305 lines
5.8 KiB
C
305 lines
5.8 KiB
C
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/* tan.c
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*
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* Circular tangent
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, tan();
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*
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* y = tan( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns the circular tangent of the radian argument x.
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*
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* Range reduction is modulo pi/4. A rational function
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* x + x**3 P(x**2)/Q(x**2)
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* is employed in the basic interval [0, pi/4].
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC +-1.07e9 44000 4.1e-17 1.0e-17
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* IEEE +-1.07e9 30000 2.9e-16 8.1e-17
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* tan total loss x > 1.073741824e9 0.0
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*
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*/
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/* cot.c
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*
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* Circular cotangent
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*
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*
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*
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* SYNOPSIS:
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*
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* double x, y, cot();
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*
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* y = cot( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns the circular cotangent of the radian argument x.
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*
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* Range reduction is modulo pi/4. A rational function
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* x + x**3 P(x**2)/Q(x**2)
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* is employed in the basic interval [0, pi/4].
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE +-1.07e9 30000 2.9e-16 8.2e-17
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*
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*
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* ERROR MESSAGES:
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*
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* message condition value returned
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* cot total loss x > 1.073741824e9 0.0
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* cot singularity x = 0 INFINITY
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*
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*/
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/*
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Cephes Math Library Release 2.8: June, 2000
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yright 1984, 1995, 2000 by Stephen L. Moshier
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*/
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#include "mconf.h"
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#ifdef UNK
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const static double P[] = {
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-1.30936939181383777646E4,
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1.15351664838587416140E6,
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-1.79565251976484877988E7
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};
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const static double Q[] = {
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/* 1.00000000000000000000E0,*/
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1.36812963470692954678E4,
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-1.32089234440210967447E6,
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2.50083801823357915839E7,
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-5.38695755929454629881E7
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};
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const static double DP1 = 7.853981554508209228515625E-1;
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const static double DP2 = 7.94662735614792836714E-9;
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const static double DP3 = 3.06161699786838294307E-17;
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const static double lossth = 1.073741824e9;
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#endif
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#ifdef DEC
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static unsigned short P[] = {
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0143514,0113306,0111171,0174674,
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0045214,0147545,0027744,0167346,
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0146210,0177526,0114514,0105660
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};
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static unsigned short Q[] = {
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/*0040200,0000000,0000000,0000000,*/
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0043525,0142457,0072633,0025617,
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0145241,0036742,0140525,0162256,
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0046276,0146176,0013526,0143573,
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0146515,0077401,0162762,0150607
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};
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/* 7.853981629014015197753906250000E-1 */
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static unsigned short P1[] = {0040111,0007732,0120000,0000000,};
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/* 4.960467869796758577649598009884E-10 */
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static unsigned short P2[] = {0030410,0055060,0100000,0000000,};
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/* 2.860594363054915898381331279295E-18 */
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static unsigned short P3[] = {0021523,0011431,0105056,0001560,};
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#define DP1 *(double *)P1
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#define DP2 *(double *)P2
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#define DP3 *(double *)P3
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const static double lossth = 1.073741824e9;
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#endif
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#ifdef IBMPC
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static unsigned short P[] = {
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0x3f38,0xd24f,0x92d8,0xc0c9,
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0x9ddd,0xa5fc,0x99ec,0x4131,
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0x9176,0xd329,0x1fea,0xc171
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};
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static unsigned short Q[] = {
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/*0x0000,0x0000,0x0000,0x3ff0,*/
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0x6572,0xeeb3,0xb8a5,0x40ca,
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0xbc96,0x582a,0x27bc,0xc134,
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0xd8ef,0xc2ea,0xd98f,0x4177,
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0x5a31,0x3cbe,0xafe0,0xc189
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};
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/*
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7.85398125648498535156E-1,
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3.77489470793079817668E-8,
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2.69515142907905952645E-15,
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*/
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static unsigned short P1[] = {0x0000,0x4000,0x21fb,0x3fe9};
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static unsigned short P2[] = {0x0000,0x0000,0x442d,0x3e64};
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static unsigned short P3[] = {0x5170,0x98cc,0x4698,0x3ce8};
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#define DP1 *(double *)P1
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#define DP2 *(double *)P2
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#define DP3 *(double *)P3
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const static double lossth = 1.073741824e9;
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#endif
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#ifdef MIEEE
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static unsigned short P[] = {
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0xc0c9,0x92d8,0xd24f,0x3f38,
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0x4131,0x99ec,0xa5fc,0x9ddd,
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0xc171,0x1fea,0xd329,0x9176
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};
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static unsigned short Q[] = {
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0x40ca,0xb8a5,0xeeb3,0x6572,
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0xc134,0x27bc,0x582a,0xbc96,
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0x4177,0xd98f,0xc2ea,0xd8ef,
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0xc189,0xafe0,0x3cbe,0x5a31
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};
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static unsigned short P1[] = {
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0x3fe9,0x21fb,0x4000,0x0000
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};
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static unsigned short P2[] = {
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0x3e64,0x442d,0x0000,0x0000
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};
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static unsigned short P3[] = {
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0x3ce8,0x4698,0x98cc,0x5170,
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};
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#define DP1 *(double *)P1
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#define DP2 *(double *)P2
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#define DP3 *(double *)P3
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const static double lossth = 1.073741824e9;
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#endif
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#ifdef ANSIPROT
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extern double polevl ( double, void *, int );
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extern double p1evl ( double, void *, int );
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extern double floor ( double );
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extern double ldexp ( double, int );
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extern int isnan ( double );
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extern int isfinite ( double );
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const static double tancot(double, int);
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#else
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double polevl(), p1evl(), floor(), ldexp();
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const static double tancot();
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int isnan(), isfinite();
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#endif
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extern double PIO4;
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extern double INFINITY;
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extern double NAN;
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double tan(x)
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double x;
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{
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#ifdef MINUSZERO
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if( x == 0.0 )
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return(x);
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#endif
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#ifdef NANS
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if( isnan(x) )
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return(x);
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if( !isfinite(x) )
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{
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mtherr( "tan", DOMAIN );
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return(NAN);
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}
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#endif
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return( tancot(x,0) );
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}
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double cot(x)
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double x;
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{
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if( x == 0.0 )
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{
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mtherr( "cot", SING );
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return( INFINITY );
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}
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return( tancot(x,1) );
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}
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const static double tancot( xx, cotflg )
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double xx;
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int cotflg;
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{
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double x, y, z, zz;
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int j, sign;
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/* make argument positive but save the sign */
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if( xx < 0 )
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{
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x = -xx;
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sign = -1;
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}
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else
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{
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x = xx;
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sign = 1;
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}
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if( x > lossth )
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{
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if( cotflg )
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mtherr( "cot", TLOSS );
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else
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mtherr( "tan", TLOSS );
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return(0.0);
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}
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/* compute x mod PIO4 */
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y = floor( x/PIO4 );
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/* strip high bits of integer part */
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z = ldexp( y, -3 );
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z = floor(z); /* integer part of y/8 */
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z = y - ldexp( z, 3 ); /* y - 16 * (y/16) */
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/* integer and fractional part modulo one octant */
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j = z;
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/* map zeros and singularities to origin */
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if( j & 1 )
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{
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j += 1;
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y += 1.0;
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}
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z = ((x - y * DP1) - y * DP2) - y * DP3;
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zz = z * z;
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if( zz > 1.0e-14 )
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y = z + z * (zz * polevl( zz, P, 2 )/p1evl(zz, Q, 4));
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else
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y = z;
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if( j & 2 )
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{
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if( cotflg )
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y = -y;
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else
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y = -1.0/y;
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}
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else
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{
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if( cotflg )
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y = 1.0/y;
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}
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if( sign < 0 )
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y = -y;
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return( y );
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}
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