Everyone, say hello to a real floating point emulator!

The fpemul written for Linux by W. Metzenthen: ported to NetBSD and
then to FreeBSD, and now back to OpenBSD.

1 files changed, 499 insertions, 0 deletions

diff --git a/sys/gnu/arch/i386/fpemul/wm_sqrt.s b/sys/gnu/arch/i386/fpemul/wm_sqrt.s
new file mode 100644
index 00000000000..849a11ff465
--- /dev/null
+++ b/sys/gnu/arch/i386/fpemul/wm_sqrt.s
@@ -0,0 +1,499 @@
+	.file	"wm_sqrt.S"
+/*	$OpenBSD: wm_sqrt.s,v 1.1 1996/08/27 10:33:04 downsj Exp $	*/
+/*
+ *  wm_sqrt.S
+ *
+ * Fixed point arithmetic square root evaluation.
+ *
+ * Call from C as:
+ *   void wm_sqrt(FPU_REG *n, unsigned int control_word)
+ *
+ *
+ * Copyright (C) 1992,1993,1994
+ *                       W. Metzenthen, 22 Parker St, Ormond, Vic 3163,
+ *                       Australia.  E-mail   billm@vaxc.cc.monash.edu.au
+ * All rights reserved.
+ *
+ * This copyright notice covers the redistribution and use of the
+ * FPU emulator developed by W. Metzenthen. It covers only its use
+ * in the 386BSD, FreeBSD and NetBSD operating systems. Any other
+ * use is not permitted under this copyright.
+ *
+ * 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 include information specifying
+ *    that source code for the emulator is freely available and include
+ *    either:
+ *      a) an offer to provide the source code for a nominal distribution
+ *         fee, or
+ *      b) list at least two alternative methods whereby the source
+ *         can be obtained, e.g. a publically accessible bulletin board
+ *         and an anonymous ftp site from which the software can be
+ *         downloaded.
+ * 3. All advertising materials specifically mentioning features or use of
+ *    this emulator must acknowledge that it was developed by W. Metzenthen.
+ * 4. The name of W. Metzenthen may not be used to endorse or promote
+ *    products derived from this software without specific prior written
+ *    permission.
+ *
+ * THIS SOFTWARE IS PROVIDED ``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
+ * W. METZENTHEN 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.
+ *
+ *
+ * The purpose of this copyright, based upon the Berkeley copyright, is to
+ * ensure that the covered software remains freely available to everyone.
+ *
+ * The software (with necessary differences) is also available, but under
+ * the terms of the GNU copyleft, for the Linux operating system and for
+ * the djgpp ms-dos extender.
+ *
+ * W. Metzenthen   June 1994.
+ *
+ *
+ *     $FreeBSD: wm_sqrt.s,v 1.3 1994/06/10 07:45:04 rich Exp $
+ *
+ */
+
+
+/*---------------------------------------------------------------------------+
+ |  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 <machine/asm.h>
+
+#include <gnu/arch/i386/fpemul/exception.h>
+#include <gnu/arch/i386/fpemul/fpu_asm.h>
+
+
+.data
+/*
+	Local storage:
+ */
+	.align 4,0
+accum_3:
+	.long	0		/* ms word */
+accum_2:
+	.long	0
+accum_1:
+	.long	0
+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 */
+fsqrt_arg_2:
+	.long	0		/* ms word */
+fsqrt_arg_1:
+	.long	0
+fsqrt_arg_0:
+	.long	0		/* ls word, at most the ms bit is set */
+
+.text
+	.align 2,144
+
+.globl _wm_sqrt
+
+_wm_sqrt:
+	pushl	%ebp
+	movl	%esp,%ebp
+	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.. */
+
+	cmpl	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,fsqrt_arg_2		/* ms word of n */
+	movl	%ecx,fsqrt_arg_1
+	movl	%edx,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	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	fsqrt_arg_1,%ecx
+	subl	%ecx,%eax
+	movl	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,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,accum_1
+
+	movl	%esi,%eax
+	mull	%esi
+	movl	%edx,accum_3
+	movl	%eax,accum_2
+
+	movl	%edi,%eax
+	mull	%esi
+	addl	%eax,accum_1
+	adcl	%edx,accum_2
+	adcl	$0,accum_3
+
+/*	movl	%esi,%eax*/
+/*	mull	%edi*/
+	addl	%eax,accum_1
+	adcl	%edx,accum_2
+	adcl	$0,accum_3
+
+/* guess^2 now in accum_3:accum_2:accum_1*/
+
+	movl	fsqrt_arg_0,%eax		/* get normalized n*/
+	subl	%eax,accum_1
+	movl	fsqrt_arg_1,%eax
+	sbbl	%eax,accum_2
+	movl	fsqrt_arg_2,%eax		/* ms word of normalized n*/
+	sbbl	%eax,accum_3
+	jnc	sqrt_stage_3_positive
+
+/* subtraction gives a negative result*/
+/* negate the result before division */
+	notl	accum_1
+	notl	accum_2
+	notl	accum_3
+	addl	$1,accum_1
+	adcl	$0,accum_2
+
+#ifdef PARANOID
+	adcl	$0,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	accum_2,%edx
+	movl	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	accum_2,%edx
+	movl	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
+	movl	EXP_BIAS,EXP(%edi)	/* Result is in  [1.0 .. 2.0)*/
+	movl	PARAM2,%ecx
+	jmp	FPU_round_sqrt
+
+
+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