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/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* Based on newlib/libm/math/kf_tan.c in Newlib. */
#include "amdgcnmach.h"
static const float
one = 1.0000000000e+00, /* 0x3f800000 */
pio4 = 7.8539812565e-01, /* 0x3f490fda */
pio4lo= 3.7748947079e-08, /* 0x33222168 */
T[] = {
3.3333334327e-01, /* 0x3eaaaaab */
1.3333334029e-01, /* 0x3e088889 */
5.3968254477e-02, /* 0x3d5d0dd1 */
2.1869488060e-02, /* 0x3cb327a4 */
8.8632395491e-03, /* 0x3c11371f */
3.5920790397e-03, /* 0x3b6b6916 */
1.4562094584e-03, /* 0x3abede48 */
5.8804126456e-04, /* 0x3a1a26c8 */
2.4646313977e-04, /* 0x398137b9 */
7.8179444245e-05, /* 0x38a3f445 */
7.1407252108e-05, /* 0x3895c07a */
-1.8558637748e-05, /* 0xb79bae5f */
2.5907305826e-05, /* 0x37d95384 */
};
#if defined (__has_builtin) && __has_builtin (__builtin_gcn_fabsvf)
static v64sf
v64sf_kernel_tanf (v64sf x, v64sf y, v64si iy, v64si __mask)
{
FUNCTION_INIT (v64sf);
v64si hx;
GET_FLOAT_WORD(hx, x, NO_COND);
v64si ix = hx & 0x7fffffff; /* high word of |x| */
VECTOR_IF(ix<0x31800000, cond) /* x < 2**-28 */
VECTOR_IF2(__builtin_convertvector (x, v64si)==0, cond2, cond) /* generate inexact */
VECTOR_RETURN (1.0f / __builtin_gcn_fabsvf (x), (ix|(iy+1))==0);
VECTOR_RETURN (x, cond2 & (iy == 1));
VECTOR_RETURN (-1.0f / x, cond2);
VECTOR_ENDIF
VECTOR_ENDIF
VECTOR_IF(ix>=0x3f2ca140, cond) /* |x|>=0.6744 */
VECTOR_COND_MOVE (x, -x, cond & (hx < 0));
VECTOR_COND_MOVE (y, -y, cond & (hx < 0));
v64sf z = pio4-x;
v64sf w = pio4lo-y;
VECTOR_COND_MOVE (x, z+w, cond);
VECTOR_COND_MOVE (y, VECTOR_INIT (0.0f), cond);
VECTOR_ENDIF
v64sf z = x*x;
v64sf w = z*z;
/* Break x^5*(T[1]+x^2*T[2]+...) into
* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
*/
v64sf r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
v64sf v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
v64sf s = z*x;
r = y + z*(s*(r+v)+y);
r += T[0]*s;
w = x+r;
VECTOR_IF(ix>=0x3f2ca140, cond)
v = __builtin_convertvector (iy, v64sf);
VECTOR_RETURN (__builtin_convertvector (1-((hx>>30)&2), v64sf)
* (v-2.0f*(x-(w*w/(w+v)-r))), cond);
VECTOR_ENDIF
VECTOR_RETURN (w, iy == 1);
/* if allow error up to 2 ulp,
simply return -1.0/(x+r) here */
/* compute -1.0/(x+r) accurately */
z = w;
v64si i;
GET_FLOAT_WORD(i,z, NO_COND);
SET_FLOAT_WORD(z,i&0xfffff000, NO_COND);
v = r - (z - x); /* z+v = r+x */
v64sf a, t;
t = a = -1.0f/w; /* a = -1.0/w */
GET_FLOAT_WORD(i,t, NO_COND);
SET_FLOAT_WORD(t,i&0xfffff000, NO_COND);
s = 1.0f+t*z;
VECTOR_RETURN (t+a*(s+t*v), NO_COND);
FUNCTION_RETURN;
}
static v64si
v64sf_rem_pio2f (v64sf x, v64sf *y)
{
/* Work in double-precision for better accuracy. */
v64df dx = __builtin_convertvector (x, v64df);
v64df r = dx * __INV_PI_OVER_TWO_2_24;
v64si n = (__builtin_convertvector (r, v64si) + 0x800000) >> 24;
dx = dx - __builtin_convertvector (n, v64df) * __PI_OVER_TWO;
y[0] = __builtin_convertvector (dx, v64sf);
y[1] = __builtin_convertvector (dx, v64sf) - y[0];
return n;
}
DEF_VS_MATH_FUNC (v64sf, tanf, v64sf x)
{
FUNCTION_INIT (v64sf);
v64si ix;
GET_FLOAT_WORD (ix, x, NO_COND);
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
VECTOR_RETURN (v64sf_kernel_tanf (x, VECTOR_INIT (0.0f), VECTOR_INIT (1), __mask),
ix <= 0x3f490fda);
/* tan(Inf or NaN) is NaN */
VECTOR_RETURN (x-x, ~FLT_UWORD_IS_FINITE(ix)); /* NaN */
/* argument reduction needed */
v64sf y[2];
v64si n = v64sf_rem_pio2f (x,y);
VECTOR_RETURN (v64sf_kernel_tanf (y[0], y[1], 1-((n&1)<<1), __mask), // 1 -- n even
NO_COND); // -1 -- n odd
FUNCTION_RETURN;
}
DEF_VARIANTS (tanf, sf, sf)
#endif
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