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-rw-r--r--src/math/acosh.go5
-rw-r--r--src/math/big/arith.go89
-rw-r--r--src/math/big/arith_386.s27
-rw-r--r--src/math/big/arith_amd64.s26
-rw-r--r--src/math/big/arith_arm.s11
-rw-r--r--src/math/big/arith_arm64.s9
-rw-r--r--src/math/big/arith_decl.go2
-rw-r--r--src/math/big/arith_decl_pure.go8
-rw-r--r--src/math/big/arith_mips64x.s5
-rw-r--r--src/math/big/arith_mipsx.s5
-rw-r--r--src/math/big/arith_ppc64x.s40
-rw-r--r--src/math/big/arith_riscv64.s5
-rw-r--r--src/math/big/arith_s390x.s225
-rw-r--r--src/math/big/arith_test.go107
-rw-r--r--src/math/big/arith_wasm.s5
-rw-r--r--src/math/big/decimal.go3
-rw-r--r--src/math/big/link_test.go4
-rw-r--r--src/math/big/nat.go5
-rw-r--r--src/math/bits/make_examples.go4
-rw-r--r--src/math/bits/make_tables.go4
20 files changed, 200 insertions, 389 deletions
diff --git a/src/math/acosh.go b/src/math/acosh.go
index cc8195ce32..41ca87123c 100644
--- a/src/math/acosh.go
+++ b/src/math/acosh.go
@@ -42,10 +42,7 @@ package math
func Acosh(x float64) float64
func acosh(x float64) float64 {
- const (
- Ln2 = 6.93147180559945286227e-01 // 0x3FE62E42FEFA39EF
- Large = 1 << 28 // 2**28
- )
+ const Large = 1 << 28 // 2**28
// first case is special case
switch {
case x < 1 || IsNaN(x):
diff --git a/src/math/big/arith.go b/src/math/big/arith.go
index b0885f261f..750ce8aa39 100644
--- a/src/math/big/arith.go
+++ b/src/math/big/arith.go
@@ -60,12 +60,6 @@ func nlz(x Word) uint {
return uint(bits.LeadingZeros(uint(x)))
}
-// q = (u1<<_W + u0 - r)/v
-func divWW_g(u1, u0, v Word) (q, r Word) {
- qq, rr := bits.Div(uint(u1), uint(u0), uint(v))
- return Word(qq), Word(rr)
-}
-
// The resulting carry c is either 0 or 1.
func addVV_g(z, x, y []Word) (c Word) {
// The comment near the top of this file discusses this for loop condition.
@@ -207,10 +201,87 @@ func addMulVVW_g(z, x []Word, y Word) (c Word) {
return
}
-func divWVW_g(z []Word, xn Word, x []Word, y Word) (r Word) {
+// q = ( x1 << _W + x0 - r)/y. m = floor(( _B^2 - 1 ) / d - _B). Requiring x1<y.
+// An approximate reciprocal with a reference to "Improved Division by Invariant Integers
+// (IEEE Transactions on Computers, 11 Jun. 2010)"
+func divWW(x1, x0, y, m Word) (q, r Word) {
+ s := nlz(y)
+ if s != 0 {
+ x1 = x1<<s | x0>>(_W-s)
+ x0 <<= s
+ y <<= s
+ }
+ d := uint(y)
+ // We know that
+ // m = ⎣(B^2-1)/d⎦-B
+ // ⎣(B^2-1)/d⎦ = m+B
+ // (B^2-1)/d = m+B+delta1 0 <= delta1 <= (d-1)/d
+ // B^2/d = m+B+delta2 0 <= delta2 <= 1
+ // The quotient we're trying to compute is
+ // quotient = ⎣(x1*B+x0)/d⎦
+ // = ⎣(x1*B*(B^2/d)+x0*(B^2/d))/B^2⎦
+ // = ⎣(x1*B*(m+B+delta2)+x0*(m+B+delta2))/B^2⎦
+ // = ⎣(x1*m+x1*B+x0)/B + x0*m/B^2 + delta2*(x1*B+x0)/B^2⎦
+ // The latter two terms of this three-term sum are between 0 and 1.
+ // So we can compute just the first term, and we will be low by at most 2.
+ t1, t0 := bits.Mul(uint(m), uint(x1))
+ _, c := bits.Add(t0, uint(x0), 0)
+ t1, _ = bits.Add(t1, uint(x1), c)
+ // The quotient is either t1, t1+1, or t1+2.
+ // We'll try t1 and adjust if needed.
+ qq := t1
+ // compute remainder r=x-d*q.
+ dq1, dq0 := bits.Mul(d, qq)
+ r0, b := bits.Sub(uint(x0), dq0, 0)
+ r1, _ := bits.Sub(uint(x1), dq1, b)
+ // The remainder we just computed is bounded above by B+d:
+ // r = x1*B + x0 - d*q.
+ // = x1*B + x0 - d*⎣(x1*m+x1*B+x0)/B⎦
+ // = x1*B + x0 - d*((x1*m+x1*B+x0)/B-alpha) 0 <= alpha < 1
+ // = x1*B + x0 - x1*d/B*m - x1*d - x0*d/B + d*alpha
+ // = x1*B + x0 - x1*d/B*⎣(B^2-1)/d-B⎦ - x1*d - x0*d/B + d*alpha
+ // = x1*B + x0 - x1*d/B*⎣(B^2-1)/d-B⎦ - x1*d - x0*d/B + d*alpha
+ // = x1*B + x0 - x1*d/B*((B^2-1)/d-B-beta) - x1*d - x0*d/B + d*alpha 0 <= beta < 1
+ // = x1*B + x0 - x1*B + x1/B + x1*d + x1*d/B*beta - x1*d - x0*d/B + d*alpha
+ // = x0 + x1/B + x1*d/B*beta - x0*d/B + d*alpha
+ // = x0*(1-d/B) + x1*(1+d*beta)/B + d*alpha
+ // < B*(1-d/B) + d*B/B + d because x0<B (and 1-d/B>0), x1<d, 1+d*beta<=B, alpha<1
+ // = B - d + d + d
+ // = B+d
+ // So r1 can only be 0 or 1. If r1 is 1, then we know q was too small.
+ // Add 1 to q and subtract d from r. That guarantees that r is <B, so
+ // we no longer need to keep track of r1.
+ if r1 != 0 {
+ qq++
+ r0 -= d
+ }
+ // If the remainder is still too large, increment q one more time.
+ if r0 >= d {
+ qq++
+ r0 -= d
+ }
+ return Word(qq), Word(r0 >> s)
+}
+
+func divWVW(z []Word, xn Word, x []Word, y Word) (r Word) {
r = xn
+ if len(x) == 1 {
+ qq, rr := bits.Div(uint(r), uint(x[0]), uint(y))
+ z[0] = Word(qq)
+ return Word(rr)
+ }
+ rec := reciprocalWord(y)
for i := len(z) - 1; i >= 0; i-- {
- z[i], r = divWW_g(r, x[i], y)
+ z[i], r = divWW(r, x[i], y, rec)
}
- return
+ return r
+}
+
+// reciprocalWord return the reciprocal of the divisor. rec = floor(( _B^2 - 1 ) / u - _B). u = d1 << nlz(d1).
+func reciprocalWord(d1 Word) Word {
+ u := uint(d1 << nlz(d1))
+ x1 := ^u
+ x0 := uint(_M)
+ rec, _ := bits.Div(x1, x0, u) // (_B^2-1)/U-_B = (_B*(_M-C)+_M)/U
+ return Word(rec)
}
diff --git a/src/math/big/arith_386.s b/src/math/big/arith_386.s
index f61da2aba7..d0ea949fe6 100644
--- a/src/math/big/arith_386.s
+++ b/src/math/big/arith_386.s
@@ -18,16 +18,6 @@ TEXT ·mulWW(SB),NOSPLIT,$0
RET
-// func divWW(x1, x0, y Word) (q, r Word)
-TEXT ·divWW(SB),NOSPLIT,$0
- MOVL x1+0(FP), DX
- MOVL x0+4(FP), AX
- DIVL y+8(FP)
- MOVL AX, q+12(FP)
- MOVL DX, r+16(FP)
- RET
-
-
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
MOVL z+0(FP), DI
@@ -251,21 +241,4 @@ E6: CMPL BX, $0 // i < 0
RET
-// func divWVW(z* Word, xn Word, x []Word, y Word) (r Word)
-TEXT ·divWVW(SB),NOSPLIT,$0
- MOVL z+0(FP), DI
- MOVL xn+12(FP), DX // r = xn
- MOVL x+16(FP), SI
- MOVL y+28(FP), CX
- MOVL z_len+4(FP), BX // i = z
- JMP E7
-L7: MOVL (SI)(BX*4), AX
- DIVL CX
- MOVL AX, (DI)(BX*4)
-
-E7: SUBL $1, BX // i--
- JGE L7 // i >= 0
-
- MOVL DX, r+32(FP)
- RET
diff --git a/src/math/big/arith_amd64.s b/src/math/big/arith_amd64.s
index b75639f540..61043ca2d9 100644
--- a/src/math/big/arith_amd64.s
+++ b/src/math/big/arith_amd64.s
@@ -18,14 +18,6 @@ TEXT ·mulWW(SB),NOSPLIT,$0
RET
-// func divWW(x1, x0, y Word) (q, r Word)
-TEXT ·divWW(SB),NOSPLIT,$0
- MOVQ x1+0(FP), DX
- MOVQ x0+8(FP), AX
- DIVQ y+16(FP)
- MOVQ AX, q+24(FP)
- MOVQ DX, r+32(FP)
- RET
// The carry bit is saved with SBBQ Rx, Rx: if the carry was set, Rx is -1, otherwise it is 0.
// It is restored with ADDQ Rx, Rx: if Rx was -1 the carry is set, otherwise it is cleared.
@@ -531,21 +523,3 @@ adx_short:
-// func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
-TEXT ·divWVW(SB),NOSPLIT,$0
- MOVQ z+0(FP), R10
- MOVQ xn+24(FP), DX // r = xn
- MOVQ x+32(FP), R8
- MOVQ y+56(FP), R9
- MOVQ z_len+8(FP), BX // i = z
- JMP E7
-
-L7: MOVQ (R8)(BX*8), AX
- DIVQ R9
- MOVQ AX, (R10)(BX*8)
-
-E7: SUBQ $1, BX // i--
- JGE L7 // i >= 0
-
- MOVQ DX, r+64(FP)
- RET
diff --git a/src/math/big/arith_arm.s b/src/math/big/arith_arm.s
index 33aa36f709..cbf7445e7a 100644
--- a/src/math/big/arith_arm.s
+++ b/src/math/big/arith_arm.s
@@ -272,17 +272,6 @@ E9:
RET
-// func divWVW(z* Word, xn Word, x []Word, y Word) (r Word)
-TEXT ·divWVW(SB),NOSPLIT,$0
- // ARM has no multiword division, so use portable code.
- B ·divWVW_g(SB)
-
-
-// func divWW(x1, x0, y Word) (q, r Word)
-TEXT ·divWW(SB),NOSPLIT,$0
- // ARM has no multiword division, so use portable code.
- B ·divWW_g(SB)
-
// func mulWW(x, y Word) (z1, z0 Word)
TEXT ·mulWW(SB),NOSPLIT,$0
diff --git a/src/math/big/arith_arm64.s b/src/math/big/arith_arm64.s
index da6e408e19..22357d088e 100644
--- a/src/math/big/arith_arm64.s
+++ b/src/math/big/arith_arm64.s
@@ -23,11 +23,6 @@ TEXT ·mulWW(SB),NOSPLIT,$0
RET
-// func divWW(x1, x0, y Word) (q, r Word)
-TEXT ·divWW(SB),NOSPLIT,$0
- B ·divWW_g(SB) // ARM64 has no multiword division
-
-
// func addVV(z, x, y []Word) (c Word)
TEXT ·addVV(SB),NOSPLIT,$0
MOVD z_len+8(FP), R0
@@ -585,6 +580,4 @@ done:
MOVD R4, c+56(FP)
RET
-// func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
-TEXT ·divWVW(SB),NOSPLIT,$0
- B ·divWVW_g(SB)
+
diff --git a/src/math/big/arith_decl.go b/src/math/big/arith_decl.go
index 41e592334c..d519bdc87b 100644
--- a/src/math/big/arith_decl.go
+++ b/src/math/big/arith_decl.go
@@ -8,7 +8,6 @@ package big
// implemented in arith_$GOARCH.s
func mulWW(x, y Word) (z1, z0 Word)
-func divWW(x1, x0, y Word) (q, r Word)
func addVV(z, x, y []Word) (c Word)
func subVV(z, x, y []Word) (c Word)
func addVW(z, x []Word, y Word) (c Word)
@@ -17,4 +16,3 @@ func shlVU(z, x []Word, s uint) (c Word)
func shrVU(z, x []Word, s uint) (c Word)
func mulAddVWW(z, x []Word, y, r Word) (c Word)
func addMulVVW(z, x []Word, y Word) (c Word)
-func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
diff --git a/src/math/big/arith_decl_pure.go b/src/math/big/arith_decl_pure.go
index 305f7ee03b..5faa3bd281 100644
--- a/src/math/big/arith_decl_pure.go
+++ b/src/math/big/arith_decl_pure.go
@@ -10,10 +10,6 @@ func mulWW(x, y Word) (z1, z0 Word) {
return mulWW_g(x, y)
}
-func divWW(x1, x0, y Word) (q, r Word) {
- return divWW_g(x1, x0, y)
-}
-
func addVV(z, x, y []Word) (c Word) {
return addVV_g(z, x, y)
}
@@ -55,7 +51,3 @@ func mulAddVWW(z, x []Word, y, r Word) (c Word) {
func addMulVVW(z, x []Word, y Word) (c Word) {
return addMulVVW_g(z, x, y)
}
-
-func divWVW(z []Word, xn Word, x []Word, y Word) (r Word) {
- return divWVW_g(z, xn, x, y)
-}
diff --git a/src/math/big/arith_mips64x.s b/src/math/big/arith_mips64x.s
index 983510ee3d..804b9fe06e 100644
--- a/src/math/big/arith_mips64x.s
+++ b/src/math/big/arith_mips64x.s
@@ -12,9 +12,6 @@
TEXT ·mulWW(SB),NOSPLIT,$0
JMP ·mulWW_g(SB)
-TEXT ·divWW(SB),NOSPLIT,$0
- JMP ·divWW_g(SB)
-
TEXT ·addVV(SB),NOSPLIT,$0
JMP ·addVV_g(SB)
@@ -39,5 +36,3 @@ TEXT ·mulAddVWW(SB),NOSPLIT,$0
TEXT ·addMulVVW(SB),NOSPLIT,$0
JMP ·addMulVVW_g(SB)
-TEXT ·divWVW(SB),NOSPLIT,$0
- JMP ·divWVW_g(SB)
diff --git a/src/math/big/arith_mipsx.s b/src/math/big/arith_mipsx.s
index 54cafbd9c0..efdecb80f3 100644
--- a/src/math/big/arith_mipsx.s
+++ b/src/math/big/arith_mipsx.s
@@ -12,9 +12,6 @@
TEXT ·mulWW(SB),NOSPLIT,$0
JMP ·mulWW_g(SB)
-TEXT ·divWW(SB),NOSPLIT,$0
- JMP ·divWW_g(SB)
-
TEXT ·addVV(SB),NOSPLIT,$0
JMP ·addVV_g(SB)
@@ -39,5 +36,3 @@ TEXT ·mulAddVWW(SB),NOSPLIT,$0
TEXT ·addMulVVW(SB),NOSPLIT,$0
JMP ·addMulVVW_g(SB)
-TEXT ·divWVW(SB),NOSPLIT,$0
- JMP ·divWVW_g(SB)
diff --git a/src/math/big/arith_ppc64x.s b/src/math/big/arith_ppc64x.s
index 409e10ab48..b299ccc2fb 100644
--- a/src/math/big/arith_ppc64x.s
+++ b/src/math/big/arith_ppc64x.s
@@ -478,44 +478,4 @@ done:
MOVD R4, c+56(FP)
RET
-// func divWW(x1, x0, y Word) (q, r Word)
-TEXT ·divWW(SB), NOSPLIT, $0
- MOVD x1+0(FP), R4
- MOVD x0+8(FP), R5
- MOVD y+16(FP), R6
- CMPU R4, R6
- BGE divbigger
-
- // from the programmer's note in ch. 3 of the ISA manual, p.74
- DIVDEU R6, R4, R3
- DIVDU R6, R5, R7
- MULLD R6, R3, R8
- MULLD R6, R7, R20
- SUB R20, R5, R10
- ADD R7, R3, R3
- SUB R8, R10, R4
- CMPU R4, R10
- BLT adjust
- CMPU R4, R6
- BLT end
-
-adjust:
- MOVD $1, R21
- ADD R21, R3, R3
- SUB R6, R4, R4
-
-end:
- MOVD R3, q+24(FP)
- MOVD R4, r+32(FP)
-
- RET
-
-divbigger:
- MOVD $-1, R7
- MOVD R7, q+24(FP)
- MOVD R7, r+32(FP)
- RET
-
-TEXT ·divWVW(SB), NOSPLIT, $0
- BR ·divWVW_g(SB)
diff --git a/src/math/big/arith_riscv64.s b/src/math/big/arith_riscv64.s
index 59065c3f7b..a2f7666c7b 100644
--- a/src/math/big/arith_riscv64.s
+++ b/src/math/big/arith_riscv64.s
@@ -19,9 +19,6 @@ TEXT ·mulWW(SB),NOSPLIT,$0
MOV X8, z0+24(FP)
RET
-// func divWW(x1, x0, y Word) (q, r Word)
-TEXT ·divWW(SB),NOSPLIT,$0
- JMP ·divWW_g(SB) // riscv64 has no multiword division
TEXT ·addVV(SB),NOSPLIT,$0
JMP ·addVV_g(SB)
@@ -47,5 +44,3 @@ TEXT ·mulAddVWW(SB),NOSPLIT,$0
TEXT ·addMulVVW(SB),NOSPLIT,$0
JMP ·addMulVVW_g(SB)
-TEXT ·divWVW(SB),NOSPLIT,$0
- JMP ·divWVW_g(SB)
diff --git a/src/math/big/arith_s390x.s b/src/math/big/arith_s390x.s
index 4891768111..caa4db0829 100644
--- a/src/math/big/arith_s390x.s
+++ b/src/math/big/arith_s390x.s
@@ -17,15 +17,6 @@ TEXT ·mulWW(SB), NOSPLIT, $0
MOVD R11, z0+24(FP)
RET
-// func divWW(x1, x0, y Word) (q, r Word)
-TEXT ·divWW(SB), NOSPLIT, $0
- MOVD x1+0(FP), R10
- MOVD x0+8(FP), R11
- MOVD y+16(FP), R5
- WORD $0xb98700a5 // dlgr r10,r5
- MOVD R11, q+24(FP)
- MOVD R10, r+32(FP)
- RET
// DI = R3, CX = R4, SI = r10, r8 = r8, r9=r9, r10 = r2 , r11 = r5, r12 = r6, r13 = r7, r14 = r1 (R0 set to 0) + use R11
// func addVV(z, x, y []Word) (c Word)
@@ -702,199 +693,11 @@ returnC:
// func shlVU(z, x []Word, s uint) (c Word)
TEXT ·shlVU(SB), NOSPLIT, $0
- MOVD z_len+8(FP), R5
- MOVD $0, R0
- SUB $1, R5 // n--
- BLT X8b // n < 0 (n <= 0)
-
- // n > 0
- MOVD s+48(FP), R4
- CMPBEQ R0, R4, Z80 // handle 0 case beq
- MOVD $64, R6
- CMPBEQ R6, R4, Z864 // handle 64 case beq
- MOVD z+0(FP), R2
- MOVD x+24(FP), R8
- SLD $3, R5 // n = n*8
- SUB R4, R6, R7
- MOVD (R8)(R5*1), R10 // w1 = x[i-1]
- SRD R7, R10, R3
- MOVD R3, c+56(FP)
-
- MOVD $0, R1 // i = 0
- BR E8
-
- // i < n-1
-L8:
- MOVD R10, R3 // w = w1
- MOVD -8(R8)(R5*1), R10 // w1 = x[i+1]
-
- SLD R4, R3 // w<<s | w1>>ŝ
- SRD R7, R10, R6
- OR R6, R3
- MOVD R3, (R2)(R5*1) // z[i] = w<<s | w1>>ŝ
- SUB $8, R5 // i--
-
-E8:
- CMPBGT R5, R0, L8 // i < n-1
-
- // i >= n-1
-X8a:
- SLD R4, R10 // w1<<s
- MOVD R10, (R2) // z[0] = w1<<s
- RET
-
-X8b:
- MOVD R0, c+56(FP)
- RET
-
-Z80:
- MOVD z+0(FP), R2
- MOVD x+24(FP), R8
- SLD $3, R5 // n = n*8
-
- MOVD (R8), R10
- MOVD $0, R3
- MOVD R3, c+56(FP)
-
- MOVD $0, R1 // i = 0
- BR E8Z
+ BR ·shlVU_g(SB)
- // i < n-1
-L8Z:
- MOVD R10, R3
- MOVD 8(R8)(R1*1), R10
-
- MOVD R3, (R2)(R1*1)
- ADD $8, R1
-
-E8Z:
- CMPBLT R1, R5, L8Z
-
- // i >= n-1
- MOVD R10, (R2)(R5*1)
- RET
-
-Z864:
- MOVD z+0(FP), R2
- MOVD x+24(FP), R8
- SLD $3, R5 // n = n*8
- MOVD (R8)(R5*1), R3 // w1 = x[n-1]
- MOVD R3, c+56(FP) // z[i] = x[n-1]
-
- BR E864
-
- // i < n-1
-L864:
- MOVD -8(R8)(R5*1), R3
-
- MOVD R3, (R2)(R5*1) // z[i] = x[n-1]
- SUB $8, R5 // i--
-
-E864:
- CMPBGT R5, R0, L864 // i < n-1
-
- MOVD R0, (R2) // z[n-1] = 0
- RET
-
-// CX = R4, r8 = r8, r10 = r2 , r11 = r5, DX = r3, AX = r10 , BX = R1 , 64-count = r7 (R0 set to 0) temp = R6
// func shrVU(z, x []Word, s uint) (c Word)
TEXT ·shrVU(SB), NOSPLIT, $0
- MOVD z_len+8(FP), R5
- MOVD $0, R0
- SUB $1, R5 // n--
- BLT X9b // n < 0 (n <= 0)
-
- // n > 0
- MOVD s+48(FP), R4
- CMPBEQ R0, R4, ZB0 // handle 0 case beq
- MOVD $64, R6
- CMPBEQ R6, R4, ZB64 // handle 64 case beq
- MOVD z+0(FP), R2
- MOVD x+24(FP), R8
- SLD $3, R5 // n = n*8
- SUB R4, R6, R7
- MOVD (R8), R10 // w1 = x[0]
- SLD R7, R10, R3
- MOVD R3, c+56(FP)
-
- MOVD $0, R1 // i = 0
- BR E9
-
- // i < n-1
-L9:
- MOVD R10, R3 // w = w1
- MOVD 8(R8)(R1*1), R10 // w1 = x[i+1]
-
- SRD R4, R3 // w>>s | w1<<s
- SLD R7, R10, R6
- OR R6, R3
- MOVD R3, (R2)(R1*1) // z[i] = w>>s | w1<<s
- ADD $8, R1 // i++
-
-E9:
- CMPBLT R1, R5, L9 // i < n-1
-
- // i >= n-1
-X9a:
- SRD R4, R10 // w1>>s
- MOVD R10, (R2)(R5*1) // z[n-1] = w1>>s
- RET
-
-X9b:
- MOVD R0, c+56(FP)
- RET
-
-ZB0:
- MOVD z+0(FP), R2
- MOVD x+24(FP), R8
- SLD $3, R5 // n = n*8
-
- MOVD (R8), R10 // w1 = x[0]
- MOVD $0, R3 // R10 << 64
- MOVD R3, c+56(FP)
-
- MOVD $0, R1 // i = 0
- BR E9Z
-
- // i < n-1
-L9Z:
- MOVD R10, R3 // w = w1
- MOVD 8(R8)(R1*1), R10 // w1 = x[i+1]
-
- MOVD R3, (R2)(R1*1) // z[i] = w>>s | w1<<s
- ADD $8, R1 // i++
-
-E9Z:
- CMPBLT R1, R5, L9Z // i < n-1
-
- // i >= n-1
- MOVD R10, (R2)(R5*1) // z[n-1] = w1>>s
- RET
-
-ZB64:
- MOVD z+0(FP), R2
- MOVD x+24(FP), R8
- SLD $3, R5 // n = n*8
- MOVD (R8), R3 // w1 = x[0]
- MOVD R3, c+56(FP)
-
- MOVD $0, R1 // i = 0
- BR E964
-
- // i < n-1
-L964:
- MOVD 8(R8)(R1*1), R3 // w1 = x[i+1]
-
- MOVD R3, (R2)(R1*1) // z[i] = w>>s | w1<<s
- ADD $8, R1 // i++
-
-E964:
- CMPBLT R1, R5, L964 // i < n-1
-
- // i >= n-1
- MOVD $0, R10 // w1>>s
- MOVD R10, (R2)(R5*1) // z[n-1] = w1>>s
- RET
+ BR ·shrVU_g(SB)
// CX = R4, r8 = r8, r9=r9, r10 = r2 , r11 = r5, DX = r3, AX = r6 , BX = R1 , (R0 set to 0) + use R11 + use R7 for i
// func mulAddVWW(z, x []Word, y, r Word) (c Word)
@@ -990,27 +793,3 @@ E6:
MOVD R4, c+56(FP)
RET
-// func divWVW(z []Word, xn Word, x []Word, y Word) (r Word)
-// CX = R4, r8 = r8, r9=r9, r10 = r2 , r11 = r5, AX = r11, DX = R6, r12=r12, BX = R1(*8) , (R0 set to 0) + use R11 + use R7 for i
-TEXT ·divWVW(SB), NOSPLIT, $0
- MOVD z+0(FP), R2
- MOVD xn+24(FP), R10 // r = xn
- MOVD x+32(FP), R8
- MOVD y+56(FP), R9
- MOVD z_len+8(FP), R7 // i = z
- SLD $3, R7, R1 // i*8
- MOVD $0, R0 // make sure it's zero
- BR E7
-
-L7:
- MOVD (R8)(R1*1), R11
- WORD $0xB98700A9 // DLGR R10,R9
- MOVD R11, (R2)(R1*1)
-
-E7:
- SUB $1, R7 // i--
- SUB $8, R1
- BGE L7 // i >= 0
-
- MOVD R10, r+64(FP)
- RET
diff --git a/src/math/big/arith_test.go b/src/math/big/arith_test.go
index fc205934c5..2aca0effde 100644
--- a/src/math/big/arith_test.go
+++ b/src/math/big/arith_test.go
@@ -7,6 +7,7 @@ package big
import (
"fmt"
"internal/testenv"
+ "math/bits"
"math/rand"
"strings"
"testing"
@@ -284,20 +285,56 @@ type argVU struct {
m string // message.
}
+var argshlVUIn = []Word{1, 2, 4, 8, 16, 32, 64, 0, 0, 0}
+var argshlVUr0 = []Word{1, 2, 4, 8, 16, 32, 64}
+var argshlVUr1 = []Word{2, 4, 8, 16, 32, 64, 128}
+var argshlVUrWm1 = []Word{1 << (_W - 1), 0, 1, 2, 4, 8, 16}
+
var argshlVU = []argVU{
// test cases for shlVU
{[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0}, 7, 0, 0, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "complete overlap of shlVU"},
{[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0, 0, 0, 0}, 7, 0, 3, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "partial overlap by half of shlVU"},
{[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0, 0, 0, 0, 0, 0, 0}, 7, 0, 6, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "partial overlap by 1 Word of shlVU"},
{[]Word{1, _M, _M, _M, _M, _M, 3 << (_W - 2), 0, 0, 0, 0, 0, 0, 0, 0}, 7, 0, 7, 1, []Word{2, _M - 1, _M, _M, _M, _M, 1<<(_W-1) + 1}, 1, "no overlap of shlVU"},
+ // additional test cases with shift values of 0, 1 and (_W-1)
+ {argshlVUIn, 7, 0, 0, 0, argshlVUr0, 0, "complete overlap of shlVU and shift of 0"},
+ {argshlVUIn, 7, 0, 0, 1, argshlVUr1, 0, "complete overlap of shlVU and shift of 1"},
+ {argshlVUIn, 7, 0, 0, _W - 1, argshlVUrWm1, 32, "complete overlap of shlVU and shift of _W - 1"},
+ {argshlVUIn, 7, 0, 1, 0, argshlVUr0, 0, "partial overlap by 6 Words of shlVU and shift of 0"},
+ {argshlVUIn, 7, 0, 1, 1, argshlVUr1, 0, "partial overlap by 6 Words of shlVU and shift of 1"},
+ {argshlVUIn, 7, 0, 1, _W - 1, argshlVUrWm1, 32, "partial overlap by 6 Words of shlVU and shift of _W - 1"},
+ {argshlVUIn, 7, 0, 2, 0, argshlVUr0, 0, "partial overlap by 5 Words of shlVU and shift of 0"},
+ {argshlVUIn, 7, 0, 2, 1, argshlVUr1, 0, "partial overlap by 5 Words of shlVU and shift of 1"},
+ {argshlVUIn, 7, 0, 2, _W - 1, argshlVUrWm1, 32, "partial overlap by 5 Words of shlVU abd shift of _W - 1"},
+ {argshlVUIn, 7, 0, 3, 0, argshlVUr0, 0, "partial overlap by 4 Words of shlVU and shift of 0"},
+ {argshlVUIn, 7, 0, 3, 1, argshlVUr1, 0, "partial overlap by 4 Words of shlVU and shift of 1"},
+ {argshlVUIn, 7, 0, 3, _W - 1, argshlVUrWm1, 32, "partial overlap by 4 Words of shlVU and shift of _W - 1"},
}
+var argshrVUIn = []Word{0, 0, 0, 1, 2, 4, 8, 16, 32, 64}
+var argshrVUr0 = []Word{1, 2, 4, 8, 16, 32, 64}
+var argshrVUr1 = []Word{0, 1, 2, 4, 8, 16, 32}
+var argshrVUrWm1 = []Word{4, 8, 16, 32, 64, 128, 0}
+
var argshrVU = []argVU{
// test cases for shrVU
{[]Word{0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 1, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "complete overlap of shrVU"},
{[]Word{0, 0, 0, 0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 4, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "partial overlap by half of shrVU"},
{[]Word{0, 0, 0, 0, 0, 0, 0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 7, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "partial overlap by 1 Word of shrVU"},
{[]Word{0, 0, 0, 0, 0, 0, 0, 0, 3, _M, _M, _M, _M, _M, 1 << (_W - 1)}, 7, 8, 1, 1, []Word{1<<(_W-1) + 1, _M, _M, _M, _M, _M >> 1, 1 << (_W - 2)}, 1 << (_W - 1), "no overlap of shrVU"},
+ // additional test cases with shift values of 0, 1 and (_W-1)
+ {argshrVUIn, 7, 3, 3, 0, argshrVUr0, 0, "complete overlap of shrVU and shift of 0"},
+ {argshrVUIn, 7, 3, 3, 1, argshrVUr1, 1 << (_W - 1), "complete overlap of shrVU and shift of 1"},
+ {argshrVUIn, 7, 3, 3, _W - 1, argshrVUrWm1, 2, "complete overlap of shrVU and shift of _W - 1"},
+ {argshrVUIn, 7, 3, 2, 0, argshrVUr0, 0, "partial overlap by 6 Words of shrVU and shift of 0"},
+ {argshrVUIn, 7, 3, 2, 1, argshrVUr1, 1 << (_W - 1), "partial overlap by 6 Words of shrVU and shift of 1"},
+ {argshrVUIn, 7, 3, 2, _W - 1, argshrVUrWm1, 2, "partial overlap by 6 Words of shrVU and shift of _W - 1"},
+ {argshrVUIn, 7, 3, 1, 0, argshrVUr0, 0, "partial overlap by 5 Words of shrVU and shift of 0"},
+ {argshrVUIn, 7, 3, 1, 1, argshrVUr1, 1 << (_W - 1), "partial overlap by 5 Words of shrVU and shift of 1"},
+ {argshrVUIn, 7, 3, 1, _W - 1, argshrVUrWm1, 2, "partial overlap by 5 Words of shrVU and shift of _W - 1"},
+ {argshrVUIn, 7, 3, 0, 0, argshrVUr0, 0, "partial overlap by 4 Words of shrVU and shift of 0"},
+ {argshrVUIn, 7, 3, 0, 1, argshrVUr1, 1 << (_W - 1), "partial overlap by 4 Words of shrVU and shift of 1"},
+ {argshrVUIn, 7, 3, 0, _W - 1, argshrVUrWm1, 2, "partial overlap by 4 Words of shrVU and shift of _W - 1"},
}
func testShiftFunc(t *testing.T, f func(z, x []Word, s uint) Word, a argVU) {
@@ -334,11 +371,24 @@ func TestIssue31084(t *testing.T) {
// compute 10^n via 5^n << n.
const n = 165
p := nat(nil).expNN(nat{5}, nat{n}, nil)
- p = p.shl(p, uint(n))
+ p = p.shl(p, n)
got := string(p.utoa(10))
want := "1" + strings.Repeat("0", n)
if got != want {
- t.Errorf("shl(%v, %v)\n\tgot %s; want %s\n", p, uint(n), got, want)
+ t.Errorf("shl(%v, %v)\n\tgot %s\n\twant %s", p, n, got, want)
+ }
+}
+
+const issue42838Value = "159309191113245227702888039776771180559110455519261878607388585338616290151305816094308987472018268594098344692611135542392730712890625"
+
+func TestIssue42838(t *testing.T) {
+ const s = 192
+ z, _, _, _ := nat(nil).scan(strings.NewReader(issue42838Value), 0, false)
+ z = z.shl(z, s)
+ got := string(z.utoa(10))
+ want := "1" + strings.Repeat("0", s)
+ if got != want {
+ t.Errorf("shl(%v, %v)\n\tgot %s\n\twant %s", z, s, got, want)
}
}
@@ -493,7 +543,6 @@ func TestFunVWW(t *testing.T) {
if a.y != 0 && a.r < a.y {
arg := argWVW{a.x, a.c, a.z, a.y, a.r}
- testFunWVW(t, "divWVW_g", divWVW_g, arg)
testFunWVW(t, "divWVW", divWVW, arg)
}
}
@@ -536,6 +585,42 @@ func TestMulAddWWW(t *testing.T) {
}
}
+var divWWTests = []struct {
+ x1, x0, y Word
+ q, r Word
+}{
+ {_M >> 1, 0, _M, _M >> 1, _M >> 1},
+ {_M - (1 << (_W - 2)), _M, 3 << (_W - 2), _M, _M - (1 << (_W - 2))},
+}
+
+const testsNumber = 1 << 16
+
+func TestDivWW(t *testing.T) {
+ i := 0
+ for i, test := range divWWTests {
+ rec := reciprocalWord(test.y)
+ q, r := divWW(test.x1, test.x0, test.y, rec)
+ if q != test.q || r != test.r {
+ t.Errorf("#%d got (%x, %x) want (%x, %x)", i, q, r, test.q, test.r)
+ }
+ }
+ //random tests
+ for ; i < testsNumber; i++ {
+ x1 := rndW()
+ x0 := rndW()
+ y := rndW()
+ if x1 >= y {
+ continue
+ }
+ rec := reciprocalWord(y)
+ qGot, rGot := divWW(x1, x0, y, rec)
+ qWant, rWant := bits.Div(uint(x1), uint(x0), uint(y))
+ if uint(qGot) != qWant || uint(rGot) != rWant {
+ t.Errorf("#%d got (%x, %x) want (%x, %x)", i, qGot, rGot, qWant, rWant)
+ }
+ }
+}
+
func BenchmarkMulAddVWW(b *testing.B) {
for _, n := range benchSizes {
if isRaceBuilder && n > 1e3 {
@@ -570,3 +655,19 @@ func BenchmarkAddMulVVW(b *testing.B) {
})
}
}
+func BenchmarkDivWVW(b *testing.B) {
+ for _, n := range benchSizes {
+ if isRaceBuilder && n > 1e3 {
+ continue
+ }
+ x := rndV(n)
+ y := rndW()
+ z := make([]Word, n)
+ b.Run(fmt.Sprint(n), func(b *testing.B) {
+ b.SetBytes(int64(n * _W))
+ for i := 0; i < b.N; i++ {
+ divWVW(z, 0, x, y)
+ }
+ })
+ }
+}
diff --git a/src/math/big/arith_wasm.s b/src/math/big/arith_wasm.s
index 382597c694..add1064469 100644
--- a/src/math/big/arith_wasm.s
+++ b/src/math/big/arith_wasm.s
@@ -9,9 +9,6 @@
TEXT ·mulWW(SB),NOSPLIT,$0
JMP ·mulWW_g(SB)
-TEXT ·divWW(SB),NOSPLIT,$0
- JMP ·divWW_g(SB)
-
TEXT ·addVV(SB),NOSPLIT,$0
JMP ·addVV_g(SB)
@@ -36,5 +33,3 @@ TEXT ·mulAddVWW(SB),NOSPLIT,$0
TEXT ·addMulVVW(SB),NOSPLIT,$0
JMP ·addMulVVW_g(SB)
-TEXT ·divWVW(SB),NOSPLIT,$0
- JMP ·divWVW_g(SB)
diff --git a/src/math/big/decimal.go b/src/math/big/decimal.go
index ae9ffb5db6..716f03bfa4 100644
--- a/src/math/big/decimal.go
+++ b/src/math/big/decimal.go
@@ -166,18 +166,21 @@ func (x *decimal) String() string {
switch {
case x.exp <= 0:
// 0.00ddd
+ buf = make([]byte, 0, 2+(-x.exp)+len(x.mant))
buf = append(buf, "0."...)
buf = appendZeros(buf, -x.exp)
buf = append(buf, x.mant...)
case /* 0 < */ x.exp < len(x.mant):
// dd.ddd
+ buf = make([]byte, 0, 1+len(x.mant))
buf = append(buf, x.mant[:x.exp]...)
buf = append(buf, '.')
buf = append(buf, x.mant[x.exp:]...)
default: // len(x.mant) <= x.exp
// ddd00
+ buf = make([]byte, 0, x.exp)
buf = append(buf, x.mant...)
buf = appendZeros(buf, x.exp-len(x.mant))
}
diff --git a/src/math/big/link_test.go b/src/math/big/link_test.go
index 2212bd444f..42f9cefca0 100644
--- a/src/math/big/link_test.go
+++ b/src/math/big/link_test.go
@@ -7,7 +7,7 @@ package big
import (
"bytes"
"internal/testenv"
- "io/ioutil"
+ "os"
"os/exec"
"path/filepath"
"testing"
@@ -27,7 +27,7 @@ func TestLinkerGC(t *testing.T) {
import _ "math/big"
func main() {}
`)
- if err := ioutil.WriteFile(goFile, file, 0644); err != nil {
+ if err := os.WriteFile(goFile, file, 0644); err != nil {
t.Fatal(err)
}
cmd := exec.Command(goBin, "build", "-o", "x.exe", "x.go")
diff --git a/src/math/big/nat.go b/src/math/big/nat.go
index 6a3989bf9d..068176e1c1 100644
--- a/src/math/big/nat.go
+++ b/src/math/big/nat.go
@@ -751,6 +751,7 @@ func (q nat) divBasic(u, v nat) {
// D2.
vn1 := v[n-1]
+ rec := reciprocalWord(vn1)
for j := m; j >= 0; j-- {
// D3.
qhat := Word(_M)
@@ -760,7 +761,7 @@ func (q nat) divBasic(u, v nat) {
}
if ujn != vn1 {
var rhat Word
- qhat, rhat = divWW(ujn, u[j+n-1], vn1)
+ qhat, rhat = divWW(ujn, u[j+n-1], vn1, rec)
// x1 | x2 = q̂v_{n-2}
vn2 := v[n-2]
@@ -928,7 +929,7 @@ func (z nat) divRecursiveStep(u, v nat, depth int, tmp *nat, temps []*nat) {
// Now u < (v<<B), compute lower bits in the same way.
// Choose shift = B-1 again.
- s := B
+ s := B - 1
qhat := *temps[depth]
qhat.clear()
qhat.divRecursiveStep(u[s:].norm(), v[s:], depth+1, tmp, temps)
diff --git a/src/math/bits/make_examples.go b/src/math/bits/make_examples.go
index cd81cd6c4d..1d3ad53fe6 100644
--- a/src/math/bits/make_examples.go
+++ b/src/math/bits/make_examples.go
@@ -11,9 +11,9 @@ package main
import (
"bytes"
"fmt"
- "io/ioutil"
"log"
"math/bits"
+ "os"
)
const header = `// Copyright 2017 The Go Authors. All rights reserved.
@@ -106,7 +106,7 @@ func main() {
}
}
- if err := ioutil.WriteFile("example_test.go", w.Bytes(), 0666); err != nil {
+ if err := os.WriteFile("example_test.go", w.Bytes(), 0666); err != nil {
log.Fatal(err)
}
}
diff --git a/src/math/bits/make_tables.go b/src/math/bits/make_tables.go
index ff2fe2e385..b068d5e0e3 100644
--- a/src/math/bits/make_tables.go
+++ b/src/math/bits/make_tables.go
@@ -13,8 +13,8 @@ import (
"fmt"
"go/format"
"io"
- "io/ioutil"
"log"
+ "os"
)
var header = []byte(`// Copyright 2017 The Go Authors. All rights reserved.
@@ -40,7 +40,7 @@ func main() {
log.Fatal(err)
}
- err = ioutil.WriteFile("bits_tables.go", out, 0666)
+ err = os.WriteFile("bits_tables.go", out, 0666)
if err != nil {
log.Fatal(err)
}
generated by cgit v1.3 (git 2.53.0) at 2026-04-15 19:43:55 +0000