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Diffstat (limited to 'newlib/libm/machine/spu/headers/cos_sin.h')
| -rw-r--r-- | newlib/libm/machine/spu/headers/cos_sin.h | 216 |
1 files changed, 216 insertions, 0 deletions
diff --git a/newlib/libm/machine/spu/headers/cos_sin.h b/newlib/libm/machine/spu/headers/cos_sin.h new file mode 100644 index 000000000..4769d06a3 --- /dev/null +++ b/newlib/libm/machine/spu/headers/cos_sin.h @@ -0,0 +1,216 @@ +/* -------------------------------------------------------------- */ +/* (C)Copyright 2006,2007, */ +/* 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. */ +/* 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__ */ + + |