Home | History | Annotate | Line # | Download | only in i387
s_log1pf.S revision 1.8 
      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  1.8  wennmach RCSID("$NetBSD: s_log1pf.S,v 1.8 2003/09/10 16:45:43 wennmach 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  1.8  wennmach  *
     41  1.1       jtc  */
     42  1.2       jtc 
     43  1.8  wennmach .section	.rodata
     44  1.8  wennmach 	.align 8
     45  1.8  wennmach BOUND:
     46  1.8  wennmach 	.long 0x0,0x3fd00000		/* (double)0.25 */
     47  1.8  wennmach 
     48  1.8  wennmach .text
     49  1.8  wennmach 	.align 4
     50  1.1       jtc ENTRY(log1pf)
     51  1.6      fvdl 	XMM_ONE_ARG_FLOAT_PROLOGUE
     52  1.8  wennmach 	flds	ARG_FLOAT_ONE
     53  1.8  wennmach 	fabs
     54  1.8  wennmach 	fldl	BOUND
     55  1.8  wennmach 	fcompp
     56  1.8  wennmach 	fnstsw %ax
     57  1.8  wennmach 	andb $69,%ah
     58  1.8  wennmach 	jne .l1
     59  1.8  wennmach 	jmp .l2
     60  1.8  wennmach 	.align 4
     61  1.8  wennmach .l1:
     62  1.8  wennmach 	fldln2
     63  1.8  wennmach         flds	ARG_FLOAT_ONE
     64  1.8  wennmach         fld1
     65  1.8  wennmach         faddp
     66  1.8  wennmach         fyl2x
     67  1.8  wennmach 	XMM_FLOAT_EPILOGUE
     68  1.8  wennmach         ret
     69  1.8  wennmach 	.align 4
     70  1.8  wennmach .l2:
     71  1.1       jtc 	fldln2
     72  1.6      fvdl 	flds	ARG_FLOAT_ONE
     73  1.8  wennmach 	fyl2xp1
     74  1.6      fvdl 	XMM_FLOAT_EPILOGUE
     75  1.1       jtc 	ret
     76