[444] | 1 | |
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| 2 | /* @(#)z_atangentf.c 1.0 98/08/13 */ |
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| 3 | /****************************************************************** |
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| 4 | * The following routines are coded directly from the algorithms |
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| 5 | * and coefficients given in "Software Manual for the Elementary |
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| 6 | * Functions" by William J. Cody, Jr. and William Waite, Prentice |
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| 7 | * Hall, 1980. |
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| 8 | ******************************************************************/ |
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| 9 | /****************************************************************** |
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| 10 | * Arctangent |
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| 11 | * |
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| 12 | * Input: |
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| 13 | * x - floating point value |
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| 14 | * |
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| 15 | * Output: |
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| 16 | * arctangent of x |
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| 17 | * |
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| 18 | * Description: |
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| 19 | * This routine calculates arctangents. |
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| 20 | * |
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| 21 | *****************************************************************/ |
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| 22 | |
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| 23 | #include <float.h> |
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| 24 | #include "fdlibm.h" |
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| 25 | #include "zmath.h" |
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| 26 | |
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| 27 | static const float ROOT3 = 1.732050807; |
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| 28 | static const float a[] = { 0.0, 0.523598775, 1.570796326, |
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| 29 | 1.047197551 }; |
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| 30 | static const float q[] = { 0.1412500740e+1 }; |
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| 31 | static const float p[] = { -0.4708325141, -0.5090958253e-1 }; |
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| 32 | |
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| 33 | float |
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| 34 | atangentf (float x, |
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| 35 | float v, |
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| 36 | float u, |
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| 37 | int arctan2) |
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| 38 | { |
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| 39 | float f, g, R, P, Q, A, res; |
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| 40 | int N; |
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| 41 | int branch = 0; |
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| 42 | int expv, expu; |
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| 43 | |
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| 44 | /* Preparation for calculating arctan2. */ |
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| 45 | if (arctan2) |
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| 46 | { |
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| 47 | if (u == 0.0) |
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| 48 | if (v == 0.0) |
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| 49 | { |
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| 50 | errno = ERANGE; |
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| 51 | return (z_notanum_f.f); |
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| 52 | } |
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| 53 | else |
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| 54 | { |
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| 55 | branch = 1; |
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| 56 | res = __PI_OVER_TWO; |
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| 57 | } |
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| 58 | |
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| 59 | if (!branch) |
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| 60 | { |
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| 61 | int e; |
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| 62 | /* Get the exponent values of the inputs. */ |
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| 63 | g = frexpf (v, &expv); |
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| 64 | g = frexpf (u, &expu); |
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| 65 | |
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| 66 | /* See if a divide will overflow. */ |
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| 67 | e = expv - expu; |
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| 68 | if (e > FLT_MAX_EXP) |
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| 69 | { |
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| 70 | branch = 1; |
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| 71 | res = __PI_OVER_TWO; |
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| 72 | } |
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| 73 | |
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| 74 | /* Also check for underflow. */ |
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| 75 | else if (e < FLT_MIN_EXP) |
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| 76 | { |
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| 77 | branch = 2; |
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| 78 | res = 0.0; |
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| 79 | } |
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| 80 | } |
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| 81 | } |
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| 82 | |
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| 83 | if (!branch) |
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| 84 | { |
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| 85 | if (arctan2) |
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| 86 | f = fabsf (v / u); |
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| 87 | else |
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| 88 | f = fabsf (x); |
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| 89 | |
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| 90 | if (f > 1.0) |
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| 91 | { |
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| 92 | f = 1.0 / f; |
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| 93 | N = 2; |
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| 94 | } |
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| 95 | else |
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| 96 | N = 0; |
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| 97 | |
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| 98 | if (f > (2.0 - ROOT3)) |
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| 99 | { |
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| 100 | A = ROOT3 - 1.0; |
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| 101 | f = (((A * f - 0.5) - 0.5) + f) / (ROOT3 + f); |
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| 102 | N++; |
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| 103 | } |
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| 104 | |
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| 105 | /* Check for values that are too small. */ |
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| 106 | if (-z_rooteps_f < f && f < z_rooteps_f) |
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| 107 | res = f; |
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| 108 | |
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| 109 | /* Calculate the Taylor series. */ |
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| 110 | else |
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| 111 | { |
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| 112 | g = f * f; |
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| 113 | P = (p[1] * g + p[0]) * g; |
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| 114 | Q = g + q[0]; |
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| 115 | R = P / Q; |
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| 116 | |
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| 117 | res = f + f * R; |
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| 118 | } |
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| 119 | |
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| 120 | if (N > 1) |
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| 121 | res = -res; |
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| 122 | |
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| 123 | res += a[N]; |
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| 124 | } |
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| 125 | |
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| 126 | if (arctan2) |
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| 127 | { |
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| 128 | if (u < 0.0) |
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| 129 | res = __PI - res; |
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| 130 | if (v < 0.0) |
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| 131 | res = -res; |
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| 132 | } |
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| 133 | else if (x < 0.0) |
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| 134 | { |
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| 135 | res = -res; |
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| 136 | } |
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| 137 | |
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| 138 | return (res); |
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| 139 | } |
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