/*
* 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_pow(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 = (!xpos & (inty == 0)) ? QNANBITPATT_SP32 : ret;
ret = ax < 0x3f800000 & iy == NINFBITPATT_SP32 ? PINFBITPATT_SP32 : ret;
ret = ax > 0x3f800000 & iy == NINFBITPATT_SP32 ? 0 : ret;
ret = ax < 0x3f800000 & iy == PINFBITPATT_SP32 ? 0 : ret;
ret = ax > 0x3f800000 & iy == PINFBITPATT_SP32 ? PINFBITPATT_SP32 : ret;
int xinf = xpos ? PINFBITPATT_SP32 : NINFBITPATT_SP32;
ret = ((ax == 0) & !ypos & (inty == 1)) ? xinf : ret;
ret = ((ax == 0) & !ypos & (inty != 1)) ? PINFBITPATT_SP32 : ret;
int xzero = xpos ? 0 : 0x80000000;
ret = ((ax == 0) & ypos & (inty == 1)) ? xzero : ret;
ret = ((ax == 0) & ypos & (inty != 1)) ? 0 : ret;
ret = ((ax == 0) & (iy == NINFBITPATT_SP32)) ? PINFBITPATT_SP32 : ret;
ret = ((ix == 0xbf800000) & (ay == PINFBITPATT_SP32)) ? 0x3f800000 : ret;
ret = ((ix == NINFBITPATT_SP32) & !ypos & (inty == 1)) ? 0x80000000 : ret;
ret = ((ix == NINFBITPATT_SP32) & !ypos & (inty != 1)) ? 0 : ret;
ret = ((ix == NINFBITPATT_SP32) & ypos & (inty == 1)) ? NINFBITPATT_SP32 : ret;
ret = ((ix == NINFBITPATT_SP32) & ypos & (inty != 1)) ? PINFBITPATT_SP32 : ret;
ret = ((ix == PINFBITPATT_SP32) & !ypos) ? 0 : ret;
ret = ((ix == PINFBITPATT_SP32) & ypos) ? PINFBITPATT_SP32 : ret;
ret = (ax > PINFBITPATT_SP32) ? ix : ret;
ret = (ay > PINFBITPATT_SP32) ? iy : ret;
ret = ay == 0 ? 0x3f800000 : ret;
ret = ix == 0x3f800000 ? 0x3f800000 : ret;
return as_float(ret);
}
_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_pow, float, float)
#ifdef cl_khr_fp64
_CLC_DEF _CLC_OVERLOAD double __clc_pow(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 = !xpos & (inty == 0) ? QNANBITPATT_DP64 : ret;
ret = ax < 0x3ff0000000000000L & uy == NINFBITPATT_DP64 ? PINFBITPATT_DP64 : ret;
ret = ax > 0x3ff0000000000000L & uy == NINFBITPATT_DP64 ? 0L : ret;
ret = ax < 0x3ff0000000000000L & uy == PINFBITPATT_DP64 ? 0L : ret;
ret = ax > 0x3ff0000000000000L & uy == PINFBITPATT_DP64 ? PINFBITPATT_DP64 : ret;
long xinf = xpos ? PINFBITPATT_DP64 : NINFBITPATT_DP64;
ret = ((ax == 0L) & !ypos & (inty == 1)) ? xinf : ret;
ret = ((ax == 0L) & !ypos & (inty != 1)) ? PINFBITPATT_DP64 : ret;
long xzero = xpos ? 0L : 0x8000000000000000L;
ret = ((ax == 0L) & ypos & (inty == 1)) ? xzero : ret;
ret = ((ax == 0L) & ypos & (inty != 1)) ? 0L : ret;
ret = ((ax == 0L) & (uy == NINFBITPATT_DP64)) ? PINFBITPATT_DP64 : ret;
ret = ((ux == 0xbff0000000000000L) & (ay == PINFBITPATT_DP64)) ? 0x3ff0000000000000L : 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 = ay > PINFBITPATT_DP64 ? uy : ret;
ret = ay == 0L ? 0x3ff0000000000000L : ret;
ret = ux == 0x3ff0000000000000L ? 0x3ff0000000000000L : ret;
return as_double(ret);
}
_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_pow, double, double)
#endif
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