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11210 libm should be cstyle(1ONBLD) clean
@@ -16,13 +16,15 @@
* 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.
*/
@@ -34,114 +36,123 @@
* Part of the algorithm is based on W. Cody's lgamma function.
*/
#include "libm.h"
-static const double
-one = 1.0,
-zero = 0.0,
-hln2pi = 0.9189385332046727417803297, /* log(2*pi)/2 */
-pi = 3.1415926535897932384626434,
-two52 = 4503599627370496.0, /* 43300000,00000000 (used by sin_pi) */
+static const double one = 1.0,
+ zero = 0.0,
+ hln2pi = 0.9189385332046727417803297, /* log(2*pi)/2 */
+ pi = 3.1415926535897932384626434,
+ two52 = 4503599627370496.0, /* 43300000,00000000 (used by sin_pi) */
+
/*
* Numerator and denominator coefficients for rational minimax Approximation
* P/Q over (0.5,1.5).
*/
-D1 = -5.772156649015328605195174e-1,
-p7 = 4.945235359296727046734888e0,
-p6 = 2.018112620856775083915565e2,
-p5 = 2.290838373831346393026739e3,
-p4 = 1.131967205903380828685045e4,
-p3 = 2.855724635671635335736389e4,
-p2 = 3.848496228443793359990269e4,
-p1 = 2.637748787624195437963534e4,
-p0 = 7.225813979700288197698961e3,
-q7 = 6.748212550303777196073036e1,
-q6 = 1.113332393857199323513008e3,
-q5 = 7.738757056935398733233834e3,
-q4 = 2.763987074403340708898585e4,
-q3 = 5.499310206226157329794414e4,
-q2 = 6.161122180066002127833352e4,
-q1 = 3.635127591501940507276287e4,
-q0 = 8.785536302431013170870835e3,
+ D1 = -5.772156649015328605195174e-1,
+ p7 = 4.945235359296727046734888e0,
+ p6 = 2.018112620856775083915565e2,
+ p5 = 2.290838373831346393026739e3,
+ p4 = 1.131967205903380828685045e4,
+ p3 = 2.855724635671635335736389e4,
+ p2 = 3.848496228443793359990269e4,
+ p1 = 2.637748787624195437963534e4,
+ p0 = 7.225813979700288197698961e3,
+ q7 = 6.748212550303777196073036e1,
+ q6 = 1.113332393857199323513008e3,
+ q5 = 7.738757056935398733233834e3,
+ q4 = 2.763987074403340708898585e4,
+ q3 = 5.499310206226157329794414e4,
+ q2 = 6.161122180066002127833352e4,
+ q1 = 3.635127591501940507276287e4,
+ q0 = 8.785536302431013170870835e3,
+
/*
* Numerator and denominator coefficients for rational minimax Approximation
* G/H over (1.5,4.0).
*/
-D2 = 4.227843350984671393993777e-1,
-g7 = 4.974607845568932035012064e0,
-g6 = 5.424138599891070494101986e2,
-g5 = 1.550693864978364947665077e4,
-g4 = 1.847932904445632425417223e5,
-g3 = 1.088204769468828767498470e6,
-g2 = 3.338152967987029735917223e6,
-g1 = 5.106661678927352456275255e6,
-g0 = 3.074109054850539556250927e6,
-h7 = 1.830328399370592604055942e2,
-h6 = 7.765049321445005871323047e3,
-h5 = 1.331903827966074194402448e5,
-h4 = 1.136705821321969608938755e6,
-h3 = 5.267964117437946917577538e6,
-h2 = 1.346701454311101692290052e7,
-h1 = 1.782736530353274213975932e7,
-h0 = 9.533095591844353613395747e6,
+ D2 = 4.227843350984671393993777e-1,
+ g7 = 4.974607845568932035012064e0,
+ g6 = 5.424138599891070494101986e2,
+ g5 = 1.550693864978364947665077e4,
+ g4 = 1.847932904445632425417223e5,
+ g3 = 1.088204769468828767498470e6,
+ g2 = 3.338152967987029735917223e6,
+ g1 = 5.106661678927352456275255e6,
+ g0 = 3.074109054850539556250927e6,
+ h7 = 1.830328399370592604055942e2,
+ h6 = 7.765049321445005871323047e3,
+ h5 = 1.331903827966074194402448e5,
+ h4 = 1.136705821321969608938755e6,
+ h3 = 5.267964117437946917577538e6,
+ h2 = 1.346701454311101692290052e7,
+ h1 = 1.782736530353274213975932e7,
+ h0 = 9.533095591844353613395747e6,
+
/*
* Numerator and denominator coefficients for rational minimax Approximation
* U/V over (4.0,12.0).
*/
-D4 = 1.791759469228055000094023e0,
-u7 = 1.474502166059939948905062e4,
-u6 = 2.426813369486704502836312e6,
-u5 = 1.214755574045093227939592e8,
-u4 = 2.663432449630976949898078e9,
-u3 = 2.940378956634553899906876e10,
-u2 = 1.702665737765398868392998e11,
-u1 = 4.926125793377430887588120e11,
-u0 = 5.606251856223951465078242e11,
-v7 = 2.690530175870899333379843e3,
-v6 = 6.393885654300092398984238e5,
-v5 = 4.135599930241388052042842e7,
-v4 = 1.120872109616147941376570e9,
-v3 = 1.488613728678813811542398e10,
-v2 = 1.016803586272438228077304e11,
-v1 = 3.417476345507377132798597e11,
-v0 = 4.463158187419713286462081e11,
+ D4 = 1.791759469228055000094023e0,
+ u7 = 1.474502166059939948905062e4,
+ u6 = 2.426813369486704502836312e6,
+ u5 = 1.214755574045093227939592e8,
+ u4 = 2.663432449630976949898078e9,
+ u3 = 2.940378956634553899906876e10,
+ u2 = 1.702665737765398868392998e11,
+ u1 = 4.926125793377430887588120e11,
+ u0 = 5.606251856223951465078242e11,
+ v7 = 2.690530175870899333379843e3,
+ v6 = 6.393885654300092398984238e5,
+ v5 = 4.135599930241388052042842e7,
+ v4 = 1.120872109616147941376570e9,
+ v3 = 1.488613728678813811542398e10,
+ v2 = 1.016803586272438228077304e11,
+ v1 = 3.417476345507377132798597e11,
+ v0 = 4.463158187419713286462081e11,
+
/*
* Coefficients for minimax approximation over (12, INF).
*/
-c5 = -1.910444077728e-03,
-c4 = 8.4171387781295e-04,
-c3 = -5.952379913043012e-04,
-c2 = 7.93650793500350248e-04,
-c1 = -2.777777777777681622553e-03,
-c0 = 8.333333333333333331554247e-02,
-c6 = 5.7083835261e-03;
+ c5 = -1.910444077728e-03,
+ c4 = 8.4171387781295e-04,
+ c3 = -5.952379913043012e-04,
+ c2 = 7.93650793500350248e-04,
+ c1 = -2.777777777777681622553e-03,
+ c0 = 8.333333333333333331554247e-02,
+ c6 = 5.7083835261e-03;
/*
* Return sin(pi*x). We assume x is finite and negative, and if it
* is an integer, then the sign of the zero returned doesn't matter.
*/
static double
-sin_pi(double x) {
+sin_pi(double x)
+{
double y, z;
int n;
y = -x;
+
if (y <= 0.25)
return (__k_sin(pi * x, 0.0));
+
if (y >= two52)
return (zero);
+
z = floor(y);
+
if (y == z)
return (zero);
/* argument reduction: set y = |x| mod 2 */
y *= 0.5;
y = 2.0 * (y - floor(y));
/* now floor(y * 4) tells which octant y is in */
n = (int)(y * 4.0);
+
switch (n) {
case 0:
y = __k_sin(pi * y, 0.0);
break;
case 1:
@@ -158,17 +169,20 @@
break;
default:
y = __k_sin(pi * (y - 2.0), 0.0);
break;
}
+
return (-y);
}
static double
-neg(double z, int *signgamp) {
+neg(double z, int *signgamp)
+{
double t, p;
+ /* BEGIN CSTYLED */
/*
* written by K.C. Ng, Feb 2, 1989.
*
* Since
* -z*G(-z)*G(z) = pi/sin(pi*z),
@@ -185,41 +199,52 @@
* if (z+1.0 == 1.0) ...tiny z
* return -log(z);
* else
* return log(pi/(t*z))-__k_lgamma(z, signgamp);
*/
+ /* END CSTYLED */
t = sin_pi(z); /* t := sin(pi*z) */
+
if (t == zero) /* return 1.0/0.0 = +INF */
return (one / fabs(t));
+
z = -z;
p = z + one;
+
if (p == one)
p = -log(z);
else
p = log(pi / (fabs(t) * z)) - __k_lgamma(z, signgamp);
+
if (t < zero)
*signgamp = -1;
+
return (p);
}
double
-__k_lgamma(double x, int *signgamp) {
+__k_lgamma(double x, int *signgamp)
+{
double t, p, q, cr, y;
/* purge off +-inf, NaN and negative arguments */
if (!finite(x))
return (x * x);
+
*signgamp = 1;
+
if (signbit(x))
return (neg(x, signgamp));
/* lgamma(x) ~ log(1/x) for really tiny x */
t = one + x;
+
if (t == one) {
if (x == zero)
return (one / x);
+
return (-log(x));
}
/* for tiny < x < inf */
if (x <= 1.5) {
@@ -232,38 +257,47 @@
}
if (x <= 0.5 || x >= 0.6796875) {
if (x == one)
return (zero);
- p = p0+y*(p1+y*(p2+y*(p3+y*(p4+y*(p5+y*(p6+y*p7))))));
- q = q0+y*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*(q6+y*
- (q7+y)))))));
- return (cr+y*(D1+y*(p/q)));
+
+ p = p0 + y * (p1 + y * (p2 + y * (p3 + y * (p4 + y *
+ (p5 + y * (p6 + y * p7))))));
+ q = q0 + y * (q1 + y * (q2 + y * (q3 + y * (q4 + y *
+ (q5 + y * (q6 + y * (q7 + y)))))));
+ return (cr + y * (D1 + y * (p / q)));
} else {
y = x - one;
- p = g0+y*(g1+y*(g2+y*(g3+y*(g4+y*(g5+y*(g6+y*g7))))));
- q = h0+y*(h1+y*(h2+y*(h3+y*(h4+y*(h5+y*(h6+y*
- (h7+y)))))));
- return (cr+y*(D2+y*(p/q)));
+ p = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y *
+ (g5 + y * (g6 + y * g7))))));
+ q = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y *
+ (h5 + y * (h6 + y * (h7 + y)))))));
+ return (cr + y * (D2 + y * (p / q)));
}
} else if (x <= 4.0) {
if (x == 2.0)
return (zero);
+
y = x - 2.0;
- p = g0+y*(g1+y*(g2+y*(g3+y*(g4+y*(g5+y*(g6+y*g7))))));
- q = h0+y*(h1+y*(h2+y*(h3+y*(h4+y*(h5+y*(h6+y*(h7+y)))))));
- return (y*(D2+y*(p/q)));
+ p = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y *
+ (g6 + y * g7))))));
+ q = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y * (h5 + y *
+ (h6 + y * (h7 + y)))))));
+ return (y * (D2 + y * (p / q)));
} else if (x <= 12.0) {
y = x - 4.0;
- p = u0+y*(u1+y*(u2+y*(u3+y*(u4+y*(u5+y*(u6+y*u7))))));
- q = v0+y*(v1+y*(v2+y*(v3+y*(v4+y*(v5+y*(v6+y*(v7-y)))))));
- return (D4+y*(p/q));
+ p = u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y *
+ (u6 + y * u7))))));
+ q = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y *
+ (v6 + y * (v7 - y)))))));
+ return (D4 + y * (p / q));
} else if (x <= 1.0e17) { /* x ~< 2**(prec+3) */
t = one / x;
y = t * t;
- p = hln2pi+t*(c0+y*(c1+y*(c2+y*(c3+y*(c4+y*(c5+y*c6))))));
+ p = hln2pi + t * (c0 + y * (c1 + y * (c2 + y * (c3 + y * (c4 +
+ y * (c5 + y * c6))))));
q = log(x);
- return (x*(q-one)-(0.5*q-p));
+ return (x * (q - one) - (0.5 * q - p));
} else { /* may overflow */
return (x * (log(x) - 1.0));
}
}