diff options
Diffstat (limited to 'usr/src/lib/libmvec/common/__vpowf.c')
| -rw-r--r-- | usr/src/lib/libmvec/common/__vpowf.c | 824 |
1 files changed, 824 insertions, 0 deletions
diff --git a/usr/src/lib/libmvec/common/__vpowf.c b/usr/src/lib/libmvec/common/__vpowf.c new file mode 100644 index 0000000000..93ba70e7e9 --- /dev/null +++ b/usr/src/lib/libmvec/common/__vpowf.c @@ -0,0 +1,824 @@ +/* + * CDDL HEADER START + * + * The contents of this file are subject to the terms of the + * Common Development and Distribution License (the "License"). + * You may not use this file except in compliance with the License. + * + * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE + * or http://www.opensolaris.org/os/licensing. + * See the License for the specific language governing permissions + * and limitations under the License. + * + * When distributing Covered Code, include this CDDL HEADER in each + * file and include the License file at usr/src/OPENSOLARIS.LICENSE. + * If applicable, add the following below this CDDL HEADER, with the + * fields enclosed by brackets "[]" replaced with your own identifying + * information: Portions Copyright [yyyy] [name of copyright owner] + * + * CDDL HEADER END + */ + +/* + * Copyright 2011 Nexenta Systems, Inc. All rights reserved. + */ +/* + * Copyright 2006 Sun Microsystems, Inc. All rights reserved. + * Use is subject to license terms. + */ + +#ifdef __RESTRICT +#define restrict _Restrict +#else +#define restrict +#endif + +/* float powf(float x, float y) + * + * Method : + * 1. Special cases: + * for (anything) ** 0 => 1 + * for (anything) ** NaN => QNaN + invalid + * for NaN ** (anything) => QNaN + invalid + * for +-1 ** +-Inf => QNaN + invalid + * for +-(|x| < 1) ** +Inf => +0 + * for +-(|x| < 1) ** -Inf => +Inf + * for +-(|x| > 1) ** +Inf => +Inf + * for +-(|x| > 1) ** -Inf => +0 + * for +Inf ** (negative) => +0 + * for +Inf ** (positive) => +Inf + * for -Inf ** (negative except odd integer) => +0 + * for -Inf ** (negative odd integer) => -0 + * for -Inf ** (positive except odd integer) => +Inf + * for -Inf ** (positive odd integer) => -Inf + * for (negative) ** (non-integer) => QNaN + invalid + * for +0 ** (negative) => +Inf + overflow + * for +0 ** (positive) => +0 + * for -0 ** (negative except odd integer) => +Inf + overflow + * for -0 ** (negative odd integer) => -Inf + overflow + * for -0 ** (positive except odd integer) => +0 + * for -0 ** (positive odd integer) => -0 + * 2. Computes x**y from: + * x**y = 2**(y*log2(x)) = 2**(w/256), where w = 256*log2(|x|)*y. + * 3. Computes w = 256 * log2(|x|) * y from + * |x| = m * 2**n => log2(|x|) = n + log2(m). + * Let m = m0 + dm, where m0 = 1 + k / 128, + * k = [0, 128], + * dm = [-1/256, 1/256]. + * Then 256*log2(m) = 256*log2(m0 + dm) = 256*log2(m0) + 256*log2(1+z), + * where z = dm*(1/m0), z = [-1/258, 1/256]. + * Then + * 1/m0 is looked up in a table of 1, 1/(1+1/128), ..., 1/(1+128/128). + * 256*log2(m0) is looked up in a table of 256*log2(1), 256*log2(1+1/128), + * ..., 256*log2(1+128/128). + * 256*log2(1+z) is computed using approximation: + * 256*log2(1+z) = (((a3*z + a2)*z + a1)*z + a0)*z. + * 3. For w >= 32768 + * then for (negative) ** (odd integer) => -Inf + overflow + * else => +Inf + overflow + * For w <= -38400 + * then for (negative) ** (odd integer) => -0 + underflow + * else => +0 + underflow + * 4. Computes 2 ** (w/256) from: + * 2 ** (w/256) = 2**a * 2**(k/256) * 2**(r/256) + * Where: + * a = int ( w ) >> 8; + * k = int ( w ) & 0xFF; + * r = frac ( w ). + * Note that: + * k = 0, 1, ..., 255; + * r = (-1, 1). + * Then: + * 2**(k/256) is looked up in a table of 2**0, 2**1/256, ... + * 2**(r/256) is computed using approximation: + * 2**(r/256) = a0 + a1 * r + a2 * r**2 + * Multiplication by 2**a is done by adding "a" to + * the biased exponent. + * 5. For (negative) ** (odd integer) => -(2**(w/256)) + * otherwise => 2**(w/256) + * + * Accuracy: + * Max. relative aproximation error < 2**(-37.35) for 256*log2(1+z). + * Max. relative aproximation error < 2**(-29.18) for 2**(r/256). + * All calculations are done in double precision. + * Maximum error observed: less than 0.528 ulp after 700.000.000 + * results. + */ + +static void __vpowfx(int n, float * restrict px, float * restrict py, + int stridey, float * restrict pz, int stridez); + +static void __vpowf_n(int n, float * restrict px, int stridex, float * restrict py, + int stridey, float * restrict pz, int stridez); + +static void __vpowfx_n(int n, double yy, float * restrict py, + int stridey, float * restrict pz, int stridez); + +#pragma no_inline(__vpowfx) +#pragma no_inline(__vpowf_n) +#pragma no_inline(__vpowfx_n) + +static const double __TBL_exp2f[] = { + /* 2^(i/256), i = [0, 255] */ +1.000000000000000000e+00, 1.002711275050202522e+00, 1.005429901112802726e+00, 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+1.869099989941238604e+00, 1.874167634110299963e+00, 1.879249018056560194e+00, +1.884344179032334532e+00, 1.889453154390939194e+00, 1.894575981586965607e+00, +1.899712698176555303e+00, 1.904863341817674138e+00, 1.910027950270389852e+00, +1.915206561397147400e+00, 1.920399213163047403e+00, 1.925605943636125028e+00, +1.930826790987627106e+00, 1.936061793492294347e+00, 1.941310989528640452e+00, +1.946574417579233218e+00, 1.951852116230978318e+00, 1.957144124175400179e+00, +1.962450480208927317e+00, 1.967771223233175881e+00, 1.973106392255234320e+00, +1.978456026387950928e+00, 1.983820164850219392e+00, 1.989198846967266343e+00, +1.994592112170940235e+00 +}; + +static const double __TBL_log2f[] = { + /* __TBL_log2f[2*i] = 256*log2(1+i/128), i = [0, 128] */ + /* __TBL_log2f[2*i+1] = 2**(-23)/(1+i/128), i = [0, 128] */ +0.000000000000000000e+00, 1.192092895507812500e-07, 2.874177388353054585e+00, +1.182851865310077503e-07, 5.726160135284354524e+00, 1.173753004807692373e-07, 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2.099658143782880586e+02, 6.751676576327433535e-08, +2.115964127464742432e+02, 6.721933507709251725e-08, 2.132198436261738550e+02, +6.692451343201754014e-08, 2.148361697528176535e+02, 6.663226664847161225e-08, +2.164454530417600608e+02, 6.634256114130434863e-08, 2.180477546025107358e+02, +6.605536390692640687e-08, 2.196431347526584545e+02, 6.577064251077586116e-08, +2.212316530314957390e+02, 6.548836507510729591e-08, 2.228133682133515663e+02, +6.520850026709402365e-08, 2.243883383206399174e+02, 6.493101728723404362e-08, +2.259566206366313565e+02, 6.465588585805084723e-08, 2.275182717179543204e+02, +6.438307621308016336e-08, 2.290733474068335340e+02, 6.411255908613445100e-08, +2.306219028430716378e+02, 6.384430570083681460e-08, 2.321639924757807307e+02, +6.357828776041666578e-08, 2.336996700748701699e+02, 6.331447743775933615e-08, +2.352289887422961954e+02, 6.305284736570248109e-08, 2.367520009230799189e+02, +6.279337062757202180e-08, 2.382687584160988763e+02, 6.253602074795082293e-08, +2.397793123846580556e+02, 6.228077168367347501e-08, 2.412837133668454044e+02, +6.202759781504065697e-08, 2.427820112856774699e+02, 6.177647393724696421e-08, +2.442742554590400630e+02, 6.152737525201612732e-08, 2.457604946094287186e+02, +6.128027735943774537e-08, 2.472407768734942692e+02, 6.103515625000000127e-08, +2.487151498113976231e+02, 6.079198829681274795e-08, 2.501836604159786077e+02, +6.055075024801586965e-08, 2.516463551217433974e+02, 6.031141921936758485e-08, +2.531032798136744475e+02, 6.007397268700787318e-08, 2.545544798358676246e+02, +5.983838848039215603e-08, 2.560000000000000000e+02, 5.960464477539062500e-08 +}; + +static const double __TBL_expfb[] = { +7.006492321624085355e-46, 1.401298464324817071e-45, 2.802596928649634142e-45, +5.605193857299268284e-45, 1.121038771459853657e-44, 2.242077542919707313e-44, +4.484155085839414627e-44, 8.968310171678829254e-44, 1.793662034335765851e-43, +3.587324068671531702e-43, 7.174648137343063403e-43, 1.434929627468612681e-42, +2.869859254937225361e-42, 5.739718509874450723e-42, 1.147943701974890145e-41, +2.295887403949780289e-41, 4.591774807899560578e-41, 9.183549615799121156e-41, +1.836709923159824231e-40, 3.673419846319648462e-40, 7.346839692639296925e-40, +1.469367938527859385e-39, 2.938735877055718770e-39, 5.877471754111437540e-39, +1.175494350822287508e-38, 2.350988701644575016e-38, 4.701977403289150032e-38, +9.403954806578300064e-38, 1.880790961315660013e-37, 3.761581922631320025e-37, +7.523163845262640051e-37, 1.504632769052528010e-36, 3.009265538105056020e-36, +6.018531076210112041e-36, 1.203706215242022408e-35, 2.407412430484044816e-35, +4.814824860968089633e-35, 9.629649721936179265e-35, 1.925929944387235853e-34, +3.851859888774471706e-34, 7.703719777548943412e-34, 1.540743955509788682e-33, +3.081487911019577365e-33, 6.162975822039154730e-33, 1.232595164407830946e-32, +2.465190328815661892e-32, 4.930380657631323784e-32, 9.860761315262647568e-32, +1.972152263052529514e-31, 3.944304526105059027e-31, 7.888609052210118054e-31, +1.577721810442023611e-30, 3.155443620884047222e-30, 6.310887241768094443e-30, +1.262177448353618889e-29, 2.524354896707237777e-29, 5.048709793414475555e-29, +1.009741958682895111e-28, 2.019483917365790222e-28, 4.038967834731580444e-28, +8.077935669463160887e-28, 1.615587133892632177e-27, 3.231174267785264355e-27, +6.462348535570528710e-27, 1.292469707114105742e-26, 2.584939414228211484e-26, +5.169878828456422968e-26, 1.033975765691284594e-25, 2.067951531382569187e-25, +4.135903062765138374e-25, 8.271806125530276749e-25, 1.654361225106055350e-24, +3.308722450212110699e-24, 6.617444900424221399e-24, 1.323488980084844280e-23, +2.646977960169688560e-23, 5.293955920339377119e-23, 1.058791184067875424e-22, +2.117582368135750848e-22, 4.235164736271501695e-22, 8.470329472543003391e-22, +1.694065894508600678e-21, 3.388131789017201356e-21, 6.776263578034402713e-21, +1.355252715606880543e-20, 2.710505431213761085e-20, 5.421010862427522170e-20, +1.084202172485504434e-19, 2.168404344971008868e-19, 4.336808689942017736e-19, +8.673617379884035472e-19, 1.734723475976807094e-18, 3.469446951953614189e-18, +6.938893903907228378e-18, 1.387778780781445676e-17, 2.775557561562891351e-17, +5.551115123125782702e-17, 1.110223024625156540e-16, 2.220446049250313081e-16, +4.440892098500626162e-16, 8.881784197001252323e-16, 1.776356839400250465e-15, +3.552713678800500929e-15, 7.105427357601001859e-15, 1.421085471520200372e-14, +2.842170943040400743e-14, 5.684341886080801487e-14, 1.136868377216160297e-13, +2.273736754432320595e-13, 4.547473508864641190e-13, 9.094947017729282379e-13, +1.818989403545856476e-12, 3.637978807091712952e-12, 7.275957614183425903e-12, +1.455191522836685181e-11, 2.910383045673370361e-11, 5.820766091346740723e-11, +1.164153218269348145e-10, 2.328306436538696289e-10, 4.656612873077392578e-10, +9.313225746154785156e-10, 1.862645149230957031e-09, 3.725290298461914062e-09, +7.450580596923828125e-09, 1.490116119384765625e-08, 2.980232238769531250e-08, +5.960464477539062500e-08, 1.192092895507812500e-07, 2.384185791015625000e-07, +4.768371582031250000e-07, 9.536743164062500000e-07, 1.907348632812500000e-06, +3.814697265625000000e-06, 7.629394531250000000e-06, 1.525878906250000000e-05, +3.051757812500000000e-05, 6.103515625000000000e-05, 1.220703125000000000e-04, +2.441406250000000000e-04, 4.882812500000000000e-04, 9.765625000000000000e-04, +1.953125000000000000e-03, 3.906250000000000000e-03, 7.812500000000000000e-03, +1.562500000000000000e-02, 3.125000000000000000e-02, 6.250000000000000000e-02, +1.250000000000000000e-01, 2.500000000000000000e-01, 5.000000000000000000e-01, +1.000000000000000000e+00, 2.000000000000000000e+00, 4.000000000000000000e+00, +8.000000000000000000e+00, 1.600000000000000000e+01, 3.200000000000000000e+01, +6.400000000000000000e+01, 1.280000000000000000e+02, 2.560000000000000000e+02, +5.120000000000000000e+02, 1.024000000000000000e+03, 2.048000000000000000e+03, +4.096000000000000000e+03, 8.192000000000000000e+03, 1.638400000000000000e+04, +3.276800000000000000e+04, 6.553600000000000000e+04, 1.310720000000000000e+05, +2.621440000000000000e+05, 5.242880000000000000e+05, 1.048576000000000000e+06, +2.097152000000000000e+06, 4.194304000000000000e+06, 8.388608000000000000e+06, +1.677721600000000000e+07, 3.355443200000000000e+07, 6.710886400000000000e+07, +1.342177280000000000e+08, 2.684354560000000000e+08, 5.368709120000000000e+08, +1.073741824000000000e+09, 2.147483648000000000e+09, 4.294967296000000000e+09, +8.589934592000000000e+09, 1.717986918400000000e+10, 3.435973836800000000e+10, +6.871947673600000000e+10, 1.374389534720000000e+11, 2.748779069440000000e+11, +5.497558138880000000e+11, 1.099511627776000000e+12, 2.199023255552000000e+12, +4.398046511104000000e+12, 8.796093022208000000e+12, 1.759218604441600000e+13, +3.518437208883200000e+13, 7.036874417766400000e+13, 1.407374883553280000e+14, +2.814749767106560000e+14, 5.629499534213120000e+14, 1.125899906842624000e+15, +2.251799813685248000e+15, 4.503599627370496000e+15, 9.007199254740992000e+15, +1.801439850948198400e+16, 3.602879701896396800e+16, 7.205759403792793600e+16, +1.441151880758558720e+17, 2.882303761517117440e+17, 5.764607523034234880e+17, +1.152921504606846976e+18, 2.305843009213693952e+18, 4.611686018427387904e+18, +9.223372036854775808e+18, 1.844674407370955162e+19, 3.689348814741910323e+19, +7.378697629483820646e+19, 1.475739525896764129e+20, 2.951479051793528259e+20, +5.902958103587056517e+20, 1.180591620717411303e+21, 2.361183241434822607e+21, +4.722366482869645214e+21, 9.444732965739290427e+21, 1.888946593147858085e+22, +3.777893186295716171e+22, 7.555786372591432342e+22, 1.511157274518286468e+23, +3.022314549036572937e+23, 6.044629098073145874e+23, 1.208925819614629175e+24, +2.417851639229258349e+24, 4.835703278458516699e+24, 9.671406556917033398e+24, +1.934281311383406680e+25, 3.868562622766813359e+25, 7.737125245533626718e+25, +1.547425049106725344e+26, 3.094850098213450687e+26, 6.189700196426901374e+26, +1.237940039285380275e+27, 2.475880078570760550e+27, 4.951760157141521100e+27, +9.903520314283042199e+27, 1.980704062856608440e+28, 3.961408125713216880e+28, +7.922816251426433759e+28, 1.584563250285286752e+29, 3.169126500570573504e+29, +6.338253001141147007e+29, 1.267650600228229401e+30, 2.535301200456458803e+30, +5.070602400912917606e+30, 1.014120480182583521e+31, 2.028240960365167042e+31, +4.056481920730334085e+31, 8.112963841460668170e+31, 1.622592768292133634e+32, +3.245185536584267268e+32, 6.490371073168534536e+32, 1.298074214633706907e+33, +2.596148429267413814e+33, 5.192296858534827629e+33, 1.038459371706965526e+34, +2.076918743413931051e+34, 4.153837486827862103e+34, 8.307674973655724206e+34, +1.661534994731144841e+35, 3.323069989462289682e+35, 6.646139978924579365e+35, +1.329227995784915873e+36, 2.658455991569831746e+36, 5.316911983139663492e+36, +1.063382396627932698e+37, 2.126764793255865397e+37, 4.253529586511730793e+37, +8.507059173023461587e+37, 1.701411834604692317e+38, 3.402823669209384635e+38 +}; + +static const double + KA3 = -3.60659926599003171364e-01*256.0, + KA2 = 4.80902715189356683026e-01*256.0, + KA1 = -7.21347520569871841065e-01*256.0, + KA0 = 1.44269504088069658645e+00*256.0, + KB2 = 3.66556671660783833261e-06, + KB1 = 2.70760782821392980564e-03, + DONE = 1.0, + HTHRESH = 32768.0, + LTHRESH = -38400.0; + +#define RETURN(ret) \ +{ \ + *pz = (ret); \ + px += stridex; \ + py += stridey; \ + pz += stridez; \ + if (n_n == 0) \ + { \ + spx = px; spy = py; spz = pz; \ + continue; \ + } \ + n--; \ + break; \ +} + +void +__vpowf(int n, float * restrict px, int stridex, float * restrict py, + int stridey, float * restrict pz, int stridez) +{ + float *spx, *spy, *spz; + double y0, yy0; + long long di0; + unsigned ux, sx, uy, ay, ax0; + int exp, i0, ind0, exp0, yisint0, n_n; + +#ifndef NOPOWFIX + if (stridex == 0) + { + unsigned hx = *(unsigned*)px; + + if ((hx >= 0x00800000) && /* x not zero or subnormal */ + (hx < 0x7f800000) && /* x not inf, nan or negative sign bit */ + (hx != 0x3f800000)) /* x not 1 */ + { + __vpowfx(n, px, py, stridey, pz, stridez); + return; + } + } +#endif + + while (n > 0) + { + n_n = 0; + spx = px; + spy = py; + spz = pz; + for (; n > 0 ; n--) + { + uy = *(unsigned int*)py; + ux = *(unsigned int*)px; + ay = uy & 0x7fffffff; + ax0 = ux & 0x7fffffff; + sx = ux >> 31; + yisint0 = 0; /* Y - non-integer */ + + /* |X| or |Y| = Inf,Nan */ + if (ax0 >= 0x7f800000 || ay >= 0x7f800000) + { + if (ay == 0) + RETURN(1.0f) /* pow(X,0) */ + /* |X| or |Y| = Nan */ + if (ax0 > 0x7f800000 || ay > 0x7f800000) + RETURN (*px + *py) + if (ay == 0x7f800000) /* |Y| = Inf */ + { + float fy; + if (ax0 == 0x3f800000) + fy = *py - *py; /* +-1 ** +-Inf = NaN */ + else + fy = ((ax0 < 0x3f800000) != (uy >> 31)) ? 0.0f : *(float*) &ay; + RETURN(fy) + } + if (sx) /* X = -Inf */ + { + exp = ay >> 23; + if (exp >= 0x97) /* |Y| >= 2^24 */ + yisint0 = 2; /* Y - even */ + else if (exp >= 0x7f) /* |Y| >= 1 */ + { + i0 = ay >> ((0x7f + 23) - exp); + if ((i0 << ((0x7f + 23) - exp)) == ay) + yisint0 = 2 - (i0 & 1); + } + } + if (uy >> 31) + ax0 = 0; + ax0 += yisint0 << 31; + RETURN(*(float*)&ax0) + } + + if ((int)ux < 0x00800000) /* X = denormal or negative */ + { + if (ay == 0) + RETURN(1.0f) /* pow(X,0) */ + exp0 = (ax0 >> 23) - 127; + + if ((int)ax0 < 0x00800000) /* X = denormal */ + { + *((float*) &ax0) = (float) (int)ax0; + exp0 = (ax0 >> 23) - (127 + 149); + } + + if ((int)ux <= 0) /* X <= 0 */ + { + exp = ay >> 23; + if (exp >= 0x97) /* |Y| >= 2^24 */ + yisint0 = 2; /* Y - even */ + else if (exp >= 0x7f) /* |Y| >= 1 */ + { + i0 = ay >> ((0x7f + 23) - exp); + if ((i0 << ((0x7f + 23) - exp)) == ay) + yisint0 = 2 - (i0 & 1); + } + + if (ax0 == 0) /* pow(0,Y) */ + { + float fy; + fy = (uy >> 31) ? 1.0f / 0.0f : 0.0f; + if (sx & yisint0) + fy = -fy; + RETURN(fy) + } + + if (yisint0 == 0) /* pow(neg,non-integer) */ + RETURN(0.0f / 0.0f) /* NaN */ + } + + /* perform yy0 = 256*log2(xi)*yi */ + ax0 &= 0x007fffff; + i0 = (ax0 + 0x8000) & 0xffff0000; + ind0 = i0 >> 15; + i0 = ax0 - i0; + y0 = (double) i0 * __TBL_log2f[ind0 + 1]; + yy0 = __TBL_log2f[ind0] + (double) (exp0 << 8); + yy0 += (((KA3 * y0 + KA2) * y0 + KA1) * y0 + KA0) * y0; + yy0 = (double)py[0] * yy0; + + /* perform 2 ** (yy0/256) */ + if (yy0 >= HTHRESH) + yy0 = HTHRESH; + if (yy0 <= LTHRESH) + yy0 = LTHRESH; + ind0 = (int) yy0; + y0 = yy0 - (double)ind0; + yy0 = (KB2 * y0 + KB1) * y0 + DONE; + di0 = ((long long)((ind0 >> 8) + (yisint0 << 11))) << 52; + di0 += ((long long*)__TBL_exp2f)[ind0 & 255]; + RETURN((float) (yy0 * *(double*)&di0)) + } + px += stridex; + py += stridey; + pz += stridez; + n_n++; + } + if (n_n > 0) + __vpowf_n(n_n, spx, stridex, spy, stridey, spz, stridez); + } +} + + +static void +__vpowf_n(int n, float * restrict px, int stridex, float * restrict py, + int stridey, float * restrict pz, int stridez) +{ + double y0, yy0; + double di0; + int ind0, i0, exp0; + unsigned ax0; + double y1, yy1; + double di1; + int ind1, i1, exp1; + unsigned ax1; + double y2, yy2; + double di2; + int ind2, i2, exp2; + unsigned ax2; + + for (; n > 2 ; n -= 3) + { + /* perform yy0 = 256*log2(xi)*yi */ + ax0 = ((int*)px)[0]; + px += stridex; + ax1 = ((int*)px)[0]; + px += stridex; + ax2 = ((int*)px)[0]; + px += stridex; + exp0 = ((ax0 & 0x7fffffff) >> 23) - 127; + exp1 = ((ax1 & 0x7fffffff) >> 23) - 127; + exp2 = ((ax2 & 0x7fffffff) >> 23) - 127; + ax0 &= 0x007fffff; + ax1 &= 0x007fffff; + ax2 &= 0x007fffff; + i0 = (ax0 + 0x8000) & 0xffff0000; + i1 = (ax1 + 0x8000) & 0xffff0000; + i2 = (ax2 + 0x8000) & 0xffff0000; + ind0 = i0 >> 15; + ind1 = i1 >> 15; + ind2 = i2 >> 15; + i0 = ax0 - i0; + i1 = ax1 - i1; + i2 = ax2 - i2; + y0 = (double) i0 * __TBL_log2f[ind0 + 1]; + y1 = (double) i1 * __TBL_log2f[ind1 + 1]; + y2 = (double) i2 * __TBL_log2f[ind2 + 1]; + yy0 = __TBL_log2f[ind0] + (double) (exp0 << 8); + yy1 = __TBL_log2f[ind1] + (double) (exp1 << 8); + yy2 = __TBL_log2f[ind2] + (double) (exp2 << 8); + yy0 += (((KA3 * y0 + KA2) * y0 + KA1) * y0 + KA0) * y0; + yy1 += (((KA3 * y1 + KA2) * y1 + KA1) * y1 + KA0) * y1; + yy2 += (((KA3 * y2 + KA2) * y2 + KA1) * y2 + KA0) * y2; + yy0 = (double)py[0] * yy0; + py += stridey; + yy1 = (double)py[0] * yy1; + py += stridey; + yy2 = (double)py[0] * yy2; + py += stridey; + + /* perform 2 ** (yy0/256) */ + if (yy0 >= HTHRESH) + yy0 = HTHRESH; + if (yy0 <= LTHRESH) + yy0 = LTHRESH; + if (yy1 >= HTHRESH) + yy1 = HTHRESH; + if (yy1 <= LTHRESH) + yy1 = LTHRESH; + if (yy2 >= HTHRESH) + yy2 = HTHRESH; + if (yy2 <= LTHRESH) + yy2 = LTHRESH; + + ind0 = (int) yy0; + ind1 = (int) yy1; + ind2 = (int) yy2; + y0 = yy0 - (double)ind0; + y1 = yy1 - (double)ind1; + y2 = yy2 - (double)ind2; + yy0 = (KB2 * y0 + KB1) * y0 + DONE; + yy1 = (KB2 * y1 + KB1) * y1 + DONE; + yy2 = (KB2 * y2 + KB1) * y2 + DONE; + di0 = (__TBL_expfb + 150)[ind0 >> 8]; + di1 = (__TBL_expfb + 150)[ind1 >> 8]; + di2 = (__TBL_expfb + 150)[ind2 >> 8]; + di0 *= __TBL_exp2f[ind0 & 255]; + di1 *= __TBL_exp2f[ind1 & 255]; + di2 *= __TBL_exp2f[ind2 & 255]; + pz[0] = (float) (yy0 * di0); + pz += stridez; + pz[0] = (float) (yy1 * di1); + pz += stridez; + pz[0] = (float) (yy2 * di2); + pz += stridez; + } + + for (; n > 0 ; n--) + { + /* perform yy0 = 256*log2(xi)*yi */ + ax0 = ((int*)px)[0]; + exp0 = ((ax0 & 0x7fffffff) >> 23) - 127; + ax0 &= 0x007fffff; + i0 = (ax0 + 0x8000) & 0xffff0000; + ind0 = i0 >> 15; + i0 = ax0 - i0; + y0 = (double) i0 * __TBL_log2f[ind0 + 1]; + yy0 = __TBL_log2f[ind0] + (double) (exp0 << 8); + yy0 += (((KA3 * y0 + KA2) * y0 + KA1) * y0 + KA0) * y0; + yy0 = (double)py[0] * yy0; + + /* perform 2 ** (yy0/256) */ + if (yy0 >= HTHRESH) + yy0 = HTHRESH; + if (yy0 <= LTHRESH) + yy0 = LTHRESH; + ind0 = (int) yy0; + y0 = yy0 - (double)ind0; + yy0 = (KB2 * y0 + KB1) * y0 + DONE; + di0 = (__TBL_expfb + 150)[ind0 >> 8]; + di0 *= __TBL_exp2f[ind0 & 255]; + pz[0] = (float) (yy0 * di0); + px += stridex; + py += stridey; + pz += stridez; + } +} + + +static void +__vpowfx(int n, float * restrict px, float * restrict py, + int stridey, float * restrict pz, int stridez) +{ + float *spy, *spz; + double yy, y0; + int ind0, exp0, i0, n_n; + unsigned ux, ax, ax0, uy, ay; + + /* perform yy = 256*log2(xi)*yi */ + ux = *(unsigned int*)px; + ax = ux & 0x7fffffff; + exp0 = (ax >> 23) - 127; + ax0 = ux & 0x007fffff; + i0 = (ax0 + 0x8000) & 0xffff0000; + ind0 = i0 >> 15; + i0 = ax0 - i0; + y0 = (double) i0 * __TBL_log2f[ind0 + 1]; + yy = __TBL_log2f[ind0] + (double) (exp0 << 8); + yy += (((KA3 * y0 + KA2) * y0 + KA1) * y0 + KA0) * y0; + + while (n > 0) + { + n_n = 0; + spy = py; + spz = pz; + for (; n > 0 ; n--) + { + uy = *(unsigned int*)py; + ay = uy & 0x7fffffff; + + if (ay >= 0x7f800000) /* |Y| = Inf or Nan */ + { + float fy; + if (ay > 0x7f800000) + fy = *py + *py; /* |Y| = Nan */ + else + fy = ((ax < 0x3f800000) != (uy >> 31)) ? 0.0f : *(float*)&ay; + *pz = fy; + py += stridey; + pz += stridez; + if (n_n == 0) + { + spy = py; + spz = pz; + continue; + } + n--; + break; + } + py += stridey; + pz += stridez; + n_n++; + } + if (n_n > 0) + __vpowfx_n(n_n, yy, spy, stridey, spz, stridez); + } +} + + +static void +__vpowfx_n(int n, double yy, float * restrict py, + int stridey, float * restrict pz, int stridez) +{ + double y0, yy0, di0; + double y1, yy1, di1; + double y2, yy2, di2; + int ind0, ind1, ind2; + + for (; n > 2 ; n-= 3) + { + /* perform 2 ** (yy/256) */ + yy0 = (double)py[0] * yy; + py += stridey; + yy1 = (double)py[0] * yy; + py += stridey; + yy2 = (double)py[0] * yy; + py += stridey; + if (yy0 >= HTHRESH) + yy0 = HTHRESH; + if (yy0 <= LTHRESH) + yy0 = LTHRESH; + if (yy1 >= HTHRESH) + yy1 = HTHRESH; + if (yy1 <= LTHRESH) + yy1 = LTHRESH; + if (yy2 >= HTHRESH) + yy2 = HTHRESH; + if (yy2 <= LTHRESH) + yy2 = LTHRESH; + ind0 = (int) yy0; + ind1 = (int) yy1; + ind2 = (int) yy2; + y0 = yy0 - (double)ind0; + y1 = yy1 - (double)ind1; + y2 = yy2 - (double)ind2; + yy0 = (KB2 * y0 + KB1) * y0 + DONE; + yy1 = (KB2 * y1 + KB1) * y1 + DONE; + yy2 = (KB2 * y2 + KB1) * y2 + DONE; + di0 = (__TBL_expfb + 150)[ind0 >> 8]; + di1 = (__TBL_expfb + 150)[ind1 >> 8]; + di2 = (__TBL_expfb + 150)[ind2 >> 8]; + di0 *= __TBL_exp2f[ind0 & 255]; + di1 *= __TBL_exp2f[ind1 & 255]; + di2 *= __TBL_exp2f[ind2 & 255]; + pz[0] = (float) (yy0 * di0); + pz += stridez; + pz[0] = (float) (yy1 * di1); + pz += stridez; + pz[0] = (float) (yy2 * di2); + pz += stridez; + } + for (; n > 0 ; n--) + { + /* perform 2 ** (yy/256) */ + yy0 = (double)py[0] * yy; + if (yy0 >= HTHRESH) + yy0 = HTHRESH; + if (yy0 <= LTHRESH) + yy0 = LTHRESH; + ind0 = (int) yy0; + y0 = yy0 - (double)ind0; + yy0 = (KB2 * y0 + KB1) * y0 + DONE; + di0 = (__TBL_expfb + 150)[ind0 >> 8]; + di0 *= __TBL_exp2f[ind0 & 255]; + pz[0] = (float) (yy0 * di0); + py += stridey; + pz += stridez; + } +} |