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audacia/src/SseMathFuncs.cpp

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/**********************************************************************
Audacity: A Digital Audio Editor
SseMathFuncs.cpp
Stephen Moshier (wrote original C version, The Cephes Library)
Julien Pommier (converted to use SSE)
Andrew Hallendorff (adapted for Audacity)
*******************************************************************//**
\file SseMathfuncs.cpp
\brief SSE maths functions (for FFTs)
*//****************************************************************/
#include "SseMathFuncs.h"
/* JKC: The trig functions use Taylor's series, on the range 0 to Pi/4
* computing both Sin and Cos, and using one or the other (in the
* solo functions), or both in the more useful for us for FFTs sincos
* function.
* The constants minus_cephes_DP1 to minus_cephes_DP3 are used in the
* angle reduction modulo function.
* 4 sincos are done at a time.
* If we wanted to do just sin or just cos, we could speed things up
* by queuing up the Sines and Cosines into batches of 4 separately.*/
#ifndef USE_SSE2 //sry this is all sse2 now
#define USE_SSE2
#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 = { (float)Val, (float)Val, (float)Val, (float)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, (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);
#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
*/
__m128 log_ps(v4sfu *xPtr) {
__m128 x=*((__m128 *)xPtr);
#ifdef USE_SSE2
__m128i emm0;
#else
__m64 mm0, mm1;
#endif
__m128 one = *(__m128*)_ps_1;
__m128 invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps());
x = _mm_max_ps(x, *(__m128*)_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, *(__m128*)_ps_inv_mant_mask);
x = _mm_or_ps(x, *(__m128*)_ps_0p5);
#ifndef USE_SSE2
/* now e=mm0:mm1 contain the really base-2 exponent */
mm0 = _mm_sub_pi32(mm0, *(__m64*)_pi32_0x7f);
mm1 = _mm_sub_pi32(mm1, *(__m64*)_pi32_0x7f);
__m128 e = _mm_cvtpi32x2_ps(mm0, mm1);
_mm_empty(); /* bye bye mmx */
#else
emm0 = _mm_sub_epi32(emm0, *(__m128i*)_pi32_0x7f);
__m128 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; }
*/
__m128 mask = _mm_cmplt_ps(x, *(__m128*)_ps_cephes_SQRTHF);
__m128 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);
__m128 z = _mm_mul_ps(x,x);
__m128 y = *(__m128*)_ps_cephes_log_p0;
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_log_p1);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_log_p2);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_log_p3);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_log_p4);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_log_p5);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_log_p6);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_log_p7);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_log_p8);
y = _mm_mul_ps(y, x);
y = _mm_mul_ps(y, z);
tmp = _mm_mul_ps(e, *(__m128*)_ps_cephes_log_q1);
y = _mm_add_ps(y, tmp);
tmp = _mm_mul_ps(z, *(__m128*)_ps_0p5);
y = _mm_sub_ps(y, tmp);
tmp = _mm_mul_ps(e, *(__m128*)_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);
__m128 exp_ps(v4sfu *xPtr) {
__m128 x=*((__m128 *)xPtr);
__m128 tmp = _mm_setzero_ps(), fx;
#ifdef USE_SSE2
__m128i emm0;
#else
__m64 mm0, mm1;
#endif
__m128 one = *(__m128*)_ps_1;
x = _mm_min_ps(x, *(__m128*)_ps_exp_hi);
x = _mm_max_ps(x, *(__m128*)_ps_exp_lo);
/* express exp(x) as exp(g + n*log(2)) */
fx = _mm_mul_ps(x, *(__m128*)_ps_cephes_LOG2EF);
fx = _mm_add_ps(fx, *(__m128*)_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 */
__m128 mask = _mm_cmpgt_ps(tmp, fx);
mask = _mm_and_ps(mask, one);
fx = _mm_sub_ps(tmp, mask);
tmp = _mm_mul_ps(fx, *(__m128*)_ps_cephes_exp_C1);
__m128 z = _mm_mul_ps(fx, *(__m128*)_ps_cephes_exp_C2);
x = _mm_sub_ps(x, tmp);
x = _mm_sub_ps(x, z);
z = _mm_mul_ps(x,x);
__m128 y = *(__m128*)_ps_cephes_exp_p0;
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_exp_p1);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_exp_p2);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_exp_p3);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_ps_cephes_exp_p4);
y = _mm_mul_ps(y, x);
y = _mm_add_ps(y, *(__m128*)_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, *(__m64*)_pi32_0x7f);
mm1 = _mm_add_pi32(mm1, *(__m64*)_pi32_0x7f);
mm0 = _mm_slli_pi32(mm0, 23);
mm1 = _mm_slli_pi32(mm1, 23);
__m128 pow2n;
COPY_MM_TO_XMM(mm0, mm1, pow2n);
_mm_empty();
#else
emm0 = _mm_cvttps_epi32(fx);
emm0 = _mm_add_epi32(emm0, *(__m128i*)_pi32_0x7f);
emm0 = _mm_slli_epi32(emm0, 23);
__m128 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.
*/
__m128 sin_ps(v4sfu *xPtr) { // any x
__m128 x=*((__m128 *)xPtr);
__m128 xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
#ifdef USE_SSE2
__m128i emm0, emm2;
#else
__m64 mm0, mm1, mm2, mm3;
#endif
sign_bit = x;
/* take the absolute value */
x = _mm_and_ps(x, *(__m128*)_ps_inv_sign_mask);
/* extract the sign bit (upper one) */
sign_bit = _mm_and_ps(sign_bit, *(__m128*)_ps_sign_mask);
/* scale by 4/Pi */
y = _mm_mul_ps(x, *(__m128*)_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, *(__m128i*)_pi32_1);
emm2 = _mm_and_si128(emm2, *(__m128i*)_pi32_inv1);
y = _mm_cvtepi32_ps(emm2);
/* get the swap sign flag */
emm0 = _mm_and_si128(emm2, *(__m128i*)_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, *(__m128i*)_pi32_2);
emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
__m128 swap_sign_bit = _mm_castsi128_ps(emm0);
__m128 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, *(__m64*)_pi32_1);
mm3 = _mm_add_pi32(mm3, *(__m64*)_pi32_1);
mm2 = _mm_and_si64(mm2, *(__m64*)_pi32_inv1);
mm3 = _mm_and_si64(mm3, *(__m64*)_pi32_inv1);
y = _mm_cvtpi32x2_ps(mm2, mm3);
/* get the swap sign flag */
mm0 = _mm_and_si64(mm2, *(__m64*)_pi32_4);
mm1 = _mm_and_si64(mm3, *(__m64*)_pi32_4);
mm0 = _mm_slli_pi32(mm0, 29);
mm1 = _mm_slli_pi32(mm1, 29);
/* get the polynom selection mask */
mm2 = _mm_and_si64(mm2, *(__m64*)_pi32_2);
mm3 = _mm_and_si64(mm3, *(__m64*)_pi32_2);
mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64());
mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64());
__m128 swap_sign_bit, poly_mask;
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 = *(__m128*)_ps_minus_cephes_DP1;
xmm2 = *(__m128*)_ps_minus_cephes_DP2;
xmm3 = *(__m128*)_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 = *(__m128*)_ps_coscof_p0;
__m128 z = _mm_mul_ps(x,x);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(__m128*)_ps_coscof_p1);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(__m128*)_ps_coscof_p2);
y = _mm_mul_ps(y, z);
y = _mm_mul_ps(y, z);
__m128 tmp = _mm_mul_ps(z, *(__m128*)_ps_0p5);
y = _mm_sub_ps(y, tmp);
y = _mm_add_ps(y, *(__m128*)_ps_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
__m128 y2 = *(__m128*)_ps_sincof_p0;
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(__m128*)_ps_sincof_p1);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(__m128*)_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 */
__m128 cos_ps(v4sfu *xPtr) { // any x
__m128 x=*((__m128 *)xPtr);
__m128 xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
#ifdef USE_SSE2
__m128i emm0, emm2;
#else
__m64 mm0, mm1, mm2, mm3;
#endif
/* take the absolute value */
x = _mm_and_ps(x, *(__m128*)_ps_inv_sign_mask);
/* scale by 4/Pi */
y = _mm_mul_ps(x, *(__m128*)_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, *(__m128i*)_pi32_1);
emm2 = _mm_and_si128(emm2, *(__m128i*)_pi32_inv1);
y = _mm_cvtepi32_ps(emm2);
emm2 = _mm_sub_epi32(emm2, *(__m128i*)_pi32_2);
/* get the swap sign flag */
emm0 = _mm_andnot_si128(emm2, *(__m128i*)_pi32_4);
emm0 = _mm_slli_epi32(emm0, 29);
/* get the polynom selection mask */
emm2 = _mm_and_si128(emm2, *(__m128i*)_pi32_2);
emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
__m128 sign_bit = _mm_castsi128_ps(emm0);
__m128 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, *(__m64*)_pi32_1);
mm3 = _mm_add_pi32(mm3, *(__m64*)_pi32_1);
mm2 = _mm_and_si64(mm2, *(__m64*)_pi32_inv1);
mm3 = _mm_and_si64(mm3, *(__m64*)_pi32_inv1);
y = _mm_cvtpi32x2_ps(mm2, mm3);
mm2 = _mm_sub_pi32(mm2, *(__m64*)_pi32_2);
mm3 = _mm_sub_pi32(mm3, *(__m64*)_pi32_2);
/* get the swap sign flag in mm0:mm1 and the
polynom selection mask in mm2:mm3 */
mm0 = _mm_andnot_si64(mm2, *(__m64*)_pi32_4);
mm1 = _mm_andnot_si64(mm3, *(__m64*)_pi32_4);
mm0 = _mm_slli_pi32(mm0, 29);
mm1 = _mm_slli_pi32(mm1, 29);
mm2 = _mm_and_si64(mm2, *(__m64*)_pi32_2);
mm3 = _mm_and_si64(mm3, *(__m64*)_pi32_2);
mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64());
mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64());
__m128 sign_bit, poly_mask;
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 = *(__m128*)_ps_minus_cephes_DP1;
xmm2 = *(__m128*)_ps_minus_cephes_DP2;
xmm3 = *(__m128*)_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 = *(__m128*)_ps_coscof_p0;
__m128 z = _mm_mul_ps(x,x);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(__m128*)_ps_coscof_p1);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(__m128*)_ps_coscof_p2);
y = _mm_mul_ps(y, z);
y = _mm_mul_ps(y, z);
__m128 tmp = _mm_mul_ps(z, *(__m128*)_ps_0p5);
y = _mm_sub_ps(y, tmp);
y = _mm_add_ps(y, *(__m128*)_ps_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
__m128 y2 = *(__m128*)_ps_sincof_p0;
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(__m128*)_ps_sincof_p1);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(__m128*)_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(v4sfu *xptr, v4sfu *sptr, v4sfu *cptr) {
__m128 x=*((__m128 *)xptr), *s=(__m128 *)sptr, *c=(__m128 *)cptr, xmm1, xmm2, xmm3 = _mm_setzero_ps(), sign_bit_sin, y;
#ifdef USE_SSE2
__m128i emm0, emm2, emm4;
#else
__m64 mm0, mm1, mm2, mm3, mm4, mm5;
#endif
sign_bit_sin = x;
/* take the absolute value */
x = _mm_and_ps(x, *(__m128*)_ps_inv_sign_mask);
/* extract the sign bit (upper one) */
sign_bit_sin = _mm_and_ps(sign_bit_sin, *(__m128*)_ps_sign_mask);
/* scale by 4/Pi */
y = _mm_mul_ps(x, *(__m128*)_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, *(__m128i*)_pi32_1);
emm2 = _mm_and_si128(emm2, *(__m128i*)_pi32_inv1);
y = _mm_cvtepi32_ps(emm2);
emm4 = emm2;
/* get the swap sign flag for the sine */
emm0 = _mm_and_si128(emm2, *(__m128i*)_pi32_4);
emm0 = _mm_slli_epi32(emm0, 29);
__m128 swap_sign_bit_sin = _mm_castsi128_ps(emm0);
/* get the polynom selection mask for the sine*/
emm2 = _mm_and_si128(emm2, *(__m128i*)_pi32_2);
emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
__m128 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, *(__m64*)_pi32_1);
mm3 = _mm_add_pi32(mm3, *(__m64*)_pi32_1);
mm2 = _mm_and_si64(mm2, *(__m64*)_pi32_inv1);
mm3 = _mm_and_si64(mm3, *(__m64*)_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, *(__m64*)_pi32_4);
mm1 = _mm_and_si64(mm3, *(__m64*)_pi32_4);
mm0 = _mm_slli_pi32(mm0, 29);
mm1 = _mm_slli_pi32(mm1, 29);
__m128 swap_sign_bit_sin;
COPY_MM_TO_XMM(mm0, mm1, swap_sign_bit_sin);
/* get the polynom selection mask for the sine */
mm2 = _mm_and_si64(mm2, *(__m64*)_pi32_2);
mm3 = _mm_and_si64(mm3, *(__m64*)_pi32_2);
mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64());
mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64());
__m128 poly_mask;
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 = *(__m128*)_ps_minus_cephes_DP1;
xmm2 = *(__m128*)_ps_minus_cephes_DP2;
xmm3 = *(__m128*)_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, *(__m128i*)_pi32_2);
emm4 = _mm_andnot_si128(emm4, *(__m128i*)_pi32_4);
emm4 = _mm_slli_epi32(emm4, 29);
__m128 sign_bit_cos = _mm_castsi128_ps(emm4);
#else
/* get the sign flag for the cosine */
mm4 = _mm_sub_pi32(mm4, *(__m64*)_pi32_2);
mm5 = _mm_sub_pi32(mm5, *(__m64*)_pi32_2);
mm4 = _mm_andnot_si64(mm4, *(__m64*)_pi32_4);
mm5 = _mm_andnot_si64(mm5, *(__m64*)_pi32_4);
mm4 = _mm_slli_pi32(mm4, 29);
mm5 = _mm_slli_pi32(mm5, 29);
__m128 sign_bit_cos;
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) */
__m128 z = _mm_mul_ps(x,x);
y = *(__m128*)_ps_coscof_p0;
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(__m128*)_ps_coscof_p1);
y = _mm_mul_ps(y, z);
y = _mm_add_ps(y, *(__m128*)_ps_coscof_p2);
y = _mm_mul_ps(y, z);
y = _mm_mul_ps(y, z);
__m128 tmp = _mm_mul_ps(z, *(__m128*)_ps_0p5);
y = _mm_sub_ps(y, tmp);
y = _mm_add_ps(y, *(__m128*)_ps_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
__m128 y2 = *(__m128*)_ps_sincof_p0;
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(__m128*)_ps_sincof_p1);
y2 = _mm_mul_ps(y2, z);
y2 = _mm_add_ps(y2, *(__m128*)_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;
__m128 ysin2 = _mm_and_ps(xmm3, y2);
__m128 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);
}
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