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vectormath_lib.h
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vectormath_lib.h
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/**************************** vectormath_lib.h *****************************
* Author: Agner Fog
* Date created: 2012-05-30
* Last modified: 2022-08-02
* Version: 2.02.00
* Project: vector class library
* Description:
* Header file defining mathematical functions on floating point vectors
* using Intel SVML (Short Vector Math Library)
*
* Include this file if you want to use SVML for math functions on vectors
* See vcl_manual.pdf for details on how to obtain the SVML library and link to it.
* Alternatively, use the inline math functions by including
* vectormath_exp.h for power and exponential functions,
* vectormath_trig.h for trigonometric functions,
* vectormath_hyp.h for hyperbolic functions
*
* For detailed instructions, see vcl_manual.pdf
*
* (c) Copyright 2012-2022 Agner Fog.
* Apache License version 2.0 or later.
\*****************************************************************************/
// check combination of header files
#ifndef VECTORMATH_LIB_H
#define VECTORMATH_LIB_H 202
#ifdef VECTORMATH_COMMON_H
#error conflicting header files. More than one implementation of mathematical functions included
#else
#include "vectorclass.h" // make sure vector classes are defined first
#ifdef VCL_NAMESPACE
namespace VCL_NAMESPACE { // optional name space
#endif
#if defined(__INTEL_COMPILER) || defined(__INTEL_LLVM_COMPILER)
#define USE_SVML_INTRINSICS // Intel compilers have intrinsic functions of access to SVML library
#endif
#if !(defined(USE_SVML_INTRINSICS))
// sinpi, cospi, and tanpi functions are included in SVML, but undocumented
// (The "Classic" version of Intel compiler accepts the intrinsics of these functions even though they are not in the header files)
#define TRIGPI_FUNCTIONS
#endif
#if defined(__clang__) || defined (__GNUC__)
#define SINCOS_ASM // sincos can be fixed with inline assembly
#else
// MS compiler does not support inline assembly. sincos not available
#endif
#ifdef USE_SVML_INTRINSICS
/*****************************************************************************
*
* 128-bit vector functions using Intel compiler intrinsic functions
*
*****************************************************************************/
// exponential and power functions
static inline Vec4f exp(Vec4f const x) { // exponential function
return _mm_exp_ps(x);
}
static inline Vec2d exp(Vec2d const x) { // exponential function
return _mm_exp_pd(x);
}
static inline Vec4f expm1(Vec4f const x) { // exp(x)-1. Avoids loss of precision if x is close to 1
return _mm_expm1_ps(x);
}
static inline Vec2d expm1(Vec2d const x) { // exp(x)-1. Avoids loss of precision if x is close to 1
return _mm_expm1_pd(x);
}
static inline Vec4f exp2(Vec4f const x) { // pow(2,x)
return _mm_exp2_ps(x);
}
static inline Vec2d exp2(Vec2d const x) { // pow(2,x)
return _mm_exp2_pd(x);
}
static inline Vec4f exp10(Vec4f const x) { // pow(10,x)
return _mm_exp10_ps(x);
}
static inline Vec2d exp10(Vec2d const x) { // pow(10,x)
return _mm_exp10_pd(x);
}
static inline Vec4f pow(Vec4f const a, Vec4f const b) { // pow(a,b) = a to the power of b
return _mm_pow_ps(a, b);
}
static inline Vec4f pow(Vec4f const a, float const b) { // pow(a,b) = a to the power of b
return _mm_pow_ps(a, Vec4f(b));
}
static inline Vec2d pow(Vec2d const a, Vec2d const b) { // pow(a,b) = a to the power of b
return _mm_pow_pd(a, b);
}
static inline Vec2d pow(Vec2d const a, double const b) { // pow(a,b) = a to the power of b
return _mm_pow_pd(a, Vec2d(b));
}
static inline Vec4f cbrt(Vec4f const x) { // pow(x,1/3)
return _mm_cbrt_ps(x);
}
static inline Vec2d cbrt(Vec2d const x) { // pow(x,1/3)
return _mm_cbrt_pd(x);
}
// logarithms
static inline Vec4f log(Vec4f const x) { // natural logarithm
return _mm_log_ps(x);
}
static inline Vec2d log(Vec2d const x) { // natural logarithm
return _mm_log_pd(x);
}
static inline Vec4f log1p(Vec4f const x) { // log(1+x). Avoids loss of precision if 1+x is close to 1
return _mm_log1p_ps(x);
}
static inline Vec2d log1p(Vec2d const x) { // log(1+x). Avoids loss of precision if 1+x is close to 1
return _mm_log1p_pd(x);
}
static inline Vec4f log2(Vec4f const x) { // logarithm base 2
return _mm_log2_ps(x);
}
static inline Vec2d log2(Vec2d const x) { // logarithm base 2
return _mm_log2_pd(x);
}
static inline Vec4f log10(Vec4f const x) { // logarithm base 10
return _mm_log10_ps(x);
}
static inline Vec2d log10(Vec2d const x) { // logarithm base 10
return _mm_log10_pd(x);
}
// trigonometric functions
static inline Vec4f sin(Vec4f const x) { // sine
return _mm_sin_ps(x);
}
static inline Vec2d sin(Vec2d const x) { // sine
return _mm_sin_pd(x);
}
static inline Vec4f cos(Vec4f const x) { // cosine
return _mm_cos_ps(x);
}
static inline Vec2d cos(Vec2d const x) { // cosine
return _mm_cos_pd(x);
}
static inline Vec4f sincos(Vec4f * pcos, Vec4f const x) { // sine and cosine. sin(x) returned, cos(x) in pcos
__m128 r_sin, r_cos;
r_sin = _mm_sincos_ps(&r_cos, x);
*pcos = r_cos;
return r_sin;
}
static inline Vec2d sincos(Vec2d * pcos, Vec2d const x) { // sine and cosine. sin(x) returned, cos(x) in pcos
__m128d r_sin, r_cos;
r_sin = _mm_sincos_pd(&r_cos, x);
*pcos = r_cos;
return r_sin;
}
static inline Vec4f tan(Vec4f const x) { // tangent
return _mm_tan_ps(x);
}
static inline Vec2d tan(Vec2d const x) { // tangent
return _mm_tan_pd(x);
}
#ifdef TRIGPI_FUNCTIONS
static inline Vec4f sinpi(Vec4f const x) { // sine
return _mm_sinpi_ps(x);
}
static inline Vec2d sinpi(Vec2d const x) { // sine
return _mm_sinpi_pd(x);
}
static inline Vec4f cospi(Vec4f const x) { // cosine
return _mm_cospi_ps(x);
}
static inline Vec2d cospi(Vec2d const x) { // cosine
return _mm_cospi_pd(x);
}
static inline Vec4f tanpi(Vec4f const x) { // tangent
return _mm_tanpi_ps(x);
}
static inline Vec2d tanpi(Vec2d const x) { // tangent
return _mm_tanpi_pd(x);
}
#endif // TRIGPI_FUNCTIONS
// inverse trigonometric functions
static inline Vec4f asin(Vec4f const x) { // inverse sine
return _mm_asin_ps(x);
}
static inline Vec2d asin(Vec2d const x) { // inverse sine
return _mm_asin_pd(x);
}
static inline Vec4f acos(Vec4f const x) { // inverse cosine
return _mm_acos_ps(x);
}
static inline Vec2d acos(Vec2d const x) { // inverse cosine
return _mm_acos_pd(x);
}
static inline Vec4f atan(Vec4f const x) { // inverse tangent
return _mm_atan_ps(x);
}
static inline Vec2d atan(Vec2d const x) { // inverse tangent
return _mm_atan_pd(x);
}
static inline Vec4f atan2(Vec4f const a, Vec4f const b) { // inverse tangent of a/b
return _mm_atan2_ps(a, b);
}
static inline Vec2d atan2(Vec2d const a, Vec2d const b) { // inverse tangent of a/b
return _mm_atan2_pd(a, b);
}
// hyperbolic functions and inverse hyperbolic functions
static inline Vec4f sinh(Vec4f const x) { // hyperbolic sine
return _mm_sinh_ps(x);
}
static inline Vec2d sinh(Vec2d const x) { // hyperbolic sine
return _mm_sinh_pd(x);
}
static inline Vec4f cosh(Vec4f const x) { // hyperbolic cosine
return _mm_cosh_ps(x);
}
static inline Vec2d cosh(Vec2d const x) { // hyperbolic cosine
return _mm_cosh_pd(x);
}
static inline Vec4f tanh(Vec4f const x) { // hyperbolic tangent
return _mm_tanh_ps(x);
}
static inline Vec2d tanh(Vec2d const x) { // hyperbolic tangent
return _mm_tanh_pd(x);
}
static inline Vec4f asinh(Vec4f const x) { // inverse hyperbolic sine
return _mm_asinh_ps(x);
}
static inline Vec2d asinh(Vec2d const x) { // inverse hyperbolic sine
return _mm_asinh_pd(x);
}
static inline Vec4f acosh(Vec4f const x) { // inverse hyperbolic cosine
return _mm_acosh_ps(x);
}
static inline Vec2d acosh(Vec2d const x) { // inverse hyperbolic cosine
return _mm_acosh_pd(x);
}
static inline Vec4f atanh(Vec4f const x) { // inverse hyperbolic tangent
return _mm_atanh_ps(x);
}
static inline Vec2d atanh(Vec2d const x) { // inverse hyperbolic tangent
return _mm_atanh_pd(x);
}
// error function
static inline Vec4f erf(Vec4f const x) { // error function
return _mm_erf_ps(x);
}
static inline Vec2d erf(Vec2d const x) { // error function
return _mm_erf_pd(x);
}
static inline Vec4f erfc(Vec4f const x) { // error function complement
return _mm_erfc_ps(x);
}
static inline Vec2d erfc(Vec2d const x) { // error function complement
return _mm_erfc_pd(x);
}
static inline Vec4f erfinv(Vec4f const x) { // inverse error function
return _mm_erfinv_ps(x);
}
static inline Vec2d erfinv(Vec2d const x) { // inverse error function
return _mm_erfinv_pd(x);
}
static inline Vec4f cdfnorm(Vec4f const x) { // cumulative normal distribution function
return _mm_cdfnorm_ps(x);
}
static inline Vec2d cdfnorm(Vec2d const x) { // cumulative normal distribution function
return _mm_cdfnorm_pd(x);
}
static inline Vec4f cdfnorminv(Vec4f const x) { // inverse cumulative normal distribution function
return _mm_cdfnorminv_ps(x);
}
static inline Vec2d cdfnorminv(Vec2d const x) { // inverse cumulative normal distribution function
return _mm_cdfnorminv_pd(x);
}
#else
/*************************************************************************************
*
* 128-bit vector functions using other compiler than Intel C++ compiler "Classic"
*
*************************************************************************************/
#if (defined(_WIN64) && !defined(USE_SVML_INTRINSICS) )
// (call with one parameter may work without __vectorcall because the parameter happens to be in zmm0, but that would be unsafe)
#define V_VECTORCALL __vectorcall // fix calling convention, one parameter.
#define V_VECTORCALL2 __vectorcall // fix calling convention, two parameters or two returns
#else
#define V_VECTORCALL
#define V_VECTORCALL2
#endif
// External function prototypes for SVML library, 128-bit vectors
extern "C" {
extern __m128 V_VECTORCALL __svml_expf4 (__m128);
extern __m128d V_VECTORCALL __svml_exp2 (__m128d);
extern __m128 V_VECTORCALL __svml_expm1f4 (__m128);
extern __m128d V_VECTORCALL __svml_expm12 (__m128d);
extern __m128 V_VECTORCALL __svml_exp2f4 (__m128);
extern __m128d V_VECTORCALL __svml_exp22 (__m128d);
extern __m128 V_VECTORCALL __svml_exp10f4 (__m128);
extern __m128d V_VECTORCALL __svml_exp102 (__m128d);
extern __m128 V_VECTORCALL2 __svml_powf4 (__m128, __m128);
extern __m128d V_VECTORCALL2 __svml_pow2 (__m128d, __m128d);
extern __m128 V_VECTORCALL __svml_cbrtf4 (__m128);
extern __m128d V_VECTORCALL __svml_cbrt2 (__m128d);
extern __m128 V_VECTORCALL __svml_invsqrtf4 (__m128);
extern __m128d V_VECTORCALL __svml_invsqrt2 (__m128d);
extern __m128 V_VECTORCALL __svml_logf4 (__m128);
extern __m128d V_VECTORCALL __svml_log2 (__m128d);
extern __m128 V_VECTORCALL __svml_log1pf4 (__m128);
extern __m128d V_VECTORCALL __svml_log1p2 (__m128d);
extern __m128 V_VECTORCALL __svml_log2f4 (__m128);
extern __m128d V_VECTORCALL __svml_log22 (__m128d);
extern __m128 V_VECTORCALL __svml_log10f4 (__m128);
extern __m128d V_VECTORCALL __svml_log102 (__m128d);
extern __m128 V_VECTORCALL __svml_sinf4 (__m128);
extern __m128d V_VECTORCALL __svml_sin2 (__m128d);
extern __m128 V_VECTORCALL __svml_cosf4 (__m128);
extern __m128d V_VECTORCALL __svml_cos2 (__m128d);
extern __m128 V_VECTORCALL2 __svml_sincosf4 (__m128); // cos returned in xmm1
extern __m128d V_VECTORCALL2 __svml_sincos2 (__m128d); // cos returned in xmm1
extern __m128 V_VECTORCALL __svml_tanf4 (__m128);
extern __m128d V_VECTORCALL __svml_tan2 (__m128d);
extern __m128 V_VECTORCALL __svml_sinpif4 (__m128);
extern __m128d V_VECTORCALL __svml_sinpi2 (__m128d);
extern __m128 V_VECTORCALL __svml_cospif4 (__m128);
extern __m128d V_VECTORCALL __svml_cospi2 (__m128d);
//extern __m128 V_VECTORCALL2 __svml_sincospif4 (__m128); // not in library
//extern __m128d V_VECTORCALL2 __svml_sincospi2 (__m128d);// not in library
extern __m128 V_VECTORCALL __svml_tanpif4 (__m128);
extern __m128d V_VECTORCALL __svml_tanpi2 (__m128d);
extern __m128 V_VECTORCALL __svml_asinf4 (__m128);
extern __m128d V_VECTORCALL __svml_asin2 (__m128d);
extern __m128 V_VECTORCALL __svml_acosf4 (__m128);
extern __m128d V_VECTORCALL __svml_acos2 (__m128d);
extern __m128 V_VECTORCALL __svml_atanf4 (__m128);
extern __m128d V_VECTORCALL __svml_atan2 (__m128d);
extern __m128 V_VECTORCALL2 __svml_atan2f4 (__m128, __m128);
extern __m128d V_VECTORCALL2 __svml_atan22 (__m128d, __m128d);
extern __m128 V_VECTORCALL __svml_sinhf4 (__m128);
extern __m128d V_VECTORCALL __svml_sinh2 (__m128d);
extern __m128 V_VECTORCALL __svml_coshf4 (__m128);
extern __m128d V_VECTORCALL __svml_cosh2 (__m128d);
extern __m128 V_VECTORCALL __svml_tanhf4 (__m128);
extern __m128d V_VECTORCALL __svml_tanh2 (__m128d);
extern __m128 V_VECTORCALL __svml_asinhf4 (__m128);
extern __m128d V_VECTORCALL __svml_asinh2 (__m128d);
extern __m128 V_VECTORCALL __svml_acoshf4 (__m128);
extern __m128d V_VECTORCALL __svml_acosh2 (__m128d);
extern __m128 V_VECTORCALL __svml_atanhf4 (__m128);
extern __m128d V_VECTORCALL __svml_atanh2 (__m128d);
extern __m128 V_VECTORCALL __svml_erff4 (__m128);
extern __m128d V_VECTORCALL __svml_erf2 (__m128d);
extern __m128 V_VECTORCALL __svml_erfcf4 (__m128);
extern __m128d V_VECTORCALL __svml_erfc2 (__m128d);
extern __m128 V_VECTORCALL __svml_erfinvf4 (__m128);
extern __m128d V_VECTORCALL __svml_erfinv2 (__m128d);
extern __m128 V_VECTORCALL __svml_cdfnormf4 (__m128);
extern __m128d V_VECTORCALL __svml_cdfnorm2 (__m128d);
extern __m128 V_VECTORCALL __svml_cdfnorminvf4(__m128);
extern __m128d V_VECTORCALL __svml_cdfnorminv2 (__m128d);
extern __m128 V_VECTORCALL __svml_cexpf4 (__m128);
extern __m128d V_VECTORCALL __svml_cexp2 (__m128d);
}
/*****************************************************************************
*
* Function definitions
*
*****************************************************************************/
// exponential and power functions
static inline Vec4f exp (Vec4f const x) { // exponential function
return __svml_expf4(x);
}
static inline Vec2d exp (Vec2d const x) { // exponential function
return __svml_exp2(x);
}
static inline Vec4f expm1 (Vec4f const x) { // exp(x)-1
return __svml_expm1f4(x);
}
static inline Vec2d expm1 (Vec2d const x) { // exp(x)-1
return __svml_expm12(x);
}
static inline Vec4f exp2 (Vec4f const x) { // pow(2,x)
return __svml_exp2f4(x);
}
static inline Vec2d exp2 (Vec2d const x) { // pow(2,x)
return __svml_exp22(x);
}
static inline Vec4f exp10 (Vec4f const x) { // pow(10,x)
return __svml_exp10f4(x);
}
static inline Vec2d exp10 (Vec2d const x) { // pow(10,x)
return __svml_exp102(x);
}
static inline Vec4f pow (Vec4f const a, Vec4f const b) { // pow(a,b) = a to the power of b
return __svml_powf4(a,b);
}
static inline Vec4f pow (Vec4f const a, float const b) { // pow(a,b)
return __svml_powf4(a,Vec4f(b));
}
static inline Vec2d pow (Vec2d const a, Vec2d const b) { // pow(a,b)
return __svml_pow2(a,b);
}
static inline Vec2d pow (Vec2d const a, double const b) { // pow(a,b)
return __svml_pow2(a,Vec2d(b));
}
static inline Vec4f cbrt (Vec4f const x) { // pow(x,1/3)
return __svml_cbrtf4(x);
}
static inline Vec2d cbrt (Vec2d const x) { // pow(x,1/3)
return __svml_cbrt2(x);
}
// logarithms
static inline Vec4f log (Vec4f const x) { // natural logarithm
return __svml_logf4(x);
}
static inline Vec2d log (Vec2d const x) { // natural logarithm
return __svml_log2(x);
}
static inline Vec4f log1p (Vec4f const x) { // log(1+x)
return __svml_log1pf4(x);
}
static inline Vec2d log1p (Vec2d const x) { // log(1+x)
return __svml_log1p2(x);
}
static inline Vec4f log2 (Vec4f const x) { // logarithm base 2
return __svml_log2f4(x);
}
static inline Vec2d log2 (Vec2d const x) { // logarithm base 2
return __svml_log22(x);
}
static inline Vec4f log10 (Vec4f const x) { // logarithm base 10
return __svml_log10f4(x);
}
static inline Vec2d log10 (Vec2d const x) { // logarithm base 10
return __svml_log102(x);
}
// trigonometric functions (angles in radians)
static inline Vec4f sin (Vec4f const x) { // sine
return __svml_sinf4(x);
}
static inline Vec2d sin (Vec2d const x) { // sine
return __svml_sin2(x);
}
static inline Vec4f cos (Vec4f const x) { // cosine
return __svml_cosf4(x);
}
static inline Vec2d cos (Vec2d const x) { // cosine
return __svml_cos2(x);
}
// sincos function. sin(x) returned, cos(x) in pcos
#ifdef SINCOS_ASM // sincos can be fixed with inline assembly
static inline Vec4f sincos (Vec4f * pcos, Vec4f const x) {
__m128 r_sin, r_cos;
// __asm__ ( "call __svml_sincosf4 \n movaps %%xmm0, %0 \n movaps %%xmm1, %1" : "=m"(r_sin), "=m"(r_cos) : "xmm0"(x) );
r_sin = __svml_sincosf4(x); // fix calling convention in windows and linux using assembly
__asm__ __volatile__ ( "movaps %%xmm1, %0":"=m"(r_cos));
*pcos = r_cos;
return r_sin;
}
static inline Vec2d sincos (Vec2d * pcos, Vec2d const x) { // sine and cosine. sin(x) returned, cos(x) in pcos
__m128d r_sin, r_cos;
r_sin = __svml_sincos2(x);
__asm__ __volatile__ ( "movaps %%xmm1, %0":"=m"(r_cos));
*pcos = r_cos;
return r_sin;
}
#endif // inline assembly available
static inline Vec4f tan (Vec4f const x) { // tangent
return __svml_tanf4(x);
}
static inline Vec2d tan (Vec2d const x) { // tangent
return __svml_tan2(x);
}
static inline Vec4f sinpi (Vec4f const x) { // sine
return __svml_sinpif4(x);
}
static inline Vec2d sinpi (Vec2d const x) { // sine
return __svml_sinpi2(x);
}
static inline Vec4f cospi (Vec4f const x) { // cosine
return __svml_cospif4(x);
}
static inline Vec2d cospi (Vec2d const x) { // cosine
return __svml_cospi2(x);
}
static inline Vec4f tanpi (Vec4f const x) { // tangent
return __svml_tanpif4(x);
}
static inline Vec2d tanpi (Vec2d const x) { // tangent
return __svml_tanpi2(x);
}
// inverse trigonometric functions
static inline Vec4f asin (Vec4f const x) { // inverse sine
return __svml_asinf4(x);
}
static inline Vec2d asin (Vec2d const x) { // inverse sine
return __svml_asin2(x);
}
static inline Vec4f acos (Vec4f const x) { // inverse cosine
return __svml_acosf4(x);
}
static inline Vec2d acos (Vec2d const x) { // inverse cosine
return __svml_acos2(x);
}
static inline Vec4f atan (Vec4f const x) { // inverse tangent
return __svml_atanf4(x);
}
static inline Vec2d atan (Vec2d const x) { // inverse tangent
return __svml_atan2(x);
}
static inline Vec4f atan2 (Vec4f const a, Vec4f const b) { // inverse tangent of a/b
return __svml_atan2f4(a,b);
}
static inline Vec2d atan2 (Vec2d const a, Vec2d const b) { // inverse tangent of a/b
return __svml_atan22(a,b);
}
// hyperbolic functions and inverse hyperbolic functions
static inline Vec4f sinh (Vec4f const x) { // hyperbolic sine
return __svml_sinhf4(x);
}
static inline Vec2d sinh (Vec2d const x) { // hyperbolic sine
return __svml_sinh2(x);
}
static inline Vec4f cosh (Vec4f const x) { // hyperbolic cosine
return __svml_coshf4(x);
}
static inline Vec2d cosh (Vec2d const x) { // hyperbolic cosine
return __svml_cosh2(x);
}
static inline Vec4f tanh (Vec4f const x) { // hyperbolic tangent
return __svml_tanhf4(x);
}
static inline Vec2d tanh (Vec2d const x) { // hyperbolic tangent
return __svml_tanh2(x);
}
static inline Vec4f asinh (Vec4f const x) { // inverse hyperbolic sine
return __svml_asinhf4(x);
}
static inline Vec2d asinh (Vec2d const x) { // inverse hyperbolic sine
return __svml_asinh2(x);
}
static inline Vec4f acosh (Vec4f const x) { // inverse hyperbolic cosine
return __svml_acoshf4(x);
}
static inline Vec2d acosh (Vec2d const x) { // inverse hyperbolic cosine
return __svml_acosh2(x);
}
static inline Vec4f atanh (Vec4f const x) { // inverse hyperbolic tangent
return __svml_atanhf4(x);
}
static inline Vec2d atanh (Vec2d const x) { // inverse hyperbolic tangent
return __svml_atanh2(x);
}
// error function
static inline Vec4f erf (Vec4f const x) { // error function
return __svml_erff4(x);
}
static inline Vec2d erf (Vec2d const x) { // error function
return __svml_erf2(x);
}
static inline Vec4f erfc (Vec4f const x) { // error function complement
return __svml_erfcf4(x);
}
static inline Vec2d erfc (Vec2d const x) { // error function complement
return __svml_erfc2(x);
}
static inline Vec4f erfinv (Vec4f const x) { // inverse error function
return __svml_erfinvf4(x);
}
static inline Vec2d erfinv (Vec2d const x) { // inverse error function
return __svml_erfinv2(x);
}
static inline Vec4f cdfnorm (Vec4f const x) { // cumulative normal distribution function
return __svml_cdfnormf4(x);
}
static inline Vec2d cdfnorm (Vec2d const x) { // cumulative normal distribution function
return __svml_cdfnorm2(x);
}
static inline Vec4f cdfnorminv (Vec4f const x) { // inverse cumulative normal distribution function
return __svml_cdfnorminvf4(x);
}
static inline Vec2d cdfnorminv (Vec2d const x) { // inverse cumulative normal distribution function
return __svml_cdfnorminv2(x);
}
#endif // USE_SVML_INTRINSICS
#if defined (MAX_VECTOR_SIZE) && MAX_VECTOR_SIZE >= 256 // 256 bit vectors
#if defined (VECTORF256_H) // 256-bit vector registers supported
#ifdef USE_SVML_INTRINSICS
/*****************************************************************************
*
* 256-bit vector functions using Intel compiler intrinsic functions
*
*****************************************************************************/
// exponential and power functions
static inline Vec8f exp(Vec8f const x) { // exponential function
return _mm256_exp_ps(x);
}
static inline Vec4d exp(Vec4d const x) { // exponential function
return _mm256_exp_pd(x);
}
static inline Vec8f expm1(Vec8f const x) { // exp(x)-1. Avoids loss of precision if x is close to 1
return _mm256_expm1_ps(x);
}
static inline Vec4d expm1(Vec4d const x) { // exp(x)-1. Avoids loss of precision if x is close to 1
return _mm256_expm1_pd(x);
}
static inline Vec8f exp2(Vec8f const x) { // pow(2,x)
return _mm256_exp2_ps(x);
}
static inline Vec4d exp2(Vec4d const x) { // pow(2,x)
return _mm256_exp2_pd(x);
}
static inline Vec8f exp10(Vec8f const x) { // pow(10,x)
return _mm256_exp10_ps(x);
}
static inline Vec4d exp10(Vec4d const x) { // pow(10,x)
return _mm256_exp10_pd(x);
}
static inline Vec8f pow(Vec8f const a, Vec8f const b) { // pow(a,b) = a to the power of b
return _mm256_pow_ps(a, b);
}
static inline Vec8f pow(Vec8f const a, float const b) { // pow(a,b) = a to the power of b
return _mm256_pow_ps(a, Vec8f(b));
}
static inline Vec4d pow(Vec4d const a, Vec4d const b) { // pow(a,b) = a to the power of b
return _mm256_pow_pd(a, b);
}
static inline Vec4d pow(Vec4d const a, double const b) { // pow(a,b) = a to the power of b
return _mm256_pow_pd(a, Vec4d(b));
}
static inline Vec8f cbrt(Vec8f const x) { // pow(x,1/3)
return _mm256_cbrt_ps(x);
}
static inline Vec4d cbrt(Vec4d const x) { // pow(x,1/3)
return _mm256_cbrt_pd(x);
}
// logarithms
static inline Vec8f log(Vec8f const x) { // natural logarithm
return _mm256_log_ps(x);
}
static inline Vec4d log(Vec4d const x) { // natural logarithm
return _mm256_log_pd(x);
}
static inline Vec8f log1p(Vec8f const x) { // log(1+x). Avoids loss of precision if 1+x is close to 1
return _mm256_log1p_ps(x);
}
static inline Vec4d log1p(Vec4d const x) { // log(1+x). Avoids loss of precision if 1+x is close to 1
return _mm256_log1p_pd(x);
}
static inline Vec8f log2(Vec8f const x) { // logarithm base 2
return _mm256_log2_ps(x);
}
static inline Vec4d log2(Vec4d const x) { // logarithm base 2
return _mm256_log2_pd(x);
}
static inline Vec8f log10(Vec8f const x) { // logarithm base 10
return _mm256_log10_ps(x);
}
static inline Vec4d log10(Vec4d const x) { // logarithm base 10
return _mm256_log10_pd(x);
}
// trigonometric functions
static inline Vec8f sin(Vec8f const x) { // sine
return _mm256_sin_ps(x);
}
static inline Vec4d sin(Vec4d const x) { // sine
return _mm256_sin_pd(x);
}
static inline Vec8f cos(Vec8f const x) { // cosine
return _mm256_cos_ps(x);
}
static inline Vec4d cos(Vec4d const x) { // cosine
return _mm256_cos_pd(x);
}
static inline Vec8f sincos(Vec8f * pcos, Vec8f const x) { // sine and cosine. sin(x) returned, cos(x) in pcos
__m256 r_sin, r_cos;
r_sin = _mm256_sincos_ps(&r_cos, x);
*pcos = r_cos;
return r_sin;
}
static inline Vec4d sincos(Vec4d * pcos, Vec4d const x) { // sine and cosine. sin(x) returned, cos(x) in pcos
__m256d r_sin, r_cos;
r_sin = _mm256_sincos_pd(&r_cos, x);
*pcos = r_cos;
return r_sin;
}
static inline Vec8f tan(Vec8f const x) { // tangent
return _mm256_tan_ps(x);
}
static inline Vec4d tan(Vec4d const x) { // tangent
return _mm256_tan_pd(x);
}
#ifdef TRIGPI_FUNCTIONS
static inline Vec8f sinpi(Vec8f const x) { // sine
return _mm256_sinpi_ps(x);
}
static inline Vec4d sinpi(Vec4d const x) { // sine
return _mm256_sinpi_pd(x);
}
static inline Vec8f cospi(Vec8f const x) { // cosine
return _mm256_cospi_ps(x);
}
static inline Vec4d cospi(Vec4d const x) { // cosine
return _mm256_cospi_pd(x);
}
static inline Vec8f tanpi(Vec8f const x) { // tangent
return _mm256_tanpi_ps(x);
}
static inline Vec4d tanpi(Vec4d const x) { // tangent
return _mm256_tanpi_pd(x);
}
#endif // TRIGPI_FUNCTIONS
// inverse trigonometric functions
static inline Vec8f asin(Vec8f const x) { // inverse sine
return _mm256_asin_ps(x);
}
static inline Vec4d asin(Vec4d const x) { // inverse sine
return _mm256_asin_pd(x);
}
static inline Vec8f acos(Vec8f const x) { // inverse cosine
return _mm256_acos_ps(x);
}
static inline Vec4d acos(Vec4d const x) { // inverse cosine
return _mm256_acos_pd(x);
}
static inline Vec8f atan(Vec8f const x) { // inverse tangent
return _mm256_atan_ps(x);
}
static inline Vec4d atan(Vec4d const x) { // inverse tangent
return _mm256_atan_pd(x);
}
static inline Vec8f atan2(Vec8f const a, Vec8f const b) { // inverse tangent of a/b
return _mm256_atan2_ps(a, b);
}
static inline Vec4d atan2(Vec4d const a, Vec4d const b) { // inverse tangent of a/b
return _mm256_atan2_pd(a, b);
}
// hyperbolic functions and inverse hyperbolic functions
static inline Vec8f sinh(Vec8f const x) { // hyperbolic sine
return _mm256_sinh_ps(x);
}
static inline Vec4d sinh(Vec4d const x) { // hyperbolic sine
return _mm256_sinh_pd(x);
}
static inline Vec8f cosh(Vec8f const x) { // hyperbolic cosine
return _mm256_cosh_ps(x);
}
static inline Vec4d cosh(Vec4d const x) { // hyperbolic cosine
return _mm256_cosh_pd(x);
}
static inline Vec8f tanh(Vec8f const x) { // hyperbolic tangent
return _mm256_tanh_ps(x);
}
static inline Vec4d tanh(Vec4d const x) { // hyperbolic tangent
return _mm256_tanh_pd(x);
}
static inline Vec8f asinh(Vec8f const x) { // inverse hyperbolic sine
return _mm256_asinh_ps(x);
}
static inline Vec4d asinh(Vec4d const x) { // inverse hyperbolic sine
return _mm256_asinh_pd(x);
}
static inline Vec8f acosh(Vec8f const x) { // inverse hyperbolic cosine
return _mm256_acosh_ps(x);
}
static inline Vec4d acosh(Vec4d const x) { // inverse hyperbolic cosine
return _mm256_acosh_pd(x);
}
static inline Vec8f atanh(Vec8f const x) { // inverse hyperbolic tangent
return _mm256_atanh_ps(x);
}
static inline Vec4d atanh(Vec4d const x) { // inverse hyperbolic tangent
return _mm256_atanh_pd(x);
}
// error function
static inline Vec8f erf(Vec8f const x) { // error function
return _mm256_erf_ps(x);
}
static inline Vec4d erf(Vec4d const x) { // error function
return _mm256_erf_pd(x);
}
static inline Vec8f erfc(Vec8f const x) { // error function complement
return _mm256_erfc_ps(x);
}
static inline Vec4d erfc(Vec4d const x) { // error function complement
return _mm256_erfc_pd(x);
}
static inline Vec8f erfinv(Vec8f const x) { // inverse error function
return _mm256_erfinv_ps(x);
}
static inline Vec4d erfinv(Vec4d const x) { // inverse error function
return _mm256_erfinv_pd(x);
}
static inline Vec8f cdfnorm(Vec8f const x) { // cumulative normal distribution function
return _mm256_cdfnorm_ps(x);
}
static inline Vec4d cdfnorm(Vec4d const x) { // cumulative normal distribution function
return _mm256_cdfnorm_pd(x);
}
static inline Vec8f cdfnorminv(Vec8f const x) {// inverse cumulative normal distribution function
return _mm256_cdfnorminv_ps(x);
}
static inline Vec4d cdfnorminv(Vec4d const x) {// inverse cumulative normal distribution function
return _mm256_cdfnorminv_pd(x);
}
#else // not USE_SVML_INTRINSICS
/*****************************************************************************
*
* 256-bit vector functions using other compiler than Intel
*
*****************************************************************************/
// External function prototypes for SVML library, 256-bit vectors
extern "C" {
extern __m256 V_VECTORCALL __svml_expf8 (__m256);
extern __m256d V_VECTORCALL __svml_exp4 (__m256d);
extern __m256 V_VECTORCALL __svml_expm1f8 (__m256);
extern __m256d V_VECTORCALL __svml_expm14 (__m256d);
extern __m256 V_VECTORCALL __svml_exp2f8 (__m256);
extern __m256d V_VECTORCALL __svml_exp24 (__m256d);
extern __m256 V_VECTORCALL __svml_exp10f8 (__m256);
extern __m256d V_VECTORCALL __svml_exp104 (__m256d);
extern __m256 V_VECTORCALL2 __svml_powf8 (__m256, __m256);
extern __m256d V_VECTORCALL2 __svml_pow4 (__m256d, __m256d);
extern __m256 V_VECTORCALL __svml_cbrtf8 (__m256);
extern __m256d V_VECTORCALL __svml_cbrt4 (__m256d);
extern __m256 V_VECTORCALL __svml_invsqrtf8 (__m256);
extern __m256d V_VECTORCALL __svml_invsqrt4 (__m256d);
extern __m256 V_VECTORCALL __svml_logf8 (__m256);
extern __m256d V_VECTORCALL __svml_log4 (__m256d);
extern __m256 V_VECTORCALL __svml_log1pf8 (__m256);
extern __m256d V_VECTORCALL __svml_log1p4 (__m256d);
extern __m256 V_VECTORCALL __svml_log2f8 (__m256);
extern __m256d V_VECTORCALL __svml_log24 (__m256d);
extern __m256 V_VECTORCALL __svml_log10f8 (__m256);
extern __m256d V_VECTORCALL __svml_log104 (__m256d);
extern __m256 V_VECTORCALL __svml_sinf8 (__m256);
extern __m256d V_VECTORCALL __svml_sin4 (__m256d);
extern __m256 V_VECTORCALL __svml_cosf8 (__m256);
extern __m256d V_VECTORCALL __svml_cos4 (__m256d);
extern __m256 V_VECTORCALL2 __svml_sincosf8 (__m256); // cos returned in ymm1
extern __m256d V_VECTORCALL2 __svml_sincos4 (__m256d); // cos returned in ymm1
extern __m256 V_VECTORCALL __svml_tanf8 (__m256);
extern __m256d V_VECTORCALL __svml_tan4 (__m256d);
extern __m256 V_VECTORCALL __svml_sinpif8 (__m256);
extern __m256d V_VECTORCALL __svml_sinpi4 (__m256d);
extern __m256 V_VECTORCALL __svml_cospif8 (__m256);
extern __m256d V_VECTORCALL __svml_cospi4 (__m256d);
extern __m256 V_VECTORCALL __svml_tanpif8 (__m256);
extern __m256d V_VECTORCALL __svml_tanpi4 (__m256d);
extern __m256 V_VECTORCALL __svml_asinf8 (__m256);
extern __m256d V_VECTORCALL __svml_asin4 (__m256d);
extern __m256 V_VECTORCALL __svml_acosf8 (__m256);
extern __m256d V_VECTORCALL __svml_acos4 (__m256d);
extern __m256 V_VECTORCALL __svml_atanf8 (__m256);
extern __m256d V_VECTORCALL __svml_atan4 (__m256d);
extern __m256 V_VECTORCALL2 __svml_atan2f8 (__m256, __m256);
extern __m256d V_VECTORCALL2 __svml_atan24 (__m256d, __m256d);
extern __m256 V_VECTORCALL __svml_sinhf8 (__m256);
extern __m256d V_VECTORCALL __svml_sinh4 (__m256d);
extern __m256 V_VECTORCALL __svml_coshf8 (__m256);
extern __m256d V_VECTORCALL __svml_cosh4 (__m256d);
extern __m256 V_VECTORCALL __svml_tanhf8 (__m256);
extern __m256d V_VECTORCALL __svml_tanh4 (__m256d);
extern __m256 V_VECTORCALL __svml_asinhf8 (__m256);
extern __m256d V_VECTORCALL __svml_asinh4 (__m256d);
extern __m256 V_VECTORCALL __svml_acoshf8 (__m256);
extern __m256d V_VECTORCALL __svml_acosh4 (__m256d);
extern __m256 V_VECTORCALL __svml_atanhf8 (__m256);
extern __m256d V_VECTORCALL __svml_atanh4 (__m256d);
extern __m256 V_VECTORCALL __svml_erff8 (__m256);
extern __m256d V_VECTORCALL __svml_erf4 (__m256d);
extern __m256 V_VECTORCALL __svml_erfcf8 (__m256);
extern __m256d V_VECTORCALL __svml_erfc4 (__m256d);
extern __m256 V_VECTORCALL __svml_erfinvf8 (__m256);
extern __m256d V_VECTORCALL __svml_erfinv4 (__m256d);
extern __m256 V_VECTORCALL __svml_cdfnorminvf8(__m256);
extern __m256d V_VECTORCALL __svml_cdfnorminv4 (__m256d);
extern __m256 V_VECTORCALL __svml_cdfnormf8 (__m256);
extern __m256d V_VECTORCALL __svml_cdfnorm4 (__m256d);
//extern __m256 V_VECTORCALL __svml_cexpf8 (__m256);
//extern __m256d V_VECTORCALL __svml_cexp4 (__m256d);
}
// exponential and power functions
static inline Vec8f exp (Vec8f const x) { // exponential function
return __svml_expf8(x);
}
static inline Vec4d exp (Vec4d const x) { // exponential function
return __svml_exp4(x);
}
static inline Vec8f expm1 (Vec8f const x) { // exp(x)-1
return __svml_expm1f8(x);
}
static inline Vec4d expm1 (Vec4d const x) { // exp(x)-1
return __svml_expm14(x);
}
static inline Vec8f exp2 (Vec8f const x) { // pow(2,x)
return __svml_exp2f8(x);
}
static inline Vec4d exp2 (Vec4d const x) { // pow(2,x)
return __svml_exp24(x);
}
static inline Vec8f exp10 (Vec8f const x) { // pow(10,x)
return __svml_exp10f8(x);
}
static inline Vec4d exp10 (Vec4d const x) { // pow(10,x)
return __svml_exp104(x);
}
static inline Vec8f pow (Vec8f const a, Vec8f const b) { // pow(a,b) = a to the power of b
return __svml_powf8(a,b);
}
static inline Vec8f pow (Vec8f const a, float const b) { // pow(a,b)
return __svml_powf8(a,Vec8f(b));
}
static inline Vec4d pow (Vec4d const a, Vec4d const b) { // pow(a,b)
return __svml_pow4(a,b);
}
static inline Vec4d pow (Vec4d const a, double const b) { // pow(a,b)
return __svml_pow4(a,Vec4d(b));
}
static inline Vec8f cbrt (Vec8f const x) { // pow(x,1/3)
return __svml_cbrtf8(x);
}
static inline Vec4d cbrt (Vec4d const x) { // pow(x,1/3)
return __svml_cbrt4(x);
}
// logarithms
static inline Vec8f log (Vec8f const x) { // natural logarithm
return __svml_logf8(x);
}
static inline Vec4d log (Vec4d const x) { // natural logarithm
return __svml_log4(x);