From 1077fa4d772832f77a677ce7fb7c2d513b959e3f Mon Sep 17 00:00:00 2001 From: Eric Andersen Date: Thu, 10 May 2001 00:40:28 +0000 Subject: uClibc now has a math library. muahahahaha! -Erik --- libm/ldouble/powl.c | 739 ++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 739 insertions(+) create mode 100644 libm/ldouble/powl.c (limited to 'libm/ldouble/powl.c') diff --git a/libm/ldouble/powl.c b/libm/ldouble/powl.c new file mode 100644 index 000000000..bad380696 --- /dev/null +++ b/libm/ldouble/powl.c @@ -0,0 +1,739 @@ +/* powl.c + * + * Power function, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, z, powl(); + * + * z = powl( x, y ); + * + * + * + * DESCRIPTION: + * + * Computes x raised to the yth power. Analytically, + * + * x**y = exp( y log(x) ). + * + * Following Cody and Waite, this program uses a lookup table + * of 2**-i/32 and pseudo extended precision arithmetic to + * obtain several extra bits of accuracy in both the logarithm + * and the exponential. + * + * + * + * ACCURACY: + * + * The relative error of pow(x,y) can be estimated + * by y dl ln(2), where dl is the absolute error of + * the internally computed base 2 logarithm. At the ends + * of the approximation interval the logarithm equal 1/32 + * and its relative error is about 1 lsb = 1.1e-19. Hence + * the predicted relative error in the result is 2.3e-21 y . + * + * Relative error: + * arithmetic domain # trials peak rms + * + * IEEE +-1000 40000 2.8e-18 3.7e-19 + * .001 < x < 1000, with log(x) uniformly distributed. + * -1000 < y < 1000, y uniformly distributed. + * + * IEEE 0,8700 60000 6.5e-18 1.0e-18 + * 0.99 < x < 1.01, 0 < y < 8700, uniformly distributed. + * + * + * ERROR MESSAGES: + * + * message condition value returned + * pow overflow x**y > MAXNUM INFINITY + * pow underflow x**y < 1/MAXNUM 0.0 + * pow domain x<0 and y noninteger 0.0 + * + */ + +/* +Cephes Math Library Release 2.7: May, 1998 +Copyright 1984, 1991, 1998 by Stephen L. Moshier +*/ + + +#include + +static char fname[] = {"powl"}; + +/* Table size */ +#define NXT 32 +/* log2(Table size) */ +#define LNXT 5 + +#ifdef UNK +/* log(1+x) = x - .5x^2 + x^3 * P(z)/Q(z) + * on the domain 2^(-1/32) - 1 <= x <= 2^(1/32) - 1 + */ +static long double P[] = { + 8.3319510773868690346226E-4L, + 4.9000050881978028599627E-1L, + 1.7500123722550302671919E0L, + 1.4000100839971580279335E0L, +}; +static long double Q[] = { +/* 1.0000000000000000000000E0L,*/ + 5.2500282295834889175431E0L, + 8.4000598057587009834666E0L, + 4.2000302519914740834728E0L, +}; +/* A[i] = 2^(-i/32), rounded to IEEE long double precision. + * If i is even, A[i] + B[i/2] gives additional accuracy. + */ +static long double A[33] = { + 1.0000000000000000000000E0L, + 9.7857206208770013448287E-1L, + 9.5760328069857364691013E-1L, + 9.3708381705514995065011E-1L, + 9.1700404320467123175367E-1L, + 8.9735453750155359320742E-1L, + 8.7812608018664974155474E-1L, + 8.5930964906123895780165E-1L, + 8.4089641525371454301892E-1L, + 8.2287773907698242225554E-1L, + 8.0524516597462715409607E-1L, + 7.8799042255394324325455E-1L, + 7.7110541270397041179298E-1L, + 7.5458221379671136985669E-1L, + 7.3841307296974965571198E-1L, + 7.2259040348852331001267E-1L, + 7.0710678118654752438189E-1L, + 6.9195494098191597746178E-1L, + 6.7712777346844636413344E-1L, + 6.6261832157987064729696E-1L, + 6.4841977732550483296079E-1L, + 6.3452547859586661129850E-1L, + 6.2092890603674202431705E-1L, + 6.0762367999023443907803E-1L, + 5.9460355750136053334378E-1L, + 5.8186242938878875689693E-1L, + 5.6939431737834582684856E-1L, + 5.5719337129794626814472E-1L, + 5.4525386633262882960438E-1L, + 5.3357020033841180906486E-1L, + 5.2213689121370692017331E-1L, + 5.1094857432705833910408E-1L, + 5.0000000000000000000000E-1L, +}; +static long double B[17] = { + 0.0000000000000000000000E0L, + 2.6176170809902549338711E-20L, +-1.0126791927256478897086E-20L, + 1.3438228172316276937655E-21L, + 1.2207982955417546912101E-20L, +-6.3084814358060867200133E-21L, + 1.3164426894366316434230E-20L, +-1.8527916071632873716786E-20L, + 1.8950325588932570796551E-20L, + 1.5564775779538780478155E-20L, + 6.0859793637556860974380E-21L, +-2.0208749253662532228949E-20L, + 1.4966292219224761844552E-20L, + 3.3540909728056476875639E-21L, +-8.6987564101742849540743E-22L, +-1.2327176863327626135542E-20L, + 0.0000000000000000000000E0L, +}; + +/* 2^x = 1 + x P(x), + * on the interval -1/32 <= x <= 0 + */ +static long double R[] = { + 1.5089970579127659901157E-5L, + 1.5402715328927013076125E-4L, + 1.3333556028915671091390E-3L, + 9.6181291046036762031786E-3L, + 5.5504108664798463044015E-2L, + 2.4022650695910062854352E-1L, + 6.9314718055994530931447E-1L, +}; + +#define douba(k) A[k] +#define doubb(k) B[k] +#define MEXP (NXT*16384.0L) +/* The following if denormal numbers are supported, else -MEXP: */ +#ifdef DENORMAL +#define MNEXP (-NXT*(16384.0L+64.0L)) +#else +#define MNEXP (-NXT*16384.0L) +#endif +/* log2(e) - 1 */ +#define LOG2EA 0.44269504088896340735992L +#endif + + +#ifdef IBMPC +static short P[] = { +0xb804,0xa8b7,0xc6f4,0xda6a,0x3ff4, XPD +0x7de9,0xcf02,0x58c0,0xfae1,0x3ffd, XPD +0x405a,0x3722,0x67c9,0xe000,0x3fff, XPD +0xcd99,0x6b43,0x87ca,0xb333,0x3fff, XPD +}; +static short Q[] = { +/* 0x0000,0x0000,0x0000,0x8000,0x3fff, */ +0x6307,0xa469,0x3b33,0xa800,0x4001, XPD +0xfec2,0x62d7,0xa51c,0x8666,0x4002, XPD +0xda32,0xd072,0xa5d7,0x8666,0x4001, XPD +}; +static short A[] = { +0x0000,0x0000,0x0000,0x8000,0x3fff, XPD +0x033a,0x722a,0xb2db,0xfa83,0x3ffe, XPD +0xcc2c,0x2486,0x7d15,0xf525,0x3ffe, XPD +0xf5cb,0xdcda,0xb99b,0xefe4,0x3ffe, XPD +0x392f,0xdd24,0xc6e7,0xeac0,0x3ffe, XPD +0x48a8,0x7c83,0x06e7,0xe5b9,0x3ffe, XPD +0xe111,0x2a94,0xdeec,0xe0cc,0x3ffe, XPD +0x3755,0xdaf2,0xb797,0xdbfb,0x3ffe, XPD +0x6af4,0xd69d,0xfcca,0xd744,0x3ffe, XPD +0xe45a,0xf12a,0x1d91,0xd2a8,0x3ffe, XPD +0x80e4,0x1f84,0x8c15,0xce24,0x3ffe, XPD +0x27a3,0x6e2f,0xbd86,0xc9b9,0x3ffe, XPD +0xdadd,0x5506,0x2a11,0xc567,0x3ffe, XPD +0x9456,0x6670,0x4cca,0xc12c,0x3ffe, XPD +0x36bf,0x580c,0xa39f,0xbd08,0x3ffe, XPD +0x9ee9,0x62fb,0xaf47,0xb8fb,0x3ffe, XPD +0x6484,0xf9de,0xf333,0xb504,0x3ffe, XPD +0x2590,0xd2ac,0xf581,0xb123,0x3ffe, XPD +0x4ac6,0x42a1,0x3eea,0xad58,0x3ffe, XPD +0x0ef8,0xea7c,0x5ab4,0xa9a1,0x3ffe, XPD +0x38ea,0xb151,0xd6a9,0xa5fe,0x3ffe, XPD +0x6819,0x0c49,0x4303,0xa270,0x3ffe, XPD +0x11ae,0x91a1,0x3260,0x9ef5,0x3ffe, XPD +0x5539,0xd54e,0x39b9,0x9b8d,0x3ffe, XPD +0xa96f,0x8db8,0xf051,0x9837,0x3ffe, XPD +0x0961,0xfef7,0xefa8,0x94f4,0x3ffe, XPD +0xc336,0xab11,0xd373,0x91c3,0x3ffe, XPD +0x53c0,0x45cd,0x398b,0x8ea4,0x3ffe, XPD +0xd6e7,0xea8b,0xc1e3,0x8b95,0x3ffe, XPD +0x8527,0x92da,0x0e80,0x8898,0x3ffe, XPD +0x7b15,0xcc48,0xc367,0x85aa,0x3ffe, XPD +0xa1d7,0xac2b,0x8698,0x82cd,0x3ffe, XPD +0x0000,0x0000,0x0000,0x8000,0x3ffe, XPD +}; +static short B[] = { +0x0000,0x0000,0x0000,0x0000,0x0000, XPD +0x1f87,0xdb30,0x18f5,0xf73a,0x3fbd, XPD +0xac15,0x3e46,0x2932,0xbf4a,0xbfbc, XPD +0x7944,0xba66,0xa091,0xcb12,0x3fb9, XPD +0xff78,0x40b4,0x2ee6,0xe69a,0x3fbc, XPD +0xc895,0x5069,0xe383,0xee53,0xbfbb, XPD +0x7cde,0x9376,0x4325,0xf8ab,0x3fbc, XPD +0xa10c,0x25e0,0xc093,0xaefd,0xbfbd, XPD +0x7d3e,0xea95,0x1366,0xb2fb,0x3fbd, XPD +0x5d89,0xeb34,0x5191,0x9301,0x3fbd, XPD +0x80d9,0xb883,0xfb10,0xe5eb,0x3fbb, XPD +0x045d,0x288c,0xc1ec,0xbedd,0xbfbd, XPD +0xeded,0x5c85,0x4630,0x8d5a,0x3fbd, XPD +0x9d82,0xe5ac,0x8e0a,0xfd6d,0x3fba, XPD +0x6dfd,0xeb58,0xaf14,0x8373,0xbfb9, XPD +0xf938,0x7aac,0x91cf,0xe8da,0xbfbc, XPD +0x0000,0x0000,0x0000,0x0000,0x0000, XPD +}; +static short R[] = { +0xa69b,0x530e,0xee1d,0xfd2a,0x3fee, XPD +0xc746,0x8e7e,0x5960,0xa182,0x3ff2, XPD +0x63b6,0xadda,0xfd6a,0xaec3,0x3ff5, XPD +0xc104,0xfd99,0x5b7c,0x9d95,0x3ff8, XPD +0xe05e,0x249d,0x46b8,0xe358,0x3ffa, XPD +0x5d1d,0x162c,0xeffc,0xf5fd,0x3ffc, XPD +0x79aa,0xd1cf,0x17f7,0xb172,0x3ffe, XPD +}; + +/* 10 byte sizes versus 12 byte */ +#define douba(k) (*(long double *)(&A[(sizeof( long double )/2)*(k)])) +#define doubb(k) (*(long double *)(&B[(sizeof( long double )/2)*(k)])) +#define MEXP (NXT*16384.0L) +#ifdef DENORMAL +#define MNEXP (-NXT*(16384.0L+64.0L)) +#else +#define MNEXP (-NXT*16384.0L) +#endif +static short L[] = {0xc2ef,0x705f,0xeca5,0xe2a8,0x3ffd, XPD}; +#define LOG2EA (*(long double *)(&L[0])) +#endif + +#ifdef MIEEE +static long P[] = { +0x3ff40000,0xda6ac6f4,0xa8b7b804, +0x3ffd0000,0xfae158c0,0xcf027de9, +0x3fff0000,0xe00067c9,0x3722405a, +0x3fff0000,0xb33387ca,0x6b43cd99, +}; +static long Q[] = { +/* 0x3fff0000,0x80000000,0x00000000, */ +0x40010000,0xa8003b33,0xa4696307, +0x40020000,0x8666a51c,0x62d7fec2, +0x40010000,0x8666a5d7,0xd072da32, +}; +static long A[] = { +0x3fff0000,0x80000000,0x00000000, +0x3ffe0000,0xfa83b2db,0x722a033a, +0x3ffe0000,0xf5257d15,0x2486cc2c, +0x3ffe0000,0xefe4b99b,0xdcdaf5cb, +0x3ffe0000,0xeac0c6e7,0xdd24392f, +0x3ffe0000,0xe5b906e7,0x7c8348a8, +0x3ffe0000,0xe0ccdeec,0x2a94e111, +0x3ffe0000,0xdbfbb797,0xdaf23755, +0x3ffe0000,0xd744fcca,0xd69d6af4, +0x3ffe0000,0xd2a81d91,0xf12ae45a, +0x3ffe0000,0xce248c15,0x1f8480e4, +0x3ffe0000,0xc9b9bd86,0x6e2f27a3, +0x3ffe0000,0xc5672a11,0x5506dadd, +0x3ffe0000,0xc12c4cca,0x66709456, +0x3ffe0000,0xbd08a39f,0x580c36bf, +0x3ffe0000,0xb8fbaf47,0x62fb9ee9, +0x3ffe0000,0xb504f333,0xf9de6484, +0x3ffe0000,0xb123f581,0xd2ac2590, +0x3ffe0000,0xad583eea,0x42a14ac6, +0x3ffe0000,0xa9a15ab4,0xea7c0ef8, +0x3ffe0000,0xa5fed6a9,0xb15138ea, +0x3ffe0000,0xa2704303,0x0c496819, +0x3ffe0000,0x9ef53260,0x91a111ae, +0x3ffe0000,0x9b8d39b9,0xd54e5539, +0x3ffe0000,0x9837f051,0x8db8a96f, +0x3ffe0000,0x94f4efa8,0xfef70961, +0x3ffe0000,0x91c3d373,0xab11c336, +0x3ffe0000,0x8ea4398b,0x45cd53c0, +0x3ffe0000,0x8b95c1e3,0xea8bd6e7, +0x3ffe0000,0x88980e80,0x92da8527, +0x3ffe0000,0x85aac367,0xcc487b15, +0x3ffe0000,0x82cd8698,0xac2ba1d7, +0x3ffe0000,0x80000000,0x00000000, +}; +static long B[51] = { +0x00000000,0x00000000,0x00000000, +0x3fbd0000,0xf73a18f5,0xdb301f87, +0xbfbc0000,0xbf4a2932,0x3e46ac15, +0x3fb90000,0xcb12a091,0xba667944, +0x3fbc0000,0xe69a2ee6,0x40b4ff78, +0xbfbb0000,0xee53e383,0x5069c895, +0x3fbc0000,0xf8ab4325,0x93767cde, +0xbfbd0000,0xaefdc093,0x25e0a10c, +0x3fbd0000,0xb2fb1366,0xea957d3e, +0x3fbd0000,0x93015191,0xeb345d89, +0x3fbb0000,0xe5ebfb10,0xb88380d9, +0xbfbd0000,0xbeddc1ec,0x288c045d, +0x3fbd0000,0x8d5a4630,0x5c85eded, +0x3fba0000,0xfd6d8e0a,0xe5ac9d82, +0xbfb90000,0x8373af14,0xeb586dfd, +0xbfbc0000,0xe8da91cf,0x7aacf938, +0x00000000,0x00000000,0x00000000, +}; +static long R[] = { +0x3fee0000,0xfd2aee1d,0x530ea69b, +0x3ff20000,0xa1825960,0x8e7ec746, +0x3ff50000,0xaec3fd6a,0xadda63b6, +0x3ff80000,0x9d955b7c,0xfd99c104, +0x3ffa0000,0xe35846b8,0x249de05e, +0x3ffc0000,0xf5fdeffc,0x162c5d1d, +0x3ffe0000,0xb17217f7,0xd1cf79aa, +}; + +#define douba(k) (*(long double *)&A[3*(k)]) +#define doubb(k) (*(long double *)&B[3*(k)]) +#define MEXP (NXT*16384.0L) +#ifdef DENORMAL +#define MNEXP (-NXT*(16384.0L+64.0L)) +#else +#define MNEXP (-NXT*16382.0L) +#endif +static long L[3] = {0x3ffd0000,0xe2a8eca5,0x705fc2ef}; +#define LOG2EA (*(long double *)(&L[0])) +#endif + + +#define F W +#define Fa Wa +#define Fb Wb +#define G W +#define Ga Wa +#define Gb u +#define H W +#define Ha Wb +#define Hb Wb + +extern long double MAXNUML; +static VOLATILE long double z; +static long double w, W, Wa, Wb, ya, yb, u; +#ifdef ANSIPROT +extern long double floorl ( long double ); +extern long double fabsl ( long double ); +extern long double frexpl ( long double, int * ); +extern long double ldexpl ( long double, int ); +extern long double polevll ( long double, void *, int ); +extern long double p1evll ( long double, void *, int ); +extern long double powil ( long double, int ); +extern int isnanl ( long double ); +extern int isfinitel ( long double ); +static long double reducl( long double ); +extern int signbitl ( long double ); +#else +long double floorl(), fabsl(), frexpl(), ldexpl(); +long double polevll(), p1evll(), powil(); +static long double reducl(); +int isnanl(), isfinitel(), signbitl(); +#endif + +#ifdef INFINITIES +extern long double INFINITYL; +#else +#define INFINITYL MAXNUML +#endif + +#ifdef NANS +extern long double NANL; +#endif +#ifdef MINUSZERO +extern long double NEGZEROL; +#endif + +long double powl( x, y ) +long double x, y; +{ +/* double F, Fa, Fb, G, Ga, Gb, H, Ha, Hb */ +int i, nflg, iyflg, yoddint; +long e; + +if( y == 0.0L ) + return( 1.0L ); + +#ifdef NANS +if( isnanl(x) ) + return( x ); +if( isnanl(y) ) + return( y ); +#endif + +if( y == 1.0L ) + return( x ); + +#ifdef INFINITIES +if( !isfinitel(y) && (x == -1.0L || x == 1.0L) ) + { + mtherr( "powl", DOMAIN ); +#ifdef NANS + return( NANL ); +#else + return( INFINITYL ); +#endif + } +#endif + +if( x == 1.0L ) + return( 1.0L ); + +if( y >= MAXNUML ) + { +#ifdef INFINITIES + if( x > 1.0L ) + return( INFINITYL ); +#else + if( x > 1.0L ) + return( MAXNUML ); +#endif + if( x > 0.0L && x < 1.0L ) + return( 0.0L ); +#ifdef INFINITIES + if( x < -1.0L ) + return( INFINITYL ); +#else + if( x < -1.0L ) + return( MAXNUML ); +#endif + if( x > -1.0L && x < 0.0L ) + return( 0.0L ); + } +if( y <= -MAXNUML ) + { + if( x > 1.0L ) + return( 0.0L ); +#ifdef INFINITIES + if( x > 0.0L && x < 1.0L ) + return( INFINITYL ); +#else + if( x > 0.0L && x < 1.0L ) + return( MAXNUML ); +#endif + if( x < -1.0L ) + return( 0.0L ); +#ifdef INFINITIES + if( x > -1.0L && x < 0.0L ) + return( INFINITYL ); +#else + if( x > -1.0L && x < 0.0L ) + return( MAXNUML ); +#endif + } +if( x >= MAXNUML ) + { +#if INFINITIES + if( y > 0.0L ) + return( INFINITYL ); +#else + if( y > 0.0L ) + return( MAXNUML ); +#endif + return( 0.0L ); + } + +w = floorl(y); +/* Set iyflg to 1 if y is an integer. */ +iyflg = 0; +if( w == y ) + iyflg = 1; + +/* Test for odd integer y. */ +yoddint = 0; +if( iyflg ) + { + ya = fabsl(y); + ya = floorl(0.5L * ya); + yb = 0.5L * fabsl(w); + if( ya != yb ) + yoddint = 1; + } + +if( x <= -MAXNUML ) + { + if( y > 0.0L ) + { +#ifdef INFINITIES + if( yoddint ) + return( -INFINITYL ); + return( INFINITYL ); +#else + if( yoddint ) + return( -MAXNUML ); + return( MAXNUML ); +#endif + } + if( y < 0.0L ) + { +#ifdef MINUSZERO + if( yoddint ) + return( NEGZEROL ); +#endif + return( 0.0 ); + } + } + + +nflg = 0; /* flag = 1 if x<0 raised to integer power */ +if( x <= 0.0L ) + { + if( x == 0.0L ) + { + if( y < 0.0 ) + { +#ifdef MINUSZERO + if( signbitl(x) && yoddint ) + return( -INFINITYL ); +#endif +#ifdef INFINITIES + return( INFINITYL ); +#else + return( MAXNUML ); +#endif + } + if( y > 0.0 ) + { +#ifdef MINUSZERO + if( signbitl(x) && yoddint ) + return( NEGZEROL ); +#endif + return( 0.0 ); + } + if( y == 0.0L ) + return( 1.0L ); /* 0**0 */ + else + return( 0.0L ); /* 0**y */ + } + else + { + if( iyflg == 0 ) + { /* noninteger power of negative number */ + mtherr( fname, DOMAIN ); +#ifdef NANS + return(NANL); +#else + return(0.0L); +#endif + } + nflg = 1; + } + } + +/* Integer power of an integer. */ + +if( iyflg ) + { + i = w; + w = floorl(x); + if( (w == x) && (fabsl(y) < 32768.0) ) + { + w = powil( x, (int) y ); + return( w ); + } + } + + +if( nflg ) + x = fabsl(x); + +/* separate significand from exponent */ +x = frexpl( x, &i ); +e = i; + +/* find significand in antilog table A[] */ +i = 1; +if( x <= douba(17) ) + i = 17; +if( x <= douba(i+8) ) + i += 8; +if( x <= douba(i+4) ) + i += 4; +if( x <= douba(i+2) ) + i += 2; +if( x >= douba(1) ) + i = -1; +i += 1; + + +/* Find (x - A[i])/A[i] + * in order to compute log(x/A[i]): + * + * log(x) = log( a x/a ) = log(a) + log(x/a) + * + * log(x/a) = log(1+v), v = x/a - 1 = (x-a)/a + */ +x -= douba(i); +x -= doubb(i/2); +x /= douba(i); + + +/* rational approximation for log(1+v): + * + * log(1+v) = v - v**2/2 + v**3 P(v) / Q(v) + */ +z = x*x; +w = x * ( z * polevll( x, P, 3 ) / p1evll( x, Q, 3 ) ); +w = w - ldexpl( z, -1 ); /* w - 0.5 * z */ + +/* Convert to base 2 logarithm: + * multiply by log2(e) = 1 + LOG2EA + */ +z = LOG2EA * w; +z += w; +z += LOG2EA * x; +z += x; + +/* Compute exponent term of the base 2 logarithm. */ +w = -i; +w = ldexpl( w, -LNXT ); /* divide by NXT */ +w += e; +/* Now base 2 log of x is w + z. */ + +/* Multiply base 2 log by y, in extended precision. */ + +/* separate y into large part ya + * and small part yb less than 1/NXT + */ +ya = reducl(y); +yb = y - ya; + +/* (w+z)(ya+yb) + * = w*ya + w*yb + z*y + */ +F = z * y + w * yb; +Fa = reducl(F); +Fb = F - Fa; + +G = Fa + w * ya; +Ga = reducl(G); +Gb = G - Ga; + +H = Fb + Gb; +Ha = reducl(H); +w = ldexpl( Ga+Ha, LNXT ); + +/* Test the power of 2 for overflow */ +if( w > MEXP ) + { +/* printf( "w = %.4Le ", w ); */ + mtherr( fname, OVERFLOW ); + return( MAXNUML ); + } + +if( w < MNEXP ) + { +/* printf( "w = %.4Le ", w ); */ + mtherr( fname, UNDERFLOW ); + return( 0.0L ); + } + +e = w; +Hb = H - Ha; + +if( Hb > 0.0L ) + { + e += 1; + Hb -= (1.0L/NXT); /*0.0625L;*/ + } + +/* Now the product y * log2(x) = Hb + e/NXT. + * + * Compute base 2 exponential of Hb, + * where -0.0625 <= Hb <= 0. + */ +z = Hb * polevll( Hb, R, 6 ); /* z = 2**Hb - 1 */ + +/* Express e/NXT as an integer plus a negative number of (1/NXT)ths. + * Find lookup table entry for the fractional power of 2. + */ +if( e < 0 ) + i = 0; +else + i = 1; +i = e/NXT + i; +e = NXT*i - e; +w = douba( e ); +z = w * z; /* 2**-e * ( 1 + (2**Hb-1) ) */ +z = z + w; +z = ldexpl( z, i ); /* multiply by integer power of 2 */ + +if( nflg ) + { +/* For negative x, + * find out if the integer exponent + * is odd or even. + */ + w = ldexpl( y, -1 ); + w = floorl(w); + w = ldexpl( w, 1 ); + if( w != y ) + z = -z; /* odd exponent */ + } + +return( z ); +} + + +/* Find a multiple of 1/NXT that is within 1/NXT of x. */ +static long double reducl(x) +long double x; +{ +long double t; + +t = ldexpl( x, LNXT ); +t = floorl( t ); +t = ldexpl( t, -LNXT ); +return(t); +} -- cgit v1.2.3