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Diffstat (limited to 'src/gallium/drivers/llvmpipe/sse_mathfun.h')
| -rw-r--r-- | src/gallium/drivers/llvmpipe/sse_mathfun.h | 773 |
1 files changed, 773 insertions, 0 deletions
diff --git a/src/gallium/drivers/llvmpipe/sse_mathfun.h b/src/gallium/drivers/llvmpipe/sse_mathfun.h new file mode 100644 index 00000000000..8ac2064b7bb --- /dev/null +++ b/src/gallium/drivers/llvmpipe/sse_mathfun.h @@ -0,0 +1,773 @@ +/* SIMD (SSE1+MMX or SSE2) implementation of sin, cos, exp and log + + Inspired by Intel Approximate Math library, and based on the + corresponding algorithms of the cephes math library + + The default is to use the SSE1 version. If you define USE_SSE2 the + the SSE2 intrinsics will be used in place of the MMX intrinsics. Do + not expect any significant performance improvement with SSE2. +*/ + +/* Copyright (C) 2007 Julien Pommier + + This software is provided 'as-is', without any express or implied + warranty. In no event will the authors be held liable for any damages + arising from the use of this software. + + Permission is granted to anyone to use this software for any purpose, + including commercial applications, and to alter it and redistribute it + freely, subject to the following restrictions: + + 1. The origin of this software must not be misrepresented; you must not + claim that you wrote the original software. If you use this software + in a product, an acknowledgment in the product documentation would be + appreciated but is not required. + 2. Altered source versions must be plainly marked as such, and must not be + misrepresented as being the original software. + 3. This notice may not be removed or altered from any source distribution. + + (this is the zlib license) +*/ + +#include <xmmintrin.h> + +/* yes I know, the top of this file is quite ugly */ + +#ifdef _MSC_VER /* visual c++ */ +# define ALIGN16_BEG __declspec(align(16)) +# define ALIGN16_END +#else /* gcc or icc */ +# define ALIGN16_BEG +# define ALIGN16_END __attribute__((aligned(16))) +#endif + +/* __m128 is ugly to write */ +typedef __m128 v4sf; // vector of 4 float (sse1) + +#ifdef USE_SSE2 +# include <emmintrin.h> +typedef __m128i v4si; // vector of 4 int (sse2) +#else +typedef __m64 v2si; // vector of 2 int (mmx) +#endif + +/* declare some SSE constants -- why can't I figure a better way to do that? */ +#define _PS_CONST(Name, Val) \ + static const ALIGN16_BEG float _ps_##Name[4] ALIGN16_END = { Val, Val, Val, Val } +#define _PI32_CONST(Name, Val) \ + static const ALIGN16_BEG int _pi32_##Name[4] ALIGN16_END = { Val, Val, Val, Val } +#define _PS_CONST_TYPE(Name, Type, Val) \ + static const ALIGN16_BEG Type _ps_##Name[4] ALIGN16_END = { Val, Val, Val, Val } + +_PS_CONST(1 , 1.0f); +_PS_CONST(0p5, 0.5f); +/* the smallest non denormalized float number */ +_PS_CONST_TYPE(min_norm_pos, int, 0x00800000); +_PS_CONST_TYPE(mant_mask, int, 0x7f800000); +_PS_CONST_TYPE(inv_mant_mask, int, ~0x7f800000); + +_PS_CONST_TYPE(sign_mask, int, 0x80000000); +_PS_CONST_TYPE(inv_sign_mask, int, ~0x80000000); + +_PI32_CONST(1, 1); +_PI32_CONST(inv1, ~1); +_PI32_CONST(2, 2); +_PI32_CONST(4, 4); +_PI32_CONST(0x7f, 0x7f); + +_PS_CONST(cephes_SQRTHF, 0.707106781186547524); +_PS_CONST(cephes_log_p0, 7.0376836292E-2); +_PS_CONST(cephes_log_p1, - 1.1514610310E-1); +_PS_CONST(cephes_log_p2, 1.1676998740E-1); +_PS_CONST(cephes_log_p3, - 1.2420140846E-1); +_PS_CONST(cephes_log_p4, + 1.4249322787E-1); +_PS_CONST(cephes_log_p5, - 1.6668057665E-1); +_PS_CONST(cephes_log_p6, + 2.0000714765E-1); +_PS_CONST(cephes_log_p7, - 2.4999993993E-1); +_PS_CONST(cephes_log_p8, + 3.3333331174E-1); +_PS_CONST(cephes_log_q1, -2.12194440e-4); +_PS_CONST(cephes_log_q2, 0.693359375); + +v4sf log_ps(v4sf x); +v4sf exp_ps(v4sf x); +v4sf sin_ps(v4sf x); +v4sf cos_ps(v4sf x); +void sincos_ps(v4sf x, v4sf *s, v4sf *c); + +#if defined (__MINGW32__) + +/* the ugly part below: many versions of gcc used to be completely buggy with respect to some intrinsics + The movehl_ps is fixed in mingw 3.4.5, but I found out that all the _mm_cmp* intrinsics were completely + broken on my mingw gcc 3.4.5 ... + + Note that the bug on _mm_cmp* does occur only at -O0 optimization level +*/ + +inline __m128 my_movehl_ps(__m128 a, const __m128 b) { + asm ( + "movhlps %2,%0\n\t" + : "=x" (a) + : "0" (a), "x"(b) + ); + return a; } +#warning "redefined _mm_movehl_ps (see gcc bug 21179)" +#define _mm_movehl_ps my_movehl_ps + +inline __m128 my_cmplt_ps(__m128 a, const __m128 b) { + asm ( + "cmpltps %2,%0\n\t" + : "=x" (a) + : "0" (a), "x"(b) + ); + return a; + } +inline __m128 my_cmpgt_ps(__m128 a, const __m128 b) { + asm ( + "cmpnleps %2,%0\n\t" + : "=x" (a) + : "0" (a), "x"(b) + ); + return a; +} +inline __m128 my_cmpeq_ps(__m128 a, const __m128 b) { + asm ( + "cmpeqps %2,%0\n\t" + : "=x" (a) + : "0" (a), "x"(b) + ); + return a; +} +#warning "redefined _mm_cmpxx_ps functions..." +#define _mm_cmplt_ps my_cmplt_ps +#define _mm_cmpgt_ps my_cmpgt_ps +#define _mm_cmpeq_ps my_cmpeq_ps +#endif + +#ifndef USE_SSE2 +typedef union xmm_mm_union { + __m128 xmm; + __m64 mm[2]; +} xmm_mm_union; + +#define COPY_XMM_TO_MM(xmm_, mm0_, mm1_) { \ + xmm_mm_union u; u.xmm = xmm_; \ + mm0_ = u.mm[0]; \ + mm1_ = u.mm[1]; \ +} + +#define COPY_MM_TO_XMM(mm0_, mm1_, xmm_) { \ + xmm_mm_union u; u.mm[0]=mm0_; u.mm[1]=mm1_; xmm_ = u.xmm; \ + } + +#endif // USE_SSE2 + +/* natural logarithm computed for 4 simultaneous float + return NaN for x <= 0 +*/ +v4sf log_ps(v4sf x) { +#ifdef USE_SSE2 + v4si emm0; +#else + v2si mm0, mm1; +#endif + v4sf one = *(v4sf*)_ps_1; + + v4sf invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps()); + v4sf e, mask, tmp, z, y; + + x = _mm_max_ps(x, *(v4sf*)_ps_min_norm_pos); /* cut off denormalized stuff */ + +#ifndef USE_SSE2 + /* part 1: x = frexpf(x, &e); */ + COPY_XMM_TO_MM(x, mm0, mm1); + mm0 = _mm_srli_pi32(mm0, 23); + mm1 = _mm_srli_pi32(mm1, 23); +#else + emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23); +#endif + /* keep only the fractional part */ + x = _mm_and_ps(x, *(v4sf*)_ps_inv_mant_mask); + x = _mm_or_ps(x, *(v4sf*)_ps_0p5); + +#ifndef USE_SSE2 + /* now e=mm0:mm1 contain the really base-2 exponent */ + mm0 = _mm_sub_pi32(mm0, *(v2si*)_pi32_0x7f); + mm1 = _mm_sub_pi32(mm1, *(v2si*)_pi32_0x7f); + e = _mm_cvtpi32x2_ps(mm0, mm1); + _mm_empty(); /* bye bye mmx */ +#else + emm0 = _mm_sub_epi32(emm0, *(v4si*)_pi32_0x7f); + e = _mm_cvtepi32_ps(emm0); +#endif + + e = _mm_add_ps(e, one); + + /* part2: + if( x < SQRTHF ) { + e -= 1; + x = x + x - 1.0; + } else { x = x - 1.0; } + */ + + mask = _mm_cmplt_ps(x, *(v4sf*)_ps_cephes_SQRTHF); + tmp = _mm_and_ps(x, mask); + x = _mm_sub_ps(x, one); + e = _mm_sub_ps(e, _mm_and_ps(one, mask)); + x = _mm_add_ps(x, tmp); + + + z = _mm_mul_ps(x,x); + + y = *(v4sf*)_ps_cephes_log_p0; + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p1); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p2); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p3); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p4); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p5); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p6); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p7); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_log_p8); + y = _mm_mul_ps(y, x); + + y = _mm_mul_ps(y, z); + + + tmp = _mm_mul_ps(e, *(v4sf*)_ps_cephes_log_q1); + y = _mm_add_ps(y, tmp); + + + tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5); + y = _mm_sub_ps(y, tmp); + + tmp = _mm_mul_ps(e, *(v4sf*)_ps_cephes_log_q2); + x = _mm_add_ps(x, y); + x = _mm_add_ps(x, tmp); + x = _mm_or_ps(x, invalid_mask); // negative arg will be NAN + return x; +} + +_PS_CONST(exp_hi, 88.3762626647949f); +_PS_CONST(exp_lo, -88.3762626647949f); + +_PS_CONST(cephes_LOG2EF, 1.44269504088896341); +_PS_CONST(cephes_exp_C1, 0.693359375); +_PS_CONST(cephes_exp_C2, -2.12194440e-4); + +_PS_CONST(cephes_exp_p0, 1.9875691500E-4); +_PS_CONST(cephes_exp_p1, 1.3981999507E-3); +_PS_CONST(cephes_exp_p2, 8.3334519073E-3); +_PS_CONST(cephes_exp_p3, 4.1665795894E-2); +_PS_CONST(cephes_exp_p4, 1.6666665459E-1); +_PS_CONST(cephes_exp_p5, 5.0000001201E-1); + +v4sf exp_ps(v4sf x) { + v4sf tmp = _mm_setzero_ps(), fx; +#ifdef USE_SSE2 + v4si emm0; +#else + v2si mm0, mm1; +#endif + v4sf one = *(v4sf*)_ps_1; + v4sf mask, z, y, pow2n; + + x = _mm_min_ps(x, *(v4sf*)_ps_exp_hi); + x = _mm_max_ps(x, *(v4sf*)_ps_exp_lo); + + /* express exp(x) as exp(g + n*log(2)) */ + fx = _mm_mul_ps(x, *(v4sf*)_ps_cephes_LOG2EF); + fx = _mm_add_ps(fx, *(v4sf*)_ps_0p5); + + /* how to perform a floorf with SSE: just below */ +#ifndef USE_SSE2 + /* step 1 : cast to int */ + tmp = _mm_movehl_ps(tmp, fx); + mm0 = _mm_cvttps_pi32(fx); + mm1 = _mm_cvttps_pi32(tmp); + /* step 2 : cast back to float */ + tmp = _mm_cvtpi32x2_ps(mm0, mm1); +#else + emm0 = _mm_cvttps_epi32(fx); + tmp = _mm_cvtepi32_ps(emm0); +#endif + /* if greater, substract 1 */ + mask = _mm_cmpgt_ps(tmp, fx); + mask = _mm_and_ps(mask, one); + fx = _mm_sub_ps(tmp, mask); + + tmp = _mm_mul_ps(fx, *(v4sf*)_ps_cephes_exp_C1); + z = _mm_mul_ps(fx, *(v4sf*)_ps_cephes_exp_C2); + x = _mm_sub_ps(x, tmp); + x = _mm_sub_ps(x, z); + + z = _mm_mul_ps(x,x); + + y = *(v4sf*)_ps_cephes_exp_p0; + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p1); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p2); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p3); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p4); + y = _mm_mul_ps(y, x); + y = _mm_add_ps(y, *(v4sf*)_ps_cephes_exp_p5); + y = _mm_mul_ps(y, z); + y = _mm_add_ps(y, x); + y = _mm_add_ps(y, one); + + /* build 2^n */ +#ifndef USE_SSE2 + z = _mm_movehl_ps(z, fx); + mm0 = _mm_cvttps_pi32(fx); + mm1 = _mm_cvttps_pi32(z); + mm0 = _mm_add_pi32(mm0, *(v2si*)_pi32_0x7f); + mm1 = _mm_add_pi32(mm1, *(v2si*)_pi32_0x7f); + mm0 = _mm_slli_pi32(mm0, 23); + mm1 = _mm_slli_pi32(mm1, 23); + + COPY_MM_TO_XMM(mm0, mm1, pow2n); + _mm_empty(); +#else + emm0 = _mm_cvttps_epi32(fx); + emm0 = _mm_add_epi32(emm0, *(v4si*)_pi32_0x7f); + emm0 = _mm_slli_epi32(emm0, 23); + pow2n = _mm_castsi128_ps(emm0); +#endif + y = _mm_mul_ps(y, pow2n); + return y; +} + +_PS_CONST(minus_cephes_DP1, -0.78515625); +_PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4); +_PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8); +_PS_CONST(sincof_p0, -1.9515295891E-4); +_PS_CONST(sincof_p1, 8.3321608736E-3); +_PS_CONST(sincof_p2, -1.6666654611E-1); +_PS_CONST(coscof_p0, 2.443315711809948E-005); +_PS_CONST(coscof_p1, -1.388731625493765E-003); +_PS_CONST(coscof_p2, 4.166664568298827E-002); +_PS_CONST(cephes_FOPI, 1.27323954473516); // 4 / M_PI + + +/* evaluation of 4 sines at onces, using only SSE1+MMX intrinsics so + it runs also on old athlons XPs and the pentium III of your grand + mother. + + The code is the exact rewriting of the cephes sinf function. + Precision is excellent as long as x < 8192 (I did not bother to + take into account the special handling they have for greater values + -- it does not return garbage for arguments over 8192, though, but + the extra precision is missing). + + Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the + surprising but correct result. + + Performance is also surprisingly good, 1.33 times faster than the + macos vsinf SSE2 function, and 1.5 times faster than the + __vrs4_sinf of amd's ACML (which is only available in 64 bits). Not + too bad for an SSE1 function (with no special tuning) ! + However the latter libraries probably have a much better handling of NaN, + Inf, denormalized and other special arguments.. + + On my core 1 duo, the execution of this function takes approximately 95 cycles. + + From what I have observed on the experiments with Intel AMath lib, switching to an + SSE2 version would improve the perf by only 10%. + + Since it is based on SSE intrinsics, it has to be compiled at -O2 to + deliver full speed. +*/ +v4sf sin_ps(v4sf x) { // any x + v4sf xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y; + +#ifdef USE_SSE2 + v4si emm0, emm2; +#else + v2si mm0, mm1, mm2, mm3; +#endif + v4sf swap_sign_bit, poly_mask, z, tmp, y2; + + sign_bit = x; + /* take the absolute value */ + x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask); + /* extract the sign bit (upper one) */ + sign_bit = _mm_and_ps(sign_bit, *(v4sf*)_ps_sign_mask); + + /* scale by 4/Pi */ + y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI); + + //printf("plop:"); print4(y); +#ifdef USE_SSE2 + /* store the integer part of y in mm0 */ + emm2 = _mm_cvttps_epi32(y); + /* j=(j+1) & (~1) (see the cephes sources) */ + emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1); + emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1); + y = _mm_cvtepi32_ps(emm2); + /* get the swap sign flag */ + emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4); + emm0 = _mm_slli_epi32(emm0, 29); + /* get the polynom selection mask + there is one polynom for 0 <= x <= Pi/4 + and another one for Pi/4<x<=Pi/2 + + Both branches will be computed. + */ + emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2); + emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128()); + + swap_sign_bit = _mm_castsi128_ps(emm0); + poly_mask = _mm_castsi128_ps(emm2); + sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit); +#else + /* store the integer part of y in mm0:mm1 */ + xmm2 = _mm_movehl_ps(xmm2, y); + mm2 = _mm_cvttps_pi32(y); + mm3 = _mm_cvttps_pi32(xmm2); + /* j=(j+1) & (~1) (see the cephes sources) */ + mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1); + mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1); + mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1); + mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1); + y = _mm_cvtpi32x2_ps(mm2, mm3); + /* get the swap sign flag */ + mm0 = _mm_and_si64(mm2, *(v2si*)_pi32_4); + mm1 = _mm_and_si64(mm3, *(v2si*)_pi32_4); + mm0 = _mm_slli_pi32(mm0, 29); + mm1 = _mm_slli_pi32(mm1, 29); + /* get the polynom selection mask */ + mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2); + mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2); + mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64()); + mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64()); + + COPY_MM_TO_XMM(mm0, mm1, swap_sign_bit); + COPY_MM_TO_XMM(mm2, mm3, poly_mask); + sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit); + _mm_empty(); /* good-bye mmx */ +#endif + + /* The magic pass: "Extended precision modular arithmetic" + x = ((x - y * DP1) - y * DP2) - y * DP3; */ + xmm1 = *(v4sf*)_ps_minus_cephes_DP1; + xmm2 = *(v4sf*)_ps_minus_cephes_DP2; + xmm3 = *(v4sf*)_ps_minus_cephes_DP3; + xmm1 = _mm_mul_ps(y, xmm1); + xmm2 = _mm_mul_ps(y, xmm2); + xmm3 = _mm_mul_ps(y, xmm3); + x = _mm_add_ps(x, xmm1); + x = _mm_add_ps(x, xmm2); + x = _mm_add_ps(x, xmm3); + + /* Evaluate the first polynom (0 <= x <= Pi/4) */ + y = *(v4sf*)_ps_coscof_p0; + z = _mm_mul_ps(x,x); + + y = _mm_mul_ps(y, z); + y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1); + y = _mm_mul_ps(y, z); + y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2); + y = _mm_mul_ps(y, z); + y = _mm_mul_ps(y, z); + tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5); + y = _mm_sub_ps(y, tmp); + y = _mm_add_ps(y, *(v4sf*)_ps_1); + + /* Evaluate the second polynom (Pi/4 <= x <= 0) */ + + y2 = *(v4sf*)_ps_sincof_p0; + y2 = _mm_mul_ps(y2, z); + y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1); + y2 = _mm_mul_ps(y2, z); + y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2); + y2 = _mm_mul_ps(y2, z); + y2 = _mm_mul_ps(y2, x); + y2 = _mm_add_ps(y2, x); + + /* select the correct result from the two polynoms */ + xmm3 = poly_mask; + y2 = _mm_and_ps(xmm3, y2); //, xmm3); + y = _mm_andnot_ps(xmm3, y); + y = _mm_add_ps(y,y2); + /* update the sign */ + y = _mm_xor_ps(y, sign_bit); + + return y; +} + +/* almost the same as sin_ps */ +v4sf cos_ps(v4sf x) { // any x + v4sf xmm1, xmm2 = _mm_setzero_ps(), xmm3, y; +#ifdef USE_SSE2 + v4si emm0, emm2; +#else + v2si mm0, mm1, mm2, mm3; +#endif + v4sf sign_bit, poly_mask, z, tmp, y2; + + /* take the absolute value */ + x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask); + + /* scale by 4/Pi */ + y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI); + +#ifdef USE_SSE2 + /* store the integer part of y in mm0 */ + emm2 = _mm_cvttps_epi32(y); + /* j=(j+1) & (~1) (see the cephes sources) */ + emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1); + emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1); + y = _mm_cvtepi32_ps(emm2); + + emm2 = _mm_sub_epi32(emm2, *(v4si*)_pi32_2); + + /* get the swap sign flag */ + emm0 = _mm_andnot_si128(emm2, *(v4si*)_pi32_4); + emm0 = _mm_slli_epi32(emm0, 29); + /* get the polynom selection mask */ + emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2); + emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128()); + + sign_bit = _mm_castsi128_ps(emm0); + poly_mask = _mm_castsi128_ps(emm2); +#else + /* store the integer part of y in mm0:mm1 */ + xmm2 = _mm_movehl_ps(xmm2, y); + mm2 = _mm_cvttps_pi32(y); + mm3 = _mm_cvttps_pi32(xmm2); + + /* j=(j+1) & (~1) (see the cephes sources) */ + mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1); + mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1); + mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1); + mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1); + + y = _mm_cvtpi32x2_ps(mm2, mm3); + + + mm2 = _mm_sub_pi32(mm2, *(v2si*)_pi32_2); + mm3 = _mm_sub_pi32(mm3, *(v2si*)_pi32_2); + + /* get the swap sign flag in mm0:mm1 and the + polynom selection mask in mm2:mm3 */ + + mm0 = _mm_andnot_si64(mm2, *(v2si*)_pi32_4); + mm1 = _mm_andnot_si64(mm3, *(v2si*)_pi32_4); + mm0 = _mm_slli_pi32(mm0, 29); + mm1 = _mm_slli_pi32(mm1, 29); + + mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2); + mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2); + + mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64()); + mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64()); + + COPY_MM_TO_XMM(mm0, mm1, sign_bit); + COPY_MM_TO_XMM(mm2, mm3, poly_mask); + _mm_empty(); /* good-bye mmx */ +#endif + /* The magic pass: "Extended precision modular arithmetic" + x = ((x - y * DP1) - y * DP2) - y * DP3; */ + xmm1 = *(v4sf*)_ps_minus_cephes_DP1; + xmm2 = *(v4sf*)_ps_minus_cephes_DP2; + xmm3 = *(v4sf*)_ps_minus_cephes_DP3; + xmm1 = _mm_mul_ps(y, xmm1); + xmm2 = _mm_mul_ps(y, xmm2); + xmm3 = _mm_mul_ps(y, xmm3); + x = _mm_add_ps(x, xmm1); + x = _mm_add_ps(x, xmm2); + x = _mm_add_ps(x, xmm3); + + /* Evaluate the first polynom (0 <= x <= Pi/4) */ + y = *(v4sf*)_ps_coscof_p0; + z = _mm_mul_ps(x,x); + + y = _mm_mul_ps(y, z); + y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1); + y = _mm_mul_ps(y, z); + y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2); + y = _mm_mul_ps(y, z); + y = _mm_mul_ps(y, z); + tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5); + y = _mm_sub_ps(y, tmp); + y = _mm_add_ps(y, *(v4sf*)_ps_1); + + /* Evaluate the second polynom (Pi/4 <= x <= 0) */ + + y2 = *(v4sf*)_ps_sincof_p0; + y2 = _mm_mul_ps(y2, z); + y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1); + y2 = _mm_mul_ps(y2, z); + y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2); + y2 = _mm_mul_ps(y2, z); + y2 = _mm_mul_ps(y2, x); + y2 = _mm_add_ps(y2, x); + + /* select the correct result from the two polynoms */ + xmm3 = poly_mask; + y2 = _mm_and_ps(xmm3, y2); //, xmm3); + y = _mm_andnot_ps(xmm3, y); + y = _mm_add_ps(y,y2); + /* update the sign */ + y = _mm_xor_ps(y, sign_bit); + + return y; +} + +/* since sin_ps and cos_ps are almost identical, sincos_ps could replace both of them.. + it is almost as fast, and gives you a free cosine with your sine */ +void sincos_ps(v4sf x, v4sf *s, v4sf *c) { + v4sf xmm1, xmm2, xmm3 = _mm_setzero_ps(), sign_bit_sin, y; +#ifdef USE_SSE2 + v4si emm0, emm2, emm4; +#else + v2si mm0, mm1, mm2, mm3, mm4, mm5; +#endif + v4sf swap_sign_bit_sin, poly_mask, z, tmp, y2, ysin1, ysin2; + v4sf sign_bit_cos; + + sign_bit_sin = x; + /* take the absolute value */ + x = _mm_and_ps(x, *(v4sf*)_ps_inv_sign_mask); + /* extract the sign bit (upper one) */ + sign_bit_sin = _mm_and_ps(sign_bit_sin, *(v4sf*)_ps_sign_mask); + + /* scale by 4/Pi */ + y = _mm_mul_ps(x, *(v4sf*)_ps_cephes_FOPI); + +#ifdef USE_SSE2 + /* store the integer part of y in emm2 */ + emm2 = _mm_cvttps_epi32(y); + + /* j=(j+1) & (~1) (see the cephes sources) */ + emm2 = _mm_add_epi32(emm2, *(v4si*)_pi32_1); + emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_inv1); + y = _mm_cvtepi32_ps(emm2); + + emm4 = emm2; + + /* get the swap sign flag for the sine */ + emm0 = _mm_and_si128(emm2, *(v4si*)_pi32_4); + emm0 = _mm_slli_epi32(emm0, 29); + swap_sign_bit_sin = _mm_castsi128_ps(emm0); + + /* get the polynom selection mask for the sine*/ + emm2 = _mm_and_si128(emm2, *(v4si*)_pi32_2); + emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128()); + poly_mask = _mm_castsi128_ps(emm2); +#else + /* store the integer part of y in mm2:mm3 */ + xmm3 = _mm_movehl_ps(xmm3, y); + mm2 = _mm_cvttps_pi32(y); + mm3 = _mm_cvttps_pi32(xmm3); + + /* j=(j+1) & (~1) (see the cephes sources) */ + mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1); + mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1); + mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1); + mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1); + + y = _mm_cvtpi32x2_ps(mm2, mm3); + + mm4 = mm2; + mm5 = mm3; + + /* get the swap sign flag for the sine */ + mm0 = _mm_and_si64(mm2, *(v2si*)_pi32_4); + mm1 = _mm_and_si64(mm3, *(v2si*)_pi32_4); + mm0 = _mm_slli_pi32(mm0, 29); + mm1 = _mm_slli_pi32(mm1, 29); + + COPY_MM_TO_XMM(mm0, mm1, swap_sign_bit_sin); + + /* get the polynom selection mask for the sine */ + + mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2); + mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2); + mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64()); + mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64()); + + COPY_MM_TO_XMM(mm2, mm3, poly_mask); +#endif + + /* The magic pass: "Extended precision modular arithmetic" + x = ((x - y * DP1) - y * DP2) - y * DP3; */ + xmm1 = *(v4sf*)_ps_minus_cephes_DP1; + xmm2 = *(v4sf*)_ps_minus_cephes_DP2; + xmm3 = *(v4sf*)_ps_minus_cephes_DP3; + xmm1 = _mm_mul_ps(y, xmm1); + xmm2 = _mm_mul_ps(y, xmm2); + xmm3 = _mm_mul_ps(y, xmm3); + x = _mm_add_ps(x, xmm1); + x = _mm_add_ps(x, xmm2); + x = _mm_add_ps(x, xmm3); + +#ifdef USE_SSE2 + emm4 = _mm_sub_epi32(emm4, *(v4si*)_pi32_2); + emm4 = _mm_andnot_si128(emm4, *(v4si*)_pi32_4); + emm4 = _mm_slli_epi32(emm4, 29); + sign_bit_cos = _mm_castsi128_ps(emm4); +#else + /* get the sign flag for the cosine */ + mm4 = _mm_sub_pi32(mm4, *(v2si*)_pi32_2); + mm5 = _mm_sub_pi32(mm5, *(v2si*)_pi32_2); + mm4 = _mm_andnot_si64(mm4, *(v2si*)_pi32_4); + mm5 = _mm_andnot_si64(mm5, *(v2si*)_pi32_4); + mm4 = _mm_slli_pi32(mm4, 29); + mm5 = _mm_slli_pi32(mm5, 29); + COPY_MM_TO_XMM(mm4, mm5, sign_bit_cos); + _mm_empty(); /* good-bye mmx */ +#endif + + sign_bit_sin = _mm_xor_ps(sign_bit_sin, swap_sign_bit_sin); + + + /* Evaluate the first polynom (0 <= x <= Pi/4) */ + z = _mm_mul_ps(x,x); + y = *(v4sf*)_ps_coscof_p0; + + y = _mm_mul_ps(y, z); + y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1); + y = _mm_mul_ps(y, z); + y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2); + y = _mm_mul_ps(y, z); + y = _mm_mul_ps(y, z); + tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5); + y = _mm_sub_ps(y, tmp); + y = _mm_add_ps(y, *(v4sf*)_ps_1); + + /* Evaluate the second polynom (Pi/4 <= x <= 0) */ + + y2 = *(v4sf*)_ps_sincof_p0; + y2 = _mm_mul_ps(y2, z); + y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1); + y2 = _mm_mul_ps(y2, z); + y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2); + y2 = _mm_mul_ps(y2, z); + y2 = _mm_mul_ps(y2, x); + y2 = _mm_add_ps(y2, x); + + /* select the correct result from the two polynoms */ + xmm3 = poly_mask; + ysin2 = _mm_and_ps(xmm3, y2); + ysin1 = _mm_andnot_ps(xmm3, y); + y2 = _mm_sub_ps(y2,ysin2); + y = _mm_sub_ps(y, ysin1); + + xmm1 = _mm_add_ps(ysin1,ysin2); + xmm2 = _mm_add_ps(y,y2); + + /* update the sign */ + *s = _mm_xor_ps(xmm1, sign_bit_sin); + *c = _mm_xor_ps(xmm2, sign_bit_cos); +} + |