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sleefsseavx.c
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sleefsseavx.c
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#ifndef SLEEFSSEAVX
#define SLEEFSSEAVX
#include <assert.h>
#include <math.h>
//#include <bits/nan.h>
//#include <bits/inf.h>
//#include "sleefsseavx.h"
#ifdef __SSE2__
#include "helpersse2.h"
#ifdef ENABLE_AVX
#include "helperavx.h"
#endif
#ifdef __GNUC__
#define INLINE __inline
#else
#define INLINE inline
#endif
//
#define PI4_A .7853981554508209228515625
#define PI4_B .794662735614792836713604629039764404296875e-8
#define PI4_C .306161699786838294306516483068750264552437361480769e-16
#define M_4_PI 1.273239544735162542821171882678754627704620361328125
#define L2U .69314718055966295651160180568695068359375
#define L2L .28235290563031577122588448175013436025525412068e-12
#define R_LN2 1.442695040888963407359924681001892137426645954152985934135449406931
//
#define PI4_Af 0.78515625f
#define PI4_Bf 0.00024127960205078125f
#define PI4_Cf 6.3329935073852539062e-07f
#define PI4_Df 4.9604681473525147339e-10f
#define L2Uf 0.693145751953125f
#define L2Lf 1.428606765330187045e-06f
#define R_LN2f 1.442695040888963407359924681001892137426645954152985934135449406931f
#define INFINITYf ((float)INFINITY)
#define NANf ((float)NAN)
//
static INLINE vdouble vadd3(vdouble v0, vdouble v1, vdouble v2) {
return vadd(vadd(v0, v1), v2);
}
static INLINE vdouble vadd4(vdouble v0, vdouble v1, vdouble v2, vdouble v3) {
return vadd3(vadd(v0, v1), v2, v3);
}
static INLINE vdouble vadd5(vdouble v0, vdouble v1, vdouble v2, vdouble v3, vdouble v4) {
return vadd4(vadd(v0, v1), v2, v3, v4);
}
static INLINE vdouble vadd6(vdouble v0, vdouble v1, vdouble v2, vdouble v3, vdouble v4, vdouble v5) {
return vadd5(vadd(v0, v1), v2, v3, v4, v5);
}
static INLINE vdouble vadd7(vdouble v0, vdouble v1, vdouble v2, vdouble v3, vdouble v4, vdouble v5, vdouble v6) {
return vadd6(vadd(v0, v1), v2, v3, v4, v5, v6);
}
static INLINE vdouble vsub3(vdouble v0, vdouble v1, vdouble v2) {
return vsub(vsub(v0, v1), v2);
}
static INLINE vdouble vsub4(vdouble v0, vdouble v1, vdouble v2, vdouble v3) {
return vsub3(vsub(v0, v1), v2, v3);
}
static INLINE vdouble vsub5(vdouble v0, vdouble v1, vdouble v2, vdouble v3, vdouble v4) {
return vsub4(vsub(v0, v1), v2, v3, v4);
}
//
static INLINE vdouble2 normalize_d(vdouble2 t) {
vdouble2 s;
s.x = vadd(t.x, t.y);
s.y = vadd(vsub(t.x, s.x), t.y);
return s;
}
static INLINE vdouble2 scale_d(vdouble2 d, vdouble s) {
vdouble2 r = {vmul(d.x, s), vmul(d.y, s)};
return r;
}
static INLINE vdouble2 add_ss(vdouble x, vdouble y) {
vdouble2 r;
r.x = vadd(x, y);
r.y = vadd(vsub(x, r.x), y);
return r;
}
static INLINE vdouble2 add2_ss(vdouble x, vdouble y) {
vdouble2 r;
r.x = vadd(x, y);
vdouble v = vsub(r.x, x);
r.y = vadd(vsub(x, vsub(r.x, v)), vsub(y, v));
return r;
}
static INLINE vdouble2 add_ds(vdouble2 x, vdouble y) {
vdouble2 r;
r.x = vadd(x.x, y);
r.y = vadd3(vsub(x.x, r.x), y, x.y);
return r;
}
static INLINE vdouble2 add2_ds(vdouble2 x, vdouble y) {
vdouble2 r;
r.x = vadd(x.x, y);
vdouble v = vsub(r.x, x.x);
r.y = vadd(vsub(x.x, vsub(r.x, v)), vsub(y, v));
r.y = vadd(r.y, x.y);
return r;
}
static INLINE vdouble2 add_sd(vdouble x, vdouble2 y) {
vdouble2 r;
r.x = vadd(x, y.x);
r.y = vadd3(vsub(x, r.x), y.x, y.y);
return r;
}
static INLINE vdouble2 add_dd(vdouble2 x, vdouble2 y) {
// |x| >= |y|
vdouble2 r;
r.x = vadd(x.x, y.x);
r.y = vadd4(vsub(x.x, r.x), y.x, x.y, y.y);
return r;
}
static INLINE vdouble2 add2_dd(vdouble2 x, vdouble2 y) {
vdouble2 r;
r.x = vadd(x.x, y.x);
vdouble v = vsub(r.x, x.x);
r.y = vadd(vsub(x.x, vsub(r.x, v)), vsub(y.x, v));
r.y = vadd(r.y, vadd(x.y, y.y));
return r;
}
static INLINE vdouble2 div_dd(vdouble2 n, vdouble2 d) {
vdouble t = vrec(d.x);
vdouble dh = vupper(d.x), dl = vsub(d.x, dh);
vdouble th = vupper(t ), tl = vsub(t , th);
vdouble nhh = vupper(n.x), nhl = vsub(n.x, nhh);
vdouble2 q;
q.x = vmul(n.x, t);
vdouble u = vadd5(vsub(vmul(nhh, th), q.x), vmul(nhh, tl), vmul(nhl, th), vmul(nhl, tl),
vmul(q.x, vsub5(vcast_vd_d(1), vmul(dh, th), vmul(dh, tl), vmul(dl, th), vmul(dl, tl))));
q.y = vadd(vmul(t, vsub(n.y, vmul(q.x, d.y))), u);
return q;
}
static INLINE vdouble2 mul_ss(vdouble x, vdouble y) {
vdouble xh = vupper(x), xl = vsub(x, xh);
vdouble yh = vupper(y), yl = vsub(y, yh);
vdouble2 r;
r.x = vmul(x, y);
r.y = vadd5(vmul(xh, yh), vneg(r.x), vmul(xl, yh), vmul(xh, yl), vmul(xl, yl));
return r;
}
static INLINE vdouble2 mul_ds(vdouble2 x, vdouble y) {
vdouble xh = vupper(x.x), xl = vsub(x.x, xh);
vdouble yh = vupper(y ), yl = vsub(y , yh);
vdouble2 r;
r.x = vmul(x.x, y);
r.y = vadd6(vmul(xh, yh), vneg(r.x), vmul(xl, yh), vmul(xh, yl), vmul(xl, yl), vmul(x.y, y));
return r;
}
static INLINE vdouble2 mul_dd(vdouble2 x, vdouble2 y) {
vdouble xh = vupper(x.x), xl = vsub(x.x, xh);
vdouble yh = vupper(y.x), yl = vsub(y.x, yh);
vdouble2 r;
r.x = vmul(x.x, y.x);
r.y = vadd7(vmul(xh, yh), vneg(r.x), vmul(xl, yh), vmul(xh, yl), vmul(xl, yl), vmul(x.x, y.y), vmul(x.y, y.x));
return r;
}
static INLINE vdouble2 squ_d(vdouble2 x) {
vdouble xh = vupper(x.x), xl = vsub(x.x, xh);
vdouble2 r;
r.x = vmul(x.x, x.x);
r.y = vadd5(vmul(xh, xh), vneg(r.x), vmul(vadd(xh, xh), xl), vmul(xl, xl), vmul(x.x, vadd(x.y, x.y)));
return r;
}
static INLINE vdouble2 rec_s(vdouble d) {
vdouble t = vrec(d);
vdouble dh = vupper(d), dl = vsub(d, dh);
vdouble th = vupper(t), tl = vsub(t, th);
vdouble2 q;
q.x = t;
q.y = vmul(t, vsub5(vcast_vd_d(1), vmul(dh, th), vmul(dh, tl), vmul(dl, th), vmul(dl, tl)));
return q;
}
static INLINE vdouble2 sqrt_d(vdouble2 d) {
vdouble t = vsqrt(vadd(d.x, d.y));
return scale_d(mul_dd(add2_dd(d, mul_ss(t, t)), rec_s(t)), vcast_vd_d(0.5));
}
//
static INLINE vdouble xldexp(vdouble x, vint q) { return vldexp(x, q); }
static INLINE vint xilogb(vdouble d) {
vdouble e = vcast_vd_vi(vsubi(vilogbp1(vabs(d)), vcast_vi_i(1)));
e = vsel(vmask_eq(d, vcast_vd_d(0)), vcast_vd_d(-2147483648.0), e);
e = vsel(vmask_eq(vabs(d), vcast_vd_d(INFINITY)), vcast_vd_d(2147483647), e);
return vrint_vi_vd(e);
}
static INLINE vdouble xsin(vdouble d) {
vint q;
vdouble u, s;
q = vrint_vi_vd(vmul(d, vcast_vd_d(M_1_PI)));
u = vcast_vd_vi(q);
d = vadd(d, vmul(u, vcast_vd_d(-PI4_A*4)));
d = vadd(d, vmul(u, vcast_vd_d(-PI4_B*4)));
d = vadd(d, vmul(u, vcast_vd_d(-PI4_C*4)));
s = vmul(d, d);
d = vsel(vmaski_eq(vandi(q, vcast_vi_i(1)), vcast_vi_i(1)), vneg(d), d);
u = vcast_vd_d(-7.97255955009037868891952e-18);
u = vmla(u, s, vcast_vd_d(2.81009972710863200091251e-15));
u = vmla(u, s, vcast_vd_d(-7.64712219118158833288484e-13));
u = vmla(u, s, vcast_vd_d(1.60590430605664501629054e-10));
u = vmla(u, s, vcast_vd_d(-2.50521083763502045810755e-08));
u = vmla(u, s, vcast_vd_d(2.75573192239198747630416e-06));
u = vmla(u, s, vcast_vd_d(-0.000198412698412696162806809));
u = vmla(u, s, vcast_vd_d(0.00833333333333332974823815));
u = vmla(u, s, vcast_vd_d(-0.166666666666666657414808));
u = vmla(s, vmul(u, d), d);
return u;
}
static INLINE vdouble xcos(vdouble d) {
vint q;
vdouble u, s;
q = vrint_vi_vd(vsub(vmul(d, vcast_vd_d(M_1_PI)), vcast_vd_d(0.5)));
q = vaddi(vaddi(q, q), vcast_vi_i(1));
u = vcast_vd_vi(q);
d = vadd(d, vmul(u, vcast_vd_d(-PI4_A*2)));
d = vadd(d, vmul(u, vcast_vd_d(-PI4_B*2)));
d = vadd(d, vmul(u, vcast_vd_d(-PI4_C*2)));
s = vmul(d, d);
d = vsel(vmaski_eq(vandi(q, vcast_vi_i(2)), vcast_vi_i(0)), vneg(d), d);
u = vcast_vd_d(-7.97255955009037868891952e-18);
u = vmla(u, s, vcast_vd_d(2.81009972710863200091251e-15));
u = vmla(u, s, vcast_vd_d(-7.64712219118158833288484e-13));
u = vmla(u, s, vcast_vd_d(1.60590430605664501629054e-10));
u = vmla(u, s, vcast_vd_d(-2.50521083763502045810755e-08));
u = vmla(u, s, vcast_vd_d(2.75573192239198747630416e-06));
u = vmla(u, s, vcast_vd_d(-0.000198412698412696162806809));
u = vmla(u, s, vcast_vd_d(0.00833333333333332974823815));
u = vmla(u, s, vcast_vd_d(-0.166666666666666657414808));
u = vmla(s, vmul(u, d), d);
return u;
}
static INLINE vdouble2 xsincos(vdouble d) {
vint q;
vmask m;
vdouble u, s, t, rx, ry;
vdouble2 r;
q = vrint_vi_vd(vmul(d, vcast_vd_d(M_2_PI)));
s = d;
u = vcast_vd_vi(q);
s = vmla(u, vcast_vd_d(-PI4_A*2), s);
s = vmla(u, vcast_vd_d(-PI4_B*2), s);
s = vmla(u, vcast_vd_d(-PI4_C*2), s);
t = s;
s = vmul(s, s);
u = vcast_vd_d(1.58938307283228937328511e-10);
u = vmla(u, s, vcast_vd_d(-2.50506943502539773349318e-08));
u = vmla(u, s, vcast_vd_d(2.75573131776846360512547e-06));
u = vmla(u, s, vcast_vd_d(-0.000198412698278911770864914));
u = vmla(u, s, vcast_vd_d(0.0083333333333191845961746));
u = vmla(u, s, vcast_vd_d(-0.166666666666666130709393));
u = vmul(vmul(u, s), t);
rx = vadd(t, u);
u = vcast_vd_d(-1.13615350239097429531523e-11);
u = vmla(u, s, vcast_vd_d(2.08757471207040055479366e-09));
u = vmla(u, s, vcast_vd_d(-2.75573144028847567498567e-07));
u = vmla(u, s, vcast_vd_d(2.48015872890001867311915e-05));
u = vmla(u, s, vcast_vd_d(-0.00138888888888714019282329));
u = vmla(u, s, vcast_vd_d(0.0416666666666665519592062));
u = vmla(u, s, vcast_vd_d(-0.5));
ry = vadd(vcast_vd_d(1), vmul(s, u));
m = vmaski_eq(vandi(q, vcast_vi_i(1)), vcast_vi_i(0));
r.x = vsel(m, rx, ry);
r.y = vsel(m, ry, rx);
m = vmaski_eq(vandi(q, vcast_vi_i(2)), vcast_vi_i(2));
r.x = vreinterpret_vd_vm(vxorm(vandm(m, vreinterpret_vm_vd(vcast_vd_d(-0.0))), vreinterpret_vm_vd(r.x)));
m = vmaski_eq(vandi(vaddi(q, vcast_vi_i(1)), vcast_vi_i(2)), vcast_vi_i(2));
r.y = vreinterpret_vd_vm(vxorm(vandm(m, vreinterpret_vm_vd(vcast_vd_d(-0.0))), vreinterpret_vm_vd(r.y)));
m = vmask_isinf(d);
r.x = vsel(m, vcast_vd_d(NAN), r.x);
r.y = vsel(m, vcast_vd_d(NAN), r.y);
return r;
}
static INLINE vdouble xtan(vdouble d) {
vint q;
vdouble u, s, x;
vmask m;
q = vrint_vi_vd(vmul(d, vcast_vd_d(M_2_PI)));
u = vcast_vd_vi(q);
x = vadd(d, vmul(u, vcast_vd_d(-PI4_A*2)));
x = vadd(x, vmul(u, vcast_vd_d(-PI4_B*2)));
x = vadd(x, vmul(u, vcast_vd_d(-PI4_C*2)));
s = vmul(x, x);
m = vmaski_eq(vandi(q, vcast_vi_i(1)), vcast_vi_i(1));
x = vsel(m, vneg(x), x);
u = vcast_vd_d(1.01419718511083373224408e-05);
u = vmla(u, s, vcast_vd_d(-2.59519791585924697698614e-05));
u = vmla(u, s, vcast_vd_d(5.23388081915899855325186e-05));
u = vmla(u, s, vcast_vd_d(-3.05033014433946488225616e-05));
u = vmla(u, s, vcast_vd_d(7.14707504084242744267497e-05));
u = vmla(u, s, vcast_vd_d(8.09674518280159187045078e-05));
u = vmla(u, s, vcast_vd_d(0.000244884931879331847054404));
u = vmla(u, s, vcast_vd_d(0.000588505168743587154904506));
u = vmla(u, s, vcast_vd_d(0.00145612788922812427978848));
u = vmla(u, s, vcast_vd_d(0.00359208743836906619142924));
u = vmla(u, s, vcast_vd_d(0.00886323944362401618113356));
u = vmla(u, s, vcast_vd_d(0.0218694882853846389592078));
u = vmla(u, s, vcast_vd_d(0.0539682539781298417636002));
u = vmla(u, s, vcast_vd_d(0.133333333333125941821962));
u = vmla(u, s, vcast_vd_d(0.333333333333334980164153));
u = vmla(s, vmul(u, x), x);
u = vsel(m, vrec(u), u);
u = vsel(vmask_isinf(d), vcast_vd_d(NAN), u);
return u;
}
static INLINE vdouble atan2k(vdouble y, vdouble x) {
vdouble s, t, u;
vint q;
vmask p;
q = vseli_lt(x, vcast_vd_d(0), vcast_vi_i(-2), vcast_vi_i(0));
x = vabs(x);
q = vseli_lt(x, y, vaddi(q, vcast_vi_i(1)), q);
p = vmask_lt(x, y);
s = vsel (p, vneg(x), y);
t = vmax (x, y);
s = vdiv(s, t);
t = vmul(s, s);
u = vcast_vd_d(-1.88796008463073496563746e-05);
u = vmla(u, t, vcast_vd_d(0.000209850076645816976906797));
u = vmla(u, t, vcast_vd_d(-0.00110611831486672482563471));
u = vmla(u, t, vcast_vd_d(0.00370026744188713119232403));
u = vmla(u, t, vcast_vd_d(-0.00889896195887655491740809));
u = vmla(u, t, vcast_vd_d(0.016599329773529201970117));
u = vmla(u, t, vcast_vd_d(-0.0254517624932312641616861));
u = vmla(u, t, vcast_vd_d(0.0337852580001353069993897));
u = vmla(u, t, vcast_vd_d(-0.0407629191276836500001934));
u = vmla(u, t, vcast_vd_d(0.0466667150077840625632675));
u = vmla(u, t, vcast_vd_d(-0.0523674852303482457616113));
u = vmla(u, t, vcast_vd_d(0.0587666392926673580854313));
u = vmla(u, t, vcast_vd_d(-0.0666573579361080525984562));
u = vmla(u, t, vcast_vd_d(0.0769219538311769618355029));
u = vmla(u, t, vcast_vd_d(-0.090908995008245008229153));
u = vmla(u, t, vcast_vd_d(0.111111105648261418443745));
u = vmla(u, t, vcast_vd_d(-0.14285714266771329383765));
u = vmla(u, t, vcast_vd_d(0.199999999996591265594148));
u = vmla(u, t, vcast_vd_d(-0.333333333333311110369124));
t = vadd(s, vmul(s, vmul(t, u)));
t = vadd(t, vmul(vcast_vd_vi(q), vcast_vd_d(M_PI/2)));
return t;
}
static INLINE vdouble xatan2(vdouble y, vdouble x) {
vdouble r = atan2k(vabs(y), x);
r = vmulsign(r, x);
r = vsel(vorm(vmask_isinf(x), vmask_eq(x, vcast_vd_d(0))), vsub(vcast_vd_d(M_PI/2), visinf2(x, vmulsign(vcast_vd_d(M_PI/2), x))), r);
r = vsel(vmask_isinf(y), vsub(vcast_vd_d(M_PI/2), visinf2(x, vmulsign(vcast_vd_d(M_PI/4), x))), r);
r = vsel(vmask_eq(y, vcast_vd_d(0)), vsel(vmask_eq(vsign(x), vcast_vd_d(-1.0)), vcast_vd_d(M_PI), vcast_vd_d(0)), r);
return vsel(vorm(vmask_isnan(x), vmask_isnan(y)), vcast_vd_d(NAN), vmulsign(r, y));
}
static INLINE vdouble xasin(vdouble d) {
vdouble x, y;
x = vadd(vcast_vd_d(1), d);
y = vsub(vcast_vd_d(1), d);
x = vmul(x, y);
x = vsqrt(x);
x = vsel(vmask_isnan(x), vcast_vd_d(NAN), atan2k(vabs(d), x));
return vmulsign(x, d);
}
static INLINE vdouble xacos(vdouble d) {
vdouble x, y;
x = vadd(vcast_vd_d(1), d);
y = vsub(vcast_vd_d(1), d);
x = vmul(x, y);
x = vsqrt(x);
x = vmulsign(atan2k(x, vabs(d)), d);
y = (vdouble)vandm(vmask_lt(d, vcast_vd_d(0)), (vmask)vcast_vd_d(M_PI));
x = vadd(x, y);
return x;
}
static INLINE vdouble xatan(vdouble s) {
vdouble t, u;
vint q;
q = vseli_lt(s, vcast_vd_d(0), vcast_vi_i(2), vcast_vi_i(0));
s = vabs(s);
q = vseli_lt(vcast_vd_d(1), s, vaddi(q, vcast_vi_i(1)), q);
s = vsel(vmask_lt(vcast_vd_d(1), s), vdiv(vcast_vd_d(1), s), s);
t = vmul(s, s);
u = vcast_vd_d(-1.88796008463073496563746e-05);
u = vmla(u, t, vcast_vd_d(0.000209850076645816976906797));
u = vmla(u, t, vcast_vd_d(-0.00110611831486672482563471));
u = vmla(u, t, vcast_vd_d(0.00370026744188713119232403));
u = vmla(u, t, vcast_vd_d(-0.00889896195887655491740809));
u = vmla(u, t, vcast_vd_d(0.016599329773529201970117));
u = vmla(u, t, vcast_vd_d(-0.0254517624932312641616861));
u = vmla(u, t, vcast_vd_d(0.0337852580001353069993897));
u = vmla(u, t, vcast_vd_d(-0.0407629191276836500001934));
u = vmla(u, t, vcast_vd_d(0.0466667150077840625632675));
u = vmla(u, t, vcast_vd_d(-0.0523674852303482457616113));
u = vmla(u, t, vcast_vd_d(0.0587666392926673580854313));
u = vmla(u, t, vcast_vd_d(-0.0666573579361080525984562));
u = vmla(u, t, vcast_vd_d(0.0769219538311769618355029));
u = vmla(u, t, vcast_vd_d(-0.090908995008245008229153));
u = vmla(u, t, vcast_vd_d(0.111111105648261418443745));
u = vmla(u, t, vcast_vd_d(-0.14285714266771329383765));
u = vmla(u, t, vcast_vd_d(0.199999999996591265594148));
u = vmla(u, t, vcast_vd_d(-0.333333333333311110369124));
t = vadd(s, vmul(s, vmul(t, u)));
t = vsel(vmaski_eq(vandi(q, vcast_vi_i(1)), vcast_vi_i(1)), vsub(vcast_vd_d(M_PI/2), t), t);
t = vsel(vmaski_eq(vandi(q, vcast_vi_i(2)), vcast_vi_i(2)), vneg(t), t);
return t;
}
static INLINE vdouble xlog(vdouble d) {
vdouble x, x2;
vdouble t, m;
vint e;
e = vilogbp1(vmul(d, vcast_vd_d(0.7071)));
m = vldexp(d, vsubi(vcast_vi_i(0), e));
x = vdiv(vadd(vcast_vd_d(-1), m), vadd(vcast_vd_d(1), m));
x2 = vmul(x, x);
t = vcast_vd_d(0.148197055177935105296783);
t = vmla(t, x2, vcast_vd_d(0.153108178020442575739679));
t = vmla(t, x2, vcast_vd_d(0.181837339521549679055568));
t = vmla(t, x2, vcast_vd_d(0.22222194152736701733275));
t = vmla(t, x2, vcast_vd_d(0.285714288030134544449368));
t = vmla(t, x2, vcast_vd_d(0.399999999989941956712869));
t = vmla(t, x2, vcast_vd_d(0.666666666666685503450651));
t = vmla(t, x2, vcast_vd_d(2));
x = vadd(vmul(x, t), vmul(vcast_vd_d(0.693147180559945286226764), vcast_vd_vi(e)));
x = vsel(vmask_ispinf(d), vcast_vd_d(INFINITY), x);
x = vsel(vmask_gt(vcast_vd_d(0), d), vcast_vd_d(NAN), x);
x = vsel(vmask_eq(d, vcast_vd_d(0)), vcast_vd_d(-INFINITY), x);
return x;
}
static INLINE vdouble xexp(vdouble d) {
vint q = vrint_vi_vd(vmul(d, vcast_vd_d(R_LN2)));
vdouble s, u;
s = vadd(d, vmul(vcast_vd_vi(q), vcast_vd_d(-L2U)));
s = vadd(s, vmul(vcast_vd_vi(q), vcast_vd_d(-L2L)));
u = vcast_vd_d(2.08860621107283687536341e-09);
u = vmla(u, s, vcast_vd_d(2.51112930892876518610661e-08));
u = vmla(u, s, vcast_vd_d(2.75573911234900471893338e-07));
u = vmla(u, s, vcast_vd_d(2.75572362911928827629423e-06));
u = vmla(u, s, vcast_vd_d(2.4801587159235472998791e-05));
u = vmla(u, s, vcast_vd_d(0.000198412698960509205564975));
u = vmla(u, s, vcast_vd_d(0.00138888888889774492207962));
u = vmla(u, s, vcast_vd_d(0.00833333333331652721664984));
u = vmla(u, s, vcast_vd_d(0.0416666666666665047591422));
u = vmla(u, s, vcast_vd_d(0.166666666666666851703837));
u = vmla(u, s, vcast_vd_d(0.5));
u = vadd(vcast_vd_d(1), vadd(s, vmul(vmul(s, s), u)));
u = vldexp(u, q);
u = vsel(vmask_isminf(d), vcast_vd_d(0), u);
return u;
}
static INLINE vdouble2 logk(vdouble d) {
vdouble2 x, x2;
vdouble t, m;
vint e;
e = vilogbp1(vmul(d, vcast_vd_d(0.7071)));
m = vldexp(d, vsubi(vcast_vi_i(0), e));
x = div_dd(add2_ss(vcast_vd_d(-1), m), add2_ss(vcast_vd_d(1), m));
x2 = squ_d(x);
x2 = normalize_d(x2);
t = vcast_vd_d(0.134601987501262130076155);
t = vmla(t, x2.x, vcast_vd_d(0.132248509032032670243288));
t = vmla(t, x2.x, vcast_vd_d(0.153883458318096079652524));
t = vmla(t, x2.x, vcast_vd_d(0.181817427573705403298686));
t = vmla(t, x2.x, vcast_vd_d(0.222222231326187414840781));
t = vmla(t, x2.x, vcast_vd_d(0.285714285651261412873718));
t = vmla(t, x2.x, vcast_vd_d(0.400000000000222439910458));
t = vmla(t, x2.x, vcast_vd_d(0.666666666666666371239645));
return add2_dd(mul_ds(dd(vcast_vd_d(0.693147180559945286226764), vcast_vd_d(2.319046813846299558417771e-17)),
vcast_vd_vi(e)),
add2_dd(scale_d(x, vcast_vd_d(2)), mul_ds(mul_dd(x2, x), t)));
}
static INLINE vdouble expk(vdouble2 d) {
vdouble u = vmul(vadd(d.x, d.y), vcast_vd_d(R_LN2));
vint q = vrint_vi_vd(u);
vdouble2 s, t;
s = add2_ds(d, vmul(vcast_vd_vi(q), vcast_vd_d(-L2U)));
s = add2_ds(s, vmul(vcast_vd_vi(q), vcast_vd_d(-L2L)));
q = vrint_vi_vd(vmin(vmax(vcast_vd_d(-2047.49), u), vcast_vd_d(2047.49)));
s = normalize_d(s);
u = vcast_vd_d(2.51069683420950419527139e-08);
u = vmla(u, s.x, vcast_vd_d(2.76286166770270649116855e-07));
u = vmla(u, s.x, vcast_vd_d(2.75572496725023574143864e-06));
u = vmla(u, s.x, vcast_vd_d(2.48014973989819794114153e-05));
u = vmla(u, s.x, vcast_vd_d(0.000198412698809069797676111));
u = vmla(u, s.x, vcast_vd_d(0.0013888888939977128960529));
u = vmla(u, s.x, vcast_vd_d(0.00833333333332371417601081));
u = vmla(u, s.x, vcast_vd_d(0.0416666666665409524128449));
u = vmla(u, s.x, vcast_vd_d(0.166666666666666740681535));
u = vmla(u, s.x, vcast_vd_d(0.500000000000000999200722));
t = add_dd(s, mul_ds(squ_d(s), u));
t = add_sd(vcast_vd_d(1), t);
u = vadd(t.x, t.y);
u = vldexp(u, q);
return u;
}
static INLINE vdouble xpow(vdouble x, vdouble y) {
#if 1
vmask yisint = vmask_eq(vcast_vd_vi(vrint_vi_vd(y)), y);
vmask yisodd = vandm(vmaski_eq(vandi(vrint_vi_vd(y), vcast_vi_i(1)), vcast_vi_i(1)), yisint);
vdouble result = expk(mul_ds(logk(vabs(x)), y));
//result = vsel(vmask_isnan(result), vcast_vd_d(INFINITY), result);
result = vmul(result,
vsel(vmask_gt(x, vcast_vd_d(0)),
vcast_vd_d(1),
vsel(yisint,
vsel(yisodd,
vcast_vd_d(-1),
vcast_vd_d(1)),
vcast_vd_d(NAN))));
vdouble efx = vreinterpret_vd_vm(vxorm(vreinterpret_vm_vd(vsub(vabs(x), vcast_vd_d(1))), vsignbit(y)));
result = vsel(vmask_isinf(y),
vsel(vmask_lt(efx, vcast_vd_d(0)),
vcast_vd_d(0),
vsel(vmask_eq(efx, vcast_vd_d(0)),
vcast_vd_d(1.0),
vcast_vd_d(INFINITY))),
result);
result = vsel(vorm(vmask_isinf(x), vmask_eq(x, vcast_vd_d(0))),
vmul(vsel(yisodd, vsign(x), vcast_vd_d(1)),
vsel(vmask_lt(vsel(vmask_eq(x, vcast_vd_d(0)), vneg(y), y), vcast_vd_d(0)),
vcast_vd_d(0),
vcast_vd_d(INFINITY))),
result);
result = vsel(vorm(vmask_isnan(x), vmask_isnan(y)), vcast_vd_d(NAN), result);
result = vsel(vorm(vmask_eq(y, vcast_vd_d(0)), vmask_eq(x, vcast_vd_d(1))), vcast_vd_d(1), result);
return result;
#else
return expk(mul_ds(logk(x), y));
#endif
}
static INLINE vdouble2 expk2(vdouble2 d) {
vdouble u = vmul(vadd(d.x, d.y), vcast_vd_d(R_LN2));
vint q = vrint_vi_vd(u);
vdouble2 s, t;
s = add2_ds(d, vmul(vcast_vd_vi(q), vcast_vd_d(-L2U)));
s = add2_ds(s, vmul(vcast_vd_vi(q), vcast_vd_d(-L2L)));
q = vrint_vi_vd(vmin(vmax(vcast_vd_d(-2047.49), u), vcast_vd_d(2047.49)));
s = normalize_d(s);
u = vcast_vd_d(2.51069683420950419527139e-08);
u = vmla(u, s.x, vcast_vd_d(2.76286166770270649116855e-07));
u = vmla(u, s.x, vcast_vd_d(2.75572496725023574143864e-06));
u = vmla(u, s.x, vcast_vd_d(2.48014973989819794114153e-05));
u = vmla(u, s.x, vcast_vd_d(0.000198412698809069797676111));
u = vmla(u, s.x, vcast_vd_d(0.0013888888939977128960529));
u = vmla(u, s.x, vcast_vd_d(0.00833333333332371417601081));
u = vmla(u, s.x, vcast_vd_d(0.0416666666665409524128449));
u = vmla(u, s.x, vcast_vd_d(0.166666666666666740681535));
u = vmla(u, s.x, vcast_vd_d(0.500000000000000999200722));
t = add_dd(s, mul_ds(squ_d(s), u));
t = add_sd(vcast_vd_d(1), t);
return dd(vldexp(t.x, q), vldexp(t.y, q));
}
static INLINE vdouble xsinh(vdouble x) {
vdouble y = vabs(x);
vdouble2 d = expk2(dd(y, vcast_vd_d(0)));
d = add2_dd(d, div_dd(dd(vcast_vd_d(-1), vcast_vd_d(0)), d));
y = vmul(vadd(d.x, d.y), vcast_vd_d(0.5));
y = vsel(vorm(vmask_isinf(x), vmask_isnan(y)), vcast_vd_d(INFINITY), y);
y = vmulsign(y, x);
y = vsel(vmask_isnan(x), vcast_vd_d(NAN), y);
return y;
}
static INLINE vdouble xcosh(vdouble x) {
vdouble2 d = expk2(dd(x, vcast_vd_d(0)));
d = add2_dd(d, div_dd(dd(vcast_vd_d(1), vcast_vd_d(0)), d));
vdouble y = vmul(vadd(d.x, d.y), vcast_vd_d(0.5));
y = vsel(vorm(vmask_isinf(x), vmask_isnan(y)), vcast_vd_d(INFINITY), y);
y = vsel(vmask_isnan(x), vcast_vd_d(NAN), y);
return y;
}
static INLINE vdouble xtanh(vdouble x) {
vdouble y = vabs(x);
vdouble2 d = expk2(dd(y, vcast_vd_d(0)));
vdouble2 e = div_dd(dd(vcast_vd_d(1), vcast_vd_d(0)), d);
d = div_dd(add2_dd(d, scale_d(e, vcast_vd_d(-1))), add2_dd(d, e));
y = d.x + d.y;
y = vsel(vorm(vmask_isinf(x), vmask_isnan(y)), vcast_vd_d(1.0), y);
y = vmulsign(y, x);
y = vsel(vmask_isnan(x), vcast_vd_d(NAN), y);
return y;
}
static INLINE vdouble2 logk2(vdouble2 d) {
vdouble2 x, x2, m;
vdouble t;
vint e;
d = normalize_d(d);
e = vilogbp1(vmul(d.x, vcast_vd_d(0.7071)));
m = scale_d(d, vldexp(vcast_vd_d(1), vsubi(vcast_vi_i(0), e)));
x = div_dd(add2_ds(m, vcast_vd_d(-1)), add2_ds(m, vcast_vd_d(1)));
x2 = squ_d(x);
x2 = normalize_d(x2);
t = vcast_vd_d(0.134601987501262130076155);
t = vmla(t, x2.x, vcast_vd_d(0.132248509032032670243288));
t = vmla(t, x2.x, vcast_vd_d(0.153883458318096079652524));
t = vmla(t, x2.x, vcast_vd_d(0.181817427573705403298686));
t = vmla(t, x2.x, vcast_vd_d(0.222222231326187414840781));
t = vmla(t, x2.x, vcast_vd_d(0.285714285651261412873718));
t = vmla(t, x2.x, vcast_vd_d(0.400000000000222439910458));
t = vmla(t, x2.x, vcast_vd_d(0.666666666666666371239645));
return add2_dd(mul_ds(dd(vcast_vd_d(0.693147180559945286226764), vcast_vd_d(2.319046813846299558417771e-17)),
vcast_vd_vi(e)),
add2_dd(scale_d(x, vcast_vd_d(2)), mul_ds(mul_dd(x2, x), t)));
}
static INLINE vdouble xasinh(vdouble x) {
vdouble y = vabs(x);
vdouble2 d = logk2(add2_ds(sqrt_d(add2_ds(mul_ss(y, y), vcast_vd_d(1))), y));
y = vadd(d.x, d.y);
y = vsel(vorm(vmask_isinf(x), vmask_isnan(y)), vcast_vd_d(INFINITY), y);
y = vmulsign(y, x);
y = vsel(vmask_isnan(x), vcast_vd_d(NAN), y);
return y;
}
static INLINE vdouble xacosh(vdouble x) {
vdouble2 d = logk2(add2_ds(sqrt_d(add2_ds(mul_ss(x, x), vcast_vd_d(-1))), x));
vdouble y = vadd(d.x, d.y);
y = vsel(vorm(vmask_isinf(x), vmask_isnan(y)), vcast_vd_d(INFINITY), y);
y = vsel(vmask_eq(x, vcast_vd_d(1.0)), vcast_vd_d(0.0), y);
y = vsel(vmask_lt(x, vcast_vd_d(1.0)), vcast_vd_d(NAN), y);
y = vsel(vmask_isnan(x), vcast_vd_d(NAN), y);
return y;
}
static INLINE vdouble xatanh(vdouble x) {
vdouble y = vabs(x);
vdouble2 d = logk2(div_dd(add2_ss(vcast_vd_d(1), y), add2_ss(vcast_vd_d(1), -y)));
y = vsel(vmask_gt(y, vcast_vd_d(1.0)), vcast_vd_d(NAN), vsel(vmask_eq(y, vcast_vd_d(1.0)), vcast_vd_d(INFINITY), vmul(vadd(d.x, d.y), vcast_vd_d(0.5))));
y = vsel(vorm(vmask_isinf(x), vmask_isnan(y)), vcast_vd_d(NAN), y);
y = vmulsign(y, x);
y = vsel(vmask_isnan(x), vcast_vd_d(NAN), y);
return y;
}
static INLINE vdouble xcbrt(vdouble d) {
vdouble x, y, q = vcast_vd_d(1.0);
vint e, qu, re;
vdouble t;
e = vilogbp1(vabs(d));
d = vldexp(d, vsubi(vcast_vi_i(0), e));
t = vadd(vcast_vd_vi(e), vcast_vd_d(6144));
qu = vtruncate_vi_vd(vdiv(t, vcast_vd_d(3)));
re = vtruncate_vi_vd(vsub(t, vmul(vcast_vd_vi(qu), vcast_vd_d(3))));
q = vsel(vmaski_eq(re, vcast_vi_i(1)), vcast_vd_d(1.2599210498948731647672106), q);
q = vsel(vmaski_eq(re, vcast_vi_i(2)), vcast_vd_d(1.5874010519681994747517056), q);
q = vldexp(q, vsubi(qu, vcast_vi_i(2048)));
q = vmulsign(q, d);
d = vabs(d);
x = vcast_vd_d(-0.640245898480692909870982);
x = vmla(x, d, vcast_vd_d(2.96155103020039511818595));
x = vmla(x, d, vcast_vd_d(-5.73353060922947843636166));
x = vmla(x, d, vcast_vd_d(6.03990368989458747961407));
x = vmla(x, d, vcast_vd_d(-3.85841935510444988821632));
x = vmla(x, d, vcast_vd_d(2.2307275302496609725722));
y = vmul(x, x); y = vmul(y, y); x = vsub(x, vmul(vmla(d, y, vneg(x)), vcast_vd_d(1.0 / 3.0)));
y = vmul(vmul(d, x), x);
y = vmul(vsub(y, vmul(vmul(vcast_vd_d(2.0 / 3.0), y), vmla(y, x, vcast_vd_d(-1.0)))), q);
return y;
}
static INLINE vdouble xexp2(vdouble a) {
vdouble u = expk(mul_ds(dd(vcast_vd_d(0.69314718055994528623), vcast_vd_d(2.3190468138462995584e-17)), a));
u = vsel(vmask_ispinf(a), vcast_vd_d(INFINITY), u);
u = vsel(vmask_isminf(a), vcast_vd_d(0), u);
return u;
}
static INLINE vdouble xexp10(vdouble a) {
vdouble u = expk(mul_ds(dd(vcast_vd_d(2.3025850929940459011), vcast_vd_d(-2.1707562233822493508e-16)), a));
u = vsel(vmask_ispinf(a), vcast_vd_d(INFINITY), u);
u = vsel(vmask_isminf(a), vcast_vd_d(0), u);
return u;
}
static INLINE vdouble xexpm1(vdouble a) {
vdouble2 d = add2_ds(expk2(dd(a, vcast_vd_d(0))), vcast_vd_d(-1.0));
vdouble x = d.x + d.y;
x = vsel(vmask_ispinf(a), vcast_vd_d(INFINITY), x);
x = vsel(vmask_isminf(a), vcast_vd_d(-1), x);
return x;
}
static INLINE vdouble xlog10(vdouble a) {
vdouble2 d = mul_dd(logk(a), dd(vcast_vd_d(0.43429448190325176116), vcast_vd_d(6.6494347733425473126e-17)));
vdouble x = d.x + d.y;
x = vsel(vmask_ispinf(a), vcast_vd_d(INFINITY), x);
x = vsel(vmask_gt(vcast_vd_d(0), a), vcast_vd_d(NAN), x);
x = vsel(vmask_eq(a, vcast_vd_d(0)), vcast_vd_d(-INFINITY), x);
return x;
}
static INLINE vdouble xlog1p(vdouble a) {
vdouble2 d = logk2(add2_ss(a, vcast_vd_d(1)));
vdouble x = d.x + d.y;
x = vsel(vmask_ispinf(a), vcast_vd_d(INFINITY), x);
x = vsel(vmask_gt(vcast_vd_d(-1), a), vcast_vd_d(NAN), x);
x = vsel(vmask_eq(a, vcast_vd_d(-1)), vcast_vd_d(-INFINITY), x);
return x;
}
//
typedef struct {
vfloat x, y;
} vfloat2;
static INLINE vfloat vmlaf(vfloat x, vfloat y, vfloat z) { return vaddf(vmulf(x, y), z); }
static INLINE vfloat vabsf(vfloat f) { return (vfloat)vandnotm((vmask)vcast_vf_f(-0.0f), (vmask)f); }
static INLINE vfloat vnegf(vfloat f) { return (vfloat)vxorm((vmask)f, (vmask)vcast_vf_f(-0.0f)); }
static INLINE vfloat vself(vmask mask, vfloat x, vfloat y) {
return (vfloat)vorm(vandm(mask, (vmask)x), vandnotm(mask, (vmask)y));
}
static INLINE vint2 vseli2_lt(vfloat f0, vfloat f1, vint2 x, vint2 y) {
vint2 m2 = vcast_vi2_vm(vmaskf_lt(f0, f1));
return vori2(vandi2(m2, x), vandnoti2(m2, y));
}
static INLINE vmask vsignbitf(vfloat f) {
return vandm((vmask)f, (vmask)vcast_vf_f(-0.0f));
}
static INLINE vfloat vmulsignf(vfloat x, vfloat y) {
return (vfloat)vxorm((vmask)x, vsignbitf(y));
}
static INLINE vfloat vsignf(vfloat f) {
return (vfloat)vorm((vmask)vcast_vf_f(1.0f), vandm((vmask)vcast_vf_f(-0.0f), (vmask)f));
}
static INLINE vmask vmaskf_isinf(vfloat d) { return vmaskf_eq(vabsf(d), vcast_vf_f(INFINITYf)); }
static INLINE vmask vmaskf_ispinf(vfloat d) { return vmaskf_eq(d, vcast_vf_f(INFINITYf)); }
static INLINE vmask vmaskf_isminf(vfloat d) { return vmaskf_eq(d, vcast_vf_f(-INFINITYf)); }
static INLINE vmask vmaskf_isnan(vfloat d) { return vmaskf_neq(d, d); }
static INLINE vfloat visinf2f(vfloat d, vfloat m) { return (vfloat)vandm(vmaskf_isinf(d), vorm(vsignbitf(d), (vmask)m)); }
static INLINE vfloat visinff(vfloat d) { return visinf2f(d, vcast_vf_f(1.0f)); }
static INLINE vint2 vilogbp1f(vfloat d) {
vmask m = vmaskf_lt(d, vcast_vf_f(5.421010862427522E-20f));
d = vself(m, vmulf(vcast_vf_f(1.8446744073709552E19f), d), d);
vint2 q = vandi2(vsrli2(vcast_vi2_vm(vreinterpret_vm_vf(d)), 23), vcast_vi2_i(0xff));
q = vsubi2(q, vseli2(m, vcast_vi2_i(64 + 0x7e), vcast_vi2_i(0x7e)));
return q;
}
static INLINE vfloat vldexpf(vfloat x, vint2 q) {
vfloat u;
vint2 m = vsrai2(q, 31);
m = vslli2(vsubi2(vsrai2(vaddi2(m, q), 6), m), 4);
q = vsubi2(q, vslli2(m, 2));
u = vreinterpret_vf_vm(vcast_vm_vi2(vslli2(vaddi2(m, vcast_vi2_i(0x7f)), 23)));
x = vmulf(vmulf(vmulf(vmulf(x, u), u), u), u);
u = vreinterpret_vf_vm(vcast_vm_vi2(vslli2(vaddi2(q, vcast_vi2_i(0x7f)), 23)));
return vmulf(x, u);
}
static INLINE vfloat xsinf(vfloat d) {
vint2 q;
vfloat u, s;
q = vrint_vi2_vf(vmulf(d, vcast_vf_f((float)M_1_PI)));
u = vcast_vf_vi2(q);
d = vmlaf(u, vcast_vf_f(-PI4_Af*4), d);
d = vmlaf(u, vcast_vf_f(-PI4_Bf*4), d);
d = vmlaf(u, vcast_vf_f(-PI4_Cf*4), d);
d = vmlaf(u, vcast_vf_f(-PI4_Df*4), d);
s = vmulf(d, d);
d = vself(vmaski2_eq(vandi2(q, vcast_vi2_i(1)), vcast_vi2_i(1)), vnegf(d), d);
u = vcast_vf_f(2.6083159809786593541503e-06f);
u = vmlaf(u, s, vcast_vf_f(-0.0001981069071916863322258f));
u = vmlaf(u, s, vcast_vf_f(0.00833307858556509017944336f));
u = vmlaf(u, s, vcast_vf_f(-0.166666597127914428710938f));
u = vmlaf(s, vmulf(u, d), d);
return u;
}
static INLINE vfloat xcosf(vfloat d) {
vint2 q;
vfloat u, s;
q = vrint_vi2_vf(vsubf(vmulf(d, vcast_vf_f((float)M_1_PI)), vcast_vf_f(0.5f)));
q = vaddi2(vaddi2(q, q), vcast_vi2_i(1));
u = vcast_vf_vi2(q);
d = vmlaf(u, vcast_vf_f(-PI4_Af*2), d);
d = vmlaf(u, vcast_vf_f(-PI4_Bf*2), d);
d = vmlaf(u, vcast_vf_f(-PI4_Cf*2), d);
d = vmlaf(u, vcast_vf_f(-PI4_Df*2), d);
s = vmulf(d, d);
d = vself(vmaski2_eq(vandi2(q, vcast_vi2_i(2)), vcast_vi2_i(2)), d, vnegf(d));
u = vcast_vf_f(2.6083159809786593541503e-06f);
u = vmlaf(u, s, vcast_vf_f(-0.0001981069071916863322258f));