simd_math.h File Reference

#include "config.h"
#include <math.h>
#include "gromacs/math/utilities.h"
#include "gromacs/simd/simd.h"

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Description

Math functions for SIMD datatypes.

Attention

This file is generic for all SIMD architectures, so you cannot assume that any of the optional SIMD features (as defined in simd.h) are present. In particular, this means you cannot assume support for integers, logical operations (neither on floating-point nor integer values), shifts, and the architecture might only have SIMD for either float or double. Second, to keep this file clean and general, any additions to this file must work for all possible SIMD architectures in both single and double precision (if they support it), and you cannot make any assumptions about SIMD width.

Author

Erik Lindahl erik..nosp@m.lind.nosp@m.ahl@s.nosp@m.cili.nosp@m.felab.nosp@m..se

SIMD4 math functions
#define	gmx_simd4_sum4_r   gmx_simd4_sum4_f
	SIMD4 utility function to sum a+b+c+d for SIMD4 reals. More...
#define	gmx_simd4_invsqrt_r   gmx_simd4_invsqrt_f
	Calculate 1/sqrt(x) for SIMD4 real. More...
#define	gmx_simd4_invsqrt_singleaccuracy_r   gmx_simd4_invsqrt_f
	1/sqrt(x) for SIMD4 real. Single accuracy, even for double prec. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd4_sum4_f (gmx_simd_float_t a, gmx_simd_float_t b, gmx_simd_float_t c, gmx_simd_float_t d)
	SIMD4 utility function to sum a+b+c+d for SIMD4 floats. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd4_rsqrt_iter_f (gmx_simd_float_t lu, gmx_simd_float_t x)
	Perform one Newton-Raphson iteration to improve 1/sqrt(x) for SIMD4 float. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd4_invsqrt_f (gmx_simd_float_t x)
	Calculate 1/sqrt(x) for SIMD4 float. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd4_sum4_d (gmx_simd_double_t a, gmx_simd_double_t b, gmx_simd_double_t c, gmx_simd_double_t d)
	SIMD4 utility function to sum a+b+c+d for SIMD4 doubles. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd4_rsqrt_iter_d (gmx_simd_double_t lu, gmx_simd_double_t x)
	Perform one Newton-Raphson iteration to improve 1/sqrt(x) for SIMD4 double. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd4_invsqrt_d (gmx_simd_double_t x)
	Calculate 1/sqrt(x) for SIMD4 double. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd4_invsqrt_singleaccuracy_d (gmx_simd_double_t x)
	Calculate 1/sqrt(x) for SIMD4 double, but in single accuracy. More...

Macros
Real-precision SIMD math functions
These are the ones you should typically call in Gromacs.
#define	gmx_simd_sum4_r   gmx_simd_sum4_f
	SIMD utility function to sum a+b+c+d for SIMD reals. More...
#define	gmx_simd_xor_sign_r   gmx_simd_xor_sign_f
	Return -a if b is negative, SIMD real. More...
#define	gmx_simd_invsqrt_r   gmx_simd_invsqrt_f
	Calculate 1/sqrt(x) for SIMD real. More...
#define	gmx_simd_invsqrt_pair_r   gmx_simd_invsqrt_pair_f
	Calculate 1/sqrt(x) for two SIMD reals. More...
#define	gmx_simd_sqrt_r   gmx_simd_sqrt_f
	Calculate sqrt(x) correctly for SIMD real, including argument 0.0. More...
#define	gmx_simd_inv_r   gmx_simd_inv_f
	Calculate 1/x for SIMD real. More...
#define	gmx_simd_log_r   gmx_simd_log_f
	SIMD real log(x). This is the natural logarithm. More...
#define	gmx_simd_exp2_r   gmx_simd_exp2_f
	SIMD real 2^x. More...
#define	gmx_simd_exp_r   gmx_simd_exp_f
	SIMD real e^x. More...
#define	gmx_simd_erf_r   gmx_simd_erf_f
	SIMD real erf(x). More...
#define	gmx_simd_erfc_r   gmx_simd_erfc_f
	SIMD real erfc(x). More...
#define	gmx_simd_sincos_r   gmx_simd_sincos_f
	SIMD real sin & cos. More...
#define	gmx_simd_sin_r   gmx_simd_sin_f
	SIMD real sin(x). More...
#define	gmx_simd_cos_r   gmx_simd_cos_f
	SIMD real cos(x). More...
#define	gmx_simd_tan_r   gmx_simd_tan_f
	SIMD real tan(x). More...
#define	gmx_simd_asin_r   gmx_simd_asin_f
	SIMD real asin(x). More...
#define	gmx_simd_acos_r   gmx_simd_acos_f
	SIMD real acos(x). More...
#define	gmx_simd_atan_r   gmx_simd_atan_f
	SIMD real atan(x). More...
#define	gmx_simd_atan2_r   gmx_simd_atan2_f
	SIMD real atan2(y,x). More...
#define	gmx_simd_pmecorrF_r   gmx_simd_pmecorrF_f
	SIMD Analytic PME force correction. More...
#define	gmx_simd_pmecorrV_r   gmx_simd_pmecorrV_f
	SIMD Analytic PME potential correction. More...
#define	gmx_simd_invsqrt_singleaccuracy_r   gmx_simd_invsqrt_f
	Calculate 1/sqrt(x) for SIMD, only targeting single accuracy. More...
#define	gmx_simd_invsqrt_pair_singleaccuracy_r   gmx_simd_invsqrt_pair_f
	Calculate 1/sqrt(x) for SIMD pair, only targeting single accuracy. More...
#define	gmx_simd_sqrt_singleaccuracy_r   gmx_simd_sqrt_f
	Calculate sqrt(x), only targeting single accuracy. More...
#define	gmx_simd_inv_singleaccuracy_r   gmx_simd_inv_f
	Calculate 1/x for SIMD real, only targeting single accuracy. More...
#define	gmx_simd_log_singleaccuracy_r   gmx_simd_log_f
	SIMD real log(x), only targeting single accuracy. More...
#define	gmx_simd_exp2_singleaccuracy_r   gmx_simd_exp2_f
	SIMD real 2^x, only targeting single accuracy. More...
#define	gmx_simd_exp_singleaccuracy_r   gmx_simd_exp_f
	SIMD real e^x, only targeting single accuracy. More...
#define	gmx_simd_erf_singleaccuracy_r   gmx_simd_erf_f
	SIMD real erf(x), only targeting single accuracy. More...
#define	gmx_simd_erfc_singleaccuracy_r   gmx_simd_erfc_f
	SIMD real erfc(x), only targeting single accuracy. More...
#define	gmx_simd_sincos_singleaccuracy_r   gmx_simd_sincos_f
	SIMD real sin & cos, only targeting single accuracy. More...
#define	gmx_simd_sin_singleaccuracy_r   gmx_simd_sin_f
	SIMD real sin(x), only targeting single accuracy. More...
#define	gmx_simd_cos_singleaccuracy_r   gmx_simd_cos_f
	SIMD real cos(x), only targeting single accuracy. More...
#define	gmx_simd_tan_singleaccuracy_r   gmx_simd_tan_f
	SIMD real tan(x), only targeting single accuracy. More...
#define	gmx_simd_asin_singleaccuracy_r   gmx_simd_asin_f
	SIMD real asin(x), only targeting single accuracy. More...
#define	gmx_simd_acos_singleaccuracy_r   gmx_simd_acos_f
	SIMD real acos(x), only targeting single accuracy. More...
#define	gmx_simd_atan_singleaccuracy_r   gmx_simd_atan_f
	SIMD real atan(x), only targeting single accuracy. More...
#define	gmx_simd_atan2_singleaccuracy_r   gmx_simd_atan2_f
	SIMD real atan2(y,x), only targeting single accuracy. More...
#define	gmx_simd_pmecorrF_singleaccuracy_r   gmx_simd_pmecorrF_f
	SIMD Analytic PME force corr., only targeting single accuracy. More...
#define	gmx_simd_pmecorrV_singleaccuracy_r   gmx_simd_pmecorrV_f
	SIMD Analytic PME potential corr., only targeting single accuracy. More...

Functions
Single precision SIMD math functions
Note In most cases you should use the real-precision functions instead.
static gmx_simd_float_t gmx_simdcall	gmx_simd_sum4_f (gmx_simd_float_t a, gmx_simd_float_t b, gmx_simd_float_t c, gmx_simd_float_t d)
	SIMD float utility to sum a+b+c+d. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_xor_sign_f (gmx_simd_float_t a, gmx_simd_float_t b)
	Return -a if b is negative, SIMD float. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_rsqrt_iter_f (gmx_simd_float_t lu, gmx_simd_float_t x)
	Perform one Newton-Raphson iteration to improve 1/sqrt(x) for SIMD float. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_invsqrt_f (gmx_simd_float_t x)
	Calculate 1/sqrt(x) for SIMD float. More...
static gmx_simd_float_t	gmx_simd_invsqrt_maskfpe_f (gmx_simd_float_t x, gmx_simd_fbool_t m)
	Calculate 1/sqrt(x) for masked entries of SIMD float. More...
static gmx_simd_float_t	gmx_simd_invsqrt_notmaskfpe_f (gmx_simd_float_t x, gmx_simd_fbool_t m)
	Calculate 1/sqrt(x) for non-masked entries of SIMD float. More...
static void gmx_simdcall	gmx_simd_invsqrt_pair_f (gmx_simd_float_t x0, gmx_simd_float_t x1, gmx_simd_float_t *out0, gmx_simd_float_t *out1)
	Calculate 1/sqrt(x) for two SIMD floats. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_rcp_iter_f (gmx_simd_float_t lu, gmx_simd_float_t x)
	Perform one Newton-Raphson iteration to improve 1/x for SIMD float. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_inv_f (gmx_simd_float_t x)
	Calculate 1/x for SIMD float. More...
static gmx_simd_float_t	gmx_simd_inv_maskfpe_f (gmx_simd_float_t x, gmx_simd_fbool_t m)
	Calculate 1/x for masked entries of SIMD float. More...
static gmx_simd_float_t	gmx_simd_inv_notmaskfpe_f (gmx_simd_float_t x, gmx_simd_fbool_t m)
	Calculate 1/x for non-masked entries of SIMD float. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_sqrt_f (gmx_simd_float_t x)
	Calculate sqrt(x) correctly for SIMD floats, including argument 0.0. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_log_f (gmx_simd_float_t x)
	SIMD float log(x). This is the natural logarithm. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_exp2_f (gmx_simd_float_t x)
	SIMD float 2^x. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_exp_f (gmx_simd_float_t x)
	SIMD float exp(x). More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_erf_f (gmx_simd_float_t x)
	SIMD float erf(x). More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_erfc_f (gmx_simd_float_t x)
	SIMD float erfc(x). More...
static void gmx_simdcall	gmx_simd_sincos_f (gmx_simd_float_t x, gmx_simd_float_t *sinval, gmx_simd_float_t *cosval)
	SIMD float sin & cos. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_sin_f (gmx_simd_float_t x)
	SIMD float sin(x). More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_cos_f (gmx_simd_float_t x)
	SIMD float cos(x). More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_tan_f (gmx_simd_float_t x)
	SIMD float tan(x). More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_asin_f (gmx_simd_float_t x)
	SIMD float asin(x). More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_acos_f (gmx_simd_float_t x)
	SIMD float acos(x). More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_atan_f (gmx_simd_float_t x)
	SIMD float asin(x). More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_atan2_f (gmx_simd_float_t y, gmx_simd_float_t x)
	SIMD float atan2(y,x). More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_pmecorrF_f (gmx_simd_float_t z2)
	Calculate the force correction due to PME analytically in SIMD float. More...
static gmx_simd_float_t gmx_simdcall	gmx_simd_pmecorrV_f (gmx_simd_float_t z2)
	Calculate the potential correction due to PME analytically in SIMD float. More...
Double precision SIMD math functions
Note In most cases you should use the real-precision functions instead.
static gmx_simd_double_t gmx_simdcall	gmx_simd_sum4_d (gmx_simd_double_t a, gmx_simd_double_t b, gmx_simd_double_t c, gmx_simd_double_t d)
	SIMD utility function to sum a+b+c+d for SIMD doubles. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_xor_sign_d (gmx_simd_double_t a, gmx_simd_double_t b)
	Return -a if b is negative, SIMD double. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_rsqrt_iter_d (gmx_simd_double_t lu, gmx_simd_double_t x)
	Perform one Newton-Raphson iteration to improve 1/sqrt(x) for SIMD double. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_invsqrt_d (gmx_simd_double_t x)
	Calculate 1/sqrt(x) for SIMD double. More...
static gmx_simd_double_t	gmx_simd_invsqrt_maskfpe_d (gmx_simd_double_t x, gmx_simd_dbool_t m)
	Calculate 1/sqrt(x) for masked entries of SIMD double. More...
static gmx_simd_double_t	gmx_simd_invsqrt_notmaskfpe_d (gmx_simd_double_t x, gmx_simd_dbool_t m)
	Calculate 1/sqrt(x) for non-masked entries of SIMD double. More...
static void gmx_simdcall	gmx_simd_invsqrt_pair_d (gmx_simd_double_t x0, gmx_simd_double_t x1, gmx_simd_double_t *out0, gmx_simd_double_t *out1)
	Calculate 1/sqrt(x) for two SIMD doubles. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_rcp_iter_d (gmx_simd_double_t lu, gmx_simd_double_t x)
	Perform one Newton-Raphson iteration to improve 1/x for SIMD double. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_inv_d (gmx_simd_double_t x)
	Calculate 1/x for SIMD double. More...
static gmx_simd_double_t	gmx_simd_inv_maskfpe_d (gmx_simd_double_t x, gmx_simd_dbool_t m)
	Calculate 1/x for masked entries of SIMD double. More...
static gmx_simd_double_t	gmx_simd_inv_notmaskfpe_d (gmx_simd_double_t x, gmx_simd_dbool_t m)
	Calculate 1/x for non-masked entries of SIMD double. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_sqrt_d (gmx_simd_double_t x)
	Calculate sqrt(x) correctly for SIMD doubles, including argument 0.0. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_log_d (gmx_simd_double_t x)
	SIMD double log(x). This is the natural logarithm. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_exp2_d (gmx_simd_double_t x)
	SIMD double 2^x. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_exp_d (gmx_simd_double_t x)
	SIMD double exp(x). More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_erf_d (gmx_simd_double_t x)
	SIMD double erf(x). More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_erfc_d (gmx_simd_double_t x)
	SIMD double erfc(x). More...
static void gmx_simdcall	gmx_simd_sincos_d (gmx_simd_double_t x, gmx_simd_double_t *sinval, gmx_simd_double_t *cosval)
	SIMD double sin & cos. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_sin_d (gmx_simd_double_t x)
	SIMD double sin(x). More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_cos_d (gmx_simd_double_t x)
	SIMD double cos(x). More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_tan_d (gmx_simd_double_t x)
	SIMD double tan(x). More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_asin_d (gmx_simd_double_t x)
	SIMD double asin(x). More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_acos_d (gmx_simd_double_t x)
	SIMD double acos(x). More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_atan_d (gmx_simd_double_t x)
	SIMD double atan(x). More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_atan2_d (gmx_simd_double_t y, gmx_simd_double_t x)
	SIMD double atan2(y,x). More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_pmecorrF_d (gmx_simd_double_t z2)
	Calculate the force correction due to PME analytically for SIMD double. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_pmecorrV_d (gmx_simd_double_t z2)
	Calculate the potential correction due to PME analytically for SIMD double. More...
SIMD math functions for double prec. data, single prec. accuracy
Note In some cases we do not need full double accuracy of individual SIMD math functions, although the data is stored in double precision SIMD registers. This might be the case for special algorithms, or if the architecture does not support single precision. Since the full double precision evaluation of math functions typically require much more expensive polynomial approximations these functions implement the algorithms used in the single precision SIMD math functions, but they operate on double precision SIMD variables. You should normally not use these functions directly, but the real-precision wrappers instead. When Gromacs is compiled in single precision, those will be aliases to the normal single precision SIMD math functions.
static gmx_simd_double_t gmx_simdcall	gmx_simd_invsqrt_singleaccuracy_d (gmx_simd_double_t x)
	Calculate 1/sqrt(x) for SIMD double, but in single accuracy. More...
static gmx_simd_double_t	gmx_simd_invsqrt_maskfpe_singleaccuracy_d (gmx_simd_double_t x, gmx_simd_dbool_t m)
	1/sqrt(x) for masked entries of SIMD double, but in single accuracy. More...
static gmx_simd_double_t	gmx_simd_invsqrt_notmaskfpe_singleaccuracy_d (gmx_simd_double_t x, gmx_simd_dbool_t m)
	1/sqrt(x) for non-masked entries of SIMD double, in single accuracy. More...
static void gmx_simdcall	gmx_simd_invsqrt_pair_singleaccuracy_d (gmx_simd_double_t x0, gmx_simd_double_t x1, gmx_simd_double_t *out0, gmx_simd_double_t *out1)
	Calculate 1/sqrt(x) for two SIMD doubles, but single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_inv_singleaccuracy_d (gmx_simd_double_t x)
	Calculate 1/x for SIMD double, but in single accuracy. More...
static gmx_simd_double_t	gmx_simd_inv_maskfpe_singleaccuracy_d (gmx_simd_double_t x, gmx_simd_dbool_t m)
	1/x for masked entries of SIMD double, single accuracy. More...
static gmx_simd_double_t	gmx_simd_inv_notmaskfpe_singleaccuracy_d (gmx_simd_double_t x, gmx_simd_dbool_t m)
	1/x for non-masked entries of SIMD double, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_sqrt_singleaccuracy_d (gmx_simd_double_t x)
	Calculate sqrt(x) (correct for 0.0) for SIMD double, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_log_singleaccuracy_d (gmx_simd_double_t x)
	SIMD log(x). Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_exp2_singleaccuracy_d (gmx_simd_double_t x)
	SIMD 2^x. Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_exp_singleaccuracy_d (gmx_simd_double_t x)
	SIMD exp(x). Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_erf_singleaccuracy_d (gmx_simd_double_t x)
	SIMD erf(x). Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_erfc_singleaccuracy_d (gmx_simd_double_t x)
	SIMD erfc(x). Double precision SIMD data, single accuracy. More...
static void gmx_simdcall	gmx_simd_sincos_singleaccuracy_d (gmx_simd_double_t x, gmx_simd_double_t *sinval, gmx_simd_double_t *cosval)
	SIMD sin & cos. Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_sin_singleaccuracy_d (gmx_simd_double_t x)
	SIMD sin(x). Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_cos_singleaccuracy_d (gmx_simd_double_t x)
	SIMD cos(x). Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_tan_singleaccuracy_d (gmx_simd_double_t x)
	SIMD tan(x). Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_asin_singleaccuracy_d (gmx_simd_double_t x)
	SIMD asin(x). Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_acos_singleaccuracy_d (gmx_simd_double_t x)
	SIMD acos(x). Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_atan_singleaccuracy_d (gmx_simd_double_t x)
	SIMD asin(x). Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_atan2_singleaccuracy_d (gmx_simd_double_t y, gmx_simd_double_t x)
	SIMD atan2(y,x). Double precision SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_pmecorrF_singleaccuracy_d (gmx_simd_double_t z2)
	Analytical PME force correction, double SIMD data, single accuracy. More...
static gmx_simd_double_t gmx_simdcall	gmx_simd_pmecorrV_singleaccuracy_d (gmx_simd_double_t z2)
	Analytical PME potential correction, double SIMD data, single accuracy. More...