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291 lines
6.8 KiB
291 lines
6.8 KiB
/***
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*atan.c - arctangent of x and x/y
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*
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* Copyright (c) 1991-2001, Microsoft Corporation. All rights reserved.
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*
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*Purpose:
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*
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*Revision History:
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* 8-15-91 GDP written
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* 12-30-91 GDP support IEEE exceptions
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* 3-27-92 GDP support UNDERFLOW
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* 02-06-95 JWM Mac merge
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* 10-07-97 RDL Added IA64.
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*
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*******************************************************************************/
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#include <math.h>
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#include <trans.h>
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#if defined(_M_IA64)
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#pragma function(atan, atan2)
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#endif
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static double _atanhlp(double x);
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static double const a[4] = {
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0.0,
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0.52359877559829887308, /* pi/6 */
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1.57079632679489661923, /* pi/2 */
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1.04719755119659774615 /* pi/3 */
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};
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/* constants */
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static double const EPS = 1.05367121277235079465e-8; /* 2^(-53/2) */
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static double const PI_OVER_TWO = 1.57079632679489661923;
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static double const PI = 3.14159265358979323846;
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static double const TWO_M_SQRT3 = 0.26794919243112270647;
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static double const SQRT3_M_ONE = 0.73205080756887729353;
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static double const SQRT3 = 1.73205080756887729353;
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/* chose MAX_ARG s.t. 1/MAX_ARG does not underflow */
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static double const MAX_ARG = 4.494232837155790e+307;
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/* constants for rational approximation */
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static double const p0 = -0.13688768894191926929e+2;
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static double const p1 = -0.20505855195861651981e+2;
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static double const p2 = -0.84946240351320683534e+1;
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static double const p3 = -0.83758299368150059274e+0;
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static double const q0 = 0.41066306682575781263e+2;
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static double const q1 = 0.86157349597130242515e+2;
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static double const q2 = 0.59578436142597344465e+2;
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static double const q3 = 0.15024001160028576121e+2;
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static double const q4 = 0.10000000000000000000e+1;
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#define Q(g) (((((g) + q3) * (g) + q2) * (g) + q1) * (g) + q0)
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#define R(g) ((((p3 * (g) + p2) * (g) + p1) * (g) + p0) * (g)) / Q(g)
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/***
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*double atan(double x) - arctangent
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*
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*Purpose:
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*
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*Entry:
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*
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*Exit:
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*
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*Exceptions:
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* P, I
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\*******************************************************************************/
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double atan(double x)
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{
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uintptr_t savedcw;
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double result;
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/* save user fp control word */
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savedcw = _maskfp();
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/* check for infinity or NAN */
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if (IS_D_SPECIAL(x)){
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switch(_sptype(x)) {
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case T_PINF:
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result = PI_OVER_TWO;
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break;
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case T_NINF:
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result = -PI_OVER_TWO;
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break;
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case T_QNAN:
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return _handle_qnan1(OP_ATAN,x,savedcw);
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default: //T_SNAN
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return _except1(FP_I,OP_ATAN,x,_s2qnan(x),savedcw);
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}
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}
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if (x == 0.0)
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RETURN(savedcw,x);
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result = _atanhlp(x);
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RETURN_INEXACT1(OP_ATAN,x,result,savedcw);
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}
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/***
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*double atan2(double x, double y) - arctangent (x/y)
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*
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*Purpose:
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*
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*Entry:
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*
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*Exit:
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*
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*Exceptions:
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* NAN or both args 0: DOMAIN error
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*******************************************************************************/
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double atan2(double v, double u)
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{
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uintptr_t savedcw;
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double result;
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/* save user fp control word */
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savedcw = _maskfp();
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/* check for infinity or NAN */
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if (IS_D_SPECIAL(v) || IS_D_SPECIAL(u)){
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if (IS_D_SNAN(v) || IS_D_SNAN(u)){
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return _except2(FP_I,OP_ATAN2,v,u,_d_snan2(v,u),savedcw);
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}
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if (IS_D_QNAN(v) || IS_D_QNAN(u)){
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return _handle_qnan2(OP_ATAN2,v,u,savedcw);
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}
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if ((IS_D_INF(v) || IS_D_MINF(v)) &&
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(IS_D_INF(u) || IS_D_MINF(u))){
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return _except2(FP_I,OP_ATAN2,v,u,QNAN_ATAN2,savedcw);
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}
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/* the other combinations of infinities will be handled
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* later by the division v/u
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*/
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}
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if (u == 0) {
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if (v == 0) {
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return _except2(FP_I,OP_ATAN2,v,u,QNAN_ATAN2,savedcw);
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}
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else {
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result = PI_OVER_TWO;
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}
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}
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else if (INTEXP(v) - INTEXP(u) > MAXEXP - 3) {
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/* v/u overflow */
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result = PI_OVER_TWO;
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}
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else {
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double arg = v/u;
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if (ABS(arg) < D_MIN) {
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if (v == 0.0 || IS_D_INF(u) || IS_D_MINF(u)) {
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result = (u < 0) ? PI : 0;
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if (v < 0) {
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result = -result;
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}
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if (result == 0) {
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RETURN(savedcw, result);
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}
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else {
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RETURN_INEXACT2(OP_ATAN2,v,u,result,savedcw);
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}
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}
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else {
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double v1, u1;
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int vexp, uexp;
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int exc_flags;
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//
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// in this case an underflow has occurred
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// re-compute the result in order to raise
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// an IEEE underflow exception
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//
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if (u < 0) {
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result = v < 0 ? -PI: PI;
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RETURN_INEXACT2(OP_ATAN2,v,u,result,savedcw);
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}
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v1 = _decomp(v, &vexp);
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u1 = _decomp(u, &uexp);
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result = _add_exp(v1/u1, vexp-uexp+IEEE_ADJUST);
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result = ABS(result);
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if (v < 0) {
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result = -result;
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}
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// this is not a perfect solution. In the future
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// we may want to have a way to let the division
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// generate an exception and propagate the IEEE result
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// to the user's handler
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exc_flags = FP_U;
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if (_statfp() & ISW_INEXACT) {
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exc_flags |= FP_P;
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}
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return _except2(exc_flags,OP_ATAN2,v,u,result,savedcw);
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}
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}
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else {
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result = _atanhlp( ABS(arg) );
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}
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}
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/* set sign of the result */
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if (u < 0) {
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result = PI - result;
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}
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if (v < 0) {
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result = -result;
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}
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RETURN_INEXACT2(OP_ATAN2,v,u,result,savedcw);
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}
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/***
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*double _atanhlp(double x) - arctangent helper
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*
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*Purpose:
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* Compute arctangent of x, assuming x is a valid, non infinite
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* number.
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* The algorithm (reduction / rational approximation) is
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* taken from Cody & Waite.
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*
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*Entry:
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*
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*Exit:
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*
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*Exceptions:
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*
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*******************************************************************************/
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static double _atanhlp(double x)
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{
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double f,g,result;
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int n;
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f = ABS(x);
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if (f > MAX_ARG) {
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// if this step is ommited, 1.0/f might underflow in the
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// following block
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return x > 0.0 ? PI_OVER_TWO : -PI_OVER_TWO;
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}
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if (f > 1.0) {
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f = 1.0/f;
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n = 2;
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}
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else {
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n = 0;
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}
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if (f > TWO_M_SQRT3) {
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f = (((SQRT3_M_ONE * f - .5) - .5) + f) / (SQRT3 + f);
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n++;
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}
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if (ABS(f) < EPS) {
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result = f;
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}
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else {
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g = f*f;
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result = f + f * R(g);
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}
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if (n > 1)
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result = -result;
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result += a[n];
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if (x < 0.0)
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result = -result;
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return result;
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}
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