 = lth_near1 + ltt_near1;
	float lh_near1 = -r;
	float l_near1 = lh_near1 + lt_near1;

	// Computations for x not near 1
	int m = (int)(ax >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
	float mf = (float)m;
	int ixs = as_int(as_float(ax \| 0x3f800000) - 1.0f);
	float mfs = (float)((ixs >> EXPSHIFTBITS_SP32) - 253);
	int c = m == -127;
	int ixn = c ? ixs : ax;
	float mfn = c ? mfs : mf;

	int indx = (ixn & 0x007f0000) + ((ixn & 0x00008000) << 1);

	// F - Y
	float f = as_float(0x3f000000 \| indx) - as_float(0x3f000000 \| (ixn & MANTBITS_SP32));

	indx = indx >> 16;
	float2 tv = USE_TABLE(log_inv_tbl_ep, indx);
	float rh = f * tv.s0;
	float rt = f * tv.s1;
	r = rh + rt;

	poly = mad(r, mad(r, 0x1.0p-2f, 0x1.555556p-2f), 0x1.0p-1f) * (r*r);
	poly += (rh - r) + rt;

	const float LOG2_HEAD = 0x1.62e000p-1f; // 0.693115234
	const float LOG2_TAIL = 0x1.0bfbe8p-15f; // 0.0000319461833
	tv = USE_TABLE(loge_tbl, indx);
	float lth = -r;
	float ltt = mad(mfn, LOG2_TAIL, -poly) + tv.s1;
	float lt = lth + ltt;
	float lh = mad(mfn, LOG2_HEAD, tv.s0);
	float l = lh + lt;

	// Select near 1 or not
	lth = near1 ? lth_near1 : lth;
	ltt = near1 ? ltt_near1 : ltt;
	lt = near1 ? lt_near1 : lt;
	lh = near1 ? lh_near1 : lh;
	l = near1 ? l_near1 : l;

	float gh = as_float(as_int(l) & 0xfffff000);
	float gt = ((ltt - (lt - lth)) + ((lh - l) + lt)) + (l - gh);

	float yh = as_float(iy & 0xfffff000);

	float yt = y - yh;

	float ylogx_s = mad(gt, yh, mad(gh, yt, yt*gt));
	float ylogx = mad(yh, gh, ylogx_s);
	float ylogx_t = mad(yh, gh, -ylogx) + ylogx_s;

	// Extra precise exp of ylogx
	const float R_64_BY_LOG2 = 0x1.715476p+6f; // 64/log2 : 92.332482616893657
	int n = convert_int(ylogx * R_64_BY_LOG2);
	float nf = (float) n;

	int j = n & 0x3f;
	m = n >> 6;
	int m2 = m << EXPSHIFTBITS_SP32;

	const float R_LOG2_BY_64_LD = 0x1.620000p-7f; // log2/64 lead: 0.0108032227
	const float R_LOG2_BY_64_TL = 0x1.c85fdep-16f; // log2/64 tail: 0.0000272020388
	r = mad(nf, -R_LOG2_BY_64_TL, mad(nf, -R_LOG2_BY_64_LD, ylogx)) + ylogx_t;

	// Truncated Taylor series for e^r
	poly = mad(mad(mad(r, 0x1.555556p-5f, 0x1.555556p-3f), r, 0x1.000000p-1f), r*r, r);

	tv = USE_TABLE(exp_tbl_ep, j);

	float expylogx = mad(tv.s0, poly, mad(tv.s1, poly, tv.s1)) + tv.s0;
	float sexpylogx = expylogx * as_float(0x1 << (m + 149));
	float texpylogx = as_float(as_int(expylogx) + m2);
	expylogx = m < -125 ? sexpylogx : texpylogx;

	// Result is +-Inf if (ylogx + ylogx_t) > 128*log2
	expylogx = ((ylogx > 0x1.62e430p+6f) \| (ylogx == 0x1.62e430p+6f & ylogx_t > -0x1.05c610p-22f)) ? as_float(PINFBITPATT_SP32) : expylogx;

	// Result is 0 if ylogx < -149*log2
	expylogx = ylogx < -0x1.9d1da0p+6f ? 0.0f : expylogx;

	// Classify y:
	// inty = 0 means not an integer.
	// inty = 1 means odd integer.
	// inty = 2 means even integer.

	int yexp = (int)(ay >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32 + 1;
	int mask = (1 << (24 - yexp)) - 1;
	int yodd = ((iy >> (24 - yexp)) & 0x1) != 0;
	int inty = yodd ? 1 : 2;
	inty = (iy & mask) != 0 ? 0 : inty;
	inty = yexp < 1 ? 0 : inty;
	inty = yexp > 24 ? 2 : inty;

	float signval = as_float((as_uint(expylogx) ^ SIGNBIT_SP32));
	expylogx = ((inty == 1) & !xpos) ? signval : expylogx;
	int ret = as_int(expylogx);

	// Corner case handling
	ret = ax < 0x3f800000 & iy == NINFBITPATT_SP32 ? PINFBITPATT_SP32 : ret;
	ret = ax < 0x3f800000 & iy == PINFBITPATT_SP32 ? 0 : ret;
	ret = ax == 0x3f800000 & ay < PINFBITPATT_SP32 ? 0x3f800000 : ret;
	ret = ax == 0x3f800000 & ay == PINFBITPATT_SP32 ? QNANBITPATT_SP32 : ret;
	ret = ax > 0x3f800000 & iy == NINFBITPATT_SP32 ? 0 : ret;
	ret = ax > 0x3f800000 & iy == PINFBITPATT_SP32 ? PINFBITPATT_SP32 : ret;
	ret = ((ix < PINFBITPATT_SP32) & (ay == 0)) ? 0x3f800000 : ret;
	ret = ((ax == PINFBITPATT_SP32) & !ypos) ? 0 : ret;
	ret = ((ax == PINFBITPATT_SP32) & ypos) ? PINFBITPATT_SP32 : ret;
	ret = ((ax == PINFBITPATT_SP32) & (iy == PINFBITPATT_SP32)) ? PINFBITPATT_SP32 : ret;
	ret = ((ax == PINFBITPATT_SP32) & (ay == 0)) ? QNANBITPATT_SP32 : ret;
	ret = ((ax == 0) & !ypos) ? PINFBITPATT_SP32 : ret;
	ret = ((ax == 0) & ypos) ? 0 : ret;
	ret = ((ax == 0) & (ay == 0)) ? QNANBITPATT_SP32 : ret;
	ret = ((ax != 0) & !xpos) ? QNANBITPATT_SP32 : ret;
	ret = ax > PINFBITPATT_SP32 ? ix : ret;
	ret = ay > PINFBITPATT_SP32 ? iy : ret;

	return as_float(ret);
	}
	_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_powr, float, float)

	#ifdef cl_khr_fp64
	_CLC_DEF _CLC_OVERLOAD double __clc_powr(double x, double y)
	{
	const double real_log2_tail = 5.76999904754328540596e-08;
	const double real_log2_lead = 6.93147122859954833984e-01;

	long ux = as_long(x);
	long ax = ux & (~SIGNBIT_DP64);
	int xpos = ax == ux;

	long uy = as_long(y);
	long ay = uy & (~SIGNBIT_DP64);
	int ypos = ay == uy;

	// Extended precision log
	double v, vt;
	{
	int exp = (int)(ax >> 52) - 1023;
	int mask_exp_1023 = exp == -1023;
	double xexp = (double) exp;
	long mantissa = ax & 0x000FFFFFFFFFFFFFL;

	long temp_ux = as_long(as_double(0x3ff0000000000000L \| mantissa) - 1.0);
	exp = ((temp_ux & 0x7FF0000000000000L) >> 52) - 2045;
	double xexp1 = (double) exp;
	long mantissa1 = temp_ux & 0x000FFFFFFFFFFFFFL;

	xexp = mask_exp_1023 ? xexp1 : xexp;
	mantissa = mask_exp_1023 ? mantissa1 : mantissa;

	long rax = (mantissa & 0x000ff00000000000) + ((mantissa & 0x0000080000000000) << 1);
	int index = rax >> 44;

	double F = as_double(rax \| 0x3FE0000000000000L);
	double Y = as_double(mantissa \| 0x3FE0000000000000L);
	double f = F - Y;
	double2 tv = USE_TABLE(log_f_inv_tbl, index);
	double log_h = tv.s0;
	double log_t = tv.s1;
	double f_inv = (log_h + log_t) * f;
	double r1 = as_double(as_long(f_inv) & 0xfffffffff8000000L);
	double r2 = fma(-F, r1, f) * (log_h + log_t);
	double r = r1 + r2;

	double poly = fma(r,
	fma(r,
	fma(r,
	fma(r, 1.0/7.0, 1.0/6.0),
	1.0/5.0),
	1.0/4.0),
	1.0/3.0);
	poly = poly * r * r * r;

	double hr1r1 = 0.5r1r1;
	double poly0h = r1 + hr1r1;
	double poly0t = r1 - poly0h + hr1r1;
	poly = fma(r1, r2, fma(0.5*r2, r2, poly)) + r2 + poly0t;

	tv = USE_TABLE(powlog_tbl, index);
	log_h = tv.s0;
	log_t = tv.s1;

	double resT_t = fma(xexp, real_log2_tail, + log_t) - poly;
	double resT = resT_t - poly0h;
	double resH = fma(xexp, real_log2_lead, log_h);
	double resT_h = poly0h;

	double H = resT + resH;
	double H_h = as_double(as_long(H) & 0xfffffffff8000000L);
	double T = (resH - H + resT) + (resT_t - (resT + resT_h)) + (H - H_h);
	H = H_h;

	double y_head = as_double(uy & 0xfffffffff8000000L);
	double y_tail = y - y_head;

	double temp = fma(y_tail, H, fma(y_head, T, y_tail*T));
	v = fma(y_head, H, temp);
	vt = fma(y_head, H, -v) + temp;
	}

	// Now calculate exp of (v,vt)

	double expv;
	{
	const double max_exp_arg = 709.782712893384;
	const double min_exp_arg = -745.1332191019411;
	const double sixtyfour_by_lnof2 = 92.33248261689366;
	const double lnof2_by_64_head = 0.010830424260348081;
	const double lnof2_by_64_tail = -4.359010638708991e-10;

	double temp = v * sixtyfour_by_lnof2;
	int n = (int)temp;
	double dn = (double)n;
	int j = n & 0x0000003f;
	int m = n >> 6;

	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;
	{
	int yexp = (int)(ay >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64 + 1;
	inty = yexp < 1 ? 0 : 2;
	inty = yexp > 53 ? 2 : inty;
	long mask = (1L << (53 - yexp)) - 1L;
	int inty1 = (((ay & ~mask) >> (53 - yexp)) & 1L) == 1L ? 1 : 2;
	inty1 = (ay & mask) != 0 ? 0 : inty1;
	inty = !(yexp < 1) & !(yexp > 53) ? inty1 : inty;
	}

	expv *= ((inty == 1) & !xpos) ? -1.0 : 1.0;

	long ret = as_long(expv);

	// Now all the edge cases
	ret = ax < 0x3ff0000000000000L & uy == NINFBITPATT_DP64 ? PINFBITPATT_DP64 : ret;
	ret = ax < 0x3ff0000000000000L & uy == PINFBITPATT_DP64 ? 0L : ret;
	ret = ax == 0x3ff0000000000000L & ay < PINFBITPATT_DP64 ? 0x3ff0000000000000L : ret;
	ret = ax == 0x3ff0000000000000L & ay == PINFBITPATT_DP64 ? QNANBITPATT_DP64 : ret;
	ret = ax > 0x3ff0000000000000L & uy == NINFBITPATT_DP64 ? 0L : ret;
	ret = ax > 0x3ff0000000000000L & uy == PINFBITPATT_DP64 ? PINFBITPATT_DP64 : ret;
	ret = ux < PINFBITPATT_DP64 & ay == 0L ? 0x3ff0000000000000L : ret;
	ret = ((ax == PINFBITPATT_DP64) & !ypos) ? 0L : ret;
	ret = ((ax == PINFBITPATT_DP64) & ypos) ? PINFBITPATT_DP64 : ret;
	ret = ((ax == PINFBITPATT_DP64) & (uy == PINFBITPATT_DP64)) ? PINFBITPATT_DP64 : ret;
	ret = ((ax == PINFBITPATT_DP64) & (ay == 0L)) ? QNANBITPATT_DP64 : ret;
	ret = ((ax == 0L) & !ypos) ? PINFBITPATT_DP64 : ret;
	ret = ((ax == 0L) & ypos) ? 0L : ret;
	ret = ((ax == 0L) & (ay == 0L)) ? QNANBITPATT_DP64 : ret;
	ret = ((ax != 0L) & !xpos) ? QNANBITPATT_DP64 : ret;
	ret = ax > PINFBITPATT_DP64 ? ux : ret;
	ret = ay > PINFBITPATT_DP64 ? uy : ret;

	return as_double(ret);
	}
	_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_powr, double, double)
	#endif