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77e97be151a2d3fd135f17ecf74b00b7e5fc8d1c
rawTherapee/rtengine/sleef.c
Hombre 8b2eac9a3d Pipette and "On Preview Widgets" branch. See issue 227 
The pipette part is already working quite nice but need to be finished. The widgets part needs more work...
2014-01-21 23:37:36 +01:00

1239 lines
29 KiB
C
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#ifndef _SLEEFC_
#define _SLEEFC_
#include <assert.h>
#include <stdint.h>
#include <math.h>
//#include <bits/nan.h>
//#include <bits/inf.h>
#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
__inline int64_t doubleToRawLongBits(double d) {
union {
double f;
int64_t i;
} tmp;
tmp.f = d;
return tmp.i;
}
__inline double longBitsToDouble(int64_t i) {
union {
double f;
int64_t i;
} tmp;
tmp.i = i;
return tmp.f;
}
__inline double xfabs(double x) {
return longBitsToDouble(0x7fffffffffffffffLL & doubleToRawLongBits(x));
}
__inline double mulsign(double x, double y) {
return longBitsToDouble(doubleToRawLongBits(x) ^ (doubleToRawLongBits(y) & (1LL << 63)));
}
__inline double sign(double d) { return mulsign(1, d); }
__inline double mla(double x, double y, double z) { return x * y + z; }
__inline double xrint(double x) { return x < 0 ? (int)(x - 0.5) : (int)(x + 0.5); }
__inline int xisnan(double x) { return x != x; }
__inline int xisinf(double x) { return x == INFINITY || x == -INFINITY; }
__inline int xisminf(double x) { return x == -INFINITY; }
__inline int xispinf(double x) { return x == INFINITY; }
__inline double ldexpk(double x, int q) {
double u;
int m;
m = q >> 31;
m = (((m + q) >> 9) - m) << 7;
q = q - (m << 2);
u = longBitsToDouble(((int64_t)(m + 0x3ff)) << 52);
x = x * u * u * u * u;
u = longBitsToDouble(((int64_t)(q + 0x3ff)) << 52);
return x * u;
}
__inline double xldexp(double x, int q) { return ldexpk(x, q); }
__inline int ilogbp1(double d) {
int m = d < 4.9090934652977266E-91;
d = m ? 2.037035976334486E90 * d : d;
int q = (doubleToRawLongBits(d) >> 52) & 0x7ff;
q = m ? q - (300 + 0x03fe) : q - 0x03fe;
return q;
}
__inline int xilogb(double d) {
int e = ilogbp1(xfabs(d)) - 1;
e = d == 0 ? -2147483648.0 : e;
e = d == INFINITY || d == -INFINITY ? 2147483647 : e;
return e;
}
__inline double upper(double d) {
return longBitsToDouble(doubleToRawLongBits(d) & 0xfffffffff8000000LL);
}
typedef struct {
double x, y;
} double2;
typedef struct {
float x, y;
} float2;
__inline double2 dd(double h, double l) {
double2 ret;
ret.x = h; ret.y = l;
return ret;
}
__inline double2 normalize_d(double2 t) {
double2 s;
s.x = t.x + t.y;
s.y = t.x - s.x + t.y;
return s;
}
__inline double2 scale_d(double2 d, double s) {
double2 r;
r.x = d.x * s;
r.y = d.y * s;
return r;
}
__inline double2 add2_ss(double x, double y) {
double2 r;
r.x = x + y;
double v = r.x - x;
r.y = (x - (r.x - v)) + (y - v);
return r;
}
__inline double2 add_ds(double2 x, double y) {
// |x| >= |y|
double2 r;
assert(xisnan(x.x) || xisnan(y) || xfabs(x.x) >= xfabs(y));
r.x = x.x + y;
r.y = x.x - r.x + y + x.y;
return r;
}
__inline double2 add2_ds(double2 x, double y) {
// |x| >= |y|
double2 r;
r.x = x.x + y;
double v = r.x - x.x;
r.y = (x.x - (r.x - v)) + (y - v);
r.y += x.y;
return r;
}
__inline double2 add_sd(double x, double2 y) {
// |x| >= |y|
double2 r;
assert(xisnan(x) || xisnan(y.x) || xfabs(x) >= xfabs(y.x));
r.x = x + y.x;
r.y = x - r.x + y.x + y.y;
return r;
}
__inline double2 add_dd(double2 x, double2 y) {
// |x| >= |y|
double2 r;
assert(xisnan(x.x) || xisnan(y.x) || xfabs(x.x) >= xfabs(y.x));
r.x = x.x + y.x;
r.y = x.x - r.x + y.x + x.y + y.y;
return r;
}
__inline double2 add2_dd(double2 x, double2 y) {
double2 r;
r.x = x.x + y.x;
double v = r.x - x.x;
r.y = (x.x - (r.x - v)) + (y.x - v);
r.y += x.y + y.y;
return r;
}
__inline double2 div_dd(double2 n, double2 d) {
double t = 1.0 / d.x;
double dh = upper(d.x), dl = d.x - dh;
double th = upper(t ), tl = t - th;
double nhh = upper(n.x), nhl = n.x - nhh;
double2 q;
q.x = n.x * t;
double u = -q.x + nhh * th + nhh * tl + nhl * th + nhl * tl +
q.x * (1 - dh * th - dh * tl - dl * th - dl * tl);
q.y = t * (n.y - q.x * d.y) + u;
return q;
}
__inline double2 mul_ss(double x, double y) {
double xh = upper(x), xl = x - xh;
double yh = upper(y), yl = y - yh;
double2 r;
r.x = x * y;
r.y = xh * yh - r.x + xl * yh + xh * yl + xl * yl;
return r;
}
__inline double2 mul_ds(double2 x, double y) {
double xh = upper(x.x), xl = x.x - xh;
double yh = upper(y ), yl = y - yh;
double2 r;
r.x = x.x * y;
r.y = xh * yh - r.x + xl * yh + xh * yl + xl * yl + x.y * y;
return r;
}
__inline double2 mul_dd(double2 x, double2 y) {
double xh = upper(x.x), xl = x.x - xh;
double yh = upper(y.x), yl = y.x - yh;
double2 r;
r.x = x.x * y.x;
r.y = xh * yh - r.x + xl * yh + xh * yl + xl * yl + x.x * y.y + x.y * y.x;
return r;
}
__inline double2 squ_d(double2 x) {
double xh = upper(x.x), xl = x.x - xh;
double2 r;
r.x = x.x * x.x;
r.y = xh * xh - r.x + (xh + xh) * xl + xl * xl + x.x * (x.y + x.y);
return r;
}
__inline double2 rec_s(double d) {
double t = 1.0 / d;
double dh = upper(d), dl = d - dh;
double th = upper(t), tl = t - th;
double2 q;
q.x = t;
q.y = t * (1 - dh * th - dh * tl - dl * th - dl * tl);
return q;
}
__inline double2 sqrt_d(double2 d) {
double t = sqrt(d.x + d.y);
return scale_d(mul_dd(add2_dd(d, mul_ss(t, t)), rec_s(t)), 0.5);
}
__inline double atan2k(double y, double x) {
double s, t, u;
int q = 0;
if (x < 0) { x = -x; q = -2; }
if (y > x) { t = x; x = y; y = -t; q += 1; }
s = y / x;
t = s * s;
u = -1.88796008463073496563746e-05;
u = u * t + (0.000209850076645816976906797);
u = u * t + (-0.00110611831486672482563471);
u = u * t + (0.00370026744188713119232403);
u = u * t + (-0.00889896195887655491740809);
u = u * t + (0.016599329773529201970117);
u = u * t + (-0.0254517624932312641616861);
u = u * t + (0.0337852580001353069993897);
u = u * t + (-0.0407629191276836500001934);
u = u * t + (0.0466667150077840625632675);
u = u * t + (-0.0523674852303482457616113);
u = u * t + (0.0587666392926673580854313);
u = u * t + (-0.0666573579361080525984562);
u = u * t + (0.0769219538311769618355029);
u = u * t + (-0.090908995008245008229153);
u = u * t + (0.111111105648261418443745);
u = u * t + (-0.14285714266771329383765);
u = u * t + (0.199999999996591265594148);
u = u * t + (-0.333333333333311110369124);
t = u * t * s + s;
t = q * (M_PI/2) + t;
return t;
}
__inline double xatan2(double y, double x) {
double r = atan2k(xfabs(y), x);
r = mulsign(r, x);
if (xisinf(x) || x == 0) r = M_PI/2 - (xisinf(x) ? (sign(x) * (M_PI /2)) : 0);
if (xisinf(y) ) r = M_PI/2 - (xisinf(x) ? (sign(x) * (M_PI*1/4)) : 0);
if ( y == 0) r = (sign(x) == -1 ? M_PI : 0);
return xisnan(x) || xisnan(y) ? NAN : mulsign(r, y);
}
__inline double xasin(double d) {
return mulsign(atan2k(xfabs(d), sqrt((1+d)*(1-d))), d);
}
__inline double xacos(double d) {
return mulsign(atan2k(sqrt((1+d)*(1-d)), xfabs(d)), d) + (d < 0 ? M_PI : 0);
}
__inline double xatan(double s) {
double t, u;
int q = 0;
if (s < 0) { s = -s; q = 2; }
if (s > 1) { s = 1.0 / s; q |= 1; }
t = s * s;
u = -1.88796008463073496563746e-05;
u = u * t + (0.000209850076645816976906797);
u = u * t + (-0.00110611831486672482563471);
u = u * t + (0.00370026744188713119232403);
u = u * t + (-0.00889896195887655491740809);
u = u * t + (0.016599329773529201970117);
u = u * t + (-0.0254517624932312641616861);
u = u * t + (0.0337852580001353069993897);
u = u * t + (-0.0407629191276836500001934);
u = u * t + (0.0466667150077840625632675);
u = u * t + (-0.0523674852303482457616113);
u = u * t + (0.0587666392926673580854313);
u = u * t + (-0.0666573579361080525984562);
u = u * t + (0.0769219538311769618355029);
u = u * t + (-0.090908995008245008229153);
u = u * t + (0.111111105648261418443745);
u = u * t + (-0.14285714266771329383765);
u = u * t + (0.199999999996591265594148);
u = u * t + (-0.333333333333311110369124);
t = s + s * (t * u);
if ((q & 1) != 0) t = 1.570796326794896557998982 - t;
if ((q & 2) != 0) t = -t;
return t;
}
__inline double xsin(double d) {
int q;
double u, s;
q = (int)xrint(d * M_1_PI);
d = mla(q, -PI4_A*4, d);
d = mla(q, -PI4_B*4, d);
d = mla(q, -PI4_C*4, d);
s = d * d;
if ((q & 1) != 0) d = -d;
u = -7.97255955009037868891952e-18;
u = mla(u, s, 2.81009972710863200091251e-15);
u = mla(u, s, -7.64712219118158833288484e-13);
u = mla(u, s, 1.60590430605664501629054e-10);
u = mla(u, s, -2.50521083763502045810755e-08);
u = mla(u, s, 2.75573192239198747630416e-06);
u = mla(u, s, -0.000198412698412696162806809);
u = mla(u, s, 0.00833333333333332974823815);
u = mla(u, s, -0.166666666666666657414808);
u = mla(s, u * d, d);
return u;
}
__inline double xcos(double d) {
int q;
double u, s;
q = 1 + 2*(int)xrint(d * M_1_PI - 0.5);
d = mla(q, -PI4_A*2, d);
d = mla(q, -PI4_B*2, d);
d = mla(q, -PI4_C*2, d);
s = d * d;
if ((q & 2) == 0) d = -d;
u = -7.97255955009037868891952e-18;
u = mla(u, s, 2.81009972710863200091251e-15);
u = mla(u, s, -7.64712219118158833288484e-13);
u = mla(u, s, 1.60590430605664501629054e-10);
u = mla(u, s, -2.50521083763502045810755e-08);
u = mla(u, s, 2.75573192239198747630416e-06);
u = mla(u, s, -0.000198412698412696162806809);
u = mla(u, s, 0.00833333333333332974823815);
u = mla(u, s, -0.166666666666666657414808);
u = mla(s, u * d, d);
return u;
}
__inline double2 xsincos(double d) {
int q;
double u, s, t;
double2 r;
q = (int)xrint(d * (2 * M_1_PI));
s = d;
s = mla(-q, PI4_A*2, s);
s = mla(-q, PI4_B*2, s);
s = mla(-q, PI4_C*2, s);
t = s;
s = s * s;
u = 1.58938307283228937328511e-10;
u = mla(u, s, -2.50506943502539773349318e-08);
u = mla(u, s, 2.75573131776846360512547e-06);
u = mla(u, s, -0.000198412698278911770864914);
u = mla(u, s, 0.0083333333333191845961746);
u = mla(u, s, -0.166666666666666130709393);
u = u * s * t;
r.x = t + u;
u = -1.13615350239097429531523e-11;
u = mla(u, s, 2.08757471207040055479366e-09);
u = mla(u, s, -2.75573144028847567498567e-07);
u = mla(u, s, 2.48015872890001867311915e-05);
u = mla(u, s, -0.00138888888888714019282329);
u = mla(u, s, 0.0416666666666665519592062);
u = mla(u, s, -0.5);
r.y = u * s + 1;
if ((q & 1) != 0) { s = r.y; r.y = r.x; r.x = s; }
if ((q & 2) != 0) { r.x = -r.x; }
if (((q+1) & 2) != 0) { r.y = -r.y; }
if (xisinf(d)) { r.x = r.y = NAN; }
return r;
}
__inline double xtan(double d) {
int q;
double u, s, x;
q = (int)xrint(d * (2 * M_1_PI));
x = mla(q, -PI4_A*2, d);
x = mla(q, -PI4_B*2, x);
x = mla(q, -PI4_C*2, x);
s = x * x;
if ((q & 1) != 0) x = -x;
u = 1.01419718511083373224408e-05;
u = mla(u, s, -2.59519791585924697698614e-05);
u = mla(u, s, 5.23388081915899855325186e-05);
u = mla(u, s, -3.05033014433946488225616e-05);
u = mla(u, s, 7.14707504084242744267497e-05);
u = mla(u, s, 8.09674518280159187045078e-05);
u = mla(u, s, 0.000244884931879331847054404);
u = mla(u, s, 0.000588505168743587154904506);
u = mla(u, s, 0.00145612788922812427978848);
u = mla(u, s, 0.00359208743836906619142924);
u = mla(u, s, 0.00886323944362401618113356);
u = mla(u, s, 0.0218694882853846389592078);
u = mla(u, s, 0.0539682539781298417636002);
u = mla(u, s, 0.133333333333125941821962);
u = mla(u, s, 0.333333333333334980164153);
u = mla(s, u * x, x);
if ((q & 1) != 0) u = 1.0 / u;
if (xisinf(d)) u = NAN;
return u;
}
__inline double xlog(double d) {
double x, x2, t, m;
int e;
e = ilogbp1(d * 0.7071);
m = ldexpk(d, -e);
x = (m-1) / (m+1);
x2 = x * x;
t = 0.148197055177935105296783;
t = mla(t, x2, 0.153108178020442575739679);
t = mla(t, x2, 0.181837339521549679055568);
t = mla(t, x2, 0.22222194152736701733275);
t = mla(t, x2, 0.285714288030134544449368);
t = mla(t, x2, 0.399999999989941956712869);
t = mla(t, x2, 0.666666666666685503450651);
t = mla(t, x2, 2);
x = x * t + 0.693147180559945286226764 * e;
if (xisinf(d)) x = INFINITY;
if (d < 0) x = NAN;
if (d == 0) x = -INFINITY;
return x;
}
__inline double xexp(double d) {
int q = (int)xrint(d * R_LN2);
double s, u;
s = mla(q, -L2U, d);
s = mla(q, -L2L, s);
u = 2.08860621107283687536341e-09;
u = mla(u, s, 2.51112930892876518610661e-08);
u = mla(u, s, 2.75573911234900471893338e-07);
u = mla(u, s, 2.75572362911928827629423e-06);
u = mla(u, s, 2.4801587159235472998791e-05);
u = mla(u, s, 0.000198412698960509205564975);
u = mla(u, s, 0.00138888888889774492207962);
u = mla(u, s, 0.00833333333331652721664984);
u = mla(u, s, 0.0416666666666665047591422);
u = mla(u, s, 0.166666666666666851703837);
u = mla(u, s, 0.5);
u = s * s * u + s + 1;
u = ldexpk(u, q);
if (xisminf(d)) u = 0;
return u;
}
__inline double2 logk(double d) {
double2 x, x2;
double m, t;
int e;
e = ilogbp1(d * 0.7071);
m = ldexpk(d, -e);
x = div_dd(add2_ss(-1, m), add2_ss(1, m));
x2 = squ_d(x);
t = 0.134601987501262130076155;
t = mla(t, x2.x, 0.132248509032032670243288);
t = mla(t, x2.x, 0.153883458318096079652524);
t = mla(t, x2.x, 0.181817427573705403298686);
t = mla(t, x2.x, 0.222222231326187414840781);
t = mla(t, x2.x, 0.285714285651261412873718);
t = mla(t, x2.x, 0.400000000000222439910458);
t = mla(t, x2.x, 0.666666666666666371239645);
return add2_dd(mul_ds(dd(0.693147180559945286226764, 2.319046813846299558417771e-17), e),
add2_dd(scale_d(x, 2), mul_ds(mul_dd(x2, x), t)));
}
__inline double expk(double2 d) {
int q = (int)rint((d.x + d.y) * R_LN2);
double2 s, t;
double u;
s = add2_ds(d, q * -L2U);
s = add2_ds(s, q * -L2L);
s = normalize_d(s);
u = 2.51069683420950419527139e-08;
u = mla(u, s.x, 2.76286166770270649116855e-07);
u = mla(u, s.x, 2.75572496725023574143864e-06);
u = mla(u, s.x, 2.48014973989819794114153e-05);
u = mla(u, s.x, 0.000198412698809069797676111);
u = mla(u, s.x, 0.0013888888939977128960529);
u = mla(u, s.x, 0.00833333333332371417601081);
u = mla(u, s.x, 0.0416666666665409524128449);
u = mla(u, s.x, 0.166666666666666740681535);
u = mla(u, s.x, 0.500000000000000999200722);
t = add_dd(s, mul_ds(squ_d(s), u));
t = add_sd(1, t);
return ldexpk(t.x + t.y, q);
}
__inline double xpow(double x, double y) {
int yisint = (int)y == y;
int yisodd = (1 & (int)y) != 0 && yisint;
double result = expk(mul_ds(logk(xfabs(x)), y));
result = xisnan(result) ? INFINITY : result;
result *= (x >= 0 ? 1 : (!yisint ? NAN : (yisodd ? -1 : 1)));
double efx = mulsign(xfabs(x) - 1, y);
if (xisinf(y)) result = efx < 0 ? 0.0 : (efx == 0 ? 1.0 : INFINITY);
if (xisinf(x) || x == 0) result = (yisodd ? sign(x) : 1) * ((x == 0 ? -y : y) < 0 ? 0 : INFINITY);
if (xisnan(x) || xisnan(y)) result = NAN;
if (y == 0 || x == 1) result = 1;
return result;
}
__inline double2 expk2(double2 d) {
int q = (int)rint((d.x + d.y) * R_LN2);
double2 s, t;
double u;
s = add2_ds(d, q * -L2U);
s = add2_ds(s, q * -L2L);
s = normalize_d(s);
u = 2.51069683420950419527139e-08;
u = mla(u, s.x, 2.76286166770270649116855e-07);
u = mla(u, s.x, 2.75572496725023574143864e-06);
u = mla(u, s.x, 2.48014973989819794114153e-05);
u = mla(u, s.x, 0.000198412698809069797676111);
u = mla(u, s.x, 0.0013888888939977128960529);
u = mla(u, s.x, 0.00833333333332371417601081);
u = mla(u, s.x, 0.0416666666665409524128449);
u = mla(u, s.x, 0.166666666666666740681535);
u = mla(u, s.x, 0.500000000000000999200722);
t = add_dd(s, mul_ds(squ_d(s), u));
t = add_sd(1, t);
return dd(ldexpk(t.x, q), ldexpk(t.y, q));
}
__inline double xsinh(double x) {
double y = xfabs(x);
double2 d = expk2(dd(y, 0));
d = add2_dd(d, div_dd(dd(-1, 0), d));
y = (d.x + d.y) * 0.5;
y = xisinf(x) || xisnan(y) ? INFINITY : y;
y = mulsign(y, x);
y = xisnan(x) ? NAN : y;
return y;
}
__inline double xcosh(double x) {
double2 d = expk2(dd(x, 0));
d = add2_dd(d, div_dd(dd(1, 0), d));
double y = (d.x + d.y) * 0.5;
y = xisinf(x) || xisnan(y) ? INFINITY : y;
y = xisnan(x) ? NAN : y;
return y;
}
__inline double xtanh(double x) {
double y = xfabs(x);
double2 d = expk2(dd(y, 0));
double2 e = div_dd(dd(1, 0), d);
d = div_dd(add2_dd(d, scale_d(e, -1)), add2_dd(d, e));
y = d.x + d.y;
y = xisinf(x) || xisnan(y) ? 1.0 : y;
y = mulsign(y, x);
y = xisnan(x) ? NAN : y;
return y;
}
__inline double2 logk2(double2 d) {
double2 x, x2, m;
double t;
int e;
d = normalize_d(d);
e = ilogbp1(d.x * 0.7071);
m = scale_d(d, ldexpk(1, -e));
x = div_dd(add2_ds(m, -1), add2_ds(m, 1));
x2 = squ_d(x);
t = 0.134601987501262130076155;
t = mla(t, x2.x, 0.132248509032032670243288);
t = mla(t, x2.x, 0.153883458318096079652524);
t = mla(t, x2.x, 0.181817427573705403298686);
t = mla(t, x2.x, 0.222222231326187414840781);
t = mla(t, x2.x, 0.285714285651261412873718);
t = mla(t, x2.x, 0.400000000000222439910458);
t = mla(t, x2.x, 0.666666666666666371239645);
return add2_dd(mul_ds(dd(0.693147180559945286226764, 2.319046813846299558417771e-17), e),
add2_dd(scale_d(x, 2), mul_ds(mul_dd(x2, x), t)));
}
__inline double xasinh(double x) {
double y = xfabs(x);
double2 d = logk2(add2_ds(sqrt_d(add2_ds(mul_ss(y, y), 1)), y));
y = d.x + d.y;
y = xisinf(x) || xisnan(y) ? INFINITY : y;
y = mulsign(y, x);
y = xisnan(x) ? NAN : y;
return y;
}
__inline double xacosh(double x) {
double2 d = logk2(add2_ds(sqrt_d(add2_ds(mul_ss(x, x), -1)), x));
double y = d.x + d.y;
y = xisinf(x) || xisnan(y) ? INFINITY : y;
y = x == 1.0 ? 0.0 : y;
y = x < 1.0 ? NAN : y;
y = xisnan(x) ? NAN : y;
return y;
}
__inline double xatanh(double x) {
double y = xfabs(x);
double2 d = logk2(div_dd(add2_ss(1, y), add2_ss(1, -y)));
y = y > 1.0 ? NAN : (y == 1.0 ? INFINITY : (d.x + d.y) * 0.5);
y = xisinf(x) || xisnan(y) ? NAN : y;
y = mulsign(y, x);
y = xisnan(x) ? NAN : y;
return y;
}
//
__inline double xfma(double x, double y, double z) {
union {
double f;
long long int i;
} tmp;
tmp.f = x;
tmp.i = (tmp.i + 0x4000000) & 0xfffffffff8000000LL;
double xh = tmp.f, xl = x - xh;
tmp.f = y;
tmp.i = (tmp.i + 0x4000000) & 0xfffffffff8000000LL;
double yh = tmp.f, yl = y - yh;
double h = x * y;
double l = xh * yh - h + xl * yh + xh * yl + xl * yl;
double h2, l2, v;
h2 = h + z;
v = h2 - h;
l2 = (h - (h2 - v)) + (z - v) + l;
return h2 + l2;
}
__inline double xsqrt(double d) { // max error : 0.5 ulp
double q = 1;
if (d < 8.636168555094445E-78) {
d *= 1.157920892373162E77;
q = 2.9387358770557188E-39;
}
// http://en.wikipedia.org/wiki/Fast_inverse_square_root
double x = longBitsToDouble(0x5fe6ec85e7de30da - (doubleToRawLongBits(d + 1e-320) >> 1));
x = x * (1.5 - 0.5 * d * x * x);
x = x * (1.5 - 0.5 * d * x * x);
x = x * (1.5 - 0.5 * d * x * x);
// You can change xfma to fma if fma is correctly implemented
x = xfma(d * x, d * x, -d) * (x * -0.5) + d * x;
return d == INFINITY ? INFINITY : x * q;
}
__inline double xcbrt(double d) { // max error : 2 ulps
double x, y, q = 1.0;
int e, r;
e = ilogbp1(d);
d = ldexpk(d, -e);
r = (e + 6144) % 3;
q = (r == 1) ? 1.2599210498948731647672106 : q;
q = (r == 2) ? 1.5874010519681994747517056 : q;
q = ldexpk(q, (e + 6144) / 3 - 2048);
q = mulsign(q, d);
d = xfabs(d);
x = -0.640245898480692909870982;
x = x * d + 2.96155103020039511818595;
x = x * d + -5.73353060922947843636166;
x = x * d + 6.03990368989458747961407;
x = x * d + -3.85841935510444988821632;
x = x * d + 2.2307275302496609725722;
y = x * x; y = y * y; x -= (d * y - x) * (1.0 / 3.0);
y = d * x * x;
y = (y - (2.0 / 3.0) * y * (y * x - 1)) * q;
return y;
}
__inline double xexp2(double a) {
double u = expk(mul_ds(dd(0.69314718055994528623, 2.3190468138462995584e-17), a));
if (xispinf(a)) u = INFINITY;
if (xisminf(a)) u = 0;
return u;
}
__inline double xexp10(double a) {
double u = expk(mul_ds(dd(2.3025850929940459011, -2.1707562233822493508e-16), a));
if (xispinf(a)) u = INFINITY;
if (xisminf(a)) u = 0;
return u;
}
__inline double xexpm1(double a) {
double2 d = add2_ds(expk2(dd(a, 0)), -1.0);
double x = d.x + d.y;
if (xispinf(a)) x = INFINITY;
if (xisminf(a)) x = -1;
return x;
}
__inline double xlog10(double a) {
double2 d = mul_dd(logk(a), dd(0.43429448190325176116, 6.6494347733425473126e-17));
double x = d.x + d.y;
if (xisinf(a)) x = INFINITY;
if (a < 0) x = NAN;
if (a == 0) x = -INFINITY;
return x;
}
__inline double xlog1p(double a) {
double2 d = logk2(add2_ss(a, 1));
double x = d.x + d.y;
if (xisinf(a)) x = INFINITY;
if (a < -1) x = NAN;
if (a == -1) x = -INFINITY;
return x;
}
///////////////////////////////////////////
#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 M_PIf ((float)M_PI)
#define INFINITYf ((float)INFINITY)
#define NANf ((float)NAN)
__inline int32_t floatToRawIntBits(float d) {
union {
float f;
int32_t i;
} tmp;
tmp.f = d;
return tmp.i;
}
__inline float intBitsToFloat(int32_t i) {
union {
float f;
int32_t i;
} tmp;
tmp.i = i;
return tmp.f;
}
__inline float xfabsf(float x) {
return intBitsToFloat(0x7fffffffL & floatToRawIntBits(x));
}
__inline float mulsignf(float x, float y) {
return intBitsToFloat(floatToRawIntBits(x) ^ (floatToRawIntBits(y) & (1 << 31)));
}
__inline float signf(float d) { return mulsignf(1, d); }
__inline float mlaf(float x, float y, float z) { return x * y + z; }
__inline float xrintf(float x) { return x < 0 ? (int)(x - 0.5f) : (int)(x + 0.5f); }
__inline int xisnanf(float x) { return x != x; }
__inline int xisinff(float x) { return x == INFINITYf || x == -INFINITYf; }
__inline int xisminff(float x) { return x == -INFINITYf; }
__inline int xispinff(float x) { return x == INFINITYf; }
__inline int ilogbp1f(float d) {
int m = d < 5.421010862427522E-20f;
d = m ? 1.8446744073709552E19f * d : d;
int q = (floatToRawIntBits(d) >> 23) & 0xff;
q = m ? q - (64 + 0x7e) : q - 0x7e;
return q;
}
__inline float ldexpkf(float x, int q) {
float u;
int m;
m = q >> 31;
m = (((m + q) >> 6) - m) << 4;
q = q - (m << 2);
u = intBitsToFloat(((int32_t)(m + 0x7f)) << 23);
x = x * u * u * u * u;
u = intBitsToFloat(((int32_t)(q + 0x7f)) << 23);
return x * u;
}
__inline float xcbrtf(float d) { // max error : 2 ulps
float x, y, q = 1.0f;
int e, r;
e = ilogbp1f(d);
d = ldexpkf(d, -e);
r = (e + 6144) % 3;
q = (r == 1) ? 1.2599210498948731647672106f : q;
q = (r == 2) ? 1.5874010519681994747517056f : q;
q = ldexpkf(q, (e + 6144) / 3 - 2048);
q = mulsignf(q, d);
d = xfabsf(d);
x = -0.601564466953277587890625f;
x = mlaf(x, d, 2.8208892345428466796875f);
x = mlaf(x, d, -5.532182216644287109375f);
x = mlaf(x, d, 5.898262500762939453125f);
x = mlaf(x, d, -3.8095417022705078125f);
x = mlaf(x, d, 2.2241256237030029296875f);
y = d * x * x;
y = (y - (2.0f / 3.0f) * y * (y * x - 1.0f)) * q;
return y;
}
__inline float xsinf(float d) {
int q;
float u, s;
q = (int)xrintf(d * (float)M_1_PI);
d = mlaf(q, -PI4_Af*4, d);
d = mlaf(q, -PI4_Bf*4, d);
d = mlaf(q, -PI4_Cf*4, d);
d = mlaf(q, -PI4_Df*4, d);
s = d * d;
if ((q & 1) != 0) d = -d;
u = 2.6083159809786593541503e-06f;
u = mlaf(u, s, -0.0001981069071916863322258f);
u = mlaf(u, s, 0.00833307858556509017944336f);
u = mlaf(u, s, -0.166666597127914428710938f);
u = mlaf(s, u * d, d);
return u;
}
__inline float xcosf(float d) {
int q;
float u, s;
q = 1 + 2*(int)xrintf(d * (float)M_1_PI - 0.5f);
d = mlaf(q, -PI4_Af*2, d);
d = mlaf(q, -PI4_Bf*2, d);
d = mlaf(q, -PI4_Cf*2, d);
d = mlaf(q, -PI4_Df*2, d);
s = d * d;
if ((q & 2) == 0) d = -d;
u = 2.6083159809786593541503e-06f;
u = mlaf(u, s, -0.0001981069071916863322258f);
u = mlaf(u, s, 0.00833307858556509017944336f);
u = mlaf(u, s, -0.166666597127914428710938f);
u = mlaf(s, u * d, d);
return u;
}
__inline float2 xsincosf(float d) {
int q;
float u, s, t;
float2 r;
q = (int)rint(d * ((float)(2 * M_1_PI)));
s = d;
s = mlaf(q, -PI4_Af*2, s);
s = mlaf(q, -PI4_Bf*2, s);
s = mlaf(q, -PI4_Cf*2, s);
s = mlaf(q, -PI4_Df*2, s);
t = s;
s = s * s;
u = -0.000195169282960705459117889f;
u = mlaf(u, s, 0.00833215750753879547119141f);
u = mlaf(u, s, -0.166666537523269653320312f);
u = u * s * t;
r.x = t + u;
u = -2.71811842367242206819355e-07f;
u = mlaf(u, s, 2.47990446951007470488548e-05f);
u = mlaf(u, s, -0.00138888787478208541870117f);
u = mlaf(u, s, 0.0416666641831398010253906f);
u = mlaf(u, s, -0.5f);
r.y = u * s + 1;
if ((q & 1) != 0) { s = r.y; r.y = r.x; r.x = s; }
if ((q & 2) != 0) { r.x = -r.x; }
if (((q+1) & 2) != 0) { r.y = -r.y; }
if (xisinff(d)) { r.x = r.y = NANf; }
return r;
}
__inline float xtanf(float d) {
int q;
float u, s, x;
q = (int)xrintf(d * (float)(2 * M_1_PI));
x = d;
x = mlaf(q, -PI4_Af*2, x);
x = mlaf(q, -PI4_Bf*2, x);
x = mlaf(q, -PI4_Cf*2, x);
x = mlaf(q, -PI4_Df*2, x);
s = x * x;
if ((q & 1) != 0) x = -x;
u = 0.00927245803177356719970703f;
u = mlaf(u, s, 0.00331984995864331722259521f);
u = mlaf(u, s, 0.0242998078465461730957031f);
u = mlaf(u, s, 0.0534495301544666290283203f);
u = mlaf(u, s, 0.133383005857467651367188f);
u = mlaf(u, s, 0.333331853151321411132812f);
u = mlaf(s, u * x, x);
if ((q & 1) != 0) u = 1.0f / u;
if (xisinff(d)) u = NANf;
return u;
}
__inline float xatanf(float s) {
float t, u;
int q = 0;
if (s < 0) { s = -s; q = 2; }
if (s > 1) { s = 1.0f / s; q |= 1; }
t = s * s;
u = 0.00282363896258175373077393f;
u = mlaf(u, t, -0.0159569028764963150024414f);
u = mlaf(u, t, 0.0425049886107444763183594f);
u = mlaf(u, t, -0.0748900920152664184570312f);
u = mlaf(u, t, 0.106347933411598205566406f);
u = mlaf(u, t, -0.142027363181114196777344f);
u = mlaf(u, t, 0.199926957488059997558594f);
u = mlaf(u, t, -0.333331018686294555664062f);
t = s + s * (t * u);
if ((q & 1) != 0) t = 1.570796326794896557998982f - t;
if ((q & 2) != 0) t = -t;
return t;
}
__inline float atan2kf(float y, float x) {
float s, t, u;
int q = 0;
if (x < 0) { x = -x; q = -2; }
if (y > x) { t = x; x = y; y = -t; q += 1; }
s = y / x;
t = s * s;
u = 0.00282363896258175373077393f;
u = mlaf(u, t, -0.0159569028764963150024414f);
u = mlaf(u, t, 0.0425049886107444763183594f);
u = mlaf(u, t, -0.0748900920152664184570312f);
u = mlaf(u, t, 0.106347933411598205566406f);
u = mlaf(u, t, -0.142027363181114196777344f);
u = mlaf(u, t, 0.199926957488059997558594f);
u = mlaf(u, t, -0.333331018686294555664062f);
t = u * t * s + s;
t = q * (float)(M_PI/2) + t;
return t;
}
__inline float xatan2f(float y, float x) {
float r = atan2kf(xfabsf(y), x);
r = mulsignf(r, x);
if (xisinff(x) || x == 0) r = M_PIf/2 - (xisinff(x) ? (signf(x) * (float)(M_PI /2)) : 0);
if (xisinff(y) ) r = M_PIf/2 - (xisinff(x) ? (signf(x) * (float)(M_PI*1/4)) : 0);
if ( y == 0) r = (signf(x) == -1 ? M_PIf : 0);
return xisnanf(x) || xisnanf(y) ? NANf : mulsignf(r, y);
}
__inline float xasinf(float d) {
return mulsignf(atan2kf(fabsf(d), sqrtf((1.0f+d)*(1.0f-d))), d);
}
__inline float xacosf(float d) {
return mulsignf(atan2kf(sqrtf((1.0f+d)*(1.0f-d)), fabsf(d)), d) + (d < 0 ? (float)M_PI : 0.0f);
}
__inline float xlogf(float d) {
float x, x2, t, m;
int e;
e = ilogbp1f(d * 0.7071f);
m = ldexpkf(d, -e);
x = (m-1.0f) / (m+1.0f);
x2 = x * x;
t = 0.2371599674224853515625f;
t = mlaf(t, x2, 0.285279005765914916992188f);
t = mlaf(t, x2, 0.400005519390106201171875f);
t = mlaf(t, x2, 0.666666567325592041015625f);
t = mlaf(t, x2, 2.0f);
x = x * t + 0.693147180559945286226764f * e;
if (xisinff(d)) x = INFINITYf;
if (d < 0) x = NANf;
if (d == 0) x = -INFINITYf;
return x;
}
__inline float xexpf(float d) {
if(d<=-104.0f) return 0.0f;
int q = (int)xrintf(d * R_LN2f);
float s, u;
s = mlaf(q, -L2Uf, d);
s = mlaf(q, -L2Lf, s);
u = 0.00136324646882712841033936f;
u = mlaf(u, s, 0.00836596917361021041870117f);
u = mlaf(u, s, 0.0416710823774337768554688f);
u = mlaf(u, s, 0.166665524244308471679688f);
u = mlaf(u, s, 0.499999850988388061523438f);
u = s * s * u + s + 1.0f;
u = ldexpkf(u, q);
// if (xisminff(d)) u = 0;
return u;
}
__inline float xmul2f(float d) {
if (*(int*)&d & 0x7FFFFFFF) { // if f==0 do nothing
*(int*)&d += 1 << 23; // add 1 to the exponent
}
return d;
}
__inline float xdiv2f(float d) {
if (*(int*)&d & 0x7FFFFFFF) { // if f==0 do nothing
*(int*)&d -= 1 << 23; // sub 1 from the exponent
}
return d;
}
__inline float xdivf( float d, int n){
if (*(int*)&d & 0x7FFFFFFF) { // if f==0 do nothing
*(int*)&d -= n << 23; // add n to the exponent
}
return d;
}
#endif
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