Import libkern arm specific bits.
This commit is contained in:
Olivier Houchard
parent
59315819d5
commit
03f110294b
Notes:
svn2git
2020-12-20 02:59:44 +00:00
svn path=/head/; revision=129210
387
sys/libkern/arm/divsi3.S
Normal file
387
sys/libkern/arm/divsi3.S
Normal file
@ -0,0 +1,387 @@
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/* $NetBSD: divsi3.S,v 1.4 2003/04/05 23:27:15 bjh21 Exp $ */
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/*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#include <machine/asm.h>
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__FBSDID("$FreeBSD$");
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/*
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* stack is aligned as there's a possibility of branching to L_overflow
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* which makes a C call
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*/
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ENTRY(__umodsi3)
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stmfd sp!, {lr}
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sub sp, sp, #4 /* align stack */
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bl .L_udivide
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add sp, sp, #4 /* unalign stack */
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mov r0, r1
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ldmfd sp!, {pc}
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ENTRY(__modsi3)
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stmfd sp!, {lr}
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sub sp, sp, #4 /* align stack */
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bl .L_divide
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add sp, sp, #4 /* unalign stack */
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mov r0, r1
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ldmfd sp!, {pc}
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.L_overflow:
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#if !defined(_KERNEL) && !defined(_STANDALONE)
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mov r0, #8 /* SIGFPE */
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bl PIC_SYM(_C_LABEL(raise), PLT) /* raise it */
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mov r0, #0
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#else
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/* XXX should cause a fatal error */
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mvn r0, #0
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#endif
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mov pc, lr
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ENTRY(__udivsi3)
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.L_udivide: /* r0 = r0 / r1; r1 = r0 % r1 */
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eor r0, r1, r0
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eor r1, r0, r1
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eor r0, r1, r0
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/* r0 = r1 / r0; r1 = r1 % r0 */
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cmp r0, #1
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bcc .L_overflow
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beq .L_divide_l0
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mov ip, #0
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movs r1, r1
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bpl .L_divide_l1
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orr ip, ip, #0x20000000 /* ip bit 0x20000000 = -ve r1 */
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movs r1, r1, lsr #1
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orrcs ip, ip, #0x10000000 /* ip bit 0x10000000 = bit 0 of r1 */
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b .L_divide_l1
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.L_divide_l0: /* r0 == 1 */
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mov r0, r1
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mov r1, #0
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mov pc, lr
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ENTRY(__divsi3)
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.L_divide: /* r0 = r0 / r1; r1 = r0 % r1 */
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eor r0, r1, r0
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eor r1, r0, r1
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eor r0, r1, r0
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/* r0 = r1 / r0; r1 = r1 % r0 */
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cmp r0, #1
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bcc .L_overflow
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beq .L_divide_l0
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ands ip, r0, #0x80000000
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rsbmi r0, r0, #0
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ands r2, r1, #0x80000000
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eor ip, ip, r2
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rsbmi r1, r1, #0
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orr ip, r2, ip, lsr #1 /* ip bit 0x40000000 = -ve division */
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/* ip bit 0x80000000 = -ve remainder */
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.L_divide_l1:
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mov r2, #1
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mov r3, #0
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/*
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* If the highest bit of the dividend is set, we have to be
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* careful when shifting the divisor. Test this.
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*/
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movs r1,r1
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bpl .L_old_code
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/*
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* At this point, the highest bit of r1 is known to be set.
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* We abuse this below in the tst instructions.
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*/
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tst r1, r0 /*, lsl #0 */
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bmi .L_divide_b1
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tst r1, r0, lsl #1
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bmi .L_divide_b2
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tst r1, r0, lsl #2
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bmi .L_divide_b3
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tst r1, r0, lsl #3
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bmi .L_divide_b4
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tst r1, r0, lsl #4
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bmi .L_divide_b5
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tst r1, r0, lsl #5
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bmi .L_divide_b6
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tst r1, r0, lsl #6
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bmi .L_divide_b7
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tst r1, r0, lsl #7
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bmi .L_divide_b8
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tst r1, r0, lsl #8
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bmi .L_divide_b9
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tst r1, r0, lsl #9
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bmi .L_divide_b10
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tst r1, r0, lsl #10
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bmi .L_divide_b11
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tst r1, r0, lsl #11
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bmi .L_divide_b12
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tst r1, r0, lsl #12
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bmi .L_divide_b13
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tst r1, r0, lsl #13
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bmi .L_divide_b14
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tst r1, r0, lsl #14
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bmi .L_divide_b15
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tst r1, r0, lsl #15
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bmi .L_divide_b16
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tst r1, r0, lsl #16
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bmi .L_divide_b17
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tst r1, r0, lsl #17
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bmi .L_divide_b18
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tst r1, r0, lsl #18
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bmi .L_divide_b19
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tst r1, r0, lsl #19
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bmi .L_divide_b20
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tst r1, r0, lsl #20
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bmi .L_divide_b21
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tst r1, r0, lsl #21
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bmi .L_divide_b22
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tst r1, r0, lsl #22
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bmi .L_divide_b23
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tst r1, r0, lsl #23
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bmi .L_divide_b24
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tst r1, r0, lsl #24
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bmi .L_divide_b25
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tst r1, r0, lsl #25
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bmi .L_divide_b26
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tst r1, r0, lsl #26
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bmi .L_divide_b27
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tst r1, r0, lsl #27
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bmi .L_divide_b28
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tst r1, r0, lsl #28
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bmi .L_divide_b29
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tst r1, r0, lsl #29
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bmi .L_divide_b30
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tst r1, r0, lsl #30
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bmi .L_divide_b31
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/*
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* instead of:
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* tst r1, r0, lsl #31
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* bmi .L_divide_b32
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*/
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b .L_divide_b32
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.L_old_code:
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cmp r1, r0
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bcc .L_divide_b0
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cmp r1, r0, lsl #1
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bcc .L_divide_b1
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cmp r1, r0, lsl #2
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bcc .L_divide_b2
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cmp r1, r0, lsl #3
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bcc .L_divide_b3
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cmp r1, r0, lsl #4
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bcc .L_divide_b4
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cmp r1, r0, lsl #5
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bcc .L_divide_b5
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cmp r1, r0, lsl #6
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bcc .L_divide_b6
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cmp r1, r0, lsl #7
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bcc .L_divide_b7
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cmp r1, r0, lsl #8
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bcc .L_divide_b8
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cmp r1, r0, lsl #9
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bcc .L_divide_b9
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cmp r1, r0, lsl #10
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bcc .L_divide_b10
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cmp r1, r0, lsl #11
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bcc .L_divide_b11
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cmp r1, r0, lsl #12
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bcc .L_divide_b12
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cmp r1, r0, lsl #13
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bcc .L_divide_b13
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cmp r1, r0, lsl #14
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bcc .L_divide_b14
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cmp r1, r0, lsl #15
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bcc .L_divide_b15
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cmp r1, r0, lsl #16
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bcc .L_divide_b16
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cmp r1, r0, lsl #17
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bcc .L_divide_b17
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cmp r1, r0, lsl #18
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bcc .L_divide_b18
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cmp r1, r0, lsl #19
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bcc .L_divide_b19
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cmp r1, r0, lsl #20
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bcc .L_divide_b20
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cmp r1, r0, lsl #21
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bcc .L_divide_b21
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cmp r1, r0, lsl #22
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bcc .L_divide_b22
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cmp r1, r0, lsl #23
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bcc .L_divide_b23
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cmp r1, r0, lsl #24
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bcc .L_divide_b24
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cmp r1, r0, lsl #25
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bcc .L_divide_b25
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cmp r1, r0, lsl #26
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bcc .L_divide_b26
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cmp r1, r0, lsl #27
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bcc .L_divide_b27
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cmp r1, r0, lsl #28
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bcc .L_divide_b28
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cmp r1, r0, lsl #29
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bcc .L_divide_b29
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cmp r1, r0, lsl #30
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bcc .L_divide_b30
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.L_divide_b32:
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cmp r1, r0, lsl #31
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subhs r1, r1,r0, lsl #31
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addhs r3, r3,r2, lsl #31
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.L_divide_b31:
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cmp r1, r0, lsl #30
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subhs r1, r1,r0, lsl #30
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addhs r3, r3,r2, lsl #30
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.L_divide_b30:
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cmp r1, r0, lsl #29
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subhs r1, r1,r0, lsl #29
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addhs r3, r3,r2, lsl #29
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.L_divide_b29:
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cmp r1, r0, lsl #28
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subhs r1, r1,r0, lsl #28
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addhs r3, r3,r2, lsl #28
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.L_divide_b28:
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cmp r1, r0, lsl #27
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subhs r1, r1,r0, lsl #27
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addhs r3, r3,r2, lsl #27
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.L_divide_b27:
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cmp r1, r0, lsl #26
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subhs r1, r1,r0, lsl #26
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addhs r3, r3,r2, lsl #26
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.L_divide_b26:
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cmp r1, r0, lsl #25
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subhs r1, r1,r0, lsl #25
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addhs r3, r3,r2, lsl #25
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.L_divide_b25:
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cmp r1, r0, lsl #24
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subhs r1, r1,r0, lsl #24
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addhs r3, r3,r2, lsl #24
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.L_divide_b24:
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cmp r1, r0, lsl #23
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subhs r1, r1,r0, lsl #23
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addhs r3, r3,r2, lsl #23
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.L_divide_b23:
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cmp r1, r0, lsl #22
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subhs r1, r1,r0, lsl #22
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addhs r3, r3,r2, lsl #22
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.L_divide_b22:
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cmp r1, r0, lsl #21
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subhs r1, r1,r0, lsl #21
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addhs r3, r3,r2, lsl #21
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.L_divide_b21:
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cmp r1, r0, lsl #20
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subhs r1, r1,r0, lsl #20
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addhs r3, r3,r2, lsl #20
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.L_divide_b20:
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cmp r1, r0, lsl #19
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subhs r1, r1,r0, lsl #19
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addhs r3, r3,r2, lsl #19
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.L_divide_b19:
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cmp r1, r0, lsl #18
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subhs r1, r1,r0, lsl #18
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addhs r3, r3,r2, lsl #18
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.L_divide_b18:
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cmp r1, r0, lsl #17
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subhs r1, r1,r0, lsl #17
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addhs r3, r3,r2, lsl #17
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.L_divide_b17:
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cmp r1, r0, lsl #16
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subhs r1, r1,r0, lsl #16
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addhs r3, r3,r2, lsl #16
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.L_divide_b16:
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cmp r1, r0, lsl #15
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subhs r1, r1,r0, lsl #15
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addhs r3, r3,r2, lsl #15
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.L_divide_b15:
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cmp r1, r0, lsl #14
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subhs r1, r1,r0, lsl #14
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addhs r3, r3,r2, lsl #14
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.L_divide_b14:
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cmp r1, r0, lsl #13
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subhs r1, r1,r0, lsl #13
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addhs r3, r3,r2, lsl #13
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.L_divide_b13:
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cmp r1, r0, lsl #12
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subhs r1, r1,r0, lsl #12
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addhs r3, r3,r2, lsl #12
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.L_divide_b12:
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cmp r1, r0, lsl #11
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subhs r1, r1,r0, lsl #11
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addhs r3, r3,r2, lsl #11
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.L_divide_b11:
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cmp r1, r0, lsl #10
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subhs r1, r1,r0, lsl #10
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addhs r3, r3,r2, lsl #10
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.L_divide_b10:
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cmp r1, r0, lsl #9
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subhs r1, r1,r0, lsl #9
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addhs r3, r3,r2, lsl #9
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.L_divide_b9:
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cmp r1, r0, lsl #8
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subhs r1, r1,r0, lsl #8
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addhs r3, r3,r2, lsl #8
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.L_divide_b8:
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cmp r1, r0, lsl #7
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subhs r1, r1,r0, lsl #7
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addhs r3, r3,r2, lsl #7
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.L_divide_b7:
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cmp r1, r0, lsl #6
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subhs r1, r1,r0, lsl #6
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addhs r3, r3,r2, lsl #6
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.L_divide_b6:
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cmp r1, r0, lsl #5
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subhs r1, r1,r0, lsl #5
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addhs r3, r3,r2, lsl #5
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.L_divide_b5:
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cmp r1, r0, lsl #4
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subhs r1, r1,r0, lsl #4
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addhs r3, r3,r2, lsl #4
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.L_divide_b4:
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cmp r1, r0, lsl #3
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subhs r1, r1,r0, lsl #3
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addhs r3, r3,r2, lsl #3
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.L_divide_b3:
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cmp r1, r0, lsl #2
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subhs r1, r1,r0, lsl #2
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addhs r3, r3,r2, lsl #2
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.L_divide_b2:
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cmp r1, r0, lsl #1
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subhs r1, r1,r0, lsl #1
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addhs r3, r3,r2, lsl #1
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.L_divide_b1:
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cmp r1, r0
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subhs r1, r1, r0
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addhs r3, r3, r2
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.L_divide_b0:
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tst ip, #0x20000000
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bne .L_udivide_l1
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mov r0, r3
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cmp ip, #0
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rsbmi r1, r1, #0
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movs ip, ip, lsl #1
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bicmi r0, r0, #0x80000000 /* Fix incase we divided 0x80000000 */
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rsbmi r0, r0, #0
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mov pc, lr
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.L_udivide_l1:
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tst ip, #0x10000000
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mov r1, r1, lsl #1
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orrne r1, r1, #1
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mov r3, r3, lsl #1
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cmp r1, r0
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subhs r1, r1, r0
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addhs r3, r3, r2
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mov r0, r3
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mov pc, lr
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77
sys/libkern/arm/ffs.S
Normal file
77
sys/libkern/arm/ffs.S
Normal file
@ -0,0 +1,77 @@
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/* $NetBSD: ffs.S,v 1.3 2003/04/05 23:27:15 bjh21 Exp $ */
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/*
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* Copyright (c) 2001 Christopher Gilbert
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
* 3. The name of the company nor the name of the author may be used to
|
||||
* endorse or promote products derived from this software without specific
|
||||
* prior written permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
|
||||
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
|
||||
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
|
||||
* IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
|
||||
* INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
|
||||
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
|
||||
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <machine/asm.h>
|
||||
__FBSDID("$FreeBSD$");
|
||||
|
||||
|
||||
/*
|
||||
* ffs - find first set bit, this algorithm isolates the first set
|
||||
* bit, then multiplies the number by 0x0450fbaf which leaves the top
|
||||
* 6 bits as an index into the table. This algorithm should be a win
|
||||
* over the checking each bit in turn as per the C compiled version.
|
||||
*
|
||||
* under ARMv5 there's an instruction called CLZ (count leading Zero's) that
|
||||
* could be used
|
||||
*
|
||||
* This is the ffs algorithm devised by d.seal and posted to comp.sys.arm on
|
||||
* 16 Feb 1994.
|
||||
*/
|
||||
|
||||
ENTRY(ffs)
|
||||
/* Standard trick to isolate bottom bit in r0 or 0 if r0 = 0 on entry */
|
||||
rsb r1, r0, #0
|
||||
ands r0, r0, r1
|
||||
/*
|
||||
* now r0 has at most one set bit, call this X
|
||||
* if X = 0, all further instructions are skipped
|
||||
*/
|
||||
adrne r2, .L_ffs_table
|
||||
orrne r0, r0, r0, lsl #4 /* r0 = X * 0x11 */
|
||||
orrne r0, r0, r0, lsl #6 /* r0 = X * 0x451 */
|
||||
rsbne r0, r0, r0, lsl #16 /* r0 = X * 0x0450fbaf */
|
||||
|
||||
/* now lookup in table indexed on top 6 bits of r0 */
|
||||
ldrneb r0, [ r2, r0, lsr #26 ]
|
||||
|
||||
mov pc, lr
|
||||
.text;
|
||||
.type .L_ffs_table, _ASM_TYPE_OBJECT;
|
||||
.L_ffs_table:
|
||||
/* 0 1 2 3 4 5 6 7 */
|
||||
.byte 0, 1, 2, 13, 3, 7, 0, 14 /* 0- 7 */
|
||||
.byte 4, 0, 8, 0, 0, 0, 0, 15 /* 8-15 */
|
||||
.byte 11, 5, 0, 0, 9, 0, 0, 26 /* 16-23 */
|
||||
.byte 0, 0, 0, 0, 0, 22, 28, 16 /* 24-31 */
|
||||
.byte 32, 12, 6, 0, 0, 0, 0, 0 /* 32-39 */
|
||||
.byte 10, 0, 0, 25, 0, 0, 21, 27 /* 40-47 */
|
||||
.byte 31, 0, 0, 0, 0, 24, 0, 20 /* 48-55 */
|
||||
.byte 30, 0, 23, 19, 29, 18, 17, 0 /* 56-63 */
|
||||
|
||||
249
sys/libkern/arm/muldi3.c
Normal file
249
sys/libkern/arm/muldi3.c
Normal file
@ -0,0 +1,249 @@
|
||||
/* $NetBSD: muldi3.c,v 1.8 2003/08/07 16:32:09 agc Exp $ */
|
||||
|
||||
/*-
|
||||
* Copyright (c) 1992, 1993
|
||||
* The Regents of the University of California. All rights reserved.
|
||||
*
|
||||
* This software was developed by the Computer Systems Engineering group
|
||||
* at Lawrence Berkeley Laboratory under DARPA contract BG 91-66 and
|
||||
* contributed to Berkeley.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions
|
||||
* are met:
|
||||
* 1. Redistributions of source code must retain the above copyright
|
||||
* notice, this list of conditions and the following disclaimer.
|
||||
* 2. Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
* 3. Neither the name of the University nor the names of its contributors
|
||||
* may be used to endorse or promote products derived from this software
|
||||
* without specific prior written permission.
|
||||
*
|
||||
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
|
||||
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
|
||||
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
|
||||
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
|
||||
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
||||
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
|
||||
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
|
||||
* SUCH DAMAGE.
|
||||
*/
|
||||
|
||||
#include <sys/cdefs.h>
|
||||
#if defined(LIBC_SCCS) && !defined(lint)
|
||||
#if 0
|
||||
static char sccsid[] = "@(#)muldi3.c 8.1 (Berkeley) 6/4/93";
|
||||
#else
|
||||
__FBSDID("$FreeBSD$");
|
||||
#endif
|
||||
#endif /* LIBC_SCCS and not lint */
|
||||
|
||||
#include <libkern/quad.h>
|
||||
|
||||
/*
|
||||
* Multiply two quads.
|
||||
*
|
||||
* Our algorithm is based on the following. Split incoming quad values
|
||||
* u and v (where u,v >= 0) into
|
||||
*
|
||||
* u = 2^n u1 * u0 (n = number of bits in `u_int', usu. 32)
|
||||
*
|
||||
* and
|
||||
*
|
||||
* v = 2^n v1 * v0
|
||||
*
|
||||
* Then
|
||||
*
|
||||
* uv = 2^2n u1 v1 + 2^n u1 v0 + 2^n v1 u0 + u0 v0
|
||||
* = 2^2n u1 v1 + 2^n (u1 v0 + v1 u0) + u0 v0
|
||||
*
|
||||
* Now add 2^n u1 v1 to the first term and subtract it from the middle,
|
||||
* and add 2^n u0 v0 to the last term and subtract it from the middle.
|
||||
* This gives:
|
||||
*
|
||||
* uv = (2^2n + 2^n) (u1 v1) +
|
||||
* (2^n) (u1 v0 - u1 v1 + u0 v1 - u0 v0) +
|
||||
* (2^n + 1) (u0 v0)
|
||||
*
|
||||
* Factoring the middle a bit gives us:
|
||||
*
|
||||
* uv = (2^2n + 2^n) (u1 v1) + [u1v1 = high]
|
||||
* (2^n) (u1 - u0) (v0 - v1) + [(u1-u0)... = mid]
|
||||
* (2^n + 1) (u0 v0) [u0v0 = low]
|
||||
*
|
||||
* The terms (u1 v1), (u1 - u0) (v0 - v1), and (u0 v0) can all be done
|
||||
* in just half the precision of the original. (Note that either or both
|
||||
* of (u1 - u0) or (v0 - v1) may be negative.)
|
||||
*
|
||||
* This algorithm is from Knuth vol. 2 (2nd ed), section 4.3.3, p. 278.
|
||||
*
|
||||
* Since C does not give us a `int * int = quad' operator, we split
|
||||
* our input quads into two ints, then split the two ints into two
|
||||
* shorts. We can then calculate `short * short = int' in native
|
||||
* arithmetic.
|
||||
*
|
||||
* Our product should, strictly speaking, be a `long quad', with 128
|
||||
* bits, but we are going to discard the upper 64. In other words,
|
||||
* we are not interested in uv, but rather in (uv mod 2^2n). This
|
||||
* makes some of the terms above vanish, and we get:
|
||||
*
|
||||
* (2^n)(high) + (2^n)(mid) + (2^n + 1)(low)
|
||||
*
|
||||
* or
|
||||
*
|
||||
* (2^n)(high + mid + low) + low
|
||||
*
|
||||
* Furthermore, `high' and `mid' can be computed mod 2^n, as any factor
|
||||
* of 2^n in either one will also vanish. Only `low' need be computed
|
||||
* mod 2^2n, and only because of the final term above.
|
||||
*/
|
||||
static quad_t __lmulq(u_int, u_int);
|
||||
|
||||
quad_t __muldi3(quad_t, quad_t);
|
||||
quad_t
|
||||
__muldi3(quad_t a, quad_t b)
|
||||
{
|
||||
union uu u, v, low, prod;
|
||||
u_int high, mid, udiff, vdiff;
|
||||
int negall, negmid;
|
||||
#define u1 u.ul[H]
|
||||
#define u0 u.ul[L]
|
||||
#define v1 v.ul[H]
|
||||
#define v0 v.ul[L]
|
||||
|
||||
/*
|
||||
* Get u and v such that u, v >= 0. When this is finished,
|
||||
* u1, u0, v1, and v0 will be directly accessible through the
|
||||
* int fields.
|
||||
*/
|
||||
if (a >= 0)
|
||||
u.q = a, negall = 0;
|
||||
else
|
||||
u.q = -a, negall = 1;
|
||||
if (b >= 0)
|
||||
v.q = b;
|
||||
else
|
||||
v.q = -b, negall ^= 1;
|
||||
|
||||
if (u1 == 0 && v1 == 0) {
|
||||
/*
|
||||
* An (I hope) important optimization occurs when u1 and v1
|
||||
* are both 0. This should be common since most numbers
|
||||
* are small. Here the product is just u0*v0.
|
||||
*/
|
||||
prod.q = __lmulq(u0, v0);
|
||||
} else {
|
||||
/*
|
||||
* Compute the three intermediate products, remembering
|
||||
* whether the middle term is negative. We can discard
|
||||
* any upper bits in high and mid, so we can use native
|
||||
* u_int * u_int => u_int arithmetic.
|
||||
*/
|
||||
low.q = __lmulq(u0, v0);
|
||||
|
||||
if (u1 >= u0)
|
||||
negmid = 0, udiff = u1 - u0;
|
||||
else
|
||||
negmid = 1, udiff = u0 - u1;
|
||||
if (v0 >= v1)
|
||||
vdiff = v0 - v1;
|
||||
else
|
||||
vdiff = v1 - v0, negmid ^= 1;
|
||||
mid = udiff * vdiff;
|
||||
|
||||
high = u1 * v1;
|
||||
|
||||
/*
|
||||
* Assemble the final product.
|
||||
*/
|
||||
prod.ul[H] = high + (negmid ? -mid : mid) + low.ul[L] +
|
||||
low.ul[H];
|
||||
prod.ul[L] = low.ul[L];
|
||||
}
|
||||
return (negall ? -prod.q : prod.q);
|
||||
#undef u1
|
||||
#undef u0
|
||||
#undef v1
|
||||
#undef v0
|
||||
}
|
||||
|
||||
/*
|
||||
* Multiply two 2N-bit ints to produce a 4N-bit quad, where N is half
|
||||
* the number of bits in an int (whatever that is---the code below
|
||||
* does not care as long as quad.h does its part of the bargain---but
|
||||
* typically N==16).
|
||||
*
|
||||
* We use the same algorithm from Knuth, but this time the modulo refinement
|
||||
* does not apply. On the other hand, since N is half the size of an int,
|
||||
* we can get away with native multiplication---none of our input terms
|
||||
* exceeds (UINT_MAX >> 1).
|
||||
*
|
||||
* Note that, for u_int l, the quad-precision result
|
||||
*
|
||||
* l << N
|
||||
*
|
||||
* splits into high and low ints as HHALF(l) and LHUP(l) respectively.
|
||||
*/
|
||||
static quad_t
|
||||
__lmulq(u_int u, u_int v)
|
||||
{
|
||||
u_int u1, u0, v1, v0, udiff, vdiff, high, mid, low;
|
||||
u_int prodh, prodl, was;
|
||||
union uu prod;
|
||||
int neg;
|
||||
|
||||
u1 = HHALF(u);
|
||||
u0 = LHALF(u);
|
||||
v1 = HHALF(v);
|
||||
v0 = LHALF(v);
|
||||
|
||||
low = u0 * v0;
|
||||
|
||||
/* This is the same small-number optimization as before. */
|
||||
if (u1 == 0 && v1 == 0)
|
||||
return (low);
|
||||
|
||||
if (u1 >= u0)
|
||||
udiff = u1 - u0, neg = 0;
|
||||
else
|
||||
udiff = u0 - u1, neg = 1;
|
||||
if (v0 >= v1)
|
||||
vdiff = v0 - v1;
|
||||
else
|
||||
vdiff = v1 - v0, neg ^= 1;
|
||||
mid = udiff * vdiff;
|
||||
|
||||
high = u1 * v1;
|
||||
|
||||
/* prod = (high << 2N) + (high << N); */
|
||||
prodh = high + HHALF(high);
|
||||
prodl = LHUP(high);
|
||||
|
||||
/* if (neg) prod -= mid << N; else prod += mid << N; */
|
||||
if (neg) {
|
||||
was = prodl;
|
||||
prodl -= LHUP(mid);
|
||||
prodh -= HHALF(mid) + (prodl > was);
|
||||
} else {
|
||||
was = prodl;
|
||||
prodl += LHUP(mid);
|
||||
prodh += HHALF(mid) + (prodl < was);
|
||||
}
|
||||
|
||||
/* prod += low << N */
|
||||
was = prodl;
|
||||
prodl += LHUP(low);
|
||||
prodh += HHALF(low) + (prodl < was);
|
||||
/* ... + low; */
|
||||
if ((prodl += low) < low)
|
||||
prodh++;
|
||||
|
||||
/* return 4N-bit product */
|
||||
prod.ul[H] = prodh;
|
||||
prod.ul[L] = prodl;
|
||||
return (prod.q);
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user