lbn960jx.s
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上传日期:2007-01-08
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- # Assembly-language bignum primitives for the i960 Jx series.
- #
- # The Jx series is fairly straightforward single-instruction-issue
- # implementation, with a 1-cycle-issue 4-cycle-latency non-pipelined
- # multiplier that we can use. Note also that loads which hit in the
- # cache have 2 cycles of latency and stores stall until all pending
- # loads are done.
- #
- # What is intensely annoying about the i960 is that it uses the same
- # flags for all conditional branches (even compare-and-branch sets the
- # flags) AND for the carry bit. Further, it is hard to manipulate
- # that bit.
- #
- # Calling conventions:
- # The r registers are all local, if you set them up. There's an alternative
- # calling convention that uses bal (branch and link) and doesn't set them up.
- # Currently, all of these functions are designed to work that way.
- # g0-g7 are argument registers and volatile across calls. return in g0-g3.
- # g8-g11 are extra argument registers, and volatile if used, but
- # preserved if not. Here, they are not.
- # g12 is used for PIC, and is preserved.
- # g13 is a pointer to a structure return value, if used, and is volatile.
- # g14 is magic, and is used as a return address in the branch-and-link
- # convention, and as a pointer to an argument block if the arguments
- # won't fit in registers, but is usually hardwired 0 and must be
- # returned set to zero (0).
- # g15 is the frame pointer, and shouldn't be messed with.
- # The AC (condition codes) are all volatile.
- # The fp registers are all volatile, but irrelevant.
- #
- # BNWORD32
- # lbnMultAdd1_32(BNWORD32 *out, BNWORD32 const *in, unsigned len, BNWORD32 k)
- # This adds "k" * "in" to "len" words of "out" and returns the word of
- # carry.
- #
- # For doing multiply-add, the 960 is a bit annoying because it uses
- # the same status bits for the carry flag and for the loop indexing
- # computation, and doesn't have an "add with carry out but not carry in"
- # instruction. Fortunately, we can arrange to have the loop indexing
- # leave the carry bit clear most of the time.
- #
- # The basic sequence of the loop is:
- # 1. Multiply k * *in++ -> high, low
- # 2. Addc carry word and carry bit to low
- # 3. Addc carry bit to high, producing carry word (note: cannot generate carry!)
- # 4. Addc low to *out++
- #
- # Note that the carry bit set in step 4 is used in step 2. The only place
- # in this loop that the carry flag isn't in use is between steps 3 and 4,
- # so we have to rotate the loop to place the loop indexing operations here.
- # (Which consist of a compare-and-decrement and a conditional branch.)
- # The loop above ignores the details of when to do loads and stores, which
- # have some flexibility, but must be carefully scheduled to avoid stalls.
- #
- # The first iteration has no carry word in, so it requires only steps 1 and 4,
- # and since we begin the loop with step 4, it boils down to just step 1
- # followed by the loop indexing (which clears the carry bit in preparation
- # for step 4).
- #
- # Arguments are passed as follows:
- # g0 - out pointer
- # g1 - in pointer
- # g2 - length
- # g3 - k
- # The other registers are used as follows.
- # g4 - low word of product
- # g5 - high word of product
- # g6 - current word of "out"
- # g7 - carry word
- # g13 - current word of "in"
- .globl _lbnMulAdd1_32
- _lbnMulAdd1_32:
- ld (g1),g13 # Fetch *in
- addo g1,4,g1 # Increment in
- emul g13,g3,g4 # Do multiply (step 1)
- ld (g0),g6 # Fetch *out
- chkbit 0,g2 # Check if loop counter was odd
- shro 1,g2,g2 # Divide loop counter by 2
- mov g5,g7 # Move high word to carry
- bno ma_loop1 # If even, jump to ma_loop1
- cmpo 0,g2 # If odd, was it 1 (now 0)?
- be ma_done # If equal (carry set), jump to ending code
- # Entered with carry bit clear
- ma_loop:
- ld (g1),g13 # Fetch *in
- addc g4,g6,g6 # Add low to *out (step 4), generate carry
- emul g13,g3,g4 # Do multiply (step 1)
- st g6,(g0) # Write out *out
- addo g0,4,g0 # Increment out
- addo g1,4,g1 # Increment in
- ld (g0),g6 # Fetch next *out
- addc g7,g4,g4 # Add carries to low (step 2)
- addc g5,0,g7 # Add carry bit to high (step 3) & clear carry
- ma_loop1:
- ld (g1),g13 # Fetch *in
- addc g4,g6,g6 # Add low to *out (step 4), generate carry
- emul g13,g3,g4 # Do multiply (step 1)
- st g6,(g0) # Write out *out
- addo g0,4,g0 # Increment out
- addo g1,4,g1 # Increment in
- ld (g0),g6 # Fetch next *out
- addc g7,g4,g4 # Add carries to low (step 2)
- addc g5,0,g7 # Add carry bit to high (step 3) & clear carry
- cmpdeco 1,g2,g2
- bne ma_loop
- # When we come here, carry is *set*, and we stil have to do step 4
- ma_done:
- cmpi 0,1 # Clear carry (equal flag)
- addc g4,g6,g6 # Add low to *out (step 4), generate carry
- st g6,(g0) # Write out *out
- addc g7,0,g0 # Add carry bit and word to produce return value
- ret
- # Now, multiply N by 1 is similarly annoying. We only have one add in the
- # whole loop, which should just be able to leave its carry output in the
- # carry flag for the next iteration, but we need the condition codes to do
- # loop testing. *Sigh*.
- #
- # void
- # lbnMultN1_32(BNWORD32 *out, BNWORD32 const *in, unsigned len, BNWORD32 k)
- # This stores len+1 words of "k" * len words of "in" and stores the result
- # in "out".
- #
- # To avoid having to do a move after the first iteration, for the first
- # step, g4/g5 is the product. For second step, g6/g7 is used for product
- # storage and g5 is the carry in. It alternates from then on.
- .globl _lbnMulN1_32
- _lbnMulN1_32:
- ld (g1),g13 # Fetch *in
- addo g1,4,g1 # Increment in
- emul g13,g3,g4 # Do multiply (step 1)
- chkbit 0,g2 # Check if loop counter was odd
- shro 1,g2,g2 # Divide loop counter by 2
- bno m_loop1 # If even, jump to ma_loop1
- mov g4,g6
- cmpo 0,g2 # If counter was odd, was it 1 (now 0)?
- mov g5,g7
- be m_done # If equal (carry set), jump to ending code
- # Entered with carry bit clear
- m_loop:
- # Result in g6, carry word in g7
- ld (g1),g13 # Fetch *in
- addo g1,4,g1 # Increment in
- emul g13,g3,g4 # Do multiply (step 1)
- st g6,(g0) # Write out *out
- addo g0,4,g0 # Increment out
- addc g7,g4,g4 # Add carries to low (step 2)
- # No need to add carry bit here, because it'll get remembered until next addc.
- # addc g5,0,g5 # Add carry bit to high (step 3)
- m_loop1:
- # Carry word in g5
- ld (g1),g13 # Fetch *in
- addo g1,4,g1 # Increment in
- emul g13,g3,g6 # Do multiply (step 1)
- st g4,(g0) # Write out *out
- addo g0,4,g0 # Increment out
- addc g5,g6,g6 # Add carries to low (step 2)
- addc g7,0,g7 # Add carry bit to high (step 3)
- cmpdeco 1,g2,g2
- bne m_loop
- # When we come here, we have to store g6 and the carry word in g7.
- m_done:
- st g6,(g0) # Write out *out
- st g7,4(g0) # Write out *out
- ret
- # BNWORD32
- # lbnMultSub1_32(BNWORD32 *out, BNWORD32 const *in, unsigned len, BNWORD32 k)
- # This subtracts "k" * "in" from "len" words of "out" and returns the word of
- # borrow.
- #
- # This is similar to multiply-add, but actually a bit more obnoxious,
- # because of the carry situation. The 960 uses a carry (rather than a borrow)
- # bit on subtracts, so the carry bit should be 1 for a subc to do the
- # same thing as an ordinary subo. So we use two carry chains: one from
- # the add of the low-order words to the high-order carry word, and a second,
- # which uses an extra register, to connect the subtracts. This avoids
- # the need to fiddle with inverting the bit in the usual case.
- #
- # Arguments are passed as follows:
- # g0 - out pointer
- # g1 - in pointer
- # g2 - length
- # g3 - k
- # The other registers are used as follows.
- # g4 - low word of product
- # g5 - high word of product
- # g6 - current word of "out"
- # g7 - carry word
- # g13 - current word of "in"
- # g14 - remembered carry bit
- .globl _lbnMulSub1_32
- _lbnMulSub1_32:
- ld (g1),g13 # Fetch *in
- addo g1,4,g1 # Increment in
- emul g13,g3,g4 # Do multiply (step 1)
- ld (g0),g6 # Fetch *out
- chkbit 0,g2 # Check if loop counter was odd
- mov 1,g14 # Set remembered carry for first iteration
- shro 1,g2,g2 # Divide loop counter by 2
- mov g5,g7 # Move high word to carry
- bno ms_loop1 # If even, jump to ma_loop1
- cmpo 0,g2 # If odd, was it 1 (now 0)?
- be ms_done # If equal (carry set), jump to ending code
- # Entered with carry bit clear
- ms_loop:
- ld (g1),g13 # Fetch *in
- cmpi g14,1 # Set carry flag
- subc g4,g6,g6 # Subtract low from *out (step 4), gen. carry
- emul g13,g3,g4 # Do multiply (step 1)
- addc 0,0,g14 # g14 = carry, then clear carry
- st g6,(g0) # Write out *out
- addo g0,4,g0 # Increment out
- addo g1,4,g1 # Increment in
- ld (g0),g6 # Fetch next *out
- addc g7,g4,g4 # Add carries to low (step 2)
- addc g5,0,g7 # Add carry bit to high (step 3)
- ms_loop1:
- ld (g1),g13 # Fetch *in
- cmpi g14,1 # Set carry flag for subtrsct
- subc g4,g6,g6 # Subtract low from *out (step 4), gen. carry
- emul g13,g3,g4 # Do multiply (step 1)
- addc 0,0,g14 # g14 = carry, then clear carry
- st g6,(g0) # Write out *out
- addo g0,4,g0 # Increment out
- addo g1,4,g1 # Increment in
- ld (g0),g6 # Fetch next *out
- addc g7,g4,g4 # Add carries to low (step 2)
- addc g5,0,g7 # Add carry bit to high (step 3)
- cmpdeco 1,g2,g2
- bne ms_loop
- # When we come here, carry is *set*, and we stil have to do step 4
- ms_done:
- cmpi g14,1 # set carry (equal flag)
- subc g4,g6,g6 # Add low to *out (step 4), generate carry
- st g6,(g0) # Write out *out
- subc 0,0,g14 # g14 = -1 if no carry (borrow), 0 if carry
- subo g14,g7,g0 # Add borrow bit to produce return value
- mov 0,g14 # Restore g14 to 0 for return
- ret