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Diffstat (limited to 'arch/i386/math-emu/wm_sqrt.S')
| -rw-r--r-- | arch/i386/math-emu/wm_sqrt.S | 470 |
1 files changed, 0 insertions, 470 deletions
diff --git a/arch/i386/math-emu/wm_sqrt.S b/arch/i386/math-emu/wm_sqrt.S deleted file mode 100644 index d258f59564e..00000000000 --- a/arch/i386/math-emu/wm_sqrt.S +++ /dev/null @@ -1,470 +0,0 @@ - .file "wm_sqrt.S" -/*---------------------------------------------------------------------------+ - | wm_sqrt.S | - | | - | Fixed point arithmetic square root evaluation. | - | | - | Copyright (C) 1992,1993,1995,1997 | - | W. Metzenthen, 22 Parker St, Ormond, Vic 3163, | - | Australia. E-mail billm@suburbia.net | - | | - | Call from C as: | - | int wm_sqrt(FPU_REG *n, unsigned int control_word) | - | | - +---------------------------------------------------------------------------*/ - -/*---------------------------------------------------------------------------+ - | wm_sqrt(FPU_REG *n, unsigned int control_word) | - | returns the square root of n in n. | - | | - | Use Newton's method to compute the square root of a number, which must | - | be in the range [1.0 .. 4.0), to 64 bits accuracy. | - | Does not check the sign or tag of the argument. | - | Sets the exponent, but not the sign or tag of the result. | - | | - | The guess is kept in %esi:%edi | - +---------------------------------------------------------------------------*/ - -#include "exception.h" -#include "fpu_emu.h" - - -#ifndef NON_REENTRANT_FPU -/* Local storage on the stack: */ -#define FPU_accum_3 -4(%ebp) /* ms word */ -#define FPU_accum_2 -8(%ebp) -#define FPU_accum_1 -12(%ebp) -#define FPU_accum_0 -16(%ebp) - -/* - * The de-normalised argument: - * sq_2 sq_1 sq_0 - * b b b b b b b ... b b b b b b .... b b b b 0 0 0 ... 0 - * ^ binary point here - */ -#define FPU_fsqrt_arg_2 -20(%ebp) /* ms word */ -#define FPU_fsqrt_arg_1 -24(%ebp) -#define FPU_fsqrt_arg_0 -28(%ebp) /* ls word, at most the ms bit is set */ - -#else -/* Local storage in a static area: */ -.data - .align 4,0 -FPU_accum_3: - .long 0 /* ms word */ -FPU_accum_2: - .long 0 -FPU_accum_1: - .long 0 -FPU_accum_0: - .long 0 - -/* The de-normalised argument: - sq_2 sq_1 sq_0 - b b b b b b b ... b b b b b b .... b b b b 0 0 0 ... 0 - ^ binary point here - */ -FPU_fsqrt_arg_2: - .long 0 /* ms word */ -FPU_fsqrt_arg_1: - .long 0 -FPU_fsqrt_arg_0: - .long 0 /* ls word, at most the ms bit is set */ -#endif /* NON_REENTRANT_FPU */ - - -.text -ENTRY(wm_sqrt) - pushl %ebp - movl %esp,%ebp -#ifndef NON_REENTRANT_FPU - subl $28,%esp -#endif /* NON_REENTRANT_FPU */ - pushl %esi - pushl %edi - pushl %ebx - - movl PARAM1,%esi - - movl SIGH(%esi),%eax - movl SIGL(%esi),%ecx - xorl %edx,%edx - -/* We use a rough linear estimate for the first guess.. */ - - cmpw EXP_BIAS,EXP(%esi) - jnz sqrt_arg_ge_2 - - shrl $1,%eax /* arg is in the range [1.0 .. 2.0) */ - rcrl $1,%ecx - rcrl $1,%edx - -sqrt_arg_ge_2: -/* From here on, n is never accessed directly again until it is - replaced by the answer. */ - - movl %eax,FPU_fsqrt_arg_2 /* ms word of n */ - movl %ecx,FPU_fsqrt_arg_1 - movl %edx,FPU_fsqrt_arg_0 - -/* Make a linear first estimate */ - shrl $1,%eax - addl $0x40000000,%eax - movl $0xaaaaaaaa,%ecx - mull %ecx - shll %edx /* max result was 7fff... */ - testl $0x80000000,%edx /* but min was 3fff... */ - jnz sqrt_prelim_no_adjust - - movl $0x80000000,%edx /* round up */ - -sqrt_prelim_no_adjust: - movl %edx,%esi /* Our first guess */ - -/* We have now computed (approx) (2 + x) / 3, which forms the basis - for a few iterations of Newton's method */ - - movl FPU_fsqrt_arg_2,%ecx /* ms word */ - -/* - * From our initial estimate, three iterations are enough to get us - * to 30 bits or so. This will then allow two iterations at better - * precision to complete the process. - */ - -/* Compute (g + n/g)/2 at each iteration (g is the guess). */ - shrl %ecx /* Doing this first will prevent a divide */ - /* overflow later. */ - - movl %ecx,%edx /* msw of the arg / 2 */ - divl %esi /* current estimate */ - shrl %esi /* divide by 2 */ - addl %eax,%esi /* the new estimate */ - - movl %ecx,%edx - divl %esi - shrl %esi - addl %eax,%esi - - movl %ecx,%edx - divl %esi - shrl %esi - addl %eax,%esi - -/* - * Now that an estimate accurate to about 30 bits has been obtained (in %esi), - * we improve it to 60 bits or so. - * - * The strategy from now on is to compute new estimates from - * guess := guess + (n - guess^2) / (2 * guess) - */ - -/* First, find the square of the guess */ - movl %esi,%eax - mull %esi -/* guess^2 now in %edx:%eax */ - - movl FPU_fsqrt_arg_1,%ecx - subl %ecx,%eax - movl FPU_fsqrt_arg_2,%ecx /* ms word of normalized n */ - sbbl %ecx,%edx - jnc sqrt_stage_2_positive - -/* Subtraction gives a negative result, - negate the result before division. */ - notl %edx - notl %eax - addl $1,%eax - adcl $0,%edx - - divl %esi - movl %eax,%ecx - - movl %edx,%eax - divl %esi - jmp sqrt_stage_2_finish - -sqrt_stage_2_positive: - divl %esi - movl %eax,%ecx - - movl %edx,%eax - divl %esi - - notl %ecx - notl %eax - addl $1,%eax - adcl $0,%ecx - -sqrt_stage_2_finish: - sarl $1,%ecx /* divide by 2 */ - rcrl $1,%eax - - /* Form the new estimate in %esi:%edi */ - movl %eax,%edi - addl %ecx,%esi - - jnz sqrt_stage_2_done /* result should be [1..2) */ - -#ifdef PARANOID -/* It should be possible to get here only if the arg is ffff....ffff */ - cmp $0xffffffff,FPU_fsqrt_arg_1 - jnz sqrt_stage_2_error -#endif /* PARANOID */ - -/* The best rounded result. */ - xorl %eax,%eax - decl %eax - movl %eax,%edi - movl %eax,%esi - movl $0x7fffffff,%eax - jmp sqrt_round_result - -#ifdef PARANOID -sqrt_stage_2_error: - pushl EX_INTERNAL|0x213 - call EXCEPTION -#endif /* PARANOID */ - -sqrt_stage_2_done: - -/* Now the square root has been computed to better than 60 bits. */ - -/* Find the square of the guess. */ - movl %edi,%eax /* ls word of guess */ - mull %edi - movl %edx,FPU_accum_1 - - movl %esi,%eax - mull %esi - movl %edx,FPU_accum_3 - movl %eax,FPU_accum_2 - - movl %edi,%eax - mull %esi - addl %eax,FPU_accum_1 - adcl %edx,FPU_accum_2 - adcl $0,FPU_accum_3 - -/* movl %esi,%eax */ -/* mull %edi */ - addl %eax,FPU_accum_1 - adcl %edx,FPU_accum_2 - adcl $0,FPU_accum_3 - -/* guess^2 now in FPU_accum_3:FPU_accum_2:FPU_accum_1 */ - - movl FPU_fsqrt_arg_0,%eax /* get normalized n */ - subl %eax,FPU_accum_1 - movl FPU_fsqrt_arg_1,%eax - sbbl %eax,FPU_accum_2 - movl FPU_fsqrt_arg_2,%eax /* ms word of normalized n */ - sbbl %eax,FPU_accum_3 - jnc sqrt_stage_3_positive - -/* Subtraction gives a negative result, - negate the result before division */ - notl FPU_accum_1 - notl FPU_accum_2 - notl FPU_accum_3 - addl $1,FPU_accum_1 - adcl $0,FPU_accum_2 - -#ifdef PARANOID - adcl $0,FPU_accum_3 /* This must be zero */ - jz sqrt_stage_3_no_error - -sqrt_stage_3_error: - pushl EX_INTERNAL|0x207 - call EXCEPTION - -sqrt_stage_3_no_error: -#endif /* PARANOID */ - - movl FPU_accum_2,%edx - movl FPU_accum_1,%eax - divl %esi - movl %eax,%ecx - - movl %edx,%eax - divl %esi - - sarl $1,%ecx /* divide by 2 */ - rcrl $1,%eax - - /* prepare to round the result */ - - addl %ecx,%edi - adcl $0,%esi - - jmp sqrt_stage_3_finished - -sqrt_stage_3_positive: - movl FPU_accum_2,%edx - movl FPU_accum_1,%eax - divl %esi - movl %eax,%ecx - - movl %edx,%eax - divl %esi - - sarl $1,%ecx /* divide by 2 */ - rcrl $1,%eax - - /* prepare to round the result */ - - notl %eax /* Negate the correction term */ - notl %ecx - addl $1,%eax - adcl $0,%ecx /* carry here ==> correction == 0 */ - adcl $0xffffffff,%esi - - addl %ecx,%edi - adcl $0,%esi - -sqrt_stage_3_finished: - -/* - * The result in %esi:%edi:%esi should be good to about 90 bits here, - * and the rounding information here does not have sufficient accuracy - * in a few rare cases. - */ - cmpl $0xffffffe0,%eax - ja sqrt_near_exact_x - - cmpl $0x00000020,%eax - jb sqrt_near_exact - - cmpl $0x7fffffe0,%eax - jb sqrt_round_result - - cmpl $0x80000020,%eax - jb sqrt_get_more_precision - -sqrt_round_result: -/* Set up for rounding operations */ - movl %eax,%edx - movl %esi,%eax - movl %edi,%ebx - movl PARAM1,%edi - movw EXP_BIAS,EXP(%edi) /* Result is in [1.0 .. 2.0) */ - jmp fpu_reg_round - - -sqrt_near_exact_x: -/* First, the estimate must be rounded up. */ - addl $1,%edi - adcl $0,%esi - -sqrt_near_exact: -/* - * This is an easy case because x^1/2 is monotonic. - * We need just find the square of our estimate, compare it - * with the argument, and deduce whether our estimate is - * above, below, or exact. We use the fact that the estimate - * is known to be accurate to about 90 bits. - */ - movl %edi,%eax /* ls word of guess */ - mull %edi - movl %edx,%ebx /* 2nd ls word of square */ - movl %eax,%ecx /* ls word of square */ - - movl %edi,%eax - mull %esi - addl %eax,%ebx - addl %eax,%ebx - -#ifdef PARANOID - cmp $0xffffffb0,%ebx - jb sqrt_near_exact_ok - - cmp $0x00000050,%ebx - ja sqrt_near_exact_ok - - pushl EX_INTERNAL|0x214 - call EXCEPTION - -sqrt_near_exact_ok: -#endif /* PARANOID */ - - or %ebx,%ebx - js sqrt_near_exact_small - - jnz sqrt_near_exact_large - - or %ebx,%edx - jnz sqrt_near_exact_large - -/* Our estimate is exactly the right answer */ - xorl %eax,%eax - jmp sqrt_round_result - -sqrt_near_exact_small: -/* Our estimate is too small */ - movl $0x000000ff,%eax - jmp sqrt_round_result - -sqrt_near_exact_large: -/* Our estimate is too large, we need to decrement it */ - subl $1,%edi - sbbl $0,%esi - movl $0xffffff00,%eax - jmp sqrt_round_result - - -sqrt_get_more_precision: -/* This case is almost the same as the above, except we start - with an extra bit of precision in the estimate. */ - stc /* The extra bit. */ - rcll $1,%edi /* Shift the estimate left one bit */ - rcll $1,%esi - - movl %edi,%eax /* ls word of guess */ - mull %edi - movl %edx,%ebx /* 2nd ls word of square */ - movl %eax,%ecx /* ls word of square */ - - movl %edi,%eax - mull %esi - addl %eax,%ebx - addl %eax,%ebx - -/* Put our estimate back to its original value */ - stc /* The ms bit. */ - rcrl $1,%esi /* Shift the estimate left one bit */ - rcrl $1,%edi - -#ifdef PARANOID - cmp $0xffffff60,%ebx - jb sqrt_more_prec_ok - - cmp $0x000000a0,%ebx - ja sqrt_more_prec_ok - - pushl EX_INTERNAL|0x215 - call EXCEPTION - -sqrt_more_prec_ok: -#endif /* PARANOID */ - - or %ebx,%ebx - js sqrt_more_prec_small - - jnz sqrt_more_prec_large - - or %ebx,%ecx - jnz sqrt_more_prec_large - -/* Our estimate is exactly the right answer */ - movl $0x80000000,%eax - jmp sqrt_round_result - -sqrt_more_prec_small: -/* Our estimate is too small */ - movl $0x800000ff,%eax - jmp sqrt_round_result - -sqrt_more_prec_large: -/* Our estimate is too large */ - movl $0x7fffff00,%eax - jmp sqrt_round_result |