| /* |
| * 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_rootn(float x, int ny) |
| { |
| float y = MATH_RECIP((float)ny); |
| |
| 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 fny = (float)ny; |
| float fnyh = as_float(as_int(fny) & 0xfffff000); |
| float fnyt = (float)(ny - (int)fnyh); |
| float yt = MATH_DIVIDE(mad(-fnyt, yh, mad(-fnyh, yh, 1.0f)), fny); |
| |
| 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 = __clc_fp32_subnormals_supported() ? expylogx * as_float(0x1 << (m + 149)) : 0.0f; |
| |
| 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 inty = 2 - (ny & 1); |
| |
| 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 == 2)) ? QNANBITPATT_SP32 : ret; |
| int xinf = xpos ? PINFBITPATT_SP32 : NINFBITPATT_SP32; |
| ret = ((ax == 0) & !ypos & (inty == 1)) ? xinf : ret; |
| ret = ((ax == 0) & !ypos & (inty == 2)) ? PINFBITPATT_SP32 : ret; |
| ret = ((ax == 0) & ypos & (inty == 2)) ? 0 : ret; |
| int xzero = xpos ? 0 : 0x80000000; |
| ret = ((ax == 0) & ypos & (inty == 1)) ? xzero : ret; |
| ret = ((ix == NINFBITPATT_SP32) & ypos & (inty == 1)) ? NINFBITPATT_SP32 : ret; |
| ret = ((ix == NINFBITPATT_SP32) & !ypos & (inty == 1)) ? 0x80000000 : ret; |
| ret = ((ix == PINFBITPATT_SP32) & !ypos) ? 0 : ret; |
| ret = ((ix == PINFBITPATT_SP32) & ypos) ? PINFBITPATT_SP32 : ret; |
| ret = ax > PINFBITPATT_SP32 ? ix : ret; |
| ret = ny == 0 ? QNANBITPATT_SP32 : ret; |
| |
| return as_float(ret); |
| } |
| _CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, float, __clc_rootn, float, int) |
| |
| #ifdef cl_khr_fp64 |
| _CLC_DEF _CLC_OVERLOAD double __clc_rootn(double x, int ny) |
| { |
| const double real_log2_tail = 5.76999904754328540596e-08; |
| const double real_log2_lead = 6.93147122859954833984e-01; |
| |
| double dny = (double)ny; |
| double y = 1.0 / dny; |
| |
| 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 fnyh = as_double(as_long(dny) & 0xfffffffffff00000); |
| double fnyt = (double)(ny - (int)fnyh); |
| y_tail = fma(-fnyt, y_head, fma(-fnyh, y_head, 1.0))/ dny; |
| |
| 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 = 2 - (ny & 1); |
| |
| expv *= ((inty == 1) & !xpos) ? -1.0 : 1.0; |
| |
| long ret = as_long(expv); |
| |
| // Now all the edge cases |
| ret = (!xpos & (inty == 2)) ? QNANBITPATT_DP64 : ret; |
| 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 ? 0L : 0x8000000000000000L; |
| ret = ((ax == 0L) & ypos & (inty == 1)) ? xzero : ret; |
| ret = ((ux == NINFBITPATT_DP64) & ypos & (inty == 1)) ? NINFBITPATT_DP64 : ret; |
| ret = ((ux == NINFBITPATT_DP64) & !ypos & (inty == 1)) ? 0x8000000000000000L : 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 ? QNANBITPATT_DP64 : ret; |
| return as_double(ret); |
| } |
| _CLC_BINARY_VECTORIZE(_CLC_DEF _CLC_OVERLOAD, double, __clc_rootn, double, int) |
| #endif |