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Diffstat (limited to 'usr/src/lib/libmvec/common/__vrsqrtf.c')
-rw-r--r-- | usr/src/lib/libmvec/common/__vrsqrtf.c | 506 |
1 files changed, 506 insertions, 0 deletions
diff --git a/usr/src/lib/libmvec/common/__vrsqrtf.c b/usr/src/lib/libmvec/common/__vrsqrtf.c new file mode 100644 index 0000000000..54572a8a33 --- /dev/null +++ b/usr/src/lib/libmvec/common/__vrsqrtf.c @@ -0,0 +1,506 @@ +/* + * 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. + */ + +#include "libm_synonyms.h" +#include "libm_inlines.h" + +#ifdef __RESTRICT +#define restrict _Restrict +#else +#define restrict +#endif + +/* float rsqrtf(float x) + * + * Method : + * 1. Special cases: + * for x = NaN => QNaN; + * for x = +Inf => 0; + * for x is negative, -Inf => QNaN + invalid; + * for x = +0 => +Inf + divide-by-zero; + * for x = -0 => -Inf + divide-by-zero. + * 2. Computes reciprocal square root from: + * x = m * 2**n + * Where: + * m = [0.5, 2), + * n = ((exponent + 1) & ~1). + * Then: + * rsqrtf(x) = 1/sqrt( m * 2**n ) = (2 ** (-n/2)) * (1/sqrt(m)) + * 2. Computes 1/sqrt(m) from: + * 1/sqrt(m) = (1/sqrt(m0)) * (1/sqrt(1 + (1/m0)*dm)) + * Where: + * m = m0 + dm, + * m0 = 0.5 * (1 + k/64) for m = [0.5, 0.5+127/256), k = [0, 63]; + * m0 = 1.0 * (0 + k/64) for m = [0.5+127/256, 1.0+127/128), k = [64, 127]; + * Then: + * 1/sqrt(m0), 1/m0 are looked up in a table, + * 1/sqrt(1 + (1/m0)*dm) is computed using approximation: + * 1/sqrt(1 + z) = ((a3 * z + a2) * z + a1) * z + a0 + * where z = [-1/64, 1/64]. + * + * Accuracy: + * The maximum relative error for the approximating + * polynomial is 2**(-27.87). + * Maximum error observed: less than 0.534 ulp for the + * whole float type range. + */ + +#define sqrtf __sqrtf + +extern float sqrtf(float); + +static const double __TBL_rsqrtf[] = { +/* +i = [0,63] + TBL[2*i ] = 1 / (*(double*)&(0x3fe0000000000000ULL + (i << 46))) * 2**-24; + TBL[2*i+1] = 1 / sqrtl(*(double*)&(0x3fe0000000000000ULL + (i << 46))); +i = [64,127] + TBL[2*i ] = 1 / (*(double*)&(0x3fe0000000000000ULL + (i << 46))) * 2**-23; + TBL[2*i+1] = 1 / sqrtl(*(double*)&(0x3fe0000000000000ULL + (i << 46))); +*/ + 1.1920928955078125000e-07, 1.4142135623730951455e+00, + 1.1737530048076923728e-07, 1.4032928308912466786e+00, + 1.1559688683712121533e-07, 1.3926212476455828160e+00, + 1.1387156016791044559e-07, 1.3821894809301762397e+00, + 1.1219697840073529256e-07, 1.3719886811400707760e+00, + 1.1057093523550724772e-07, 1.3620104492139977204e+00, + 1.0899135044642856803e-07, 1.3522468075656264297e+00, + 1.0745626100352112918e-07, 1.3426901732747025253e+00, + 1.0596381293402777190e-07, 1.3333333333333332593e+00, + 1.0451225385273972023e-07, 1.3241694217637887121e+00, + 1.0309992609797297870e-07, 1.3151918984428583315e+00, + 1.0172526041666667320e-07, 1.3063945294843617440e+00, + 1.0038677014802631022e-07, 1.2977713690461003537e+00, + 9.9083045860389616921e-08, 1.2893167424406084542e+00, + 9.7812750400641022247e-08, 1.2810252304406970492e+00, + 9.6574614319620251657e-08, 1.2728916546811681609e+00, + 9.5367431640625005294e-08, 1.2649110640673517647e+00, + 9.4190055941358019463e-08, 1.2570787221094177344e+00, + 9.3041396722560978838e-08, 1.2493900951088485751e+00, + 9.1920416039156631290e-08, 1.2418408411301324890e+00, + 9.0826125372023804482e-08, 1.2344267996967352996e+00, + 8.9757582720588234048e-08, 1.2271439821557927896e+00, + 8.8713889898255812722e-08, 1.2199885626608373279e+00, + 8.7694190014367814875e-08, 1.2129568697262453902e+00, + 8.6697665127840911497e-08, 1.2060453783110545167e+00, + 8.5723534058988761666e-08, 1.1992507023933782762e+00, + 8.4771050347222225457e-08, 1.1925695879998878812e+00, + 8.3839500343406599951e-08, 1.1859989066577618644e+00, + 8.2928201426630432481e-08, 1.1795356492391770864e+00, + 8.2036500336021511923e-08, 1.1731769201708264205e+00, + 8.1163771609042551220e-08, 1.1669199319831564665e+00, + 8.0309416118421050820e-08, 1.1607620001760186046e+00, + 7.9472859700520828922e-08, 1.1547005383792514621e+00, + 7.8653551868556699530e-08, 1.1487330537883810866e+00, + 7.7850964604591830522e-08, 1.1428571428571427937e+00, + 7.7064591224747481298e-08, 1.1370704872299222110e+00, + 7.6293945312500001588e-08, 1.1313708498984760276e+00, + 7.5538559715346535571e-08, 1.1257560715684669095e+00, + 7.4797985600490195040e-08, 1.1202240672224077489e+00, + 7.4071791565533974158e-08, 1.1147728228665882977e+00, + 7.3359562800480773303e-08, 1.1094003924504582947e+00, + 7.2660900297619054173e-08, 1.1041048949477667573e+00, + 7.1975420106132072725e-08, 1.0988845115895122806e+00, + 7.1302752628504667579e-08, 1.0937374832394612945e+00, + 7.0642541956018514597e-08, 1.0886621079036347126e+00, + 6.9994445240825691959e-08, 1.0836567383657542685e+00, + 6.9358132102272723904e-08, 1.0787197799411873955e+00, + 6.8733284065315314719e-08, 1.0738496883424388795e+00, + 6.8119594029017853361e-08, 1.0690449676496975862e+00, + 6.7516765763274335346e-08, 1.0643041683803828867e+00, + 6.6924513432017540145e-08, 1.0596258856520350822e+00, + 6.6342561141304348632e-08, 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1.1057093523550724772e-07, 9.6308682468615358641e-01, + 1.0899135044642856803e-07, 9.5618288746751489704e-01, + 1.0745626100352112918e-07, 9.4942532655508271588e-01, + 1.0596381293402777190e-07, 9.4280904158206335630e-01, + 1.0451225385273972023e-07, 9.3632917756904454620e-01, + 1.0309992609797297870e-07, 9.2998110995055427441e-01, + 1.0172526041666667320e-07, 9.2376043070340119190e-01, + 1.0038677014802631022e-07, 9.1766293548224708854e-01, + 9.9083045860389616921e-08, 9.1168461167710357351e-01, + 9.7812750400641022247e-08, 9.0582162731567661407e-01, + 9.6574614319620251657e-08, 9.0007032074081916306e-01, + 9.5367431640625005294e-08, 8.9442719099991585541e-01, + 9.4190055941358019463e-08, 8.8888888888888883955e-01, + 9.3041396722560978838e-08, 8.8345220859877238162e-01, + 9.1920416039156631290e-08, 8.7811407991752277180e-01, + 9.0826125372023804482e-08, 8.7287156094396955996e-01, + 8.9757582720588234048e-08, 8.6772183127462465535e-01, + 8.8713889898255812722e-08, 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7.3359562800480773303e-08, 7.8446454055273617811e-01, + 7.2660900297619054173e-08, 7.8072005835882651859e-01, + 7.1975420106132072725e-08, 7.7702868988581130782e-01, + 7.1302752628504667579e-08, 7.7338919123653082632e-01, + 7.0642541956018514597e-08, 7.6980035891950104876e-01, + 6.9994445240825691959e-08, 7.6626102817692109959e-01, + 6.9358132102272723904e-08, 7.6277007139647390321e-01, + 6.8733284065315314719e-08, 7.5932639660199918730e-01, + 6.8119594029017853361e-08, 7.5592894601845450619e-01, + 6.7516765763274335346e-08, 7.5257669470687782454e-01, + 6.6924513432017540145e-08, 7.4926864926535519107e-01, + 6.6342561141304348632e-08, 7.4600384659225105199e-01, + 6.5770642510775861156e-08, 7.4278135270820744296e-01, + 6.5208500267094023655e-08, 7.3960026163363878915e-01, + 6.4655885858050847233e-08, 7.3645969431865865307e-01, + 6.4112559086134451001e-08, 7.3335879762256905856e-01, + 6.3578287760416665784e-08, 7.3029674334022143256e-01, + 6.3052847365702481089e-08, 7.2727272727272729291e-01, + 6.2536020747950822927e-08, 7.2428596834014824513e-01, + 6.2027597815040656970e-08, 7.2133570773394584119e-01, + 6.1527375252016127325e-08, 7.1842120810709964029e-01, + 6.1035156250000001271e-08, 7.1554175279993270653e-01, + 6.0550750248015869655e-08, 7.1269664509979835376e-01, + 6.0073972687007873182e-08, 7.0988520753289097165e-01, +}; + +static const unsigned long long LCONST[] = { +0x3feffffffee7f18fULL, /* A0 = 9.99999997962321453275e-01 */ +0xbfdffffffe07e52fULL, /* A1 =-4.99999998166077580600e-01 */ +0x3fd801180ca296d9ULL, /* A2 = 3.75066768969515586277e-01 */ +0xbfd400fc0bbb8e78ULL, /* A3 =-3.12560092408808548438e-01 */ +}; + +static void +__vrsqrtf_n(int n, float * restrict px, int stridex, float * restrict py, int stridey); + +#pragma no_inline(__vrsqrtf_n) + +#define RETURN(ret) \ +{ \ + *py = (ret); \ + py += stridey; \ + if (n_n == 0) \ + { \ + spx = px; spy = py; \ + ax0 = *(int*)px; \ + continue; \ + } \ + n--; \ + break; \ +} + +void +__vrsqrtf(int n, float * restrict px, int stridex, float * restrict py, int stridey) +{ + float *spx, *spy; + int ax0, n_n; + float res; + float FONE = 1.0f, FTWO = 2.0f; + + while (n > 1) + { + n_n = 0; + spx = px; + spy = py; + ax0 = *(int*)px; + for (; n > 1 ; n--) + { + px += stridex; + if (ax0 >= 0x7f800000) /* X = NaN or Inf */ + { + res = *(px - stridex); + RETURN (FONE / res) + } + + py += stridey; + + if (ax0 < 0x00800000) /* X = denormal, zero or negative */ + { + py -= stridey; + res = *(px - stridex); + + if ((ax0 & 0x7fffffff) == 0) /* |X| = zero */ + { + RETURN (FONE / res) + } + else if (ax0 >= 0) /* X = denormal */ + { + double A0 = ((double*)LCONST)[0]; /* 9.99999997962321453275e-01 */ + double A1 = ((double*)LCONST)[1]; /* -4.99999998166077580600e-01 */ + double A2 = ((double*)LCONST)[2]; /* 3.75066768969515586277e-01 */ + double A3 = ((double*)LCONST)[3]; /* -3.12560092408808548438e-01 */ + + double res0, xx0, tbl_div0, tbl_sqrt0; + float fres0; + int iax0, si0, iexp0; + + res = *(int*)&res; + res *= FTWO; + ax0 = *(int*)&res; + iexp0 = ax0 >> 24; + iexp0 = 0x3f + 0x4b - iexp0; + iexp0 = iexp0 << 23; + + si0 = (ax0 >> 13) & 0x7f0; + + tbl_div0 = ((double*)((char*)__TBL_rsqrtf + si0))[0]; + tbl_sqrt0 = ((double*)((char*)__TBL_rsqrtf + si0))[1]; + iax0 = ax0 & 0x7ffe0000; + iax0 = ax0 - iax0; + xx0 = iax0 * tbl_div0; + res0 = tbl_sqrt0 * (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0); + + fres0 = res0; + iexp0 += *(int*)&fres0; + RETURN(*(float*)&iexp0) + } + else /* X = negative */ + { + RETURN (sqrtf(res)) + } + } + n_n++; + ax0 = *(int*)px; + } + if (n_n > 0) + __vrsqrtf_n(n_n, spx, stridex, spy, stridey); + } + + if (n > 0) + { + ax0 = *(int*)px; + + if (ax0 >= 0x7f800000) /* X = NaN or Inf */ + { + res = *px; + *py = FONE / res; + } + else if (ax0 < 0x00800000) /* X = denormal, zero or negative */ + { + res = *px; + + if ((ax0 & 0x7fffffff) == 0) /* |X| = zero */ + { + *py = FONE / res; + } + else if (ax0 >= 0) /* X = denormal */ + { + double A0 = ((double*)LCONST)[0]; /* 9.99999997962321453275e-01 */ + double A1 = ((double*)LCONST)[1]; /* -4.99999998166077580600e-01 */ + double A2 = ((double*)LCONST)[2]; /* 3.75066768969515586277e-01 */ + double A3 = ((double*)LCONST)[3]; /* -3.12560092408808548438e-01 */ + double res0, xx0, tbl_div0, tbl_sqrt0; + float fres0; + int iax0, si0, iexp0; + + res = *(int*)&res; + res *= FTWO; + ax0 = *(int*)&res; + iexp0 = ax0 >> 24; + iexp0 = 0x3f + 0x4b - iexp0; + iexp0 = iexp0 << 23; + + si0 = (ax0 >> 13) & 0x7f0; + + tbl_div0 = ((double*)((char*)__TBL_rsqrtf + si0))[0]; + tbl_sqrt0 = ((double*)((char*)__TBL_rsqrtf + si0))[1]; + iax0 = ax0 & 0x7ffe0000; + iax0 = ax0 - iax0; + xx0 = iax0 * tbl_div0; + res0 = tbl_sqrt0 * (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0); + + fres0 = res0; + iexp0 += *(int*)&fres0; + + *(int*)py = iexp0; + } + else /* X = negative */ + { + *py = sqrtf(res); + } + } + else + { + double A0 = ((double*)LCONST)[0]; /* 9.99999997962321453275e-01 */ + double A1 = ((double*)LCONST)[1]; /* -4.99999998166077580600e-01 */ + double A2 = ((double*)LCONST)[2]; /* 3.75066768969515586277e-01 */ + double A3 = ((double*)LCONST)[3]; /* -3.12560092408808548438e-01 */ + double res0, xx0, tbl_div0, tbl_sqrt0; + float fres0; + int iax0, si0, iexp0; + + iexp0 = ax0 >> 24; + iexp0 = 0x3f - iexp0; + iexp0 = iexp0 << 23; + + si0 = (ax0 >> 13) & 0x7f0; + + tbl_div0 = ((double*)((char*)__TBL_rsqrtf + si0))[0]; + tbl_sqrt0 = ((double*)((char*)__TBL_rsqrtf + si0))[1]; + iax0 = ax0 & 0x7ffe0000; + iax0 = ax0 - iax0; + xx0 = iax0 * tbl_div0; + res0 = tbl_sqrt0 * (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0); + + fres0 = res0; + iexp0 += *(int*)&fres0; + + *(int*)py = iexp0; + } + } +} + +void +__vrsqrtf_n(int n, float * restrict px, int stridex, float * restrict py, int stridey) +{ + double A0 = ((double*)LCONST)[0]; /* 9.99999997962321453275e-01 */ + double A1 = ((double*)LCONST)[1]; /* -4.99999998166077580600e-01 */ + double A2 = ((double*)LCONST)[2]; /* 3.75066768969515586277e-01 */ + double A3 = ((double*)LCONST)[3]; /* -3.12560092408808548438e-01 */ + double res0, xx0, tbl_div0, tbl_sqrt0; + float fres0; + int iax0, ax0, si0, iexp0; + +#if defined(ARCH_v7) || defined(ARCH_v8) + double res1, xx1, tbl_div1, tbl_sqrt1; + double res2, xx2, tbl_div2, tbl_sqrt2; + float fres1, fres2; + int iax1, ax1, si1, iexp1; + int iax2, ax2, si2, iexp2; + + for(; n > 2 ; n -= 3) + { + ax0 = *(int*)px; + px += stridex; + + ax1 = *(int*)px; + px += stridex; + + ax2 = *(int*)px; + px += stridex; + + iexp0 = ax0 >> 24; + iexp1 = ax1 >> 24; + iexp2 = ax2 >> 24; + iexp0 = 0x3f - iexp0; + iexp1 = 0x3f - iexp1; + iexp2 = 0x3f - iexp2; + + iexp0 = iexp0 << 23; + iexp1 = iexp1 << 23; + iexp2 = iexp2 << 23; + + si0 = (ax0 >> 13) & 0x7f0; + si1 = (ax1 >> 13) & 0x7f0; + si2 = (ax2 >> 13) & 0x7f0; + + tbl_div0 = ((double*)((char*)__TBL_rsqrtf + si0))[0]; + tbl_div1 = ((double*)((char*)__TBL_rsqrtf + si1))[0]; + tbl_div2 = ((double*)((char*)__TBL_rsqrtf + si2))[0]; + tbl_sqrt0 = ((double*)((char*)__TBL_rsqrtf + si0))[1]; + tbl_sqrt1 = ((double*)((char*)__TBL_rsqrtf + si1))[1]; + tbl_sqrt2 = ((double*)((char*)__TBL_rsqrtf + si2))[1]; + iax0 = ax0 & 0x7ffe0000; + iax1 = ax1 & 0x7ffe0000; + iax2 = ax2 & 0x7ffe0000; + iax0 = ax0 - iax0; + iax1 = ax1 - iax1; + iax2 = ax2 - iax2; + xx0 = iax0 * tbl_div0; + xx1 = iax1 * tbl_div1; + xx2 = iax2 * tbl_div2; + res0 = tbl_sqrt0 * (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0); + res1 = tbl_sqrt1 * (((A3 * xx1 + A2) * xx1 + A1) * xx1 + A0); + res2 = tbl_sqrt2 * (((A3 * xx2 + A2) * xx2 + A1) * xx2 + A0); + + fres0 = res0; + fres1 = res1; + fres2 = res2; + + iexp0 += *(int*)&fres0; + iexp1 += *(int*)&fres1; + iexp2 += *(int*)&fres2; + *(int*)py = iexp0; + py += stridey; + *(int*)py = iexp1; + py += stridey; + *(int*)py = iexp2; + py += stridey; + } +#endif + for(; n > 0 ; n--) + { + ax0 = *(int*)px; + px += stridex; + + iexp0 = ax0 >> 24; + iexp0 = 0x3f - iexp0; + iexp0 = iexp0 << 23; + + si0 = (ax0 >> 13) & 0x7f0; + + tbl_div0 = ((double*)((char*)__TBL_rsqrtf + si0))[0]; + tbl_sqrt0 = ((double*)((char*)__TBL_rsqrtf + si0))[1]; + iax0 = ax0 & 0x7ffe0000; + iax0 = ax0 - iax0; + xx0 = iax0 * tbl_div0; + res0 = tbl_sqrt0 * (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0); + + fres0 = res0; + iexp0 += *(int*)&fres0; + *(int*)py = iexp0; + py += stridey; + } +} + |