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_powr(float x, float y) { 68 int ix = as_int(x); 69 int ax = ix & EXSIGNBIT_SP32; 70 int xpos = ix == ax; 71 72 int iy = as_int(y); 73 int ay = iy & EXSIGNBIT_SP32; 74 int ypos = iy == ay; 75 76 // Extra precise log calculation 77 // First handle case that x is close to 1 78 float r = 1.0f - as_float(ax); 79 int near1 = __clc_fabs(r) < 0x1.0p-4f; 80 float r2 = r * r; 81 82 // Coefficients are just 1/3, 1/4, 1/5 and 1/6 83 float poly = __clc_mad( 84 r, 85 __clc_mad(r, 86 __clc_mad(r, __clc_mad(r, 0x1.24924ap-3f, 0x1.555556p-3f), 87 0x1.99999ap-3f), 88 0x1.000000p-2f), 89 0x1.555556p-2f); 90 91 poly *= r2 * r; 92 93 float lth_near1 = -r2 * 0.5f; 94 float ltt_near1 = -poly; 95 float lt_near1 = lth_near1 + ltt_near1; 96 float lh_near1 = -r; 97 float l_near1 = lh_near1 + lt_near1; 98 99 // Computations for x not near 1 100 int m = (int)(ax >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; 101 float mf = (float)m; 102 int ixs = as_int(as_float(ax | 0x3f800000) - 1.0f); 103 float mfs = (float)((ixs >> EXPSHIFTBITS_SP32) - 253); 104 int c = m == -127; 105 int ixn = c ? ixs : ax; 106 float mfn = c ? mfs : mf; 107 108 int indx = (ixn & 0x007f0000) + ((ixn & 0x00008000) << 1); 109 110 // F - Y 111 float f = as_float(0x3f000000 | indx) - 112 as_float(0x3f000000 | (ixn & MANTBITS_SP32)); 113 114 indx = indx >> 16; 115 float2 tv = USE_TABLE(log_inv_tbl_ep, indx); 116 float rh = f * tv.s0; 117 float rt = f * tv.s1; 118 r = rh + rt; 119 120 poly = __clc_mad(r, __clc_mad(r, 0x1.0p-2f, 0x1.555556p-2f), 0x1.0p-1f) * 121 (r * r); 122 poly += (rh - r) + rt; 123 124 const float LOG2_HEAD = 0x1.62e000p-1f; // 0.693115234 125 const float LOG2_TAIL = 0x1.0bfbe8p-15f; // 0.0000319461833 126 tv = USE_TABLE(loge_tbl, indx); 127 float lth = -r; 128 float ltt = __clc_mad(mfn, LOG2_TAIL, -poly) + tv.s1; 129 float lt = lth + ltt; 130 float lh = __clc_mad(mfn, LOG2_HEAD, tv.s0); 131 float l = lh + lt; 132 133 // Select near 1 or not 134 lth = near1 ? lth_near1 : lth; 135 ltt = near1 ? ltt_near1 : ltt; 136 lt = near1 ? lt_near1 : lt; 137 lh = near1 ? lh_near1 : lh; 138 l = near1 ? l_near1 : l; 139 140 float gh = as_float(as_int(l) & 0xfffff000); 141 float gt = ((ltt - (lt - lth)) + ((lh - l) + lt)) + (l - gh); 142 143 float yh = as_float(iy & 0xfffff000); 144 145 float yt = y - yh; 146 147 float ylogx_s = __clc_mad(gt, yh, __clc_mad(gh, yt, yt * gt)); 148 float ylogx = __clc_mad(yh, gh, ylogx_s); 149 float ylogx_t = __clc_mad(yh, gh, -ylogx) + ylogx_s; 150 151 // Extra precise exp of ylogx 152 // 64/log2 : 92.332482616893657 153 const float R_64_BY_LOG2 = 0x1.715476p+6f; 154 int n = convert_int(ylogx * R_64_BY_LOG2); 155 float nf = (float)n; 156 157 int j = n & 0x3f; 158 m = n >> 6; 159 int m2 = m << EXPSHIFTBITS_SP32; 160 // log2/64 lead: 0.0108032227 161 const float R_LOG2_BY_64_LD = 0x1.620000p-7f; 162 // log2/64 tail: 0.0000272020388 163 const float R_LOG2_BY_64_TL = 0x1.c85fdep-16f; 164 r = __clc_mad(nf, -R_LOG2_BY_64_TL, __clc_mad(nf, -R_LOG2_BY_64_LD, ylogx)) + 165 ylogx_t; 166 167 // Truncated Taylor series for e^r 168 poly = __clc_mad(__clc_mad(__clc_mad(r, 0x1.555556p-5f, 0x1.555556p-3f), r, 169 0x1.000000p-1f), 170 r * r, r); 171 172 tv = USE_TABLE(exp_tbl_ep, j); 173 174 float expylogx = 175 __clc_mad(tv.s0, poly, __clc_mad(tv.s1, poly, tv.s1)) + tv.s0; 176 float sexpylogx = expylogx * as_float(0x1 << (m + 149)); 177 float texpylogx = as_float(as_int(expylogx) + m2); 178 expylogx = m < -125 ? sexpylogx : texpylogx; 179 180 // Result is +-Inf if (ylogx + ylogx_t) > 128*log2 181 expylogx = ((ylogx > 0x1.62e430p+6f) | 182 (ylogx == 0x1.62e430p+6f & ylogx_t > -0x1.05c610p-22f)) 183 ? as_float(PINFBITPATT_SP32) 184 : expylogx; 185 186 // Result is 0 if ylogx < -149*log2 187 expylogx = ylogx < -0x1.9d1da0p+6f ? 0.0f : expylogx; 188 189 // Classify y: 190 // inty = 0 means not an integer. 191 // inty = 1 means odd integer. 192 // inty = 2 means even integer. 193 194 int yexp = (int)(ay >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32 + 1; 195 int mask = (1 << (24 - yexp)) - 1; 196 int yodd = ((iy >> (24 - yexp)) & 0x1) != 0; 197 int inty = yodd ? 1 : 2; 198 inty = (iy & mask) != 0 ? 0 : inty; 199 inty = yexp < 1 ? 0 : inty; 200 inty = yexp > 24 ? 2 : inty; 201 202 float signval = as_float((as_uint(expylogx) ^ SIGNBIT_SP32)); 203 expylogx = ((inty == 1) & !xpos) ? signval : expylogx; 204 int ret = as_int(expylogx); 205 206 // Corner case handling 207 ret = ax < 0x3f800000 & iy == NINFBITPATT_SP32 ? PINFBITPATT_SP32 : ret; 208 ret = ax < 0x3f800000 & iy == PINFBITPATT_SP32 ? 0 : ret; 209 ret = ax == 0x3f800000 & ay < PINFBITPATT_SP32 ? 0x3f800000 : ret; 210 ret = ax == 0x3f800000 & ay == PINFBITPATT_SP32 ? QNANBITPATT_SP32 : ret; 211 ret = ax > 0x3f800000 & iy == NINFBITPATT_SP32 ? 0 : ret; 212 ret = ax > 0x3f800000 & iy == PINFBITPATT_SP32 ? PINFBITPATT_SP32 : ret; 213 ret = ((ix < PINFBITPATT_SP32) & (ay == 0)) ? 0x3f800000 : ret; 214 ret = ((ax == PINFBITPATT_SP32) & !ypos) ? 0 : ret; 215 ret = ((ax == PINFBITPATT_SP32) & ypos) ? PINFBITPATT_SP32 : ret; 216 ret = ((ax == PINFBITPATT_SP32) & (iy == PINFBITPATT_SP32)) ? PINFBITPATT_SP32 217 : ret; 218 ret = ((ax == PINFBITPATT_SP32) & (ay == 0)) ? QNANBITPATT_SP32 : ret; 219 ret = ((ax == 0) & !ypos) ? PINFBITPATT_SP32 : ret; 220 ret = ((ax == 0) & ypos) ? 0 : ret; 221 ret = ((ax == 0) & (ay == 0)) ? QNANBITPATT_SP32 : ret; 222 ret = ((ax != 0) & !xpos) ? QNANBITPATT_SP32 : ret; 223 ret = ax > PINFBITPATT_SP32 ? ix : ret; 224 ret = ay > PINFBITPATT_SP32 ? iy : ret; 225 226 return as_float(ret); 227} 228_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_powr, float, float) 229 230#ifdef cl_khr_fp64 231_CLC_DEF _CLC_OVERLOAD double __clc_powr(double x, double y) { 232 const double real_log2_tail = 5.76999904754328540596e-08; 233 const double real_log2_lead = 6.93147122859954833984e-01; 234 235 long ux = as_long(x); 236 long ax = ux & (~SIGNBIT_DP64); 237 int xpos = ax == ux; 238 239 long uy = as_long(y); 240 long ay = uy & (~SIGNBIT_DP64); 241 int ypos = ay == uy; 242 243 // Extended precision log 244 double v, vt; 245 { 246 int exp = (int)(ax >> 52) - 1023; 247 int mask_exp_1023 = exp == -1023; 248 double xexp = (double)exp; 249 long mantissa = ax & 0x000FFFFFFFFFFFFFL; 250 251 long temp_ux = as_long(as_double(0x3ff0000000000000L | mantissa) - 1.0); 252 exp = ((temp_ux & 0x7FF0000000000000L) >> 52) - 2045; 253 double xexp1 = (double)exp; 254 long mantissa1 = temp_ux & 0x000FFFFFFFFFFFFFL; 255 256 xexp = mask_exp_1023 ? xexp1 : xexp; 257 mantissa = mask_exp_1023 ? mantissa1 : mantissa; 258 259 long rax = (mantissa & 0x000ff00000000000) + 260 ((mantissa & 0x0000080000000000) << 1); 261 int index = rax >> 44; 262 263 double F = as_double(rax | 0x3FE0000000000000L); 264 double Y = as_double(mantissa | 0x3FE0000000000000L); 265 double f = F - Y; 266 double2 tv = USE_TABLE(log_f_inv_tbl, index); 267 double log_h = tv.s0; 268 double log_t = tv.s1; 269 double f_inv = (log_h + log_t) * f; 270 double r1 = as_double(as_long(f_inv) & 0xfffffffff8000000L); 271 double r2 = fma(-F, r1, f) * (log_h + log_t); 272 double r = r1 + r2; 273 274 double poly = fma( 275 r, fma(r, fma(r, fma(r, 1.0 / 7.0, 1.0 / 6.0), 1.0 / 5.0), 1.0 / 4.0), 276 1.0 / 3.0); 277 poly = poly * r * r * r; 278 279 double hr1r1 = 0.5 * r1 * r1; 280 double poly0h = r1 + hr1r1; 281 double poly0t = r1 - poly0h + hr1r1; 282 poly = fma(r1, r2, fma(0.5 * r2, r2, poly)) + r2 + poly0t; 283 284 tv = USE_TABLE(powlog_tbl, index); 285 log_h = tv.s0; 286 log_t = tv.s1; 287 288 double resT_t = fma(xexp, real_log2_tail, +log_t) - poly; 289 double resT = resT_t - poly0h; 290 double resH = fma(xexp, real_log2_lead, log_h); 291 double resT_h = poly0h; 292 293 double H = resT + resH; 294 double H_h = as_double(as_long(H) & 0xfffffffff8000000L); 295 double T = (resH - H + resT) + (resT_t - (resT + resT_h)) + (H - H_h); 296 H = H_h; 297 298 double y_head = as_double(uy & 0xfffffffff8000000L); 299 double y_tail = y - y_head; 300 301 double temp = fma(y_tail, H, fma(y_head, T, y_tail * T)); 302 v = fma(y_head, H, temp); 303 vt = fma(y_head, H, -v) + temp; 304 } 305 306 // Now calculate exp of (v,vt) 307 308 double expv; 309 { 310 const double max_exp_arg = 709.782712893384; 311 const double min_exp_arg = -745.1332191019411; 312 const double sixtyfour_by_lnof2 = 92.33248261689366; 313 const double lnof2_by_64_head = 0.010830424260348081; 314 const double lnof2_by_64_tail = -4.359010638708991e-10; 315 316 double temp = v * sixtyfour_by_lnof2; 317 int n = (int)temp; 318 double dn = (double)n; 319 int j = n & 0x0000003f; 320 int m = n >> 6; 321 322 double2 tv = USE_TABLE(two_to_jby64_ep_tbl, j); 323 double f1 = tv.s0; 324 double f2 = tv.s1; 325 double f = f1 + f2; 326 327 double r1 = fma(dn, -lnof2_by_64_head, v); 328 double r2 = dn * lnof2_by_64_tail; 329 double r = (r1 + r2) + vt; 330 331 double q = fma( 332 r, 333 fma(r, 334 fma(r, 335 fma(r, 1.38889490863777199667e-03, 8.33336798434219616221e-03), 336 4.16666666662260795726e-02), 337 1.66666666665260878863e-01), 338 5.00000000000000008883e-01); 339 q = fma(r * r, q, r); 340 341 expv = fma(f, q, f2) + f1; 342 expv = ldexp(expv, m); 343 344 expv = v > max_exp_arg ? as_double(0x7FF0000000000000L) : expv; 345 expv = v < min_exp_arg ? 0.0 : expv; 346 } 347 348 // See whether y is an integer. 349 // inty = 0 means not an integer. 350 // inty = 1 means odd integer. 351 // inty = 2 means even integer. 352 353 int inty; 354 { 355 int yexp = (int)(ay >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64 + 1; 356 inty = yexp < 1 ? 0 : 2; 357 inty = yexp > 53 ? 2 : inty; 358 long mask = (1L << (53 - yexp)) - 1L; 359 int inty1 = (((ay & ~mask) >> (53 - yexp)) & 1L) == 1L ? 1 : 2; 360 inty1 = (ay & mask) != 0 ? 0 : inty1; 361 inty = !(yexp < 1) & !(yexp > 53) ? inty1 : inty; 362 } 363 364 expv *= ((inty == 1) & !xpos) ? -1.0 : 1.0; 365 366 long ret = as_long(expv); 367 368 // Now all the edge cases 369 ret = ax < 0x3ff0000000000000L & uy == NINFBITPATT_DP64 ? PINFBITPATT_DP64 370 : ret; 371 ret = ax < 0x3ff0000000000000L & uy == PINFBITPATT_DP64 ? 0L : ret; 372 ret = ax == 0x3ff0000000000000L & ay < PINFBITPATT_DP64 ? 0x3ff0000000000000L 373 : ret; 374 ret = ax == 0x3ff0000000000000L & ay == PINFBITPATT_DP64 ? QNANBITPATT_DP64 375 : ret; 376 ret = ax > 0x3ff0000000000000L & uy == NINFBITPATT_DP64 ? 0L : ret; 377 ret = ax > 0x3ff0000000000000L & uy == PINFBITPATT_DP64 ? PINFBITPATT_DP64 378 : ret; 379 ret = ux < PINFBITPATT_DP64 & ay == 0L ? 0x3ff0000000000000L : ret; 380 ret = ((ax == PINFBITPATT_DP64) & !ypos) ? 0L : ret; 381 ret = ((ax == PINFBITPATT_DP64) & ypos) ? PINFBITPATT_DP64 : ret; 382 ret = ((ax == PINFBITPATT_DP64) & (uy == PINFBITPATT_DP64)) ? PINFBITPATT_DP64 383 : ret; 384 ret = ((ax == PINFBITPATT_DP64) & (ay == 0L)) ? QNANBITPATT_DP64 : ret; 385 ret = ((ax == 0L) & !ypos) ? PINFBITPATT_DP64 : ret; 386 ret = ((ax == 0L) & ypos) ? 0L : ret; 387 ret = ((ax == 0L) & (ay == 0L)) ? QNANBITPATT_DP64 : ret; 388 ret = ((ax != 0L) & !xpos) ? QNANBITPATT_DP64 : ret; 389 ret = ax > PINFBITPATT_DP64 ? ux : ret; 390 ret = ay > PINFBITPATT_DP64 ? uy : ret; 391 392 return as_double(ret); 393} 394_CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_powr, double, double) 395#endif 396