math: p_atan: Implement atan Function

README.md

@@ -210,7 +210,8 @@ FUNCTION     | NOTES
 [p_acos()](src/math/p_acos.c)         | arc cosine  
 [p_acosh()](src/math/p_acosh.c)       | arc hyperbolic cosine  
 [p_asin()](src/math/p_asin.c)         | arc sine  
-[p_asinh()](src/math/p_asinh.c)       | arc hyperbolic sine  
+[p_asinh()](src/math/p_asinh.c)       | arc hyperbolic sine 
+[p_atan()](src/math/p_atan.c)         | arc tan  
 [p_cbrt()](src/math/p_cbrt.c)         | cubic root                    
 [p_cos()](src/math/p_cos.c)           | cosine  
 [p_cosh()](src/math/p_cosh.c)         | hyperbolic cosine  

src/math/p_atan.c

@@ -1,26 +1,6 @@
-#include <pal.h>
-
 /*
- * -1 <= x <= 1
- * atan x = a1 * x + a3 * x^3 + ... + a9 * x^9 + e(x)
- * |e(x)| <= 10^-5
- */
-static inline float _p_atan(const float x)
-{
-    const float a1 =  0.9998660f;
-    const float a3 = -0.3302995f;
-    const float a5 =  0.1801410f;
-    const float a7 = -0.0851330f;
-    const float a9 =  0.0208351f;
-    float x2 = x * x;
-    return x * (a1 + x2 * (a3 + x2 * (a5 + x2 * (a7 + x2 * a9))));
-}
-
-/**
  *
- * Calculates inverse tangent (arc tangent) of the input value. The function
- * returns a value between -pi/2 to pi/2 but does not check for illegal input
- * values.
+ * Calculates inverse tangent (arc tangent). 
  *
  * @param a     Pointer to input vector
  *
@@ -31,11 +11,34 @@ static inline float _p_atan(const float x)
  * @return      None
  *
  */
+
 void p_atan_f32(const float *a, float *c, int n)
 {
+    int i;int sign; float ff; float x;
+    float r,r2,r4,r6,r8;
+    float pi4 = 0.78539816339f;                      // constant=pi/4
+
+    for ( i = 0; i < n; i++)
+      {
+       const float *pa = (a+i);
+             float *pc = (c+i);
+       ff = *pa;
+       if (ff >= 0) sign = 1.0; else sign = -1.0;     // store sign of input variable
+       if (ff < 0) x = ff * (-1.0f); else x = ff;     // this is equivalent of x=abs(a)
+
+       r  = (x-1)/(x+1);
+       r2 = r * r ; r4 = r2*r2 ; r6 = r4*r2 ; r8 = r4*r4 ;
+
+       float z = pi4
+        +    (+0.9999993329f*r
+        +r2 *(-0.3332985605f*r
+        +r  *(+0.1994653599f*r2
+        +    (-0.1390853351f*r4
+        +    (+0.0964200441f*r6
+        +    (-0.0559098861f*r8
+        +r4 *(+0.0218612288f*r6
+        +    (-0.0040540580f*r8))))))));
 
-    int i;
-    for (i = 0; i < n; i++) {
-        c[i] = _p_atan(a[i]);
-    }
+       *pc = sign*z;
+      }
 }

tests/math/gold/p_atan_f32.dat

@@ -1,100 +1,100 @@
--0.107358,-0.049577,0.000000,-0.106948
-0.051781,-0.265425,0.000000,0.051735
-0.941475,-0.975603,0.000000,0.755263
--0.770979,-0.360797,0.000000,-0.656793
-0.738044,-0.380252,0.000000,0.635805
-0.608158,-0.123753,0.000000,0.546396
--0.066886,0.380368,0.000000,-0.066787
-0.465099,0.210297,0.000000,0.435339
-0.968926,0.910675,0.000000,0.769617
--0.207846,-0.573708,0.000000,-0.204928
--0.971535,-0.123731,0.000000,-0.770961
--0.782373,-0.992383,0.000000,-0.663900
-0.682603,0.521601,0.000000,0.598954
--0.536897,0.615399,0.000000,-0.492728
--0.076406,-0.549893,0.000000,-0.076258
--0.683411,0.816236,0.000000,-0.599505
-0.400530,0.368370,0.000000,0.380963
--0.449189,0.342005,0.000000,-0.422179
-0.392768,-0.220168,0.000000,0.374256
-0.981208,0.130812,0.000000,0.775913
-0.399579,0.589365,0.000000,0.380143
--0.992941,-0.667307,0.000000,-0.781856
--0.030266,0.472158,0.000000,-0.030257
-0.542991,-0.061340,0.000000,0.497446
-0.382832,-0.664855,0.000000,0.365619
-0.364952,0.411298,0.000000,0.349932
-0.211414,0.582579,0.000000,0.208346
-0.418914,-0.105983,0.000000,0.396704
-0.104180,0.882017,0.000000,0.103806
--0.490584,-0.972226,0.000000,-0.456086
--0.667876,-0.173995,0.000000,-0.588839
-0.844010,0.732653,0.000000,0.701006
--0.805625,-0.605179,0.000000,-0.678161
-0.074658,0.587143,0.000000,0.074520
-0.174653,0.055866,0.000000,0.172909
--0.282045,-0.425768,0.000000,-0.274904
--0.354768,-0.274987,0.000000,-0.340916
--0.093074,0.614965,0.000000,-0.092807
--0.802829,-0.550084,0.000000,-0.676464
--0.446374,0.580004,0.000000,-0.419834
--0.214939,0.918578,0.000000,-0.211718
--0.008699,0.996475,0.000000,-0.008699
-0.501157,-0.589785,0.000000,0.464573
--0.109508,-0.394662,0.000000,-0.109073
--0.707768,0.399907,0.000000,-0.615920
--0.366888,-0.375644,0.000000,-0.351640
--0.774088,-0.522878,0.000000,-0.658740
--0.642991,-0.579713,0.000000,-0.571432
--0.128057,0.431668,0.000000,-0.127364
--0.992570,-0.953404,0.000000,-0.781669
--0.512466,-0.274615,0.000000,-0.473571
--0.379171,0.132765,0.000000,-0.362422
-0.450398,0.527754,0.000000,0.423185
--0.252269,0.647569,0.000000,-0.247113
-0.977671,0.301357,0.000000,0.774108
-0.227573,-0.237268,0.000000,0.223762
-0.219935,-0.781126,0.000000,0.216488
--0.240793,-0.278908,0.000000,-0.236295
--0.370910,0.649699,0.000000,-0.355180
-0.326430,-0.078678,0.000000,0.315525
-0.049606,0.959542,0.000000,0.049565
-0.545678,0.275518,0.000000,0.499519
--0.563335,0.902687,0.000000,-0.513024
-0.695806,0.308608,0.000000,0.607906
-0.334355,0.703236,0.000000,0.322670
-0.355204,0.821889,0.000000,0.341303
--0.571379,0.976033,0.000000,-0.519109
--0.045346,0.879019,0.000000,-0.045315
-0.503788,0.702385,0.000000,0.466673
-0.526589,0.481458,0.000000,0.484692
-0.003741,-0.245838,0.000000,0.003741
--0.755809,-0.776324,0.000000,-0.647209
--0.026964,0.003398,0.000000,-0.026957
--0.055232,0.602126,0.000000,-0.055176
--0.346903,-0.728802,0.000000,-0.333913
--0.476552,0.702704,0.000000,-0.444714
--0.769260,-0.930874,0.000000,-0.655714
--0.021778,-0.332595,0.000000,-0.021775
-0.971813,-0.325972,0.000000,0.771104
-0.976013,0.306168,0.000000,0.773260
--0.622736,0.331217,0.000000,-0.556970
-0.128056,-0.194115,0.000000,0.127363
-0.307250,-0.917290,0.000000,0.298095
--0.315096,-0.188962,0.000000,-0.305248
-0.785095,-0.788507,0.000000,0.665586
--0.707504,-0.211164,0.000000,-0.615744
--0.034345,-0.463313,0.000000,-0.034332
-0.012512,0.938691,0.000000,0.012511
-0.540085,0.957280,0.000000,0.495199
-0.540816,-0.806818,0.000000,0.495765
--0.771522,-0.935736,0.000000,-0.657134
-0.895886,-0.540781,0.000000,0.730538
--0.866610,-0.125892,0.000000,-0.714058
-0.126623,-0.894797,0.000000,0.125953
-0.548136,0.102636,0.000000,0.501411
-0.411370,0.925400,0.000000,0.390270
--0.566147,-0.460574,0.000000,-0.515156
--0.268715,0.741103,0.000000,-0.262514
--0.377863,0.416189,0.000000,-0.361278
--0.447859,-0.592769,0.000000,-0.421072
+4.963864,0.000000,0.000000,1.372001
+0.913008,0.000000,0.000000,0.739956
+2.429646,0.000000,0.000000,1.180345
+3.647594,0.000000,0.000000,1.303217
+5.567312,0.000000,0.000000,1.393072
+6.265069,0.000000,0.000000,1.412516
+0.715971,0.000000,0.000000,0.621365
+5.052592,0.000000,0.000000,1.375403
+5.577939,0.000000,0.000000,1.393403
+0.907919,0.000000,0.000000,0.737173
+0.379105,0.000000,0.000000,0.362365
+0.720684,0.000000,0.000000,0.624473
+0.674235,0.000000,0.000000,0.593224
+0.520856,0.000000,0.000000,0.480193
+0.345032,0.000000,0.000000,0.332242
+0.361974,0.000000,0.000000,0.347302
+0.361479,0.000000,0.000000,0.346864
+0.455790,0.000000,0.000000,0.427658
+0.582766,0.000000,0.000000,0.527651
+0.511593,0.000000,0.000000,0.472879
+0.022779,0.000000,0.000000,0.022775
+0.045248,0.000000,0.000000,0.045217
+0.093859,0.000000,0.000000,0.093585
+0.080974,0.000000,0.000000,0.080798
+0.092150,0.000000,0.000000,0.091890
+0.022109,0.000000,0.000000,0.022105
+0.000462,0.000000,0.000000,0.000462
+0.046636,0.000000,0.000000,0.046602
+0.040523,0.000000,0.000000,0.040501
+0.097185,0.000000,0.000000,0.096881
+0.009579,0.000000,0.000000,0.009579
+0.000739,0.000000,0.000000,0.000739
+0.006546,0.000000,0.000000,0.006546
+0.009225,0.000000,0.000000,0.009225
+0.008334,0.000000,0.000000,0.008334
+0.003858,0.000000,0.000000,0.003858
+0.000647,0.000000,0.000000,0.000647
+0.000657,0.000000,0.000000,0.000657
+0.002802,0.000000,0.000000,0.002802
+0.008586,0.000000,0.000000,0.008586
+0.000576,0.000000,0.000000,0.000576
+0.000907,0.000000,0.000000,0.000907
+0.000270,0.000000,0.000000,0.000270
+0.000811,0.000000,0.000000,0.000811
+0.000115,0.000000,0.000000,0.000115
+0.000302,0.000000,0.000000,0.000302
+0.000785,0.000000,0.000000,0.000785
+0.000594,0.000000,0.000000,0.000594
+0.000445,0.000000,0.000000,0.000445
+0.000903,0.000000,0.000000,0.000903
+-0.952188,0.000000,0.000000,-0.760912
+-1.959224,0.000000,0.000000,-1.098858
+-2.589151,0.000000,0.000000,-1.202219
+-2.562399,0.000000,0.000000,-1.198715
+-0.256550,0.000000,0.000000,-0.251134
+-1.581301,0.000000,0.000000,-1.006900
+-3.784508,0.000000,0.000000,-1.312465
+-4.273364,0.000000,0.000000,-1.340925
+-4.727937,0.000000,0.000000,-1.362360
+-2.341383,0.000000,0.000000,-1.167150
+-0.370549,0.000000,0.000000,-0.354863
+-0.337516,0.000000,0.000000,-0.325510
+-0.862123,0.000000,0.000000,-0.711490
+-0.413447,0.000000,0.000000,-0.392045
+-0.893094,0.000000,0.000000,-0.728987
+-0.030457,0.000000,0.000000,-0.030448
+-0.507305,0.000000,0.000000,-0.469475
+-0.713741,0.000000,0.000000,-0.619889
+-0.431114,0.000000,0.000000,-0.407038
+-0.170107,0.000000,0.000000,-0.168494
+-0.028679,0.000000,0.000000,-0.028671
+-0.056042,0.000000,0.000000,-0.055983
+-0.028366,0.000000,0.000000,-0.028358
+-0.047950,0.000000,0.000000,-0.047913
+-0.055205,0.000000,0.000000,-0.055149
+-0.023834,0.000000,0.000000,-0.023829
+-0.028604,0.000000,0.000000,-0.028596
+-0.016342,0.000000,0.000000,-0.016341
+-0.064428,0.000000,0.000000,-0.064339
+-0.081401,0.000000,0.000000,-0.081222
+-0.000246,0.000000,0.000000,-0.000246
+-0.002968,0.000000,0.000000,-0.002968
+-0.006977,0.000000,0.000000,-0.006977
+-0.009397,0.000000,0.000000,-0.009397
+-0.005367,0.000000,0.000000,-0.005367
+-0.003527,0.000000,0.000000,-0.003527
+-0.000699,0.000000,0.000000,-0.000699
+-0.006228,0.000000,0.000000,-0.006228
+-0.006891,0.000000,0.000000,-0.006891
+-0.004988,0.000000,0.000000,-0.004988
+-0.000611,0.000000,0.000000,-0.000611
+-0.000793,0.000000,0.000000,-0.000793
+-0.000857,0.000000,0.000000,-0.000857
+-0.000734,0.000000,0.000000,-0.000734
+-0.000240,0.000000,0.000000,-0.000240
+-0.000951,0.000000,0.000000,-0.000951
+-0.000543,0.000000,0.000000,-0.000543
+-0.000546,0.000000,0.000000,-0.000546
+-0.000044,0.000000,0.000000,-0.000044
+-0.000009,0.000000,0.000000,-0.000009