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/******************************************************************************
** File Name: sin_cos.h *
** Author: shan.he *
** DATE: 2010-11-22 *
** Copyright: 2010 Spreadtrum, Incoporated. All Rights Reserved. *
** Description: *
** Note: *
*****************************************************************************/
/******************************************************************************
** Edit History *
**---------------------------------------------------------------------------*
** DATE NAME DESCRIPTION *
*****************************************************************************/
/**---------------------------------------------------------------------------*
** Dependencies *
**---------------------------------------------------------------------------*/
#include "sin_cos.h"
/**---------------------------------------------------------------------------*
** Macros *
**---------------------------------------------------------------------------*/
//typedef long long __int64
#define SINCOS_BIT_31 (1 << 31)
#define SINCOS_BIT_30 (1 << 30)
//#define SMULL(x, y) ((__int64)(x) * (__int64)(y))
#define SMULL(x, y) ((int64_t)(x) * (int64_t)(y))
/**---------------------------------------------------------------------------*
** static variable *
**---------------------------------------------------------------------------*/
static const uint32_t cossin_tbl[64] =
{
0x3ffec42d, 0x00c90e90, 0x3ff4e5e0, 0x025b0caf,
0x3fe12acb, 0x03ecadcf, 0x3fc395f9, 0x057db403,
0x3f9c2bfb, 0x070de172, 0x3f6af2e3, 0x089cf867,
0x3f2ff24a, 0x0a2abb59, 0x3eeb3347, 0x0bb6ecef,
0x3e9cc076, 0x0d415013, 0x3e44a5ef, 0x0ec9a7f3,
0x3de2f148, 0x104fb80e, 0x3d77b192, 0x11d3443f,
0x3d02f757, 0x135410c3, 0x3c84d496, 0x14d1e242,
0x3bfd5cc4, 0x164c7ddd, 0x3b6ca4c4, 0x17c3a931,
0x3ad2c2e8, 0x19372a64, 0x3a2fcee8, 0x1aa6c82b,
0x3983e1e8, 0x1c1249d8, 0x38cf1669, 0x1d79775c,
0x3811884d, 0x1edc1953, 0x374b54ce, 0x2039f90f,
0x367c9a7e, 0x2192e09b, 0x35a5793c, 0x22e69ac8,
0x34c61236, 0x2434f332, 0x33de87de, 0x257db64c,
0x32eefdea, 0x26c0b162, 0x31f79948, 0x27fdb2a7,
0x30f8801f, 0x29348937, 0x2ff1d9c7, 0x2a650525,
0x2ee3cebe, 0x2b8ef77d, 0x2dce88aa, 0x2cb2324c
};
/**---------------------------------------------------------------------------*
** static Functions *
**---------------------------------------------------------------------------*/
// s(x) = sin(2*PI*x*2^(-32)) =s(a) * cos(PI*(x-a)*2^(-31)) + c(a) * sin(PI*(x-a)*2^(-31))
// b = x - a, A = PI*a*2^(-31), B = PI*(x-a)*2^(-32)
// PI / 128 <= A < PI/4, 0 <= B < PI / 128
// sin(B) = B - B ^ 3 / 6; cos(B)=1 - B ^ 2 / 2;
// s(x) = sin(A) * cos(B) + cos(A) * sin(B)
// s(x) = sin(A) - sin(A) * B^2 / 2 + cos(A) * B - cos(A) * B * B^2 / 6
// s(x) = S1 - S2 + S3 + S4;
// S1 = sin(A), S2 = sin(A) * B^2 / 2, S3 = cos(A) * B, S4 = - cos(A) * B * B^2 / 6
// T1 = B^2;
/*lint --e{647}*/
static int32_t sin_core(int32_t arc_q33, int32_t sign)
{
int32_t a, b, B;
int32_t sin_a, cos_a;
int32_t S1, S2, S3, S4, T1;
int32_t R = 0;
int32_t C1 = 0x6487ed51; //round(2 * PI * 2 ^ 28)
int32_t C2 = -715827882; //0xd5555556; //round(-2^32/6)
a = arc_q33 >> 25;
cos_a = cossin_tbl[2 * a];
sin_a = cossin_tbl[2 * a + 1];
cos_a ^= (sign >> 31);
sin_a ^= (sign >> 31);
a = a << 25;
b = arc_q33 - a;
b -= (1 << 24);
B = SMULL((b << 3), C1) >> 32; //B at Q32
T1 = SMULL(B, B) >> 32; //B^2 at Q32
S1 = sin_a;
S2 = SMULL(sin_a, T1 >> 1) >> 32; //S2 at Q30
S3 = SMULL(cos_a, B) >> 32; //S3 at Q30
S4 = SMULL(T1, C2) >> 32; //-B^2 / 6 at Q32
S4 = SMULL(S3, S4) >> 32; //S4 at Q30
R = S1 - S2 + S3 + S4;
return R;
}
// c(x) = cos(2*PI*x*2^(-32)) = c(a) * cos(PI*(x-a)*2^(-31)) + s(a) * sin(PI*(x-a)*2^(-31))
// b = x - a, A = PI*a*2^(-31), B = PI*(x-a)*2^(-32)
// PI / 128 <= A < PI/4, 0 <= B < PI / 128
// sin(B) = B - B ^ 3 / 6; cos(B)=1 - B ^ 2 / 2;
// s(x) = cos(A) * cos(B) - sin(A) * sin(B)
// s(x) = cos(A) - cos(A) * B^2 / 2 - sin(A) * B + sin(A) * B * B^2 / 6;
// s(x) = S1 - S2 - S3 + S4;
// S1 = cos(A), S2 = cos(A) * B^2 / 2, S3 = sin(A) * B, S4 = sin(A) * B * B^2 / 6
// T1 = B^2;
/*lint --e{647}*/
static int32_t cos_core(int32_t arc_q33, int32_t sign)
{
int32_t a, b, B;
int32_t sin_a, cos_a;
int32_t S1, S2, S3, S4, T1;
int32_t R = 0;
int32_t C1 = 0x6487ed51; //round(2 * PI * 2 ^ 28)
int32_t C2 = 0x2aaaaaab; //round(2^32/6)
a = arc_q33 >> 25;
cos_a = cossin_tbl[a * 2];
sin_a = cossin_tbl[a * 2 + 1];
cos_a ^= (sign >> 31); //correct the sign
sin_a ^= (sign >> 31); //correct the sign
a = a << 25;
b = arc_q33 - a;
b -= (1 << 24);
B = SMULL((b << 3), C1) >> 32; //B at Q32
T1 = SMULL(B, B) >> 32; //B^2 at Q32
S1 = cos_a;
S2 = SMULL(cos_a, T1 >> 1) >> 32; //S2 at Q30
S3 = SMULL(sin_a, B) >> 32; //S3 at Q30
S4 = SMULL(T1, C2) >> 32; //B^2 / 6 at Q32
S4 = SMULL(S3, S4) >> 32; //S4 at Q30
R = S1 - S2 - S3 + S4;
return R;
}
/**---------------------------------------------------------------------------*
** Public Functions *
**---------------------------------------------------------------------------*/
/****************************************************************************/
/* Purpose: get the sin value of an arc at Q32 */
/* Author: */
/* Input: arc at Q32 */
/* Output: none */
/* Return: sin value at Q30 */
/* Note: arc at Q32 = arc * (2 ^ 32) */
/* value at Q30 = value * (2 ^ 30) */
/****************************************************************************/
/*lint --e{648}*/
int32_t dcam_sin_32(int32_t n)
{
int32_t s = n & SINCOS_BIT_31; //if s equal to 1, the sin value is negative
n = n << 1; //angle in revolutions at Q33, the BIT_31 only indicates the sign
if (0 == n) // == pi, 0
{
return 0;
}
if (SINCOS_BIT_31 == (n & SINCOS_BIT_31)) // >= pi/2
{
n &= ~SINCOS_BIT_31; //-= pi/2
if (n < SINCOS_BIT_30) // < pi/4
{
return cos_core(n, s);
}
else if (n == SINCOS_BIT_30) // == pi/4
{
n -= 1;
}
else if (n > SINCOS_BIT_30) // > pi/4
{
n = SINCOS_BIT_31 - n; // pi/2 - n
}
return sin_core(n, s);
}
else
{
if (n < SINCOS_BIT_30) // < pi/4
{
return sin_core(n, s);
}
if (n == SINCOS_BIT_30) // == pi/4
{
n -= 1;
}
else if (n > SINCOS_BIT_30) // > pi/4
{
n = SINCOS_BIT_31 - n; // pi/2 - n
}
return cos_core(n, s);
}
}
/****************************************************************************/
/* Purpose: get the cos value of an arc at Q32 */
/* Author: */
/* Input: arc at Q32 */
/* Output: none */
/* Return: cos value at Q30 */
/* Note: arc at Q32 = arc * (2 ^ 32) */
/* value at Q30 = value * (2 ^ 30) */
/****************************************************************************/
/*lint --e{648}*/
int32_t dcam_cos_32(int32_t n)
{
int32_t s = n & SINCOS_BIT_31; //if s equal to 1, the sin value is negative
n = n << 1; //angle in revolutions at Q33, the BIT_31 only indicates the sign
if (n == SINCOS_BIT_31)
{
return 0;
}
if (SINCOS_BIT_31 == (n & SINCOS_BIT_31)) // >= pi/2
{
n &= ~SINCOS_BIT_31; //-= pi/2
if (n < SINCOS_BIT_30) // < pi/4
{
return -sin_core(n, s);
}
else if (n == SINCOS_BIT_30) // == pi/4
{
n -= 1;
}
else if (n > SINCOS_BIT_30) // > pi/4
{
n = SINCOS_BIT_31 - n; // pi/2 - n
}
return -cos_core(n, s);
}
else
{
if (n < SINCOS_BIT_30) // < pi/4
{
return cos_core(n, s);
}
if (n == SINCOS_BIT_30) // == pi/4
{
n -= 1;
}
else if (n > SINCOS_BIT_30) // > pi/4
{
n = SINCOS_BIT_31 - n; // pi/2 - n
}
return sin_core(n, s);
}
}
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