diff options
Diffstat (limited to 'newlib/libm/machine/amdgcn/v64sf_pow.c')
| -rw-r--r-- | newlib/libm/machine/amdgcn/v64sf_pow.c | 292 |
1 files changed, 292 insertions, 0 deletions
diff --git a/newlib/libm/machine/amdgcn/v64sf_pow.c b/newlib/libm/machine/amdgcn/v64sf_pow.c new file mode 100644 index 000000000..2a404a9e5 --- /dev/null +++ b/newlib/libm/machine/amdgcn/v64sf_pow.c @@ -0,0 +1,292 @@ +/* + * ==================================================== + * 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/ef_pow.c in Newlib. */ + +#include "amdgcnmach.h" + +static const float +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ +dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ +zero = 0.0, +one = 1.0, +two = 2.0, +two24 = 16777216.0, /* 0x4b800000 */ + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 6.0000002384e-01, /* 0x3f19999a */ +L2 = 4.2857143283e-01, /* 0x3edb6db7 */ +L3 = 3.3333334327e-01, /* 0x3eaaaaab */ +L4 = 2.7272811532e-01, /* 0x3e8ba305 */ +L5 = 2.3066075146e-01, /* 0x3e6c3255 */ +L6 = 2.0697501302e-01, /* 0x3e53f142 */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08, /* 0x3331bb4c */ +lg2 = 6.9314718246e-01, /* 0x3f317218 */ +lg2_h = 6.93145752e-01, /* 0x3f317200 */ +lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ +ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ +cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ +cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */ +cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */ +ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ +ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ +ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ + +v64sf v64sf_sqrtf_aux (v64sf, v64si); +v64sf v64sf_scalbnf_aux (v64sf, v64si, v64si); + +#if defined (__has_builtin) && __has_builtin (__builtin_gcn_fabsvf) + +DEF_VS_MATH_FUNC (v64sf, powf, v64sf x, v64sf y) +{ + FUNCTION_INIT (v64sf); + + v64si hx, hy; + GET_FLOAT_WORD (hx,x, NO_COND); + GET_FLOAT_WORD (hy,y, NO_COND); + v64si ix = hx&0x7fffffff; + v64si iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + VECTOR_IF (FLT_UWORD_IS_ZERO(iy), cond) + VECTOR_RETURN (x + y, cond & v64sf_issignalingf_inline(x)); + VECTOR_RETURN (VECTOR_INIT (1.0f), cond); + VECTOR_ENDIF + + /* x|y==NaN return NaN unless x==1 then return 1 */ + VECTOR_IF (FLT_UWORD_IS_NAN(ix) | FLT_UWORD_IS_NAN(iy), cond) + VECTOR_IF2 (hx==0x3f800000 & ~v64sf_issignalingf_inline(y), cond2, cond) + VECTOR_RETURN (VECTOR_INIT (1.0f), cond2); + VECTOR_ELSE2 (cond2, cond) + VECTOR_RETURN (x + y, cond2); + VECTOR_ENDIF + VECTOR_ENDIF + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + v64si yisint = VECTOR_INIT (0); + + VECTOR_IF (hx < 0, cond) + VECTOR_IF2 (iy >= 0x4b800000, cond2, cond) + VECTOR_COND_MOVE (yisint, VECTOR_INIT (2), cond2); /* even integer y */ + VECTOR_ELSEIF2 (iy >= 0x3f800000, cond2, cond) + v64si k = (iy>>23)-0x7f; /* exponent */ + v64si j = iy>>(23-k); + VECTOR_COND_MOVE (yisint, 2-(j&1), cond2 & (j<<(23-k))==iy); + VECTOR_ENDIF + VECTOR_ENDIF + + /* special value of y */ + VECTOR_IF (FLT_UWORD_IS_INFINITE(iy), cond) /* y is +-inf */ + VECTOR_IF2 (ix==0x3f800000, cond2, cond) + VECTOR_RETURN (VECTOR_INIT (1.0f), cond2); /* +-1**+-inf = 1 */ + VECTOR_ELSEIF2 (ix > 0x3f800000, cond2, cond) /* (|x|>1)**+-inf = inf,0 */ + VECTOR_RETURN (y, cond2 & (hy >= 0)); + VECTOR_RETURN (VECTOR_INIT (0.0f), cond2); + VECTOR_ELSE2 (cond2, cond) /* (|x|<1)**-,+inf = inf,0 */ + VECTOR_RETURN (-y, cond2 & (hy<0)); + VECTOR_RETURN (VECTOR_INIT (0.0f), cond2); + VECTOR_ENDIF + VECTOR_ENDIF + VECTOR_IF (iy==0x3f800000, cond) /* y is +-1 */ + VECTOR_RETURN (VECTOR_INIT (1.0f) / x, cond & (hy<0)); + VECTOR_RETURN (x, cond); + VECTOR_ENDIF + + VECTOR_RETURN (x*x, hy==0x40000000); /* y is 2 */ + /* y is 0.5 */ + /* x >= +0 */ + VECTOR_RETURN (v64sf_sqrtf_aux (x, __mask), (hy==0x3f000000) & (hx >= 0)); + + v64sf ax = __builtin_gcn_fabsvf(x); + /* special value of x */ + VECTOR_IF (FLT_UWORD_IS_INFINITE(ix)|FLT_UWORD_IS_ZERO(ix)|ix==0x3f800000, cond) + v64sf z = ax; /*x is +-0,+-inf,+-1*/ + VECTOR_COND_MOVE (z, VECTOR_INIT (1.0f) / z, cond & (hy < 0)); /* z = (1/|x|) */ + VECTOR_IF2 (hx<0, cond2, cond) + VECTOR_IF2 (((ix-0x3f800000)|yisint)==0, cond3, cond2) + /* (-1)**non-int is NaN */ + VECTOR_COND_MOVE (z, (z-z)/(z-z), cond3); + VECTOR_ELSEIF2 (yisint==1, cond3, cond2) + /* (x<0)**odd = -(|x|**odd) */ + VECTOR_COND_MOVE (z, -z, cond3); + VECTOR_ENDIF + VECTOR_ENDIF + VECTOR_RETURN (z, cond); + VECTOR_ENDIF + + /* (x<0)**(non-int) is NaN */ + VECTOR_RETURN ((x-x)/(x-x), ((((hx >> 31) & 1) - 1)|yisint)==0); + + v64sf t1, t2; + + /* |y| is huge */ + VECTOR_IF (iy>0x4d000000, cond) /* if |y| > 2**27 */ + /* over/underflow if x is not close to one */ + VECTOR_IF2(ix<0x3f7ffff4, cond2, cond) + VECTOR_RETURN (v64sf_math_oflowf(VECTOR_INIT (0)), cond2 & (hy < 0)); + VECTOR_RETURN (v64sf_math_uflowf(VECTOR_INIT (0)), cond2); + VECTOR_ENDIF + VECTOR_IF2(ix>0x3f800007, cond2, cond) + VECTOR_RETURN (v64sf_math_oflowf(VECTOR_INIT (0)), cond2 & (hy > 0)); + VECTOR_RETURN (v64sf_math_uflowf(VECTOR_INIT (0)), cond2); + VECTOR_ENDIF + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + v64sf t = ax-1; /* t has 20 trailing zeros */ + v64sf w = (t*t)*(0.5f-t*(0.333333333333f-t*0.25f)); + v64sf u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ + v64sf v = t*ivln2_l-w*ivln2; + VECTOR_COND_MOVE (t1, u+v, cond); + v64si is; + GET_FLOAT_WORD(is,t1, cond); + SET_FLOAT_WORD(t1,is&0xfffff000, cond); + VECTOR_COND_MOVE (t2, v-(t1-u), cond); + VECTOR_RETURN (VECTOR_INIT (0.123456f), cond); + VECTOR_ELSE (cond) + v64si n = VECTOR_INIT (0); + /* take care subnormal number */ + VECTOR_IF2 (FLT_UWORD_IS_SUBNORMAL(ix), cond2, cond) + VECTOR_COND_MOVE (ax, ax * two24, cond); + VECTOR_COND_MOVE (n, n - 24, cond2); + GET_FLOAT_WORD(ix,ax, cond2); + VECTOR_ENDIF + n += (ix>>23)-0x7f; + v64si j = ix&0x007fffff; + /* determine interval */ + v64si ix = j|0x3f800000; /* normalize ix */ + v64si k; + VECTOR_IF2 (j<=0x1cc471, cond2, cond) + VECTOR_COND_MOVE (k, VECTOR_INIT (0), cond2); /* |x|<sqrt(3/2) */ + VECTOR_ELSEIF2 (j<0x5db3d7, cond2, cond) + VECTOR_COND_MOVE (k, VECTOR_INIT (1), cond2); /* |x|<sqrt(3) */ + VECTOR_ELSE2 (cond2, cond) + VECTOR_COND_MOVE (k, VECTOR_INIT (0), cond2); + VECTOR_COND_MOVE (n, n + 1, cond2); + VECTOR_COND_MOVE (ix, ix - 0x00800000, cond2); + VECTOR_ENDIF + SET_FLOAT_WORD(ax,ix, cond); + + /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + /* bp[0]=1.0, bp[1]=1.5 */ + v64sf bp_k = VECTOR_MERGE (VECTOR_INIT (bp[1]), VECTOR_INIT (bp[0]), k == 1); + v64sf u = ax-bp_k; + v64sf v = 1.0f/(ax+bp_k); + v64sf s = u*v; + v64sf s_h = s; + v64si is; + GET_FLOAT_WORD(is,s_h, cond); + SET_FLOAT_WORD(s_h,is&0xfffff000, cond); + /* t_h=ax+bp[k] High */ + v64sf t_h; + SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21), cond); + v64sf t_l = ax - (t_h-bp_k); + v64sf s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + v64sf s2 = s*s; + v64sf r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+s); + s2 = s_h*s_h; + t_h = __builtin_convertvector(3.0f+s2+r, v64sf); + GET_FLOAT_WORD(is,t_h, cond); + SET_FLOAT_WORD(t_h,is&0xfffff000, cond); + t_l = r-((t_h-3.0f)-s2); + /* u+v = s*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*s; + /* 2/(3log2)*(s+...) */ + v64sf p_h = u+v; + GET_FLOAT_WORD(is,p_h, cond); + SET_FLOAT_WORD(p_h,is&0xfffff000, cond); + v64sf p_l = v-(p_h-u); + v64sf z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + v64sf dp_l_k = VECTOR_MERGE (VECTOR_INIT (dp_l[1]), VECTOR_INIT (dp_l[0]), k == 1); + v64sf z_l = cp_l*p_h+p_l*cp+dp_l_k; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + v64sf t = __builtin_convertvector (n, v64sf); + v64sf dp_h_k = VECTOR_MERGE (VECTOR_INIT (dp_h[1]), VECTOR_INIT (dp_h[0]), k == 1); + VECTOR_COND_MOVE (t1, (((z_h+z_l)+dp_h_k)+t), cond); + GET_FLOAT_WORD(is,t1, cond); + SET_FLOAT_WORD(t1,is&0xfffff000, cond); + VECTOR_COND_MOVE (t2, z_l-(((t1-t)-dp_h_k)-z_h), cond); + VECTOR_ENDIF + + v64sf s = VECTOR_INIT (1.0f); /* s (sign of result -ve**odd) = -1 else = 1 */ + VECTOR_COND_MOVE (s, VECTOR_INIT (-1.0f), /* (-ve)**(odd int) */ + ((hx>>31) != 0)&(yisint == 1)); + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + v64si is; + GET_FLOAT_WORD(is,y, NO_COND); + v64sf y1; + SET_FLOAT_WORD(y1,is&0xfffff000, NO_COND); + v64sf p_l = (y-y1)*t1+y*t2; + v64sf p_h = y1*t1; + v64sf z = p_l+p_h; + v64si j; + GET_FLOAT_WORD(j,z, NO_COND); + v64si i = j&0x7fffffff; + VECTOR_IF (j>0, cond) + VECTOR_RETURN (v64sf_math_oflowf(s<0), cond & i>FLT_UWORD_EXP_MAX); /* overflow */ + VECTOR_RETURN (v64sf_math_oflowf(s<0), cond & (i==FLT_UWORD_EXP_MAX) + & (p_l+ovt>z-p_h)); /* overflow */ + VECTOR_ELSE (cond) + VECTOR_RETURN (v64sf_math_uflowf(s<0), cond & (i>FLT_UWORD_EXP_MIN)); /* underflow */ + VECTOR_RETURN (v64sf_math_uflowf(s<0), cond & (i==FLT_UWORD_EXP_MIN) + & (p_l<=z-p_h)); /* underflow */ + VECTOR_ENDIF + /* + * compute 2**(p_h+p_l) + */ + v64si k = (i>>23)-0x7f; + v64si n = VECTOR_INIT (0); + VECTOR_IF (i>0x3f000000, cond) /* if |z| > 0.5, set n = [z+0.5] */ + VECTOR_COND_MOVE (n, j+(0x00800000>>(k+1)), cond); + k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ + v64sf t; + SET_FLOAT_WORD(t,n&~(0x007fffff>>k), cond); + VECTOR_COND_MOVE (n, ((n&0x007fffff)|0x00800000)>>(23-k), cond); + VECTOR_COND_MOVE (n, -n, cond & (j<0)); + VECTOR_COND_MOVE (p_h, p_h - t, cond); + VECTOR_ENDIF + v64sf t = p_l+p_h; + GET_FLOAT_WORD(is,t, NO_COND); + SET_FLOAT_WORD(t,is&0xfffff000, NO_COND); + v64sf u = t*lg2_h; + v64sf v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + v64sf w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + v64sf r = (z*t1)/(t1-2.0f)-(w+z*w); + z = VECTOR_INIT (1.0f)-(r-z); + GET_FLOAT_WORD(j,z, NO_COND); + j += (n<<23); + VECTOR_IF ((j>>23)<=0, cond) + VECTOR_COND_MOVE (z, v64sf_scalbnf_aux(z, n, __mask), cond); /* subnormal output */ + VECTOR_ELSE (cond) + SET_FLOAT_WORD(z, j, cond); + VECTOR_ENDIF + VECTOR_RETURN (s*z, NO_COND); + + FUNCTION_RETURN; +} + +DEF_VARIANTS2 (powf, sf, sf) + +#endif |