/*      $NetBSD: fpu_trig.c,v 1.18 2017/01/16 12:05:40 isaki Exp $      */

/*
* Copyright (c) 1995  Ken Nakata
*      All rights reserved.
*
* 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. Neither the name of the author nor the names of its contributors
*    may be used to endorse or promote products derived from this software
*    without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``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 THE AUTHOR OR CONTRIBUTORS 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.
*
*      @(#)fpu_trig.c  10/24/95
*/

/*
* Copyright (c) 2011 Tetsuya Isaki. All rights reserved.
*
* 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.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``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 THE AUTHOR 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 <sys/cdefs.h>
__KERNEL_RCSID(0, "$NetBSD: fpu_trig.c,v 1.18 2017/01/16 12:05:40 isaki Exp $");

#include "fpu_emulate.h"

/*
* arccos(x) = pi/2 - arcsin(x)
*/
struct fpn *
fpu_acos(struct fpemu *fe)
{
       struct fpn *r;

       if (ISNAN(&fe->fe_f2))
               return &fe->fe_f2;
       if (ISINF(&fe->fe_f2))
               return fpu_newnan(fe);

       r = fpu_asin(fe);
       CPYFPN(&fe->fe_f2, r);

       /* pi/2 - asin(x) */
       fpu_const(&fe->fe_f1, FPU_CONST_PI);
       fe->fe_f1.fp_exp--;
       fe->fe_f2.fp_sign = !fe->fe_f2.fp_sign;
       r = fpu_add(fe);

       return r;
}

/*
*                          x
* arcsin(x) = arctan(---------------)
*                     sqrt(1 - x^2)
*/
struct fpn *
fpu_asin(struct fpemu *fe)
{
       struct fpn x;
       struct fpn *r;

       if (ISNAN(&fe->fe_f2))
               return &fe->fe_f2;
       if (ISZERO(&fe->fe_f2))
               return &fe->fe_f2;

       if (ISINF(&fe->fe_f2))
               return fpu_newnan(fe);

       CPYFPN(&x, &fe->fe_f2);

       /* x^2 */
       CPYFPN(&fe->fe_f1, &fe->fe_f2);
       r = fpu_mul(fe);

       /* 1 - x^2 */
       CPYFPN(&fe->fe_f2, r);
       fe->fe_f2.fp_sign = 1;
       fpu_const(&fe->fe_f1, FPU_CONST_1);
       r = fpu_add(fe);

       /* sqrt(1-x^2) */
       CPYFPN(&fe->fe_f2, r);
       r = fpu_sqrt(fe);

       /* x/sqrt */
       CPYFPN(&fe->fe_f2, r);
       CPYFPN(&fe->fe_f1, &x);
       r = fpu_div(fe);

       /* arctan */
       CPYFPN(&fe->fe_f2, r);
       return fpu_atan(fe);
}

/*
* arctan(x):
*
*      if (x < 0) {
*              x = abs(x);
*              sign = 1;
*      }
*      y = arctan(x);
*      if (sign) {
*              y = -y;
*      }
*/
struct fpn *
fpu_atan(struct fpemu *fe)
{
       struct fpn a;
       struct fpn x;
       struct fpn v;

       if (ISNAN(&fe->fe_f2))
               return &fe->fe_f2;
       if (ISZERO(&fe->fe_f2))
               return &fe->fe_f2;

       CPYFPN(&a, &fe->fe_f2);

       if (ISINF(&fe->fe_f2)) {
               /* f2 <- pi/2 */
               fpu_const(&fe->fe_f2, FPU_CONST_PI);
               fe->fe_f2.fp_exp--;

               fe->fe_f2.fp_sign = a.fp_sign;
               return &fe->fe_f2;
       }

       fpu_const(&x, FPU_CONST_1);
       fpu_const(&fe->fe_f2, FPU_CONST_0);
       CPYFPN(&v, &fe->fe_f2);
       fpu_cordit1(fe, &x, &a, &fe->fe_f2, &v);

       return &fe->fe_f2;
}


/*
* fe_f1 := sin(in)
* fe_f2 := cos(in)
*/
static void
__fpu_sincos_cordic(struct fpemu *fe, const struct fpn *in)
{
       struct fpn a;
       struct fpn v;

       CPYFPN(&a, in);
       fpu_const(&fe->fe_f1, FPU_CONST_0);
       CPYFPN(&fe->fe_f2, &fpu_cordic_inv_gain1);
       fpu_const(&v, FPU_CONST_1);
       v.fp_sign = 1;
       fpu_cordit1(fe, &fe->fe_f2, &fe->fe_f1, &a, &v);
}

/*
* cos(x):
*
*      if (x < 0) {
*              x = abs(x);
*      }
*      if (x > 2*pi) {
*              x %= 2*pi;
*      }
*      if (x > pi) {
*              x -= pi;
*              sign inverse;
*      }
*      if (x > pi/2) {
*              y = sin(x - pi/2);
*              sign inverse;
*      } else {
*              y = cos(x);
*      }
*      if (sign) {
*              y = -y;
*      }
*/
struct fpn *
fpu_cos(struct fpemu *fe)
{
       struct fpn x;
       struct fpn p;
       struct fpn *r;
       int sign;

       if (ISNAN(&fe->fe_f2))
               return &fe->fe_f2;
       if (ISINF(&fe->fe_f2))
               return fpu_newnan(fe);

       /* x = abs(input) */
       sign = 0;
       CPYFPN(&x, &fe->fe_f2);
       x.fp_sign = 0;

       /* p <- 2*pi */
       fpu_const(&p, FPU_CONST_PI);
       p.fp_exp++;

       /*
        * if (x > 2*pi*N)
        *  cos(x) is cos(x - 2*pi*N)
        */
       CPYFPN(&fe->fe_f1, &x);
       CPYFPN(&fe->fe_f2, &p);
       r = fpu_cmp(fe);
       if (r->fp_sign == 0) {
               CPYFPN(&fe->fe_f1, &x);
               CPYFPN(&fe->fe_f2, &p);
               r = fpu_mod(fe);
               CPYFPN(&x, r);
       }

       /* p <- pi */
       p.fp_exp--;

       /*
        * if (x > pi)
        *  cos(x) is -cos(x - pi)
        */
       CPYFPN(&fe->fe_f1, &x);
       CPYFPN(&fe->fe_f2, &p);
       fe->fe_f2.fp_sign = 1;
       r = fpu_add(fe);
       if (r->fp_sign == 0) {
               CPYFPN(&x, r);
               sign ^= 1;
       }

       /* p <- pi/2 */
       p.fp_exp--;

       /*
        * if (x > pi/2)
        *  cos(x) is -sin(x - pi/2)
        * else
        *  cos(x)
        */
       CPYFPN(&fe->fe_f1, &x);
       CPYFPN(&fe->fe_f2, &p);
       fe->fe_f2.fp_sign = 1;
       r = fpu_add(fe);
       if (r->fp_sign == 0) {
               __fpu_sincos_cordic(fe, r);
               r = &fe->fe_f1;
               sign ^= 1;
       } else {
               __fpu_sincos_cordic(fe, &x);
               r = &fe->fe_f2;
       }
       r->fp_sign = sign;
       return r;
}

/*
* sin(x):
*
*      if (x < 0) {
*              x = abs(x);
*              sign = 1;
*      }
*      if (x > 2*pi) {
*              x %= 2*pi;
*      }
*      if (x > pi) {
*              x -= pi;
*              sign inverse;
*      }
*      if (x > pi/2) {
*              y = cos(x - pi/2);
*      } else {
*              y = sin(x);
*      }
*      if (sign) {
*              y = -y;
*      }
*/
struct fpn *
fpu_sin(struct fpemu *fe)
{
       struct fpn x;
       struct fpn p;
       struct fpn *r;
       int sign;

       if (ISNAN(&fe->fe_f2))
               return &fe->fe_f2;
       if (ISINF(&fe->fe_f2))
               return fpu_newnan(fe);

       /* if x is +0/-0, return +0/-0 */
       if (ISZERO(&fe->fe_f2))
               return &fe->fe_f2;

       /* x = abs(input) */
       sign = fe->fe_f2.fp_sign;
       CPYFPN(&x, &fe->fe_f2);
       x.fp_sign = 0;

       /* p <- 2*pi */
       fpu_const(&p, FPU_CONST_PI);
       p.fp_exp++;

       /*
        * if (x > 2*pi*N)
        *  sin(x) is sin(x - 2*pi*N)
        */
       CPYFPN(&fe->fe_f1, &x);
       CPYFPN(&fe->fe_f2, &p);
       r = fpu_cmp(fe);
       if (r->fp_sign == 0) {
               CPYFPN(&fe->fe_f1, &x);
               CPYFPN(&fe->fe_f2, &p);
               r = fpu_mod(fe);
               CPYFPN(&x, r);
       }

       /* p <- pi */
       p.fp_exp--;

       /*
        * if (x > pi)
        *  sin(x) is -sin(x - pi)
        */
       CPYFPN(&fe->fe_f1, &x);
       CPYFPN(&fe->fe_f2, &p);
       fe->fe_f2.fp_sign = 1;
       r = fpu_add(fe);
       if (r->fp_sign == 0) {
               CPYFPN(&x, r);
               sign ^= 1;
       }

       /* p <- pi/2 */
       p.fp_exp--;

       /*
        * if (x > pi/2)
        *  sin(x) is cos(x - pi/2)
        * else
        *  sin(x)
        */
       CPYFPN(&fe->fe_f1, &x);
       CPYFPN(&fe->fe_f2, &p);
       fe->fe_f2.fp_sign = 1;
       r = fpu_add(fe);
       if (r->fp_sign == 0) {
               __fpu_sincos_cordic(fe, r);
               r = &fe->fe_f2;
       } else {
               __fpu_sincos_cordic(fe, &x);
               r = &fe->fe_f1;
       }
       r->fp_sign = sign;
       return r;
}

/*
* tan(x) = sin(x) / cos(x)
*/
struct fpn *
fpu_tan(struct fpemu *fe)
{
       struct fpn x;
       struct fpn s;
       struct fpn *r;

       if (ISNAN(&fe->fe_f2))
               return &fe->fe_f2;
       if (ISINF(&fe->fe_f2))
               return fpu_newnan(fe);

       /* if x is +0/-0, return +0/-0 */
       if (ISZERO(&fe->fe_f2))
               return &fe->fe_f2;

       CPYFPN(&x, &fe->fe_f2);

       /* sin(x) */
       CPYFPN(&fe->fe_f2, &x);
       r = fpu_sin(fe);
       CPYFPN(&s, r);

       /* cos(x) */
       CPYFPN(&fe->fe_f2, &x);
       r = fpu_cos(fe);
       CPYFPN(&fe->fe_f2, r);

       CPYFPN(&fe->fe_f1, &s);
       r = fpu_div(fe);
       return r;
}

struct fpn *
fpu_sincos(struct fpemu *fe, int regc)
{
       __fpu_sincos_cordic(fe, &fe->fe_f2);

       /* cos(x) */
       fpu_implode(fe, &fe->fe_f2, FTYPE_EXT, &fe->fe_fpframe->fpf_regs[regc * 3]);

       /* sin(x) */
       return &fe->fe_f1;
}

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