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| Commit | Line | Data |
|---|---|---|
| 5d130d40 RM |
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 | } |