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https://gitea.nishi.boats/pyrite-dev/milsko
synced 2026-01-10 03:13:28 +00:00
add fdlibm
git-svn-id: http://svn2.nishi.boats/svn/milsko/trunk@557 b9cfdab3-6d41-4d17-bbe4-086880011989
This commit is contained in:
NishiOwO
@@ -34,14 +34,14 @@ static void default_multiply_u8(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
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out->un.u8.h = a->un.u8.h * b->un.u8.h;
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};
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static void default_reciprocal_u8(MwLLVec* a, MwLLVec* out) {
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out->un.u8.a = nbsd_pow(a->un.u8.a, -1);
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out->un.u8.b = nbsd_pow(a->un.u8.b, -1);
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out->un.u8.c = nbsd_pow(a->un.u8.c, -1);
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out->un.u8.d = nbsd_pow(a->un.u8.d, -1);
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out->un.u8.e = nbsd_pow(a->un.u8.e, -1);
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out->un.u8.f = nbsd_pow(a->un.u8.f, -1);
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out->un.u8.g = nbsd_pow(a->un.u8.g, -1);
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out->un.u8.h = nbsd_pow(a->un.u8.h, -1);
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out->un.u8.a = pow(a->un.u8.a, -1);
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out->un.u8.b = pow(a->un.u8.b, -1);
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out->un.u8.c = pow(a->un.u8.c, -1);
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out->un.u8.d = pow(a->un.u8.d, -1);
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out->un.u8.e = pow(a->un.u8.e, -1);
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out->un.u8.f = pow(a->un.u8.f, -1);
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out->un.u8.g = pow(a->un.u8.g, -1);
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out->un.u8.h = pow(a->un.u8.h, -1);
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};
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static void default_squareRoot_u8(MwLLVec* a, MwLLVec* out) {
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out->un.u8.a = sqrt(a->un.u8.a);
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@@ -125,10 +125,10 @@ static void default_multiply_u16(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
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out->un.u16.d = a->un.u16.d * b->un.u16.d;
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}
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static void default_reciprocal_u16(MwLLVec* a, MwLLVec* out) {
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out->un.u16.a = nbsd_pow(a->un.u16.a, -1);
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out->un.u16.b = nbsd_pow(a->un.u16.b, -1);
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out->un.u16.c = nbsd_pow(a->un.u16.c, -1);
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out->un.u16.d = nbsd_pow(a->un.u16.d, -1);
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out->un.u16.a = pow(a->un.u16.a, -1);
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out->un.u16.b = pow(a->un.u16.b, -1);
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out->un.u16.c = pow(a->un.u16.c, -1);
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out->un.u16.d = pow(a->un.u16.d, -1);
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};
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static void default_squareRoot_u16(MwLLVec* a, MwLLVec* out) {
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out->un.u16.a = sqrt(a->un.u16.a);
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@@ -188,8 +188,8 @@ static void default_multiply_u32(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
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out->un.u32.b = a->un.u32.b * b->un.u32.b;
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}
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static void default_reciprocal_u32(MwLLVec* a, MwLLVec* out) {
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out->un.u32.a = nbsd_pow(a->un.u32.a, -1);
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out->un.u32.b = nbsd_pow(a->un.u32.b, -1);
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out->un.u32.a = pow(a->un.u32.a, -1);
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out->un.u32.b = pow(a->un.u32.b, -1);
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};
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static void default_squareRoot_u32(MwLLVec* a, MwLLVec* out) {
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out->un.u32.a = sqrt(a->un.u32.a);
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@@ -257,14 +257,14 @@ static void default_multiply_i8(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
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out->un.i8.h = a->un.i8.h * b->un.i8.h;
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};
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static void default_reciprocal_i8(MwLLVec* a, MwLLVec* out) {
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out->un.i8.a = nbsd_pow(a->un.i8.a, -1);
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out->un.i8.b = nbsd_pow(a->un.i8.b, -1);
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out->un.i8.c = nbsd_pow(a->un.i8.c, -1);
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out->un.i8.d = nbsd_pow(a->un.i8.d, -1);
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out->un.i8.e = nbsd_pow(a->un.i8.e, -1);
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out->un.i8.f = nbsd_pow(a->un.i8.f, -1);
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out->un.i8.g = nbsd_pow(a->un.i8.g, -1);
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out->un.i8.h = nbsd_pow(a->un.i8.h, -1);
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out->un.i8.a = pow(a->un.i8.a, -1);
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out->un.i8.b = pow(a->un.i8.b, -1);
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out->un.i8.c = pow(a->un.i8.c, -1);
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out->un.i8.d = pow(a->un.i8.d, -1);
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out->un.i8.e = pow(a->un.i8.e, -1);
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out->un.i8.f = pow(a->un.i8.f, -1);
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out->un.i8.g = pow(a->un.i8.g, -1);
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out->un.i8.h = pow(a->un.i8.h, -1);
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};
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static void default_squareRoot_i8(MwLLVec* a, MwLLVec* out) {
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out->un.i8.a = sqrt(a->un.i8.a);
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@@ -329,10 +329,10 @@ static void default_multiply_i16(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
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out->un.i16.d = a->un.i16.d * b->un.i16.d;
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}
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static void default_reciprocal_i16(MwLLVec* a, MwLLVec* out) {
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out->un.i16.a = nbsd_pow(a->un.i16.a, -1);
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out->un.i16.b = nbsd_pow(a->un.i16.b, -1);
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out->un.i16.c = nbsd_pow(a->un.i16.c, -1);
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out->un.i16.d = nbsd_pow(a->un.i16.d, -1);
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out->un.i16.a = pow(a->un.i16.a, -1);
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out->un.i16.b = pow(a->un.i16.b, -1);
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out->un.i16.c = pow(a->un.i16.c, -1);
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out->un.i16.d = pow(a->un.i16.d, -1);
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};
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static void default_squareRoot_i16(MwLLVec* a, MwLLVec* out) {
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out->un.i16.a = sqrt(a->un.i16.a);
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@@ -380,8 +380,8 @@ static void default_multiply_i32(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
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out->un.i32.b = a->un.i32.b * b->un.i32.b;
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}
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static void default_reciprocal_i32(MwLLVec* a, MwLLVec* out) {
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out->un.i32.a = nbsd_pow(a->un.i32.a, -1);
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out->un.i32.b = nbsd_pow(a->un.i32.b, -1);
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out->un.i32.a = pow(a->un.i32.a, -1);
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out->un.i32.b = pow(a->un.i32.b, -1);
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};
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static void default_squareRoot_i32(MwLLVec* a, MwLLVec* out) {
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out->un.i32.a = sqrt(a->un.i32.a);
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@@ -12,7 +12,6 @@
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#define FEATX86_SSE (1 << 25)
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#define FEATX86_SSE2 (1 << 26)
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#endif
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#include "nbsd_math.h"
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struct _MwLLMathVTable {
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void (*Add)(MwLLVec* a, MwLLVec* b, MwLLVec* out);
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@@ -1,31 +0,0 @@
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/* @(#)s_copysign.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* $Id$ */
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#include <Mw/BaseTypes.h>
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#include "math_internal.h"
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/*
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* copysign(double x, double y)
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* copysign(x,y) returns a value with the magnitude of x and
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* with the sign bit of y.
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*/
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double
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nbsd_copysign(double x, double y) {
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MwU32 hx, hy;
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GET_HIGH_WORD(hx, x);
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GET_HIGH_WORD(hy, y);
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SET_HIGH_WORD(x, (hx & 0x7fffffff) | (hy & 0x80000000));
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return x;
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}
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@@ -1,17 +0,0 @@
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/* $Id$ */
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#include <Mw/BaseTypes.h>
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#include "math_internal.h"
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static char endian = 0;
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char nbsd_endian(void) {
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unsigned short n = 1;
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if(endian != 0) return endian;
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if(1 == *(unsigned char*)&n) {
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endian = 'L';
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} else {
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endian = 'B';
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}
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return endian;
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}
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@@ -1,103 +0,0 @@
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/*
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* from: @(#)fdlibm.h 5.1 93/09/24
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* $NetBSD: math_private.h,v 1.34 2024/07/17 12:00:13 riastradh Exp $
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*/
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/* $Id$ */
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#ifndef __NBSD_MATH__
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#define __NBSD_MATH__
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#include <Mw/BaseTypes.h>
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typedef union _ieee_double_shape_type {
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double value;
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struct
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{
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MwU32 lsw;
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MwU32 msw;
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} parts;
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struct
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{
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MwU64 w;
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} xparts;
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} ieee_double_shape_type;
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/* Get two 32-bit integers from a double. */
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#define EXTRACT_WORDS(ix0, ix1, d) \
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do { \
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ieee_double_shape_type ew_u; \
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ew_u.value = (d); \
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if(nbsd_endian() == 'L') { \
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(ix0) = ew_u.parts.msw; \
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(ix1) = ew_u.parts.lsw; \
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} else { \
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(ix0) = ew_u.parts.lsw; \
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(ix1) = ew_u.parts.msw; \
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} \
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} while(0)
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/* Get the more significant 32-bit integer from a double. */
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#define GET_HIGH_WORD(i, d) \
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do { \
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ieee_double_shape_type gh_u; \
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gh_u.value = (d); \
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(i) = nbsd_endian() == 'L' ? gh_u.parts.msw : gh_u.parts.lsw; \
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} while(0)
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/* Get the less significant 32-bit integer from a double. */
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#define GET_LOW_WORD(i, d) \
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do { \
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ieee_double_shape_type gl_u; \
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gl_u.value = (d); \
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(i) = nbsd_endian() == 'L' ? gl_u.parts.lsw : gl_u.parts.msw; \
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} while(0)
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/* Set the more significant 32 bits of a double from an integer. */
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#define SET_HIGH_WORD(d, v) \
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do { \
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ieee_double_shape_type sh_u; \
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sh_u.value = (d); \
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if(nbsd_endian() == 'L') { \
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sh_u.parts.msw = (v); \
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} else { \
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sh_u.parts.lsw = (v); \
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} \
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(d) = sh_u.value; \
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} while(0)
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/* Set the less significant 32 bits of a double from an integer. */
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#define SET_LOW_WORD(d, v) \
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do { \
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ieee_double_shape_type sl_u; \
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sl_u.value = (d); \
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if(nbsd_endian() == 'L') { \
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sl_u.parts.lsw = (v); \
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} else { \
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sl_u.parts.msw = (v); \
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} \
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(d) = sl_u.value; \
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} while(0)
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double nbsd_pow(double a, double b);
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double nbsd_scalbn(double x, int n);
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double nbsd_scalbln(double x, long n);
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double nbsd_copysign(double x, double y);
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char nbsd_endian(void);
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#endif
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@@ -1,321 +0,0 @@
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/* @(#)e_pow.c 1.5 04/04/22 SMI */
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/*
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* ====================================================
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* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
|
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*
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* Permission to use, copy, modify, and distribute this
|
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* software is freely granted, provided that this notice
|
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* is preserved.
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* ====================================================
|
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*/
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/* $Id$ */
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#include <Mw/BaseTypes.h>
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#include "math_internal.h"
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/* __ieee754_pow(x,y) return x**y
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*
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* n
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* Method: Let x = 2 * (1+f)
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* 1. Compute and return log2(x) in two pieces:
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* log2(x) = w1 + w2,
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* where w1 has 53-24 = 29 bit trailing zeros.
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* 2. Perform y*log2(x) = n+y' by simulating multi-precision
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* arithmetic, where |y'|<=0.5.
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* 3. Return x**y = 2**n*exp(y'*log2)
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*
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* Special cases:
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* 1. (anything) ** 0 is 1
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* 2. (anything) ** 1 is itself
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* 3. (anything) ** NAN is NAN except 1 ** NAN = 1
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* 4. NAN ** (anything except 0) is NAN
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* 5. +-(|x| > 1) ** +INF is +INF
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* 6. +-(|x| > 1) ** -INF is +0
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* 7. +-(|x| < 1) ** +INF is +0
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* 8. +-(|x| < 1) ** -INF is +INF
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* 9. +-1 ** +-INF is 1
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* 10. +0 ** (+anything except 0, NAN) is +0
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* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
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* 12. +0 ** (-anything except 0, NAN) is +INF
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* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
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* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
|
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* 15. +INF ** (+anything except 0,NAN) is +INF
|
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* 16. +INF ** (-anything except 0,NAN) is +0
|
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* 17. -INF ** (anything) = -0 ** (-anything)
|
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* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
|
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* 19. (-anything except 0 and inf) ** (non-integer) is NAN
|
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*
|
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* Accuracy:
|
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* pow(x,y) returns x**y nearly rounded. In particular
|
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* pow(integer,integer)
|
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* always returns the correct integer provided it is
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* representable.
|
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*
|
||||
* Constants :
|
||||
* The hexadecimal values are the intended ones for the following
|
||||
* constants. The decimal values may be used, provided that the
|
||||
* compiler will convert from decimal to binary accurately enough
|
||||
* to produce the hexadecimal values shown.
|
||||
*/
|
||||
|
||||
static const double
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||||
bp[] = {
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1.0,
|
||||
1.5,
|
||||
},
|
||||
dp_h[] = {
|
||||
0.0,
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||||
5.84962487220764160156e-01,
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||||
}, /* 0x3FE2B803, 0x40000000 */
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||||
dp_l[] = {
|
||||
0.0,
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||||
1.35003920212974897128e-08,
|
||||
}, /* 0x3E4CFDEB, 0x43CFD006 */
|
||||
zero = 0.0, one = 1.0, two = 2.0, two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
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||||
hugev = 1.0e300, tinyv = 1.0e-300,
|
||||
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
||||
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
|
||||
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
|
||||
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
|
||||
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
|
||||
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
|
||||
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
|
||||
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
|
||||
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
|
||||
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
|
||||
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
|
||||
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
|
||||
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
|
||||
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
|
||||
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
|
||||
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
|
||||
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
|
||||
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
|
||||
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
|
||||
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
|
||||
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
|
||||
|
||||
double
|
||||
nbsd_pow(double x, double y) {
|
||||
double z, ax, z_h, z_l, p_h, p_l;
|
||||
double yy1, t1, t2, r, s, t, u, v, w;
|
||||
MwI32 i, j, k, yisint, n;
|
||||
MwI32 hx, hy, ix, iy;
|
||||
MwU32 lx, ly;
|
||||
|
||||
EXTRACT_WORDS(hx, lx, x);
|
||||
EXTRACT_WORDS(hy, ly, y);
|
||||
ix = hx & 0x7fffffff;
|
||||
iy = hy & 0x7fffffff;
|
||||
|
||||
/* y==zero: x**0 = 1 */
|
||||
if((iy | ly) == 0) return one;
|
||||
|
||||
/* x==1: 1**y = 1, even if y is NaN */
|
||||
if(hx == 0x3ff00000 && lx == 0) return one;
|
||||
|
||||
/* y!=zero: result is NaN if either arg is NaN */
|
||||
if(ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) ||
|
||||
iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0)))
|
||||
return (x + 0.0) + (y + 0.0);
|
||||
|
||||
/* determine if y is an odd int when x < 0
|
||||
* yisint = 0 ... y is not an integer
|
||||
* yisint = 1 ... y is an odd int
|
||||
* yisint = 2 ... y is an even int
|
||||
*/
|
||||
yisint = 0;
|
||||
if(hx < 0) {
|
||||
if(iy >= 0x43400000) yisint = 2; /* even integer y */
|
||||
else if(iy >= 0x3ff00000) {
|
||||
k = (iy >> 20) - 0x3ff; /* exponent */
|
||||
if(k > 20) {
|
||||
j = ly >> (52 - k);
|
||||
if((MwU32)(j << (52 - k)) == ly) yisint = 2 - (j & 1);
|
||||
} else if(ly == 0) {
|
||||
j = iy >> (20 - k);
|
||||
if((j << (20 - k)) == iy) yisint = 2 - (j & 1);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* special value of y */
|
||||
if(ly == 0) {
|
||||
if(iy == 0x7ff00000) { /* y is +-inf */
|
||||
if(((ix - 0x3ff00000) | lx) == 0)
|
||||
return one; /* (-1)**+-inf is 1 */
|
||||
else if(ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
|
||||
return (hy >= 0) ? y : zero;
|
||||
else /* (|x|<1)**-,+inf = inf,0 */
|
||||
return (hy < 0) ? -y : zero;
|
||||
}
|
||||
if(iy == 0x3ff00000) { /* y is +-1 */
|
||||
if(hy < 0) return one / x;
|
||||
else
|
||||
return x;
|
||||
}
|
||||
if(hy == 0x40000000) return x * x; /* y is 2 */
|
||||
if(hy == 0x3fe00000) { /* y is 0.5 */
|
||||
if(hx >= 0) /* x >= +0 */
|
||||
return sqrt(x);
|
||||
}
|
||||
}
|
||||
|
||||
ax = fabs(x);
|
||||
/* special value of x */
|
||||
if(lx == 0) {
|
||||
if(ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
|
||||
z = ax; /*x is +-0,+-inf,+-1*/
|
||||
if(hy < 0) z = one / z; /* z = (1/|x|) */
|
||||
if(hx < 0) {
|
||||
if(((ix - 0x3ff00000) | yisint) == 0) {
|
||||
z = (z - z) / (z - z); /* (-1)**non-int is NaN */
|
||||
} else if(yisint == 1)
|
||||
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
||||
}
|
||||
return z;
|
||||
}
|
||||
}
|
||||
|
||||
/* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be
|
||||
n = (hx>>31)+1;
|
||||
but ANSI C says a right shift of a signed negative quantity is
|
||||
implementation defined. */
|
||||
n = ((MwU32)hx >> 31) - 1;
|
||||
|
||||
/* (x<0)**(non-int) is NaN */
|
||||
if((n | yisint) == 0) return (x - x) / (x - x);
|
||||
|
||||
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
||||
if((n | (yisint - 1)) == 0) s = -one; /* (-ve)**(odd int) */
|
||||
|
||||
/* |y| is hugev */
|
||||
if(iy > 0x41e00000) { /* if |y| > 2**31 */
|
||||
if(iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
|
||||
if(ix <= 0x3fefffff) return (hy < 0) ? hugev * hugev : tinyv * tinyv;
|
||||
if(ix >= 0x3ff00000) return (hy > 0) ? hugev * hugev : tinyv * tinyv;
|
||||
}
|
||||
/* over/underflow if x is not close to one */
|
||||
if(ix < 0x3fefffff) return (hy < 0) ? s * hugev * hugev : s * tinyv * tinyv;
|
||||
if(ix > 0x3ff00000) return (hy > 0) ? s * hugev * hugev : s * tinyv * tinyv;
|
||||
/* now |1-x| is tinyv <= 2**-20, suffice to compute
|
||||
log(x) by x-x^2/2+x^3/3-x^4/4 */
|
||||
t = ax - one; /* t has 20 trailing zeros */
|
||||
w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
|
||||
u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
|
||||
v = t * ivln2_l - w * ivln2;
|
||||
t1 = u + v;
|
||||
SET_LOW_WORD(t1, 0);
|
||||
t2 = v - (t1 - u);
|
||||
} else {
|
||||
double ss, s2, s_h, s_l, t_h, t_l;
|
||||
n = 0;
|
||||
/* take care subnormal number */
|
||||
if(ix < 0x00100000) {
|
||||
ax *= two53;
|
||||
n -= 53;
|
||||
GET_HIGH_WORD(ix, ax);
|
||||
}
|
||||
n += ((ix) >> 20) - 0x3ff;
|
||||
j = ix & 0x000fffff;
|
||||
/* determine interval */
|
||||
ix = j | 0x3ff00000; /* normalize ix */
|
||||
if(j <= 0x3988E) k = 0; /* |x|<sqrt(3/2) */
|
||||
else if(j < 0xBB67A)
|
||||
k = 1; /* |x|<sqrt(3) */
|
||||
else {
|
||||
k = 0;
|
||||
n += 1;
|
||||
ix -= 0x00100000;
|
||||
}
|
||||
SET_HIGH_WORD(ax, ix);
|
||||
|
||||
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
||||
u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
||||
v = one / (ax + bp[k]);
|
||||
ss = u * v;
|
||||
s_h = ss;
|
||||
SET_LOW_WORD(s_h, 0);
|
||||
/* t_h=ax+bp[k] High */
|
||||
t_h = zero;
|
||||
SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
|
||||
t_l = ax - (t_h - bp[k]);
|
||||
s_l = v * ((u - s_h * t_h) - s_h * t_l);
|
||||
/* compute log(ax) */
|
||||
s2 = ss * ss;
|
||||
r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
|
||||
r += s_l * (s_h + ss);
|
||||
s2 = s_h * s_h;
|
||||
t_h = 3.0 + s2 + r;
|
||||
SET_LOW_WORD(t_h, 0);
|
||||
t_l = r - ((t_h - 3.0) - s2);
|
||||
/* u+v = ss*(1+...) */
|
||||
u = s_h * t_h;
|
||||
v = s_l * t_h + t_l * ss;
|
||||
/* 2/(3log2)*(ss+...) */
|
||||
p_h = u + v;
|
||||
SET_LOW_WORD(p_h, 0);
|
||||
p_l = v - (p_h - u);
|
||||
z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
|
||||
z_l = cp_l * p_h + p_l * cp + dp_l[k];
|
||||
/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
||||
t = (double)n;
|
||||
t1 = (((z_h + z_l) + dp_h[k]) + t);
|
||||
SET_LOW_WORD(t1, 0);
|
||||
t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
|
||||
}
|
||||
|
||||
/* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */
|
||||
yy1 = y;
|
||||
SET_LOW_WORD(yy1, 0);
|
||||
p_l = (y - yy1) * t1 + y * t2;
|
||||
p_h = yy1 * t1;
|
||||
z = p_l + p_h;
|
||||
EXTRACT_WORDS(j, i, z);
|
||||
if(j >= 0x40900000) { /* z >= 1024 */
|
||||
if(((j - 0x40900000) | i) != 0) /* if z > 1024 */
|
||||
return s * hugev * hugev; /* overflow */
|
||||
else {
|
||||
if(p_l + ovt > z - p_h) return s * hugev * hugev; /* overflow */
|
||||
}
|
||||
} else if((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
|
||||
if(((j - 0xc090cc00) | i) != 0) /* z < -1075 */
|
||||
return s * tinyv * tinyv; /* underflow */
|
||||
else {
|
||||
if(p_l <= z - p_h) return s * tinyv * tinyv; /* underflow */
|
||||
}
|
||||
}
|
||||
/*
|
||||
* compute 2**(p_h+p_l)
|
||||
*/
|
||||
i = j & 0x7fffffff;
|
||||
k = (i >> 20) - 0x3ff;
|
||||
n = 0;
|
||||
if(i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
|
||||
n = j + (0x00100000 >> (k + 1));
|
||||
k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
|
||||
t = zero;
|
||||
SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
|
||||
n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
|
||||
if(j < 0) n = -n;
|
||||
p_h -= t;
|
||||
}
|
||||
t = p_l + p_h;
|
||||
SET_LOW_WORD(t, 0);
|
||||
u = t * lg2_h;
|
||||
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
|
||||
z = u + v;
|
||||
w = v - (z - u);
|
||||
t = z * z;
|
||||
t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
|
||||
r = (z * t1) / (t1 - two) - (w + z * w);
|
||||
z = one - (r - z);
|
||||
GET_HIGH_WORD(j, z);
|
||||
j += (n << 20);
|
||||
if((j >> 20) <= 0) z = nbsd_scalbn(z, n); /* subnormal output */
|
||||
else
|
||||
SET_HIGH_WORD(z, j);
|
||||
return s * z;
|
||||
}
|
||||
@@ -1,65 +0,0 @@
|
||||
/* @(#)s_scalbn.c 5.1 93/09/24 */
|
||||
/*
|
||||
* ====================================================
|
||||
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||||
*
|
||||
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||||
* Permission to use, copy, modify, and distribute this
|
||||
* software is freely granted, provided that this notice
|
||||
* is preserved.
|
||||
* ====================================================
|
||||
*/
|
||||
|
||||
/* $Id$ */
|
||||
|
||||
#include <Mw/BaseTypes.h>
|
||||
#include "math_internal.h"
|
||||
|
||||
/*
|
||||
* scalbn (double x, int n)
|
||||
* scalbn(x,n) returns x* 2**n computed by exponent
|
||||
* manipulation rather than by actually performing an
|
||||
* exponentiation or a multiplication.
|
||||
*/
|
||||
|
||||
static const double
|
||||
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
|
||||
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
|
||||
hugev = 1.0e+300,
|
||||
tinyv = 1.0e-300;
|
||||
|
||||
double
|
||||
nbsd_scalbn(double x, int n) {
|
||||
return nbsd_scalbln(x, n);
|
||||
}
|
||||
|
||||
double
|
||||
nbsd_scalbln(double x, long n) {
|
||||
MwI32 k, hx, lx;
|
||||
EXTRACT_WORDS(hx, lx, x);
|
||||
k = ((MwU32)hx & 0x7ff00000) >> 20; /* extract exponent */
|
||||
if(k == 0) { /* 0 or subnormal x */
|
||||
if((lx | (hx & 0x7fffffff)) == 0) return x; /* +-0 */
|
||||
x *= two54;
|
||||
GET_HIGH_WORD(hx, x);
|
||||
k = (((MwU32)hx & 0x7ff00000) >> 20) - 54;
|
||||
if(n < -50000) return tinyv * x; /*underflow*/
|
||||
}
|
||||
if(k == 0x7ff) return x + x; /* NaN or Inf */
|
||||
k = k + n;
|
||||
if(k > 0x7fe) return hugev * nbsd_copysign(hugev, x); /* overflow */
|
||||
if(k > 0) /* normal result */
|
||||
{
|
||||
SET_HIGH_WORD(x, (hx & 0x800fffff) | (k << 20));
|
||||
return x;
|
||||
}
|
||||
if(k <= -54) {
|
||||
if(n > 50000) /* in case integer overflow in n+k */
|
||||
return hugev * nbsd_copysign(hugev, x); /*overflow*/
|
||||
else
|
||||
return tinyv * nbsd_copysign(tinyv, x); /*underflow*/
|
||||
}
|
||||
k += 54; /* subnormal result */
|
||||
SET_HIGH_WORD(x, (hx & 0x800fffff) | (k << 20));
|
||||
return x * twom54;
|
||||
}
|
||||
Reference in New Issue
Block a user