/* polevll.c * p1evll.c * * Evaluate polynomial * * * * SYNOPSIS: * * int N; * long double x, y, coef[N+1], polevl[]; * * y = polevll( x, coef, N ); * * * * DESCRIPTION: * * Evaluates polynomial of degree N: * * 2 N * y = C + C x + C x +...+ C x * 0 1 2 N * * Coefficients are stored in reverse order: * * coef[0] = C , ..., coef[N] = C . * N 0 * * The function p1evll() assumes that coef[N] = 1.0 and is * omitted from the array. Its calling arguments are * otherwise the same as polevll(). * * This module also contains the following globally declared constants: * MAXNUML = 1.189731495357231765021263853E4932L; * MACHEPL = 5.42101086242752217003726400434970855712890625E-20L; * MAXLOGL = 1.1356523406294143949492E4L; * MINLOGL = -1.1355137111933024058873E4L; * LOGE2L = 6.9314718055994530941723E-1L; * LOG2EL = 1.4426950408889634073599E0L; * PIL = 3.1415926535897932384626L; * PIO2L = 1.5707963267948966192313L; * PIO4L = 7.8539816339744830961566E-1L; * * SPEED: * * In the interest of speed, there are no checks for out * of bounds arithmetic. This routine is used by most of * the functions in the library. Depending on available * equipment features, the user may wish to rewrite the * program in microcode or assembly language. * */ /* Cephes Math Library Release 2.2: July, 1992 Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ #include #if UNK /* almost 2^16384 */ long double MAXNUML = 1.189731495357231765021263853E4932L; /* 2^-64 */ long double MACHEPL = 5.42101086242752217003726400434970855712890625E-20L; /* log( MAXNUML ) */ long double MAXLOGL = 1.1356523406294143949492E4L; #ifdef DENORMAL /* log(smallest denormal number = 2^-16446) */ long double MINLOGL = -1.13994985314888605586758E4L; #else /* log( underflow threshold = 2^(-16382) ) */ long double MINLOGL = -1.1355137111933024058873E4L; #endif long double LOGE2L = 6.9314718055994530941723E-1L; long double LOG2EL = 1.4426950408889634073599E0L; long double PIL = 3.1415926535897932384626L; long double PIO2L = 1.5707963267948966192313L; long double PIO4L = 7.8539816339744830961566E-1L; #ifdef INFINITIES long double NANL = 0.0L / 0.0L; long double INFINITYL = 1.0L / 0.0L; #else long double INFINITYL = 1.189731495357231765021263853E4932L; long double NANL = 0.0L; #endif #endif #if IBMPC short MAXNUML[] = {0xffff,0xffff,0xffff,0xffff,0x7ffe, XPD}; short MAXLOGL[] = {0x79ab,0xd1cf,0x17f7,0xb172,0x400c, XPD}; #ifdef INFINITIES short INFINITYL[] = {0,0,0,0x8000,0x7fff, XPD}; short NANL[] = {0,0,0,0xc000,0x7fff, XPD}; #else short INFINITYL[] = {0xffff,0xffff,0xffff,0xffff,0x7ffe, XPD}; long double NANL = 0.0L; #endif #ifdef DENORMAL short MINLOGL[] = {0xbaaa,0x09e2,0xfe7f,0xb21d,0xc00c, XPD}; #else short MINLOGL[] = {0xeb2f,0x1210,0x8c67,0xb16c,0xc00c, XPD}; #endif short MACHEPL[] = {0x0000,0x0000,0x0000,0x8000,0x3fbf, XPD}; short LOGE2L[] = {0x79ac,0xd1cf,0x17f7,0xb172,0x3ffe, XPD}; short LOG2EL[] = {0xf0bc,0x5c17,0x3b29,0xb8aa,0x3fff, XPD}; short PIL[] = {0xc235,0x2168,0xdaa2,0xc90f,0x4000, XPD}; short PIO2L[] = {0xc235,0x2168,0xdaa2,0xc90f,0x3fff, XPD}; short PIO4L[] = {0xc235,0x2168,0xdaa2,0xc90f,0x3ffe, XPD}; #endif #if MIEEE long MAXNUML[] = {0x7ffe0000,0xffffffff,0xffffffff}; long MAXLOGL[] = {0x400c0000,0xb17217f7,0xd1cf79ab}; #ifdef INFINITIES long INFINITY[] = {0x7fff0000,0x80000000,0x00000000}; long NANL[] = {0x7fff0000,0xffffffff,0xffffffff}; #else long INFINITYL[] = {0x7ffe0000,0xffffffff,0xffffffff}; long double NANL = 0.0L; #endif #ifdef DENORMAL long MINLOGL[] = {0xc00c0000,0xb21dfe7f,0x09e2baaa}; #else long MINLOGL[] = {0xc00c0000,0xb16c8c67,0x1210eb2f}; #endif long MACHEPL[] = {0x3fbf0000,0x80000000,0x00000000}; long LOGE2L[] = {0x3ffe0000,0xb17217f7,0xd1cf79ac}; long LOG2EL[] = {0x3fff0000,0xb8aa3b29,0x5c17f0bc}; long PIL[] = {0x40000000,0xc90fdaa2,0x2168c235}; long PIO2L[] = {0x3fff0000,0xc90fdaa2,0x2168c235}; long PIO4L[] = {0x3ffe0000,0xc90fdaa2,0x2168c235}; #endif #ifdef MINUSZERO long double NEGZEROL = -0.0L; #else long double NEGZEROL = 0.0L; #endif /* Polynomial evaluator: * P[0] x^n + P[1] x^(n-1) + ... + P[n] */ long double polevll( x, p, n ) long double x; void *p; int n; { register long double y; register long double *P = (long double *)p; y = *P++; do { y = y * x + *P++; } while( --n ); return(y); } /* Polynomial evaluator: * x^n + P[0] x^(n-1) + P[1] x^(n-2) + ... + P[n] */ long double p1evll( x, p, n ) long double x; void *p; int n; { register long double y; register long double *P = (long double *)p; n -= 1; y = x + *P++; do { y = y * x + *P++; } while( --n ); return( y ); }