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      1   1.1       jtc /*
      2   1.7      salo  * Written by J.T. Conklin <jtc (at) NetBSD.org>.
      3   1.3       jtc  * Public domain.
      4   1.1       jtc  */
      5   1.1       jtc 
      6   1.8  wennmach /*
      7   1.8  wennmach  * Modified by Lex Wennmacher <wennmach (at) NetBSD.org>
      8   1.8  wennmach  * Still public domain.
      9   1.8  wennmach  */
     10   1.8  wennmach 
     11   1.1       jtc #include <machine/asm.h>
     12   1.1       jtc 
     13   1.6      fvdl #include "abi.h"
     14   1.6      fvdl 
     15  1.11  riastrad RCSID("$NetBSD: s_log1pf.S,v 1.11 2024/07/16 14:52:49 riastradh Exp $")
     16   1.1       jtc 
     17   1.1       jtc /*
     18   1.8  wennmach  * The log1pf() function is provided to compute an accurate value of
     19   1.8  wennmach  * log(1 + x), even for tiny values of x. The i387 FPU provides the
     20   1.8  wennmach  * fyl2xp1 instruction for this purpose. However, the range of this
     21   1.8  wennmach  * instruction is limited to:
     22   1.8  wennmach  * 		-(1 - (sqrt(2) / 2)) <= x <= sqrt(2) - 1
     23   1.8  wennmach  *                         -0.292893 <= x <= 0.414214
     24   1.8  wennmach  * at least on older processor versions.
     25   1.8  wennmach  *
     26   1.8  wennmach  * log1pf() is implemented by testing the range of the argument.
     27   1.8  wennmach  * If it is appropriate for fyl2xp1, this instruction is used.
     28   1.8  wennmach  * Else, we compute log1pf(x) = ln(2)*ld(1 + x) the traditional way
     29   1.8  wennmach  * (using fyl2x).
     30   1.8  wennmach  *
     31   1.8  wennmach  * The range testing costs speed, but as the rationale for the very
     32   1.8  wennmach  * existence of this function is accuracy, we accept that.
     33   1.8  wennmach  *
     34   1.8  wennmach  * In order to reduce the cost for testing the range, we check if
     35   1.8  wennmach  * the argument is in the range
     36   1.8  wennmach  *                             -0.25 <= x <= 0.25
     37   1.8  wennmach  * which can be done with just one conditional branch. If x is
     38   1.8  wennmach  * inside this range, we use fyl2xp1. Outside of this range,
     39   1.8  wennmach  * the use of fyl2x is accurate enough.
     40   1.1       jtc  */
     41   1.2       jtc 
     42  1.11  riastrad WEAK_ALIAS(log1pf, _log1pf)
     43  1.11  riastrad 
     44   1.8  wennmach .text
     45  1.10  wennmach 	.align	4
     46  1.11  riastrad ENTRY(_log1pf)
     47   1.6      fvdl 	XMM_ONE_ARG_FLOAT_PROLOGUE
     48   1.8  wennmach 	flds	ARG_FLOAT_ONE
     49   1.8  wennmach 	fabs
     50  1.10  wennmach 	fld1				/* ... x 1 */
     51  1.10  wennmach 	fadd	%st(0)			/* ... x 2 */
     52  1.10  wennmach 	fadd	%st(0)			/* ... x 4 */
     53  1.10  wennmach 	fld1				/* ... 4 1 */
     54  1.10  wennmach 	fdivp				/* ... x 0.25 */
     55   1.8  wennmach 	fcompp
     56  1.10  wennmach 	fnstsw	%ax
     57  1.10  wennmach 	andb	$69,%ah
     58  1.10  wennmach 	jne	use_fyl2x
     59  1.10  wennmach 	jmp	use_fyl2xp1
     60  1.10  wennmach 
     61  1.10  wennmach 	.align	4
     62  1.10  wennmach use_fyl2x:
     63   1.8  wennmach 	fldln2
     64   1.8  wennmach         flds	ARG_FLOAT_ONE
     65   1.8  wennmach         fld1
     66   1.8  wennmach         faddp
     67   1.8  wennmach         fyl2x
     68   1.8  wennmach 	XMM_FLOAT_EPILOGUE
     69   1.8  wennmach         ret
     70  1.10  wennmach 
     71  1.10  wennmach 	.align	4
     72  1.10  wennmach use_fyl2xp1:
     73   1.1       jtc 	fldln2
     74   1.6      fvdl 	flds	ARG_FLOAT_ONE
     75   1.8  wennmach 	fyl2xp1
     76   1.6      fvdl 	XMM_FLOAT_EPILOGUE
     77   1.1       jtc 	ret
     78  1.11  riastrad END(_log1pf)
     79