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-rw-r--r--usr/src/lib/libmvec/common/__vrhypotf.c465
1 files changed, 465 insertions, 0 deletions
diff --git a/usr/src/lib/libmvec/common/__vrhypotf.c b/usr/src/lib/libmvec/common/__vrhypotf.c
new file mode 100644
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+++ b/usr/src/lib/libmvec/common/__vrhypotf.c
@@ -0,0 +1,465 @@
+/*
+ * 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 <sys/isa_defs.h>
+#include "libm_synonyms.h"
+#include "libm_inlines.h"
+
+#ifdef _LITTLE_ENDIAN
+#define HI(x) *(1+(int*)x)
+#define LO(x) *(unsigned*)x
+#else
+#define HI(x) *(int*)x
+#define LO(x) *(1+(unsigned*)x)
+#endif
+
+#ifdef __RESTRICT
+#define restrict _Restrict
+#else
+#define restrict
+#endif
+
+/* float rhypotf(float x, float y)
+ *
+ * Method :
+ * 1. Special cases:
+ * for x or y = Inf => 0;
+ * for x or y = NaN => QNaN;
+ * for x and y = 0 => +Inf + divide-by-zero;
+ * 2. Computes d = x * x + y * y;
+ * 3. Computes reciprocal square root from:
+ * d = m * 2**n
+ * Where:
+ * m = [0.5, 2),
+ * n = ((exponent + 1) & ~1).
+ * Then:
+ * rsqrtf(d) = 1/sqrt( m * 2**n ) = (2 ** (-n/2)) * (1/sqrt(m))
+ * 4. 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 0.535 ulp after 3.000.000.000
+ * results.
+ */
+
+#pragma align 32 (__vlibm_TBL_rhypotf)
+
+static const double __vlibm_TBL_rhypotf[] = {
+/*
+ i = [0,63]
+ TBL[2*i+0] = 1.0 / (*(double*)&(0x3ff0000000000000LL + (i << 46)));
+ TBL[2*i+1] = (double)(0.5/sqrtl(2) / sqrtl(*(double*)&(0x3ff0000000000000LL + (i << 46))));
+ TBL[128+2*i+0] = 1.0 / (*(double*)&(0x3ff0000000000000LL + (i << 46)));
+ TBL[128+2*i+1] = (double)(0.25 / sqrtl(*(double*)&(0x3ff0000000000000LL + (i << 46))));
+*/
+ 1.0000000000000000000e+00, 3.5355339059327378637e-01,
+ 9.8461538461538467004e-01, 3.5082320772281166965e-01,
+ 9.6969696969696972388e-01, 3.4815531191139570399e-01,
+ 9.5522388059701490715e-01, 3.4554737023254405992e-01,
+ 9.4117647058823528106e-01, 3.4299717028501769400e-01,
+ 9.2753623188405798228e-01, 3.4050261230349943009e-01,
+ 9.1428571428571425717e-01, 3.3806170189140660742e-01,
+ 9.0140845070422537244e-01, 3.3567254331867563133e-01,
+ 8.8888888888888883955e-01, 3.3333333333333331483e-01,
+ 8.7671232876712323900e-01, 3.3104235544094717802e-01,
+ 8.6486486486486491287e-01, 3.2879797461071458287e-01,
+ 8.5333333333333338810e-01, 3.2659863237109043599e-01,
+ 8.4210526315789469010e-01, 3.2444284226152508843e-01,
+ 8.3116883116883122362e-01, 3.2232918561015211356e-01,
+ 8.2051282051282048435e-01, 3.2025630761017426229e-01,
+ 8.1012658227848100001e-01, 3.1822291367029204023e-01,
+ 8.0000000000000004441e-01, 3.1622776601683794118e-01,
+ 7.9012345679012341293e-01, 3.1426968052735443360e-01,
+ 7.8048780487804880757e-01, 3.1234752377721214378e-01,
+ 7.7108433734939763049e-01, 3.1046021028253312224e-01,
+ 7.6190476190476186247e-01, 3.0860669992418382490e-01,
+ 7.5294117647058822484e-01, 3.0678599553894819740e-01,
+ 7.4418604651162789665e-01, 3.0499714066520933198e-01,
+ 7.3563218390804596680e-01, 3.0323921743156134756e-01,
+ 7.2727272727272729291e-01, 3.0151134457776362918e-01,
+ 7.1910112359550559802e-01, 2.9981267559834456904e-01,
+ 7.1111111111111113825e-01, 2.9814239699997197031e-01,
+ 7.0329670329670335160e-01, 2.9649972666444046610e-01,
+ 6.9565217391304345895e-01, 2.9488391230979427160e-01,
+ 6.8817204301075274309e-01, 2.9329423004270660513e-01,
+ 6.8085106382978721751e-01, 2.9172998299578911663e-01,
+ 6.7368421052631577428e-01, 2.9019050004400465115e-01,
+ 6.6666666666666662966e-01, 2.8867513459481286553e-01,
+ 6.5979381443298967813e-01, 2.8718326344709527165e-01,
+ 6.5306122448979586625e-01, 2.8571428571428569843e-01,
+ 6.4646464646464651960e-01, 2.8426762180748055275e-01,
+ 6.4000000000000001332e-01, 2.8284271247461900689e-01,
+ 6.3366336633663367106e-01, 2.8143901789211672737e-01,
+ 6.2745098039215685404e-01, 2.8005601680560193723e-01,
+ 6.2135922330097081989e-01, 2.7869320571664707442e-01,
+ 6.1538461538461541878e-01, 2.7735009811261457369e-01,
+ 6.0952380952380957879e-01, 2.7602622373694168934e-01,
+ 6.0377358490566035432e-01, 2.7472112789737807015e-01,
+ 5.9813084112149528249e-01, 2.7343437080986532361e-01,
+ 5.9259259259259255970e-01, 2.7216552697590867815e-01,
+ 5.8715596330275232617e-01, 2.7091418459143856712e-01,
+ 5.8181818181818178992e-01, 2.6967994498529684888e-01,
+ 5.7657657657657657158e-01, 2.6846242208560971987e-01,
+ 5.7142857142857139685e-01, 2.6726124191242439654e-01,
+ 5.6637168141592919568e-01, 2.6607604209509572168e-01,
+ 5.6140350877192979340e-01, 2.6490647141300877054e-01,
+ 5.5652173913043478937e-01, 2.6375218935831479250e-01,
+ 5.5172413793103447510e-01, 2.6261286571944508772e-01,
+ 5.4700854700854706358e-01, 2.6148818018424535570e-01,
+ 5.4237288135593220151e-01, 2.6037782196164771520e-01,
+ 5.3781512605042014474e-01, 2.5928148942086576278e-01,
+ 5.3333333333333332593e-01, 2.5819888974716115326e-01,
+ 5.2892561983471075848e-01, 2.5712973861329002645e-01,
+ 5.2459016393442625681e-01, 2.5607375986579195004e-01,
+ 5.2032520325203257539e-01, 2.5503068522533534068e-01,
+ 5.1612903225806450180e-01, 2.5400025400038100942e-01,
+ 5.1200000000000001066e-01, 2.5298221281347033074e-01,
+ 5.0793650793650790831e-01, 2.5197631533948483540e-01,
+ 5.0393700787401574104e-01, 2.5098232205526344041e-01,
+ 1.0000000000000000000e+00, 2.5000000000000000000e-01,
+ 9.8461538461538467004e-01, 2.4806946917841690703e-01,
+ 9.6969696969696972388e-01, 2.4618298195866547551e-01,
+ 9.5522388059701490715e-01, 2.4433888871261044695e-01,
+ 9.4117647058823528106e-01, 2.4253562503633296910e-01,
+ 9.2753623188405798228e-01, 2.4077170617153839660e-01,
+ 9.1428571428571425717e-01, 2.3904572186687872426e-01,
+ 9.0140845070422537244e-01, 2.3735633163877067897e-01,
+ 8.8888888888888883955e-01, 2.3570226039551583908e-01,
+ 8.7671232876712323900e-01, 2.3408229439226113655e-01,
+ 8.6486486486486491287e-01, 2.3249527748763856860e-01,
+ 8.5333333333333338810e-01, 2.3094010767585029797e-01,
+ 8.4210526315789469010e-01, 2.2941573387056177213e-01,
+ 8.3116883116883122362e-01, 2.2792115291927589338e-01,
+ 8.2051282051282048435e-01, 2.2645540682891915352e-01,
+ 8.1012658227848100001e-01, 2.2501758018520479077e-01,
+ 8.0000000000000004441e-01, 2.2360679774997896385e-01,
+ 7.9012345679012341293e-01, 2.2222222222222220989e-01,
+ 7.8048780487804880757e-01, 2.2086305214969309541e-01,
+ 7.7108433734939763049e-01, 2.1952851997938069295e-01,
+ 7.6190476190476186247e-01, 2.1821789023599238999e-01,
+ 7.5294117647058822484e-01, 2.1693045781865616384e-01,
+ 7.4418604651162789665e-01, 2.1566554640687682354e-01,
+ 7.3563218390804596680e-01, 2.1442250696755896233e-01,
+ 7.2727272727272729291e-01, 2.1320071635561044232e-01,
+ 7.1910112359550559802e-01, 2.1199957600127200541e-01,
+ 7.1111111111111113825e-01, 2.1081851067789195153e-01,
+ 7.0329670329670335160e-01, 2.0965696734438366011e-01,
+ 6.9565217391304345895e-01, 2.0851441405707477061e-01,
+ 6.8817204301075274309e-01, 2.0739033894608505104e-01,
+ 6.8085106382978721751e-01, 2.0628424925175867233e-01,
+ 6.7368421052631577428e-01, 2.0519567041703082322e-01,
+ 6.6666666666666662966e-01, 2.0412414523193150862e-01,
+ 6.5979381443298967813e-01, 2.0306923302672380549e-01,
+ 6.5306122448979586625e-01, 2.0203050891044216364e-01,
+ 6.4646464646464651960e-01, 2.0100756305184241945e-01,
+ 6.4000000000000001332e-01, 2.0000000000000001110e-01,
+ 6.3366336633663367106e-01, 1.9900743804199783060e-01,
+ 6.2745098039215685404e-01, 1.9802950859533485772e-01,
+ 6.2135922330097081989e-01, 1.9706585563285863860e-01,
+ 6.1538461538461541878e-01, 1.9611613513818404453e-01,
+ 6.0952380952380957879e-01, 1.9518001458970662965e-01,
+ 6.0377358490566035432e-01, 1.9425717247145282696e-01,
+ 5.9813084112149528249e-01, 1.9334729780913270658e-01,
+ 5.9259259259259255970e-01, 1.9245008972987526219e-01,
+ 5.8715596330275232617e-01, 1.9156525704423027490e-01,
+ 5.8181818181818178992e-01, 1.9069251784911847580e-01,
+ 5.7657657657657657158e-01, 1.8983159915049979682e-01,
+ 5.7142857142857139685e-01, 1.8898223650461362655e-01,
+ 5.6637168141592919568e-01, 1.8814417367671945613e-01,
+ 5.6140350877192979340e-01, 1.8731716231633879777e-01,
+ 5.5652173913043478937e-01, 1.8650096164806276300e-01,
+ 5.5172413793103447510e-01, 1.8569533817705186074e-01,
+ 5.4700854700854706358e-01, 1.8490006540840969729e-01,
+ 5.4237288135593220151e-01, 1.8411492357966466327e-01,
+ 5.3781512605042014474e-01, 1.8333969940564226464e-01,
+ 5.3333333333333332593e-01, 1.8257418583505535814e-01,
+ 5.2892561983471075848e-01, 1.8181818181818182323e-01,
+ 5.2459016393442625681e-01, 1.8107149208503706128e-01,
+ 5.2032520325203257539e-01, 1.8033392693348646030e-01,
+ 5.1612903225806450180e-01, 1.7960530202677491007e-01,
+ 5.1200000000000001066e-01, 1.7888543819998317663e-01,
+ 5.0793650793650790831e-01, 1.7817416127494958844e-01,
+ 5.0393700787401574104e-01, 1.7747130188322274291e-01,
+};
+
+#define fabsf __fabsf
+
+extern float fabsf(float);
+
+static const double
+ A0 = 9.99999997962321453275e-01,
+ A1 =-4.99999998166077580600e-01,
+ A2 = 3.75066768969515586277e-01,
+ A3 =-3.12560092408808548438e-01;
+
+static void
+__vrhypotf_n(int n, float * restrict px, int stridex, float * restrict py,
+ int stridey, float * restrict pz, int stridez);
+
+#pragma no_inline(__vrhypotf_n)
+
+#define RETURN(ret) \
+{ \
+ *pz = (ret); \
+ pz += stridez; \
+ if (n_n == 0) \
+ { \
+ spx = px; spy = py; spz = pz; \
+ ay0 = *(int*)py; \
+ continue; \
+ } \
+ n--; \
+ break; \
+}
+
+
+void
+__vrhypotf(int n, float * restrict px, int stridex, float * restrict py,
+ int stridey, float * restrict pz, int stridez)
+{
+ float *spx, *spy, *spz;
+ int ax0, ay0, n_n;
+ float res, x0, y0;
+
+ while (n > 1)
+ {
+ n_n = 0;
+ spx = px;
+ spy = py;
+ spz = pz;
+ ax0 = *(int*)px;
+ ay0 = *(int*)py;
+ for (; n > 1 ; n--)
+ {
+ ax0 &= 0x7fffffff;
+ ay0 &= 0x7fffffff;
+
+ px += stridex;
+
+ if (ax0 >= 0x7f800000 || ay0 >= 0x7f800000) /* X or Y = NaN or Inf */
+ {
+ x0 = *(px - stridex);
+ y0 = *py;
+ res = fabsf(x0) + fabsf(y0);
+ if (ax0 == 0x7f800000) res = 0.0f;
+ else if (ay0 == 0x7f800000) res = 0.0f;
+ ax0 = *(int*)px;
+ py += stridey;
+ RETURN (res)
+ }
+ ax0 = *(int*)px;
+ py += stridey;
+ if (ay0 == 0) /* Y = 0 */
+ {
+ int tx = *(int*)(px - stridex) & 0x7fffffff;
+ if (tx == 0) /* X = 0 */
+ {
+ RETURN (1.0f / 0.0f)
+ }
+ }
+ pz += stridez;
+ n_n++;
+ ay0 = *(int*)py;
+ }
+ if (n_n > 0)
+ __vrhypotf_n(n_n, spx, stridex, spy, stridey, spz, stridez);
+ }
+ if (n > 0)
+ {
+ ax0 = *(int*)px;
+ ay0 = *(int*)py;
+ x0 = *px;
+ y0 = *py;
+
+ ax0 &= 0x7fffffff;
+ ay0 &= 0x7fffffff;
+
+ if (ax0 >= 0x7f800000 || ay0 >= 0x7f800000) /* X or Y = NaN or Inf */
+ {
+ res = fabsf(x0) + fabsf(y0);
+ if (ax0 == 0x7f800000) res = 0.0f;
+ else if (ay0 == 0x7f800000) res = 0.0f;
+ *pz = res;
+ }
+ else if (ax0 == 0 && ay0 == 0) /* X and Y = 0 */
+ {
+ *pz = 1.0f / 0.0f;
+ }
+ else
+ {
+ double xx0, res0, hyp0, h_hi0 = 0, dbase0 = 0;
+ int ibase0, si0, hyp0h;
+
+ hyp0 = x0 * (double)x0 + y0 * (double)y0;
+
+ ibase0 = HI(&hyp0);
+
+ HI(&dbase0) = (0x60000000 - ((ibase0 & 0x7fe00000) >> 1));
+
+ hyp0h = (ibase0 & 0x000fffff) | 0x3ff00000;
+ HI(&hyp0) = hyp0h;
+ HI(&h_hi0) = hyp0h & 0x7fffc000;
+
+ ibase0 >>= 10;
+ si0 = ibase0 & 0x7f0;
+ xx0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[0];
+
+ xx0 = (hyp0 - h_hi0) * xx0;
+ res0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[1];
+ res0 *= (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0);
+ res0 *= dbase0;
+ *pz = res0;
+ }
+ }
+}
+
+static void
+__vrhypotf_n(int n, float * restrict px, int stridex, float * restrict py,
+ int stridey, float * restrict pz, int stridez)
+{
+ double xx0, res0, hyp0, h_hi0 = 0, dbase0 = 0;
+ double xx1, res1, hyp1, h_hi1 = 0, dbase1 = 0;
+ double xx2, res2, hyp2, h_hi2 = 0, dbase2 = 0;
+ float x0, y0;
+ float x1, y1;
+ float x2, y2;
+ int ibase0, si0, hyp0h;
+ int ibase1, si1, hyp1h;
+ int ibase2, si2, hyp2h;
+
+ for (; n > 2 ; n -= 3)
+ {
+ x0 = *px;
+ px += stridex;
+ x1 = *px;
+ px += stridex;
+ x2 = *px;
+ px += stridex;
+
+ y0 = *py;
+ py += stridey;
+ y1 = *py;
+ py += stridey;
+ y2 = *py;
+ py += stridey;
+
+ hyp0 = x0 * (double)x0 + y0 * (double)y0;
+ hyp1 = x1 * (double)x1 + y1 * (double)y1;
+ hyp2 = x2 * (double)x2 + y2 * (double)y2;
+
+ ibase0 = HI(&hyp0);
+ ibase1 = HI(&hyp1);
+ ibase2 = HI(&hyp2);
+
+ HI(&dbase0) = (0x60000000 - ((ibase0 & 0x7fe00000) >> 1));
+ HI(&dbase1) = (0x60000000 - ((ibase1 & 0x7fe00000) >> 1));
+ HI(&dbase2) = (0x60000000 - ((ibase2 & 0x7fe00000) >> 1));
+
+ hyp0h = (ibase0 & 0x000fffff) | 0x3ff00000;
+ hyp1h = (ibase1 & 0x000fffff) | 0x3ff00000;
+ hyp2h = (ibase2 & 0x000fffff) | 0x3ff00000;
+ HI(&hyp0) = hyp0h;
+ HI(&hyp1) = hyp1h;
+ HI(&hyp2) = hyp2h;
+ HI(&h_hi0) = hyp0h & 0x7fffc000;
+ HI(&h_hi1) = hyp1h & 0x7fffc000;
+ HI(&h_hi2) = hyp2h & 0x7fffc000;
+
+ ibase0 >>= 10;
+ ibase1 >>= 10;
+ ibase2 >>= 10;
+ si0 = ibase0 & 0x7f0;
+ si1 = ibase1 & 0x7f0;
+ si2 = ibase2 & 0x7f0;
+ xx0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[0];
+ xx1 = ((double*)((char*)__vlibm_TBL_rhypotf + si1))[0];
+ xx2 = ((double*)((char*)__vlibm_TBL_rhypotf + si2))[0];
+
+ xx0 = (hyp0 - h_hi0) * xx0;
+ xx1 = (hyp1 - h_hi1) * xx1;
+ xx2 = (hyp2 - h_hi2) * xx2;
+ res0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[1];
+ res1 = ((double*)((char*)__vlibm_TBL_rhypotf + si1))[1];
+ res2 = ((double*)((char*)__vlibm_TBL_rhypotf + si2))[1];
+ res0 *= (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0);
+ res1 *= (((A3 * xx1 + A2) * xx1 + A1) * xx1 + A0);
+ res2 *= (((A3 * xx2 + A2) * xx2 + A1) * xx2 + A0);
+ res0 *= dbase0;
+ res1 *= dbase1;
+ res2 *= dbase2;
+ *pz = res0;
+ pz += stridez;
+ *pz = res1;
+ pz += stridez;
+ *pz = res2;
+ pz += stridez;
+ }
+
+ for (; n > 0 ; n--)
+ {
+ x0 = *px;
+ px += stridex;
+
+ y0 = *py;
+ py += stridey;
+
+ hyp0 = x0 * (double)x0 + y0 * (double)y0;
+
+ ibase0 = HI(&hyp0);
+
+ HI(&dbase0) = (0x60000000 - ((ibase0 & 0x7fe00000) >> 1));
+
+ hyp0h = (ibase0 & 0x000fffff) | 0x3ff00000;
+ HI(&hyp0) = hyp0h;
+ HI(&h_hi0) = hyp0h & 0x7fffc000;
+
+ ibase0 >>= 10;
+ si0 = ibase0 & 0x7f0;
+ xx0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[0];
+
+ xx0 = (hyp0 - h_hi0) * xx0;
+ res0 = ((double*)((char*)__vlibm_TBL_rhypotf + si0))[1];
+ res0 *= (((A3 * xx0 + A2) * xx0 + A1) * xx0 + A0);
+ res0 *= dbase0;
+ *pz = res0;
+ pz += stridez;
+ }
+}
+
generated by cgit v1.2.3 (git 2.39.1) at 2025-04-27 08:43:24 +0000