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11210 libm should be cstyle(1ONBLD) clean
*** 16,28 ****
--- 16,30 ----
* 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 2005 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
*** 73,107 ****
* z[1] : the leading 24 bits of Z rounded
* z[2] : the remaining 53 bits of Z
* Note that z[0] = z[1]+z[2] rounded.
*
*/
-
static void
! mx_poly(const double *z, const double *a, double *e, int n) {
double r, s, t, p_h, p_l, z_h, z_l, p;
int i;
n = n + n;
p = e[0] + a[n];
p_l = a[n + 1];
! p_h = (double) ((float) p);
p = a[n - 2] + z[0] * p;
! z_h = z[1]; z_l = z[2];
p_l += e[0] - (p_h - a[n]);
for (i = n - 2; i >= 2; i -= 2) {
/* compute p = ai + z * p */
t = z_h * p_h;
s = z[0] * p_l + p_h * z_l;
! p_h = (double) ((float) p);
s += a[i + 1];
r = t - (p_h - a[i]);
p = a[i - 2] + z[0] * p;
p_l = r + s;
}
! e[0] = (double)((float) p);
t = z_h * p_h;
s = z[0] * p_l + p_h * z_l;
r = t - (e[0] - a[0]);
e[1] = r + s;
}
--- 75,111 ----
* z[1] : the leading 24 bits of Z rounded
* z[2] : the remaining 53 bits of Z
* Note that z[0] = z[1]+z[2] rounded.
*
*/
static void
! mx_poly(const double *z, const double *a, double *e, int n)
! {
double r, s, t, p_h, p_l, z_h, z_l, p;
int i;
n = n + n;
p = e[0] + a[n];
p_l = a[n + 1];
! p_h = (double)((float)p);
p = a[n - 2] + z[0] * p;
! z_h = z[1];
! z_l = z[2];
p_l += e[0] - (p_h - a[n]);
for (i = n - 2; i >= 2; i -= 2) {
/* compute p = ai + z * p */
t = z_h * p_h;
s = z[0] * p_l + p_h * z_l;
! p_h = (double)((float)p);
s += a[i + 1];
r = t - (p_h - a[i]);
p = a[i - 2] + z[0] * p;
p_l = r + s;
}
!
! e[0] = (double)((float)p);
t = z_h * p_h;
s = z[0] * p_l + p_h * z_l;
r = t - (e[0] - a[0]);
e[1] = r + s;
}
*** 116,194 ****
* 8.000 -- 0x40200000 (total: 97)
* By K.C. Ng, March 9, 1989
*/
static const double TBL_atan_hi[] = {
! 1.243549945467614382e-01, 1.320397616146387620e-01, 1.397088742891636204e-01,
! 1.473614810886516302e-01, 1.549967419239409727e-01, 1.626138285979485676e-01,
! 1.702119252854744080e-01, 1.777902289926760471e-01, 1.853479499956947607e-01,
! 1.928843122579746439e-01, 2.003985538258785115e-01, 2.078899272022629863e-01,
! 2.153576996977380476e-01, 2.228011537593945213e-01, 2.302195872768437179e-01,
! 2.376123138654712419e-01, 2.449786631268641435e-01, 2.596296294082575118e-01,
! 2.741674511196587893e-01, 2.885873618940774099e-01, 3.028848683749714166e-01,
! 3.170557532091470287e-01, 3.310960767041321029e-01, 3.450021772071051318e-01,
! 3.587706702705721895e-01, 3.723984466767542023e-01, 3.858826693980737521e-01,
! 3.992207695752525431e-01, 4.124104415973872673e-01, 4.254496373700422662e-01,
! 4.383365598579578304e-01, 4.510696559885234436e-01, 4.636476090008060935e-01,
! 4.883339510564055352e-01, 5.123894603107377321e-01, 5.358112379604637043e-01,
! 5.585993153435624414e-01, 5.807563535676704136e-01, 6.022873461349641522e-01,
! 6.231993299340659043e-01, 6.435011087932843710e-01, 6.632029927060932861e-01,
! 6.823165548747480713e-01, 7.008544078844501923e-01, 7.188299996216245269e-01,
! 7.362574289814280970e-01, 7.531512809621944138e-01, 7.695264804056582975e-01,
! 7.853981633974482790e-01, 8.156919233162234217e-01, 8.441539861131710509e-01,
! 8.709034570756529758e-01, 8.960553845713439269e-01, 9.197196053504168578e-01,
! 9.420000403794636101e-01, 9.629943306809362058e-01, 9.827937232473290541e-01,
! 1.001483135694234639e+00, 1.019141344266349725e+00, 1.035841253008800145e+00,
! 1.051650212548373764e+00, 1.066630365315743623e+00, 1.080839000541168327e+00,
! 1.094328907321189925e+00, 1.107148717794090409e+00, 1.130953743979160375e+00,
! 1.152571997215667610e+00, 1.172273881128476303e+00, 1.190289949682531656e+00,
! 1.206817370285252489e+00, 1.222025323210989667e+00, 1.236059489478081863e+00,
! 1.249045772398254428e+00, 1.261093382252440387e+00, 1.272297395208717319e+00,
! 1.282740879744270757e+00, 1.292496667789785336e+00, 1.301628834009196156e+00,
! 1.310193935047555547e+00, 1.318242051016837113e+00, 1.325817663668032553e+00,
! 1.339705659598999565e+00, 1.352127380920954636e+00, 1.363300100359693845e+00,
! 1.373400766945015894e+00, 1.382574821490125894e+00, 1.390942827002418447e+00,
! 1.398605512271957618e+00, 1.405647649380269870e+00, 1.412141064608495311e+00,
! 1.418146998399631542e+00, 1.423717971406494032e+00, 1.428899272190732761e+00,
! 1.433730152484709031e+00, 1.438244794498222623e+00, 1.442473099109101931e+00,
! 1.446441332248135092e+00,
};
static const double TBL_atan_lo[] = {
! -3.125324142453938311e-18, -1.276925400709959526e-17, 2.479758919089733066e-17,
! 5.409599147666297957e-18, 9.585415594114323829e-18, 7.784470643106252464e-18,
! -3.541164079802125137e-18, 2.372599351477449041e-17, 4.180692268843078977e-18,
! 2.034098543938166622e-17, 3.139954287184449286e-18, 7.333160666520898500e-18,
! 4.738160130078732886e-19, -5.498822172446843173e-18, 1.231340452914270316e-17,
! 1.058231431371112987e-17, 1.069875561873445139e-17, 1.923875492461530410e-17,
! 8.261353575163771936e-18, -1.428369957377257085e-17, -1.101082790300136900e-17,
! -1.893928924292642146e-17, -7.952610375793798701e-18, -2.293880475557830393e-17,
! 3.088733564861919217e-17, 1.961231150484565340e-17, 2.378822732491940868e-17,
! 2.246598105617042065e-17, 3.963462895355093301e-17, 2.331553074189288466e-17,
! -2.494277030626540909e-17, 3.280735600183735558e-17, 2.269877745296168709e-17,
! -1.137323618932958456e-17, -2.546278147285580353e-17, -4.063795683482557497e-18,
! -5.455630548591626394e-18, -1.441464378193066908e-17, 2.950430737228402307e-17,
! 2.672403885140095079e-17, 1.583478505144428617e-17, -3.076054864429649001e-17,
! 6.943223671560007740e-18, -1.987626234335816123e-17, -2.147838844445698302e-17,
! 3.473937648299456719e-17, -2.425693465918206812e-17, -3.704991905602721293e-17,
! 3.061616997868383018e-17, -1.071456562778743077e-17, -4.841337011934916763e-17,
! -2.269823590747287052e-17, 2.923876285774304890e-17, -4.057439412852767923e-17,
! 5.460837485846687627e-17, -3.986660595210752445e-18, 1.390331103123099845e-17,
! 9.438308023545392000e-17, 1.000401886936679889e-17, 3.194313981784503706e-17,
! -9.650564731467513515e-17, -5.956589637160374564e-17, -1.567632251135907253e-17,
! -5.490676155022364226e-18, 9.404471373566379412e-17, 7.123833804538446299e-17,
! -9.159738508900378819e-17, 8.385188614028674371e-17, 7.683333629842068806e-17,
! 4.172467638861439118e-17, -2.979162864892849274e-17, 7.879752739459421280e-17,
! -2.196203799612310905e-18, 3.242139621534960503e-17, 2.245875015034507026e-17,
! -9.283188754266129476e-18, -6.830804768926660334e-17, -1.236918499824626670e-17,
! 8.745413734780278834e-17, -6.319394031144676258e-17, -8.824429373951136321e-17,
! -2.599011860304134377e-17, 2.147674250751150961e-17, 1.093246171526936217e-16,
! -3.307710355769516504e-17, -3.561490438648230100e-17, -9.843712133488842595e-17,
! -2.324061182591627982e-17, -8.922630138234492386e-17, -9.573807110557223276e-17,
! -8.263883782511013632e-17, 8.721870922223967507e-17, -6.457134743238754385e-17,
! -4.396204466767636187e-17, -2.493019910264565554e-17, -1.105119435430315713e-16,
! 9.211323971545051565e-17,
};
/*
* mx_atan(x,err)
* Table look-up algorithm
--- 120,230 ----
* 8.000 -- 0x40200000 (total: 97)
* By K.C. Ng, March 9, 1989
*/
static const double TBL_atan_hi[] = {
! 1.243549945467614382e-01, 1.320397616146387620e-01,
! 1.397088742891636204e-01, 1.473614810886516302e-01,
! 1.549967419239409727e-01, 1.626138285979485676e-01,
! 1.702119252854744080e-01, 1.777902289926760471e-01,
! 1.853479499956947607e-01, 1.928843122579746439e-01,
! 2.003985538258785115e-01, 2.078899272022629863e-01,
! 2.153576996977380476e-01, 2.228011537593945213e-01,
! 2.302195872768437179e-01, 2.376123138654712419e-01,
! 2.449786631268641435e-01, 2.596296294082575118e-01,
! 2.741674511196587893e-01, 2.885873618940774099e-01,
! 3.028848683749714166e-01, 3.170557532091470287e-01,
! 3.310960767041321029e-01, 3.450021772071051318e-01,
! 3.587706702705721895e-01, 3.723984466767542023e-01,
! 3.858826693980737521e-01, 3.992207695752525431e-01,
! 4.124104415973872673e-01, 4.254496373700422662e-01,
! 4.383365598579578304e-01, 4.510696559885234436e-01,
! 4.636476090008060935e-01, 4.883339510564055352e-01,
! 5.123894603107377321e-01, 5.358112379604637043e-01,
! 5.585993153435624414e-01, 5.807563535676704136e-01,
! 6.022873461349641522e-01, 6.231993299340659043e-01,
! 6.435011087932843710e-01, 6.632029927060932861e-01,
! 6.823165548747480713e-01, 7.008544078844501923e-01,
! 7.188299996216245269e-01, 7.362574289814280970e-01,
! 7.531512809621944138e-01, 7.695264804056582975e-01,
! 7.853981633974482790e-01, 8.156919233162234217e-01,
! 8.441539861131710509e-01, 8.709034570756529758e-01,
! 8.960553845713439269e-01, 9.197196053504168578e-01,
! 9.420000403794636101e-01, 9.629943306809362058e-01,
! 9.827937232473290541e-01, 1.001483135694234639e+00,
! 1.019141344266349725e+00, 1.035841253008800145e+00,
! 1.051650212548373764e+00, 1.066630365315743623e+00,
! 1.080839000541168327e+00, 1.094328907321189925e+00,
! 1.107148717794090409e+00, 1.130953743979160375e+00,
! 1.152571997215667610e+00, 1.172273881128476303e+00,
! 1.190289949682531656e+00, 1.206817370285252489e+00,
! 1.222025323210989667e+00, 1.236059489478081863e+00,
! 1.249045772398254428e+00, 1.261093382252440387e+00,
! 1.272297395208717319e+00, 1.282740879744270757e+00,
! 1.292496667789785336e+00, 1.301628834009196156e+00,
! 1.310193935047555547e+00, 1.318242051016837113e+00,
! 1.325817663668032553e+00, 1.339705659598999565e+00,
! 1.352127380920954636e+00, 1.363300100359693845e+00,
! 1.373400766945015894e+00, 1.382574821490125894e+00,
! 1.390942827002418447e+00, 1.398605512271957618e+00,
! 1.405647649380269870e+00, 1.412141064608495311e+00,
! 1.418146998399631542e+00, 1.423717971406494032e+00,
! 1.428899272190732761e+00, 1.433730152484709031e+00,
! 1.438244794498222623e+00, 1.442473099109101931e+00,
! 1.446441332248135092e+00,
};
static const double TBL_atan_lo[] = {
! -3.125324142453938311e-18, -1.276925400709959526e-17,
! 2.479758919089733066e-17, 5.409599147666297957e-18,
! 9.585415594114323829e-18, 7.784470643106252464e-18,
! -3.541164079802125137e-18, 2.372599351477449041e-17,
! 4.180692268843078977e-18, 2.034098543938166622e-17,
! 3.139954287184449286e-18, 7.333160666520898500e-18,
! 4.738160130078732886e-19, -5.498822172446843173e-18,
! 1.231340452914270316e-17, 1.058231431371112987e-17,
! 1.069875561873445139e-17, 1.923875492461530410e-17,
! 8.261353575163771936e-18, -1.428369957377257085e-17,
! -1.101082790300136900e-17, -1.893928924292642146e-17,
! -7.952610375793798701e-18, -2.293880475557830393e-17,
! 3.088733564861919217e-17, 1.961231150484565340e-17,
! 2.378822732491940868e-17, 2.246598105617042065e-17,
! 3.963462895355093301e-17, 2.331553074189288466e-17,
! -2.494277030626540909e-17, 3.280735600183735558e-17,
! 2.269877745296168709e-17, -1.137323618932958456e-17,
! -2.546278147285580353e-17, -4.063795683482557497e-18,
! -5.455630548591626394e-18, -1.441464378193066908e-17,
! 2.950430737228402307e-17, 2.672403885140095079e-17,
! 1.583478505144428617e-17, -3.076054864429649001e-17,
! 6.943223671560007740e-18, -1.987626234335816123e-17,
! -2.147838844445698302e-17, 3.473937648299456719e-17,
! -2.425693465918206812e-17, -3.704991905602721293e-17,
! 3.061616997868383018e-17, -1.071456562778743077e-17,
! -4.841337011934916763e-17, -2.269823590747287052e-17,
! 2.923876285774304890e-17, -4.057439412852767923e-17,
! 5.460837485846687627e-17, -3.986660595210752445e-18,
! 1.390331103123099845e-17, 9.438308023545392000e-17,
! 1.000401886936679889e-17, 3.194313981784503706e-17,
! -9.650564731467513515e-17, -5.956589637160374564e-17,
! -1.567632251135907253e-17, -5.490676155022364226e-18,
! 9.404471373566379412e-17, 7.123833804538446299e-17,
! -9.159738508900378819e-17, 8.385188614028674371e-17,
! 7.683333629842068806e-17, 4.172467638861439118e-17,
! -2.979162864892849274e-17, 7.879752739459421280e-17,
! -2.196203799612310905e-18, 3.242139621534960503e-17,
! 2.245875015034507026e-17, -9.283188754266129476e-18,
! -6.830804768926660334e-17, -1.236918499824626670e-17,
! 8.745413734780278834e-17, -6.319394031144676258e-17,
! -8.824429373951136321e-17, -2.599011860304134377e-17,
! 2.147674250751150961e-17, 1.093246171526936217e-16,
! -3.307710355769516504e-17, -3.561490438648230100e-17,
! -9.843712133488842595e-17, -2.324061182591627982e-17,
! -8.922630138234492386e-17, -9.573807110557223276e-17,
! -8.263883782511013632e-17, 8.721870922223967507e-17,
! -6.457134743238754385e-17, -4.396204466767636187e-17,
! -2.493019910264565554e-17, -1.105119435430315713e-16,
! 9.211323971545051565e-17,
};
/*
* mx_atan(x,err)
* Table look-up algorithm
*** 240,249 ****
--- 276,286 ----
#define P5 p[9]
#define P6 p[10]
#define P7 p[11]
#define P8 p[12]
#define P9 p[13]
+
static const double p[] = {
1.0,
0.0,
-3.33333333333333314830e-01, /* p1 = BFD55555 55555555 */
-1.85030852238476921863e-17, /* p1_l = BC755525 9783A49C */
*** 256,269 ****
--- 293,308 ----
7.69230541541713053189e-02, /* p6 = 3FB3B13A B1E68DE6 */
-6.66645815401964159097e-02, /* p7 = BFB110EE 1584446A */
5.87081768778560317279e-02, /* p8 = 3FAE0EFF 87657733 */
-4.90818147456113240690e-02, /* p9 = BFA92140 6A524B5C */
};
+
#define Q1 q[2]
#define Q3 q[6]
#define Q4 q[7]
#define Q5 q[8]
+
static const double q[] = {
1.0,
0.0,
-3.33333333333333314830e-01, /* q1 = BFD55555 55555555 */
-1.85022941571278638733e-17, /* q1_l = BC7554E9 D20EFA66 */
*** 271,317 ****
-1.28782564407438833398e-17, /* q2_l = BC6DB1FB 17217417 */
-1.42857142855492280642e-01, /* q3 = BFC24924 92483C46 */
1.11111097130183356096e-01, /* q4 = 3FBC71C6 E06595CC */
-9.08553303569109294013e-02, /* q5 = BFB7424B 808CDA76 */
};
! static const double
! one = 1.0,
! pio2hi = 1.570796326794896558e+00,
! pio2lo = 6.123233995736765886e-17;
static double
! mx_atan(double x, double *err) {
! double y, z, r, s, t, w, s_h, s_l, x_h, x_l, zz[3], ee[2], z_h,
! z_l, r_h, r_l, u, v;
int ix, iy, sign, j;
! ix = ((int *) &x)[HIWORD];
sign = ix & 0x80000000;
ix ^= sign;
/* for |x| < 1/8 */
if (ix < 0x3fc00000) {
if (ix < 0x3f300000) { /* when |x| < 2**-12 */
if (ix < 0x3d800000) { /* if |x| < 2**-39 */
! *err = (double) ((int) x);
return (x);
}
z = x * x;
t = x * z * (q[2] + z * (q[4] + z * q[6]));
r = x + t;
*err = t - (r - x);
return (r);
}
z = x * x;
/* use double precision at p4 and on */
! ee[0] = z *
! (P4 + z *
! (P5 + z * (P6 + z * (P7 + z * (P8 + z * P9)))));
! x_h = (double) ((float) x);
! z_h = (double) ((float) z);
x_l = x - x_h;
z_l = (x_h * x_h - z_h);
zz[0] = z;
zz[1] = z_h;
zz[2] = z_l + x_l * (x + x_h);
--- 310,358 ----
-1.28782564407438833398e-17, /* q2_l = BC6DB1FB 17217417 */
-1.42857142855492280642e-01, /* q3 = BFC24924 92483C46 */
1.11111097130183356096e-01, /* q4 = 3FBC71C6 E06595CC */
-9.08553303569109294013e-02, /* q5 = BFB7424B 808CDA76 */
};
!
! static const double one = 1.0,
! pio2hi = 1.570796326794896558e+00,
! pio2lo = 6.123233995736765886e-17;
static double
! mx_atan(double x, double *err)
! {
! double y, z, r, s, t, w, s_h, s_l, x_h, x_l, zz[3], ee[2], z_h, z_l,
! r_h, r_l, u, v;
int ix, iy, sign, j;
! ix = ((int *)&x)[HIWORD];
sign = ix & 0x80000000;
ix ^= sign;
/* for |x| < 1/8 */
if (ix < 0x3fc00000) {
if (ix < 0x3f300000) { /* when |x| < 2**-12 */
if (ix < 0x3d800000) { /* if |x| < 2**-39 */
! *err = (double)((int)x);
return (x);
}
+
z = x * x;
t = x * z * (q[2] + z * (q[4] + z * q[6]));
r = x + t;
*err = t - (r - x);
return (r);
}
+
z = x * x;
/* use double precision at p4 and on */
! ee[0] = z * (P4 + z * (P5 + z * (P6 + z * (P7 + z * (P8 + z *
! P9)))));
! x_h = (double)((float)x);
! z_h = (double)((float)z);
x_l = x - x_h;
z_l = (x_h * x_h - z_h);
zz[0] = z;
zz[1] = z_h;
zz[2] = z_l + x_l * (x + x_h);
*** 328,426 ****
t = x * ee[1] + x_l * ee[0];
s = t + r;
*err = t - (s - r);
return (s);
}
/* for |x| >= 8.0 */
if (ix >= 0x40200000) { /* x >= 8 */
x = fabs(x);
if (ix >= 0x42600000) { /* x >= 2**39 */
! if (ix >= 0x44c00000) { /* x >= 2**77 */
y = -pio2lo;
! } else
y = one / x - pio2lo;
if (sign == 0) {
t = pio2hi - y;
*err = -(y - (pio2hi - t));
} else {
t = y - pio2hi;
*err = y - (pio2hi + t);
}
return (t);
} else {
/* compute r = 1/x */
r = one / x;
z = r * r;
- if (ix < 0x40504000) { /* 8 < x < 65 */
/* use double precision at p4 and on */
! ee[0] = z *
! (P4 + z *
! (P5 + z *
! (P6 + z * (P7 + z * (P8 + z * P9)))));
! x_h = (double) ((float) x);
! r_h = (double) ((float) r);
! z_h = (double) ((float) z);
r_l = r * ((x_h - x) * r_h - (x_h * r_h - one));
z_l = (r_h * r_h - z_h);
zz[0] = z;
zz[1] = z_h;
zz[2] = z_l + r_l * (r + r_h);
/*
* compute (1+z*(p1+z*(p2+z*(p3+e)))) by call
* mx_poly
*/
mx_poly(zz, p, ee, 3);
} else { /* x < 65 < 2**39 */
/* use double precision at q3 and on */
ee[0] = z * (Q3 + z * (Q4 + z * Q5));
! x_h = (double) ((float) x);
! r_h = (double) ((float) r);
! z_h = (double) ((float) z);
r_l = r * ((x_h - x) * r_h - (x_h * r_h - one));
z_l = (r_h * r_h - z_h);
zz[0] = z;
zz[1] = z_h;
zz[2] = z_l + r_l * (r + r_h);
/*
* compute (1+z*(q1+z*(q2+e))) by call
* mx_poly
*/
mx_poly(zz, q, ee, 2);
}
/* pio2 - r*(1+...) */
v = r_h * ee[0];
t = pio2lo - (r * ee[1] + r_l * ee[0]);
if (sign == 0) {
s = pio2hi - v;
t -= (v - (pio2hi - s));
} else {
s = v - pio2hi;
t = -(t - (v - (s + pio2hi)));
}
w = s + t;
*err = t - (w - s);
return (w);
}
}
/* now x is between 1/8 and 8 */
! ((int *) &x)[HIWORD] = ix;
iy = (ix + 0x00008000) & 0x7fff0000;
! ((int *) &y)[HIWORD] = iy;
! ((int *) &y)[LOWORD] = 0;
j = (iy - 0x3fc00000) >> 16;
w = (x - y);
v = 1 / (one + x * y);
s = w * v;
z = s * s;
/* use double precision at q3 and on */
ee[0] = z * (Q3 + z * (Q4 + z * Q5));
! s_h = (double) ((float) s);
! z_h = (double) ((float) z);
! x_h = (double) ((float) x);
! t = (double) ((float) (one + x * y));
r = -((x_h - x) * y - (x_h * y - (t - one)));
s_l = -v * (s_h * r - (w - s_h * t));
z_l = (s_h * s_h - z_h);
zz[0] = z;
zz[1] = z_h;
--- 369,475 ----
t = x * ee[1] + x_l * ee[0];
s = t + r;
*err = t - (s - r);
return (s);
}
+
/* for |x| >= 8.0 */
if (ix >= 0x40200000) { /* x >= 8 */
x = fabs(x);
+
if (ix >= 0x42600000) { /* x >= 2**39 */
! if (ix >= 0x44c00000) /* x >= 2**77 */
y = -pio2lo;
! else
y = one / x - pio2lo;
+
if (sign == 0) {
t = pio2hi - y;
*err = -(y - (pio2hi - t));
} else {
t = y - pio2hi;
*err = y - (pio2hi + t);
}
+
return (t);
} else {
/* compute r = 1/x */
r = one / x;
z = r * r;
+ if (ix < 0x40504000) { /* 8 < x < 65 */
/* use double precision at p4 and on */
! ee[0] = z * (P4 + z * (P5 + z * (P6 + z * (P7 +
! z * (P8 + z * P9)))));
! x_h = (double)((float)x);
! r_h = (double)((float)r);
! z_h = (double)((float)z);
r_l = r * ((x_h - x) * r_h - (x_h * r_h - one));
z_l = (r_h * r_h - z_h);
zz[0] = z;
zz[1] = z_h;
zz[2] = z_l + r_l * (r + r_h);
+
/*
* compute (1+z*(p1+z*(p2+z*(p3+e)))) by call
* mx_poly
*/
mx_poly(zz, p, ee, 3);
} else { /* x < 65 < 2**39 */
/* use double precision at q3 and on */
ee[0] = z * (Q3 + z * (Q4 + z * Q5));
! x_h = (double)((float)x);
! r_h = (double)((float)r);
! z_h = (double)((float)z);
r_l = r * ((x_h - x) * r_h - (x_h * r_h - one));
z_l = (r_h * r_h - z_h);
zz[0] = z;
zz[1] = z_h;
zz[2] = z_l + r_l * (r + r_h);
+
/*
* compute (1+z*(q1+z*(q2+e))) by call
* mx_poly
*/
mx_poly(zz, q, ee, 2);
}
+
/* pio2 - r*(1+...) */
v = r_h * ee[0];
t = pio2lo - (r * ee[1] + r_l * ee[0]);
+
if (sign == 0) {
s = pio2hi - v;
t -= (v - (pio2hi - s));
} else {
s = v - pio2hi;
t = -(t - (v - (s + pio2hi)));
}
+
w = s + t;
*err = t - (w - s);
return (w);
}
}
+
/* now x is between 1/8 and 8 */
! ((int *)&x)[HIWORD] = ix;
iy = (ix + 0x00008000) & 0x7fff0000;
! ((int *)&y)[HIWORD] = iy;
! ((int *)&y)[LOWORD] = 0;
j = (iy - 0x3fc00000) >> 16;
w = (x - y);
v = 1 / (one + x * y);
s = w * v;
z = s * s;
/* use double precision at q3 and on */
ee[0] = z * (Q3 + z * (Q4 + z * Q5));
! s_h = (double)((float)s);
! z_h = (double)((float)z);
! x_h = (double)((float)x);
! t = (double)((float)(one + x * y));
r = -((x_h - x) * y - (x_h * y - (t - one)));
s_l = -v * (s_h * r - (w - s_h * t));
z_l = (s_h * s_h - z_h);
zz[0] = z;
zz[1] = z_h;
*** 432,450 ****
u = TBL_atan_hi[j];
s = u + v;
t += (v - (s - u));
w = s + t;
*err = t - (w - s);
if (sign != 0) {
w = -w;
*err = -*err;
}
return (w);
}
! static const double
! twom768 = 6.441148769597133308e-232, /* 2^-768 */
two768 = 1.552518092300708935e+231, /* 2^768 */
pi = 3.1415926535897931159979634685,
pi_lo = 1.224646799147353177e-16,
pio2 = 1.570796326794896558e+00,
pio2_lo = 6.123233995736765886e-17,
--- 481,500 ----
u = TBL_atan_hi[j];
s = u + v;
t += (v - (s - u));
w = s + t;
*err = t - (w - s);
+
if (sign != 0) {
w = -w;
*err = -*err;
}
+
return (w);
}
! static const double twom768 = 6.441148769597133308e-232, /* 2^-768 */
two768 = 1.552518092300708935e+231, /* 2^768 */
pi = 3.1415926535897931159979634685,
pi_lo = 1.224646799147353177e-16,
pio2 = 1.570796326794896558e+00,
pio2_lo = 6.123233995736765886e-17,
*** 452,521 ****
pio4_lo = 3.061616997868382943e-17,
pi3o4 = 2.356194490192344836998,
pi3o4_lo = 9.184850993605148829195e-17;
double
! __k_atan2(double y, double x, double *w) {
double t, xh, th, t1, t2, w1, w2;
int ix, iy, hx, hy, lx, ly;
! hy = ((int *) &y)[HIWORD];
! ly = ((int *) &y)[LOWORD];
iy = hy & ~0x80000000;
! hx = ((int *) &x)[HIWORD];
! lx = ((int *) &x)[LOWORD];
ix = hx & ~0x80000000;
*w = 0.0;
if (ix >= 0x7ff00000 || iy >= 0x7ff00000) { /* ignore inexact */
! if (isnan(x) || isnan(y))
return (x * y);
! else if (iy < 0x7ff00000) {
if (hx >= 0) { /* ATAN2(+-finite, +inf) is +-0 */
*w *= y;
return (*w);
} else { /* ATAN2(+-finite, -inf) is +-pi */
*w = copysign(pi_lo, y);
return (copysign(pi, y));
}
} else if (ix < 0x7ff00000) {
/* ATAN2(+-inf, finite) is +-pi/2 */
! *w = (hy >= 0)? pio2_lo : -pio2_lo;
! return ((hy >= 0)? pio2 : -pio2);
} else if (hx > 0) { /* ATAN2(+-INF,+INF) = +-pi/4 */
! *w = (hy >= 0)? pio4_lo : -pio4_lo;
! return ((hy >= 0)? pio4 : -pio4);
} else { /* ATAN2(+-INF,-INF) = +-3pi/4 */
! *w = (hy >= 0)? pi3o4_lo : -pi3o4_lo;
! return ((hy >= 0)? pi3o4 : -pi3o4);
}
} else if ((ix | lx) == 0 || (iy | ly) == 0) {
if ((iy | ly) == 0) {
! if (hx >= 0) /* ATAN2(+-0, +(0 <= x <= inf)) is +-0 */
return (y);
! else { /* ATAN2(+-0, -(0 <= x <= inf)) is +-pi */
! *w = (hy >= 0)? pi_lo : -pi_lo;
! return ((hy >= 0)? pi : -pi);
}
} else { /* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2 */
! *w = (hy >= 0)? pio2_lo : -pio2_lo;
! return ((hy >= 0)? pio2 : -pio2);
}
} else if (iy - ix > 0x06400000) { /* |x/y| < 2 ** -100 */
! *w = (hy >= 0)? pio2_lo : -pio2_lo;
! return ((hy >= 0)? pio2 : -pio2);
} else if (ix - iy > 0x06400000) { /* |y/x| < 2 ** -100 */
if (hx < 0) {
! *w = (hy >= 0)? pi_lo : -pi_lo;
! return ((hy >= 0)? pi : -pi);
} else {
t = y / x;
th = t;
! ((int *) &th)[LOWORD] &= 0xf8000000;
xh = x;
! ((int *) &xh)[LOWORD] &= 0xf8000000;
t1 = (x - xh) * t + xh * (t - th);
t2 = y - xh * th;
*w = (t2 - t1) / x;
return (t);
}
--- 502,573 ----
pio4_lo = 3.061616997868382943e-17,
pi3o4 = 2.356194490192344836998,
pi3o4_lo = 9.184850993605148829195e-17;
double
! __k_atan2(double y, double x, double *w)
! {
double t, xh, th, t1, t2, w1, w2;
int ix, iy, hx, hy, lx, ly;
! hy = ((int *)&y)[HIWORD];
! ly = ((int *)&y)[LOWORD];
iy = hy & ~0x80000000;
! hx = ((int *)&x)[HIWORD];
! lx = ((int *)&x)[LOWORD];
ix = hx & ~0x80000000;
*w = 0.0;
+
if (ix >= 0x7ff00000 || iy >= 0x7ff00000) { /* ignore inexact */
! if (isnan(x) || isnan(y)) {
return (x * y);
! } else if (iy < 0x7ff00000) {
if (hx >= 0) { /* ATAN2(+-finite, +inf) is +-0 */
*w *= y;
return (*w);
} else { /* ATAN2(+-finite, -inf) is +-pi */
*w = copysign(pi_lo, y);
return (copysign(pi, y));
}
} else if (ix < 0x7ff00000) {
/* ATAN2(+-inf, finite) is +-pi/2 */
! *w = (hy >= 0) ? pio2_lo : -pio2_lo;
! return ((hy >= 0) ? pio2 : -pio2);
} else if (hx > 0) { /* ATAN2(+-INF,+INF) = +-pi/4 */
! *w = (hy >= 0) ? pio4_lo : -pio4_lo;
! return ((hy >= 0) ? pio4 : -pio4);
} else { /* ATAN2(+-INF,-INF) = +-3pi/4 */
! *w = (hy >= 0) ? pi3o4_lo : -pi3o4_lo;
! return ((hy >= 0) ? pi3o4 : -pi3o4);
}
} else if ((ix | lx) == 0 || (iy | ly) == 0) {
if ((iy | ly) == 0) {
! if (hx >= 0) { /* ATAN2(+-0, +(0 <= x <= inf)) is +-0 */
return (y);
! } else { /* ATAN2(+-0, -(0 <= x <= inf)) is +-pi */
! *w = (hy >= 0) ? pi_lo : -pi_lo;
! return ((hy >= 0) ? pi : -pi);
}
} else { /* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2 */
! *w = (hy >= 0) ? pio2_lo : -pio2_lo;
! return ((hy >= 0) ? pio2 : -pio2);
}
} else if (iy - ix > 0x06400000) { /* |x/y| < 2 ** -100 */
! *w = (hy >= 0) ? pio2_lo : -pio2_lo;
! return ((hy >= 0) ? pio2 : -pio2);
} else if (ix - iy > 0x06400000) { /* |y/x| < 2 ** -100 */
if (hx < 0) {
! *w = (hy >= 0) ? pi_lo : -pi_lo;
! return ((hy >= 0) ? pi : -pi);
} else {
t = y / x;
th = t;
! ((int *)&th)[LOWORD] &= 0xf8000000;
xh = x;
! ((int *)&xh)[LOWORD] &= 0xf8000000;
t1 = (x - xh) * t + xh * (t - th);
t2 = y - xh * th;
*w = (t2 - t1) / x;
return (t);
}
*** 525,550 ****
y *= twom768;
} else if (ix < 0x23d00000) {
x *= two768;
y *= two768;
}
y = fabs(y);
x = fabs(x);
t = y / x;
th = t;
! ((int *) &th)[LOWORD] &= 0xf8000000;
xh = x;
! ((int *) &xh)[LOWORD] &= 0xf8000000;
t1 = (x - xh) * t + xh * (t - th);
t2 = y - xh * th;
w1 = mx_atan(t, &w2);
w2 += (t2 - t1) / (x + y * t);
if (hx < 0) {
t1 = pi - w1;
t2 = pi - t1;
w2 = (pi_lo - w2) - (w1 - t2);
w1 = t1;
}
! *w = (hy >= 0)? w2 : -w2;
! return ((hy >= 0)? w1 : -w1);
}
}
--- 577,605 ----
y *= twom768;
} else if (ix < 0x23d00000) {
x *= two768;
y *= two768;
}
+
y = fabs(y);
x = fabs(x);
t = y / x;
th = t;
! ((int *)&th)[LOWORD] &= 0xf8000000;
xh = x;
! ((int *)&xh)[LOWORD] &= 0xf8000000;
t1 = (x - xh) * t + xh * (t - th);
t2 = y - xh * th;
w1 = mx_atan(t, &w2);
w2 += (t2 - t1) / (x + y * t);
+
if (hx < 0) {
t1 = pi - w1;
t2 = pi - t1;
w2 = (pi_lo - w2) - (w1 - t2);
w1 = t1;
}
!
! *w = (hy >= 0) ? w2 : -w2;
! return ((hy >= 0) ? w1 : -w1);
}
}