Why are bitwise boolean and shift operations called logical operations in CPU architecture? - cpu-architecture

This image is from the "Computer Organization and Design" book:
As you can see, the left-hand column is labeled as "logical operations", but the operations shown are all bitwise. Conventionally, && and || are known as logical operators while & and | are known as bitwise operators.
They are introducing the table with the following sentences:
It follows that operations were added to
programming languages and instruction set architectures to simplify, among other
things, the packing and unpacking of bits into words. These instructions are called
logical operations. Figure 2.8 shows logical operations in C, Java, and RISC-V.
Why do you think they write logical operators for & and |?

In computer-architecture terminology, operations on numbers are "arithmetic" (e.g. add/sub/mul/div).
Operations on bits are often called "logical" or "logic instructions" as in "boolean logic". (Arithmetic right shift, shifting in copies of the sign bit, is usually grouped with other shifts as a logic aka bitwise operation.)
For example, in the Wikipedia ALU (Arithmetic logic unit) article, the editor who wrote it says the opcode "specifies the desired arithmetic or logic operation to be performed by the ALU".
Agner Fog's instruction tables of his per-instruction performance-testing results categorizes integer instructions into Move / Arithmetic / Logic (bitwise, shifts, bit-test, setcc) / Control transfer / String (yes, x86 is funky like that) / Other (like leave and cpuid). And similarly, FP arithmetic vs. logic (yes, SIMD instruction sets provide bitwise boolean instructions for FP/SIMD registers).
CPUs don't have "logical" operations in the sense of C and Java's && or || (not even for integer inputs without considering the short-circuit eval), so in the context of computer architecture, "logical" has a different meaning than in software where they needed to distinguish bitwise from the more complicated operation of logical operators.
The computer architecture usage is older, I assume.
Your book isn't saying that & in C or Java is a "logical operator", but it is saying that an and instruction performs a "logical operation" in the computer-architecture sense of the word. The corresponding C and Java operator is the bitwise & operator.
Machine code doesn't have operators, just instructions. (Assembly language has operations on assemble-time constants, like andi x1, x2, (1<<4)-1 as an alternate way of writing andi x1, x2, 0x0f. But this is purely a feature of an assembler, and not something an ISA reference manual will discuss.)
Usage citations from random tutorials or guides that came up when I googled computer architecture logical operations
https://www.tutorialspoint.com/what-are-logic-micro-operations-in-computer-architecture "Logic operations are binary micro-operations implemented on the bits saved in the registers. These operations treated each bit independently and create them as binary variables."
https://www.sciencedirect.com/topics/computer-science/logical-operation quotes some books, like Harris & Harris: Digital Design and Computer Architecture, 2016 - "ARM logical operations include AND, ORR (OR), EOR (XOR), and BIC (bit clear)". The same authors wrote the same thing about MIPS bitwise instructions.
https://www.techtarget.com/whatis/definition/arithmetic-logic-unit-ALU

Related

Orthogonality of Instruction Set Architecture

I am studying the difference between CISC and RISC recently, and I've encountered into the term "Orthogonality". After doing some research, my understanding so far is that there are two "axes", addressing modes & operations, which are independent of each other, so it produces a maximum number of (#addressing modes * #operations) instructions in the ISA.
For CISC machine, which is a register-memory architecture, operands may come from register or memory and RISC a register-register(or load-store) one on the contrary.
So, what's the role of orthogonality playing in these two ISA? Is CISC more orthogonal than RISC or vice versa?
As the wiki describes, "Modern CPUs often simulate orthogonality in a preprocessing step before performing the actual tasks in a RISC-like core. This "simulated orthogonality" in general is a broader concept, encompassing the notions of decoupling and completeness in function libraries, like in the mathematical concept: an orthogonal function set is easy to use as a basis into expanded functions, ensuring that parts don’t affect another if we change one part." What does this paragraph mean? What is the preprocessing step, does it have anything to do with the microcode?
Any explanation are appreciated! Thanks a lot!
Maximizing total choices of possible instructions like a CISC is generally not what's meant. Instead it's more about being a simpler compiler target, without complex interactions in what makes an instruction legal or not. RISC machines are often highly orthogonal, and designed with being a compiler target in mind, not human programmers.
My understanding of the term is that orthogonality is more about any register being usable in any case where any other register is usable. Unlike x86 shl reg, cl where variable-count shifts require a specific register. (I know this is a RISC-V question, but the examples of non-orthogonality I know of come from other ISAs, primarily x86.)
And definitely not like 8086 (before 386), where if you needed to multiply, one of the operands had to be in the accumulator, AL or AX. And sign-extension was also only available there. 386 introduced movsx reg, r/m8 and r/m16. (And movzx, allowing easy and more efficient zero-extending of a byte from memory into SI or DI, without having to load 2 bytes and and si, 0x00ff.)
Even worse, 16-bit addressing modes only allow a few registers in very limited ways: [bp|bx] + [si|di] + disp0/8/16, vs. 32-bit addressing modes allowing stuff like lea eax, [ecx + ecx + 3] to use the same register twice, or address memory relative to the stack pointer without having to copy it to the base pointer (BP) register.
Or if some memory operands can use a certain addressing mode, can all memory operands use it? AArch64 ldp/stp (load-pair/store-pair of registers) I think has fewer available addressing modes than single-register loads, because it needs 5 extra bits for a second register number. Unlike ARM32 ldrd where the pair of registers is two contiguous registers, starting with an even number.
In general, the less interaction there is between a choice of one thing (like instruction) and the possible choices for another (a register), the more orthogonal.
One of the major benefits with this is being a simple compiler target. The most optimal code can more often be found with a greedy algorithm that only takes into a account one thing at a time, not interlocking tradeoffs. Not like x86-64 "if I use ECX instead of R9d for this variable, that'll save bytes in multiple instructions not needing REX prefix, but later mean I need an extra mov to copy a register for a shift count". (x86 BMI2 introduced variable-count shifts that can use a count from any register, like shlx ebx, eax, r15d)
Or far worse targeting 8086 or 286, where 16-bit addressing modes impose a lot more constraints on register allocation. And you'd more often you'd want to use instructions that needed their operands in specific registers, especially the accumulator.
But if you're not worried about every byte of code size, x86-64 is a fairly orthogonal ISA, usually you don't need to care about which register you use for what. One change in that direction beyond 386's important changes was making the low byte of every register addressable, like bpl, spl, sil, dil as the low bytes of RBP, RSP, RSI, RDI. (But those require REX prefixes, overlapping encodings with AH/CH/DH/BH which are only usable in instructions without REX prefixes.)
Another example of non-orthogonality is x86's notorious integer SIMD extensions, MMX and SSE2. Want to do minimum of unsigned integers 16 bytes at a time? In SSE2 we have pminub for unsigned byte elements. And pminsw, signed 16-bit elements. But no other combination of size and signedness until SSE4.1, several years later, which filled in the gaps allowing signed bytes and u16, as well as i32 and u32. And then AVX-512 added i64 and u64. Every min available always had a corresponding max, but other than that, SSE2 was highly non-orthogonal in that and many other ways, including signed/unsigned saturating add/sub, and pack of wider to narrower elements with signed or unsigned saturation. And FP vs. integer shuffles, e.g. there's no integer equivalent to shufps that takes two elements from one vector, two from another, using an immediate control operand. Fortunately for shuffles you can use FP shuffles on integer data.
x86 SIMD is still not very orthogonal in many ways, for example in integer multiply where not all combinations of element size are available for everything; 16-bit has 16x16 => 16-bit low half, signed high half, or unsigned high half. (And a widening multiply and horizontal-add, pmaddwd). 32-bit has signed and unsigned widening 32x32 => 64-bit, and with SSE4.1 also non-widening. 8-bit only has a multiply and horizontal-add where one operand is treated as signed, the other as unsigned.
Again, if I'm picking on x86 a lot, it's because it's what I know. And Intel painted a huge "kick me" sign on their back when they designed MMX and SSE2, only taking some steps to fix things later with SSE4.1. (I'm sure there are reasons for some of those choices, including transistor budget and opcode coding-space in x86's notoriously cramped machine-code.) But a lot of programs don't want to assume SSE4.1 as a requirement to run at all, even now, over a decade since the first SSE4.1 CPUs. Most other SIMD ISAs are more orthogonal than x86, like ARM NEON or PowerPC AltiVec.
Anyway, in general, it's more orthogonal if all operations are available in all combinations of size and signedness that exist for any operation. This isn't always a big deal for compilers per-se, more for humans not realizing that a compiler could make their code faster if this variable was unsigned or something.
Modern CPUs often simulate orthogonality in a preprocessing step before performing the actual tasks in a RISC-like core
That sounds like they're talking about decoding to uops, but I don't see how that would gain orthogonality.
Unless they're counting the concept of any instruction allowing a memory source operand as being more orthogonal. Normally you wouldn't, being a load/store architecture is basically a fixed constraint that doesn't make other things harder.
But if you do consider that more orthogonal, then yes, decoding add eax, [rdi] to 2 uops lets it run on a back-end that separates the load work from the store work, like a RISC.
I hadn't heard this term orthogonal instruction set before, however:
The VAX is perhaps the epitome of CISC.  The VAX supports many addressing modes, ranging from register itself, to memory specified by various indexing computations (some including pointer advancement, so as to do *p++ or *--p).
The VAX allows all addressing modes for all operands of any instruction.  Further, the VAX allows both 2 operand and 3 operand instructions, so addl2 is operand2 += operand1, and addl3 is operand3 = operand1 + operand2.
Basically it can encode a lot of stuff in a single instruction, so we can do for example, a[i] = *p++ + b[j]; in one instruction, assuming a, b, i, j, and p are in registers.
Other CISC-style processors limit the encoding, for example, so that we can only do two-operand instructions (no 3 operand), and some even limit the 2nd operand to a register, so only one memory operand.  I believe this is what they're getting at with the term orthogonal or not.
Meanwhile, a RISC processor instead follows a load/store architecture.  Access to memory is not allowed for any operand, but rather only via load and store instructions, and only with those instructions are there addressing modes.  Most all arithmetic operations (except the add for addressing) happen between registers alone.  (In some sense the RISC philosophy has an orthogonality since all arithmetic operations work on registers alone.)
I don't think the term orthogonality is of high value.  I wouldn't dwell on the term itself, but rather take away from that article the comparison between CISC ala VAX, vs. others CISC, vs. RISC.
#Peter also makes a good points, such as that certain registers being hard code (i.e. an implicit source/target) in some architectures for some instructions, which reduces orthogonality.
By that point I might stress that RISC architectures generally don't hard code registers, though MIPS hard codes the return address register ($31) for the jal instruction whereas RISC V does not ($sp and $ra are hard coded but only in the compressed instruction extension).  Whereas some CISC architectures (except VAX) hard code more registers. 
The MC68000 divides the registers into two sets of 8: addressing registers and data registers, which helps encoding by providing 16 registers with only 3-bit register fields, but also limits what you can do with them (and there aren't enough address registers, since one is the stack pointer and another the global pointer, leaving only 6).
CISC architecture often support byte vs. word sized arithmetic, whereas RISC architectures usually support only word sized arithmetic, so if you want byte, you have to simulate it (i.e. with range check or other).

Why does SIMD have single data instructions when it's called SIMD?

I've been wondering.. It's called SIMD as in single instruction multiple data. So why does it have single data instructions?
For example, vaddss is the single data equivalent of the multiple data vaddps. Just about every SIMD instruction have a single data version.
Why?
Why does SIMD have single data instructions when it's called SIMD?
It isn't a SIMD instruction in that sense
vaddss is a scalar FP math instruction that operates on data in the FP/SIMD registers (XMM0..15). It exists because x87 is not a very convenient compiler target with its stack-based registers that often need fxch, and other quirks. Intel added a new way to do scalar FP math along with SSE1 (float) and SSE2 (double), which is fortunately baseline for x86-64 so everyone can just use it.
People who call that a SIMD instruction are talking about one of:
Which registers it operates on. (XMM0 is 16 bytes wide and clearly a SIMD register, even when you only care about the low element holding a scalar value.)
The fact that it's an AVX instruction, so it was introduced with an ISA extension that was primarily aimed at SIMD usage, and thus is called a SIMD extension or instruction set.
Which also means it uses the MXCSR for rounding mode and FP exception recording / unmasking, and the kinds of exceptions it can take are the same as other SSE/AVX instructions which Intel documents as "SIMD Floating-Point Exceptions" as concise terminology to distinguish it from legacy x87.
Or they're talking about the use-case of doing something to just the low element when the high elements have actual data. (Quite rare, but something you could do. Maybe more likely with sd scalar double, where the low double is one half of an XMM register.)
Or they're just plain wrong if they actually mean it in terms of Flynn's taxonomy of SISD vs. SIMD vs. MIMD etc. I highly doubt anyone would actually mean that, though. The ss and sd scalar FP math instructions are SISD, single-instruction single-data. And BTW, they only exist for FP math; x86 already has instructions like add eax, ecx for scalar integer math, and doesn't have scalar versions of paddb or even xorps.
One reason for having separate scalar FP math instructions is that using addps would also operate on whatever garbage might be in the high elements of XMM registers. This can raise extra FP exceptions (usually masked, so only recorded in MXCSR (fenv.h), but if unmasked would trap to the OS.)
With the upper elements all 0.0 (which isn't required by the calling convention, BTW), addps wouldn't raise any extra exceptions, but divps would divide by zero.
With non-zero garbage like small integers, it might be a bit-pattern for a subnormal float, or a result might be subnormal, causing huge slowdowns (factor of ~100) as the CPU takes a microcode assist to get handle subnormal input or output in many cases (or when SSE1 was new in Pentium III, probably all cases of subnormals). Unless you set FTZ and DAZ (flush to zero, denormal are zero) like gcc -ffast-math does.
For instructions like xorps or paddq which don't do actual FP math, no FP exceptions or microcode assists are possible. You can just use them even if you only care about the low 32 or 64 bits of an XMM.
MMX or SSE2 had occasional uses in 32-bit code for doing scalar 64-bit integer math, with zeros or garbage in the upper bytes. MMX paddq mm0, mm1 is a SISD instruction, but SSE2 paddq xmm0, xmm1 is a SIMD instruction.
SSE1 was new in Pentium 3, where the SIMD execution units and registers were only 64 bits wide. addps decoded to 2 uops; addss decoded to 1. So there was a performance motivation, too, even in the best case.
This is also likely the reason for Intel's unfortunate design where sqrtss and cvtsi2ss and others merge into the destination, requiring either spending extra front-end bandwidth on xor-zeroing, or risking false dependencies: Why does adding an xorps instruction make this function using cvtsi2ss and addss ~5x faster? . It's a short-sighted design decision to make them single-uop on Pentium 3, which they unfortunately followed in SSE2 for double precision, and stuck to for AVX and AVX-512 when they had a chance to introduce better versions with different semantics. At least the AVX versions take a 2nd source register to merge with, so you can pick a "cold" reg as a workaround, see my answer on the linked duplicate.
It's normal for scalar FP to share registers with SIMD
It isn't necessary or useful to have yet another set of registers for scalar FP, and sharing with the x87 FPU or the general-purpose integer registers would each be worse for separate reasons.
It's totally normal on other ISAs for the SIMD registers to overlap or be the same as the scalar FP registers; Some ISAs (like ARM) that didn't have weirdo designs like x87 didn't need new architectural state to introduce SIMD. e.g. ARM's NEON q0..q15 16-byte registers map to pairs of d0..d31 double-precision FP registers that existed with VFPv3.
(I'm not sure if the partial-register aliasing was actually common in SIMD extensions for other ISAs, though. Probably some introduced new architectural state, or just used FP double-precision registers as 64-bit integer SIMD instead of 128-bit.)
In an OS kernel you often talk about saving "FPU state" on context switch (as opposed to just the general-purpose integer registers), and these days that's short-hand for FPU and SIMD state. e.g. in the Linux kernel, you need to use kernel_fpu_begin() before running instructions that use XMM/YMM/ZMM registers. (e.g. in the RAID5 / RAID6 drivers).

What accounts for most of the integer multiply instructions?

The majority of integer multiplications don't actually need multiply:
Floating-point is, and has been since the 486, normally handled by dedicated hardware.
Multiplication by a constant, such as for scaling an array index by the size of the element, can be reduced to a left shift in the common case where it's a power of two, or a sequence of left shifts and additions in the general case.
Multiplications associated with accessing a 2D array, can often be strength reduced to addition if it's in the context of a loop.
So what's left?
Certain library functions like fwrite that take a number of elements and an element size as runtime parameters.
Exact decimal arithmetic e.g. Java's BigDecimal type.
Such forms of cryptography as require multiplication and are not handled by their own dedicated hardware.
Big integers e.g. for exploring number theory.
Other cases I'm not thinking of right now.
None of these jump out at me as wildly common, yet all modern CPU architectures include integer multiply instructions. (RISC-V omits them from the minimal version of the instruction set, but has been criticized for even going this far.)
Has anyone ever analyzed a representative sample of code, such as the SPEC benchmarks, to find out exactly what use case accounts for most of the actual uses of integer multiply (as measured by dynamic rather than static frequency)?

Additive inverse of a number: subtraction from zero or multiplication by −1

Which method is faster when negating a number: -1*a or 0-a? where a is a double.
Both are terrible, just flip the sign bit with an XOR or a dedicated FP negation instruction.
IEEE-754 floating point uses a sign/magnitude representation so -x differs from x by exactly 1 bit: the sign-bit. (e.g. on x86 with SSE, using xorps How to negate (change sign) of the floating point elements in a __m128 type variable?). This flips NaN to -NaN or vice versa without changing the payload.
In C, write it as -a and see what your compiler does.
Even better, you can often optimize away a negation by later doing a subtract instead of add, or an FMSUB or FNMADD instead of FMADD, or producing a originally with an FNMSUB instead of FMADD to negate as part of the FMA.
But if you had to choose between an actual FP multiple or FP add instruction, normally subtraction has latency at least as good as multiplications.
Intel Haswell and Broadwell have multiply throughput twice as good as add throughput (running on FMA units with worse or equal latency to add), but most microarchitectures (including modern x86 Ryzen and Skylake) have balanced FP add vs. multiply throughput.
In general for non-x86 architectures, generally add will be at least as cheap as multiply. But again, most ISAs will have some special way of negating like x86's SSE1 xorps or legacy x87 fchs (CHange Sign).
Boolean AND or ANDN (or a dedicated instruction that has the "mask" built in) to unconditionally clear the sign bit is also useful as an absolute value.

Indexed addressing mode and implied addressing mode

Indexed addressing mode is usually used for accessing arrays as arrays are stored contiguosly. We have a index register which gets incremented in every iteration which when added to base address gives the array element address.
I don't understand the actual need of this addressing mode. Why can't we do this with direct addressing ? We have the base address and we can just add 1 to it every time when accessing. Why do we need indexed addressing mode which has a overhead of index register ?
I am not sure about the instruction format for implied addressing mode. Suppose we have a instruction INC AC. Is the address of AC specified in the instruction or is there a special opcode which means 'INC AC' and we don't include the address of AC (accumulator)?
I don't understand the actual need of this addressing mode. Why can't we do this with direct addressing?
You can; MIPS only has one addressing mode and compilers can still generate code for it just fine. But sometimes it has to use an extra shift + add instruction to calculate an address (if it's not just looping through an array).
The point of addressing modes is to save instructions and save registers, especially in 2-operand instruction sets like x86, where add eax, ecx overwrites eax with the result (eax += ecx), unlike MIPS or other 3-instruction ISAs where addu $t2, $t1, $t0 does t2 = t1 + t0. On x86, that would require a copy (mov) and an add. (Or in that special case, lea edx, [eax+ecx]: x86 can copy-and-add (and shift) using the same instruction-encoding it uses for memory operands.)
Consider a histogram problem: you generate array indices in unpredictable order, and have to index an array. On x86-64, add dword [rbx + rdi*4], 1 will increment a 32-bit counter in memory using a single 4-byte instruction, which decodes to only 2 uops for the front-end to issue into the out-of-order core on modern Intel CPUs. (http://agner.org/optimize/). (rbx is the base register, rdi is a scaled index). Having a scaled index is very powerful; x86 16-bit addressing modes support 2 registers, but not a scaled index.
Classic MIPS only has separate shift and add instructions, although MIPS32 did add a scaled-add instruction for address calculation. That would save an instruction here. Being a load-store machine, the loads and stores always have to be separate instructions (unlike on x86 where that add decodes as a micro-fused load+add and a store. See INC instruction vs ADD 1: Does it matter?).
Probably ARM would be a better comparison for MIPS: It's also a load-store RISC machine. But it does have a selection of addressing modes, including scaled index using the barrel shifter. So instead of needing a separate shift / add for each array index, you'd use LDR R0, [R1, R2, LSL #2], add r0, r0, #1 / str with the same addressing mode.
Often when looping through an array, it is best to just increment pointers on x86. But it's also an option to use an index, especially for loops with multiple arrays using the same index, like C[i] = A[i] + B[i]. Indexed addressing mode can sometimes be slightly less efficient in hardware, though, so when a compiler is unrolling a loop it usually should use pointers, even though it has to increment all 3 pointers separately instead of one index.
The point of instruction-set design is not merely to be Turing complete, it's to enable efficient code that gets more work done with fewer clock cycles and/or smaller code-size, or give programmers the option of aiming for either of those goals.
The minimum threshold for a computer to be programmable is extremely low, see for example various One instruction set computer architectures. (None implemented for real, just designed on paper to show that it's possible to write programs with nothing but a subtract-and-branch-if-less-than-zero instruction, with memory operands encoded in the instruction.
There's a tradeoff between easy to decode (especially to decode in parallel) vs. compact. x86 is horrible because it evolved as a series of extensions, often without a lot of planning to leave room for future extensions. If you're interested in ISA design decisions, have a look at Agner Fog's blog for interesting discussion about designing an ISA for high-performance CPUs that combines the best of x86 (lots of work with one instruction, e.g. memory operand as part of an ALU instruction) with the best features of RISC (easy to decode, lots of registers): Proposal for an ideal extensible instruction set.
There's also a tradeoff in how you spend the bits in an instruction word, especially in a fixed instruction width ISA like most RISCs. Different ISAs made different choices.
PowerPC uses lots of the coding space for powerful bitfield instructions like rlwinm (rotate left and mask off a window of bits), and lots of opcodes. IDK if the generally unpronounceable and hard-to-remember mnemonics are related to that...
ARM uses the high 4 bits for predicated execution of any instruction based on condition codes. It uses more bits for the barrel shifter (the 2nd source operand is optionally shifted or rotated by an immediate or a count from another register).
MIPS has relatively large immediate operands, and is basically simple.
x86 32/64-bit addressing modes use a variable-length encoding, with an extra byte SIB (scale/index/base) byte when there's an index, and an optional disp8 or disp32 immediate displacement. (e.g. add esi, [rax + rdx + 12340] takes 2 + 1 + 4 bytes to encode, vs. 2 bytes for add esi, [rax].
x86 16-bit addressing modes are much more limited, and pack everything except the optional disp8/disp16 displacement into the ModR/M byte.
Suppose we have a instruction INC AC. Is the address of AC specified in the instruction or is there a special opcode which means 'INC AC' and we don't include the address of AC (accumulator)?
Yes, the machine-code format for some instructions in some ISAs includes implicit operands. Many machines have push / pop instructions that implicitly use a specific register as the stack pointer. For example, in x86-64's push rax, RAX is an explicit register operand (encoded in the low 3 bits of the one-byte opcode using the push r64 short form), while RSP is an implicit operand.
Older 8-bit CPUs often had instructions like DECA (to decrement the accumulator, A). i.e. there was a specific opcode for that register. This could be the same thing as having a DEC instruction with some bits in the opcode byte specifying which register (like x86 does before x86-64 repurposed the short INC/DEC encodings as REX prefixes: note the "N.E" (Not Encodeable) in the 64-bit mode column for dec r32). But if there's no regular pattern then it can definitely be considered an implicit operand.
Sometimes putting things into neat categories breaks down, so don't worry too much about whether using bits with the opcode byte counts as implicit or explicit for x86. It's a way of spending more opcode space to save code-size for commonly used instructions while still allowing use with different registers.
Some ISAs only use a certain register as the stack pointer by convention, with no implicit uses. MIPS is like this.
ARM32 (in ARM, not Thumb mode) also uses explicit operands in push/pop. Its push/pop mnemonics are just aliases for store-multiple decrement-before / load-multiple increment-after (LDMIA / STMDB) to implement a full-descending stack. See ARM's docs for LDM/STM which explains this, and what you can do with the general case of these instructions, e.g. LDMDB to decrement a pointer and then load (in the opposite direction of POP).