Programming

Well, you guys are making some p good points. I'll probably end up sharing it, but'll give it a clean up, try to fix some bugs and improve my comments before posting it publicly. For now whoever really wants it (including you) can just ask and I'll dm it, understanding it will be a hard read and still has bugs.

I can easily check for when motion stops, but checking for when any particular face is both parallel to the floor and at the same level can be computationally expensive, particularly in the dice with more sides. What you're suggesting is likely a good idea, but I wouldn't know how to get probabilities without doing what I just mentioned. I'm sure there's an optimization i can do with this that I can't think of rn.

I didn't have the patience to do it myself bit wanted to see just how complex it would get:

fp32_mul() {
    local a=$1 b=$2
    local sa=$(( (a >> 31) & 1 ))
    local sb=$(( (b >> 31) & 1 ))
    local sign=$((sa ^ sb))

    local ea=$(( (a >> 23) & 0xff ))
    local eb=$(( (b >> 23) & 0xff ))
    local fa=$(( a & 0x7fffff ))
    local fb=$(( b & 0x7fffff ))

    # NaN / infinity / zero handling
    if (( ea == 255 )); then
        if (( fa != 0 )); then
            printf '%08x\n' $((0x7fc00000))
            return
        fi
        if (( eb == 0 && fb == 0 )); then
            printf '%08x\n' $((0x7fc00000))   # inf * 0 = NaN
            return
        fi
        printf '%08x\n' $(((sign << 31) | 0x7f800000))
        return
    fi

    if (( eb == 255 )); then
        if (( fb != 0 )); then
            printf '%08x\n' $((0x7fc00000))
            return
        fi
        if (( ea == 0 && fa == 0 )); then
            printf '%08x\n' $((0x7fc00000))
            return
        fi
        printf '%08x\n' $(((sign << 31) | 0x7f800000))
        return
    fi

    if (( ea == 0 && fa == 0 || eb == 0 && fb == 0 )); then
        printf '%08x\n' $((sign << 31))
        return
    fi

    # Convert subnormals to a normalized significand/exponent.
    # m is a 24-bit significand for normals.
    local ma mb
    if (( ea == 0 )); then
        ma=$fa
        ea=1
        while (( (ma & 0x800000) == 0 )); do
            ma=$((ma << 1))
            ((ea--))
        done
    else
        ma=$((fa | 0x800000))
    fi

    if (( eb == 0 )); then
        mb=$fb
        eb=1
        while (( (mb & 0x800000) == 0 )); do
            mb=$((mb << 1))
            ((eb--))
        done
    else
        mb=$((fb | 0x800000))
    fi

    # Multiply the two 24-bit significands.
    # Product is up to 48 bits.
    local p=$((ma * mb))
    local e=$((ea + eb - 127))

    # Normalize product.
    #
    # ma*mb has binary point after bit 46.  If bit 47 is set,
    # product is [2,4), otherwise [1,2).
    local shift
    if (( p & 0x800000000000 )); then
        shift=24
        ((e++))
    else
        shift=23
    fi

    # Extract 23 fraction bits plus guard/round/sticky information.
    local frac=$(( (p >> shift) & 0x7fffff ))
    local guard=$(( (p >> (shift - 1)) & 1 ))
    local round=$(( (p >> (shift - 2)) & 1 ))
    local sticky=0

    if (( shift >= 3 )); then
        local mask=$(( (1 << (shift - 2)) - 1 ))
        (( (p & mask) != 0 )) && sticky=1
    fi

    # Round-to-nearest, ties-to-even.
    if (( guard && (round || sticky || (frac & 1)) )); then
        ((frac++))
        if (( frac == 0x800000 )); then
            frac=0
            ((e++))
        fi
    fi

    # Overflow -> infinity.
    if (( e >= 255 )); then
        printf '%08x\n' $(((sign << 31) | 0x7f800000))
        return
    fi

    # Normal result.
    if (( e > 0 )); then
        printf '%08x\n' $(((sign << 31) | (e << 23) | frac))
        return
    fi

    # Underflow into the subnormal range.
    #
    # At this point the normalized significand represented by
    # (1.frac) must be shifted right by 1-e positions.
    local mant=$((0x800000 | frac))
    local rshift=$((1 - e))
    local lost=0
    local halfway=0
    local low=0

    if (( rshift >= 25 )); then
        # Everything rounds to zero (unless the exact value is
        # sufficiently close, which it cannot be here).
        mant=0
    else
        low=$((mant & ((1 << rshift) - 1)))
        mant=$((mant >> rshift))

        halfway=$((1 << (rshift - 1)))

        if (( low > halfway || (low == halfway && (mant & 1)) )); then
            ((mant++))
        fi
    fi

    # Rounding a subnormal can produce the smallest normal.
    if (( mant >= 0x800000 )); then
        printf '%08x\n' $(((sign << 31) | (1 << 23)))
    else
        printf '%08x\n' $(((sign << 31) | mant))
    fi
}

hahaha you seem to be familiar with the issues I ran across

Yes, the values are rendered on top of each face with "pixel" maps (ascii art) that have the character of the digit they represent as each pixel. These are later manipulated by the perspective projection.

For example on this d6 you can see the top face has 1s written down (in the shape of a sideways one) and the front one has 4s written down in the shape of a skewed and sideways 4.

In this specific color scheme there's not a lot of contrast between the values, but even in the palettes with better contrast, good readability is something I'm kind of giving up on solving well.

edit: might be clearer here: