不韋 呂 / Mbed 2 deprecated SDR_AM_Rx_CIC

AM中波放送用SDR．CICフィルタのみを使用．CQ出版社「トランジスタ技術」誌，2021年4月号に掲載

Dependencies:   mbed

SDR_Library/FastATan.hpp@1:30d9fb51dec1, 2019-09-23 (annotated)

Committer:
MikamiUitOpen
Date:
Mon Sep 23 07:32:10 2019 +0000
Revision:
1:30d9fb51dec1
Child:
2:4bec6b2be809
2

Who changed what in which revision?

UserRevisionLine numberNew contents of line
MikamiUitOpen 1:30d9fb51dec1 1 //--------------------------------------------------------------
MikamiUitOpen 1:30d9fb51dec1 2 // 高速低精度 arctan 計算
MikamiUitOpen 1:30d9fb51dec1 3 // 係数はミニマックス近似で求めたもの
MikamiUitOpen 1:30d9fb51dec1 4 // ただし，誤差は絶対誤差で評価した
MikamiUitOpen 1:30d9fb51dec1 5 //
MikamiUitOpen 1:30d9fb51dec1 6 // 2019/09/18, Copyright (c) 2019 MIKAMI, Naoki
MikamiUitOpen 1:30d9fb51dec1 7 //--------------------------------------------------------------
MikamiUitOpen 1:30d9fb51dec1 8
MikamiUitOpen 1:30d9fb51dec1 9 #include "mbed.h"
MikamiUitOpen 1:30d9fb51dec1 10
MikamiUitOpen 1:30d9fb51dec1 11 #ifndef FAST_ARCTAN_LOW_PRECISION_HPP
MikamiUitOpen 1:30d9fb51dec1 12 #define FAST_ARCTAN_LOW_PRECISION_HPP
MikamiUitOpen 1:30d9fb51dec1 13
MikamiUitOpen 1:30d9fb51dec1 14 namespace Mikami
MikamiUitOpen 1:30d9fb51dec1 15 {
MikamiUitOpen 1:30d9fb51dec1 16 inline float ATanPoly(float x);
MikamiUitOpen 1:30d9fb51dec1 17
MikamiUitOpen 1:30d9fb51dec1 18 // 引数の与え方は，atan2() と同じ
MikamiUitOpen 1:30d9fb51dec1 19 float FastATan(float y, float x)
MikamiUitOpen 1:30d9fb51dec1 20 {
MikamiUitOpen 1:30d9fb51dec1 21 static const float PI = 3.1415926536f; // π
MikamiUitOpen 1:30d9fb51dec1 22 static const float PI_4 = PI/4.0f; // π/4
MikamiUitOpen 1:30d9fb51dec1 23 static const float PI3_4 = 3.0f*PI/4.0f; // 3π/4
MikamiUitOpen 1:30d9fb51dec1 24 static const float PI_2 = PI/2.0f; // π/2
MikamiUitOpen 1:30d9fb51dec1 25
MikamiUitOpen 1:30d9fb51dec1 26 if ( (x == 0.0f) && (y == 0.0f) ) return 0.0f;
MikamiUitOpen 1:30d9fb51dec1 27 if (y == 0.0f)
MikamiUitOpen 1:30d9fb51dec1 28 {
MikamiUitOpen 1:30d9fb51dec1 29 if (x > 0.0f) return 0.0f; // 0
MikamiUitOpen 1:30d9fb51dec1 30 else return PI; // π
MikamiUitOpen 1:30d9fb51dec1 31 }
MikamiUitOpen 1:30d9fb51dec1 32 float abs_x = fabsf(x);
MikamiUitOpen 1:30d9fb51dec1 33 float abs_y = fabsf(y);
MikamiUitOpen 1:30d9fb51dec1 34
MikamiUitOpen 1:30d9fb51dec1 35 if (abs_x == abs_y)
MikamiUitOpen 1:30d9fb51dec1 36 {
MikamiUitOpen 1:30d9fb51dec1 37 if (x > 0.0f)
MikamiUitOpen 1:30d9fb51dec1 38 {
MikamiUitOpen 1:30d9fb51dec1 39 if (y > 0.0f) return PI_4; // π/4
MikamiUitOpen 1:30d9fb51dec1 40 else return -PI_4; // -π/4
MikamiUitOpen 1:30d9fb51dec1 41 }
MikamiUitOpen 1:30d9fb51dec1 42 else
MikamiUitOpen 1:30d9fb51dec1 43 {
MikamiUitOpen 1:30d9fb51dec1 44 if (y > 0.0f) return PI3_4; // 3π/4
MikamiUitOpen 1:30d9fb51dec1 45 else return -PI3_4; // -3π/4
MikamiUitOpen 1:30d9fb51dec1 46 }
MikamiUitOpen 1:30d9fb51dec1 47 }
MikamiUitOpen 1:30d9fb51dec1 48
MikamiUitOpen 1:30d9fb51dec1 49 if (abs_x > abs_y) // |θ|< π/4，3π/4<|θ|<π
MikamiUitOpen 1:30d9fb51dec1 50 {
MikamiUitOpen 1:30d9fb51dec1 51 float u = ATanPoly(y/x);
MikamiUitOpen 1:30d9fb51dec1 52 if (x > 0.0f) return u;
MikamiUitOpen 1:30d9fb51dec1 53 if (y > 0.0f) return u + PI;
MikamiUitOpen 1:30d9fb51dec1 54 else return u - PI;
MikamiUitOpen 1:30d9fb51dec1 55 }
MikamiUitOpen 1:30d9fb51dec1 56 else // π/4 <|θ|<3π/4
MikamiUitOpen 1:30d9fb51dec1 57 {
MikamiUitOpen 1:30d9fb51dec1 58 float u = ATanPoly(x/y);
MikamiUitOpen 1:30d9fb51dec1 59 if (y > 0.0f) return -u + PI_2;
MikamiUitOpen 1:30d9fb51dec1 60 else return -u - PI_2;
MikamiUitOpen 1:30d9fb51dec1 61 }
MikamiUitOpen 1:30d9fb51dec1 62 }
MikamiUitOpen 1:30d9fb51dec1 63
MikamiUitOpen 1:30d9fb51dec1 64 inline float ATanPoly(float x)
MikamiUitOpen 1:30d9fb51dec1 65 {
MikamiUitOpen 1:30d9fb51dec1 66 static const float A1 = 0.9992138f; // a1
MikamiUitOpen 1:30d9fb51dec1 67 static const float A3 = -0.3211750f; // a3
MikamiUitOpen 1:30d9fb51dec1 68 static const float A5 = 0.1462645f; // a5
MikamiUitOpen 1:30d9fb51dec1 69 static const float A7 = -0.03898651f; // a7
MikamiUitOpen 1:30d9fb51dec1 70
MikamiUitOpen 1:30d9fb51dec1 71 float x2 = x*x;
MikamiUitOpen 1:30d9fb51dec1 72 float atanx = (((A7*x2 + A5)*x2 + A3)*x2 + A1)*x;
MikamiUitOpen 1:30d9fb51dec1 73
MikamiUitOpen 1:30d9fb51dec1 74 return atanx;
MikamiUitOpen 1:30d9fb51dec1 75 }
MikamiUitOpen 1:30d9fb51dec1 76 }
MikamiUitOpen 1:30d9fb51dec1 77 #endif // FAST_ARCTAN_LOW_PRECISION_HPP