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eigen/Eigen/src/Core/arch/SSE/MathFunctions.h
Hauke Heibel 9d6afdeb22 ei_psqrt fix for zero input
2010-04-01 15:10:52 +02:00

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007 Julien Pommier
// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
/* The sin, cos, exp, and log functions of this file come from
* Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
*/
#ifndef EIGEN_MATH_FUNCTIONS_SSE_H
#define EIGEN_MATH_FUNCTIONS_SSE_H
static EIGEN_DONT_INLINE EIGEN_UNUSED Packet4f ei_plog(Packet4f x)
{
_EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
_EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
_EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
_EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
/* the smallest non denormalized float number */
_EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
/* natural logarithm computed for 4 simultaneous float
return NaN for x <= 0
*/
_EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
Packet4i emm0;
Packet4f invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps());
x = ei_pmax(x, ei_p4f_min_norm_pos); /* cut off denormalized stuff */
emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
/* keep only the fractional part */
x = _mm_and_ps(x, ei_p4f_inv_mant_mask);
x = _mm_or_ps(x, ei_p4f_half);
emm0 = _mm_sub_epi32(emm0, ei_p4i_0x7f);
Packet4f e = ei_padd(_mm_cvtepi32_ps(emm0), ei_p4f_1);
/* part2:
if( x < SQRTHF ) {
e -= 1;
x = x + x - 1.0;
} else { x = x - 1.0; }
*/
Packet4f mask = _mm_cmplt_ps(x, ei_p4f_cephes_SQRTHF);
Packet4f tmp = _mm_and_ps(x, mask);
x = ei_psub(x, ei_p4f_1);
e = ei_psub(e, _mm_and_ps(ei_p4f_1, mask));
x = ei_padd(x, tmp);
Packet4f x2 = ei_pmul(x,x);
Packet4f x3 = ei_pmul(x2,x);
Packet4f y, y1, y2;
y = ei_pmadd(ei_p4f_cephes_log_p0, x, ei_p4f_cephes_log_p1);
y1 = ei_pmadd(ei_p4f_cephes_log_p3, x, ei_p4f_cephes_log_p4);
y2 = ei_pmadd(ei_p4f_cephes_log_p6, x, ei_p4f_cephes_log_p7);
y = ei_pmadd(y , x, ei_p4f_cephes_log_p2);
y1 = ei_pmadd(y1, x, ei_p4f_cephes_log_p5);
y2 = ei_pmadd(y2, x, ei_p4f_cephes_log_p8);
y = ei_pmadd(y, x3, y1);
y = ei_pmadd(y, x3, y2);
y = ei_pmul(y, x3);
y1 = ei_pmul(e, ei_p4f_cephes_log_q1);
tmp = ei_pmul(x2, ei_p4f_half);
y = ei_padd(y, y1);
x = ei_psub(x, tmp);
y2 = ei_pmul(e, ei_p4f_cephes_log_q2);
x = ei_padd(x, y);
x = ei_padd(x, y2);
return _mm_or_ps(x, invalid_mask); // negative arg will be NAN
}
static EIGEN_DONT_INLINE EIGEN_UNUSED Packet4f ei_pexp(Packet4f x)
{
_EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
_EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
_EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
_EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647949f);
_EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
Packet4f tmp = _mm_setzero_ps(), fx;
Packet4i emm0;
// clamp x
x = ei_pmax(ei_pmin(x, ei_p4f_exp_hi), ei_p4f_exp_lo);
/* express exp(x) as exp(g + n*log(2)) */
fx = ei_pmadd(x, ei_p4f_cephes_LOG2EF, ei_p4f_half);
/* how to perform a floorf with SSE: just below */
emm0 = _mm_cvttps_epi32(fx);
tmp = _mm_cvtepi32_ps(emm0);
/* if greater, substract 1 */
Packet4f mask = _mm_cmpgt_ps(tmp, fx);
mask = _mm_and_ps(mask, ei_p4f_1);
fx = ei_psub(tmp, mask);
tmp = ei_pmul(fx, ei_p4f_cephes_exp_C1);
Packet4f z = ei_pmul(fx, ei_p4f_cephes_exp_C2);
x = ei_psub(x, tmp);
x = ei_psub(x, z);
z = ei_pmul(x,x);
Packet4f y = ei_p4f_cephes_exp_p0;
y = ei_pmadd(y, x, ei_p4f_cephes_exp_p1);
y = ei_pmadd(y, x, ei_p4f_cephes_exp_p2);
y = ei_pmadd(y, x, ei_p4f_cephes_exp_p3);
y = ei_pmadd(y, x, ei_p4f_cephes_exp_p4);
y = ei_pmadd(y, x, ei_p4f_cephes_exp_p5);
y = ei_pmadd(y, z, x);
y = ei_padd(y, ei_p4f_1);
/* build 2^n */
emm0 = _mm_cvttps_epi32(fx);
emm0 = _mm_add_epi32(emm0, ei_p4i_0x7f);
emm0 = _mm_slli_epi32(emm0, 23);
return ei_pmul(y, _mm_castsi128_ps(emm0));
}
/* evaluation of 4 sines at onces, using SSE2 intrinsics.
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.
*/
static EIGEN_DONT_INLINE EIGEN_UNUSED Packet4f ei_psin(Packet4f x)
{
_EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
_EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
_EIGEN_DECLARE_CONST_Packet4i(1, 1);
_EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
_EIGEN_DECLARE_CONST_Packet4i(2, 2);
_EIGEN_DECLARE_CONST_Packet4i(4, 4);
_EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
_EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
_EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
_EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
_EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
_EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
_EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
Packet4i emm0, emm2;
sign_bit = x;
/* take the absolute value */
x = ei_pabs(x);
/* take the modulo */
/* extract the sign bit (upper one) */
sign_bit = _mm_and_ps(sign_bit, ei_p4f_sign_mask);
/* scale by 4/Pi */
y = ei_pmul(x, ei_p4f_cephes_FOPI);
/* 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, ei_p4i_1);
emm2 = _mm_and_si128(emm2, ei_p4i_not1);
y = _mm_cvtepi32_ps(emm2);
/* get the swap sign flag */
emm0 = _mm_and_si128(emm2, ei_p4i_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, ei_p4i_2);
emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
Packet4f poly_mask = _mm_castsi128_ps(emm2);
sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
/* The magic pass: "Extended precision modular arithmetic"
x = ((x - y * DP1) - y * DP2) - y * DP3; */
xmm1 = ei_pmul(y, ei_p4f_minus_cephes_DP1);
xmm2 = ei_pmul(y, ei_p4f_minus_cephes_DP2);
xmm3 = ei_pmul(y, ei_p4f_minus_cephes_DP3);
x = ei_padd(x, xmm1);
x = ei_padd(x, xmm2);
x = ei_padd(x, xmm3);
/* Evaluate the first polynom (0 <= x <= Pi/4) */
y = ei_p4f_coscof_p0;
Packet4f z = _mm_mul_ps(x,x);
y = ei_pmadd(y, z, ei_p4f_coscof_p1);
y = ei_pmadd(y, z, ei_p4f_coscof_p2);
y = ei_pmul(y, z);
y = ei_pmul(y, z);
Packet4f tmp = ei_pmul(z, ei_p4f_half);
y = ei_psub(y, tmp);
y = ei_padd(y, ei_p4f_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
Packet4f y2 = ei_p4f_sincof_p0;
y2 = ei_pmadd(y2, z, ei_p4f_sincof_p1);
y2 = ei_pmadd(y2, z, ei_p4f_sincof_p2);
y2 = ei_pmul(y2, z);
y2 = ei_pmul(y2, x);
y2 = ei_padd(y2, x);
/* select the correct result from the two polynoms */
y2 = _mm_and_ps(poly_mask, y2);
y = _mm_andnot_ps(poly_mask, y);
y = _mm_or_ps(y,y2);
/* update the sign */
return _mm_xor_ps(y, sign_bit);
}
/* almost the same as ei_psin */
static EIGEN_DONT_INLINE EIGEN_UNUSED Packet4f ei_pcos(Packet4f x)
{
_EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
_EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
_EIGEN_DECLARE_CONST_Packet4i(1, 1);
_EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
_EIGEN_DECLARE_CONST_Packet4i(2, 2);
_EIGEN_DECLARE_CONST_Packet4i(4, 4);
_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
_EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
_EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
_EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
_EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
_EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
_EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
_EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
Packet4i emm0, emm2;
x = ei_pabs(x);
/* scale by 4/Pi */
y = ei_pmul(x, ei_p4f_cephes_FOPI);
/* get the integer part of y */
emm2 = _mm_cvttps_epi32(y);
/* j=(j+1) & (~1) (see the cephes sources) */
emm2 = _mm_add_epi32(emm2, ei_p4i_1);
emm2 = _mm_and_si128(emm2, ei_p4i_not1);
y = _mm_cvtepi32_ps(emm2);
emm2 = _mm_sub_epi32(emm2, ei_p4i_2);
/* get the swap sign flag */
emm0 = _mm_andnot_si128(emm2, ei_p4i_4);
emm0 = _mm_slli_epi32(emm0, 29);
/* get the polynom selection mask */
emm2 = _mm_and_si128(emm2, ei_p4i_2);
emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
Packet4f sign_bit = _mm_castsi128_ps(emm0);
Packet4f poly_mask = _mm_castsi128_ps(emm2);
/* The magic pass: "Extended precision modular arithmetic"
x = ((x - y * DP1) - y * DP2) - y * DP3; */
xmm1 = ei_pmul(y, ei_p4f_minus_cephes_DP1);
xmm2 = ei_pmul(y, ei_p4f_minus_cephes_DP2);
xmm3 = ei_pmul(y, ei_p4f_minus_cephes_DP3);
x = ei_padd(x, xmm1);
x = ei_padd(x, xmm2);
x = ei_padd(x, xmm3);
/* Evaluate the first polynom (0 <= x <= Pi/4) */
y = ei_p4f_coscof_p0;
Packet4f z = ei_pmul(x,x);
y = ei_pmadd(y,z,ei_p4f_coscof_p1);
y = ei_pmadd(y,z,ei_p4f_coscof_p2);
y = ei_pmul(y, z);
y = ei_pmul(y, z);
Packet4f tmp = _mm_mul_ps(z, ei_p4f_half);
y = ei_psub(y, tmp);
y = ei_padd(y, ei_p4f_1);
/* Evaluate the second polynom (Pi/4 <= x <= 0) */
Packet4f y2 = ei_p4f_sincof_p0;
y2 = ei_pmadd(y2, z, ei_p4f_sincof_p1);
y2 = ei_pmadd(y2, z, ei_p4f_sincof_p2);
y2 = ei_pmul(y2, z);
y2 = ei_pmadd(y2, x, x);
/* select the correct result from the two polynoms */
y2 = _mm_and_ps(poly_mask, y2);
y = _mm_andnot_ps(poly_mask, y);
y = _mm_or_ps(y,y2);
/* update the sign */
return _mm_xor_ps(y, sign_bit);
}
// This is Quake3's fast inverse square root.
// For detail see here: http://www.beyond3d.com/content/articles/8/
static EIGEN_UNUSED Packet4f ei_psqrt(Packet4f _x)
{
Packet4f half = ei_pmul(_x, ei_pset1(.5f));
/* select only the inverse sqrt of non-zero inputs */
Packet4f non_zero_mask = _mm_cmpgt_ps(_x, ei_pset1(std::numeric_limits<float>::epsilon()));
Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
x = ei_pmul(x, ei_psub(ei_pset1(1.5f), ei_pmul(half, ei_pmul(x,x))));
return ei_pmul(_x,x);
}
#endif // EIGEN_MATH_FUNCTIONS_SSE_H
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