/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/*
*
* This PA-RISC 2.0 function computes the product of two unsigned integers,
* and adds the result to a previously computed integer. The multiplicand
* is a 512-bit (64-byte, eight doubleword) unsigned integer, stored in
* memory in little-double-wordian order. The multiplier is an unsigned
* 64-bit integer. The previously computed integer to which the product is
* added is located in the result ("res") area, and is assumed to be a
* 576-bit (72-byte, nine doubleword) unsigned integer, stored in memory
* in little-double-wordian order. This value normally will be the result
* of a previously computed nine doubleword result. It is not necessary
* to pad the multiplicand with an additional 64-bit zero doubleword.
*
* Multiplicand, multiplier, and addend ideally should be aligned at
* 16-byte boundaries for best performance. The code will function
* correctly for alignment at eight-byte boundaries which are not 16-byte
* boundaries, but the execution may be slightly slower due to even/odd
* bank conflicts on PA-RISC 8000 processors.
*
* This function is designed to accept the same calling sequence as Bill
* Ackerman's "maxpy_little" function. The carry from the ninth doubleword
* of the result is written to the tenth word of the result, as is done by
* Bill Ackerman's function. The final carry also is returned as an
* integer, which may be ignored. The function prototype may be either
* of the following:
*
* void multacc512( int l, chunk* m, const chunk* a, chunk* res );
* or
* int multacc512( int l, chunk* m, const chunk* a, chunk* res );
*
* where: "l" originally denoted vector lengths. This parameter is
* ignored. This function always assumes a multiplicand length of
* 512 bits (eight doublewords), and addend and result lengths of
* 576 bits (nine doublewords).
*
* "m" is a pointer to the doubleword multiplier, ideally aligned
* on a 16-byte boundary.
*
* "a" is a pointer to the eight-doubleword multiplicand, stored
* in little-double-wordian order, and ideally aligned on a 16-byte
* boundary.
*
* "res" is a pointer to the nine doubleword addend, and to the
* nine-doubleword product computed by this function. The result
* also is stored in little-double-wordian order, and ideally is
* aligned on a 16-byte boundary. It is expected that the alignment
* of the "res" area may alternate between even/odd doubleword
* boundaries for successive calls for 512-bit x 512-bit
* multiplications.
*
* The code for this function has been scheduled to use the parallelism
* of the PA-RISC 8000 series microprocessors as well as the author was
* able. Comments and/or suggestions for improvement are welcomed.
*
* The code is "64-bit safe". This means it may be called in either
* the 32ILP context or the 64LP context. All 64-bits of registers are
* saved and restored.
*
* This code is self-contained. It requires no other header files in order
* to compile and to be linkable on a PA-RISC 2.0 machine. Symbolic
* definitions for registers and stack offsets are included within this
* one source file.
*
* This is a leaf routine. As such, minimal use is made of the stack area.
* Of the 192 bytes allocated, 64 bytes are used for saving/restoring eight
* general registers, and 128 bytes are used to move intermediate products
* from the floating-point registers to the general registers. Stack
* protocols assure proper alignment of these areas.
*
*/
/* ====================================================================*/
/* symbolic definitions for PA-RISC registers */
/* in the MIPS style, avoids lots of case shifts */
/* assigments (except t4) preserve register number parity */
/* ====================================================================*/
#define zero %r0 /* permanent zero */
#define t5 %r1 /* temp register, altered by addil */
#define rp %r2 /* return pointer */
#define s1 %r3 /* callee saves register*/
#define s0 %r4 /* callee saves register*/
#define s3 %r5 /* callee saves register*/
#define s2 %r6 /* callee saves register*/
#define s5 %r7 /* callee saves register*/
#define s4 %r8 /* callee saves register*/
#define s7 %r9 /* callee saves register*/
#define s6 %r10 /* callee saves register*/
#define t1 %r19 /* caller saves register*/
#define t0 %r20 /* caller saves register*/
#define t3 %r21 /* caller saves register*/
#define t2 %r22 /* caller saves register*/
#define a3 %r23 /* fourth argument register, high word */
#define a2 %r24 /* third argument register, low word*/
#define a1 %r25 /* second argument register, high word*/
#define a0 %r26 /* first argument register, low word*/
#define v0 %r28 /* high order return value*/
#define v1 %r29 /* low order return value*/
#define sp %r30 /* stack pointer*/
#define t4 %r31 /* temporary register */
#define fa0 %fr4 /* first argument register*/
#define fa1 %fr5 /* second argument register*/
#define fa2 %fr6 /* third argument register*/
#define fa3 %fr7 /* fourth argument register*/
#define fa0r %fr4R /* first argument register*/
#define fa1r %fr5R /* second argument register*/
#define fa2r %fr6R /* third argument register*/
#define fa3r %fr7R /* fourth argument register*/
#define ft0 %fr8 /* caller saves register*/
#define ft1 %fr9 /* caller saves register*/
#define ft2 %fr10 /* caller saves register*/
#define ft3 %fr11 /* caller saves register*/
#define ft0r %fr8R /* caller saves register*/
#define ft1r %fr9R /* caller saves register*/
#define ft2r %fr10R /* caller saves register*/
#define ft3r %fr11R /* caller saves register*/
#define ft4 %fr22 /* caller saves register*/
#define ft5 %fr23 /* caller saves register*/
#define ft6 %fr24 /* caller saves register*/
#define ft7 %fr25 /* caller saves register*/
#define ft8 %fr26 /* caller saves register*/
#define ft9 %fr27 /* caller saves register*/
#define ft10 %fr28 /* caller saves register*/
#define ft11 %fr29 /* caller saves register*/
#define ft12 %fr30 /* caller saves register*/
#define ft13 %fr31 /* caller saves register*/
#define ft4r %fr22R /* caller saves register*/
#define ft5r %fr23R /* caller saves register*/
#define ft6r %fr24R /* caller saves register*/
#define ft7r %fr25R /* caller saves register*/
#define ft8r %fr26R /* caller saves register*/
#define ft9r %fr27R /* caller saves register*/
#define ft10r %fr28R /* caller saves register*/
#define ft11r %fr29R /* caller saves register*/
#define ft12r %fr30R /* caller saves register*/
#define ft13r %fr31R /* caller saves register*/
/* ================================================================== */
/* functional definitions for PA-RISC registers */
/* ================================================================== */
/* general registers */
#define T1 a0 /* temp, (length parameter ignored) */
#define pM a1 /* -> 64-bit multiplier */
#define T2 a1 /* temp, (after fetching multiplier) */
#define pA a2 /* -> multiplicand vector (8 64-bit words) */
#define T3 a2 /* temp, (after fetching multiplicand) */
#define pR a3 /* -> addend vector (8 64-bit doublewords,
result vector (9 64-bit words) */
#define S0 s0 /* callee saves summand registers */
#define S1 s1
#define S2 s2
#define S3 s3
#define S4 s4
#define S5 s5
#define S6 s6
#define S7 s7
#define S8 v0 /* caller saves summand registers */
#define S9 v1
#define S10 t0
#define S11 t1
#define S12 t2
#define S13 t3
#define S14 t4
#define S15 t5
/* floating-point registers */
#define M fa0 /* multiplier double word */
#define MR fa0r /* low order half of multiplier double word */
#define ML fa0 /* high order half of multiplier double word */
#define A0 fa2 /* multiplicand double word 0 */
#define A0R fa2r /* low order half of multiplicand double word */
#define A0L fa2 /* high order half of multiplicand double word */
#define A1 fa3 /* multiplicand double word 1 */
#define A1R fa3r /* low order half of multiplicand double word */
#define A1L fa3 /* high order half of multiplicand double word */
#define A2 ft0 /* multiplicand double word 2 */
#define A2R ft0r /* low order half of multiplicand double word */
#define A2L ft0 /* high order half of multiplicand double word */
#define A3 ft1 /* multiplicand double word 3 */
#define A3R ft1r /* low order half of multiplicand double word */
#define A3L ft1 /* high order half of multiplicand double word */
#define A4 ft2 /* multiplicand double word 4 */
#define A4R ft2r /* low order half of multiplicand double word */
#define A4L ft2 /* high order half of multiplicand double word */
#define A5 ft3 /* multiplicand double word 5 */
#define A5R ft3r /* low order half of multiplicand double word */
#define A5L ft3 /* high order half of multiplicand double word */
#define A6 ft4 /* multiplicand double word 6 */
#define A6R ft4r /* low order half of multiplicand double word */
#define A6L ft4 /* high order half of multiplicand double word */
#define A7 ft5 /* multiplicand double word 7 */
#define A7R ft5r /* low order half of multiplicand double word */
#define A7L ft5 /* high order half of multiplicand double word */
#define P0 ft6 /* product word 0 */
#define P1 ft7 /* product word 0 */
#define P2 ft8 /* product word 0 */
#define P3 ft9 /* product word 0 */
#define P4 ft10 /* product word 0 */
#define P5 ft11 /* product word 0 */
#define P6 ft12 /* product word 0 */
#define P7 ft13 /* product word 0 */
/* ====================================================================== */
/* symbolic definitions for HP-UX stack offsets */
/* symbolic definitions for memory NOPs */
/* ====================================================================== */
#define ST_SZ 192 /* stack area total size */
#define SV0 -192(sp) /* general register save area */
#define SV1 -184(sp)
#define SV2 -176(sp)
#define SV3 -168(sp)
#define SV4 -160(sp)
#define SV5 -152(sp)
#define SV6 -144(sp)
#define SV7 -136(sp)
#define XF0 -128(sp) /* data transfer area */
#define XF1 -120(sp) /* for floating-pt to integer regs */
#define XF2 -112(sp)
#define XF3 -104(sp)
#define XF4 -96(sp)
#define XF5 -88(sp)
#define XF6 -80(sp)
#define XF7 -72(sp)
#define XF8 -64(sp)
#define XF9 -56(sp)
#define XF10 -48(sp)
#define XF11 -40(sp)
#define XF12 -32(sp)
#define XF13 -24(sp)
#define XF14 -16(sp)
#define XF15 -8(sp)
#define mnop proberi (sp),3,zero /* memory NOP */
/* ====================================================================== */
/* assembler formalities */
/* ====================================================================== */
#ifdef __LP64__
.level 2.0W
#else
.level 2.0
#endif
.space $TEXT$
.subspa $CODE$
.align 16
/* ====================================================================== */
/* here to compute 64-bit x 512-bit product + 512-bit addend */
/* ====================================================================== */
multacc512
.PROC
.CALLINFO
.ENTRY
fldd 0(pM),M ; multiplier double word
ldo ST_SZ(sp),sp ; push stack
fldd 0(pA),A0 ; multiplicand double word 0
std S1,SV1 ; save s1
fldd 16(pA),A2 ; multiplicand double word 2
std S3,SV3 ; save s3
fldd 32(pA),A4 ; multiplicand double word 4
std S5,SV5 ; save s5
fldd 48(pA),A6 ; multiplicand double word 6
std S7,SV7 ; save s7
std S0,SV0 ; save s0
fldd 8(pA),A1 ; multiplicand double word 1
xmpyu MR,A0L,P0 ; A0 cross 32-bit word products
xmpyu ML,A0R,P2
std S2,SV2 ; save s2
fldd 24(pA),A3 ; multiplicand double word 3
xmpyu MR,A2L,P4 ; A2 cross 32-bit word products
xmpyu ML,A2R,P6
std S4,SV4 ; save s4
fldd 40(pA),A5 ; multiplicand double word 5
std S6,SV6 ; save s6
fldd 56(pA),A7 ; multiplicand double word 7
fstd P0,XF0 ; MR * A0L
xmpyu MR,A0R,P0 ; A0 right 32-bit word product
xmpyu MR,A1L,P1 ; A1 cross 32-bit word product
fstd P2,XF2 ; ML * A0R
xmpyu ML,A0L,P2 ; A0 left 32-bit word product
xmpyu ML,A1R,P3 ; A1 cross 32-bit word product
fstd P4,XF4 ; MR * A2L
xmpyu MR,A2R,P4 ; A2 right 32-bit word product
xmpyu MR,A3L,P5 ; A3 cross 32-bit word product
fstd P6,XF6 ; ML * A2R
xmpyu ML,A2L,P6 ; A2 parallel 32-bit word product
xmpyu ML,A3R,P7 ; A3 cross 32-bit word product
ldd XF0,S0 ; MR * A0L
fstd P1,XF1 ; MR * A1L
ldd XF2,S2 ; ML * A0R
fstd P3,XF3 ; ML * A1R
ldd XF4,S4 ; MR * A2L
fstd P5,XF5 ; MR * A3L
xmpyu MR,A1R,P1 ; A1 parallel 32-bit word products
xmpyu ML,A1L,P3
ldd XF6,S6 ; ML * A2R
fstd P7,XF7 ; ML * A3R
xmpyu MR,A3R,P5 ; A3 parallel 32-bit word products
xmpyu ML,A3L,P7
fstd P0,XF0 ; MR * A0R
ldd XF1,S1 ; MR * A1L
nop
add S0,S2,T1 ; A0 cross product sum
fstd P2,XF2 ; ML * A0L
ldd XF3,S3 ; ML * A1R
add,dc zero,zero,S0 ; A0 cross product sum carry
depd,z T1,31,32,S2 ; A0 cross product sum << 32
fstd P4,XF4 ; MR * A2R
ldd XF5,S5 ; MR * A3L
shrpd S0,T1,32,S0 ; A0 carry | cross product sum >> 32
add S4,S6,T3 ; A2 cross product sum
fstd P6,XF6 ; ML * A2L
ldd XF7,S7 ; ML * A3R
add,dc zero,zero,S4 ; A2 cross product sum carry
depd,z T3,31,32,S6 ; A2 cross product sum << 32
ldd XF0,S8 ; MR * A0R
fstd P1,XF1 ; MR * A1R
xmpyu MR,A4L,P0 ; A4 cross 32-bit word product
xmpyu MR,A5L,P1 ; A5 cross 32-bit word product
ldd XF2,S10 ; ML * A0L
fstd P3,XF3 ; ML * A1L
xmpyu ML,A4R,P2 ; A4 cross 32-bit word product
xmpyu ML,A5R,P3 ; A5 cross 32-bit word product
ldd XF4,S12 ; MR * A2R
fstd P5,XF5 ; MR * A3L
xmpyu MR,A6L,P4 ; A6 cross 32-bit word product
xmpyu MR,A7L,P5 ; A7 cross 32-bit word product
ldd XF6,S14 ; ML * A2L
fstd P7,XF7 ; ML * A3L
xmpyu ML,A6R,P6 ; A6 cross 32-bit word product
xmpyu ML,A7R,P7 ; A7 cross 32-bit word product
fstd P0,XF0 ; MR * A4L
ldd XF1,S9 ; MR * A1R
shrpd S4,T3,32,S4 ; A2 carry | cross product sum >> 32
add S1,S3,T1 ; A1 cross product sum
fstd P2,XF2 ; ML * A4R
ldd XF3,S11 ; ML * A1L
add,dc zero,zero,S1 ; A1 cross product sum carry
depd,z T1,31,32,S3 ; A1 cross product sum << 32
fstd P4,XF4 ; MR * A6L
ldd XF5,S13 ; MR * A3R
shrpd S1,T1,32,S1 ; A1 carry | cross product sum >> 32
add S5,S7,T3 ; A3 cross product sum
fstd P6,XF6 ; ML * A6R
ldd XF7,S15 ; ML * A3L
add,dc zero,zero,S5 ; A3 cross product sum carry
depd,z T3,31,32,S7 ; A3 cross product sum << 32
shrpd S5,T3,32,S5 ; A3 carry | cross product sum >> 32
add S2,S8,S8 ; M * A0 right doubleword, P0 doubleword
add,dc S0,S10,S10 ; M * A0 left doubleword
add S3,S9,S9 ; M * A1 right doubleword
add,dc S1,S11,S11 ; M * A1 left doubleword
add S6,S12,S12 ; M * A2 right doubleword
ldd 24(pR),S3 ; Addend word 3
fstd P1,XF1 ; MR * A5L
add,dc S4,S14,S14 ; M * A2 left doubleword
xmpyu MR,A5R,P1 ; A5 right 32-bit word product
ldd 8(pR),S1 ; Addend word 1
fstd P3,XF3 ; ML * A5R
add S7,S13,S13 ; M * A3 right doubleword
xmpyu ML,A5L,P3 ; A5 left 32-bit word product
ldd 0(pR),S7 ; Addend word 0
fstd P5,XF5 ; MR * A7L
add,dc S5,S15,S15 ; M * A3 left doubleword
xmpyu MR,A7R,P5 ; A7 right 32-bit word product
ldd 16(pR),S5 ; Addend word 2
fstd P7,XF7 ; ML * A7R
add S10,S9,S9 ; P1 doubleword
xmpyu ML,A7L,P7 ; A7 left 32-bit word products
ldd XF0,S0 ; MR * A4L
fstd P1,XF9 ; MR * A5R
add,dc S11,S12,S12 ; P2 doubleword
xmpyu MR,A4R,P0 ; A4 right 32-bit word product
ldd XF2,S2 ; ML * A4R
fstd P3,XF11 ; ML * A5L
add,dc S14,S13,S13 ; P3 doubleword
xmpyu ML,A4L,P2 ; A4 left 32-bit word product
ldd XF6,S6 ; ML * A6R
fstd P5,XF13 ; MR * A7R
add,dc zero,S15,T2 ; P4 partial doubleword
xmpyu MR,A6R,P4 ; A6 right 32-bit word product
ldd XF4,S4 ; MR * A6L
fstd P7,XF15 ; ML * A7L
add S7,S8,S8 ; R0 + P0, new R0 doubleword
xmpyu ML,A6L,P6 ; A6 left 32-bit word product
fstd P0,XF0 ; MR * A4R
ldd XF7,S7 ; ML * A7R
add,dc S1,S9,S9 ; c + R1 + P1, new R1 doubleword
fstd P2,XF2 ; ML * A4L
ldd XF1,S1 ; MR * A5L
add,dc S5,S12,S12 ; c + R2 + P2, new R2 doubleword
fstd P4,XF4 ; MR * A6R
ldd XF5,S5 ; MR * A7L
add,dc S3,S13,S13 ; c + R3 + P3, new R3 doubleword
fstd P6,XF6 ; ML * A6L
ldd XF3,S3 ; ML * A5R
add,dc zero,T2,T2 ; c + partial P4
add S0,S2,T1 ; A4 cross product sum
std S8,0(pR) ; save R0
add,dc zero,zero,S0 ; A4 cross product sum carry
depd,z T1,31,32,S2 ; A4 cross product sum << 32
std S9,8(pR) ; save R1
shrpd S0,T1,32,S0 ; A4 carry | cross product sum >> 32
add S4,S6,T3 ; A6 cross product sum
std S12,16(pR) ; save R2
add,dc zero,zero,S4 ; A6 cross product sum carry
depd,z T3,31,32,S6 ; A6 cross product sum << 32
std S13,24(pR) ; save R3
shrpd S4,T3,32,S4 ; A6 carry | cross product sum >> 32
add S1,S3,T1 ; A5 cross product sum
ldd XF0,S8 ; MR * A4R
add,dc zero,zero,S1 ; A5 cross product sum carry
depd,z T1,31,32,S3 ; A5 cross product sum << 32
ldd XF2,S10 ; ML * A4L
ldd XF9,S9 ; MR * A5R
shrpd S1,T1,32,S1 ; A5 carry | cross product sum >> 32
add S5,S7,T3 ; A7 cross product sum
ldd XF4,S12 ; MR * A6R
ldd XF11,S11 ; ML * A5L
add,dc zero,zero,S5 ; A7 cross product sum carry
depd,z T3,31,32,S7 ; A7 cross product sum << 32
ldd XF6,S14 ; ML * A6L
ldd XF13,S13 ; MR * A7R
shrpd S5,T3,32,S5 ; A7 carry | cross product sum >> 32
add S2,S8,S8 ; M * A4 right doubleword
ldd XF15,S15 ; ML * A7L
add,dc S0,S10,S10 ; M * A4 left doubleword
add S3,S9,S9 ; M * A5 right doubleword
add,dc S1,S11,S11 ; M * A5 left doubleword
add S6,S12,S12 ; M * A6 right doubleword
ldd 32(pR),S0 ; Addend word 4
ldd 40(pR),S1 ; Addend word 5
add,dc S4,S14,S14 ; M * A6 left doubleword
add S7,S13,S13 ; M * A7 right doubleword
ldd 48(pR),S2 ; Addend word 6
ldd 56(pR),S3 ; Addend word 7
add,dc S5,S15,S15 ; M * A7 left doubleword
add S8,T2,S8 ; P4 doubleword
ldd 64(pR),S4 ; Addend word 8
ldd SV5,s5 ; restore s5
add,dc S10,S9,S9 ; P5 doubleword
add,dc S11,S12,S12 ; P6 doubleword
ldd SV6,s6 ; restore s6
ldd SV7,s7 ; restore s7
add,dc S14,S13,S13 ; P7 doubleword
add,dc zero,S15,S15 ; P8 doubleword
add S0,S8,S8 ; new R4 doubleword
ldd SV0,s0 ; restore s0
std S8,32(pR) ; save R4
add,dc S1,S9,S9 ; new R5 doubleword
ldd SV1,s1 ; restore s1
std S9,40(pR) ; save R5
add,dc S2,S12,S12 ; new R6 doubleword
ldd SV2,s2 ; restore s2
std S12,48(pR) ; save R6
add,dc S3,S13,S13 ; new R7 doubleword
ldd SV3,s3 ; restore s3
std S13,56(pR) ; save R7
add,dc S4,S15,S15 ; new R8 doubleword
ldd SV4,s4 ; restore s4
std S15,64(pR) ; save result[8]
add,dc zero,zero,v0 ; return carry from R8
CMPIB,*= 0,v0,$L0 ; if no overflow, exit
LDO 8(pR),pR
$FINAL1 ; Final carry propagation
LDD 64(pR),v0
LDO 8(pR),pR
ADDI 1,v0,v0
CMPIB,*= 0,v0,$FINAL1 ; Keep looping if there is a carry.
STD v0,56(pR)
$L0
bv zero(rp) ; -> caller
ldo -ST_SZ(sp),sp ; pop stack
/* ====================================================================== */
/* end of module */
/* ====================================================================== */
bve (rp)
.EXIT
nop
.PROCEND
.SPACE $TEXT$
.SUBSPA $CODE$
.EXPORT multacc512,ENTRY
.end