uClibc now has a math library. muahahahaha!

 -Erik

1 files changed, 417 insertions, 0 deletions

diff --git a/libm/double/ndtri.c b/libm/double/ndtri.c
new file mode 100644
index 000000000..948e36c50
--- /dev/null
+++ b/libm/double/ndtri.c
@@ -0,0 +1,417 @@
+/*							ndtri.c
+ *
+ *	Inverse of Normal distribution function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double x, y, ndtri();
+ *
+ * x = ndtri( y );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the argument, x, for which the area under the
+ * Gaussian probability density function (integrated from
+ * minus infinity to x) is equal to y.
+ *
+ *
+ * For small arguments 0 < y < exp(-2), the program computes
+ * z = sqrt( -2.0 * log(y) );  then the approximation is
+ * x = z - log(z)/z  - (1/z) P(1/z) / Q(1/z).
+ * There are two rational functions P/Q, one for 0 < y < exp(-32)
+ * and the other for y up to exp(-2).  For larger arguments,
+ * w = y - 0.5, and  x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
+ *
+ *
+ * ACCURACY:
+ *
+ *                      Relative error:
+ * arithmetic   domain        # trials      peak         rms
+ *    DEC      0.125, 1         5500       9.5e-17     2.1e-17
+ *    DEC      6e-39, 0.135     3500       5.7e-17     1.3e-17
+ *    IEEE     0.125, 1        20000       7.2e-16     1.3e-16
+ *    IEEE     3e-308, 0.135   50000       4.6e-16     9.8e-17
+ *
+ *
+ * ERROR MESSAGES:
+ *
+ *   message         condition    value returned
+ * ndtri domain       x <= 0        -MAXNUM
+ * ndtri domain       x >= 1         MAXNUM
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.8:  June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+
+#include <math.h>
+extern double MAXNUM;
+
+#ifdef UNK
+/* sqrt(2pi) */
+static double s2pi = 2.50662827463100050242E0;
+#endif
+
+#ifdef DEC
+static unsigned short s2p[] = {0040440,0066230,0177661,0034055};
+#define s2pi *(double *)s2p
+#endif
+
+#ifdef IBMPC
+static unsigned short s2p[] = {0x2706,0x1ff6,0x0d93,0x4004};
+#define s2pi *(double *)s2p
+#endif
+
+#ifdef MIEEE
+static unsigned short s2p[] = {
+0x4004,0x0d93,0x1ff6,0x2706
+};
+#define s2pi *(double *)s2p
+#endif
+
+/* approximation for 0 <= |y - 0.5| <= 3/8 */
+#ifdef UNK
+static double P0[5] = {
+-5.99633501014107895267E1,
+ 9.80010754185999661536E1,
+-5.66762857469070293439E1,
+ 1.39312609387279679503E1,
+-1.23916583867381258016E0,
+};
+static double Q0[8] = {
+/* 1.00000000000000000000E0,*/
+ 1.95448858338141759834E0,
+ 4.67627912898881538453E0,
+ 8.63602421390890590575E1,
+-2.25462687854119370527E2,
+ 2.00260212380060660359E2,
+-8.20372256168333339912E1,
+ 1.59056225126211695515E1,
+-1.18331621121330003142E0,
+};
+#endif
+#ifdef DEC
+static unsigned short P0[20] = {
+0141557,0155170,0071360,0120550,
+0041704,0000214,0172417,0067307,
+0141542,0132204,0040066,0156723,
+0041136,0163161,0157276,0007747,
+0140236,0116374,0073666,0051764,
+};
+static unsigned short Q0[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0040372,0026256,0110403,0123707,
+0040625,0122024,0020277,0026661,
+0041654,0134161,0124134,0007244,
+0142141,0073162,0133021,0131371,
+0042110,0041235,0043516,0057767,
+0141644,0011417,0036155,0137305,
+0041176,0076556,0004043,0125430,
+0140227,0073347,0152776,0067251,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P0[20] = {
+0x142d,0x0e5e,0xfb4f,0xc04d,
+0xedd9,0x9ea1,0x8011,0x4058,
+0xdbba,0x8806,0x5690,0xc04c,
+0xc1fd,0x3bd7,0xdcce,0x402b,
+0xca7e,0x8ef6,0xd39f,0xbff3,
+};
+static unsigned short Q0[36] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0x74f9,0xd220,0x4595,0x3fff,
+0xe5b6,0x8417,0xb482,0x4012,
+0x81d4,0x350b,0x970e,0x4055,
+0x365f,0x56c2,0x2ece,0xc06c,
+0xcbff,0xa8e9,0x0853,0x4069,
+0xb7d9,0xe78d,0x8261,0xc054,
+0x7563,0xc104,0xcfad,0x402f,
+0xcdd5,0xfabf,0xeedc,0xbff2,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P0[20] = {
+0xc04d,0xfb4f,0x0e5e,0x142d,
+0x4058,0x8011,0x9ea1,0xedd9,
+0xc04c,0x5690,0x8806,0xdbba,
+0x402b,0xdcce,0x3bd7,0xc1fd,
+0xbff3,0xd39f,0x8ef6,0xca7e,
+};
+static unsigned short Q0[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x3fff,0x4595,0xd220,0x74f9,
+0x4012,0xb482,0x8417,0xe5b6,
+0x4055,0x970e,0x350b,0x81d4,
+0xc06c,0x2ece,0x56c2,0x365f,
+0x4069,0x0853,0xa8e9,0xcbff,
+0xc054,0x8261,0xe78d,0xb7d9,
+0x402f,0xcfad,0xc104,0x7563,
+0xbff2,0xeedc,0xfabf,0xcdd5,
+};
+#endif
+
+
+/* Approximation for interval z = sqrt(-2 log y ) between 2 and 8
+ * i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
+ */
+#ifdef UNK
+static double P1[9] = {
+ 4.05544892305962419923E0,
+ 3.15251094599893866154E1,
+ 5.71628192246421288162E1,
+ 4.40805073893200834700E1,
+ 1.46849561928858024014E1,
+ 2.18663306850790267539E0,
+-1.40256079171354495875E-1,
+-3.50424626827848203418E-2,
+-8.57456785154685413611E-4,
+};
+static double Q1[8] = {
+/*  1.00000000000000000000E0,*/
+ 1.57799883256466749731E1,
+ 4.53907635128879210584E1,
+ 4.13172038254672030440E1,
+ 1.50425385692907503408E1,
+ 2.50464946208309415979E0,
+-1.42182922854787788574E-1,
+-3.80806407691578277194E-2,
+-9.33259480895457427372E-4,
+};
+#endif
+#ifdef DEC
+static unsigned short P1[36] = {
+0040601,0143074,0150744,0073326,
+0041374,0031554,0113253,0146016,
+0041544,0123272,0012463,0176771,
+0041460,0051160,0103560,0156511,
+0041152,0172624,0117772,0030755,
+0040413,0170713,0151545,0176413,
+0137417,0117512,0022154,0131671,
+0137017,0104257,0071432,0007072,
+0135540,0143363,0063137,0036166,
+};
+static unsigned short Q1[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0041174,0075325,0004736,0120326,
+0041465,0110044,0047561,0045567,
+0041445,0042321,0012142,0030340,
+0041160,0127074,0166076,0141051,
+0040440,0046055,0040745,0150400,
+0137421,0114146,0067330,0010621,
+0137033,0175162,0025555,0114351,
+0135564,0122773,0145750,0030357,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P1[36] = {
+0x8edb,0x9a3c,0x38c7,0x4010,
+0x7982,0x92d5,0x866d,0x403f,
+0x7fbf,0x42a6,0x94d7,0x404c,
+0x1ba9,0x10ee,0x0a4e,0x4046,
+0x463e,0x93ff,0x5eb2,0x402d,
+0xbfa1,0x7a6c,0x7e39,0x4001,
+0x9677,0x448d,0xf3e9,0xbfc1,
+0x41c7,0xee63,0xf115,0xbfa1,
+0xe78f,0x6ccb,0x18de,0xbf4c,
+};
+static unsigned short Q1[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xd41b,0xa13b,0x8f5a,0x402f,
+0x296f,0x89ee,0xb204,0x4046,
+0x461c,0x228c,0xa89a,0x4044,
+0xd845,0x9d87,0x15c7,0x402e,
+0xba20,0xa83c,0x0985,0x4004,
+0x0232,0xcddb,0x330c,0xbfc2,
+0xb31d,0x456d,0x7f4e,0xbfa3,
+0x061e,0x797d,0x94bf,0xbf4e,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P1[36] = {
+0x4010,0x38c7,0x9a3c,0x8edb,
+0x403f,0x866d,0x92d5,0x7982,
+0x404c,0x94d7,0x42a6,0x7fbf,
+0x4046,0x0a4e,0x10ee,0x1ba9,
+0x402d,0x5eb2,0x93ff,0x463e,
+0x4001,0x7e39,0x7a6c,0xbfa1,
+0xbfc1,0xf3e9,0x448d,0x9677,
+0xbfa1,0xf115,0xee63,0x41c7,
+0xbf4c,0x18de,0x6ccb,0xe78f,
+};
+static unsigned short Q1[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x402f,0x8f5a,0xa13b,0xd41b,
+0x4046,0xb204,0x89ee,0x296f,
+0x4044,0xa89a,0x228c,0x461c,
+0x402e,0x15c7,0x9d87,0xd845,
+0x4004,0x0985,0xa83c,0xba20,
+0xbfc2,0x330c,0xcddb,0x0232,
+0xbfa3,0x7f4e,0x456d,0xb31d,
+0xbf4e,0x94bf,0x797d,0x061e,
+};
+#endif
+
+/* Approximation for interval z = sqrt(-2 log y ) between 8 and 64
+ * i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
+ */
+
+#ifdef UNK
+static double P2[9] = {
+  3.23774891776946035970E0,
+  6.91522889068984211695E0,
+  3.93881025292474443415E0,
+  1.33303460815807542389E0,
+  2.01485389549179081538E-1,
+  1.23716634817820021358E-2,
+  3.01581553508235416007E-4,
+  2.65806974686737550832E-6,
+  6.23974539184983293730E-9,
+};
+static double Q2[8] = {
+/*  1.00000000000000000000E0,*/
+  6.02427039364742014255E0,
+  3.67983563856160859403E0,
+  1.37702099489081330271E0,
+  2.16236993594496635890E-1,
+  1.34204006088543189037E-2,
+  3.28014464682127739104E-4,
+  2.89247864745380683936E-6,
+  6.79019408009981274425E-9,
+};
+#endif
+#ifdef DEC
+static unsigned short P2[36] = {
+0040517,0033507,0036236,0125641,
+0040735,0044616,0014473,0140133,
+0040574,0012567,0114535,0102541,
+0040252,0120340,0143474,0150135,
+0037516,0051057,0115361,0031211,
+0036512,0131204,0101511,0125144,
+0035236,0016627,0043160,0140216,
+0033462,0060512,0060141,0010641,
+0031326,0062541,0101304,0077706,
+};
+static unsigned short Q2[32] = {
+/*0040200,0000000,0000000,0000000,*/
+0040700,0143322,0132137,0040501,
+0040553,0101155,0053221,0140257,
+0040260,0041071,0052573,0010004,
+0037535,0066472,0177261,0162330,
+0036533,0160475,0066666,0036132,
+0035253,0174533,0027771,0044027,
+0033502,0016147,0117666,0063671,
+0031351,0047455,0141663,0054751,
+};
+#endif
+#ifdef IBMPC
+static unsigned short P2[36] = {
+0xd574,0xe793,0xe6e8,0x4009,
+0x780b,0xc327,0xa931,0x401b,
+0xb0ac,0xf32b,0x82ae,0x400f,
+0x9a0c,0x18e7,0x541c,0x3ff5,
+0x2651,0xf35e,0xca45,0x3fc9,
+0x354d,0x9069,0x5650,0x3f89,
+0x1812,0xe8ce,0xc3b2,0x3f33,
+0x2234,0x4c0c,0x4c29,0x3ec6,
+0x8ff9,0x3058,0xccac,0x3e3a,
+};
+static unsigned short Q2[32] = {
+/*0x0000,0x0000,0x0000,0x3ff0,*/
+0xe828,0x568b,0x18da,0x4018,
+0x3816,0xaad2,0x704d,0x400d,
+0x6200,0x2aaf,0x0847,0x3ff6,
+0x3c9b,0x5fd6,0xada7,0x3fcb,
+0xc78b,0xadb6,0x7c27,0x3f8b,
+0x2903,0x65ff,0x7f2b,0x3f35,
+0xccf7,0xf3f6,0x438c,0x3ec8,
+0x6b3d,0xb876,0x29e5,0x3e3d,
+};
+#endif
+#ifdef MIEEE
+static unsigned short P2[36] = {
+0x4009,0xe6e8,0xe793,0xd574,
+0x401b,0xa931,0xc327,0x780b,
+0x400f,0x82ae,0xf32b,0xb0ac,
+0x3ff5,0x541c,0x18e7,0x9a0c,
+0x3fc9,0xca45,0xf35e,0x2651,
+0x3f89,0x5650,0x9069,0x354d,
+0x3f33,0xc3b2,0xe8ce,0x1812,
+0x3ec6,0x4c29,0x4c0c,0x2234,
+0x3e3a,0xccac,0x3058,0x8ff9,
+};
+static unsigned short Q2[32] = {
+/*0x3ff0,0x0000,0x0000,0x0000,*/
+0x4018,0x18da,0x568b,0xe828,
+0x400d,0x704d,0xaad2,0x3816,
+0x3ff6,0x0847,0x2aaf,0x6200,
+0x3fcb,0xada7,0x5fd6,0x3c9b,
+0x3f8b,0x7c27,0xadb6,0xc78b,
+0x3f35,0x7f2b,0x65ff,0x2903,
+0x3ec8,0x438c,0xf3f6,0xccf7,
+0x3e3d,0x29e5,0xb876,0x6b3d,
+};
+#endif
+
+#ifdef ANSIPROT
+extern double polevl ( double, void *, int );
+extern double p1evl ( double, void *, int );
+extern double log ( double );
+extern double sqrt ( double );
+#else
+double polevl(), p1evl(), log(), sqrt();
+#endif
+
+double ndtri(y0)
+double y0;
+{
+double x, y, z, y2, x0, x1;
+int code;
+
+if( y0 <= 0.0 )
+	{
+	mtherr( "ndtri", DOMAIN );
+	return( -MAXNUM );
+	}
+if( y0 >= 1.0 )
+	{
+	mtherr( "ndtri", DOMAIN );
+	return( MAXNUM );
+	}
+code = 1;
+y = y0;
+if( y > (1.0 - 0.13533528323661269189) ) /* 0.135... = exp(-2) */
+	{
+	y = 1.0 - y;
+	code = 0;
+	}
+
+if( y > 0.13533528323661269189 )
+	{
+	y = y - 0.5;
+	y2 = y * y;
+	x = y + y * (y2 * polevl( y2, P0, 4)/p1evl( y2, Q0, 8 ));
+	x = x * s2pi; 
+	return(x);
+	}
+
+x = sqrt( -2.0 * log(y) );
+x0 = x - log(x)/x;
+
+z = 1.0/x;
+if( x < 8.0 ) /* y > exp(-32) = 1.2664165549e-14 */
+	x1 = z * polevl( z, P1, 8 )/p1evl( z, Q1, 8 );
+else
+	x1 = z * polevl( z, P2, 8 )/p1evl( z, Q2, 8 );
+x = x0 - x1;
+if( code != 0 )
+	x = -x;
+return( x );
+}