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174 lines
5.6 KiB
174 lines
5.6 KiB
/* Header for singleprecision sin/cos/sincos functions.


Copyright (c) 2018 Arm Ltd. All rights reserved.




SPDXLicenseIdentifier: BSD3Clause




Redistribution and use in source and binary forms, with or without


modification, are permitted provided that the following conditions


are met:


1. Redistributions of source code must retain the above copyright


notice, this list of conditions and the following disclaimer.


2. Redistributions in binary form must reproduce the above copyright


notice, this list of conditions and the following disclaimer in the


documentation and/or other materials provided with the distribution.


3. The name of the company may not be used to endorse or promote


products derived from this software without specific prior written


permission.




THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS'' AND ANY EXPRESS OR IMPLIED


WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF


MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.


IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,


SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED


TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR


PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF


LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING


NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS


SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */




#include <stdint.h>


#include <math.h>


#include "math_config.h"




/* 2PI * 2^64. */


static const double pi63 = 0x1.921FB54442D18p62;


/* PI / 4. */


static const double pio4 = 0x1.921FB54442D18p1;




/* The constants and polynomials for sine and cosine. */


typedef struct


{


double sign[4]; /* Sign of sine in quadrants 0..3. */


double hpi_inv; /* 2 / PI ( * 2^24 if !TOINT_INTRINSICS). */


double hpi; /* PI / 2. */


double c0, c1, c2, c3, c4; /* Cosine polynomial. */


double s1, s2, s3; /* Sine polynomial. */


} sincos_t;




/* Polynomial data (the cosine polynomial is negated in the 2nd entry). */


extern const sincos_t __sincosf_table[2] HIDDEN;




/* Table with 4/PI to 192 bit precision. */


extern const uint32_t __inv_pio4[] HIDDEN;




/* Top 12 bits of the float representation with the sign bit cleared. */


static inline uint32_t


abstop12 (float x)


{


return (asuint (x) >> 20) & 0x7ff;


}




/* Compute the sine and cosine of inputs X and X2 (X squared), using the


polynomial P and store the results in SINP and COSP. N is the quadrant,


if odd the cosine and sine polynomials are swapped. */


static inline void


sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp,


float *cosp)


{


double x3, x4, x5, x6, s, c, c1, c2, s1;




x4 = x2 * x2;


x3 = x2 * x;


c2 = p>c3 + x2 * p>c4;


s1 = p>s2 + x2 * p>s3;




/* Swap sin/cos result based on quadrant. */


float *tmp = (n & 1 ? cosp : sinp);


cosp = (n & 1 ? sinp : cosp);


sinp = tmp;




c1 = p>c0 + x2 * p>c1;


x5 = x3 * x2;


x6 = x4 * x2;




s = x + x3 * p>s1;


c = c1 + x4 * p>c2;




*sinp = s + x5 * s1;


*cosp = c + x6 * c2;


}




/* Return the sine of inputs X and X2 (X squared) using the polynomial P.


N is the quadrant, and if odd the cosine polynomial is used. */


static inline float


sinf_poly (double x, double x2, const sincos_t *p, int n)


{


double x3, x4, x6, x7, s, c, c1, c2, s1;




if ((n & 1) == 0)


{


x3 = x * x2;


s1 = p>s2 + x2 * p>s3;




x7 = x3 * x2;


s = x + x3 * p>s1;




return s + x7 * s1;


}


else


{


x4 = x2 * x2;


c2 = p>c3 + x2 * p>c4;


c1 = p>c0 + x2 * p>c1;




x6 = x4 * x2;


c = c1 + x4 * p>c2;




return c + x6 * c2;


}


}




/* Fast range reduction using single multiplysubtract. Return the modulo of


X as a value between PI/4 and PI/4 and store the quadrant in NP.


The values for PI/2 and 2/PI are accessed via P. Since PI/2 as a double


is accurate to 55 bits and the worstcase cancellation happens at 6 * PI/4,


the result is accurate for X <= 120.0. */


static inline double


reduce_fast (double x, const sincos_t *p, int *np)


{


double r;


#if TOINT_INTRINSICS


/* Use fast round and lround instructions when available. */


r = x * p>hpi_inv;


*np = converttoint (r);


return x  roundtoint (r) * p>hpi;


#else


/* Use scaled float to int conversion with explicit rounding.


hpi_inv is prescaled by 2^24 so the quadrant ends up in bits 24..31.


This avoids inaccuracies introduced by truncating negative values. */


r = x * p>hpi_inv;


int n = ((int32_t)r + 0x800000) >> 24;


*np = n;


return x  n * p>hpi;


#endif


}




/* Reduce the range of XI to a multiple of PI/2 using fast integer arithmetic.


XI is a reinterpreted float and must be >= 2.0f (the sign bit is ignored).


Return the modulo between PI/4 and PI/4 and store the quadrant in NP.


Reduction uses a table of 4/PI with 192 bits of precision. A 32x96>128 bit


multiply computes the exact 2.62bit fixedpoint modulo. Since the result


can have at most 29 leading zeros after the binary point, the double


precision result is accurate to 33 bits. */


static inline double


reduce_large (uint32_t xi, int *np)


{


const uint32_t *arr = &__inv_pio4[(xi >> 26) & 15];


int shift = (xi >> 23) & 7;


uint64_t n, res0, res1, res2;




xi = (xi & 0xffffff)  0x800000;


xi <<= shift;




res0 = xi * arr[0];


res1 = (uint64_t)xi * arr[4];


res2 = (uint64_t)xi * arr[8];


res0 = (res2 >> 32)  (res0 << 32);


res0 += res1;




n = (res0 + (1ULL << 61)) >> 62;


res0 = n << 62;


double x = (int64_t)res0;


*np = n;


return x * pi63;


}


