diff --git a/stmhal/math.c b/stmhal/math.c index 61ba7280ea..9b815f1180 100644 --- a/stmhal/math.c +++ b/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 log10f(float x) { return 0.0; } -float tanhf(float x) { return 0.0; } +float log2f(float x) { return logf(x) / (float)_M_LN2; } + +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|>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 */ -P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */ +expf_P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */ +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) {