/* 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)
*/

#pragma once

#define SIMDE_ENABLE_NATIVE_ALIASES
#include <simde/x86/sse.h>
#include <limits>
#define USE_SSE2

/* 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 <simde/x86/sse2.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 = {float{Val}, float{Val}, \
                                                                float{Val}, float{Val}}
#define _PI32_CONST(Name, Val)                                                                \
    static const ALIGN16_BEG int _pi32_##Name[4] ALIGN16_END = {int{Val}, int{Val}, int{Val}, \
                                                                int{Val}}
#define _PS_CONST_TYPE(Name, Type, Val)                                                         \
    static const ALIGN16_BEG Type _ps_##Name[4] ALIGN16_END = {Type{Val}, Type{Val}, Type{Val}, \
                                                               Type{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_MIN);
_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);

_PS_CONST(neg_infinity, -std::numeric_limits<float>::infinity());

#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
*/
inline v4sf log_ps(v4sf x)
{
#ifdef USE_SSE2
    v4si emm0;
#else
    v2si mm0, mm1;
#endif
    v4sf one = *reinterpret_cast<const v4sf*>(_ps_1);

    v4sf invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps());
    v4sf zero_mask = _mm_cmpeq_ps(x, _mm_setzero_ps());

    x = _mm_max_ps(
        x, *reinterpret_cast<const 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, *reinterpret_cast<const v4sf*>(_ps_inv_mant_mask));
    x = _mm_or_ps(x, *reinterpret_cast<const v4sf*>(_ps_0p5));

#ifndef USE_SSE2
    /* now e=mm0:mm1 contain the really base-2 exponent */
    mm0 = _mm_sub_pi32(mm0, *reinterpret_cast<const v2si*>(_pi32_0x7f));
    mm1 = _mm_sub_pi32(mm1, *reinterpret_cast<const v2si*>(_pi32_0x7f));
    v4sf e = _mm_cvtpi32x2_ps(mm0, mm1);
    _mm_empty(); /* bye bye mmx */
#else
    emm0 = _mm_sub_epi32(emm0, *reinterpret_cast<const v4si*>(_pi32_0x7f));
    v4sf 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; }
  */
    v4sf mask = _mm_cmplt_ps(x, *reinterpret_cast<const v4sf*>(_ps_cephes_SQRTHF));
    v4sf 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);

    v4sf z = _mm_mul_ps(x, x);

    v4sf y = *reinterpret_cast<const v4sf*>(_ps_cephes_log_p0);
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_log_p1));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_log_p2));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_log_p3));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_log_p4));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_log_p5));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_log_p6));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_log_p7));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_log_p8));
    y = _mm_mul_ps(y, x);

    y = _mm_mul_ps(y, z);

    tmp = _mm_mul_ps(e, *reinterpret_cast<const v4sf*>(_ps_cephes_log_q1));
    y = _mm_add_ps(y, tmp);

    tmp = _mm_mul_ps(z, *reinterpret_cast<const v4sf*>(_ps_0p5));
    y = _mm_sub_ps(y, tmp);

    tmp = _mm_mul_ps(e, *reinterpret_cast<const 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

    // zero arg will be -INFINITY
    x = _mm_andnot_ps(zero_mask, x);
    x = _mm_or_ps(x, _mm_and_ps(zero_mask, *reinterpret_cast<const v4sf*>(_ps_neg_infinity)));

    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);

inline v4sf exp_ps(v4sf x)
{
    v4sf tmp = _mm_setzero_ps(), fx;
#ifdef USE_SSE2
    v4si emm0;
#else
    v2si mm0, mm1;
#endif
    v4sf one = *reinterpret_cast<const v4sf*>(_ps_1);

    x = _mm_min_ps(x, *reinterpret_cast<const v4sf*>(_ps_exp_hi));
    x = _mm_max_ps(x, *reinterpret_cast<const v4sf*>(_ps_exp_lo));

    /* express exp(x) as exp(g + n*log(2)) */
    fx = _mm_mul_ps(x, *reinterpret_cast<const v4sf*>(_ps_cephes_LOG2EF));
    fx = _mm_add_ps(fx, *reinterpret_cast<const 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 */
    v4sf mask = _mm_cmpgt_ps(tmp, fx);
    mask = _mm_and_ps(mask, one);
    fx = _mm_sub_ps(tmp, mask);

    tmp = _mm_mul_ps(fx, *reinterpret_cast<const v4sf*>(_ps_cephes_exp_C1));
    v4sf z = _mm_mul_ps(fx, *reinterpret_cast<const v4sf*>(_ps_cephes_exp_C2));
    x = _mm_sub_ps(x, tmp);
    x = _mm_sub_ps(x, z);

    z = _mm_mul_ps(x, x);

    v4sf y = *reinterpret_cast<const v4sf*>(_ps_cephes_exp_p0);
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_exp_p1));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_exp_p2));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_exp_p3));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_cephes_exp_p4));
    y = _mm_mul_ps(y, x);
    y = _mm_add_ps(y, *reinterpret_cast<const 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, *reinterpret_cast<const v2si*>(_pi32_0x7f));
    mm1 = _mm_add_pi32(mm1, *reinterpret_cast<const v2si*>(_pi32_0x7f));
    mm0 = _mm_slli_pi32(mm0, 23);
    mm1 = _mm_slli_pi32(mm1, 23);

    v4sf pow2n;
    COPY_MM_TO_XMM(mm0, mm1, pow2n);
    _mm_empty();
#else
    emm0 = _mm_cvttps_epi32(fx);
    emm0 = _mm_add_epi32(emm0, *reinterpret_cast<const v4si*>(_pi32_0x7f));
    emm0 = _mm_slli_epi32(emm0, 23);
    v4sf pow2n = _mm_castsi128_ps(emm0);
#endif
    y = _mm_mul_ps(y, pow2n);
    return y;
}

// Fast logAdd function - Patrick Marks, 2013
// Make a rough approximation of
// log(exp(x) + exp(y))
//
//	Method:
//
//  Assume x > y, then convert to
//
//  x + log(1 + exp(y-x))
//
//  then use a polynomial approximation for
//  f(d) = log(1 + exp(d)) ~ (a0 + a1 * x + a2 * x^2 + x3 * x^3)^2
// polynomial a_n is:  0.829003478 0.307939048 0.042920466 0.002439664
// polynomial is chosen to have f(-6.0) = 0 -- this is where we cutoff the
// approximation to zero

// The full calculation using the log and exp methods above take ~115
// instructions.
// This method takes ~15 instructions

_PS_CONST(logAdd_a0, 0.829003478);
_PS_CONST(logAdd_a1, 0.307939048);
_PS_CONST(logAdd_a2, 0.042920466);
_PS_CONST(logAdd_a3, 0.002439664);

/* natural logarithm computed for 4 simultaneous float
   return NaN for x <= 0
*/
#if FALSE
inline v4sf logAddApprox_ps(v4sf x, v4sf y)
{

    v4sf big = _mm_max_ps(x, y);
    v4sf small = _mm_min_ps(x, y);

    // Diff is always <= 0
    v4sf diff = _mm_sub_ps(small, big);
    diff = _mm_max_ps(diff, _mm_set_ps1(-6.0f));

    // Run the polynomial on the diff

    v4sf bn = *reinterpret_cast<const v4sf*>(_ps_logAdd_a3);

    bn = _mm_mul_ps(bn, diff);
    bn = _mm_add_ps(bn, *reinterpret_cast<const v4sf*>(_ps_logAdd_a2));

    bn = _mm_mul_ps(bn, diff);
    bn = _mm_add_ps(bn, *reinterpret_cast<const v4sf*>(_ps_logAdd_a1));

    bn = _mm_mul_ps(bn, diff);
    bn = _mm_add_ps(bn, *reinterpret_cast<const v4sf*>(_ps_logAdd_a0));

    bn = _mm_mul_ps(bn, bn);

    return _mm_add_ps(big, bn);
}

#endif

_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.
*/
inline 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
    sign_bit = x;
    /* take the absolute value */
    x = _mm_and_ps(x, *reinterpret_cast<const v4sf*>(_ps_inv_sign_mask));
    /* extract the sign bit (upper one) */
    sign_bit = _mm_and_ps(sign_bit, *reinterpret_cast<const v4sf*>(_ps_sign_mask));

    /* scale by 4/Pi */
    y = _mm_mul_ps(x, *reinterpret_cast<const 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, *reinterpret_cast<const v4si*>(_pi32_1));
    emm2 = _mm_and_si128(emm2, *reinterpret_cast<const v4si*>(_pi32_inv1));
    y = _mm_cvtepi32_ps(emm2);
    /* get the swap sign flag */
    emm0 = _mm_and_si128(emm2, *reinterpret_cast<const 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, *reinterpret_cast<const v4si*>(_pi32_2));
    emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());

    v4sf swap_sign_bit = _mm_castsi128_ps(emm0);
    v4sf 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, *reinterpret_cast<const v2si*>(_pi32_1));
    mm3 = _mm_add_pi32(mm3, *reinterpret_cast<const v2si*>(_pi32_1));
    mm2 = _mm_and_si64(mm2, *reinterpret_cast<const v2si*>(_pi32_inv1));
    mm3 = _mm_and_si64(mm3, *reinterpret_cast<const v2si*>(_pi32_inv1));
    y = _mm_cvtpi32x2_ps(mm2, mm3);
    /* get the swap sign flag */
    mm0 = _mm_and_si64(mm2, *reinterpret_cast<const v2si*>(_pi32_4));
    mm1 = _mm_and_si64(mm3, *reinterpret_cast<const 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, *reinterpret_cast<const v2si*>(_pi32_2));
    mm3 = _mm_and_si64(mm3, *reinterpret_cast<const v2si*>(_pi32_2));
    mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64());
    mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64());
    v4sf 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 = *reinterpret_cast<const v4sf*>(_ps_minus_cephes_DP1);
    xmm2 = *reinterpret_cast<const v4sf*>(_ps_minus_cephes_DP2);
    xmm3 = *reinterpret_cast<const 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 = *reinterpret_cast<const v4sf*>(_ps_coscof_p0);
    v4sf z = _mm_mul_ps(x, x);

    y = _mm_mul_ps(y, z);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_coscof_p1));
    y = _mm_mul_ps(y, z);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_coscof_p2));
    y = _mm_mul_ps(y, z);
    y = _mm_mul_ps(y, z);
    v4sf tmp = _mm_mul_ps(z, *reinterpret_cast<const v4sf*>(_ps_0p5));
    y = _mm_sub_ps(y, tmp);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_1));

    /* Evaluate the second polynom  (Pi/4 <= x <= 0) */

    v4sf y2 = *reinterpret_cast<const v4sf*>(_ps_sincof_p0);
    y2 = _mm_mul_ps(y2, z);
    y2 = _mm_add_ps(y2, *reinterpret_cast<const v4sf*>(_ps_sincof_p1));
    y2 = _mm_mul_ps(y2, z);
    y2 = _mm_add_ps(y2, *reinterpret_cast<const 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 */
inline 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
    /* take the absolute value */
    x = _mm_and_ps(x, *reinterpret_cast<const v4sf*>(_ps_inv_sign_mask));

    /* scale by 4/Pi */
    y = _mm_mul_ps(x, *reinterpret_cast<const 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, *reinterpret_cast<const v4si*>(_pi32_1));
    emm2 = _mm_and_si128(emm2, *reinterpret_cast<const v4si*>(_pi32_inv1));
    y = _mm_cvtepi32_ps(emm2);

    emm2 = _mm_sub_epi32(emm2, *reinterpret_cast<const v4si*>(_pi32_2));

    /* get the swap sign flag */
    emm0 = _mm_andnot_si128(emm2, *reinterpret_cast<const v4si*>(_pi32_4));
    emm0 = _mm_slli_epi32(emm0, 29);
    /* get the polynom selection mask */
    emm2 = _mm_and_si128(emm2, *reinterpret_cast<const v4si*>(_pi32_2));
    emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());

    v4sf sign_bit = _mm_castsi128_ps(emm0);
    v4sf 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, *reinterpret_cast<const v2si*>(_pi32_1));
    mm3 = _mm_add_pi32(mm3, *reinterpret_cast<const v2si*>(_pi32_1));
    mm2 = _mm_and_si64(mm2, *reinterpret_cast<const v2si*>(_pi32_inv1));
    mm3 = _mm_and_si64(mm3, *reinterpret_cast<const v2si*>(_pi32_inv1));

    y = _mm_cvtpi32x2_ps(mm2, mm3);

    mm2 = _mm_sub_pi32(mm2, *reinterpret_cast<const v2si*>(_pi32_2));
    mm3 = _mm_sub_pi32(mm3, *reinterpret_cast<const v2si*>(_pi32_2));

    /* get the swap sign flag in mm0:mm1 and the
     polynom selection mask in mm2:mm3 */

    mm0 = _mm_andnot_si64(mm2, *reinterpret_cast<const v2si*>(_pi32_4));
    mm1 = _mm_andnot_si64(mm3, *reinterpret_cast<const v2si*>(_pi32_4));
    mm0 = _mm_slli_pi32(mm0, 29);
    mm1 = _mm_slli_pi32(mm1, 29);

    mm2 = _mm_and_si64(mm2, *reinterpret_cast<const v2si*>(_pi32_2));
    mm3 = _mm_and_si64(mm3, *reinterpret_cast<const v2si*>(_pi32_2));

    mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64());
    mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64());

    v4sf 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 = *reinterpret_cast<const v4sf*>(_ps_minus_cephes_DP1);
    xmm2 = *reinterpret_cast<const v4sf*>(_ps_minus_cephes_DP2);
    xmm3 = *reinterpret_cast<const 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 = *reinterpret_cast<const v4sf*>(_ps_coscof_p0);
    v4sf z = _mm_mul_ps(x, x);

    y = _mm_mul_ps(y, z);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_coscof_p1));
    y = _mm_mul_ps(y, z);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_coscof_p2));
    y = _mm_mul_ps(y, z);
    y = _mm_mul_ps(y, z);
    v4sf tmp = _mm_mul_ps(z, *reinterpret_cast<const v4sf*>(_ps_0p5));
    y = _mm_sub_ps(y, tmp);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_1));

    /* Evaluate the second polynom  (Pi/4 <= x <= 0) */

    v4sf y2 = *reinterpret_cast<const v4sf*>(_ps_sincof_p0);
    y2 = _mm_mul_ps(y2, z);
    y2 = _mm_add_ps(y2, *reinterpret_cast<const v4sf*>(_ps_sincof_p1));
    y2 = _mm_mul_ps(y2, z);
    y2 = _mm_add_ps(y2, *reinterpret_cast<const 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 */
inline 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
    sign_bit_sin = x;
    /* take the absolute value */
    x = _mm_and_ps(x, *reinterpret_cast<const v4sf*>(_ps_inv_sign_mask));
    /* extract the sign bit (upper one) */
    sign_bit_sin = _mm_and_ps(sign_bit_sin, *reinterpret_cast<const v4sf*>(_ps_sign_mask));

    /* scale by 4/Pi */
    y = _mm_mul_ps(x, *reinterpret_cast<const 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, *reinterpret_cast<const v4si*>(_pi32_1));
    emm2 = _mm_and_si128(emm2, *reinterpret_cast<const v4si*>(_pi32_inv1));
    y = _mm_cvtepi32_ps(emm2);

    emm4 = emm2;

    /* get the swap sign flag for the sine */
    emm0 = _mm_and_si128(emm2, *reinterpret_cast<const v4si*>(_pi32_4));
    emm0 = _mm_slli_epi32(emm0, 29);
    v4sf swap_sign_bit_sin = _mm_castsi128_ps(emm0);

    /* get the polynom selection mask for the sine*/
    emm2 = _mm_and_si128(emm2, *reinterpret_cast<const v4si*>(_pi32_2));
    emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
    v4sf 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, *reinterpret_cast<const v2si*>(_pi32_1));
    mm3 = _mm_add_pi32(mm3, *reinterpret_cast<const v2si*>(_pi32_1));
    mm2 = _mm_and_si64(mm2, *reinterpret_cast<const v2si*>(_pi32_inv1));
    mm3 = _mm_and_si64(mm3, *reinterpret_cast<const 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, *reinterpret_cast<const v2si*>(_pi32_4));
    mm1 = _mm_and_si64(mm3, *reinterpret_cast<const v2si*>(_pi32_4));
    mm0 = _mm_slli_pi32(mm0, 29);
    mm1 = _mm_slli_pi32(mm1, 29);
    v4sf 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, *reinterpret_cast<const v2si*>(_pi32_2));
    mm3 = _mm_and_si64(mm3, *reinterpret_cast<const v2si*>(_pi32_2));
    mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64());
    mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64());
    v4sf 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 = *reinterpret_cast<const v4sf*>(_ps_minus_cephes_DP1);
    xmm2 = *reinterpret_cast<const v4sf*>(_ps_minus_cephes_DP2);
    xmm3 = *reinterpret_cast<const 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, *reinterpret_cast<const v4si*>(_pi32_2));
    emm4 = _mm_andnot_si128(emm4, *reinterpret_cast<const v4si*>(_pi32_4));
    emm4 = _mm_slli_epi32(emm4, 29);
    v4sf sign_bit_cos = _mm_castsi128_ps(emm4);
#else
    /* get the sign flag for the cosine */
    mm4 = _mm_sub_pi32(mm4, *reinterpret_cast<const v2si*>(_pi32_2));
    mm5 = _mm_sub_pi32(mm5, *reinterpret_cast<const v2si*>(_pi32_2));
    mm4 = _mm_andnot_si64(mm4, *reinterpret_cast<const v2si*>(_pi32_4));
    mm5 = _mm_andnot_si64(mm5, *reinterpret_cast<const v2si*>(_pi32_4));
    mm4 = _mm_slli_pi32(mm4, 29);
    mm5 = _mm_slli_pi32(mm5, 29);
    v4sf 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) */
    v4sf z = _mm_mul_ps(x, x);
    y = *reinterpret_cast<const v4sf*>(_ps_coscof_p0);

    y = _mm_mul_ps(y, z);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_coscof_p1));
    y = _mm_mul_ps(y, z);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_coscof_p2));
    y = _mm_mul_ps(y, z);
    y = _mm_mul_ps(y, z);
    v4sf tmp = _mm_mul_ps(z, *reinterpret_cast<const v4sf*>(_ps_0p5));
    y = _mm_sub_ps(y, tmp);
    y = _mm_add_ps(y, *reinterpret_cast<const v4sf*>(_ps_1));

    /* Evaluate the second polynom  (Pi/4 <= x <= 0) */

    v4sf y2 = *reinterpret_cast<const v4sf*>(_ps_sincof_p0);
    y2 = _mm_mul_ps(y2, z);
    y2 = _mm_add_ps(y2, *reinterpret_cast<const v4sf*>(_ps_sincof_p1));
    y2 = _mm_mul_ps(y2, z);
    y2 = _mm_add_ps(y2, *reinterpret_cast<const 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;
    v4sf ysin2 = _mm_and_ps(xmm3, y2);
    v4sf 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);
}