libm: adds powf
Bug: 30230114
Change-Id: If9899d8c4baf0d8f0c5e62859949beb01aef0f15
diff --git a/lib/libm/ef_pow.c b/lib/libm/ef_pow.c
new file mode 100644
index 0000000..b3041db
--- /dev/null
+++ b/lib/libm/ef_pow.c
@@ -0,0 +1,255 @@
+/* ef_pow.c -- float version of e_pow.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include "fdlibm.h"
+
+#ifdef __v810__
+#define const
+#endif
+
+#ifdef __STDC__
+static const float
+#else
+static float
+#endif
+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 */
+huge = 1.0e30,
+tiny = 1.0e-30,
+ /* 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*/
+
+#ifdef __STDC__
+ float __ieee754_powf(float x, float y)
+#else
+ float __ieee754_powf(x,y)
+ float x, y;
+#endif
+{
+ float z,ax,z_h,z_l,p_h,p_l;
+ float y1,t1,t2,r,s,t,u,v,w;
+ __int32_t i,j,k,yisint,n;
+ __int32_t hx,hy,ix,iy,is;
+
+ GET_FLOAT_WORD(hx,x);
+ GET_FLOAT_WORD(hy,y);
+ ix = hx&0x7fffffff; iy = hy&0x7fffffff;
+
+ /* y==zero: x**0 = 1 */
+ if(FLT_UWORD_IS_ZERO(iy)) return one;
+
+ /* x|y==NaN return NaN unless x==1 then return 1 */
+ if(FLT_UWORD_IS_NAN(ix) ||
+ FLT_UWORD_IS_NAN(iy)) {
+ if(ix==0x3f800000) return one;
+ else return nanf("");
+ }
+
+ /* 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
+ */
+ yisint = 0;
+ if(hx<0) {
+ if(iy>=0x4b800000) yisint = 2; /* even integer y */
+ else if(iy>=0x3f800000) {
+ k = (iy>>23)-0x7f; /* exponent */
+ j = iy>>(23-k);
+ if((j<<(23-k))==iy) yisint = 2-(j&1);
+ }
+ }
+
+ /* special value of y */
+ if (FLT_UWORD_IS_INFINITE(iy)) { /* y is +-inf */
+ if (ix==0x3f800000)
+ return one; /* +-1**+-inf = 1 */
+ else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
+ return (hy>=0)? y: zero;
+ else /* (|x|<1)**-,+inf = inf,0 */
+ return (hy<0)?-y: zero;
+ }
+ if(iy==0x3f800000) { /* y is +-1 */
+ if(hy<0) return one/x; else return x;
+ }
+ if(hy==0x40000000) return x*x; /* y is 2 */
+ if(hy==0x3f000000) { /* y is 0.5 */
+ if(hx>=0) /* x >= +0 */
+ return __ieee754_sqrtf(x);
+ }
+
+ ax = fabsf(x);
+ /* special value of x */
+ if(FLT_UWORD_IS_INFINITE(ix)||FLT_UWORD_IS_ZERO(ix)||ix==0x3f800000){
+ z = ax; /*x is +-0,+-inf,+-1*/
+ if(hy<0) z = one/z; /* z = (1/|x|) */
+ if(hx<0) {
+ if(((ix-0x3f800000)|yisint)==0) {
+ z = (z-z)/(z-z); /* (-1)**non-int is NaN */
+ } else if(yisint==1)
+ z = -z; /* (x<0)**odd = -(|x|**odd) */
+ }
+ return z;
+ }
+
+ /* (x<0)**(non-int) is NaN */
+ if(((((__uint32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
+
+ /* |y| is huge */
+ if(iy>0x4d000000) { /* if |y| > 2**27 */
+ /* over/underflow if x is not close to one */
+ if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
+ if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
+ /* now |1-x| is tiny <= 2**-20, suffice to compute
+ log(x) by x-x^2/2+x^3/3-x^4/4 */
+ t = ax-1; /* t has 20 trailing zeros */
+ w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
+ u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
+ v = t*ivln2_l-w*ivln2;
+ t1 = u+v;
+ GET_FLOAT_WORD(is,t1);
+ SET_FLOAT_WORD(t1,is&0xfffff000);
+ t2 = v-(t1-u);
+ } else {
+ float s2,s_h,s_l,t_h,t_l;
+ n = 0;
+ /* take care subnormal number */
+ if(FLT_UWORD_IS_SUBNORMAL(ix))
+ {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
+ n += ((ix)>>23)-0x7f;
+ j = ix&0x007fffff;
+ /* determine interval */
+ ix = j|0x3f800000; /* normalize ix */
+ if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
+ else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
+ else {k=0;n+=1;ix -= 0x00800000;}
+ SET_FLOAT_WORD(ax,ix);
+
+ /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
+ u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
+ v = one/(ax+bp[k]);
+ s = u*v;
+ s_h = s;
+ GET_FLOAT_WORD(is,s_h);
+ SET_FLOAT_WORD(s_h,is&0xfffff000);
+ /* t_h=ax+bp[k] High */
+ SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
+ t_l = ax - (t_h-bp[k]);
+ s_l = v*((u-s_h*t_h)-s_h*t_l);
+ /* compute log(ax) */
+ s2 = s*s;
+ 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 = (float)3.0+s2+r;
+ GET_FLOAT_WORD(is,t_h);
+ SET_FLOAT_WORD(t_h,is&0xfffff000);
+ t_l = r-((t_h-(float)3.0)-s2);
+ /* u+v = s*(1+...) */
+ u = s_h*t_h;
+ v = s_l*t_h+t_l*s;
+ /* 2/(3log2)*(s+...) */
+ p_h = u+v;
+ GET_FLOAT_WORD(is,p_h);
+ SET_FLOAT_WORD(p_h,is&0xfffff000);
+ p_l = v-(p_h-u);
+ z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
+ 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 */
+ t = (float)n;
+ t1 = (((z_h+z_l)+dp_h[k])+t);
+ GET_FLOAT_WORD(is,t1);
+ SET_FLOAT_WORD(t1,is&0xfffff000);
+ t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+ }
+
+ s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+ if(((((__uint32_t)hx>>31)-1)|(yisint-1))==0)
+ s = -one; /* (-ve)**(odd int) */
+
+ /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+ GET_FLOAT_WORD(is,y);
+ SET_FLOAT_WORD(y1,is&0xfffff000);
+ p_l = (y-y1)*t1+y*t2;
+ p_h = y1*t1;
+ z = p_l+p_h;
+ GET_FLOAT_WORD(j,z);
+ i = j&0x7fffffff;
+ if (j>0) {
+ if (i>FLT_UWORD_EXP_MAX)
+ return s*huge*huge; /* overflow */
+ else if (i==FLT_UWORD_EXP_MAX)
+ if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
+ } else {
+ if (i>FLT_UWORD_EXP_MIN)
+ return s*tiny*tiny; /* underflow */
+ else if (i==FLT_UWORD_EXP_MIN)
+ if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
+ }
+ /*
+ * compute 2**(p_h+p_l)
+ */
+ k = (i>>23)-0x7f;
+ n = 0;
+ if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
+ n = j+(0x00800000>>(k+1));
+ k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
+ SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
+ n = ((n&0x007fffff)|0x00800000)>>(23-k);
+ if(j<0) n = -n;
+ p_h -= t;
+ }
+ t = p_l+p_h;
+ GET_FLOAT_WORD(is,t);
+ SET_FLOAT_WORD(t,is&0xfffff000);
+ u = t*lg2_h;
+ v = (p_l-(t-p_h))*lg2+t*lg2_l;
+ z = u+v;
+ w = v-(z-u);
+ t = z*z;
+ t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+ r = (z*t1)/(t1-two)-(w+z*w);
+ z = one-(r-z);
+ GET_FLOAT_WORD(j,z);
+ j += (n<<23);
+ if((j>>23)<=0) z = scalbnf(z,(int)n); /* subnormal output */
+ else SET_FLOAT_WORD(z,j);
+ return s*z;
+}
diff --git a/lib/libm/wf_pow.c b/lib/libm/wf_pow.c
new file mode 100644
index 0000000..a30f880
--- /dev/null
+++ b/lib/libm/wf_pow.c
@@ -0,0 +1,179 @@
+/* wf_pow.c -- float version of w_pow.c.
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/*
+ * wrapper powf(x,y) return x**y
+ */
+
+#include "fdlibm.h"
+#include <errno.h>
+
+#ifdef __STDC__
+ float powf(float x, float y) /* wrapper powf */
+#else
+ float powf(x,y) /* wrapper powf */
+ float x,y;
+#endif
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_powf(x,y);
+#else
+ float z;
+ struct exception exc;
+ z=__ieee754_powf(x,y);
+ if(_LIB_VERSION == _IEEE_|| isnan(y)) return z;
+ if(isnan(x)) {
+ if(y==(float)0.0) {
+ /* powf(NaN,0.0) */
+ /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
+ exc.type = DOMAIN;
+ exc.name = "powf";
+ exc.err = 0;
+ exc.arg1 = (double)x;
+ exc.arg2 = (double)y;
+ exc.retval = 1.0;
+ if (_LIB_VERSION == _IEEE_ ||
+ _LIB_VERSION == _POSIX_) exc.retval = 1.0;
+ else if (!matherr(&exc)) {
+ errno = EDOM;
+ }
+ if (exc.err != 0)
+ errno = exc.err;
+ return (float)exc.retval;
+ } else
+ return z;
+ }
+ if(x==(float)0.0){
+ if(y==(float)0.0) {
+ /* powf(0.0,0.0) */
+ /* error only if _LIB_VERSION == _SVID_ */
+ exc.type = DOMAIN;
+ exc.name = "powf";
+ exc.err = 0;
+ exc.arg1 = (double)x;
+ exc.arg2 = (double)y;
+ exc.retval = 0.0;
+ if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
+ else if (!matherr(&exc)) {
+ errno = EDOM;
+ }
+ if (exc.err != 0)
+ errno = exc.err;
+ return (float)exc.retval;
+ }
+ if(finitef(y)&&y<(float)0.0) {
+ /* 0**neg */
+ exc.type = DOMAIN;
+ exc.name = "powf";
+ exc.err = 0;
+ exc.arg1 = (double)x;
+ exc.arg2 = (double)y;
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = 0.0;
+ else
+ exc.retval = -HUGE_VAL;
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ errno = EDOM;
+ }
+ if (exc.err != 0)
+ errno = exc.err;
+ return (float)exc.retval;
+ }
+ return z;
+ }
+ if(!finitef(z)) {
+ if(finitef(x)&&finitef(y)) {
+ if(isnan(z)) {
+ /* neg**non-integral */
+ exc.type = DOMAIN;
+ exc.name = "powf";
+ exc.err = 0;
+ exc.arg1 = (double)x;
+ exc.arg2 = (double)y;
+ if (_LIB_VERSION == _SVID_)
+ exc.retval = 0.0;
+ else
+ exc.retval = 0.0/0.0; /* X/Open allow NaN */
+ if (_LIB_VERSION == _POSIX_)
+ errno = EDOM;
+ else if (!matherr(&exc)) {
+ errno = EDOM;
+ }
+ if (exc.err != 0)
+ errno = exc.err;
+ return (float)exc.retval;
+ } else {
+ /* powf(x,y) overflow */
+ exc.type = OVERFLOW;
+ exc.name = "powf";
+ exc.err = 0;
+ exc.arg1 = (double)x;
+ exc.arg2 = (double)y;
+ if (_LIB_VERSION == _SVID_) {
+ exc.retval = HUGE;
+ y *= 0.5;
+ if(x<0.0&&rint(y)!=y) exc.retval = -HUGE;
+ } else {
+ exc.retval = HUGE_VAL;
+ y *= 0.5;
+ if(x<0.0&&rint(y)!=y) exc.retval = -HUGE_VAL;
+ }
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ if (exc.err != 0)
+ errno = exc.err;
+ return (float)exc.retval;
+ }
+ }
+ }
+ if(z==(float)0.0&&finitef(x)&&finitef(y)) {
+ /* powf(x,y) underflow */
+ exc.type = UNDERFLOW;
+ exc.name = "powf";
+ exc.err = 0;
+ exc.arg1 = (double)x;
+ exc.arg2 = (double)y;
+ exc.retval = 0.0;
+ if (_LIB_VERSION == _POSIX_)
+ errno = ERANGE;
+ else if (!matherr(&exc)) {
+ errno = ERANGE;
+ }
+ if (exc.err != 0)
+ errno = exc.err;
+ return (float)exc.retval;
+ }
+ return z;
+#endif
+}
+
+#ifdef _DOUBLE_IS_32BITS
+
+#ifdef __STDC__
+ double pow(double x, double y)
+#else
+ double pow(x,y)
+ double x,y;
+#endif
+{
+ return (double) powf((float) x, (float) y);
+}
+
+#endif /* defined(_DOUBLE_IS_32BITS) */
