newlib/newlib/libm/machine/spu/headers/cos_sin.h - native_client/nacl-toolchain - Git at Google

 /* --------------------------------------------------------------  */
 /* (C)Copyright 2001,2008,                                         */
 /* International Business Machines Corporation,                    */
 /* Sony Computer Entertainment, Incorporated,                      */
 /* Toshiba Corporation,                                            */
 /*                                                                 */
 /* All Rights Reserved.                                            */
 /*                                                                 */
 /* Redistribution and use in source and binary forms, with or      */
 /* without modification, are permitted provided that the           */
 /* following conditions are met:                                   */
 /*                                                                 */
 /* - Redistributions of source code must retain the above copyright*/
 /*   notice, this list of conditions and the following disclaimer. */
 /*                                                                 */
 /* - Redistributions in binary form must reproduce the above       */
 /*   copyright notice, this list of conditions and the following   */
 /*   disclaimer in the documentation and/or other materials        */
 /*   provided with the distribution.                               */
 /*                                                                 */
 /* - Neither the name of IBM Corporation nor the names of its      */
 /*   contributors may be used to endorse or promote products       */
 /*   derived from this software without specific prior written     */
 /*   permission.                                                   */
 /*                                                                 */
 /* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND          */
 /* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,     */
 /* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF        */
 /* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE        */
 /* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR            */
 /* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,    */
 /* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT    */
 /* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;    */
 /* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)        */
 /* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN       */
 /* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR    */
 /* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,  */
 /* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.              */
 /* --------------------------------------------------------------  */
 /* PROLOG END TAG zYx                                              */
 #ifdef __SPU__
 #ifndef _COS_SIN_H_
 #define _COS_SIN_H_	1

 #define M_PI_OVER_4_HI_32 0x3fe921fb

 #define M_PI_OVER_4	0.78539816339744827900
 #define M_FOUR_OVER_PI 	1.27323954478442180616

 #define M_PI_OVER_2	1.57079632679489655800
 #define M_PI_OVER_2_HI 	1.57079632673412561417
 #define M_PI_OVER_2_LO 	0.0000000000607710050650619224932

 #define M_PI_OVER_2F_HI   1.570312500000000000
 #define M_PI_OVER_2F_LO	  0.000483826794896558

 /* The following coefficients correspond to the Taylor series
  * coefficients for cos and sin.
  */
 #define COS_14 -0.00000000001138218794258068723867
 #define COS_12  0.000000002087614008917893178252
 #define COS_10 -0.0000002755731724204127572108
 #define COS_08  0.00002480158729870839541888
 #define COS_06 -0.001388888888888735934799
 #define COS_04  0.04166666666666666534980
 #define COS_02 -0.5000000000000000000000
 #define COS_00  1.0

 #define SIN_15 -0.00000000000076471637318198164759
 #define SIN_13  0.00000000016059043836821614599
 #define SIN_11 -0.000000025052108385441718775
 #define SIN_09  0.0000027557319223985890653
 #define SIN_07 -0.0001984126984126984127
 #define SIN_05  0.008333333333333333333
 #define SIN_03 -0.16666666666666666666
 #define SIN_01  1.0


 /* Compute the following for each floating point element of x.
  * 	x  = fmod(x, PI/4);
  *  	ix = (int)x * PI/4;
  * This allows one to compute cos / sin over the limited range
  * and select the sign and correct result based upon the octant
  * of the original angle (as defined by the ix result).
  *
  * Expected Inputs Types:
  * 	x  = vec_float4
  *	ix = vec_int4
  */
 #define MOD_PI_OVER_FOUR_F(_x, _ix) {					\
     vec_float4 fx;							\
 									\
     _ix = spu_convts(spu_mul(_x, spu_splats((float)M_FOUR_OVER_PI)), 0); \
     _ix = spu_add(_ix, spu_add(spu_rlmaska((vec_int4)_x, -31), 1));	\
 									\
     fx = spu_convtf(spu_rlmaska(_ix, -1), 0);				\
     _x  = spu_nmsub(fx, spu_splats((float)M_PI_OVER_2F_HI), _x);	\
     _x  = spu_nmsub(fx, spu_splats((float)M_PI_OVER_2F_LO), _x);	\
   }

 /* Double precision MOD_PI_OVER_FOUR
  *
  * Expected Inputs Types:
  * 	x  = vec_double2
  *	ix = vec_int4
  */
 #define MOD_PI_OVER_FOUR(_x, _ix) {					\
     vec_float4 fx;							\
     vec_double2 dix;							\
 									\
     fx = spu_roundtf(spu_mul(_x, spu_splats(M_FOUR_OVER_PI)));	\
     _ix = spu_convts(fx, 0);						\
     _ix = spu_add(_ix, spu_add(spu_rlmaska((vec_int4)fx, -31), 1));	\
 									\
     dix = spu_extend(spu_convtf(spu_rlmaska(_ix, -1), 0));		\
     _x  = spu_nmsub(spu_splats(M_PI_OVER_2_HI), dix, _x);		\
     _x  = spu_nmsub(spu_splats(M_PI_OVER_2_LO), dix, _x);		\
   }


 /* Compute the cos(x) and sin(x) for the range reduced angle x.
  * In order to compute these trig functions to full single precision
  * accuracy, we solve the Taylor series.
  *
  *   c = cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! - x^10/10!
  *   s = sin(x) = x - x^3/4! + x^5/5! - x^7/7! + x^9/9! - x^11/11!
  *
  * Expected Inputs Types:
  * 	x = vec_float4
  *	c = vec_float4
  *	s = vec_float4
  */

 #define COMPUTE_COS_SIN_F(_x, _c, _s) {					\
     vec_float4 x2, x4, x6;						\
     vec_float4 cos_hi, cos_lo;						\
     vec_float4 sin_hi, sin_lo;						\
 									\
     x2 = spu_mul(_x, _x);						\
     x4 = spu_mul(x2, x2);						\
     x6 = spu_mul(x2, x4);						\
 									\
     cos_hi = spu_madd(spu_splats((float)COS_10), x2, spu_splats((float)COS_08)); \
     cos_lo = spu_madd(spu_splats((float)COS_04), x2, spu_splats((float)COS_02)); \
     cos_hi = spu_madd(cos_hi, x2, spu_splats((float)COS_06));		\
     cos_lo = spu_madd(cos_lo, x2, spu_splats((float)COS_00));		\
     _c     = spu_madd(cos_hi, x6, cos_lo);				\
 									\
     sin_hi = spu_madd(spu_splats((float)SIN_11), x2, spu_splats((float)SIN_09)); \
     sin_lo = spu_madd(spu_splats((float)SIN_05), x2, spu_splats((float)SIN_03)); \
     sin_hi = spu_madd(sin_hi, x2, spu_splats((float)SIN_07));		\
     sin_lo = spu_madd(sin_lo, x2, spu_splats((float)SIN_01));		\
     _s    = spu_madd(sin_hi, x6, sin_lo);				\
     _s     = spu_mul(_s, _x);						\
   }


 /* Compute the cos(x) and sin(x) for the range reduced angle x.
  * This version computes the cosine and sine to double precision
  * accuracy using the Taylor series:
  *
  *   c = cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! - x^10/10! + x^12/12! - x^14/14!
  *   s = sin(x) = x - x^3/4! + x^5/5! - x^7/7! + x^9/9! - x^11/11! + x^13/13! - x^15/15!
  *
  * Expected Inputs Types:
  * 	x = vec_double2
  *	c = vec_double2
  *	s = vec_double2
  */

 #define COMPUTE_COS_SIN(_x, _c, _s) {					\
     vec_double2 x2, x4, x8;						\
     vec_double2 cos_hi, cos_lo;						\
     vec_double2 sin_hi, sin_lo;						\
 									\
     x2 = spu_mul(_x, _x);						\
     x4 = spu_mul(x2, x2);						\
     x8 = spu_mul(x4, x4);						\
 									\
     cos_hi = spu_madd(spu_splats(COS_14), x2, spu_splats(COS_12));	\
     cos_lo = spu_madd(spu_splats(COS_06), x2, spu_splats(COS_04));	\
     cos_hi = spu_madd(cos_hi, x2, spu_splats(COS_10));			\
     cos_lo = spu_madd(cos_lo, x2, spu_splats(COS_02));			\
     cos_hi = spu_madd(cos_hi, x2, spu_splats(COS_08));			\
     cos_lo = spu_madd(cos_lo, x2, spu_splats(COS_00));			\
     _c     = spu_madd(cos_hi, x8, cos_lo);				\
 									\
     sin_hi = spu_madd(spu_splats(SIN_15), x2, spu_splats(SIN_13));	\
     sin_lo = spu_madd(spu_splats(SIN_07), x2, spu_splats(SIN_05));	\
     sin_hi = spu_madd(sin_hi, x2, spu_splats(SIN_11));			\
     sin_lo = spu_madd(sin_lo, x2, spu_splats(SIN_03));			\
     sin_hi = spu_madd(sin_hi, x2, spu_splats(SIN_09));			\
     sin_lo = spu_madd(sin_lo, x2, spu_splats(SIN_01));			\
     _s     = spu_madd(sin_hi, x8, sin_lo);				\
     _s     = spu_mul(_s, _x);						\
   }


 #endif /* _COS_SIN_H_ */
 #endif /* __SPU__ */
	/* -------------------------------------------------------------- */
	/* (C)Copyright 2001,2008, */
	/* International Business Machines Corporation, */
	/* Sony Computer Entertainment, Incorporated, */
	/* Toshiba Corporation, */
	/* */
	/* All Rights Reserved. */
	/* */
	/* Redistribution and use in source and binary forms, with or */
	/* without modification, are permitted provided that the */
	/* following conditions are met: */
	/* */
	/* - Redistributions of source code must retain the above copyright*/
	/* notice, this list of conditions and the following disclaimer. */
	/* */
	/* - Redistributions in binary form must reproduce the above */
	/* copyright notice, this list of conditions and the following */
	/* disclaimer in the documentation and/or other materials */
	/* provided with the distribution. */
	/* */
	/* - Neither the name of IBM Corporation nor the names of its */
	/* contributors may be used to endorse or promote products */
	/* derived from this software without specific prior written */
	/* permission. */
	/* */
	/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
	/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
	/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
	/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
	/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
	/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
	/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
	/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
	/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
	/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
	/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
	/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
	/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
	/* -------------------------------------------------------------- */
	/* PROLOG END TAG zYx */
	#ifdef __SPU__
	#ifndef _COS_SIN_H_
	#define _COS_SIN_H_ 1

	#define M_PI_OVER_4_HI_32 0x3fe921fb

	#define M_PI_OVER_4 0.78539816339744827900
	#define M_FOUR_OVER_PI 1.27323954478442180616

	#define M_PI_OVER_2 1.57079632679489655800
	#define M_PI_OVER_2_HI 1.57079632673412561417
	#define M_PI_OVER_2_LO 0.0000000000607710050650619224932

	#define M_PI_OVER_2F_HI 1.570312500000000000
	#define M_PI_OVER_2F_LO 0.000483826794896558

	/* The following coefficients correspond to the Taylor series
	* coefficients for cos and sin.
	*/
	#define COS_14 -0.00000000001138218794258068723867
	#define COS_12 0.000000002087614008917893178252
	#define COS_10 -0.0000002755731724204127572108
	#define COS_08 0.00002480158729870839541888
	#define COS_06 -0.001388888888888735934799
	#define COS_04 0.04166666666666666534980
	#define COS_02 -0.5000000000000000000000
	#define COS_00 1.0

	#define SIN_15 -0.00000000000076471637318198164759
	#define SIN_13 0.00000000016059043836821614599
	#define SIN_11 -0.000000025052108385441718775
	#define SIN_09 0.0000027557319223985890653
	#define SIN_07 -0.0001984126984126984127
	#define SIN_05 0.008333333333333333333
	#define SIN_03 -0.16666666666666666666
	#define SIN_01 1.0


	/* Compute the following for each floating point element of x.
	* x = fmod(x, PI/4);
	* ix = (int)x * PI/4;
	* This allows one to compute cos / sin over the limited range
	* and select the sign and correct result based upon the octant
	* of the original angle (as defined by the ix result).
	*
	* Expected Inputs Types:
	* x = vec_float4
	* ix = vec_int4
	*/
	#define MOD_PI_OVER_FOUR_F(_x, _ix) { \
	vec_float4 fx; \
	\
	_ix = spu_convts(spu_mul(_x, spu_splats((float)M_FOUR_OVER_PI)), 0); \
	_ix = spu_add(_ix, spu_add(spu_rlmaska((vec_int4)_x, -31), 1)); \
	\
	fx = spu_convtf(spu_rlmaska(_ix, -1), 0); \
	_x = spu_nmsub(fx, spu_splats((float)M_PI_OVER_2F_HI), _x); \
	_x = spu_nmsub(fx, spu_splats((float)M_PI_OVER_2F_LO), _x); \
	}

	/* Double precision MOD_PI_OVER_FOUR
	*
	* Expected Inputs Types:
	* x = vec_double2
	* ix = vec_int4
	*/
	#define MOD_PI_OVER_FOUR(_x, _ix) { \
	vec_float4 fx; \
	vec_double2 dix; \
	\
	fx = spu_roundtf(spu_mul(_x, spu_splats(M_FOUR_OVER_PI))); \
	_ix = spu_convts(fx, 0); \
	_ix = spu_add(_ix, spu_add(spu_rlmaska((vec_int4)fx, -31), 1)); \
	\
	dix = spu_extend(spu_convtf(spu_rlmaska(_ix, -1), 0)); \
	_x = spu_nmsub(spu_splats(M_PI_OVER_2_HI), dix, _x); \
	_x = spu_nmsub(spu_splats(M_PI_OVER_2_LO), dix, _x); \
	}


	/* Compute the cos(x) and sin(x) for the range reduced angle x.
	* In order to compute these trig functions to full single precision
	* accuracy, we solve the Taylor series.
	*
	* c = cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! - x^10/10!
	* s = sin(x) = x - x^3/4! + x^5/5! - x^7/7! + x^9/9! - x^11/11!
	*
	* Expected Inputs Types:
	* x = vec_float4
	* c = vec_float4
	* s = vec_float4
	*/

	#define COMPUTE_COS_SIN_F(_x, _c, _s) { \
	vec_float4 x2, x4, x6; \
	vec_float4 cos_hi, cos_lo; \
	vec_float4 sin_hi, sin_lo; \
	\
	x2 = spu_mul(_x, _x); \
	x4 = spu_mul(x2, x2); \
	x6 = spu_mul(x2, x4); \
	\
	cos_hi = spu_madd(spu_splats((float)COS_10), x2, spu_splats((float)COS_08)); \
	cos_lo = spu_madd(spu_splats((float)COS_04), x2, spu_splats((float)COS_02)); \
	cos_hi = spu_madd(cos_hi, x2, spu_splats((float)COS_06)); \
	cos_lo = spu_madd(cos_lo, x2, spu_splats((float)COS_00)); \
	_c = spu_madd(cos_hi, x6, cos_lo); \
	\
	sin_hi = spu_madd(spu_splats((float)SIN_11), x2, spu_splats((float)SIN_09)); \
	sin_lo = spu_madd(spu_splats((float)SIN_05), x2, spu_splats((float)SIN_03)); \
	sin_hi = spu_madd(sin_hi, x2, spu_splats((float)SIN_07)); \
	sin_lo = spu_madd(sin_lo, x2, spu_splats((float)SIN_01)); \
	_s = spu_madd(sin_hi, x6, sin_lo); \
	_s = spu_mul(_s, _x); \
	}


	/* Compute the cos(x) and sin(x) for the range reduced angle x.
	* This version computes the cosine and sine to double precision
	* accuracy using the Taylor series:
	*
	* c = cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! - x^10/10! + x^12/12! - x^14/14!
	* s = sin(x) = x - x^3/4! + x^5/5! - x^7/7! + x^9/9! - x^11/11! + x^13/13! - x^15/15!
	*
	* Expected Inputs Types:
	* x = vec_double2
	* c = vec_double2
	* s = vec_double2
	*/

	#define COMPUTE_COS_SIN(_x, _c, _s) { \
	vec_double2 x2, x4, x8; \
	vec_double2 cos_hi, cos_lo; \
	vec_double2 sin_hi, sin_lo; \
	\
	x2 = spu_mul(_x, _x); \
	x4 = spu_mul(x2, x2); \
	x8 = spu_mul(x4, x4); \
	\
	cos_hi = spu_madd(spu_splats(COS_14), x2, spu_splats(COS_12)); \
	cos_lo = spu_madd(spu_splats(COS_06), x2, spu_splats(COS_04)); \
	cos_hi = spu_madd(cos_hi, x2, spu_splats(COS_10)); \
	cos_lo = spu_madd(cos_lo, x2, spu_splats(COS_02)); \
	cos_hi = spu_madd(cos_hi, x2, spu_splats(COS_08)); \
	cos_lo = spu_madd(cos_lo, x2, spu_splats(COS_00)); \
	_c = spu_madd(cos_hi, x8, cos_lo); \
	\
	sin_hi = spu_madd(spu_splats(SIN_15), x2, spu_splats(SIN_13)); \
	sin_lo = spu_madd(spu_splats(SIN_07), x2, spu_splats(SIN_05)); \
	sin_hi = spu_madd(sin_hi, x2, spu_splats(SIN_11)); \
	sin_lo = spu_madd(sin_lo, x2, spu_splats(SIN_03)); \
	sin_hi = spu_madd(sin_hi, x2, spu_splats(SIN_09)); \
	sin_lo = spu_madd(sin_lo, x2, spu_splats(SIN_01)); \
	_s = spu_madd(sin_hi, x8, sin_lo); \
	_s = spu_mul(_s, _x); \
	}




	#endif /* _COS_SIN_H_ */
	#endif /* __SPU__ */