stmhal: Add powf, logf, log2f, log10f.

stmhal/math.c

@@ -46,12 +46,6 @@ double __aeabi_dmul(double x , double y) {
     return 0.0;
 
 }
-/*
-double sqrt(double x) {
-    // TODO
-    return 0.0;
-}
-*/
 
 float sqrtf(float x) {
     asm volatile (
@@ -61,16 +55,18 @@ float sqrtf(float x) {
     return x;
 }
 
-// TODO we need import these functions from some library (eg musl or newlib)
-float powf(float x, float y) { return 0.0; }
-float logf(float x) { return 0.0; }
 // some compilers define log2f in terms of logf
 #ifdef log2f
 #undef log2f
 #endif
-float log2f(float x) { return 0.0; }
+float log2f(float x) { return logf(x) / (float)_M_LN2; }
-float log10f(float x) { return 0.0; }
+
-float tanhf(float x) { return 0.0; }
+static const float _M_LN10 = 2.30258509299404; // 0x40135d8e
+float log10f(float x) { return logf(x) / (float)_M_LN10; }
+
+float tanhf(float x) { return sinhf(x) / coshf(x); }
+
+// TODO we need import these functions from some library (eg musl or newlib)
 float acoshf(float x) { return 0.0; }
 float asinhf(float x) { return 0.0; }
 float atanhf(float x) { return 0.0; }
@@ -93,8 +89,11 @@ float modff(float x, float *y) { return 0.0; }
 float frexpf(float x, int *exp) { return 0.0; }
 float ldexpf(float x, int exp) { return 0.0; }
 
+/*****************************************************************************/
 /*****************************************************************************/
 // from musl-0.9.15 libm.h
+/*****************************************************************************/
+/*****************************************************************************/
 
 /* origin: FreeBSD /usr/src/lib/msun/src/math_private.h */
 /*
@@ -140,8 +139,11 @@ do {                                              \
       (d) = __u.f;                                \
 } while (0)
 
+/*****************************************************************************/
 /*****************************************************************************/
 // __fpclassifyf from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
 
 int __fpclassifyf(float x)
 {
@@ -152,8 +154,11 @@ int __fpclassifyf(float x)
 	return FP_NORMAL;
 }
 
+/*****************************************************************************/
 /*****************************************************************************/
 // scalbnf from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
 
 float scalbnf(float x, int n)
 {
@@ -184,8 +189,275 @@ float scalbnf(float x, int n)
 	return x;
 }
 
+/*****************************************************************************/
+/*****************************************************************************/
+// powf from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
+
+/* origin: FreeBSD /usr/src/lib/msun/src/e_powf.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.
+ * ====================================================
+ */
+
+static const float
+bp[]   = {1.0, 1.5,},
+dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
+dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
+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    =  9.6191406250e-01, /* 0x3f764000 =12b cp */
+cp_l    = -1.1736857402e-04, /* 0xb8f623c6 =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*/
+
+float powf(float x, float y)
+{
+	float z,ax,z_h,z_l,p_h,p_l;
+	float y1,t1,t2,r,s,sn,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;
+
+	/* x**0 = 1, even if x is NaN */
+	if (iy == 0)
+		return 1.0f;
+	/* 1**y = 1, even if y is NaN */
+	if (hx == 0x3f800000)
+		return 1.0f;
+	/* NaN if either arg is NaN */
+	if (ix > 0x7f800000 || iy > 0x7f800000)
+		return x + y;
+
+	/* 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 (iy == 0x7f800000) {  /* y is +-inf */
+		if (ix == 0x3f800000)      /* (-1)**+-inf is 1 */
+			return 1.0f;
+		else if (ix > 0x3f800000)  /* (|x|>1)**+-inf = inf,0 */
+			return hy >= 0 ? y : 0.0f;
+		else if (ix != 0)          /* (|x|<1)**+-inf = 0,inf if x!=0 */
+			return hy >= 0 ? 0.0f: -y;
+	}
+	if (iy == 0x3f800000)    /* y is +-1 */
+		return hy >= 0 ? x : 1.0f/x;
+	if (hy == 0x40000000)    /* y is 2 */
+		return x*x;
+	if (hy == 0x3f000000) {  /* y is  0.5 */
+		if (hx >= 0)     /* x >= +0 */
+			return sqrtf(x);
+	}
+
+	ax = fabsf(x);
+	/* special value of x */
+	if (ix == 0x7f800000 || ix == 0 || ix == 0x3f800000) { /* x is +-0,+-inf,+-1 */
+		z = ax;
+		if (hy < 0)  /* z = (1/|x|) */
+			z = 1.0f/z;
+		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;
+	}
+
+	sn = 1.0f; /* sign of result */
+	if (hx < 0) {
+		if (yisint == 0) /* (x<0)**(non-int) is NaN */
+			return (x-x)/(x-x);
+		if (yisint == 1) /* (x<0)**(odd int) */
+			sn = -1.0f;
+	}
+
+	/* |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 ? sn*huge*huge : sn*tiny*tiny;
+		if (ix > 0x3f800007)
+			return hy > 0 ? sn*huge*huge : sn*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)*(0.5f - t*(0.333333333333f - t*0.25f));
+		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 (ix < 0x00800000) {
+			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)       /* |x|<sqrt(3/2) */
+			k = 0;
+		else if (j < 0x5db3d7)   /* |x|<sqrt(3)   */
+			k = 1;
+		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 = 1.0f/(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 */
+		is = ((ix>>1) & 0xfffff000) | 0x20000000;
+		SET_FLOAT_WORD(t_h, is + 0x00400000 + (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 = 3.0f + s2 + r;
+		GET_FLOAT_WORD(is, t_h);
+		SET_FLOAT_WORD(t_h, is & 0xfffff000);
+		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+...) */
+		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);
+	}
+
+	/* 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);
+	if (j > 0x43000000)          /* if z > 128 */
+		return sn*huge*huge;  /* overflow */
+	else if (j == 0x43000000) {  /* if z == 128 */
+		if (p_l + ovt > z - p_h)
+			return sn*huge*huge;  /* overflow */
+	} else if ((j&0x7fffffff) > 0x43160000)  /* z < -150 */ // FIXME: check should be  (uint32_t)j > 0xc3160000
+		return sn*tiny*tiny;  /* underflow */
+	else if (j == 0xc3160000) {  /* z == -150 */
+		if (p_l <= z-p_h)
+			return sn*tiny*tiny;  /* underflow */
+	}
+	/*
+	 * compute 2**(p_h+p_l)
+	 */
+	i = j & 0x7fffffff;
+	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 & 0xffff8000);
+	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)/(t1-2.0f) - (w+z*w);
+	z = 1.0f - (r - z);
+	GET_FLOAT_WORD(j, z);
+	j += n<<23;
+	if ((j>>23) <= 0)  /* subnormal output */
+		z = scalbnf(z, n);
+	else
+		SET_FLOAT_WORD(z, j);
+	return sn*z;
+}
+
+/*****************************************************************************/
 /*****************************************************************************/
 // expf from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
 
 /* origin: FreeBSD /usr/src/lib/msun/src/e_expf.c */
 /*
@@ -211,8 +483,8 @@ invln2  = 1.4426950216e+0f,  /* 0x3fb8aa3b */
  * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
  * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
  */
-P1 =  1.6666625440e-1f, /*  0xaaaa8f.0p-26 */
+expf_P1 =  1.6666625440e-1f, /*  0xaaaa8f.0p-26 */
-P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
+expf_P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
 
 float expf(float x)
 {
@@ -260,15 +532,18 @@ float expf(float x)
 
 	/* x is now in primary range */
 	xx = x*x;
-	c = x - xx*(P1+xx*P2);
+	c = x - xx*(expf_P1+xx*expf_P2);
 	y = 1 + (x*c/(2-c) - lo + hi);
 	if (k == 0)
 		return y;
 	return scalbnf(y, k);
 }
 
+/*****************************************************************************/
 /*****************************************************************************/
 // expm1f from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
 
 /* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
 /*
@@ -380,8 +655,11 @@ float expm1f(float x)
 	return y;
 }
 
+/*****************************************************************************/
 /*****************************************************************************/
 // __expo2f from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
 
 /* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */
 static const int k = 235;
@@ -398,8 +676,82 @@ float __expo2f(float x)
 	return expf(x - kln2) * scale * scale;
 }
 
+/*****************************************************************************/
+/*****************************************************************************/
+// logf from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
+
+/* origin: FreeBSD /usr/src/lib/msun/src/e_logf.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.
+ * ====================================================
+ */
+
+static const float
+/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
+Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
+Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
+Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
+Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
+
+float logf(float x)
+{
+	union {float f; uint32_t i;} u = {x};
+	float_t hfsq,f,s,z,R,w,t1,t2,dk;
+	uint32_t ix;
+	int k;
+
+	ix = u.i;
+	k = 0;
+	if (ix < 0x00800000 || ix>>31) {  /* x < 2**-126  */
+		if (ix<<1 == 0)
+			return -1/(x*x);  /* log(+-0)=-inf */
+		if (ix>>31)
+			return (x-x)/0.0f; /* log(-#) = NaN */
+		/* subnormal number, scale up x */
+		k -= 25;
+		x *= 0x1p25f;
+		u.f = x;
+		ix = u.i;
+	} else if (ix >= 0x7f800000) {
+		return x;
+	} else if (ix == 0x3f800000)
+		return 0;
+
+	/* reduce x into [sqrt(2)/2, sqrt(2)] */
+	ix += 0x3f800000 - 0x3f3504f3;
+	k += (int)(ix>>23) - 0x7f;
+	ix = (ix&0x007fffff) + 0x3f3504f3;
+	u.i = ix;
+	x = u.f;
+
+	f = x - 1.0f;
+	s = f/(2.0f + f);
+	z = s*s;
+	w = z*z;
+	t1= w*(Lg2+w*Lg4);
+	t2= z*(Lg1+w*Lg3);
+	R = t2 + t1;
+	hfsq = 0.5f*f*f;
+	dk = k;
+	return s*(hfsq+R) + dk*ln2_lo - hfsq + f + dk*ln2_hi;
+}
+
+/*****************************************************************************/
 /*****************************************************************************/
 // coshf from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
 
 float coshf(float x)
 {
@@ -433,8 +785,11 @@ float coshf(float x)
 	return t;
 }
 
+/*****************************************************************************/
 /*****************************************************************************/
 // sinhf from musl-0.9.15
+/*****************************************************************************/
+/*****************************************************************************/
 
 float sinhf(float x)
 {