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Diffstat (limited to 'libm/double/sincos.c')
-rw-r--r-- | libm/double/sincos.c | 364 |
1 files changed, 0 insertions, 364 deletions
diff --git a/libm/double/sincos.c b/libm/double/sincos.c deleted file mode 100644 index 8a4a3784c..000000000 --- a/libm/double/sincos.c +++ /dev/null @@ -1,364 +0,0 @@ -/* sincos.c - * - * Circular sine and cosine of argument in degrees - * Table lookup and interpolation algorithm - * - * - * - * SYNOPSIS: - * - * double x, sine, cosine, flg, sincos(); - * - * sincos( x, &sine, &cosine, flg ); - * - * - * - * DESCRIPTION: - * - * Returns both the sine and the cosine of the argument x. - * Several different compile time options and minimax - * approximations are supplied to permit tailoring the - * tradeoff between computation speed and accuracy. - * - * Since range reduction is time consuming, the reduction - * of x modulo 360 degrees is also made optional. - * - * sin(i) is internally tabulated for 0 <= i <= 90 degrees. - * Approximation polynomials, ranging from linear interpolation - * to cubics in (x-i)**2, compute the sine and cosine - * of the residual x-i which is between -0.5 and +0.5 degree. - * In the case of the high accuracy options, the residual - * and the tabulated values are combined using the trigonometry - * formulas for sin(A+B) and cos(A+B). - * - * Compile time options are supplied for 5, 11, or 17 decimal - * relative accuracy (ACC5, ACC11, ACC17 respectively). - * A subroutine flag argument "flg" chooses betwen this - * accuracy and table lookup only (peak absolute error - * = 0.0087). - * - * If the argument flg = 1, then the tabulated value is - * returned for the nearest whole number of degrees. The - * approximation polynomials are not computed. At - * x = 0.5 deg, the absolute error is then sin(0.5) = 0.0087. - * - * An intermediate speed and precision can be obtained using - * the compile time option LINTERP and flg = 1. This yields - * a linear interpolation using a slope estimated from the sine - * or cosine at the nearest integer argument. The peak absolute - * error with this option is 3.8e-5. Relative error at small - * angles is about 1e-5. - * - * If flg = 0, then the approximation polynomials are computed - * and applied. - * - * - * - * SPEED: - * - * Relative speed comparisons follow for 6MHz IBM AT clone - * and Microsoft C version 4.0. These figures include - * software overhead of do loop and function calls. - * Since system hardware and software vary widely, the - * numbers should be taken as representative only. - * - * flg=0 flg=0 flg=1 flg=1 - * ACC11 ACC5 LINTERP Lookup only - * In-line 8087 (/FPi) - * sin(), cos() 1.0 1.0 1.0 1.0 - * - * In-line 8087 (/FPi) - * sincos() 1.1 1.4 1.9 3.0 - * - * Software (/FPa) - * sin(), cos() 0.19 0.19 0.19 0.19 - * - * Software (/FPa) - * sincos() 0.39 0.50 0.73 1.7 - * - * - * - * ACCURACY: - * - * The accurate approximations are designed with a relative error - * criterion. The absolute error is greatest at x = 0.5 degree. - * It decreases from a local maximum at i+0.5 degrees to full - * machine precision at each integer i degrees. With the - * ACC5 option, the relative error of 6.3e-6 is equivalent to - * an absolute angular error of 0.01 arc second in the argument - * at x = i+0.5 degrees. For small angles < 0.5 deg, the ACC5 - * accuracy is 6.3e-6 (.00063%) of reading; i.e., the absolute - * error decreases in proportion to the argument. This is true - * for both the sine and cosine approximations, since the latter - * is for the function 1 - cos(x). - * - * If absolute error is of most concern, use the compile time - * option ABSERR to obtain an absolute error of 2.7e-8 for ACC5 - * precision. This is about half the absolute error of the - * relative precision option. In this case the relative error - * for small angles will increase to 9.5e-6 -- a reasonable - * tradeoff. - */ - - -#include <math.h> - -/* Define one of the following to be 1: - */ -#define ACC5 1 -#define ACC11 0 -#define ACC17 0 - -/* Option for linear interpolation when flg = 1 - */ -#define LINTERP 1 - -/* Option for absolute error criterion - */ -#define ABSERR 1 - -/* Option to include modulo 360 function: - */ -#define MOD360 0 - -/* -Cephes Math Library Release 2.1 -Copyright 1987 by Stephen L. Moshier -Direct inquiries to 30 Frost Street, Cambridge, MA 02140 -*/ - - -/* Table of sin(i degrees) - * for 0 <= i <= 90 - */ -static double sintbl[92] = { - 0.00000000000000000000E0, - 1.74524064372835128194E-2, - 3.48994967025009716460E-2, - 5.23359562429438327221E-2, - 6.97564737441253007760E-2, - 8.71557427476581735581E-2, - 1.04528463267653471400E-1, - 1.21869343405147481113E-1, - 1.39173100960065444112E-1, - 1.56434465040230869010E-1, - 1.73648177666930348852E-1, - 1.90808995376544812405E-1, - 2.07911690817759337102E-1, - 2.24951054343864998051E-1, - 2.41921895599667722560E-1, - 2.58819045102520762349E-1, - 2.75637355816999185650E-1, - 2.92371704722736728097E-1, - 3.09016994374947424102E-1, - 3.25568154457156668714E-1, - 3.42020143325668733044E-1, - 3.58367949545300273484E-1, - 3.74606593415912035415E-1, - 3.90731128489273755062E-1, - 4.06736643075800207754E-1, - 4.22618261740699436187E-1, - 4.38371146789077417453E-1, - 4.53990499739546791560E-1, - 4.69471562785890775959E-1, - 4.84809620246337029075E-1, - 5.00000000000000000000E-1, - 5.15038074910054210082E-1, - 5.29919264233204954047E-1, - 5.44639035015027082224E-1, - 5.59192903470746830160E-1, - 5.73576436351046096108E-1, - 5.87785252292473129169E-1, - 6.01815023152048279918E-1, - 6.15661475325658279669E-1, - 6.29320391049837452706E-1, - 6.42787609686539326323E-1, - 6.56059028990507284782E-1, - 6.69130606358858213826E-1, - 6.81998360062498500442E-1, - 6.94658370458997286656E-1, - 7.07106781186547524401E-1, - 7.19339800338651139356E-1, - 7.31353701619170483288E-1, - 7.43144825477394235015E-1, - 7.54709580222771997943E-1, - 7.66044443118978035202E-1, - 7.77145961456970879980E-1, - 7.88010753606721956694E-1, - 7.98635510047292846284E-1, - 8.09016994374947424102E-1, - 8.19152044288991789684E-1, - 8.29037572555041692006E-1, - 8.38670567945424029638E-1, - 8.48048096156425970386E-1, - 8.57167300702112287465E-1, - 8.66025403784438646764E-1, - 8.74619707139395800285E-1, - 8.82947592858926942032E-1, - 8.91006524188367862360E-1, - 8.98794046299166992782E-1, - 9.06307787036649963243E-1, - 9.13545457642600895502E-1, - 9.20504853452440327397E-1, - 9.27183854566787400806E-1, - 9.33580426497201748990E-1, - 9.39692620785908384054E-1, - 9.45518575599316810348E-1, - 9.51056516295153572116E-1, - 9.56304755963035481339E-1, - 9.61261695938318861916E-1, - 9.65925826289068286750E-1, - 9.70295726275996472306E-1, - 9.74370064785235228540E-1, - 9.78147600733805637929E-1, - 9.81627183447663953497E-1, - 9.84807753012208059367E-1, - 9.87688340595137726190E-1, - 9.90268068741570315084E-1, - 9.92546151641322034980E-1, - 9.94521895368273336923E-1, - 9.96194698091745532295E-1, - 9.97564050259824247613E-1, - 9.98629534754573873784E-1, - 9.99390827019095730006E-1, - 9.99847695156391239157E-1, - 1.00000000000000000000E0, - 9.99847695156391239157E-1, -}; - -#ifdef ANSIPROT -double floor ( double ); -#else -double floor(); -#endif - -int sincos(x, s, c, flg) -double x; -double *s, *c; -int flg; -{ -int ix, ssign, csign, xsign; -double y, z, sx, sz, cx, cz; - -/* Make argument nonnegative. - */ -xsign = 1; -if( x < 0.0 ) - { - xsign = -1; - x = -x; - } - - -#if MOD360 -x = x - 360.0 * floor( x/360.0 ); -#endif - -/* Find nearest integer to x. - * Note there should be a domain error test here, - * but this is omitted to gain speed. - */ -ix = x + 0.5; -z = x - ix; /* the residual */ - -/* Look up the sine and cosine of the integer. - */ -if( ix <= 180 ) - { - ssign = 1; - csign = 1; - } -else - { - ssign = -1; - csign = -1; - ix -= 180; - } - -if( ix > 90 ) - { - csign = -csign; - ix = 180 - ix; - } - -sx = sintbl[ix]; -if( ssign < 0 ) - sx = -sx; -cx = sintbl[ 90-ix ]; -if( csign < 0 ) - cx = -cx; - -/* If the flag argument is set, then just return - * the tabulated values for arg to the nearest whole degree. - */ -if( flg ) - { -#if LINTERP - y = sx + 1.74531263774940077459e-2 * z * cx; - cx -= 1.74531263774940077459e-2 * z * sx; - sx = y; -#endif - if( xsign < 0 ) - sx = -sx; - *s = sx; /* sine */ - *c = cx; /* cosine */ - return 0; - } - - -if( ssign < 0 ) - sx = -sx; -if( csign < 0 ) - cx = -cx; - -/* Find sine and cosine - * of the residual angle between -0.5 and +0.5 degree. - */ -#if ACC5 -#if ABSERR -/* absolute error = 2.769e-8: */ -sz = 1.74531263774940077459e-2 * z; -/* absolute error = 4.146e-11: */ -cz = 1.0 - 1.52307909153324666207e-4 * z * z; -#else -/* relative error = 6.346e-6: */ -sz = 1.74531817576426662296e-2 * z; -/* relative error = 3.173e-6: */ -cz = 1.0 - 1.52308226602566149927e-4 * z * z; -#endif -#else -y = z * z; -#endif - - -#if ACC11 -sz = ( -8.86092781698004819918e-7 * y - + 1.74532925198378577601e-2 ) * z; - -cz = 1.0 - ( -3.86631403698859047896e-9 * y - + 1.52308709893047593702e-4 ) * y; -#endif - - -#if ACC17 -sz = (( 1.34959795251974073996e-11 * y - - 8.86096155697856783296e-7 ) * y - + 1.74532925199432957214e-2 ) * z; - -cz = 1.0 - (( 3.92582397764340914444e-14 * y - - 3.86632385155548605680e-9 ) * y - + 1.52308709893354299569e-4 ) * y; -#endif - - -/* Combine the tabulated part and the calculated part - * by trigonometry. - */ -y = sx * cz + cx * sz; -if( xsign < 0 ) - y = - y; -*s = y; /* sine */ - -*c = cx * cz - sx * sz; /* cosine */ -return 0; -} |