From 7ce331c01ce6eb7b3f5c715a38a24359da9c6ee2 Mon Sep 17 00:00:00 2001 From: Eric Andersen Date: Thu, 22 Nov 2001 14:04:29 +0000 Subject: Totally rework the math library, this time based on the MacOs X math library (which is itself based on the math lib from FreeBSD). -Erik --- libm/ldouble/powl.c | 739 ---------------------------------------------------- 1 file changed, 739 deletions(-) delete mode 100644 libm/ldouble/powl.c (limited to 'libm/ldouble/powl.c') diff --git a/libm/ldouble/powl.c b/libm/ldouble/powl.c deleted file mode 100644 index bad380696..000000000 --- a/libm/ldouble/powl.c +++ /dev/null @@ -1,739 +0,0 @@ -/* 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