1/* 2 * Copyright (c) 2014 Advanced Micro Devices, Inc. 3 * 4 * Permission is hereby granted, free of charge, to any person obtaining a copy 5 * of this software and associated documentation files (the "Software"), to deal 6 * in the Software without restriction, including without limitation the rights 7 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 8 * copies of the Software, and to permit persons to whom the Software is 9 * furnished to do so, subject to the following conditions: 10 * 11 * The above copyright notice and this permission notice shall be included in 12 * all copies or substantial portions of the Software. 13 * 14 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 15 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 16 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 17 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 18 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 19 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 20 * THE SOFTWARE. 21 */ 22 23#include <clc/clc.h> 24#include <clc/clcmacro.h> 25#include <clc/math/clc_fabs.h> 26#include <clc/math/clc_mad.h> 27#include <clc/math/clc_subnormal_config.h> 28#include <clc/math/math.h> 29#include <clc/math/tables.h> 30 31// compute pow using log and exp 32// x^y = exp(y * log(x)) 33// 34// we take care not to lose precision in the intermediate steps 35// 36// When computing log, calculate it in splits, 37// 38// r = f * (p_invead + p_inv_tail) 39// r = rh + rt 40// 41// calculate log polynomial using r, in end addition, do 42// poly = poly + ((rh-r) + rt) 43// 44// lth = -r 45// ltt = ((xexp * log2_t) - poly) + logT 46// lt = lth + ltt 47// 48// lh = (xexp * log2_h) + logH 49// l = lh + lt 50// 51// Calculate final log answer as gh and gt, 52// gh = l & higher-half bits 53// gt = (((ltt - (lt - lth)) + ((lh - l) + lt)) + (l - gh)) 54// 55// yh = y & higher-half bits 56// yt = y - yh 57// 58// Before entering computation of exp, 59// vs = ((yt*gt + yt*gh) + yh*gt) 60// v = vs + yh*gh 61// vt = ((yh*gh - v) + vs) 62// 63// In calculation of exp, add vt to r that is used for poly 64// At the end of exp, do 65// ((((expT * poly) + expT) + expH*poly) + expH) 66 67_CLC_DEF _CLC_OVERLOAD float __clc_pown(float x, int ny) { 68 float y = (float)ny; 69 70 int ix = as_int(x); 71 int ax = ix & EXSIGNBIT_SP32; 72 int xpos = ix == ax; 73 74 int iy = as_int(y); 75 int ay = iy & EXSIGNBIT_SP32; 76 int ypos = iy == ay; 77 78 // Extra precise log calculation 79 // First handle case that x is close to 1 80 float r = 1.0f - as_float(ax); 81 int near1 = __clc_fabs(r) < 0x1.0p-4f; 82 float r2 = r * r; 83 84 // Coefficients are just 1/3, 1/4, 1/5 and 1/6 85 float poly = __clc_mad( 86 r, 87 __clc_mad(r, 88 __clc_mad(r, __clc_mad(r, 0x1.24924ap-3f, 0x1.555556p-3f), 89 0x1.99999ap-3f), 90 0x1.000000p-2f), 91 0x1.555556p-2f); 92 93 poly *= r2 * r; 94 95 float lth_near1 = -r2 * 0.5f; 96 float ltt_near1 = -poly; 97 float lt_near1 = lth_near1 + ltt_near1; 98 float lh_near1 = -r; 99 float l_near1 = lh_near1 + lt_near1; 100 101 // Computations for x not near 1 102 int m = (int)(ax >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; 103 float mf = (float)m; 104 int ixs = as_int(as_float(ax | 0x3f800000) - 1.0f); 105 float mfs = (float)((ixs >> EXPSHIFTBITS_SP32) - 253); 106 int c = m == -127; 107 int ixn = c ? ixs : ax; 108 float mfn = c ? mfs : mf; 109 110 int indx = (ixn & 0x007f0000) + ((ixn & 0x00008000) << 1); 111 112 // F - Y 113 float f = as_float(0x3f000000 | indx) - 114 as_float(0x3f000000 | (ixn & MANTBITS_SP32)); 115 116 indx = indx >> 16; 117 float2 tv = USE_TABLE(log_inv_tbl_ep, indx); 118 float rh = f * tv.s0; 119 float rt = f * tv.s1; 120 r = rh + rt; 121 122 poly = __clc_mad(r, __clc_mad(r, 0x1.0p-2f, 0x1.555556p-2f), 0x1.0p-1f) * 123 (r * r); 124 poly += (rh - r) + rt; 125 126 const float LOG2_HEAD = 0x1.62e000p-1f; // 0.693115234 127 const float LOG2_TAIL = 0x1.0bfbe8p-15f; // 0.0000319461833 128 tv = USE_TABLE(loge_tbl, indx); 129 float lth = -r; 130 float ltt = __clc_mad(mfn, LOG2_TAIL, -poly) + tv.s1; 131 float lt = lth + ltt; 132 float lh = __clc_mad(mfn, LOG2_HEAD, tv.s0); 133 float l = lh + lt; 134 135 // Select near 1 or not 136 lth = near1 ? lth_near1 : lth; 137 ltt = near1 ? ltt_near1 : ltt; 138 lt = near1 ? lt_near1 : lt; 139 lh = near1 ? lh_near1 : lh; 140 l = near1 ? l_near1 : l; 141 142 float gh = as_float(as_int(l) & 0xfffff000); 143 float gt = ((ltt - (lt - lth)) + ((lh - l) + lt)) + (l - gh); 144 145 float yh = as_float(iy & 0xfffff000); 146 147 float yt = (float)(ny - (int)yh); 148 149 float ylogx_s = __clc_mad(gt, yh, __clc_mad(gh, yt, yt * gt)); 150 float ylogx = __clc_mad(yh, gh, ylogx_s); 151 float ylogx_t = __clc_mad(yh, gh, -ylogx) + ylogx_s; 152 153 // Extra precise exp of ylogx 154 // 64/log2 : 92.332482616893657 155 const float R_64_BY_LOG2 = 0x1.715476p+6f; 156 int n = convert_int(ylogx * R_64_BY_LOG2); 157 float nf = (float)n; 158 159 int j = n & 0x3f; 160 m = n >> 6; 161 int m2 = m << EXPSHIFTBITS_SP32; 162 163 // log2/64 lead: 0.0108032227 164 const float R_LOG2_BY_64_LD = 0x1.620000p-7f; 165 // log2/64 tail: 0.0000272020388 166 const float R_LOG2_BY_64_TL = 0x1.c85fdep-16f; 167 r = __clc_mad(nf, -R_LOG2_BY_64_TL, __clc_mad(nf, -R_LOG2_BY_64_LD, ylogx)) + 168 ylogx_t; 169 170 // Truncated Taylor series for e^r 171 poly = __clc_mad(__clc_mad(__clc_mad(r, 0x1.555556p-5f, 0x1.555556p-3f), r, 172 0x1.000000p-1f), 173 r * r, r); 174 175 tv = USE_TABLE(exp_tbl_ep, j); 176 177 float expylogx = 178 __clc_mad(tv.s0, poly, __clc_mad(tv.s1, poly, tv.s1)) + tv.s0; 179 float sexpylogx = expylogx * as_float(0x1 << (m + 149)); 180 float texpylogx = as_float(as_int(expylogx) + m2); 181 expylogx = m < -125 ? sexpylogx : texpylogx; 182 183 // Result is +-Inf if (ylogx + ylogx_t) > 128*log2 184 expylogx = ((ylogx > 0x1.62e430p+6f) | 185 (ylogx == 0x1.62e430p+6f & ylogx_t > -0x1.05c610p-22f)) 186 ? as_float(PINFBITPATT_SP32) 187 : expylogx; 188 189 // Result is 0 if ylogx < -149*log2 190 expylogx = ylogx < -0x1.9d1da0p+6f ? 0.0f : expylogx; 191 192 // Classify y: 193 // inty = 0 means not an integer. 194 // inty = 1 means odd integer. 195 // inty = 2 means even integer. 196 197 int inty = 2 - (ny & 1); 198 199 float signval = as_float((as_uint(expylogx) ^ SIGNBIT_SP32)); 200 expylogx = ((inty == 1) & !xpos) ? signval : expylogx; 201 int ret = as_int(expylogx); 202 203 // Corner case handling 204 int xinf = xpos ? PINFBITPATT_SP32 : NINFBITPATT_SP32; 205 ret = ((ax == 0) & !ypos & (inty == 1)) ? xinf : ret; 206 ret = ((ax == 0) & !ypos & (inty == 2)) ? PINFBITPATT_SP32 : ret; 207 ret = ((ax == 0) & ypos & (inty == 2)) ? 0 : ret; 208 int xzero = !xpos ? 0x80000000 : 0L; 209 ret = ((ax == 0) & ypos & (inty == 1)) ? xzero : ret; 210 ret = ((ix == NINFBITPATT_SP32) & !ypos & (inty == 1)) ? 0x80000000 : ret; 211 ret = ((ix == NINFBITPATT_SP32) & !ypos & (inty != 1)) ? 0 : ret; 212 ret = 213 ((ix == NINFBITPATT_SP32) & ypos & (inty == 1)) ? NINFBITPATT_SP32 : ret; 214 ret = 215 ((ix == NINFBITPATT_SP32) & ypos & (inty != 1)) ? PINFBITPATT_SP32 : ret; 216 ret = ((ix == PINFBITPATT_SP32) & !ypos) ? 0 : ret; 217 ret = ((ix == PINFBITPATT_SP32) & ypos) ? PINFBITPATT_SP32 : ret; 218 ret = ax > PINFBITPATT_SP32 ? ix : ret; 219 ret = ny == 0 ? 0x3f800000 : ret; 220 221 return as_float(ret); 222} 223_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_pown, float, int) 224 225#ifdef cl_khr_fp64 226_CLC_DEF _CLC_OVERLOAD double __clc_pown(double x, int ny) { 227 const double real_log2_tail = 5.76999904754328540596e-08; 228 const double real_log2_lead = 6.93147122859954833984e-01; 229 230 double y = (double)ny; 231 232 long ux = as_long(x); 233 long ax = ux & (~SIGNBIT_DP64); 234 int xpos = ax == ux; 235 236 long uy = as_long(y); 237 long ay = uy & (~SIGNBIT_DP64); 238 int ypos = ay == uy; 239 240 // Extended precision log 241 double v, vt; 242 { 243 int exp = (int)(ax >> 52) - 1023; 244 int mask_exp_1023 = exp == -1023; 245 double xexp = (double)exp; 246 long mantissa = ax & 0x000FFFFFFFFFFFFFL; 247 248 long temp_ux = as_long(as_double(0x3ff0000000000000L | mantissa) - 1.0); 249 exp = ((temp_ux & 0x7FF0000000000000L) >> 52) - 2045; 250 double xexp1 = (double)exp; 251 long mantissa1 = temp_ux & 0x000FFFFFFFFFFFFFL; 252 253 xexp = mask_exp_1023 ? xexp1 : xexp; 254 mantissa = mask_exp_1023 ? mantissa1 : mantissa; 255 256 long rax = (mantissa & 0x000ff00000000000) + 257 ((mantissa & 0x0000080000000000) << 1); 258 int index = rax >> 44; 259 260 double F = as_double(rax | 0x3FE0000000000000L); 261 double Y = as_double(mantissa | 0x3FE0000000000000L); 262 double f = F - Y; 263 double2 tv = USE_TABLE(log_f_inv_tbl, index); 264 double log_h = tv.s0; 265 double log_t = tv.s1; 266 double f_inv = (log_h + log_t) * f; 267 double r1 = as_double(as_long(f_inv) & 0xfffffffff8000000L); 268 double r2 = fma(-F, r1, f) * (log_h + log_t); 269 double r = r1 + r2; 270 271 double poly = fma( 272 r, fma(r, fma(r, fma(r, 1.0 / 7.0, 1.0 / 6.0), 1.0 / 5.0), 1.0 / 4.0), 273 1.0 / 3.0); 274 poly = poly * r * r * r; 275 276 double hr1r1 = 0.5 * r1 * r1; 277 double poly0h = r1 + hr1r1; 278 double poly0t = r1 - poly0h + hr1r1; 279 poly = fma(r1, r2, fma(0.5 * r2, r2, poly)) + r2 + poly0t; 280 281 tv = USE_TABLE(powlog_tbl, index); 282 log_h = tv.s0; 283 log_t = tv.s1; 284 285 double resT_t = fma(xexp, real_log2_tail, +log_t) - poly; 286 double resT = resT_t - poly0h; 287 double resH = fma(xexp, real_log2_lead, log_h); 288 double resT_h = poly0h; 289 290 double H = resT + resH; 291 double H_h = as_double(as_long(H) & 0xfffffffff8000000L); 292 double T = (resH - H + resT) + (resT_t - (resT + resT_h)) + (H - H_h); 293 H = H_h; 294 295 double y_head = as_double(uy & 0xfffffffff8000000L); 296 double y_tail = y - y_head; 297 298 int mask_2_24 = ay > 0x4170000000000000; // 2^24 299 int nyh = convert_int(y_head); 300 int nyt = ny - nyh; 301 double y_tail1 = (double)nyt; 302 y_tail = mask_2_24 ? y_tail1 : y_tail; 303 304 double temp = fma(y_tail, H, fma(y_head, T, y_tail * T)); 305 v = fma(y_head, H, temp); 306 vt = fma(y_head, H, -v) + temp; 307 } 308 309 // Now calculate exp of (v,vt) 310 311 double expv; 312 { 313 const double max_exp_arg = 709.782712893384; 314 const double min_exp_arg = -745.1332191019411; 315 const double sixtyfour_by_lnof2 = 92.33248261689366; 316 const double lnof2_by_64_head = 0.010830424260348081; 317 const double lnof2_by_64_tail = -4.359010638708991e-10; 318 319 double temp = v * sixtyfour_by_lnof2; 320 int n = (int)temp; 321 double dn = (double)n; 322 int j = n & 0x0000003f; 323 int m = n >> 6; 324 325 double2 tv = USE_TABLE(two_to_jby64_ep_tbl, j); 326 double f1 = tv.s0; 327 double f2 = tv.s1; 328 double f = f1 + f2; 329 330 double r1 = fma(dn, -lnof2_by_64_head, v); 331 double r2 = dn * lnof2_by_64_tail; 332 double r = (r1 + r2) + vt; 333 334 double q = fma( 335 r, 336 fma(r, 337 fma(r, 338 fma(r, 1.38889490863777199667e-03, 8.33336798434219616221e-03), 339 4.16666666662260795726e-02), 340 1.66666666665260878863e-01), 341 5.00000000000000008883e-01); 342 q = fma(r * r, q, r); 343 344 expv = fma(f, q, f2) + f1; 345 expv = ldexp(expv, m); 346 347 expv = v > max_exp_arg ? as_double(0x7FF0000000000000L) : expv; 348 expv = v < min_exp_arg ? 0.0 : expv; 349 } 350 351 // See whether y is an integer. 352 // inty = 0 means not an integer. 353 // inty = 1 means odd integer. 354 // inty = 2 means even integer. 355 356 int inty = 2 - (ny & 1); 357 358 expv *= ((inty == 1) & !xpos) ? -1.0 : 1.0; 359 360 long ret = as_long(expv); 361 362 // Now all the edge cases 363 long xinf = xpos ? PINFBITPATT_DP64 : NINFBITPATT_DP64; 364 ret = ((ax == 0L) & !ypos & (inty == 1)) ? xinf : ret; 365 ret = ((ax == 0L) & !ypos & (inty == 2)) ? PINFBITPATT_DP64 : ret; 366 ret = ((ax == 0L) & ypos & (inty == 2)) ? 0L : ret; 367 long xzero = !xpos ? 0x8000000000000000L : 0L; 368 ret = ((ax == 0L) & ypos & (inty == 1)) ? xzero : ret; 369 ret = ((ux == NINFBITPATT_DP64) & !ypos & (inty == 1)) ? 0x8000000000000000L 370 : ret; 371 ret = ((ux == NINFBITPATT_DP64) & !ypos & (inty != 1)) ? 0L : ret; 372 ret = 373 ((ux == NINFBITPATT_DP64) & ypos & (inty == 1)) ? NINFBITPATT_DP64 : ret; 374 ret = 375 ((ux == NINFBITPATT_DP64) & ypos & (inty != 1)) ? PINFBITPATT_DP64 : ret; 376 ret = ((ux == PINFBITPATT_DP64) & !ypos) ? 0L : ret; 377 ret = ((ux == PINFBITPATT_DP64) & ypos) ? PINFBITPATT_DP64 : ret; 378 ret = ax > PINFBITPATT_DP64 ? ux : ret; 379 ret = ny == 0 ? 0x3ff0000000000000L : ret; 380 381 return as_double(ret); 382} 383_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_pown, double, int) 384#endif 385 386#ifdef cl_khr_fp16 387 388#pragma OPENCL EXTENSION cl_khr_fp16 : enable 389 390_CLC_OVERLOAD _CLC_DEF half __clc_pown(half x, int y) { 391 return (half)__clc_pown((float)x, y); 392} 393 394_CLC_BINARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, half, __clc_pown, half, int); 395 396#endif 397