I think it would be a regression in technology to start having Intel Web-Compute Processors and Intel Gaming-Compute Processors but you know... that's just crazy me.
A bad format for what? Do you mean that you assume that HTML,markdown would look better in something like JSON? I want to see a "proof" for documents you write in JSON by hand.
Modern CPU have registers, caches, SIMD instructions which are tremendously important for performance. Yet I don't know no language which would explicitly provide any control over those things. You can only hope that your loop will be understood by compiler and optimized to proper SIMD instructions. And any change might break that optimization (including changes in compiler).
CUDA provides your explicit cache control through "__shared__" memory.
C commonly has low-level attributes. In particular, you have the "register" keyword in C if you really want to go that route, but compilers have a nice greedy algorithm that is damn near optimal, so its best to let the compiler perform its own analysis for register allocation.
SIMD instructions are easily provided through intrinsics: https://software.intel.com/sites/landingpage/IntrinsicsGuide...
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There's plenty of low level languages that provide the control you desire. The main reason for __shared__ memory is that compilers can't optimize memory across threads yet, so we still require the programmer to tile memory manually and think about the optimizations across the many, many threads a CUDA multiprocessor supports.
If you want to explicitly control the cache on x86 systems, use the _mm_prefetch() intrinsic. In practice though, it is pretty rare for prefetching to be useful on modern systems. (Auto-prefetchers will optimize most sequential traversals, and those that fail prefetching can still be out-of-order executed at decent speeds)
OpenCL / CUDA are good examples of languages designed around GPUs. C itself was based off of the DEC-PDP11.
Optimizing the other way: Many modern processors are based on executing C faster and faster... but other languages have begun to be targeted by CPUs. Not only this JOP, but ARM famously has the "convert to javascript floating point" instruction, to optimize our phone's handling of Javascript and HTML pages.
There's lots of engineers. Why not have all the engineers try to make everything faster? What benefit is there of doing things only one at a time as you propose?
RISCs also don't help with lexically scoped variables which languages like Pascal have but C doesn't.
A processor that was specifically designed for C was called CRISP (and was briefly sold as the AT&T Hobbit):
x86 itself has a lot of glut. Most x86 processors don't directly implement x86 in hardware but execute instructions in microcode, much like JVM and Java bytecode.