13e12c5d1SDavid du Colombier /* 23e12c5d1SDavid du Colombier floating-point arctangent 33e12c5d1SDavid du Colombier 43e12c5d1SDavid du Colombier atan returns the value of the arctangent of its 53e12c5d1SDavid du Colombier argument in the range [-pi/2,pi/2]. 63e12c5d1SDavid du Colombier 73e12c5d1SDavid du Colombier atan2 returns the arctangent of arg1/arg2 83e12c5d1SDavid du Colombier in the range [-pi,pi]. 93e12c5d1SDavid du Colombier 103e12c5d1SDavid du Colombier there are no error returns. 113e12c5d1SDavid du Colombier 123e12c5d1SDavid du Colombier coefficients are #5077 from Hart & Cheney. (19.56D) 133e12c5d1SDavid du Colombier */ 143e12c5d1SDavid du Colombier 153e12c5d1SDavid du Colombier #include <math.h> 163e12c5d1SDavid du Colombier 173e12c5d1SDavid du Colombier #define sq2p1 2.414213562373095048802e0 183e12c5d1SDavid du Colombier #define sq2m1 .414213562373095048802e0 193e12c5d1SDavid du Colombier #define pio2 1.570796326794896619231e0 203e12c5d1SDavid du Colombier #define pio4 .785398163397448309615e0 213e12c5d1SDavid du Colombier #define p4 .161536412982230228262e2 223e12c5d1SDavid du Colombier #define p3 .26842548195503973794141e3 233e12c5d1SDavid du Colombier #define p2 .11530293515404850115428136e4 243e12c5d1SDavid du Colombier #define p1 .178040631643319697105464587e4 253e12c5d1SDavid du Colombier #define p0 .89678597403663861959987488e3 263e12c5d1SDavid du Colombier #define q4 .5895697050844462222791e2 273e12c5d1SDavid du Colombier #define q3 .536265374031215315104235e3 283e12c5d1SDavid du Colombier #define q2 .16667838148816337184521798e4 293e12c5d1SDavid du Colombier #define q1 .207933497444540981287275926e4 303e12c5d1SDavid du Colombier #define q0 .89678597403663861962481162e3 313e12c5d1SDavid du Colombier 323e12c5d1SDavid du Colombier 333e12c5d1SDavid du Colombier /* 343e12c5d1SDavid du Colombier xatan evaluates a series valid in the 353e12c5d1SDavid du Colombier range [-0.414...,+0.414...]. 363e12c5d1SDavid du Colombier */ 373e12c5d1SDavid du Colombier 383e12c5d1SDavid du Colombier static 393e12c5d1SDavid du Colombier double xatan(double arg)403e12c5d1SDavid du Colombierxatan(double arg) 413e12c5d1SDavid du Colombier { 423e12c5d1SDavid du Colombier double argsq, value; 433e12c5d1SDavid du Colombier 44*7dd7cddfSDavid du Colombier /* get denormalized add in following if range arg**10 is much smaller 45*7dd7cddfSDavid du Colombier than q1, so check for that case 46*7dd7cddfSDavid du Colombier */ 47*7dd7cddfSDavid du Colombier if(-.01 < arg && arg < .01) 48*7dd7cddfSDavid du Colombier value = p0/q0; 49*7dd7cddfSDavid du Colombier else { 503e12c5d1SDavid du Colombier argsq = arg*arg; 513e12c5d1SDavid du Colombier value = ((((p4*argsq + p3)*argsq + p2)*argsq + p1)*argsq + p0); 523e12c5d1SDavid du Colombier value = value/(((((argsq + q4)*argsq + q3)*argsq + q2)*argsq + q1)*argsq + q0); 53*7dd7cddfSDavid du Colombier } 543e12c5d1SDavid du Colombier return value*arg; 553e12c5d1SDavid du Colombier } 563e12c5d1SDavid du Colombier 573e12c5d1SDavid du Colombier /* 583e12c5d1SDavid du Colombier satan reduces its argument (known to be positive) 593e12c5d1SDavid du Colombier to the range [0,0.414...] and calls xatan. 603e12c5d1SDavid du Colombier */ 613e12c5d1SDavid du Colombier 623e12c5d1SDavid du Colombier static 633e12c5d1SDavid du Colombier double satan(double arg)643e12c5d1SDavid du Colombiersatan(double arg) 653e12c5d1SDavid du Colombier { 663e12c5d1SDavid du Colombier 673e12c5d1SDavid du Colombier if(arg < sq2m1) 683e12c5d1SDavid du Colombier return xatan(arg); 693e12c5d1SDavid du Colombier if(arg > sq2p1) 703e12c5d1SDavid du Colombier return pio2 - xatan(1.0/arg); 713e12c5d1SDavid du Colombier return pio4 + xatan((arg-1.0)/(arg+1.0)); 723e12c5d1SDavid du Colombier } 733e12c5d1SDavid du Colombier 743e12c5d1SDavid du Colombier /* 753e12c5d1SDavid du Colombier atan makes its argument positive and 763e12c5d1SDavid du Colombier calls the inner routine satan. 773e12c5d1SDavid du Colombier */ 783e12c5d1SDavid du Colombier 793e12c5d1SDavid du Colombier double atan(double arg)803e12c5d1SDavid du Colombieratan(double arg) 813e12c5d1SDavid du Colombier { 823e12c5d1SDavid du Colombier 833e12c5d1SDavid du Colombier if(arg > 0) 843e12c5d1SDavid du Colombier return satan(arg); 853e12c5d1SDavid du Colombier return -satan(-arg); 863e12c5d1SDavid du Colombier } 87