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Annotation of researchv10dc/libc/math/atan.c, revision 1.1

1.1     ! root        1: 
        !             2: /*
        !             3:        floating-point arctangent
        !             4: 
        !             5:        atan returns the value of the arctangent of its
        !             6:        argument in the range [-pi/2,pi/2].
        !             7: 
        !             8:        atan2 returns the arctangent of arg1/arg2
        !             9:        in the range [-pi,pi].
        !            10: 
        !            11:        there are no error returns.
        !            12: 
        !            13:        coefficients are #5077 from Hart & Cheney. (19.56D)
        !            14: */
        !            15: 
        !            16: 
        !            17: double static sq2p1     =2.414213562373095048802e0;
        !            18: static double sq2m1     = .414213562373095048802e0;
        !            19: static double pio2      =1.570796326794896619231e0;
        !            20: static double pio4      = .785398163397448309615e0;
        !            21: static double p4        = .161536412982230228262e2;
        !            22: static double p3        = .26842548195503973794141e3;
        !            23: static double p2        = .11530293515404850115428136e4;
        !            24: static double p1        = .178040631643319697105464587e4;
        !            25: static double p0        = .89678597403663861959987488e3;
        !            26: static double q4        = .5895697050844462222791e2;
        !            27: static double q3        = .536265374031215315104235e3;
        !            28: static double q2        = .16667838148816337184521798e4;
        !            29: static double q1        = .207933497444540981287275926e4;
        !            30: static double q0        = .89678597403663861962481162e3;
        !            31: 
        !            32: 
        !            33: /*
        !            34:        atan makes its argument positive and
        !            35:        calls the inner routine satan.
        !            36: */
        !            37: 
        !            38: double
        !            39: atan(arg)
        !            40: double arg;
        !            41: {
        !            42:        double satan();
        !            43: 
        !            44:        if(arg>0)
        !            45:                return(satan(arg));
        !            46:        else
        !            47:                return(-satan(-arg));
        !            48: }
        !            49: 
        !            50: 
        !            51: /*
        !            52:        atan2 discovers what quadrant the angle
        !            53:        is in and calls atan.
        !            54: */
        !            55: 
        !            56: double
        !            57: atan2(arg1,arg2)
        !            58: double arg1,arg2;
        !            59: {
        !            60:        double satan();
        !            61: 
        !            62:        if((arg1+arg2)==arg1)
        !            63:                if(arg1 >= 0.) return(pio2);
        !            64:                else return(-pio2);
        !            65:        else if(arg2 <0.)
        !            66:                if(arg1 >= 0.)
        !            67:                        return(pio2+pio2 - satan(-arg1/arg2));
        !            68:                else
        !            69:                        return(-pio2-pio2 + satan(arg1/arg2));
        !            70:        else if(arg1>0)
        !            71:                return(satan(arg1/arg2));
        !            72:        else
        !            73:                return(-satan(-arg1/arg2));
        !            74: }
        !            75: 
        !            76: /*
        !            77:        satan reduces its argument (known to be positive)
        !            78:        to the range [0,0.414...] and calls xatan.
        !            79: */
        !            80: 
        !            81: static double
        !            82: satan(arg)
        !            83: double arg;
        !            84: {
        !            85:        double  xatan();
        !            86: 
        !            87:        if(arg < sq2m1)
        !            88:                return(xatan(arg));
        !            89:        else if(arg > sq2p1)
        !            90:                return(pio2 - xatan(1.0/arg));
        !            91:        else
        !            92:                return(pio4 + xatan((arg-1.0)/(arg+1.0)));
        !            93: }
        !            94: 
        !            95: /*
        !            96:        xatan evaluates a series valid in the
        !            97:        range [-0.414...,+0.414...].
        !            98: */
        !            99: 
        !           100: static double
        !           101: xatan(arg)
        !           102: double arg;
        !           103: {
        !           104:        double argsq;
        !           105:        double value;
        !           106: 
        !           107:        argsq = arg*arg;
        !           108:        value = ((((p4*argsq + p3)*argsq + p2)*argsq + p1)*argsq + p0);
        !           109:        value = value/(((((argsq + q4)*argsq + q3)*argsq + q2)*argsq + q1)*argsq + q0);
        !           110:        return(value*arg);
        !           111: }

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