/* * Written by J.T. Conklin <jtc@NetBSD.org>. * Public domain. */ /* * Modified by Lex Wennmacher <wennmach@NetBSD.org> * Still public domain. */ #include <machine/asm.h> #include "abi.h" RCSID("$NetBSD: s_log1pf.S,v 1.10 2003/09/16 18:17:11 wennmach Exp $") /* * The log1pf() function is provided to compute an accurate value of * log(1 + x), even for tiny values of x. The i387 FPU provides the * fyl2xp1 instruction for this purpose. However, the range of this * instruction is limited to: * -(1 - (sqrt(2) / 2)) <= x <= sqrt(2) - 1 * -0.292893 <= x <= 0.414214 * at least on older processor versions. * * log1pf() is implemented by testing the range of the argument. * If it is appropriate for fyl2xp1, this instruction is used. * Else, we compute log1pf(x) = ln(2)*ld(1 + x) the traditional way * (using fyl2x). * * The range testing costs speed, but as the rationale for the very * existence of this function is accuracy, we accept that. * * In order to reduce the cost for testing the range, we check if * the argument is in the range * -0.25 <= x <= 0.25 * which can be done with just one conditional branch. If x is * inside this range, we use fyl2xp1. Outside of this range, * the use of fyl2x is accurate enough. * */ .text .align 4 ENTRY(log1pf) XMM_ONE_ARG_FLOAT_PROLOGUE flds ARG_FLOAT_ONE fabs fld1 /* ... x 1 */ fadd %st(0) /* ... x 2 */ fadd %st(0) /* ... x 4 */ fld1 /* ... 4 1 */ fdivp /* ... x 0.25 */ fcompp fnstsw %ax andb $69,%ah jne use_fyl2x jmp use_fyl2xp1 .align 4 use_fyl2x: fldln2 flds ARG_FLOAT_ONE fld1 faddp fyl2x XMM_FLOAT_EPILOGUE ret .align 4 use_fyl2xp1: fldln2 flds ARG_FLOAT_ONE fyl2xp1 XMM_FLOAT_EPILOGUE ret |