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Diffstat (limited to 'libm/double/ndtri.c')
| -rw-r--r-- | libm/double/ndtri.c | 417 |
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 ); +} |