math/big: add partial arm64 assembly support

benchmark old ns/op new ns/op delta BenchmarkAddVV_1 18.7 14.8 -20.86% BenchmarkAddVV_2 21.8 16.6 -23.85% BenchmarkAddVV_3 26.1 17.1 -34.48% BenchmarkAddVV_4 30.4 21.9 -27.96% BenchmarkAddVV_5 35.5 19.8 -44.23% BenchmarkAddVV_1e1 63.0 28.3 -55.08% BenchmarkAddVV_1e2 593 178 -69.98% BenchmarkAddVV_1e3 5691 1490 -73.82% BenchmarkAddVV_1e4 56868 20761 -63.49% BenchmarkAddVV_1e5 569062 207679 -63.51% BenchmarkAddVW_1 15.8 12.6 -20.25% BenchmarkAddVW_2 17.8 13.1 -26.40% BenchmarkAddVW_3 21.2 13.9 -34.43% BenchmarkAddVW_4 23.6 14.7 -37.71% BenchmarkAddVW_5 26.0 15.8 -39.23% BenchmarkAddVW_1e1 41.3 21.6 -47.70% BenchmarkAddVW_1e2 383 145 -62.14% BenchmarkAddVW_1e3 3703 1264 -65.87% BenchmarkAddVW_1e4 36920 14359 -61.11% BenchmarkAddVW_1e5 370345 143046 -61.37% BenchmarkAddMulVVW_1 33.2 32.5 -2.11% BenchmarkAddMulVVW_2 58.0 57.2 -1.38% BenchmarkAddMulVVW_3 95.2 93.9 -1.37% BenchmarkAddMulVVW_4 108 106 -1.85% BenchmarkAddMulVVW_5 159 156 -1.89% BenchmarkAddMulVVW_1e1 344 340 -1.16% BenchmarkAddMulVVW_1e2 3644 3624 -0.55% BenchmarkAddMulVVW_1e3 37344 37208 -0.36% BenchmarkAddMulVVW_1e4 373295 372170 -0.30% BenchmarkAddMulVVW_1e5 3438116 3425606 -0.36% BenchmarkBitLen0 7.21 4.32 -40.08% BenchmarkBitLen1 6.49 4.32 -33.44% BenchmarkBitLen2 7.23 4.32 -40.25% BenchmarkBitLen3 6.49 4.32 -33.44% BenchmarkBitLen4 7.22 4.32 -40.17% BenchmarkBitLen5 6.52 4.33 -33.59% BenchmarkBitLen8 7.22 4.32 -40.17% BenchmarkBitLen9 6.49 4.32 -33.44% BenchmarkBitLen16 8.66 4.32 -50.12% BenchmarkBitLen17 7.95 4.32 -45.66% BenchmarkBitLen31 8.69 4.32 -50.29% BenchmarkGCD10x10 5021 5033 +0.24% BenchmarkGCD10x100 5571 5572 +0.02% BenchmarkGCD10x1000 6707 6729 +0.33% BenchmarkGCD10x10000 13526 13419 -0.79% BenchmarkGCD10x100000 85668 83242 -2.83% BenchmarkGCD100x100 24196 23936 -1.07% BenchmarkGCD100x1000 28802 27309 -5.18% BenchmarkGCD100x10000 64111 51704 -19.35% BenchmarkGCD100x100000 385840 274385 -28.89% BenchmarkGCD1000x1000 262892 236269 -10.13% BenchmarkGCD1000x10000 371393 277883 -25.18% BenchmarkGCD1000x100000 1311795 589055 -55.10% BenchmarkGCD10000x10000 9596740 6123930 -36.19% BenchmarkGCD10000x100000 16404000 7269610 -55.68% BenchmarkGCD100000x100000 776660000 419270000 -46.02% BenchmarkHilbert 13478980 13402270 -0.57% BenchmarkBinomial 9802 9440 -3.69% BenchmarkBitset 142 142 +0.00% BenchmarkBitsetNeg 328 279 -14.94% BenchmarkBitsetOrig 853 861 +0.94% BenchmarkBitsetNegOrig 1489 1444 -3.02% BenchmarkMul 420949000 410481000 -2.49% BenchmarkExp3Power0x10 1148 1229 +7.06% BenchmarkExp3Power0x40 1322 1376 +4.08% BenchmarkExp3Power0x100 2437 2486 +2.01% BenchmarkExp3Power0x400 9456 9346 -1.16% BenchmarkExp3Power0x1000 113623 108701 -4.33% BenchmarkExp3Power0x4000 1134933 1101481 -2.95% BenchmarkExp3Power0x10000 10773570 10396160 -3.50% BenchmarkExp3Power0x40000 101362100 97788300 -3.53% BenchmarkExp3Power0x100000 921114000 885249000 -3.89% BenchmarkExp3Power0x400000 8323094000 7969020000 -4.25% BenchmarkFibo 322021600 92554450 -71.26% BenchmarkScanPi 1264583 321065 -74.61% BenchmarkStringPiParallel 1644661 554216 -66.30% BenchmarkScan10Base2 1111 1080 -2.79% BenchmarkScan100Base2 6645 6345 -4.51% BenchmarkScan1000Base2 84084 62405 -25.78% BenchmarkScan10000Base2 3105998 932551 -69.98% BenchmarkScan100000Base2 257234800 40113333 -84.41% BenchmarkScan10Base8 571 573 +0.35% BenchmarkScan100Base8 2810 2543 -9.50% BenchmarkScan1000Base8 47383 25834 -45.48% BenchmarkScan10000Base8 2739518 567203 -79.30% BenchmarkScan100000Base8 253952400 36495680 -85.63% BenchmarkScan10Base10 553 556 +0.54% BenchmarkScan100Base10 2640 2385 -9.66% BenchmarkScan1000Base10 50865 24049 -52.72% BenchmarkScan10000Base10 3279916 549313 -83.25% BenchmarkScan100000Base10 309121000 36213140 -88.29% BenchmarkScan10Base16 478 483 +1.05% BenchmarkScan100Base16 2353 2144 -8.88% BenchmarkScan1000Base16 48091 24246 -49.58% BenchmarkScan10000Base16 2858886 586475 -79.49% BenchmarkScan100000Base16 266320000 38190500 -85.66% BenchmarkString10Base2 736 730 -0.82% BenchmarkString100Base2 2695 2707 +0.45% BenchmarkString1000Base2 20549 20388 -0.78% BenchmarkString10000Base2 212638 210782 -0.87% BenchmarkString100000Base2 1944963 1938033 -0.36% BenchmarkString10Base8 524 517 -1.34% BenchmarkString100Base8 1326 1320 -0.45% BenchmarkString1000Base8 8213 8249 +0.44% BenchmarkString10000Base8 72204 72092 -0.16% BenchmarkString100000Base8 769068 765993 -0.40% BenchmarkString10Base10 1018 982 -3.54% BenchmarkString100Base10 3485 3206 -8.01% BenchmarkString1000Base10 37102 18935 -48.97% BenchmarkString10000Base10 188633 88637 -53.01% BenchmarkString100000Base10 124490300 19700940 -84.17% BenchmarkString10Base16 509 502 -1.38% BenchmarkString100Base16 1084 1098 +1.29% BenchmarkString1000Base16 5641 5650 +0.16% BenchmarkString10000Base16 46900 46745 -0.33% BenchmarkString100000Base16 508957 505840 -0.61% BenchmarkLeafSize0 8934320 8149465 -8.78% BenchmarkLeafSize1 237666 118381 -50.19% BenchmarkLeafSize2 237807 117854 -50.44% BenchmarkLeafSize3 1688640 353494 -79.07% BenchmarkLeafSize4 235676 116196 -50.70% BenchmarkLeafSize5 2121896 430325 -79.72% BenchmarkLeafSize6 1682306 351775 -79.09% BenchmarkLeafSize7 1051847 251436 -76.10% BenchmarkLeafSize8 232697 115674 -50.29% BenchmarkLeafSize9 2403616 488443 -79.68% BenchmarkLeafSize10 2120975 429545 -79.75% BenchmarkLeafSize11 2023789 426525 -78.92% BenchmarkLeafSize12 1684830 351985 -79.11% BenchmarkLeafSize13 1465529 337906 -76.94% BenchmarkLeafSize14 1050498 253872 -75.83% BenchmarkLeafSize15 683228 197384 -71.11% BenchmarkLeafSize16 232496 116026 -50.10% BenchmarkLeafSize32 245841 126671 -48.47% BenchmarkLeafSize64 301728 190285 -36.93% Change-Id: I63e63297896d96b89c9a275b893c2b405a7e105d Reviewed-on: https://go-review.googlesource.com/9260Reviewed-by: David Crawshaw <crawshaw@golang.org>

math/big: add partial arm64 assembly support
benchmark old ns/op new ns/op delta BenchmarkAddVV_1 18.7 14.8 -20.86% BenchmarkAddVV_2 21.8 16.6 -23.85% BenchmarkAddVV_3 26.1 17.1 -34.48% BenchmarkAddVV_4 30.4 21.9 -27.96% BenchmarkAddVV_5 35.5 19.8 -44.23% BenchmarkAddVV_1e1 63.0 28.3 -55.08% BenchmarkAddVV_1e2 593 178 -69.98% BenchmarkAddVV_1e3 5691 1490 -73.82% BenchmarkAddVV_1e4 56868 20761 -63.49% BenchmarkAddVV_1e5 569062 207679 -63.51% BenchmarkAddVW_1 15.8 12.6 -20.25% BenchmarkAddVW_2 17.8 13.1 -26.40% BenchmarkAddVW_3 21.2 13.9 -34.43% BenchmarkAddVW_4 23.6 14.7 -37.71% BenchmarkAddVW_5 26.0 15.8 -39.23% BenchmarkAddVW_1e1 41.3 21.6 -47.70% BenchmarkAddVW_1e2 383 145 -62.14% BenchmarkAddVW_1e3 3703 1264 -65.87% BenchmarkAddVW_1e4 36920 14359 -61.11% BenchmarkAddVW_1e5 370345 143046 -61.37% BenchmarkAddMulVVW_1 33.2 32.5 -2.11% BenchmarkAddMulVVW_2 58.0 57.2 -1.38% BenchmarkAddMulVVW_3 95.2 93.9 -1.37% BenchmarkAddMulVVW_4 108 106 -1.85% BenchmarkAddMulVVW_5 159 156 -1.89% BenchmarkAddMulVVW_1e1 344 340 -1.16% BenchmarkAddMulVVW_1e2 3644 3624 -0.55% BenchmarkAddMulVVW_1e3 37344 37208 -0.36% BenchmarkAddMulVVW_1e4 373295 372170 -0.30% BenchmarkAddMulVVW_1e5 3438116 3425606 -0.36% BenchmarkBitLen0 7.21 4.32 -40.08% BenchmarkBitLen1 6.49 4.32 -33.44% BenchmarkBitLen2 7.23 4.32 -40.25% BenchmarkBitLen3 6.49 4.32 -33.44% BenchmarkBitLen4 7.22 4.32 -40.17% BenchmarkBitLen5 6.52 4.33 -33.59% BenchmarkBitLen8 7.22 4.32 -40.17% BenchmarkBitLen9 6.49 4.32 -33.44% BenchmarkBitLen16 8.66 4.32 -50.12% BenchmarkBitLen17 7.95 4.32 -45.66% BenchmarkBitLen31 8.69 4.32 -50.29% BenchmarkGCD10x10 5021 5033 +0.24% BenchmarkGCD10x100 5571 5572 +0.02% BenchmarkGCD10x1000 6707 6729 +0.33% BenchmarkGCD10x10000 13526 13419 -0.79% BenchmarkGCD10x100000 85668 83242 -2.83% BenchmarkGCD100x100 24196 23936 -1.07% BenchmarkGCD100x1000 28802 27309 -5.18% BenchmarkGCD100x10000 64111 51704 -19.35% BenchmarkGCD100x100000 385840 274385 -28.89% BenchmarkGCD1000x1000 262892 236269 -10.13% BenchmarkGCD1000x10000 371393 277883 -25.18% BenchmarkGCD1000x100000 1311795 589055 -55.10% BenchmarkGCD10000x10000 9596740 6123930 -36.19% BenchmarkGCD10000x100000 16404000 7269610 -55.68% BenchmarkGCD100000x100000 776660000 419270000 -46.02% BenchmarkHilbert 13478980 13402270 -0.57% BenchmarkBinomial 9802 9440 -3.69% BenchmarkBitset 142 142 +0.00% BenchmarkBitsetNeg 328 279 -14.94% BenchmarkBitsetOrig 853 861 +0.94% BenchmarkBitsetNegOrig 1489 1444 -3.02% BenchmarkMul 420949000 410481000 -2.49% BenchmarkExp3Power0x10 1148 1229 +7.06% BenchmarkExp3Power0x40 1322 1376 +4.08% BenchmarkExp3Power0x100 2437 2486 +2.01% BenchmarkExp3Power0x400 9456 9346 -1.16% BenchmarkExp3Power0x1000 113623 108701 -4.33% BenchmarkExp3Power0x4000 1134933 1101481 -2.95% BenchmarkExp3Power0x10000 10773570 10396160 -3.50% BenchmarkExp3Power0x40000 101362100 97788300 -3.53% BenchmarkExp3Power0x100000 921114000 885249000 -3.89% BenchmarkExp3Power0x400000 8323094000 7969020000 -4.25% BenchmarkFibo 322021600 92554450 -71.26% BenchmarkScanPi 1264583 321065 -74.61% BenchmarkStringPiParallel 1644661 554216 -66.30% BenchmarkScan10Base2 1111 1080 -2.79% BenchmarkScan100Base2 6645 6345 -4.51% BenchmarkScan1000Base2 84084 62405 -25.78% BenchmarkScan10000Base2 3105998 932551 -69.98% BenchmarkScan100000Base2 257234800 40113333 -84.41% BenchmarkScan10Base8 571 573 +0.35% BenchmarkScan100Base8 2810 2543 -9.50% BenchmarkScan1000Base8 47383 25834 -45.48% BenchmarkScan10000Base8 2739518 567203 -79.30% BenchmarkScan100000Base8 253952400 36495680 -85.63% BenchmarkScan10Base10 553 556 +0.54% BenchmarkScan100Base10 2640 2385 -9.66% BenchmarkScan1000Base10 50865 24049 -52.72% BenchmarkScan10000Base10 3279916 549313 -83.25% BenchmarkScan100000Base10 309121000 36213140 -88.29% BenchmarkScan10Base16 478 483 +1.05% BenchmarkScan100Base16 2353 2144 -8.88% BenchmarkScan1000Base16 48091 24246 -49.58% BenchmarkScan10000Base16 2858886 586475 -79.49% BenchmarkScan100000Base16 266320000 38190500 -85.66% BenchmarkString10Base2 736 730 -0.82% BenchmarkString100Base2 2695 2707 +0.45% BenchmarkString1000Base2 20549 20388 -0.78% BenchmarkString10000Base2 212638 210782 -0.87% BenchmarkString100000Base2 1944963 1938033 -0.36% BenchmarkString10Base8 524 517 -1.34% BenchmarkString100Base8 1326 1320 -0.45% BenchmarkString1000Base8 8213 8249 +0.44% BenchmarkString10000Base8 72204 72092 -0.16% BenchmarkString100000Base8 769068 765993 -0.40% BenchmarkString10Base10 1018 982 -3.54% BenchmarkString100Base10 3485 3206 -8.01% BenchmarkString1000Base10 37102 18935 -48.97% BenchmarkString10000Base10 188633 88637 -53.01% BenchmarkString100000Base10 124490300 19700940 -84.17% BenchmarkString10Base16 509 502 -1.38% BenchmarkString100Base16 1084 1098 +1.29% BenchmarkString1000Base16 5641 5650 +0.16% BenchmarkString10000Base16 46900 46745 -0.33% BenchmarkString100000Base16 508957 505840 -0.61% BenchmarkLeafSize0 8934320 8149465 -8.78% BenchmarkLeafSize1 237666 118381 -50.19% BenchmarkLeafSize2 237807 117854 -50.44% BenchmarkLeafSize3 1688640 353494 -79.07% BenchmarkLeafSize4 235676 116196 -50.70% BenchmarkLeafSize5 2121896 430325 -79.72% BenchmarkLeafSize6 1682306 351775 -79.09% BenchmarkLeafSize7 1051847 251436 -76.10% BenchmarkLeafSize8 232697 115674 -50.29% BenchmarkLeafSize9 2403616 488443 -79.68% BenchmarkLeafSize10 2120975 429545 -79.75% BenchmarkLeafSize11 2023789 426525 -78.92% BenchmarkLeafSize12 1684830 351985 -79.11% BenchmarkLeafSize13 1465529 337906 -76.94% BenchmarkLeafSize14 1050498 253872 -75.83% BenchmarkLeafSize15 683228 197384 -71.11% BenchmarkLeafSize16 232496 116026 -50.10% BenchmarkLeafSize32 245841 126671 -48.47% BenchmarkLeafSize64 301728 190285 -36.93% Change-Id: I63e63297896d96b89c9a275b893c2b405a7e105d Reviewed-on: https://go-review.googlesource.com/9260Reviewed-by: David Crawshaw <crawshaw@golang.org>
56a7c5b9 · Josh Bleecher Snyder · 1f65c9c1 · 56a7c5b9
Commit 56a7c5b9 authored Apr 21, 2015 by Josh Bleecher Snyder
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Showing with 139 additions and 8 deletions

arith_arm64.s src/math/big/arith_arm64.s +139 -8

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--- a/src/math/big/arith_arm64.s
+++ b/src/math/big/arith_arm64.s
@@ -9,38 +9,169 @@
 // This file provides fast assembly versions for the elementary
 // arithmetic operations on vectors implemented in arith.go.
+// TODO: Consider re-implementing using Advanced SIMD
+// once the assembler supports those instructions.
+// func mulWW(x, y Word) (z1, z0 Word)
 TEXT ·mulWW(SB),NOSPLIT,$0
-	B ·mulWW_g(SB)
+	MOVD	x+0(FP), R0
+	MOVD	y+8(FP), R1
+	MUL	R0, R1, R2
+	UMULH	R0, R1, R3
+	MOVD	R3, z1+16(FP)
+	MOVD	R2, z0+24(FP)
+	RET
+// func divWW(x1, x0, y Word) (q, r Word)
 TEXT ·divWW(SB),NOSPLIT,$0
-	B ·divWW_g(SB)
+	B	·divWW_g(SB) // ARM64 has no multiword division
+// func addVV(z, x, y []Word) (c Word)
 TEXT ·addVV(SB),NOSPLIT,$0
-	B ·addVV_g(SB)
+	MOVD	z+0(FP), R3
+	MOVD	z_len+8(FP), R0
+	MOVD	x+24(FP), R1
+	MOVD	y+48(FP), R2
+	ADDS	$0, R0 // clear carry flag
+loop:
+	CBZ	R0, done // careful not to touch the carry flag
+	MOVD.P	8(R1), R4
+	MOVD.P	8(R2), R5
+	ADCS	R4, R5
+	MOVD.P	R5, 8(R3)
+	SUB	$1, R0
+	B	loop
+done:
+	CSET	HS, R0 // extract carry flag
+	MOVD	R0, c+72(FP)
+	RET
+// func subVV(z, x, y []Word) (c Word)
 TEXT ·subVV(SB),NOSPLIT,$0
-	B ·subVV_g(SB)
+	MOVD	z+0(FP), R3
+	MOVD	z_len+8(FP), R0
+	MOVD	x+24(FP), R1
+	MOVD	y+48(FP), R2
+	CMP	R0, R0 // set carry flag
+loop:
+	CBZ	R0, done // careful not to touch the carry flag
+	MOVD.P	8(R1), R4
+	MOVD.P	8(R2), R5
+	SBCS	R5, R4
+	MOVD.P	R4, 8(R3)
+	SUB	$1, R0
+	B	loop
+done:
+	CSET	LO, R0 // extract carry flag
+	MOVD	R0, c+72(FP)
+	RET
+// func addVW(z, x []Word, y Word) (c Word)
 TEXT ·addVW(SB),NOSPLIT,$0
-	B ·addVW_g(SB)
+	MOVD	z+0(FP), R3
+	MOVD	z_len+8(FP), R0
+	MOVD	x+24(FP), R1
+	MOVD	y+48(FP), R2
+	CBZ	R0, return_y
+	MOVD.P	8(R1), R4
+	ADDS	R2, R4
+	MOVD.P	R4, 8(R3)
+	SUB	$1, R0
+loop:
+	CBZ	R0, done // careful not to touch the carry flag
+	MOVD.P	8(R1), R4
+	ADCS	$0, R4
+	MOVD.P	R4, 8(R3)
+	SUB	$1, R0
+	B	loop
+done:
+	CSET	HS, R0 // extract carry flag
+	MOVD	R0, c+56(FP)
+	RET
+return_y: // z is empty; copy y to c
+	MOVD	R2, c+56(FP)
+	RET
+// func subVW(z, x []Word, y Word) (c Word)
 TEXT ·subVW(SB),NOSPLIT,$0
-	B ·subVW_g(SB)
+	MOVD	z+0(FP), R3
+	MOVD	z_len+8(FP), R0
+	MOVD	x+24(FP), R1
+	MOVD	y+48(FP), R2
+	CBZ	R0, rety
+	MOVD.P	8(R1), R4
+	SUBS	R2, R4
+	MOVD.P	R4, 8(R3)
+	SUB	$1, R0
+loop:
+	CBZ	R0, done // careful not to touch the carry flag
+	MOVD.P	8(R1), R4
+	SBCS	$0, R4
+	MOVD.P	R4, 8(R3)
+	SUB	$1, R0
+	B	loop
+done:
+	CSET	LO, R0 // extract carry flag
+	MOVD	R0, c+56(FP)
+	RET
+rety: // z is empty; copy y to c
+	MOVD	R2, c+56(FP)
+	RET
+// func shlVU(z, x []Word, s uint) (c Word)
 TEXT ·shlVU(SB),NOSPLIT,$0
 	B ·shlVU_g(SB)
+// func shrVU(z, x []Word, s uint) (c Word)
 TEXT ·shrVU(SB),NOSPLIT,$0
 	B ·shrVU_g(SB)
+// func mulAddVWW(z, x []Word, y, r Word) (c Word)
 TEXT ·mulAddVWW(SB),NOSPLIT,$0
-	B ·mulAddVWW_g(SB)
+	MOVD	z+0(FP), R1
+	MOVD	z_len+8(FP), R0
+	MOVD	x+24(FP), R2
+	MOVD	y+48(FP), R3
+	MOVD	r+56(FP), R4
+loop:
+	CBZ	R0, done
+	MOVD.P	8(R2), R5
+	UMULH	R5, R3, R7
+	MUL	R5, R3, R6
+	ADDS	R4, R6
+	ADC	$0, R7
+	MOVD.P	R6, 8(R1)
+	MOVD	R7, R4
+	SUB	$1, R0
+	B	loop
+done:
+	MOVD	R4, c+64(FP)
+	RET
+// func addMulVVW(z, x []Word, y Word) (c Word)
 TEXT ·addMulVVW(SB),NOSPLIT,$0
 	B ·addMulVVW_g(SB)
+// func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
 TEXT ·divWVW(SB),NOSPLIT,$0
 	B ·divWVW_g(SB)
+// func bitLen(x Word) (n int)
 TEXT ·bitLen(SB),NOSPLIT,$0
-	B ·bitLen_g(SB)
+	MOVD	x+0(FP), R0
+	CLZ	R0, R0
+	MOVD	$64, R1
+	SUB	R0, R1, R0
+	MOVD	R0, n+8(FP)
+	RET