cephes.c - ogl_beamforming - Ultrasound Beamforming Implemented with OpenGL

cephes.c (3004B)
      1 /*
      2 Cephes Math Library Release 2.8:  June, 2000
      3 Copyright 1984, 1987, 2000 by Stephen L. Moshier
      4 */
      5 
      6 /* NOTE(rnp): modified so that the library can be included from a single translation unit
      7  * and so that it doesn't use pre-ANSI C declarations */
      8 
      9 function f64
     10 cephes_chbevl(f64 x, f64 *coefficients, i32 n)
     11 {
     12 	f64 *p = coefficients;
     13 	f64 b0 = *p++, b1 = 0.0, b2;
     14 
     15 	for (i32 i = n - 1; i > 0; i--) {
     16 		b2 = b1;
     17 		b1 = b0;
     18 		b0 = x * b1 - b2 + *p++;
     19 	}
     20 
     21 	return 0.5 * (b0 - b2);
     22 }
     23 
     24 function f64
     25 cephes_i0(f64 x)
     26 {
     27 	/* Chebyshev coefficients for exp(-x) I0(x)
     28 	 * in the interval [0,8].
     29 	 *
     30 	 * lim(x->0){ exp(-x) I0(x) } = 1.
     31 	 */
     32 	read_only local_persist f64 A[] = {
     33 		-4.41534164647933937950E-18,
     34 		 3.33079451882223809783E-17,
     35 		-2.43127984654795469359E-16,
     36 		 1.71539128555513303061E-15,
     37 		-1.16853328779934516808E-14,
     38 		 7.67618549860493561688E-14,
     39 		-4.85644678311192946090E-13,
     40 		 2.95505266312963983461E-12,
     41 		-1.72682629144155570723E-11,
     42 		 9.67580903537323691224E-11,
     43 		-5.18979560163526290666E-10,
     44 		 2.65982372468238665035E-9,
     45 		-1.30002500998624804212E-8,
     46 		 6.04699502254191894932E-8,
     47 		-2.67079385394061173391E-7,
     48 		 1.11738753912010371815E-6,
     49 		-4.41673835845875056359E-6,
     50 		 1.64484480707288970893E-5,
     51 		-5.75419501008210370398E-5,
     52 		 1.88502885095841655729E-4,
     53 		-5.76375574538582365885E-4,
     54 		 1.63947561694133579842E-3,
     55 		-4.32430999505057594430E-3,
     56 		 1.05464603945949983183E-2,
     57 		-2.37374148058994688156E-2,
     58 		 4.93052842396707084878E-2,
     59 		-9.49010970480476444210E-2,
     60 		 1.71620901522208775349E-1,
     61 		-3.04682672343198398683E-1,
     62 		 6.76795274409476084995E-1
     63 	};
     64 
     65 	/* Chebyshev coefficients for exp(-x) sqrt(x) I0(x)
     66 	 * in the inverted interval [8,infinity].
     67 	 *
     68 	 * lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
     69 	 */
     70 	read_only local_persist f64 B[] = {
     71 		-7.23318048787475395456E-18,
     72 		-4.83050448594418207126E-18,
     73 		 4.46562142029675999901E-17,
     74 		 3.46122286769746109310E-17,
     75 		-2.82762398051658348494E-16,
     76 		-3.42548561967721913462E-16,
     77 		 1.77256013305652638360E-15,
     78 		 3.81168066935262242075E-15,
     79 		-9.55484669882830764870E-15,
     80 		-4.15056934728722208663E-14,
     81 		 1.54008621752140982691E-14,
     82 		 3.85277838274214270114E-13,
     83 		 7.18012445138366623367E-13,
     84 		-1.79417853150680611778E-12,
     85 		-1.32158118404477131188E-11,
     86 		-3.14991652796324136454E-11,
     87 		 1.18891471078464383424E-11,
     88 		 4.94060238822496958910E-10,
     89 		 3.39623202570838634515E-9,
     90 		 2.26666899049817806459E-8,
     91 		 2.04891858946906374183E-7,
     92 		 2.89137052083475648297E-6,
     93 		 6.88975834691682398426E-5,
     94 		 3.36911647825569408990E-3,
     95 		 8.04490411014108831608E-1
     96 	};
     97 
     98 	f64 result;
     99 	if (x < 0) x = -x;
    100 	if (x <= 8.0) result = exp_f64(x) * cephes_chbevl(x / 2.0 - 2.0,  A, 30);
    101 	else          result = exp_f64(x) * cephes_chbevl(32.0 / x - 2.0, B, 25) / sqrt_f64(x);
    102 	return result;
    103 }
    104 
    105 #if 0
    106 function
    107 f64 cephes_i0e(f64 x)
    108 {
    109 	f64 result;
    110 	if (x < 0) x = -x;
    111 	if (x <= 8.0) result = cephes_chbevl(x / 2.0 - 2.0,  A, 30);
    112 	else          result = cephes_chbevl(32.0 / x - 2.0, B, 25) / sqrt_f64(x);
    113 	return result;
    114 }
    115 #endif