Hmm... then again ... a power function *could* be written more simply as an integer math subroutine ... or not. I have vague memories from high-school on how that was done.

/* A union which permits us to convert between a float and a 32 bit int. */typedef union{ float value; unsigned int word;} ieee_float_shape_type;/* Get a 32 bit int from a float. */#define GET_FLOAT_WORD(i,d) \do { \ ieee_float_shape_type gf_u; \ gf_u.value = (d); \ (i) = gf_u.word; \} while (0)/* Set a float from a 32 bit int. */#define SET_FLOAT_WORD(d,i) \do { \ ieee_float_shape_type sf_u; \ sf_u.word = (i); \ (d) = sf_u.value; \} while (0)#define FLT_UWORD_IS_ZERO(x) ((x)==0)#define FLT_UWORD_IS_NAN(x) ((x)>0x7f800000L)#define FLT_UWORD_IS_INFINITE(x) ((x)==0x7f800000L)#define FLT_UWORD_IS_SUBNORMAL(x) ((x)<0x00800000L)#define FLT_UWORD_EXP_MIN 0x43160000#define FLT_UWORD_LOG_MIN 0x42cff1b5static const floatbp[] = {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*/float powf(float x, float y){ float z,ax,z_h,z_l,p_h,p_l; float y1,t1,t2,r,s,t,u,v,w; int i,j,k,yisint,n; int 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; /* +-NaN return x+y */ if(FLT_UWORD_IS_NAN(ix) || FLT_UWORD_IS_NAN(iy)) 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 (FLT_UWORD_IS_INFINITE(iy)) { /* y is +-inf */ if (ix==0x3f800000) return y - y; /* inf**+-1 is NaN */ 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 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(((((unsigned int)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 = x-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(((((unsigned int)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;}

This won't help any with the calibration efforts, but I snapped this hummingbird at CHDK 1/8000, f3.5, ISO 400, full zoom with NO flash, Canon S2 IS. I think it demonstrates the potential of the high-speed shutter. Thanks again to the developers and explorers!ddedit to add: cropped it a bit to comply with attachment size, now appears the rules have changed......

What mode where you in for that shot? M, or Av set at 3.5?

Use that hint someone else found, full-press for one shot, then let off to the half-press position. Then you see the subject being exposed at the same speed as will apear on your final image.

Well, I think I confirmed it, and it's reproducible. The smaller the f/stop that you use, the higher the shutter-speed that you can use.

It looks like the shortest shutter speed is about 1/15000, because on shorter speeds there is no significant changes nether in sharpness nor in brightness of picture.Here is the gallery with shots made with shutter speed from 1/2500 to 1/100000.

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