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Diffstat (limited to 'arch/parisc/lib/milli/div_const.S')
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diff --git a/arch/parisc/lib/milli/div_const.S b/arch/parisc/lib/milli/div_const.S new file mode 100644 index 000000000000..dd660076e944 --- /dev/null +++ b/arch/parisc/lib/milli/div_const.S @@ -0,0 +1,682 @@ +/* 32 and 64-bit millicode, original author Hewlett-Packard + adapted for gcc by Paul Bame <bame@debian.org> + and Alan Modra <alan@linuxcare.com.au>. + + Copyright 2001, 2002, 2003 Free Software Foundation, Inc. + + This file is part of GCC and is released under the terms of + of the GNU General Public License as published by the Free Software + Foundation; either version 2, or (at your option) any later version. + See the file COPYING in the top-level GCC source directory for a copy + of the license. */ + +#include "milli.h" + +#ifdef L_div_const +/* ROUTINE: $$divI_2 + . $$divI_3 $$divU_3 + . $$divI_4 + . $$divI_5 $$divU_5 + . $$divI_6 $$divU_6 + . $$divI_7 $$divU_7 + . $$divI_8 + . $$divI_9 $$divU_9 + . $$divI_10 $$divU_10 + . + . $$divI_12 $$divU_12 + . + . $$divI_14 $$divU_14 + . $$divI_15 $$divU_15 + . $$divI_16 + . $$divI_17 $$divU_17 + . + . Divide by selected constants for single precision binary integers. + + INPUT REGISTERS: + . arg0 == dividend + . mrp == return pc + . sr0 == return space when called externally + + OUTPUT REGISTERS: + . arg0 = undefined + . arg1 = undefined + . ret1 = quotient + + OTHER REGISTERS AFFECTED: + . r1 = undefined + + SIDE EFFECTS: + . Causes a trap under the following conditions: NONE + . Changes memory at the following places: NONE + + PERMISSIBLE CONTEXT: + . Unwindable. + . Does not create a stack frame. + . Suitable for internal or external millicode. + . Assumes the special millicode register conventions. + + DISCUSSION: + . Calls other millicode routines using mrp: NONE + . Calls other millicode routines: NONE */ + + +/* TRUNCATED DIVISION BY SMALL INTEGERS + + We are interested in q(x) = floor(x/y), where x >= 0 and y > 0 + (with y fixed). + + Let a = floor(z/y), for some choice of z. Note that z will be + chosen so that division by z is cheap. + + Let r be the remainder(z/y). In other words, r = z - ay. + + Now, our method is to choose a value for b such that + + q'(x) = floor((ax+b)/z) + + is equal to q(x) over as large a range of x as possible. If the + two are equal over a sufficiently large range, and if it is easy to + form the product (ax), and it is easy to divide by z, then we can + perform the division much faster than the general division algorithm. + + So, we want the following to be true: + + . For x in the following range: + . + . ky <= x < (k+1)y + . + . implies that + . + . k <= (ax+b)/z < (k+1) + + We want to determine b such that this is true for all k in the + range {0..K} for some maximum K. + + Since (ax+b) is an increasing function of x, we can take each + bound separately to determine the "best" value for b. + + (ax+b)/z < (k+1) implies + + (a((k+1)y-1)+b < (k+1)z implies + + b < a + (k+1)(z-ay) implies + + b < a + (k+1)r + + This needs to be true for all k in the range {0..K}. In + particular, it is true for k = 0 and this leads to a maximum + acceptable value for b. + + b < a+r or b <= a+r-1 + + Taking the other bound, we have + + k <= (ax+b)/z implies + + k <= (aky+b)/z implies + + k(z-ay) <= b implies + + kr <= b + + Clearly, the largest range for k will be achieved by maximizing b, + when r is not zero. When r is zero, then the simplest choice for b + is 0. When r is not 0, set + + . b = a+r-1 + + Now, by construction, q'(x) = floor((ax+b)/z) = q(x) = floor(x/y) + for all x in the range: + + . 0 <= x < (K+1)y + + We need to determine what K is. Of our two bounds, + + . b < a+(k+1)r is satisfied for all k >= 0, by construction. + + The other bound is + + . kr <= b + + This is always true if r = 0. If r is not 0 (the usual case), then + K = floor((a+r-1)/r), is the maximum value for k. + + Therefore, the formula q'(x) = floor((ax+b)/z) yields the correct + answer for q(x) = floor(x/y) when x is in the range + + (0,(K+1)y-1) K = floor((a+r-1)/r) + + To be most useful, we want (K+1)y-1 = (max x) >= 2**32-1 so that + the formula for q'(x) yields the correct value of q(x) for all x + representable by a single word in HPPA. + + We are also constrained in that computing the product (ax), adding + b, and dividing by z must all be done quickly, otherwise we will be + better off going through the general algorithm using the DS + instruction, which uses approximately 70 cycles. + + For each y, there is a choice of z which satisfies the constraints + for (K+1)y >= 2**32. We may not, however, be able to satisfy the + timing constraints for arbitrary y. It seems that z being equal to + a power of 2 or a power of 2 minus 1 is as good as we can do, since + it minimizes the time to do division by z. We want the choice of z + to also result in a value for (a) that minimizes the computation of + the product (ax). This is best achieved if (a) has a regular bit + pattern (so the multiplication can be done with shifts and adds). + The value of (a) also needs to be less than 2**32 so the product is + always guaranteed to fit in 2 words. + + In actual practice, the following should be done: + + 1) For negative x, you should take the absolute value and remember + . the fact so that the result can be negated. This obviously does + . not apply in the unsigned case. + 2) For even y, you should factor out the power of 2 that divides y + . and divide x by it. You can then proceed by dividing by the + . odd factor of y. + + Here is a table of some odd values of y, and corresponding choices + for z which are "good". + + y z r a (hex) max x (hex) + + 3 2**32 1 55555555 100000001 + 5 2**32 1 33333333 100000003 + 7 2**24-1 0 249249 (infinite) + 9 2**24-1 0 1c71c7 (infinite) + 11 2**20-1 0 1745d (infinite) + 13 2**24-1 0 13b13b (infinite) + 15 2**32 1 11111111 10000000d + 17 2**32 1 f0f0f0f 10000000f + + If r is 1, then b = a+r-1 = a. This simplifies the computation + of (ax+b), since you can compute (x+1)(a) instead. If r is 0, + then b = 0 is ok to use which simplifies (ax+b). + + The bit patterns for 55555555, 33333333, and 11111111 are obviously + very regular. The bit patterns for the other values of a above are: + + y (hex) (binary) + + 7 249249 001001001001001001001001 << regular >> + 9 1c71c7 000111000111000111000111 << regular >> + 11 1745d 000000010111010001011101 << irregular >> + 13 13b13b 000100111011000100111011 << irregular >> + + The bit patterns for (a) corresponding to (y) of 11 and 13 may be + too irregular to warrant using this method. + + When z is a power of 2 minus 1, then the division by z is slightly + more complicated, involving an iterative solution. + + The code presented here solves division by 1 through 17, except for + 11 and 13. There are algorithms for both signed and unsigned + quantities given. + + TIMINGS (cycles) + + divisor positive negative unsigned + + . 1 2 2 2 + . 2 4 4 2 + . 3 19 21 19 + . 4 4 4 2 + . 5 18 22 19 + . 6 19 22 19 + . 8 4 4 2 + . 10 18 19 17 + . 12 18 20 18 + . 15 16 18 16 + . 16 4 4 2 + . 17 16 18 16 + + Now, the algorithm for 7, 9, and 14 is an iterative one. That is, + a loop body is executed until the tentative quotient is 0. The + number of times the loop body is executed varies depending on the + dividend, but is never more than two times. If the dividend is + less than the divisor, then the loop body is not executed at all. + Each iteration adds 4 cycles to the timings. + + divisor positive negative unsigned + + . 7 19+4n 20+4n 20+4n n = number of iterations + . 9 21+4n 22+4n 21+4n + . 14 21+4n 22+4n 20+4n + + To give an idea of how the number of iterations varies, here is a + table of dividend versus number of iterations when dividing by 7. + + smallest largest required + dividend dividend iterations + + . 0 6 0 + . 7 0x6ffffff 1 + 0x1000006 0xffffffff 2 + + There is some overlap in the range of numbers requiring 1 and 2 + iterations. */ + +RDEFINE(t2,r1) +RDEFINE(x2,arg0) /* r26 */ +RDEFINE(t1,arg1) /* r25 */ +RDEFINE(x1,ret1) /* r29 */ + + SUBSPA_MILLI_DIV + ATTR_MILLI + + .proc + .callinfo millicode + .entry +/* NONE of these routines require a stack frame + ALL of these routines are unwindable from millicode */ + +GSYM($$divide_by_constant) + .export $$divide_by_constant,millicode +/* Provides a "nice" label for the code covered by the unwind descriptor + for things like gprof. */ + +/* DIVISION BY 2 (shift by 1) */ +GSYM($$divI_2) + .export $$divI_2,millicode + comclr,>= arg0,0,0 + addi 1,arg0,arg0 + MILLIRET + extrs arg0,30,31,ret1 + + +/* DIVISION BY 4 (shift by 2) */ +GSYM($$divI_4) + .export $$divI_4,millicode + comclr,>= arg0,0,0 + addi 3,arg0,arg0 + MILLIRET + extrs arg0,29,30,ret1 + + +/* DIVISION BY 8 (shift by 3) */ +GSYM($$divI_8) + .export $$divI_8,millicode + comclr,>= arg0,0,0 + addi 7,arg0,arg0 + MILLIRET + extrs arg0,28,29,ret1 + +/* DIVISION BY 16 (shift by 4) */ +GSYM($$divI_16) + .export $$divI_16,millicode + comclr,>= arg0,0,0 + addi 15,arg0,arg0 + MILLIRET + extrs arg0,27,28,ret1 + +/**************************************************************************** +* +* DIVISION BY DIVISORS OF FFFFFFFF, and powers of 2 times these +* +* includes 3,5,15,17 and also 6,10,12 +* +****************************************************************************/ + +/* DIVISION BY 3 (use z = 2**32; a = 55555555) */ + +GSYM($$divI_3) + .export $$divI_3,millicode + comb,<,N x2,0,LREF(neg3) + + addi 1,x2,x2 /* this cannot overflow */ + extru x2,1,2,x1 /* multiply by 5 to get started */ + sh2add x2,x2,x2 + b LREF(pos) + addc x1,0,x1 + +LSYM(neg3) + subi 1,x2,x2 /* this cannot overflow */ + extru x2,1,2,x1 /* multiply by 5 to get started */ + sh2add x2,x2,x2 + b LREF(neg) + addc x1,0,x1 + +GSYM($$divU_3) + .export $$divU_3,millicode + addi 1,x2,x2 /* this CAN overflow */ + addc 0,0,x1 + shd x1,x2,30,t1 /* multiply by 5 to get started */ + sh2add x2,x2,x2 + b LREF(pos) + addc x1,t1,x1 + +/* DIVISION BY 5 (use z = 2**32; a = 33333333) */ + +GSYM($$divI_5) + .export $$divI_5,millicode + comb,<,N x2,0,LREF(neg5) + + addi 3,x2,t1 /* this cannot overflow */ + sh1add x2,t1,x2 /* multiply by 3 to get started */ + b LREF(pos) + addc 0,0,x1 + +LSYM(neg5) + sub 0,x2,x2 /* negate x2 */ + addi 1,x2,x2 /* this cannot overflow */ + shd 0,x2,31,x1 /* get top bit (can be 1) */ + sh1add x2,x2,x2 /* multiply by 3 to get started */ + b LREF(neg) + addc x1,0,x1 + +GSYM($$divU_5) + .export $$divU_5,millicode + addi 1,x2,x2 /* this CAN overflow */ + addc 0,0,x1 + shd x1,x2,31,t1 /* multiply by 3 to get started */ + sh1add x2,x2,x2 + b LREF(pos) + addc t1,x1,x1 + +/* DIVISION BY 6 (shift to divide by 2 then divide by 3) */ +GSYM($$divI_6) + .export $$divI_6,millicode + comb,<,N x2,0,LREF(neg6) + extru x2,30,31,x2 /* divide by 2 */ + addi 5,x2,t1 /* compute 5*(x2+1) = 5*x2+5 */ + sh2add x2,t1,x2 /* multiply by 5 to get started */ + b LREF(pos) + addc 0,0,x1 + +LSYM(neg6) + subi 2,x2,x2 /* negate, divide by 2, and add 1 */ + /* negation and adding 1 are done */ + /* at the same time by the SUBI */ + extru x2,30,31,x2 + shd 0,x2,30,x1 + sh2add x2,x2,x2 /* multiply by 5 to get started */ + b LREF(neg) + addc x1,0,x1 + +GSYM($$divU_6) + .export $$divU_6,millicode + extru x2,30,31,x2 /* divide by 2 */ + addi 1,x2,x2 /* cannot carry */ + shd 0,x2,30,x1 /* multiply by 5 to get started */ + sh2add x2,x2,x2 + b LREF(pos) + addc x1,0,x1 + +/* DIVISION BY 10 (shift to divide by 2 then divide by 5) */ +GSYM($$divU_10) + .export $$divU_10,millicode + extru x2,30,31,x2 /* divide by 2 */ + addi 3,x2,t1 /* compute 3*(x2+1) = (3*x2)+3 */ + sh1add x2,t1,x2 /* multiply by 3 to get started */ + addc 0,0,x1 +LSYM(pos) + shd x1,x2,28,t1 /* multiply by 0x11 */ + shd x2,0,28,t2 + add x2,t2,x2 + addc x1,t1,x1 +LSYM(pos_for_17) + shd x1,x2,24,t1 /* multiply by 0x101 */ + shd x2,0,24,t2 + add x2,t2,x2 + addc x1,t1,x1 + + shd x1,x2,16,t1 /* multiply by 0x10001 */ + shd x2,0,16,t2 + add x2,t2,x2 + MILLIRET + addc x1,t1,x1 + +GSYM($$divI_10) + .export $$divI_10,millicode + comb,< x2,0,LREF(neg10) + copy 0,x1 + extru x2,30,31,x2 /* divide by 2 */ + addib,TR 1,x2,LREF(pos) /* add 1 (cannot overflow) */ + sh1add x2,x2,x2 /* multiply by 3 to get started */ + +LSYM(neg10) + subi 2,x2,x2 /* negate, divide by 2, and add 1 */ + /* negation and adding 1 are done */ + /* at the same time by the SUBI */ + extru x2,30,31,x2 + sh1add x2,x2,x2 /* multiply by 3 to get started */ +LSYM(neg) + shd x1,x2,28,t1 /* multiply by 0x11 */ + shd x2,0,28,t2 + add x2,t2,x2 + addc x1,t1,x1 +LSYM(neg_for_17) + shd x1,x2,24,t1 /* multiply by 0x101 */ + shd x2,0,24,t2 + add x2,t2,x2 + addc x1,t1,x1 + + shd x1,x2,16,t1 /* multiply by 0x10001 */ + shd x2,0,16,t2 + add x2,t2,x2 + addc x1,t1,x1 + MILLIRET + sub 0,x1,x1 + +/* DIVISION BY 12 (shift to divide by 4 then divide by 3) */ +GSYM($$divI_12) + .export $$divI_12,millicode + comb,< x2,0,LREF(neg12) + copy 0,x1 + extru x2,29,30,x2 /* divide by 4 */ + addib,tr 1,x2,LREF(pos) /* compute 5*(x2+1) = 5*x2+5 */ + sh2add x2,x2,x2 /* multiply by 5 to get started */ + +LSYM(neg12) + subi 4,x2,x2 /* negate, divide by 4, and add 1 */ + /* negation and adding 1 are done */ + /* at the same time by the SUBI */ + extru x2,29,30,x2 + b LREF(neg) + sh2add x2,x2,x2 /* multiply by 5 to get started */ + +GSYM($$divU_12) + .export $$divU_12,millicode + extru x2,29,30,x2 /* divide by 4 */ + addi 5,x2,t1 /* cannot carry */ + sh2add x2,t1,x2 /* multiply by 5 to get started */ + b LREF(pos) + addc 0,0,x1 + +/* DIVISION BY 15 (use z = 2**32; a = 11111111) */ +GSYM($$divI_15) + .export $$divI_15,millicode + comb,< x2,0,LREF(neg15) + copy 0,x1 + addib,tr 1,x2,LREF(pos)+4 + shd x1,x2,28,t1 + +LSYM(neg15) + b LREF(neg) + subi 1,x2,x2 + +GSYM($$divU_15) + .export $$divU_15,millicode + addi 1,x2,x2 /* this CAN overflow */ + b LREF(pos) + addc 0,0,x1 + +/* DIVISION BY 17 (use z = 2**32; a = f0f0f0f) */ +GSYM($$divI_17) + .export $$divI_17,millicode + comb,<,n x2,0,LREF(neg17) + addi 1,x2,x2 /* this cannot overflow */ + shd 0,x2,28,t1 /* multiply by 0xf to get started */ + shd x2,0,28,t2 + sub t2,x2,x2 + b LREF(pos_for_17) + subb t1,0,x1 + +LSYM(neg17) + subi 1,x2,x2 /* this cannot overflow */ + shd 0,x2,28,t1 /* multiply by 0xf to get started */ + shd x2,0,28,t2 + sub t2,x2,x2 + b LREF(neg_for_17) + subb t1,0,x1 + +GSYM($$divU_17) + .export $$divU_17,millicode + addi 1,x2,x2 /* this CAN overflow */ + addc 0,0,x1 + shd x1,x2,28,t1 /* multiply by 0xf to get started */ +LSYM(u17) + shd x2,0,28,t2 + sub t2,x2,x2 + b LREF(pos_for_17) + subb t1,x1,x1 + + +/* DIVISION BY DIVISORS OF FFFFFF, and powers of 2 times these + includes 7,9 and also 14 + + + z = 2**24-1 + r = z mod x = 0 + + so choose b = 0 + + Also, in order to divide by z = 2**24-1, we approximate by dividing + by (z+1) = 2**24 (which is easy), and then correcting. + + (ax) = (z+1)q' + r + . = zq' + (q'+r) + + So to compute (ax)/z, compute q' = (ax)/(z+1) and r = (ax) mod (z+1) + Then the true remainder of (ax)/z is (q'+r). Repeat the process + with this new remainder, adding the tentative quotients together, + until a tentative quotient is 0 (and then we are done). There is + one last correction to be done. It is possible that (q'+r) = z. + If so, then (q'+r)/(z+1) = 0 and it looks like we are done. But, + in fact, we need to add 1 more to the quotient. Now, it turns + out that this happens if and only if the original value x is + an exact multiple of y. So, to avoid a three instruction test at + the end, instead use 1 instruction to add 1 to x at the beginning. */ + +/* DIVISION BY 7 (use z = 2**24-1; a = 249249) */ +GSYM($$divI_7) + .export $$divI_7,millicode + comb,<,n x2,0,LREF(neg7) +LSYM(7) + addi 1,x2,x2 /* cannot overflow */ + shd 0,x2,29,x1 + sh3add x2,x2,x2 + addc x1,0,x1 +LSYM(pos7) + shd x1,x2,26,t1 + shd x2,0,26,t2 + add x2,t2,x2 + addc x1,t1,x1 + + shd x1,x2,20,t1 + shd x2,0,20,t2 + add x2,t2,x2 + addc x1,t1,t1 + + /* computed <t1,x2>. Now divide it by (2**24 - 1) */ + + copy 0,x1 + shd,= t1,x2,24,t1 /* tentative quotient */ +LSYM(1) + addb,tr t1,x1,LREF(2) /* add to previous quotient */ + extru x2,31,24,x2 /* new remainder (unadjusted) */ + + MILLIRETN + +LSYM(2) + addb,tr t1,x2,LREF(1) /* adjust remainder */ + extru,= x2,7,8,t1 /* new quotient */ + +LSYM(neg7) + subi 1,x2,x2 /* negate x2 and add 1 */ +LSYM(8) + shd 0,x2,29,x1 + sh3add x2,x2,x2 + addc x1,0,x1 + +LSYM(neg7_shift) + shd x1,x2,26,t1 + shd x2,0,26,t2 + add x2,t2,x2 + addc x1,t1,x1 + + shd x1,x2,20,t1 + shd x2,0,20,t2 + add x2,t2,x2 + addc x1,t1,t1 + + /* computed <t1,x2>. Now divide it by (2**24 - 1) */ + + copy 0,x1 + shd,= t1,x2,24,t1 /* tentative quotient */ +LSYM(3) + addb,tr t1,x1,LREF(4) /* add to previous quotient */ + extru x2,31,24,x2 /* new remainder (unadjusted) */ + + MILLIRET + sub 0,x1,x1 /* negate result */ + +LSYM(4) + addb,tr t1,x2,LREF(3) /* adjust remainder */ + extru,= x2,7,8,t1 /* new quotient */ + +GSYM($$divU_7) + .export $$divU_7,millicode + addi 1,x2,x2 /* can carry */ + addc 0,0,x1 + shd x1,x2,29,t1 + sh3add x2,x2,x2 + b LREF(pos7) + addc t1,x1,x1 + +/* DIVISION BY 9 (use z = 2**24-1; a = 1c71c7) */ +GSYM($$divI_9) + .export $$divI_9,millicode + comb,<,n x2,0,LREF(neg9) + addi 1,x2,x2 /* cannot overflow */ + shd 0,x2,29,t1 + shd x2,0,29,t2 + sub t2,x2,x2 + b LREF(pos7) + subb t1,0,x1 + +LSYM(neg9) + subi 1,x2,x2 /* negate and add 1 */ + shd 0,x2,29,t1 + shd x2,0,29,t2 + sub t2,x2,x2 + b LREF(neg7_shift) + subb t1,0,x1 + +GSYM($$divU_9) + .export $$divU_9,millicode + addi 1,x2,x2 /* can carry */ + addc 0,0,x1 + shd x1,x2,29,t1 + shd x2,0,29,t2 + sub t2,x2,x2 + b LREF(pos7) + subb t1,x1,x1 + +/* DIVISION BY 14 (shift to divide by 2 then divide by 7) */ +GSYM($$divI_14) + .export $$divI_14,millicode + comb,<,n x2,0,LREF(neg14) +GSYM($$divU_14) + .export $$divU_14,millicode + b LREF(7) /* go to 7 case */ + extru x2,30,31,x2 /* divide by 2 */ + +LSYM(neg14) + subi 2,x2,x2 /* negate (and add 2) */ + b LREF(8) + extru x2,30,31,x2 /* divide by 2 */ + .exit + .procend + .end +#endif |