diff options
| author | darylm503 <darylm503@6f19259b-4bc3-4df7-8a09-765794883524> | 2011-04-27 21:42:16 +0000 |
|---|---|---|
| committer | darylm503 <darylm503@6f19259b-4bc3-4df7-8a09-765794883524> | 2011-04-27 21:42:16 +0000 |
| commit | 2aa62f2bc9a9654687b377d9ca8a8c2c860a3852 (patch) | |
| tree | 62a0991a44327154fb88bf95bd6f7522053db7bb /StdLib/LibC/Math | |
| parent | 98790d814871cc30bbd536673d3a0948047cd2f0 (diff) | |
| download | edk2-platforms-2aa62f2bc9a9654687b377d9ca8a8c2c860a3852.tar.xz | |
Standard Libraries for EDK II.
This set of three packages: AppPkg, StdLib, StdLibPrivateInternalFiles; contains the implementation of libraries based upon non-UEFI standards such as ISO/IEC-9899, the library portion of the C Language Standard, POSIX, etc.
AppPkg contains applications that make use of the standard libraries defined in the StdLib Package.
StdLib contains header (include) files and the implementations of the standard libraries.
StdLibPrivateInternalFiles contains files for the exclusive use of the library implementations in StdLib. These files should never be directly referenced from applications or other code.
git-svn-id: https://edk2.svn.sourceforge.net/svnroot/edk2/trunk/edk2@11600 6f19259b-4bc3-4df7-8a09-765794883524
Diffstat (limited to 'StdLib/LibC/Math')
47 files changed, 4760 insertions, 0 deletions
diff --git a/StdLib/LibC/Math/Math.inf b/StdLib/LibC/Math/Math.inf new file mode 100644 index 0000000000..6a48d97cac --- /dev/null +++ b/StdLib/LibC/Math/Math.inf @@ -0,0 +1,101 @@ +## @file
+# Standard C library: Math Library.
+#
+# Copyright (c) 2010, Intel Corporation. All rights reserved.<BR>
+#
+# This program and the accompanying materials
+# are licensed and made available under the terms and conditions of the BSD License
+# which accompanies this distribution. The full text of the license may be found at
+# http://opensource.org/licenses/bsd-license.php.
+# THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
+# WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
+#
+#
+##
+
+[Defines]
+ INF_VERSION = 0x00010005
+ BASE_NAME = LibMath
+ FILE_GUID = a9dc6f60-f861-47d1-8751-ecaae7d27291
+ MODULE_TYPE = UEFI_APPLICATION
+ VERSION_STRING = 1.0
+ LIBRARY_CLASS = LibMath
+
+#
+# VALID_ARCHITECTURES = IA32 X64 IPF
+#
+
+[Sources]
+ # ieee 754 specific
+ e_acos.c
+ e_asin.c
+ e_atan2.c
+ e_cosh.c
+ e_exp.c
+ e_sinh.c
+ e_log.c
+ e_log2.c
+ e_log10.c
+ e_pow.c
+ e_sqrt.c
+ e_fmod.c
+ e_rem_pio2.c
+
+ # kernel functions
+ k_cos.c
+ k_sin.c
+ k_tan.c
+ k_rem_pio2.c
+
+ # Simple, unadorned, functions
+ s_atan.c
+ s_cos.c
+ s_sin.c
+ s_tan.c
+ s_expm1.c
+ s_tanh.c
+ s_frexp.c
+ s_ldexp.c
+ s_scalbn.c
+ s_copysign.c
+ s_finite.c
+ s_infinity.c
+ s_modf.c
+ s_fabs.c
+ s_ceil.c
+ s_floor.c
+
+ # wrapper functions
+ w_acos.c
+ w_asin.c
+ w_atan2.c
+ w_cosh.c
+ w_sinh.c
+ w_exp.c
+ w_log.c
+ w_log2.c
+ w_log10.c
+ w_pow.c
+ w_sqrt.c
+ w_fmod.c
+
+[Packages]
+ StdLib/StdLib.dec
+ StdLibPrivateInternalFiles/DoNotUse.dec
+ MdePkg/MdePkg.dec
+
+[LibraryClasses]
+ LibC
+
+################################################################
+# The Build Options, below, are only used when building the C library.
+# DO NOT use them when building your application!
+# Nasty things could happen if you do.
+#
+# /Oi- is required for Microsoft VC++ to allow "intrinsic" functions to be
+# defined in this library.
+# /GL- is required so that LTCG generated references to functions in this library,
+# such as memcpy(), can be resolved.
+#
+[BuildOptions]
+ MSFT:*_*_*_CC_FLAGS = /Oi- /GL-
diff --git a/StdLib/LibC/Math/e_acos.c b/StdLib/LibC/Math/e_acos.c new file mode 100644 index 0000000000..4617729af6 --- /dev/null +++ b/StdLib/LibC/Math/e_acos.c @@ -0,0 +1,122 @@ +/** @file
+ Compute acos(x) using ieee FP math.
+
+ Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>
+ This program and the accompanying materials are licensed and made available under
+ the terms and conditions of the BSD License that accompanies this distribution.
+ The full text of the license may be found at
+ http://opensource.org/licenses/bsd-license.
+
+ THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
+ WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
+
+ * ====================================================
+ * 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.
+ * ====================================================
+
+ e_acos.c 5.1 93/09/24
+ NetBSD: e_acos.c,v 1.12 2002/05/26 22:01:47 wiz Exp
+ */
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // Keep older compilers quiet about floating-point divide-by-zero
+ #pragma warning ( disable : 4723 )
+#endif
+
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+
+/* __ieee754_acos(x)
+ * Method :
+ * acos(x) = pi/2 - asin(x)
+ * acos(-x) = pi/2 + asin(x)
+ * For |x|<=0.5
+ * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
+ * For x>0.5
+ * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
+ * = 2asin(sqrt((1-x)/2))
+ * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
+ * = 2f + (2c + 2s*z*R(z))
+ * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
+ * for f so that f+c ~ sqrt(z).
+ * For x<-0.5
+ * acos(x) = pi - 2asin(sqrt((1-|x|)/2))
+ * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ * Function needed: __ieee754_sqrt
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
+pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
+qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+double
+__ieee754_acos(double x)
+{
+ double z,p,q,r,w,s,c,df;
+ int32_t hx,ix;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x3ff00000) { /* |x| >= 1 */
+ u_int32_t lx;
+
+ GET_LOW_WORD(lx,x);
+ if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
+ if(hx>0) return 0.0; /* acos(1) = 0 */
+ else return pi+2.0*pio2_lo; /* acos(-1)= pi */
+ }
+ return (x-x)/(x-x); /* acos(|x|>1) is NaN */
+ }
+ if(ix<0x3fe00000) { /* |x| < 0.5 */
+ if(ix<=0x3c600000) return pio2_hi+pio2_lo; /*if|x|<2**-57*/
+ z = x*x;
+ p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+ q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+ r = p/q;
+ return pio2_hi - (x - (pio2_lo-x*r));
+ }
+ else if (hx<0) { /* x < -0.5 */
+ z = (one+x)*0.5;
+ p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+ q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+ s = __ieee754_sqrt(z);
+ r = p/q;
+ w = r*s-pio2_lo;
+ return pi - 2.0*(s+w);
+ }
+ else { /* x > 0.5 */
+ z = (one-x)*0.5;
+ s = __ieee754_sqrt(z);
+ df = s;
+ SET_LOW_WORD(df,0);
+ c = (z-df*df)/(s+df);
+ p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
+ q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
+ r = p/q;
+ w = r*s+c;
+ return 2.0*(df+w);
+ }
+}
diff --git a/StdLib/LibC/Math/e_asin.c b/StdLib/LibC/Math/e_asin.c new file mode 100644 index 0000000000..d1d4dc0019 --- /dev/null +++ b/StdLib/LibC/Math/e_asin.c @@ -0,0 +1,120 @@ +/* @(#)e_asin.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: e_asin.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
+#endif
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+// C4723: potential divide by zero.
+#pragma warning ( disable : 4723 )
+#endif
+
+/* __ieee754_asin(x)
+ * Method :
+ * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
+ * we approximate asin(x) on [0,0.5] by
+ * asin(x) = x + x*x^2*R(x^2)
+ * where
+ * R(x^2) is a rational approximation of (asin(x)-x)/x^3
+ * and its remez error is bounded by
+ * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
+ *
+ * For x in [0.5,1]
+ * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
+ * then for x>0.98
+ * asin(x) = pi/2 - 2*(s+s*z*R(z))
+ * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
+ * For x<=0.98, let pio4_hi = pio2_hi/2, then
+ * f = hi part of s;
+ * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
+ * and
+ * asin(x) = pi/2 - 2*(s+s*z*R(z))
+ * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
+ * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ */
+
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+huge = 1.000e+300,
+pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
+pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
+pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
+ /* coefficient for R(x^2) */
+pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
+pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
+pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
+pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
+pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
+pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
+qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
+qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
+qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
+qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
+
+double
+__ieee754_asin(double x)
+{
+ double t,w,p,q,c,r,s;
+ int32_t hx,ix;
+
+ t = 0;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>= 0x3ff00000) { /* |x|>= 1 */
+ u_int32_t lx;
+ GET_LOW_WORD(lx,x);
+ if(((ix-0x3ff00000)|lx)==0)
+ /* asin(1)=+-pi/2 with inexact */
+ return x*pio2_hi+x*pio2_lo;
+ return (x-x)/(x-x); /* asin(|x|>1) is NaN */
+ } else if (ix<0x3fe00000) { /* |x|<0.5 */
+ if(ix<0x3e400000) { /* if |x| < 2**-27 */
+ if(huge+x>one) return x;/* return x with inexact if x!=0*/
+ } else
+ t = x*x;
+ p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
+ q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+ w = p/q;
+ return x+x*w;
+ }
+ /* 1> |x|>= 0.5 */
+ w = one-fabs(x);
+ t = w*0.5;
+ p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
+ q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
+ s = __ieee754_sqrt(t);
+ if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
+ w = p/q;
+ t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
+ } else {
+ w = s;
+ SET_LOW_WORD(w,0);
+ c = (t-w*w)/(s+w);
+ r = p/q;
+ p = 2.0*s*r-(pio2_lo-2.0*c);
+ q = pio4_hi-2.0*w;
+ t = pio4_hi-(p-q);
+ }
+ if(hx>0) return t; else return -t;
+}
diff --git a/StdLib/LibC/Math/e_atan2.c b/StdLib/LibC/Math/e_atan2.c new file mode 100644 index 0000000000..309447c0a5 --- /dev/null +++ b/StdLib/LibC/Math/e_atan2.c @@ -0,0 +1,128 @@ +/* @(#)e_atan2.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: e_atan2.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
+#endif
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // unary minus operator applied to unsigned type, result still unsigned
+ #pragma warning ( disable : 4146 )
+#endif
+
+/* __ieee754_atan2(y,x)
+ * Method :
+ * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
+ * 2. Reduce x to positive by (if x and y are unexceptional):
+ * ARG (x+iy) = arctan(y/x) ... if x > 0,
+ * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
+ *
+ * Special cases:
+ *
+ * ATAN2((anything), NaN ) is NaN;
+ * ATAN2(NAN , (anything) ) is NaN;
+ * ATAN2(+-0, +(anything but NaN)) is +-0 ;
+ * ATAN2(+-0, -(anything but NaN)) is +-pi ;
+ * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
+ * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
+ * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
+ * ATAN2(+-INF,+INF ) is +-pi/4 ;
+ * ATAN2(+-INF,-INF ) is +-3pi/4;
+ * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
+ *
+ * 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.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+tiny = 1.0e-300,
+zero = 0.0,
+pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
+pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
+pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
+pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
+
+double
+__ieee754_atan2(double y, double x)
+{
+ double z;
+ int32_t k,m,hx,hy,ix,iy;
+ u_int32_t lx,ly;
+
+ EXTRACT_WORDS(hx,lx,x);
+ ix = hx&0x7fffffff;
+ EXTRACT_WORDS(hy,ly,y);
+ iy = hy&0x7fffffff;
+ if(((ix|((lx|-lx)>>31))>0x7ff00000)||
+ ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
+ return x+y;
+ if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
+ m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
+
+ /* when y = 0 */
+ if((iy|ly)==0) {
+ switch(m) {
+ case 0:
+ case 1: return y; /* atan(+-0,+anything)=+-0 */
+ case 2: return pi+tiny;/* atan(+0,-anything) = pi */
+ case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
+ }
+ }
+ /* when x = 0 */
+ if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+
+ /* when x is INF */
+ if(ix==0x7ff00000) {
+ if(iy==0x7ff00000) {
+ switch(m) {
+ case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
+ case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
+ case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
+ case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
+ }
+ } else {
+ switch(m) {
+ case 0: return zero ; /* atan(+...,+INF) */
+ case 1: return -zero ; /* atan(-...,+INF) */
+ case 2: return pi+tiny ; /* atan(+...,-INF) */
+ case 3: return -pi-tiny ; /* atan(-...,-INF) */
+ }
+ }
+ }
+ /* when y is INF */
+ if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
+
+ /* compute y/x */
+ k = (iy-ix)>>20;
+ if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
+ else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
+ else z=atan(fabs(y/x)); /* safe to do y/x */
+ switch (m) {
+ case 0: return z ; /* atan(+,+) */
+ case 1: {
+ u_int32_t zh;
+ GET_HIGH_WORD(zh,z);
+ SET_HIGH_WORD(z,zh ^ 0x80000000);
+ }
+ return z ; /* atan(-,+) */
+ case 2: return pi-(z-pi_lo);/* atan(+,-) */
+ default: /* case 3 */
+ return (z-pi_lo)-pi;/* atan(-,-) */
+ }
+}
diff --git a/StdLib/LibC/Math/e_cosh.c b/StdLib/LibC/Math/e_cosh.c new file mode 100644 index 0000000000..48ce6817d2 --- /dev/null +++ b/StdLib/LibC/Math/e_cosh.c @@ -0,0 +1,91 @@ +/* @(#)e_cosh.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: e_cosh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
+#endif
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // C4756: overflow in constant arithmetic
+ #pragma warning ( disable : 4756 )
+#endif
+
+/* __ieee754_cosh(x)
+ * Method :
+ * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
+ * 1. Replace x by |x| (cosh(x) = cosh(-x)).
+ * 2.
+ * [ exp(x) - 1 ]^2
+ * 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
+ * 2*exp(x)
+ *
+ * exp(x) + 1/exp(x)
+ * ln2/2 <= x <= 22 : cosh(x) := -------------------
+ * 2
+ * 22 <= x <= lnovft : cosh(x) := exp(x)/2
+ * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
+ * ln2ovft < x : cosh(x) := huge*huge (overflow)
+ *
+ * Special cases:
+ * cosh(x) is |x| if x is +INF, -INF, or NaN.
+ * only cosh(0)=1 is exact for finite x.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double one = 1.0, half=0.5, huge = 1.0e300;
+
+double
+__ieee754_cosh(double x)
+{
+ double t,w;
+ int32_t ix;
+ u_int32_t lx;
+
+ /* High word of |x|. */
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff;
+
+ /* x is INF or NaN */
+ if(ix>=0x7ff00000) return x*x;
+
+ /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
+ if(ix<0x3fd62e43) {
+ t = expm1(fabs(x));
+ w = one+t;
+ if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
+ return one+(t*t)/(w+w);
+ }
+
+ /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
+ if (ix < 0x40360000) {
+ t = __ieee754_exp(fabs(x));
+ return half*t+half/t;
+ }
+
+ /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
+ if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x));
+
+ /* |x| in [log(maxdouble), overflowthresold] */
+ GET_LOW_WORD(lx,x);
+ if (ix<0x408633CE ||
+ ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
+ w = __ieee754_exp(half*fabs(x));
+ t = half*w;
+ return t*w;
+ }
+
+ /* |x| > overflowthresold, cosh(x) overflow */
+ return huge*huge;
+}
diff --git a/StdLib/LibC/Math/e_exp.c b/StdLib/LibC/Math/e_exp.c new file mode 100644 index 0000000000..f05f5397e6 --- /dev/null +++ b/StdLib/LibC/Math/e_exp.c @@ -0,0 +1,167 @@ +/* @(#)e_exp.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: e_exp.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
+#endif
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // C4756: overflow in constant arithmetic
+ #pragma warning ( disable : 4756 )
+#endif
+
+/* __ieee754_exp(x)
+ * Returns the exponential of x.
+ *
+ * Method
+ * 1. Argument reduction:
+ * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
+ * Given x, find r and integer k such that
+ *
+ * x = k*ln2 + r, |r| <= 0.5*ln2.
+ *
+ * Here r will be represented as r = hi-lo for better
+ * accuracy.
+ *
+ * 2. Approximation of exp(r) by a special rational function on
+ * the interval [0,0.34658]:
+ * Write
+ * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
+ * We use a special Reme algorithm on [0,0.34658] to generate
+ * a polynomial of degree 5 to approximate R. The maximum error
+ * of this polynomial approximation is bounded by 2**-59. In
+ * other words,
+ * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
+ * (where z=r*r, and the values of P1 to P5 are listed below)
+ * and
+ * | 5 | -59
+ * | 2.0+P1*z+...+P5*z - R(z) | <= 2
+ * | |
+ * The computation of exp(r) thus becomes
+ * 2*r
+ * exp(r) = 1 + -------
+ * R - r
+ * r*R1(r)
+ * = 1 + r + ----------- (for better accuracy)
+ * 2 - R1(r)
+ * where
+ * 2 4 10
+ * R1(r) = r - (P1*r + P2*r + ... + P5*r ).
+ *
+ * 3. Scale back to obtain exp(x):
+ * From step 1, we have
+ * exp(x) = 2^k * exp(r)
+ *
+ * Special cases:
+ * exp(INF) is INF, exp(NaN) is NaN;
+ * exp(-INF) is 0, and
+ * for finite argument, only exp(0)=1 is exact.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Misc. info.
+ * For IEEE double
+ * if x > 7.09782712893383973096e+02 then exp(x) overflow
+ * if x < -7.45133219101941108420e+02 then exp(x) underflow
+ *
+ * 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.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+one = 1.0,
+halF[2] = {0.5,-0.5,},
+huge = 1.0e+300,
+twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
+o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
+u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
+ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
+ -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
+ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
+ -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
+invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
+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 */
+
+
+double
+__ieee754_exp(double x) /* default IEEE double exp */
+{
+ double y,hi,lo,c,t;
+ int32_t k,xsb;
+ u_int32_t hx;
+
+ hi = lo = 0;
+ k = 0;
+ GET_HIGH_WORD(hx,x);
+ xsb = (hx>>31)&1; /* sign bit of x */
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* filter out non-finite argument */
+ if(hx >= 0x40862E42) { /* if |x|>=709.78... */
+ if(hx>=0x7ff00000) {
+ u_int32_t lx;
+ GET_LOW_WORD(lx,x);
+ if(((hx&0xfffff)|lx)!=0)
+ return x+x; /* NaN */
+ else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
+ }
+ if(x > o_threshold) return huge*huge; /* overflow */
+ if(x < u_threshold) return twom1000*twom1000; /* underflow */
+ }
+
+ /* argument reduction */
+ if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
+ hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
+ } else {
+ k = (int32_t)(invln2*x+halF[xsb]);
+ t = k;
+ hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
+ lo = t*ln2LO[0];
+ }
+ x = hi - lo;
+ }
+ else if(hx < 0x3e300000) { /* when |x|<2**-28 */
+ if(huge+x>one) return one+x;/* trigger inexact */
+ }
+ else k = 0;
+
+ /* x is now in primary range */
+ t = x*x;
+ c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
+ if(k==0) return one-((x*c)/(c-2.0)-x);
+ else y = one-((lo-(x*c)/(2.0-c))-hi);
+ if(k >= -1021) {
+ u_int32_t hy;
+ GET_HIGH_WORD(hy,y);
+ SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */
+ return y;
+ } else {
+ u_int32_t hy;
+ GET_HIGH_WORD(hy,y);
+ SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */
+ return y*twom1000;
+ }
+}
diff --git a/StdLib/LibC/Math/e_fmod.c b/StdLib/LibC/Math/e_fmod.c new file mode 100644 index 0000000000..3cb06c12b0 --- /dev/null +++ b/StdLib/LibC/Math/e_fmod.c @@ -0,0 +1,138 @@ +/* @(#)e_fmod.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: e_fmod.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
+#endif
+
+/*
+ * __ieee754_fmod(x,y)
+ * Return x mod y in exact arithmetic
+ * Method: shift and subtract
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // unary minus operator applied to unsigned type, result still unsigned
+ #pragma warning ( disable : 4146 )
+#endif
+
+static const double one = 1.0, Zero[] = {0.0, -0.0,};
+
+double
+__ieee754_fmod(double x, double y)
+{
+ int32_t n,hx,hy,hz,ix,iy,sx,i;
+ u_int32_t lx,ly,lz;
+
+ EXTRACT_WORDS(hx,lx,x);
+ EXTRACT_WORDS(hy,ly,y);
+ sx = hx&0x80000000; /* sign of x */
+ hx ^=sx; /* |x| */
+ hy &= 0x7fffffff; /* |y| */
+
+ /* purge off exception values */
+ if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
+ ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
+ return (x*y)/(x*y);
+ if(hx<=hy) {
+ if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */
+ if(lx==ly)
+ return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
+ }
+
+ /* determine ix = ilogb(x) */
+ if(hx<0x00100000) { /* subnormal x */
+ if(hx==0) {
+ for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
+ } else {
+ for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
+ }
+ } else ix = (hx>>20)-1023;
+
+ /* determine iy = ilogb(y) */
+ if(hy<0x00100000) { /* subnormal y */
+ if(hy==0) {
+ for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
+ } else {
+ for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
+ }
+ } else iy = (hy>>20)-1023;
+
+ /* set up {hx,lx}, {hy,ly} and align y to x */
+ if(ix >= -1022)
+ hx = 0x00100000|(0x000fffff&hx);
+ else { /* subnormal x, shift x to normal */
+ n = -1022-ix;
+ if(n<=31) {
+ hx = (hx<<n)|(lx>>(32-n));
+ lx <<= n;
+ } else {
+ hx = lx<<(n-32);
+ lx = 0;
+ }
+ }
+ if(iy >= -1022)
+ hy = 0x00100000|(0x000fffff&hy);
+ else { /* subnormal y, shift y to normal */
+ n = -1022-iy;
+ if(n<=31) {
+ hy = (hy<<n)|(ly>>(32-n));
+ ly <<= n;
+ } else {
+ hy = ly<<(n-32);
+ ly = 0;
+ }
+ }
+
+ /* fix point fmod */
+ n = ix - iy;
+ while(n--) {
+ hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
+ if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
+ else {
+ if((hz|lz)==0) /* return sign(x)*0 */
+ return Zero[(u_int32_t)sx>>31];
+ hx = hz+hz+(lz>>31); lx = lz+lz;
+ }
+ }
+ hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
+ if(hz>=0) {hx=hz;lx=lz;}
+
+ /* convert back to floating value and restore the sign */
+ if((hx|lx)==0) /* return sign(x)*0 */
+ return Zero[(u_int32_t)sx>>31];
+ while(hx<0x00100000) { /* normalize x */
+ hx = hx+hx+(lx>>31); lx = lx+lx;
+ iy -= 1;
+ }
+ if(iy>= -1022) { /* normalize output */
+ hx = ((hx-0x00100000)|((iy+1023)<<20));
+ INSERT_WORDS(x,hx|sx,lx);
+ } else { /* subnormal output */
+ n = -1022 - iy;
+ if(n<=20) {
+ lx = (lx>>n)|((u_int32_t)hx<<(32-n));
+ hx >>= n;
+ } else if (n<=31) {
+ lx = (hx<<(32-n))|(lx>>n); hx = sx;
+ } else {
+ lx = hx>>(n-32); hx = sx;
+ }
+ INSERT_WORDS(x,hx|sx,lx);
+ x *= one; /* create necessary signal */
+ }
+ return x; /* exact output */
+}
diff --git a/StdLib/LibC/Math/e_log.c b/StdLib/LibC/Math/e_log.c new file mode 100644 index 0000000000..979b7f9421 --- /dev/null +++ b/StdLib/LibC/Math/e_log.c @@ -0,0 +1,155 @@ +/** @file
+ Compute the logrithm of x.
+
+ Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>
+ This program and the accompanying materials are licensed and made available under
+ the terms and conditions of the BSD License that accompanies this distribution.
+ The full text of the license may be found at
+ http://opensource.org/licenses/bsd-license.
+
+ THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
+ WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
+
+ * ====================================================
+ * 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.
+ * ====================================================
+
+ e_log.c 5.1 93/09/24
+ NetBSD: e_log.c,v 1.12 2002/05/26 22:01:51 wiz Exp
+**/
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // potential divide by 0 -- near line 118, (x-x)/zero is on purpose
+ #pragma warning ( disable : 4723 )
+#endif
+
+/* __ieee754_log(x)
+ * Return the logrithm of x
+ *
+ * Method :
+ * 1. Argument Reduction: find k and f such that
+ * x = 2^k * (1+f),
+ * where sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ * 2. Approximation of log(1+f).
+ * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+ * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+ * = 2s + s*R
+ * We use a special Reme algorithm on [0,0.1716] to generate
+ * a polynomial of degree 14 to approximate R The maximum error
+ * of this polynomial approximation is bounded by 2**-58.45. In
+ * other words,
+ * 2 4 6 8 10 12 14
+ * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
+ * (the values of Lg1 to Lg7 are listed in the program)
+ * and
+ * | 2 14 | -58.45
+ * | Lg1*s +...+Lg7*s - R(z) | <= 2
+ * | |
+ * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+ * In order to guarantee error in log below 1ulp, we compute log
+ * by
+ * log(1+f) = f - s*(f - R) (if f is not too large)
+ * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
+ *
+ * 3. Finally, log(x) = k*ln2 + log(1+f).
+ * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
+ * Here ln2 is split into two floating point number:
+ * ln2_hi + ln2_lo,
+ * where n*ln2_hi is always exact for |n| < 2000.
+ *
+ * Special cases:
+ * log(x) is NaN with signal if x < 0 (including -INF) ;
+ * log(+INF) is +INF; log(0) is -INF with signal;
+ * log(NaN) is that NaN with no signal.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * 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.
+ */
+
+#include "math.h"
+#include "math_private.h"
+#include <errno.h>
+
+static const double
+ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
+ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
+two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
+Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
+Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
+Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
+Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
+Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
+Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
+Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+static const double zero = 0.0;
+
+double
+__ieee754_log(double x)
+{
+ double hfsq,f,s,z,R,w,t1,t2,dk;
+ int32_t k,hx,i,j;
+ u_int32_t lx;
+
+ EXTRACT_WORDS(hx,lx,x);
+
+ k=0;
+ if (hx < 0x00100000) { /* x < 2**-1022 */
+ if (((hx&0x7fffffff)|lx)==0)
+ return -two54/zero; /* log(+-0)=-inf */
+ if (hx<0) {
+ errno = EDOM;
+ return (x-x)/zero; /* log(-#) = NaN */
+ }
+ k -= 54; x *= two54; /* subnormal number, scale up x */
+ GET_HIGH_WORD(hx,x);
+ }
+ if (hx >= 0x7ff00000) return x+x;
+ k += (hx>>20)-1023;
+ hx &= 0x000fffff;
+ i = (hx+0x95f64)&0x100000;
+ SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
+ k += (i>>20);
+ f = x-1.0;
+ if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
+ if(f==zero) { if(k==0) return zero; else {dk=(double)k;
+ return dk*ln2_hi+dk*ln2_lo;}
+ }
+ R = f*f*(0.5-0.33333333333333333*f);
+ if(k==0) return f-R; else {dk=(double)k;
+ return dk*ln2_hi-((R-dk*ln2_lo)-f);}
+ }
+ s = f/(2.0+f);
+ dk = (double)k;
+ z = s*s;
+ i = hx-0x6147a;
+ w = z*z;
+ j = 0x6b851-hx;
+ t1= w*(Lg2+w*(Lg4+w*Lg6));
+ t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
+ i |= j;
+ R = t2+t1;
+ if(i>0) {
+ hfsq=0.5*f*f;
+ if(k==0) return f-(hfsq-s*(hfsq+R)); else
+ return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
+ } else {
+ if(k==0) return f-s*(f-R); else
+ return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
+ }
+}
diff --git a/StdLib/LibC/Math/e_log10.c b/StdLib/LibC/Math/e_log10.c new file mode 100644 index 0000000000..141dd6752a --- /dev/null +++ b/StdLib/LibC/Math/e_log10.c @@ -0,0 +1,106 @@ +/** @file
+ Compute the base 10 logrithm of x.
+
+ Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>
+ This program and the accompanying materials are licensed and made available under
+ the terms and conditions of the BSD License that accompanies this distribution.
+ The full text of the license may be found at
+ http://opensource.org/licenses/bsd-license.
+
+ THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
+ WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
+
+ * ====================================================
+ * 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.
+ * ====================================================
+
+ e_log10.c 5.1 93/09/24
+ NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp
+**/
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+
+/* __ieee754_log10(x)
+ * Return the base 10 logarithm of x
+ *
+ * Method :
+ * Let log10_2hi = leading 40 bits of log10(2) and
+ * log10_2lo = log10(2) - log10_2hi,
+ * ivln10 = 1/log(10) rounded.
+ * Then
+ * n = ilogb(x),
+ * if(n<0) n = n+1;
+ * x = scalbn(x,-n);
+ * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
+ *
+ * Note 1:
+ * To guarantee log10(10**n)=n, where 10**n is normal, the rounding
+ * mode must set to Round-to-Nearest.
+ * Note 2:
+ * [1/log(10)] rounded to 53 bits has error .198 ulps;
+ * log10 is monotonic at all binary break points.
+ *
+ * Special cases:
+ * log10(x) is NaN with signal if x < 0;
+ * log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
+ * log10(NaN) is that NaN with no signal;
+ * log10(10**N) = N for N=0,1,...,22.
+ *
+ * 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.
+ */
+
+#include "math.h"
+#include "math_private.h"
+#include <errno.h>
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // potential divide by 0 -- near line 80, (x-x)/zero is on purpose
+ #pragma warning ( disable : 4723 )
+#endif
+
+static const double
+two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
+ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
+log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
+log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
+
+static const double zero = 0.0;
+
+double
+__ieee754_log10(double x)
+{
+ double y,z;
+ int32_t i,k,hx;
+ u_int32_t lx;
+
+ EXTRACT_WORDS(hx,lx,x);
+
+ k=0;
+ if (hx < 0x00100000) { /* x < 2**-1022 */
+ if (((hx&0x7fffffff)|lx)==0)
+ return -two54/zero; /* log(+-0)=-inf */
+ if (hx<0) {
+ errno = EDOM;
+ return (x-x)/zero; /* log(-#) = NaN */
+ }
+ k -= 54; x *= two54; /* subnormal number, scale up x */
+ GET_HIGH_WORD(hx,x);
+ }
+ if (hx >= 0x7ff00000) return x+x;
+ k += (hx>>20)-1023;
+ i = ((u_int32_t)k&0x80000000)>>31;
+ hx = (hx&0x000fffff)|((0x3ff-i)<<20);
+ y = (double)(k+i);
+ SET_HIGH_WORD(x,hx);
+ z = y*log10_2lo + ivln10*__ieee754_log(x);
+ return z+y*log10_2hi;
+}
diff --git a/StdLib/LibC/Math/e_log2.c b/StdLib/LibC/Math/e_log2.c new file mode 100644 index 0000000000..5d15cd3b01 --- /dev/null +++ b/StdLib/LibC/Math/e_log2.c @@ -0,0 +1,85 @@ +
+/* @(#)e_log.c 1.3 95/01/18 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunSoft, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: e_log2.c,v 1.1 2005/07/21 12:55:58 christos Exp $");
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // potential divide by 0 -- near line 53, (x-x)/zero is on purpose
+ #pragma warning ( disable : 4723 )
+#endif
+
+static const double
+ln2 = 0.6931471805599452862268,
+two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
+Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
+Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
+Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
+Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
+Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
+Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
+Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
+
+static const double zero = 0.0;
+
+double
+__ieee754_log2(double x)
+{
+ double hfsq,f,s,z,R,w,t1,t2,dk;
+ int32_t k,hx,i,j;
+ u_int32_t lx;
+
+ EXTRACT_WORDS(hx,lx,x);
+
+ k=0;
+ if (hx < 0x00100000) { /* x < 2**-1022 */
+ if (((hx&0x7fffffff)|lx)==0)
+ return -two54/zero; /* log(+-0)=-inf */
+ if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
+ k -= 54; x *= two54; /* subnormal number, scale up x */
+ GET_HIGH_WORD(hx,x);
+ }
+ if (hx >= 0x7ff00000) return x+x;
+ k += (hx>>20)-1023;
+ hx &= 0x000fffff;
+ i = (hx+0x95f64)&0x100000;
+ SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
+ k += (i>>20);
+ f = x-1.0;
+ dk = (double)k;
+ if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
+ if (f==zero)
+ return (dk);
+ R = f*f*(0.5-0.33333333333333333*f);
+ return (dk-(R-f)/ln2);
+ }
+ s = f/(2.0+f);
+ z = s*s;
+ i = hx-0x6147a;
+ w = z*z;
+ j = 0x6b851-hx;
+ t1= w*(Lg2+w*(Lg4+w*Lg6));
+ t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
+ i |= j;
+ R = t2+t1;
+ if(i>0) {
+ hfsq=0.5*f*f;
+ return (dk-(hfsq-s*(hfsq+R)-f)/ln2);
+ } else
+ return (dk-((s*(f-R))-f)/ln2);
+}
diff --git a/StdLib/LibC/Math/e_pow.c b/StdLib/LibC/Math/e_pow.c new file mode 100644 index 0000000000..6d2286b41a --- /dev/null +++ b/StdLib/LibC/Math/e_pow.c @@ -0,0 +1,323 @@ +/** @file
+ Compute the base 10 logrithm of x.
+
+ Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>
+ This program and the accompanying materials are licensed and made available under
+ the terms and conditions of the BSD License that accompanies this distribution.
+ The full text of the license may be found at
+ http://opensource.org/licenses/bsd-license.
+
+ THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
+ WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
+
+ * ====================================================
+ * 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.
+ * ====================================================
+
+ e_pow.c 5.1 93/09/24
+ NetBSD: e_pow.c,v 1.13 2004/06/30 18:43:15 drochner Exp
+**/
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // C4723: potential divide by zero.
+ #pragma warning ( disable : 4723 )
+ // C4756: overflow in constant arithmetic
+ #pragma warning ( disable : 4756 )
+#endif
+
+/* __ieee754_pow(x,y) return x**y
+ *
+ * n
+ * Method: Let x = 2 * (1+f)
+ * 1. Compute and return log2(x) in two pieces:
+ * log2(x) = w1 + w2,
+ * where w1 has 53-24 = 29 bit trailing zeros.
+ * 2. Perform y*log2(x) = n+y' by simulating multi-precision
+ * arithmetic, where |y'|<=0.5.
+ * 3. Return x**y = 2**n*exp(y'*log2)
+ *
+ * Special cases:
+ * 1. (anything) ** 0 is 1
+ * 2. (anything) ** 1 is itself
+ * 3. (anything) ** NAN is NAN
+ * 4. NAN ** (anything except 0) is NAN
+ * 5. +-(|x| > 1) ** +INF is +INF
+ * 6. +-(|x| > 1) ** -INF is +0
+ * 7. +-(|x| < 1) ** +INF is +0
+ * 8. +-(|x| < 1) ** -INF is +INF
+ * 9. +-1 ** +-INF is NAN
+ * 10. +0 ** (+anything except 0, NAN) is +0
+ * 11. -0 ** (+anything except 0, NAN, odd integer) is +0
+ * 12. +0 ** (-anything except 0, NAN) is +INF
+ * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
+ * 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
+ * 15. +INF ** (+anything except 0,NAN) is +INF
+ * 16. +INF ** (-anything except 0,NAN) is +0
+ * 17. -INF ** (anything) = -0 ** (-anything)
+ * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
+ * 19. (-anything except 0 and inf) ** (non-integer) is NAN
+ *
+ * Accuracy:
+ * pow(x,y) returns x**y nearly rounded. In particular
+ * pow(integer,integer)
+ * always returns the correct integer provided it is
+ * representable.
+ *
+ * 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.
+ */
+
+#include "math.h"
+#include "math_private.h"
+#include <errno.h>
+
+static const double
+bp[] = {1.0, 1.5,},
+dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
+dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
+zero = 0.0,
+one = 1.0,
+two = 2.0,
+two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
+huge = 1.0e300,
+tiny = 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
+__ieee754_pow(double x, double y)
+{
+ double z,ax,z_h,z_l,p_h,p_l;
+ double y1,t1,t2,r,s,t,u,v,w;
+ int32_t i,j,k,yisint,n;
+ int32_t hx,hy,ix,iy;
+ u_int32_t 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;
+
+ /* +-NaN return x+y */
+ if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
+ iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
+ return x+y;
+
+ /* 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((u_int32_t)(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 y - y; /* inf**+-1 is NaN */
+ 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 __ieee754_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;
+ }
+ }
+
+ n = (hx>>31)+1;
+
+ /* (x<0)**(non-int) is NaN */
+ if((n|yisint)==0) {
+ errno = EDOM;
+ 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 huge */
+ if(iy>0x41e00000) { /* if |y| > 2**31 */
+ if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
+ if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
+ if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
+ }
+ /* over/underflow if x is not close to one */
+ if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
+ if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
+ /* now |1-x| is tiny <= 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 y1+y2 and compute (y1+y2)*(t1+t2) */
+ y1 = y;
+ SET_LOW_WORD(y1,0);
+ p_l = (y-y1)*t1+y*t2;
+ p_h = y1*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*huge*huge; /* overflow */
+ else {
+ if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
+ }
+ } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
+ if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
+ return s*tiny*tiny; /* underflow */
+ else {
+ if(p_l<=z-p_h) return s*tiny*tiny; /* 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 = scalbn(z,n); /* subnormal output */
+ else SET_HIGH_WORD(z,j);
+ return s*z;
+}
diff --git a/StdLib/LibC/Math/e_rem_pio2.c b/StdLib/LibC/Math/e_rem_pio2.c new file mode 100644 index 0000000000..7b06d1775f --- /dev/null +++ b/StdLib/LibC/Math/e_rem_pio2.c @@ -0,0 +1,169 @@ +/* @(#)e_rem_pio2.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: e_rem_pio2.c,v 1.11 2002/05/26 22:01:52 wiz Exp $");
+#endif
+
+/* __ieee754_rem_pio2(x,y)
+ *
+ * return the remainder of x rem pi/2 in y[0]+y[1]
+ * use __kernel_rem_pio2()
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+/*
+ * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
+ */
+static const int32_t two_over_pi[] = {
+0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
+0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
+0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
+0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
+0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
+0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
+0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
+0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
+0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
+0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
+0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
+};
+
+static const int32_t npio2_hw[] = {
+0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
+0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
+0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
+0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
+0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
+0x404858EB, 0x404921FB,
+};
+
+/*
+ * invpio2: 53 bits of 2/pi
+ * pio2_1: first 33 bit of pi/2
+ * pio2_1t: pi/2 - pio2_1
+ * pio2_2: second 33 bit of pi/2
+ * pio2_2t: pi/2 - (pio2_1+pio2_2)
+ * pio2_3: third 33 bit of pi/2
+ * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
+ */
+
+static const double
+zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
+half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
+invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
+pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
+pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
+pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
+pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
+pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
+
+int32_t
+__ieee754_rem_pio2(double x, double *y)
+{
+ double z,w,t,r,fn;
+ double tx[3];
+ int32_t e0,i,j,nx,n,ix,hx;
+ u_int32_t low;
+
+ z = 0;
+ GET_HIGH_WORD(hx,x); /* high word of x */
+ ix = hx&0x7fffffff;
+ if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
+ {y[0] = x; y[1] = 0; return 0;}
+ if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
+ if(hx>0) {
+ z = x - pio2_1;
+ if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
+ y[0] = z - pio2_1t;
+ y[1] = (z-y[0])-pio2_1t;
+ } else { /* near pi/2, use 33+33+53 bit pi */
+ z -= pio2_2;
+ y[0] = z - pio2_2t;
+ y[1] = (z-y[0])-pio2_2t;
+ }
+ return 1;
+ } else { /* negative x */
+ z = x + pio2_1;
+ if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
+ y[0] = z + pio2_1t;
+ y[1] = (z-y[0])+pio2_1t;
+ } else { /* near pi/2, use 33+33+53 bit pi */
+ z += pio2_2;
+ y[0] = z + pio2_2t;
+ y[1] = (z-y[0])+pio2_2t;
+ }
+ return -1;
+ }
+ }
+ if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
+ t = fabs(x);
+ n = (int32_t) (t*invpio2+half);
+ fn = (double)n;
+ r = t-fn*pio2_1;
+ w = fn*pio2_1t; /* 1st round good to 85 bit */
+ if(n<32&&ix!=npio2_hw[n-1]) {
+ y[0] = r-w; /* quick check no cancellation */
+ } else {
+ u_int32_t high;
+ j = ix>>20;
+ y[0] = r-w;
+ GET_HIGH_WORD(high,y[0]);
+ i = j-((high>>20)&0x7ff);
+ if(i>16) { /* 2nd iteration needed, good to 118 */
+ t = r;
+ w = fn*pio2_2;
+ r = t-w;
+ w = fn*pio2_2t-((t-r)-w);
+ y[0] = r-w;
+ GET_HIGH_WORD(high,y[0]);
+ i = j-((high>>20)&0x7ff);
+ if(i>49) { /* 3rd iteration need, 151 bits acc */
+ t = r; /* will cover all possible cases */
+ w = fn*pio2_3;
+ r = t-w;
+ w = fn*pio2_3t-((t-r)-w);
+ y[0] = r-w;
+ }
+ }
+ }
+ y[1] = (r-y[0])-w;
+ if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
+ else return n;
+ }
+ /*
+ * all other (large) arguments
+ */
+ if(ix>=0x7ff00000) { /* x is inf or NaN */
+ y[0]=y[1]=x-x; return 0;
+ }
+ /* set z = scalbn(|x|,ilogb(x)-23) */
+ GET_LOW_WORD(low,x);
+ SET_LOW_WORD(z,low);
+ e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
+ SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
+ for(i=0;i<2;i++) {
+ tx[i] = (double)((int32_t)(z));
+ z = (z-tx[i])*two24;
+ }
+ tx[2] = z;
+ nx = 3;
+ while(tx[nx-1]==zero) nx--; /* skip zero term */
+ n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
+ if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
+ return n;
+}
diff --git a/StdLib/LibC/Math/e_sinh.c b/StdLib/LibC/Math/e_sinh.c new file mode 100644 index 0000000000..421b515cd4 --- /dev/null +++ b/StdLib/LibC/Math/e_sinh.c @@ -0,0 +1,79 @@ +/* @(#)e_sinh.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: e_sinh.c,v 1.11 2002/05/26 22:01:52 wiz Exp $");
+#endif
+
+#include "math.h"
+#include "math_private.h"
+
+/* __ieee754_sinh(x)
+ * Method :
+ * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
+ * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
+ * 2.
+ * E + E/(E+1)
+ * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
+ * 2
+ *
+ * 22 <= x <= lnovft : sinh(x) := exp(x)/2
+ * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
+ * ln2ovft < x : sinh(x) := x*shuge (overflow)
+ *
+ * Special cases:
+ * sinh(x) is |x| if x is +INF, -INF, or NaN.
+ * only sinh(0)=0 is exact for finite x.
+ */
+
+static const double one = 1.0, shuge = 1.0e307;
+
+double
+__ieee754_sinh(double x)
+{
+ double t,w,h;
+ int32_t ix,jx;
+ u_int32_t lx;
+
+ /* High word of |x|. */
+ GET_HIGH_WORD(jx,x);
+ ix = jx&0x7fffffff;
+
+ /* x is INF or NaN */
+ if(ix>=0x7ff00000) return x+x;
+
+ h = 0.5;
+ if (jx<0) h = -h;
+ /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
+ if (ix < 0x40360000) { /* |x|<22 */
+ if (ix<0x3e300000) /* |x|<2**-28 */
+ if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
+ t = expm1(fabs(x));
+ if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
+ return h*(t+t/(t+one));
+ }
+
+ /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
+ if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x));
+
+ /* |x| in [log(maxdouble), overflowthresold] */
+ GET_LOW_WORD(lx,x);
+ if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
+ w = __ieee754_exp(0.5*fabs(x));
+ t = h*w;
+ return t*w;
+ }
+
+ /* |x| > overflowthresold, sinh(x) overflow */
+ return x*shuge;
+}
diff --git a/StdLib/LibC/Math/e_sqrt.c b/StdLib/LibC/Math/e_sqrt.c new file mode 100644 index 0000000000..2a772f60b4 --- /dev/null +++ b/StdLib/LibC/Math/e_sqrt.c @@ -0,0 +1,464 @@ +/** @file
+ Compute the logrithm of x.
+
+ Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>
+ This program and the accompanying materials are licensed and made available under
+ the terms and conditions of the BSD License that accompanies this distribution.
+ The full text of the license may be found at
+ http://opensource.org/licenses/bsd-license.
+
+ THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
+ WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
+
+ * ====================================================
+ * 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.
+ * ====================================================
+
+ e_sqrt.c 5.1 93/09/24
+ NetBSD: e_sqrt.c,v 1.12 2002/05/26 22:01:52 wiz Exp
+**/
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+
+#include <errno.h>
+#include "math.h"
+#include "math_private.h"
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+// potential divide by 0 -- near line 129, (x-x)/(x-x) is on purpose
+#pragma warning ( disable : 4723 )
+#endif
+
+/* __ieee754_sqrt(x)
+ * Return correctly rounded sqrt.
+ * ------------------------------------------
+ * | Use the hardware sqrt if you have one |
+ * ------------------------------------------
+ * Method:
+ * Bit by bit method using integer arithmetic. (Slow, but portable)
+ * 1. Normalization
+ * Scale x to y in [1,4) with even powers of 2:
+ * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then
+ * sqrt(x) = 2^k * sqrt(y)
+ * 2. Bit by bit computation
+ * Let q = sqrt(y) truncated to i bit after binary point (q = 1),
+ * i 0
+ * i+1 2
+ * s = 2*q , and y = 2 * ( y - q ). (1)
+ * i i i i
+ *
+ * To compute q from q , one checks whether
+ * i+1 i
+ *
+ * -(i+1) 2
+ * (q + 2 ) <= y. (2)
+ * i
+ * -(i+1)
+ * If (2) is false, then q = q ; otherwise q = q + 2 .
+ * i+1 i i+1 i
+ *
+ * With some algebric manipulation, it is not difficult to see
+ * that (2) is equivalent to
+ * -(i+1)
+ * s + 2 <= y (3)
+ * i i
+ *
+ * The advantage of (3) is that s and y can be computed by
+ * i i
+ * the following recurrence formula:
+ * if (3) is false
+ *
+ * s = s , y = y ; (4)
+ * i+1 i i+1 i
+ *
+ * otherwise,
+ * -i -(i+1)
+ * s = s + 2 , y = y - s - 2 (5)
+ * i+1 i i+1 i i
+ *
+ * One may easily use induction to prove (4) and (5).
+ * Note. Since the left hand side of (3) contain only i+2 bits,
+ * it does not necessary to do a full (53-bit) comparison
+ * in (3).
+ * 3. Final rounding
+ * After generating the 53 bits result, we compute one more bit.
+ * Together with the remainder, we can decide whether the
+ * result is exact, bigger than 1/2ulp, or less than 1/2ulp
+ * (it will never equal to 1/2ulp).
+ * The rounding mode can be detected by checking whether
+ * huge + tiny is equal to huge, and whether huge - tiny is
+ * equal to huge for some floating point number "huge" and "tiny".
+ *
+ * Special cases:
+ * sqrt(+-0) = +-0 ... exact
+ * sqrt(inf) = inf
+ * sqrt(-ve) = NaN ... with invalid signal
+ * sqrt(NaN) = NaN ... with invalid signal for signaling NaN
+ *
+ * Other methods : see the appended file at the end of the program below.
+ *---------------
+ */
+
+static const double one = 1.0, tiny=1.0e-300;
+
+double
+__ieee754_sqrt(double x)
+{
+ double z;
+ int32_t sign = (int)0x80000000;
+ int32_t ix0,s0,q,m,t,i;
+ u_int32_t r,t1,s1,ix1,q1;
+
+ EXTRACT_WORDS(ix0,ix1,x);
+
+ /* take care of Inf and NaN */
+ if((ix0&0x7ff00000)==0x7ff00000) {
+ return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
+ sqrt(-inf)=sNaN */
+ }
+ /* take care of zero */
+ if(ix0<=0) {
+ if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
+ else if(ix0<0) {
+ errno = EDOM;
+ return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
+ }
+ }
+ /* normalize x */
+ m = (ix0>>20);
+ if(m==0) { /* subnormal x */
+ while(ix0==0) {
+ m -= 21;
+ ix0 |= (ix1>>11); ix1 <<= 21;
+ }
+ for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
+ m -= i-1;
+ ix0 |= (ix1>>(32-i));
+ ix1 <<= i;
+ }
+ m -= 1023; /* unbias exponent */
+ ix0 = (ix0&0x000fffff)|0x00100000;
+ if(m&1){ /* odd m, double x to make it even */
+ ix0 += ix0 + ((ix1&sign)>>31);
+ ix1 += ix1;
+ }
+ m >>= 1; /* m = [m/2] */
+
+ /* generate sqrt(x) bit by bit */
+ ix0 += ix0 + ((ix1&sign)>>31);
+ ix1 += ix1;
+ q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
+ r = 0x00200000; /* r = moving bit from right to left */
+
+ while(r!=0) {
+ t = s0+r;
+ if(t<=ix0) {
+ s0 = t+r;
+ ix0 -= t;
+ q += r;
+ }
+ ix0 += ix0 + ((ix1&sign)>>31);
+ ix1 += ix1;
+ r>>=1;
+ }
+
+ r = sign;
+ while(r!=0) {
+ t1 = s1+r;
+ t = s0;
+ if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
+ s1 = t1+r;
+ if(((t1&sign)==(u_int32_t)sign)&&(s1&sign)==0) s0 += 1;
+ ix0 -= t;
+ if (ix1 < t1) ix0 -= 1;
+ ix1 -= t1;
+ q1 += r;
+ }
+ ix0 += ix0 + ((ix1&sign)>>31);
+ ix1 += ix1;
+ r>>=1;
+ }
+
+ /* use floating add to find out rounding direction */
+ if((ix0|ix1)!=0) {
+ z = one-tiny; /* trigger inexact flag */
+ if (z>=one) {
+ z = one+tiny;
+ if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;}
+ else if (z>one) {
+ if (q1==(u_int32_t)0xfffffffe) q+=1;
+ q1+=2;
+ } else
+ q1 += (q1&1);
+ }
+ }
+ ix0 = (q>>1)+0x3fe00000;
+ ix1 = q1>>1;
+ if ((q&1)==1) ix1 |= sign;
+ ix0 += (m <<20);
+ INSERT_WORDS(z,ix0,ix1);
+ return z;
+}
+
+/*
+Other methods (use floating-point arithmetic)
+-------------
+(This is a copy of a drafted paper by Prof W. Kahan
+and K.C. Ng, written in May, 1986)
+
+ Two algorithms are given here to implement sqrt(x)
+ (IEEE double precision arithmetic) in software.
+ Both supply sqrt(x) correctly rounded. The first algorithm (in
+ Section A) uses newton iterations and involves four divisions.
+ The second one uses reciproot iterations to avoid division, but
+ requires more multiplications. Both algorithms need the ability
+ to chop results of arithmetic operations instead of round them,
+ and the INEXACT flag to indicate when an arithmetic operation
+ is executed exactly with no roundoff error, all part of the
+ standard (IEEE 754-1985). The ability to perform shift, add,
+ subtract and logical AND operations upon 32-bit words is needed
+ too, though not part of the standard.
+
+A. sqrt(x) by Newton Iteration
+
+ (1) Initial approximation
+
+ Let x0 and x1 be the leading and the trailing 32-bit words of
+ a floating point number x (in IEEE double format) respectively
+
+ 1 11 52 ...widths
+ ------------------------------------------------------
+ x: |s| e | f |
+ ------------------------------------------------------
+ msb lsb msb lsb ...order
+
+
+ ------------------------ ------------------------
+ x0: |s| e | f1 | x1: | f2 |
+ ------------------------ ------------------------
+
+ By performing shifts and subtracts on x0 and x1 (both regarded
+ as integers), we obtain an 8-bit approximation of sqrt(x) as
+ follows.
+
+ k := (x0>>1) + 0x1ff80000;
+ y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits
+ Here k is a 32-bit integer and T1[] is an integer array containing
+ correction terms. Now magically the floating value of y (y's
+ leading 32-bit word is y0, the value of its trailing word is 0)
+ approximates sqrt(x) to almost 8-bit.
+
+ Value of T1:
+ static int T1[32]= {
+ 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592,
+ 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215,
+ 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581,
+ 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,};
+
+ (2) Iterative refinement
+
+ Apply Heron's rule three times to y, we have y approximates
+ sqrt(x) to within 1 ulp (Unit in the Last Place):
+
+ y := (y+x/y)/2 ... almost 17 sig. bits
+ y := (y+x/y)/2 ... almost 35 sig. bits
+ y := y-(y-x/y)/2 ... within 1 ulp
+
+
+ Remark 1.
+ Another way to improve y to within 1 ulp is:
+
+ y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x)
+ y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x)
+
+ 2
+ (x-y )*y
+ y := y + 2* ---------- ...within 1 ulp
+ 2
+ 3y + x
+
+
+ This formula has one division fewer than the one above; however,
+ it requires more multiplications and additions. Also x must be
+ scaled in advance to avoid spurious overflow in evaluating the
+ expression 3y*y+x. Hence it is not recommended uless division
+ is slow. If division is very slow, then one should use the
+ reciproot algorithm given in section B.
+
+ (3) Final adjustment
+
+ By twiddling y's last bit it is possible to force y to be
+ correctly rounded according to the prevailing rounding mode
+ as follows. Let r and i be copies of the rounding mode and
+ inexact flag before entering the square root program. Also we
+ use the expression y+-ulp for the next representable floating
+ numbers (up and down) of y. Note that y+-ulp = either fixed
+ point y+-1, or multiply y by nextafter(1,+-inf) in chopped
+ mode.
+
+ I := FALSE; ... reset INEXACT flag I
+ R := RZ; ... set rounding mode to round-toward-zero
+ z := x/y; ... chopped quotient, possibly inexact
+ If(not I) then { ... if the quotient is exact
+ if(z=y) {
+ I := i; ... restore inexact flag
+ R := r; ... restore rounded mode
+ return sqrt(x):=y.
+ } else {
+ z := z - ulp; ... special rounding
+ }
+ }
+ i := TRUE; ... sqrt(x) is inexact
+ If (r=RN) then z=z+ulp ... rounded-to-nearest
+ If (r=RP) then { ... round-toward-+inf
+ y = y+ulp; z=z+ulp;
+ }
+ y := y+z; ... chopped sum
+ y0:=y0-0x00100000; ... y := y/2 is correctly rounded.
+ I := i; ... restore inexact flag
+ R := r; ... restore rounded mode
+ return sqrt(x):=y.
+
+ (4) Special cases
+
+ Square root of +inf, +-0, or NaN is itself;
+ Square root of a negative number is NaN with invalid signal.
+
+
+B. sqrt(x) by Reciproot Iteration
+
+ (1) Initial approximation
+
+ Let x0 and x1 be the leading and the trailing 32-bit words of
+ a floating point number x (in IEEE double format) respectively
+ (see section A). By performing shifs and subtracts on x0 and y0,
+ we obtain a 7.8-bit approximation of 1/sqrt(x) as follows.
+
+ k := 0x5fe80000 - (x0>>1);
+ y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits
+
+ Here k is a 32-bit integer and T2[] is an integer array
+ containing correction terms. Now magically the floating
+ value of y (y's leading 32-bit word is y0, the value of
+ its trailing word y1 is set to zero) approximates 1/sqrt(x)
+ to almost 7.8-bit.
+
+ Value of T2:
+ static int T2[64]= {
+ 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866,
+ 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f,
+ 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d,
+ 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0,
+ 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989,
+ 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd,
+ 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e,
+ 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,};
+
+ (2) Iterative refinement
+
+ Apply Reciproot iteration three times to y and multiply the
+ result by x to get an approximation z that matches sqrt(x)
+ to about 1 ulp. To be exact, we will have
+ -1ulp < sqrt(x)-z<1.0625ulp.
+
+ ... set rounding mode to Round-to-nearest
+ y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x)
+ y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x)
+ ... special arrangement for better accuracy
+ z := x*y ... 29 bits to sqrt(x), with z*y<1
+ z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x)
+
+ Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that
+ (a) the term z*y in the final iteration is always less than 1;
+ (b) the error in the final result is biased upward so that
+ -1 ulp < sqrt(x) - z < 1.0625 ulp
+ instead of |sqrt(x)-z|<1.03125ulp.
+
+ (3) Final adjustment
+
+ By twiddling y's last bit it is possible to force y to be
+ correctly rounded according to the prevailing rounding mode
+ as follows. Let r and i be copies of the rounding mode and
+ inexact flag before entering the square root program. Also we
+ use the expression y+-ulp for the next representable floating
+ numbers (up and down) of y. Note that y+-ulp = either fixed
+ point y+-1, or multiply y by nextafter(1,+-inf) in chopped
+ mode.
+
+ R := RZ; ... set rounding mode to round-toward-zero
+ switch(r) {
+ case RN: ... round-to-nearest
+ if(x<= z*(z-ulp)...chopped) z = z - ulp; else
+ if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp;
+ break;
+ case RZ:case RM: ... round-to-zero or round-to--inf
+ R:=RP; ... reset rounding mod to round-to-+inf
+ if(x<z*z ... rounded up) z = z - ulp; else
+ if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp;
+ break;
+ case RP: ... round-to-+inf
+ if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else
+ if(x>z*z ...chopped) z = z+ulp;
+ break;
+ }
+
+ Remark 3. The above comparisons can be done in fixed point. For
+ example, to compare x and w=z*z chopped, it suffices to compare
+ x1 and w1 (the trailing parts of x and w), regarding them as
+ two's complement integers.
+
+ ...Is z an exact square root?
+ To determine whether z is an exact square root of x, let z1 be the
+ trailing part of z, and also let x0 and x1 be the leading and
+ trailing parts of x.
+
+ If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0
+ I := 1; ... Raise Inexact flag: z is not exact
+ else {
+ j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2
+ k := z1 >> 26; ... get z's 25-th and 26-th
+ fraction bits
+ I := i or (k&j) or ((k&(j+j+1))!=(x1&3));
+ }
+ R:= r ... restore rounded mode
+ return sqrt(x):=z.
+
+ If multiplication is cheaper than the foregoing red tape, the
+ Inexact flag can be evaluated by
+
+ I := i;
+ I := (z*z!=x) or I.
+
+ Note that z*z can overwrite I; this value must be sensed if it is
+ True.
+
+ Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be
+ zero.
+
+ --------------------
+ z1: | f2 |
+ --------------------
+ bit 31 bit 0
+
+ Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd
+ or even of logb(x) have the following relations:
+
+ -------------------------------------------------
+ bit 27,26 of z1 bit 1,0 of x1 logb(x)
+ -------------------------------------------------
+ 00 00 odd and even
+ 01 01 even
+ 10 10 odd
+ 10 00 even
+ 11 01 even
+ -------------------------------------------------
+
+ (4) Special cases (see (4) of Section A).
+
+ */
+
diff --git a/StdLib/LibC/Math/k_cos.c b/StdLib/LibC/Math/k_cos.c new file mode 100644 index 0000000000..e1746a11d3 --- /dev/null +++ b/StdLib/LibC/Math/k_cos.c @@ -0,0 +1,89 @@ +/* @(#)k_cos.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: k_cos.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");
+#endif
+
+/*
+ * __kernel_cos( x, y )
+ * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ *
+ * Algorithm
+ * 1. Since cos(-x) = cos(x), we need only to consider positive x.
+ * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
+ * 3. cos(x) is approximated by a polynomial of degree 14 on
+ * [0,pi/4]
+ * 4 14
+ * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
+ * where the remez error is
+ *
+ * | 2 4 6 8 10 12 14 | -58
+ * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
+ * | |
+ *
+ * 4 6 8 10 12 14
+ * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
+ * cos(x) = 1 - x*x/2 + r
+ * since cos(x+y) ~ cos(x) - sin(x)*y
+ * ~ cos(x) - x*y,
+ * a correction term is necessary in cos(x) and hence
+ * cos(x+y) = 1 - (x*x/2 - (r - x*y))
+ * For better accuracy when x > 0.3, let qx = |x|/4 with
+ * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
+ * Then
+ * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
+ * Note that 1-qx and (x*x/2-qx) is EXACT here, and the
+ * magnitude of the latter is at least a quarter of x*x/2,
+ * thus, reducing the rounding error in the subtraction.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
+C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
+C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
+C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
+C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
+C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
+C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
+
+double
+__kernel_cos(double x, double y)
+{
+ double a,hz,z,r,qx;
+ int32_t ix;
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff; /* ix = |x|'s high word*/
+ if(ix<0x3e400000) { /* if x < 2**27 */
+ if(((int)x)==0) return one; /* generate inexact */
+ }
+ z = x*x;
+ r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
+ if(ix < 0x3FD33333) /* if |x| < 0.3 */
+ return one - (0.5*z - (z*r - x*y));
+ else {
+ if(ix > 0x3fe90000) { /* x > 0.78125 */
+ qx = 0.28125;
+ } else {
+ INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */
+ }
+ hz = 0.5*z-qx;
+ a = one-qx;
+ return a - (hz - (z*r-x*y));
+ }
+}
diff --git a/StdLib/LibC/Math/k_rem_pio2.c b/StdLib/LibC/Math/k_rem_pio2.c new file mode 100644 index 0000000000..af2857778d --- /dev/null +++ b/StdLib/LibC/Math/k_rem_pio2.c @@ -0,0 +1,305 @@ +/* @(#)k_rem_pio2.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: k_rem_pio2.c,v 1.11 2003/01/04 23:43:03 wiz Exp $");
+#endif
+
+/*
+ * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
+ * double x[],y[]; int e0,nx,prec; int ipio2[];
+ *
+ * __kernel_rem_pio2 return the last three digits of N with
+ * y = x - N*pi/2
+ * so that |y| < pi/2.
+ *
+ * The method is to compute the integer (mod 8) and fraction parts of
+ * (2/pi)*x without doing the full multiplication. In general we
+ * skip the part of the product that are known to be a huge integer (
+ * more accurately, = 0 mod 8 ). Thus the number of operations are
+ * independent of the exponent of the input.
+ *
+ * (2/pi) is represented by an array of 24-bit integers in ipio2[].
+ *
+ * Input parameters:
+ * x[] The input value (must be positive) is broken into nx
+ * pieces of 24-bit integers in double precision format.
+ * x[i] will be the i-th 24 bit of x. The scaled exponent
+ * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
+ * match x's up to 24 bits.
+ *
+ * Example of breaking a double positive z into x[0]+x[1]+x[2]:
+ * e0 = ilogb(z)-23
+ * z = scalbn(z,-e0)
+ * for i = 0,1,2
+ * x[i] = floor(z)
+ * z = (z-x[i])*2**24
+ *
+ *
+ * y[] output result in an array of double precision numbers.
+ * The dimension of y[] is:
+ * 24-bit precision 1
+ * 53-bit precision 2
+ * 64-bit precision 2
+ * 113-bit precision 3
+ * The actual value is the sum of them. Thus for 113-bit
+ * precison, one may have to do something like:
+ *
+ * long double t,w,r_head, r_tail;
+ * t = (long double)y[2] + (long double)y[1];
+ * w = (long double)y[0];
+ * r_head = t+w;
+ * r_tail = w - (r_head - t);
+ *
+ * e0 The exponent of x[0]
+ *
+ * nx dimension of x[]
+ *
+ * prec an integer indicating the precision:
+ * 0 24 bits (single)
+ * 1 53 bits (double)
+ * 2 64 bits (extended)
+ * 3 113 bits (quad)
+ *
+ * ipio2[]
+ * integer array, contains the (24*i)-th to (24*i+23)-th
+ * bit of 2/pi after binary point. The corresponding
+ * floating value is
+ *
+ * ipio2[i] * 2^(-24(i+1)).
+ *
+ * External function:
+ * double scalbn(), floor();
+ *
+ *
+ * Here is the description of some local variables:
+ *
+ * jk jk+1 is the initial number of terms of ipio2[] needed
+ * in the computation. The recommended value is 2,3,4,
+ * 6 for single, double, extended,and quad.
+ *
+ * jz local integer variable indicating the number of
+ * terms of ipio2[] used.
+ *
+ * jx nx - 1
+ *
+ * jv index for pointing to the suitable ipio2[] for the
+ * computation. In general, we want
+ * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
+ * is an integer. Thus
+ * e0-3-24*jv >= 0 or (e0-3)/24 >= jv
+ * Hence jv = max(0,(e0-3)/24).
+ *
+ * jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
+ *
+ * q[] double array with integral value, representing the
+ * 24-bits chunk of the product of x and 2/pi.
+ *
+ * q0 the corresponding exponent of q[0]. Note that the
+ * exponent for q[i] would be q0-24*i.
+ *
+ * PIo2[] double precision array, obtained by cutting pi/2
+ * into 24 bits chunks.
+ *
+ * f[] ipio2[] in floating point
+ *
+ * iq[] integer array by breaking up q[] in 24-bits chunk.
+ *
+ * fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
+ *
+ * ih integer. If >0 it indicates q[] is >= 0.5, hence
+ * it also indicates the *sign* of the result.
+ *
+ */
+
+
+/*
+ * 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.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
+
+static const double PIo2[] = {
+ 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
+ 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
+ 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
+ 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
+ 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
+ 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
+ 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
+ 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
+};
+
+static const double
+zero = 0.0,
+one = 1.0,
+two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
+twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
+
+int
+__kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2)
+{
+ int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
+ double z,fw,f[20],fq[20],q[20];
+
+ /* initialize jk*/
+ jk = init_jk[prec];
+ jp = jk;
+
+ /* determine jx,jv,q0, note that 3>q0 */
+ jx = nx-1;
+ jv = (e0-3)/24; if(jv<0) jv=0;
+ q0 = e0-24*(jv+1);
+
+ /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
+ j = jv-jx; m = jx+jk;
+ for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
+
+ /* compute q[0],q[1],...q[jk] */
+ for (i=0;i<=jk;i++) {
+ for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
+ }
+
+ jz = jk;
+recompute:
+ /* distill q[] into iq[] reversingly */
+ for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
+ fw = (double)((int32_t)(twon24* z));
+ iq[i] = (int32_t)(z-two24*fw);
+ z = q[j-1]+fw;
+ }
+
+ /* compute n */
+ z = scalbn(z,q0); /* actual value of z */
+ z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
+ n = (int32_t) z;
+ z -= (double)n;
+ ih = 0;
+ if(q0>0) { /* need iq[jz-1] to determine n */
+ i = (iq[jz-1]>>(24-q0)); n += i;
+ iq[jz-1] -= i<<(24-q0);
+ ih = iq[jz-1]>>(23-q0);
+ }
+ else if(q0==0) ih = iq[jz-1]>>23;
+ else if(z>=0.5) ih=2;
+
+ if(ih>0) { /* q > 0.5 */
+ n += 1; carry = 0;
+ for(i=0;i<jz ;i++) { /* compute 1-q */
+ j = iq[i];
+ if(carry==0) {
+ if(j!=0) {
+ carry = 1; iq[i] = 0x1000000- j;
+ }
+ } else iq[i] = 0xffffff - j;
+ }
+ if(q0>0) { /* rare case: chance is 1 in 12 */
+ switch(q0) {
+ case 1:
+ iq[jz-1] &= 0x7fffff; break;
+ case 2:
+ iq[jz-1] &= 0x3fffff; break;
+ }
+ }
+ if(ih==2) {
+ z = one - z;
+ if(carry!=0) z -= scalbn(one,q0);
+ }
+ }
+
+ /* check if recomputation is needed */
+ if(z==zero) {
+ j = 0;
+ for (i=jz-1;i>=jk;i--) j |= iq[i];
+ if(j==0) { /* need recomputation */
+ for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
+
+ for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
+ f[jx+i] = (double) ipio2[jv+i];
+ for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
+ q[i] = fw;
+ }
+ jz += k;
+ goto recompute;
+ }
+ }
+
+ /* chop off zero terms */
+ if(z==0.0) {
+ jz -= 1; q0 -= 24;
+ while(iq[jz]==0) { jz--; q0-=24;}
+ } else { /* break z into 24-bit if necessary */
+ z = scalbn(z,-q0);
+ if(z>=two24) {
+ fw = (double)((int32_t)(twon24*z));
+ iq[jz] = (int32_t)(z-two24*fw);
+ jz += 1; q0 += 24;
+ iq[jz] = (int32_t) fw;
+ } else iq[jz] = (int32_t) z ;
+ }
+
+ /* convert integer "bit" chunk to floating-point value */
+ fw = scalbn(one,q0);
+ for(i=jz;i>=0;i--) {
+ q[i] = fw*(double)iq[i]; fw*=twon24;
+ }
+
+ /* compute PIo2[0,...,jp]*q[jz,...,0] */
+ for(i=jz;i>=0;i--) {
+ for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
+ fq[jz-i] = fw;
+ }
+
+ /* compress fq[] into y[] */
+ switch(prec) {
+ case 0:
+ fw = 0.0;
+ for (i=jz;i>=0;i--) fw += fq[i];
+ y[0] = (ih==0)? fw: -fw;
+ break;
+ case 1:
+ case 2:
+ fw = 0.0;
+ for (i=jz;i>=0;i--) fw += fq[i];
+ y[0] = (ih==0)? fw: -fw;
+ fw = fq[0]-fw;
+ for (i=1;i<=jz;i++) fw += fq[i];
+ y[1] = (ih==0)? fw: -fw;
+ break;
+ case 3: /* painful */
+ for (i=jz;i>0;i--) {
+ fw = fq[i-1]+fq[i];
+ fq[i] += fq[i-1]-fw;
+ fq[i-1] = fw;
+ }
+ for (i=jz;i>1;i--) {
+ fw = fq[i-1]+fq[i];
+ fq[i] += fq[i-1]-fw;
+ fq[i-1] = fw;
+ }
+ for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
+ if(ih==0) {
+ y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
+ } else {
+ y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
+ }
+ }
+ return n&7;
+}
diff --git a/StdLib/LibC/Math/k_sin.c b/StdLib/LibC/Math/k_sin.c new file mode 100644 index 0000000000..9e4c22d03d --- /dev/null +++ b/StdLib/LibC/Math/k_sin.c @@ -0,0 +1,72 @@ +/* @(#)k_sin.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: k_sin.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");
+#endif
+
+/* __kernel_sin( x, y, iy)
+ * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
+ *
+ * Algorithm
+ * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
+ * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
+ * 3. sin(x) is approximated by a polynomial of degree 13 on
+ * [0,pi/4]
+ * 3 13
+ * sin(x) ~ x + S1*x + ... + S6*x
+ * where
+ *
+ * |sin(x) 2 4 6 8 10 12 | -58
+ * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
+ * | x |
+ *
+ * 4. sin(x+y) = sin(x) + sin'(x')*y
+ * ~ sin(x) + (1-x*x/2)*y
+ * For better accuracy, let
+ * 3 2 2 2 2
+ * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
+ * then 3 2
+ * sin(x) = x + (S1*x + (x *(r-y/2)+y))
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
+S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
+S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
+S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
+S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
+S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
+S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
+
+double
+__kernel_sin(double x, double y, int iy)
+{
+ double z,r,v;
+ int32_t ix;
+ GET_HIGH_WORD(ix,x);
+ ix &= 0x7fffffff; /* high word of x */
+ if(ix<0x3e400000) /* |x| < 2**-27 */
+ {if((int)x==0) return x;} /* generate inexact */
+ z = x*x;
+ v = z*x;
+ r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
+ if(iy==0) return x+v*(S1+z*r);
+ else return x-((z*(half*y-v*r)-y)-v*S1);
+}
diff --git a/StdLib/LibC/Math/k_tan.c b/StdLib/LibC/Math/k_tan.c new file mode 100644 index 0000000000..ad83a21d3b --- /dev/null +++ b/StdLib/LibC/Math/k_tan.c @@ -0,0 +1,156 @@ +/* @(#)k_tan.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: k_tan.c,v 1.12 2004/07/22 18:24:09 drochner Exp $");
+#endif
+
+/* __kernel_tan( x, y, k )
+ * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ * Input k indicates whether tan (if k=1) or
+ * -1/tan (if k= -1) is returned.
+ *
+ * Algorithm
+ * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
+ * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
+ * 3. tan(x) is approximated by a odd polynomial of degree 27 on
+ * [0,0.67434]
+ * 3 27
+ * tan(x) ~ x + T1*x + ... + T13*x
+ * where
+ *
+ * |tan(x) 2 4 26 | -59.2
+ * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
+ * | x |
+ *
+ * Note: tan(x+y) = tan(x) + tan'(x)*y
+ * ~ tan(x) + (1+x*x)*y
+ * Therefore, for better accuracy in computing tan(x+y), let
+ * 3 2 2 2 2
+ * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
+ * then
+ * 3 2
+ * tan(x+y) = x + (T1*x + (x *(r+y)+y))
+ *
+ * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
+ * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
+ * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double xxx[] = {
+ 3.33333333333334091986e-01, /* 3FD55555, 55555563 */
+ 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */
+ 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */
+ 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */
+ 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */
+ 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */
+ 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */
+ 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */
+ 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */
+ 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */
+ 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */
+ -1.85586374855275456654e-05, /* BEF375CB, DB605373 */
+ 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */
+/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
+/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
+/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */
+};
+#define one xxx[13]
+#define pio4 xxx[14]
+#define pio4lo xxx[15]
+#define T xxx
+
+double
+__kernel_tan(double x, double y, int iy)
+{
+ double z, r, v, w, s;
+ int32_t ix, hx;
+
+ GET_HIGH_WORD(hx, x); /* high word of x */
+ ix = hx & 0x7fffffff; /* high word of |x| */
+ if (ix < 0x3e300000) { /* x < 2**-28 */
+ if ((int) x == 0) { /* generate inexact */
+ u_int32_t low;
+ GET_LOW_WORD(low, x);
+ if(((ix | low) | (iy + 1)) == 0)
+ return one / fabs(x);
+ else {
+ if (iy == 1)
+ return x;
+ else { /* compute -1 / (x+y) carefully */
+ double a, t;
+
+ z = w = x + y;
+ SET_LOW_WORD(z, 0);
+ v = y - (z - x);
+ t = a = -one / w;
+ SET_LOW_WORD(t, 0);
+ s = one + t * z;
+ return t + a * (s + t * v);
+ }
+ }
+ }
+ }
+ if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */
+ if (hx < 0) {
+ x = -x;
+ y = -y;
+ }
+ z = pio4 - x;
+ w = pio4lo - y;
+ x = z + w;
+ y = 0.0;
+ }
+ z = x * x;
+ w = z * z;
+ /*
+ * Break x^5*(T[1]+x^2*T[2]+...) into
+ * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
+ * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
+ */
+ r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] +
+ w * T[11]))));
+ v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] +
+ w * T[12])))));
+ s = z * x;
+ r = y + z * (s * (r + v) + y);
+ r += T[0] * s;
+ w = x + r;
+ if (ix >= 0x3FE59428) {
+ v = (double) iy;
+ return (double) (1 - ((hx >> 30) & 2)) *
+ (v - 2.0 * (x - (w * w / (w + v) - r)));
+ }
+ if (iy == 1)
+ return w;
+ else {
+ /*
+ * if allow error up to 2 ulp, simply return
+ * -1.0 / (x+r) here
+ */
+ /* compute -1.0 / (x+r) accurately */
+ double a, t;
+ z = w;
+ SET_LOW_WORD(z, 0);
+ v = r - (z - x); /* z+v = r+x */
+ t = a = -1.0 / w; /* a = -1.0/w */
+ SET_LOW_WORD(t, 0);
+ s = 1.0 + t * z;
+ return t + a * (s + t * v);
+ }
+}
diff --git a/StdLib/LibC/Math/math_private.h b/StdLib/LibC/Math/math_private.h new file mode 100644 index 0000000000..0aed7e7950 --- /dev/null +++ b/StdLib/LibC/Math/math_private.h @@ -0,0 +1,229 @@ +/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/*
+ * from: @(#)fdlibm.h 5.1 93/09/24
+ * $NetBSD: math_private.h,v 1.12 2005/07/21 12:55:58 christos Exp $
+ */
+
+#ifndef _MATH_PRIVATE_H_
+#define _MATH_PRIVATE_H_
+
+#include <sys/types.h>
+
+/* The original fdlibm code used statements like:
+ n0 = ((*(int*)&one)>>29)^1; * index of high word *
+ ix0 = *(n0+(int*)&x); * high word of x *
+ ix1 = *((1-n0)+(int*)&x); * low word of x *
+ to dig two 32 bit words out of the 64 bit IEEE floating point
+ value. That is non-ANSI, and, moreover, the gcc instruction
+ scheduler gets it wrong. We instead use the following macros.
+ Unlike the original code, we determine the endianness at compile
+ time, not at run time; I don't see much benefit to selecting
+ endianness at run time. */
+
+/* A union which permits us to convert between a double and two 32 bit
+ ints. */
+
+/*
+ * The ARM ports are little endian except for the FPA word order which is
+ * big endian.
+ */
+
+#if (BYTE_ORDER == BIG_ENDIAN) || (defined(__arm__) && !defined(__VFP_FP__))
+
+typedef union
+{
+ double value;
+ struct
+ {
+ u_int32_t msw;
+ u_int32_t lsw;
+ } parts;
+} ieee_double_shape_type;
+
+#endif
+
+#if (BYTE_ORDER == LITTLE_ENDIAN) && \
+ !(defined(__arm__) && !defined(__VFP_FP__))
+
+typedef union
+{
+ double value;
+ struct
+ {
+ u_int32_t lsw;
+ u_int32_t msw;
+ } parts;
+} ieee_double_shape_type;
+
+#endif
+
+/* Get two 32 bit ints from a double. */
+
+#define EXTRACT_WORDS(ix0,ix1,d) \
+do { \
+ ieee_double_shape_type ew_u; \
+ ew_u.value = (d); \
+ (ix0) = ew_u.parts.msw; \
+ (ix1) = ew_u.parts.lsw; \
+} while (0)
+
+/* Get the more significant 32 bit int from a double. */
+
+#define GET_HIGH_WORD(i,d) \
+do { \
+ ieee_double_shape_type gh_u; \
+ gh_u.value = (d); \
+ (i) = gh_u.parts.msw; \
+} while (0)
+
+/* Get the less significant 32 bit int from a double. */
+
+#define GET_LOW_WORD(i,d) \
+do { \
+ ieee_double_shape_type gl_u; \
+ gl_u.value = (d); \
+ (i) = gl_u.parts.lsw; \
+} while (0)
+
+/* Set a double from two 32 bit ints. */
+
+#define INSERT_WORDS(d,ix0,ix1) \
+do { \
+ ieee_double_shape_type iw_u; \
+ iw_u.parts.msw = (ix0); \
+ iw_u.parts.lsw = (ix1); \
+ (d) = iw_u.value; \
+} while (0)
+
+/* Set the more significant 32 bits of a double from an int. */
+
+#define SET_HIGH_WORD(d,v) \
+do { \
+ ieee_double_shape_type sh_u; \
+ sh_u.value = (d); \
+ sh_u.parts.msw = (v); \
+ (d) = sh_u.value; \
+} while (0)
+
+/* Set the less significant 32 bits of a double from an int. */
+
+#define SET_LOW_WORD(d,v) \
+do { \
+ ieee_double_shape_type sl_u; \
+ sl_u.value = (d); \
+ sl_u.parts.lsw = (v); \
+ (d) = sl_u.value; \
+} while (0)
+
+/* A union which permits us to convert between a float and a 32 bit
+ int. */
+
+typedef union
+{
+ float value;
+ u_int32_t word;
+} ieee_float_shape_type;
+
+/* Get a 32 bit int from a float. */
+
+#define GET_FLOAT_WORD(i,d) \
+do { \
+ ieee_float_shape_type gf_u; \
+ gf_u.value = (d); \
+ (i) = gf_u.word; \
+} while (0)
+
+/* Set a float from a 32 bit int. */
+
+#define SET_FLOAT_WORD(d,i) \
+do { \
+ ieee_float_shape_type sf_u; \
+ sf_u.word = (i); \
+ (d) = sf_u.value; \
+} while (0)
+
+/* ieee style elementary functions */
+extern double __ieee754_sqrt (double);
+extern double __ieee754_acos (double);
+extern double __ieee754_acosh (double);
+extern double __ieee754_log (double);
+extern double __ieee754_atanh (double);
+extern double __ieee754_asin (double);
+extern double __ieee754_atan2 (double, double);
+extern double __ieee754_exp (double);
+extern double __ieee754_cosh (double);
+extern double __ieee754_fmod (double, double);
+extern double __ieee754_pow (double, double);
+extern double __ieee754_lgamma_r (double, int *);
+extern double __ieee754_gamma_r (double, int *);
+extern double __ieee754_lgamma (double);
+extern double __ieee754_gamma (double);
+extern double __ieee754_log10 (double);
+extern double __ieee754_log2 (double);
+extern double __ieee754_sinh (double);
+extern double __ieee754_hypot (double, double);
+extern double __ieee754_j0 (double);
+extern double __ieee754_j1 (double);
+extern double __ieee754_y0 (double);
+extern double __ieee754_y1 (double);
+extern double __ieee754_jn (int, double);
+extern double __ieee754_yn (int, double);
+extern double __ieee754_remainder (double, double);
+extern int __ieee754_rem_pio2 (double,double*);
+extern double __ieee754_scalb (double, double);
+
+/* fdlibm kernel function */
+extern double __kernel_standard (double, double, int);
+extern double __kernel_sin (double, double, int);
+extern double __kernel_cos (double, double);
+extern double __kernel_tan (double, double, int);
+extern int __kernel_rem_pio2 (double*,double*,int,int,int,const int*);
+
+
+///* ieee style elementary float functions */
+//extern float __ieee754_sqrtf __P((float));
+//extern float __ieee754_acosf __P((float));
+//extern float __ieee754_acoshf __P((float));
+//extern float __ieee754_logf __P((float));
+//extern float __ieee754_atanhf __P((float));
+//extern float __ieee754_asinf __P((float));
+//extern float __ieee754_atan2f __P((float,float));
+//extern float __ieee754_expf __P((float));
+//extern float __ieee754_coshf __P((float));
+//extern float __ieee754_fmodf __P((float,float));
+//extern float __ieee754_powf __P((float,float));
+//extern float __ieee754_lgammaf_r __P((float,int *));
+//extern float __ieee754_gammaf_r __P((float,int *));
+//extern float __ieee754_lgammaf __P((float));
+//extern float __ieee754_gammaf __P((float));
+//extern float __ieee754_log10f __P((float));
+//extern float __ieee754_log2f __P((float));
+//extern float __ieee754_sinhf __P((float));
+//extern float __ieee754_hypotf __P((float,float));
+//extern float __ieee754_j0f __P((float));
+//extern float __ieee754_j1f __P((float));
+//extern float __ieee754_y0f __P((float));
+//extern float __ieee754_y1f __P((float));
+//extern float __ieee754_jnf __P((int,float));
+//extern float __ieee754_ynf __P((int,float));
+//extern float __ieee754_remainderf __P((float,float));
+//extern int __ieee754_rem_pio2f __P((float,float*));
+//extern float __ieee754_scalbf __P((float,float));
+
+///* float versions of fdlibm kernel functions */
+//extern float __kernel_sinf __P((float,float,int));
+//extern float __kernel_cosf __P((float,float));
+//extern float __kernel_tanf __P((float,float,int));
+//extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const int*));
+
+#endif /* _MATH_PRIVATE_H_ */
diff --git a/StdLib/LibC/Math/s_atan.c b/StdLib/LibC/Math/s_atan.c new file mode 100644 index 0000000000..cbaf359936 --- /dev/null +++ b/StdLib/LibC/Math/s_atan.c @@ -0,0 +1,120 @@ +/* @(#)s_atan.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_atan.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
+#endif
+
+/* atan(x)
+ * Method
+ * 1. Reduce x to positive by atan(x) = -atan(-x).
+ * 2. According to the integer k=4t+0.25 chopped, t=x, the argument
+ * is further reduced to one of the following intervals and the
+ * arctangent of t is evaluated by the corresponding formula:
+ *
+ * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
+ * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
+ * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
+ * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
+ * [39/16,INF] atan(x) = atan(INF) + atan( -1/t )
+ *
+ * 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.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double atanhi[] = {
+ 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
+ 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
+ 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
+ 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
+};
+
+static const double atanlo[] = {
+ 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
+ 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
+ 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
+ 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
+};
+
+static const double aT[] = {
+ 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
+ -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
+ 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
+ -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
+ 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
+ -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
+ 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
+ -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
+ 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
+ -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
+ 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
+};
+
+ static const double
+one = 1.0,
+huge = 1.0e300;
+
+double
+atan(double x)
+{
+ double w,s1,s2,z;
+ int32_t ix,hx,id;
+
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ if(ix>=0x44100000) { /* if |x| >= 2^66 */
+ u_int32_t low;
+ GET_LOW_WORD(low,x);
+ if(ix>0x7ff00000||
+ (ix==0x7ff00000&&(low!=0)))
+ return x+x; /* NaN */
+ if(hx>0) return atanhi[3]+atanlo[3];
+ else return -atanhi[3]-atanlo[3];
+ } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */
+ if (ix < 0x3e200000) { /* |x| < 2^-29 */
+ if(huge+x>one) return x; /* raise inexact */
+ }
+ id = -1;
+ } else {
+ x = fabs(x);
+ if (ix < 0x3ff30000) { /* |x| < 1.1875 */
+ if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */
+ id = 0; x = (2.0*x-one)/(2.0+x);
+ } else { /* 11/16<=|x|< 19/16 */
+ id = 1; x = (x-one)/(x+one);
+ }
+ } else {
+ if (ix < 0x40038000) { /* |x| < 2.4375 */
+ id = 2; x = (x-1.5)/(one+1.5*x);
+ } else { /* 2.4375 <= |x| < 2^66 */
+ id = 3; x = -1.0/x;
+ }
+ }}
+ /* end of argument reduction */
+ z = x*x;
+ w = z*z;
+ /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
+ s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
+ s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
+ if (id<0) return x - x*(s1+s2);
+ else {
+ z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
+ return (hx<0)? -z:z;
+ }
+}
diff --git a/StdLib/LibC/Math/s_ceil.c b/StdLib/LibC/Math/s_ceil.c new file mode 100644 index 0000000000..e9579fab72 --- /dev/null +++ b/StdLib/LibC/Math/s_ceil.c @@ -0,0 +1,74 @@ +/* @(#)s_ceil.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_ceil.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
+#endif
+
+/*
+ * ceil(x)
+ * Return x rounded toward -inf to integral value
+ * Method:
+ * Bit twiddling.
+ * Exception:
+ * Inexact flag raised if x not equal to ceil(x).
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double huge = 1.0e300;
+
+double
+ceil(double x)
+{
+ int32_t i0,i1,j0;
+ u_int32_t i,j;
+
+ EXTRACT_WORDS(i0,i1,x);
+ j0 = ((i0>>20)&0x7ff)-0x3ff;
+ if(j0<20) {
+ if(j0<0) { /* raise inexact if x != 0 */
+ if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
+ if(i0<0) {i0=0x80000000;i1=0;}
+ else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;}
+ }
+ } else {
+ i = (0x000fffff)>>j0;
+ if(((i0&i)|i1)==0) return x; /* x is integral */
+ if(huge+x>0.0) { /* raise inexact flag */
+ if(i0>0) i0 += (0x00100000)>>j0;
+ i0 &= (~i); i1=0;
+ }
+ }
+ } else if (j0>51) {
+ if(j0==0x400) return x+x; /* inf or NaN */
+ else return x; /* x is integral */
+ } else {
+ i = ((u_int32_t)(0xffffffff))>>(j0-20);
+ if((i1&i)==0) return x; /* x is integral */
+ if(huge+x>0.0) { /* raise inexact flag */
+ if(i0>0) {
+ if(j0==20) i0+=1;
+ else {
+ j = i1 + (1<<(52-j0));
+ if((int32_t)j<i1) i0+=1; /* got a carry */
+ i1 = j;
+ }
+ }
+ i1 &= (~i);
+ }
+ }
+ INSERT_WORDS(x,i0,i1);
+ return x;
+}
diff --git a/StdLib/LibC/Math/s_copysign.c b/StdLib/LibC/Math/s_copysign.c new file mode 100644 index 0000000000..31a80af28f --- /dev/null +++ b/StdLib/LibC/Math/s_copysign.c @@ -0,0 +1,35 @@ +/* @(#)s_copysign.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_copysign.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
+#endif
+
+/*
+ * copysign(double x, double y)
+ * copysign(x,y) returns a value with the magnitude of x and
+ * with the sign bit of y.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+double
+copysign(double x, double y)
+{
+ u_int32_t hx,hy;
+ GET_HIGH_WORD(hx,x);
+ GET_HIGH_WORD(hy,y);
+ SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000));
+ return x;
+}
diff --git a/StdLib/LibC/Math/s_cos.c b/StdLib/LibC/Math/s_cos.c new file mode 100644 index 0000000000..ef04e5d34c --- /dev/null +++ b/StdLib/LibC/Math/s_cos.c @@ -0,0 +1,79 @@ +/* @(#)s_cos.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_cos.c,v 1.10 2002/05/26 22:01:54 wiz Exp $");
+#endif
+
+/* cos(x)
+ * Return cosine function of x.
+ *
+ * kernel function:
+ * __kernel_sin ... sine function on [-pi/4,pi/4]
+ * __kernel_cos ... cosine function on [-pi/4,pi/4]
+ * __ieee754_rem_pio2 ... argument reduction routine
+ *
+ * Method.
+ * Let S,C and T denote the sin, cos and tan respectively on
+ * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ * in [-pi/4 , +pi/4], and let n = k mod 4.
+ * We have
+ *
+ * n sin(x) cos(x) tan(x)
+ * ----------------------------------------------------------
+ * 0 S C T
+ * 1 C -S -1/T
+ * 2 -S -C T
+ * 3 -C S -1/T
+ * ----------------------------------------------------------
+ *
+ * Special cases:
+ * Let trig be any of sin, cos, or tan.
+ * trig(+-INF) is NaN, with signals;
+ * trig(NaN) is that NaN;
+ *
+ * Accuracy:
+ * TRIG(x) returns trig(x) nearly rounded
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+double
+cos(double x)
+{
+ double y[2],z=0.0;
+ int32_t n, ix;
+
+ /* High word of x. */
+ GET_HIGH_WORD(ix,x);
+
+ /* |x| ~< pi/4 */
+ ix &= 0x7fffffff;
+ if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
+
+ /* cos(Inf or NaN) is NaN */
+ else if (ix>=0x7ff00000) return x-x;
+
+ /* argument reduction needed */
+ else {
+ n = __ieee754_rem_pio2(x,y);
+ switch(n&3) {
+ case 0: return __kernel_cos(y[0],y[1]);
+ case 1: return -__kernel_sin(y[0],y[1],1);
+ case 2: return -__kernel_cos(y[0],y[1]);
+ default:
+ return __kernel_sin(y[0],y[1],1);
+ }
+ }
+}
diff --git a/StdLib/LibC/Math/s_expm1.c b/StdLib/LibC/Math/s_expm1.c new file mode 100644 index 0000000000..338f377fa4 --- /dev/null +++ b/StdLib/LibC/Math/s_expm1.c @@ -0,0 +1,228 @@ +/* @(#)s_expm1.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_expm1.c,v 1.12 2002/05/26 22:01:55 wiz Exp $");
+#endif
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // C4756: overflow in constant arithmetic
+ #pragma warning ( disable : 4756 )
+#endif
+
+/* expm1(x)
+ * Returns exp(x)-1, the exponential of x minus 1.
+ *
+ * Method
+ * 1. Argument reduction:
+ * Given x, find r and integer k such that
+ *
+ * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658
+ *
+ * Here a correction term c will be computed to compensate
+ * the error in r when rounded to a floating-point number.
+ *
+ * 2. Approximating expm1(r) by a special rational function on
+ * the interval [0,0.34658]:
+ * Since
+ * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ...
+ * we define R1(r*r) by
+ * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r)
+ * That is,
+ * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r)
+ * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r))
+ * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ...
+ * We use a special Reme algorithm on [0,0.347] to generate
+ * a polynomial of degree 5 in r*r to approximate R1. The
+ * maximum error of this polynomial approximation is bounded
+ * by 2**-61. In other words,
+ * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5
+ * where Q1 = -1.6666666666666567384E-2,
+ * Q2 = 3.9682539681370365873E-4,
+ * Q3 = -9.9206344733435987357E-6,
+ * Q4 = 2.5051361420808517002E-7,
+ * Q5 = -6.2843505682382617102E-9;
+ * (where z=r*r, and the values of Q1 to Q5 are listed below)
+ * with error bounded by
+ * | 5 | -61
+ * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2
+ * | |
+ *
+ * expm1(r) = exp(r)-1 is then computed by the following
+ * specific way which minimize the accumulation rounding error:
+ * 2 3
+ * r r [ 3 - (R1 + R1*r/2) ]
+ * expm1(r) = r + --- + --- * [--------------------]
+ * 2 2 [ 6 - r*(3 - R1*r/2) ]
+ *
+ * To compensate the error in the argument reduction, we use
+ * expm1(r+c) = expm1(r) + c + expm1(r)*c
+ * ~ expm1(r) + c + r*c
+ * Thus c+r*c will be added in as the correction terms for
+ * expm1(r+c). Now rearrange the term to avoid optimization
+ * screw up:
+ * ( 2 2 )
+ * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r )
+ * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- )
+ * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 )
+ * ( )
+ *
+ * = r - E
+ * 3. Scale back to obtain expm1(x):
+ * From step 1, we have
+ * expm1(x) = either 2^k*[expm1(r)+1] - 1
+ * = or 2^k*[expm1(r) + (1-2^-k)]
+ * 4. Implementation notes:
+ * (A). To save one multiplication, we scale the coefficient Qi
+ * to Qi*2^i, and replace z by (x^2)/2.
+ * (B). To achieve maximum accuracy, we compute expm1(x) by
+ * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf)
+ * (ii) if k=0, return r-E
+ * (iii) if k=-1, return 0.5*(r-E)-0.5
+ * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E)
+ * else return 1.0+2.0*(r-E);
+ * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1)
+ * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else
+ * (vii) return 2^k(1-((E+2^-k)-r))
+ *
+ * Special cases:
+ * expm1(INF) is INF, expm1(NaN) is NaN;
+ * expm1(-INF) is -1, and
+ * for finite argument, only expm1(0)=0 is exact.
+ *
+ * Accuracy:
+ * according to an error analysis, the error is always less than
+ * 1 ulp (unit in the last place).
+ *
+ * Misc. info.
+ * For IEEE double
+ * if x > 7.09782712893383973096e+02 then expm1(x) overflow
+ *
+ * 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.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+one = 1.0,
+huge = 1.0e+300,
+tiny = 1.0e-300,
+o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
+ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
+ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
+invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
+ /* scaled coefficients related to expm1 */
+Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
+Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
+Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
+Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
+Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
+
+double
+expm1(double x)
+{
+ double y,hi,lo,c,t,e,hxs,hfx,r1;
+ int32_t k,xsb;
+ u_int32_t hx;
+
+ c = 0;
+ GET_HIGH_WORD(hx,x);
+ xsb = hx&0x80000000; /* sign bit of x */
+ if(xsb==0) y=x; else y= -x; /* y = |x| */
+ hx &= 0x7fffffff; /* high word of |x| */
+
+ /* filter out huge and non-finite argument */
+ if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
+ if(hx >= 0x40862E42) { /* if |x|>=709.78... */
+ if(hx>=0x7ff00000) {
+ u_int32_t low;
+ GET_LOW_WORD(low,x);
+ if(((hx&0xfffff)|low)!=0)
+ return x+x; /* NaN */
+ else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
+ }
+ if(x > o_threshold) return huge*huge; /* overflow */
+ }
+ if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
+ if(x+tiny<0.0) /* raise inexact */
+ return tiny-one; /* return -1 */
+ }
+ }
+
+ /* argument reduction */
+ if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
+ if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
+ if(xsb==0)
+ {hi = x - ln2_hi; lo = ln2_lo; k = 1;}
+ else
+ {hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
+ } else {
+ k = (int32_t)(invln2*x+((xsb==0)?0.5:-0.5));
+ t = k;
+ hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
+ lo = t*ln2_lo;
+ }
+ x = hi - lo;
+ c = (hi-x)-lo;
+ }
+ else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */
+ t = huge+x; /* return x with inexact flags when x!=0 */
+ return x - (t-(huge+x));
+ }
+ else k = 0;
+
+ /* x is now in primary range */
+ hfx = 0.5*x;
+ hxs = x*hfx;
+ r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
+ t = 3.0-r1*hfx;
+ e = hxs*((r1-t)/(6.0 - x*t));
+ if(k==0) return x - (x*e-hxs); /* c is 0 */
+ else {
+ e = (x*(e-c)-c);
+ e -= hxs;
+ if(k== -1) return 0.5*(x-e)-0.5;
+ if(k==1) {
+ if(x < -0.25) return -2.0*(e-(x+0.5));
+ else return one+2.0*(x-e);
+ }
+ if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
+ u_int32_t high;
+ y = one-(e-x);
+ GET_HIGH_WORD(high,y);
+ SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
+ return y-one;
+ }
+ t = one;
+ if(k<20) {
+ u_int32_t high;
+ SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */
+ y = t-(e-x);
+ GET_HIGH_WORD(high,y);
+ SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
+ } else {
+ u_int32_t high;
+ SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */
+ y = x-(e+t);
+ y += one;
+ GET_HIGH_WORD(high,y);
+ SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
+ }
+ }
+ return y;
+}
diff --git a/StdLib/LibC/Math/s_fabs.c b/StdLib/LibC/Math/s_fabs.c new file mode 100644 index 0000000000..4cd5a5e52a --- /dev/null +++ b/StdLib/LibC/Math/s_fabs.c @@ -0,0 +1,32 @@ +/* @(#)s_fabs.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_fabs.c,v 1.10 2002/05/26 22:01:55 wiz Exp $");
+#endif
+
+/*
+ * fabs(x) returns the absolute value of x.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+double
+fabs(double x)
+{
+ u_int32_t high;
+ GET_HIGH_WORD(high,x);
+ SET_HIGH_WORD(x,high&0x7fffffff);
+ return x;
+}
diff --git a/StdLib/LibC/Math/s_finite.c b/StdLib/LibC/Math/s_finite.c new file mode 100644 index 0000000000..3f66feb981 --- /dev/null +++ b/StdLib/LibC/Math/s_finite.c @@ -0,0 +1,32 @@ +/* @(#)s_finite.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_finite.c,v 1.11 2002/05/26 22:01:55 wiz Exp $");
+#endif
+
+/*
+ * finite(x) returns 1 is x is finite, else 0;
+ * no branching!
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+int
+finite(double x)
+{
+ int32_t hx;
+ GET_HIGH_WORD(hx,x);
+ return (int)((u_int32_t)((hx&0x7fffffff)-0x7ff00000)>>31);
+}
diff --git a/StdLib/LibC/Math/s_floor.c b/StdLib/LibC/Math/s_floor.c new file mode 100644 index 0000000000..d63ef13c0d --- /dev/null +++ b/StdLib/LibC/Math/s_floor.c @@ -0,0 +1,74 @@ +/* @(#)s_floor.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_floor.c,v 1.11 2002/05/26 22:01:56 wiz Exp $");
+#endif
+
+/*
+ * floor(x)
+ * Return x rounded toward -inf to integral value
+ * Method:
+ * Bit twiddling.
+ * Exception:
+ * Inexact flag raised if x not equal to floor(x).
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double huge = 1.0e300;
+
+double
+floor(double x)
+{
+ int32_t i0,i1,j0;
+ u_int32_t i,j;
+ EXTRACT_WORDS(i0,i1,x);
+ j0 = ((i0>>20)&0x7ff)-0x3ff;
+ if(j0<20) {
+ if(j0<0) { /* raise inexact if x != 0 */
+ if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
+ if(i0>=0) {i0=i1=0;}
+ else if(((i0&0x7fffffff)|i1)!=0)
+ { i0=0xbff00000;i1=0;}
+ }
+ } else {
+ i = (0x000fffff)>>j0;
+ if(((i0&i)|i1)==0) return x; /* x is integral */
+ if(huge+x>0.0) { /* raise inexact flag */
+ if(i0<0) i0 += (0x00100000)>>j0;
+ i0 &= (~i); i1=0;
+ }
+ }
+ } else if (j0>51) {
+ if(j0==0x400) return x+x; /* inf or NaN */
+ else return x; /* x is integral */
+ } else {
+ i = ((u_int32_t)(0xffffffff))>>(j0-20);
+ if((i1&i)==0) return x; /* x is integral */
+ if(huge+x>0.0) { /* raise inexact flag */
+ if(i0<0) {
+ if(j0==20) i0+=1;
+ else {
+ j = i1+(1<<(52-j0));
+ if((int32_t)j<i1) i0 +=1 ; /* got a carry */
+ i1=j;
+ }
+ }
+ i1 &= (~i);
+ }
+ }
+ INSERT_WORDS(x,i0,i1);
+ return x;
+}
diff --git a/StdLib/LibC/Math/s_frexp.c b/StdLib/LibC/Math/s_frexp.c new file mode 100644 index 0000000000..8e93600ef9 --- /dev/null +++ b/StdLib/LibC/Math/s_frexp.c @@ -0,0 +1,52 @@ +/* @(#)s_frexp.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_frexp.c,v 1.12 2002/05/26 22:01:56 wiz Exp $");
+#endif
+
+/*
+ * for non-zero x
+ * x = frexp(arg,&exp);
+ * return a double fp quantity x such that 0.5 <= |x| <1.0
+ * and the corresponding binary exponent "exp". That is
+ * arg = x*2^exp.
+ * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg
+ * with *exp=0.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */
+
+double
+frexp(double x, int *eptr)
+{
+ int32_t hx, ix, lx;
+ EXTRACT_WORDS(hx,lx,x);
+ ix = 0x7fffffff&hx;
+ *eptr = 0;
+ if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */
+ if (ix<0x00100000) { /* subnormal */
+ x *= two54;
+ GET_HIGH_WORD(hx,x);
+ ix = hx&0x7fffffff;
+ *eptr = -54;
+ }
+ *eptr += (ix>>20)-1022;
+ hx = (hx&0x800fffff)|0x3fe00000;
+ SET_HIGH_WORD(x,hx);
+ return x;
+}
diff --git a/StdLib/LibC/Math/s_infinity.c b/StdLib/LibC/Math/s_infinity.c new file mode 100644 index 0000000000..9ee1abd0b4 --- /dev/null +++ b/StdLib/LibC/Math/s_infinity.c @@ -0,0 +1,27 @@ +/* $NetBSD: s_infinity.c,v 1.5 2003/07/26 19:25:05 salo Exp $ */
+
+/*
+ * Written by J.T. Conklin <jtc@NetBSD.org>.
+ * Public domain.
+ */
+#include <LibConfig.h>
+
+#include <sys/types.h>
+
+#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
+ // Force 8-byte alignment
+ #define ALIGN8 __declspec(align(8))
+
+ // C4742: identifier has different alignment in 'X' and 'Y'
+ #pragma warning ( disable : 4742 )
+ // C4744: identifier has different type in 'X' and 'Y'
+ #pragma warning ( disable : 4744 )
+#else
+ #define ALIGN8
+#endif
+
+#if BYTE_ORDER == LITTLE_ENDIAN
+ALIGN8 char __infinity[] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf0, 0x7f };
+#else
+ALIGN8 char __infinity[] = { 0x7f, 0xf0, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 };
+#endif
diff --git a/StdLib/LibC/Math/s_ldexp.c b/StdLib/LibC/Math/s_ldexp.c new file mode 100644 index 0000000000..6c843c7fe9 --- /dev/null +++ b/StdLib/LibC/Math/s_ldexp.c @@ -0,0 +1,29 @@ +/* @(#)s_ldexp.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_ldexp.c,v 1.9 2002/05/26 22:01:56 wiz Exp $");
+#endif
+
+#include <errno.h>
+#include "math.h"
+#include "math_private.h"
+
+double
+ldexp(double value, int exp)
+{
+ if(!finite(value)||value==0.0) return value;
+ value = scalbn(value,exp);
+ if(!finite(value)||value==0.0) errno = ERANGE;
+ return value;
+}
diff --git a/StdLib/LibC/Math/s_modf.c b/StdLib/LibC/Math/s_modf.c new file mode 100644 index 0000000000..bf4faf42e0 --- /dev/null +++ b/StdLib/LibC/Math/s_modf.c @@ -0,0 +1,76 @@ +/* @(#)s_modf.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_modf.c,v 1.11 2002/05/26 22:01:57 wiz Exp $");
+#endif
+
+/*
+ * modf(double x, double *iptr)
+ * return fraction part of x, and return x's integral part in *iptr.
+ * Method:
+ * Bit twiddling.
+ *
+ * Exception:
+ * No exception.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double one = 1.0;
+
+double
+modf(double x, double *iptr)
+{
+ int32_t i0,i1,j0;
+ u_int32_t i;
+ EXTRACT_WORDS(i0,i1,x);
+ j0 = ((i0>>20)&0x7ff)-0x3ff; /* exponent of x */
+ if(j0<20) { /* integer part in high x */
+ if(j0<0) { /* |x|<1 */
+ INSERT_WORDS(*iptr,i0&0x80000000,0); /* *iptr = +-0 */
+ return x;
+ } else {
+ i = (0x000fffff)>>j0;
+ if(((i0&i)|i1)==0) { /* x is integral */
+ u_int32_t high;
+ *iptr = x;
+ GET_HIGH_WORD(high,x);
+ INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */
+ return x;
+ } else {
+ INSERT_WORDS(*iptr,i0&(~i),0);
+ return x - *iptr;
+ }
+ }
+ } else if (j0>51) { /* no fraction part */
+ u_int32_t high;
+ *iptr = x*one;
+ GET_HIGH_WORD(high,x);
+ INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */
+ return x;
+ } else { /* fraction part in low x */
+ i = ((u_int32_t)(0xffffffff))>>(j0-20);
+ if((i1&i)==0) { /* x is integral */
+ u_int32_t high;
+ *iptr = x;
+ GET_HIGH_WORD(high,x);
+ INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */
+ return x;
+ } else {
+ INSERT_WORDS(*iptr,i0,i1&(~i));
+ return x - *iptr;
+ }
+ }
+}
diff --git a/StdLib/LibC/Math/s_scalbn.c b/StdLib/LibC/Math/s_scalbn.c new file mode 100644 index 0000000000..072f1c7c89 --- /dev/null +++ b/StdLib/LibC/Math/s_scalbn.c @@ -0,0 +1,60 @@ +/* @(#)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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_scalbn.c,v 1.12 2002/05/26 22:01:58 wiz Exp $");
+#endif
+
+/*
+ * scalbn (double x, int n)
+ * scalbn(x,n) returns x* 2**n computed by exponent
+ * manipulation rather than by actually performing an
+ * exponentiation or a multiplication.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
+twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
+huge = 1.0e+300,
+tiny = 1.0e-300;
+
+double
+scalbn(double x, int n)
+{
+ int32_t k,hx,lx;
+ EXTRACT_WORDS(hx,lx,x);
+ k = (hx&0x7ff00000)>>20; /* extract exponent */
+ if (k==0) { /* 0 or subnormal x */
+ if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
+ x *= two54;
+ GET_HIGH_WORD(hx,x);
+ k = ((hx&0x7ff00000)>>20) - 54;
+ if (n< -50000) return tiny*x; /*underflow*/
+ }
+ if (k==0x7ff) return x+x; /* NaN or Inf */
+ k = k+n;
+ if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */
+ if (k > 0) /* normal result */
+ {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;}
+ if (k <= -54) {
+ if (n > 50000) /* in case integer overflow in n+k */
+ return huge*copysign(huge,x); /*overflow*/
+ else return tiny*copysign(tiny,x); /*underflow*/
+ }
+ k += 54; /* subnormal result */
+ SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20));
+ return x*twom54;
+}
diff --git a/StdLib/LibC/Math/s_sin.c b/StdLib/LibC/Math/s_sin.c new file mode 100644 index 0000000000..2f373c984e --- /dev/null +++ b/StdLib/LibC/Math/s_sin.c @@ -0,0 +1,79 @@ +/* @(#)s_sin.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_sin.c,v 1.10 2002/05/26 22:01:58 wiz Exp $");
+#endif
+
+/* sin(x)
+ * Return sine function of x.
+ *
+ * kernel function:
+ * __kernel_sin ... sine function on [-pi/4,pi/4]
+ * __kernel_cos ... cose function on [-pi/4,pi/4]
+ * __ieee754_rem_pio2 ... argument reduction routine
+ *
+ * Method.
+ * Let S,C and T denote the sin, cos and tan respectively on
+ * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ * in [-pi/4 , +pi/4], and let n = k mod 4.
+ * We have
+ *
+ * n sin(x) cos(x) tan(x)
+ * ----------------------------------------------------------
+ * 0 S C T
+ * 1 C -S -1/T
+ * 2 -S -C T
+ * 3 -C S -1/T
+ * ----------------------------------------------------------
+ *
+ * Special cases:
+ * Let trig be any of sin, cos, or tan.
+ * trig(+-INF) is NaN, with signals;
+ * trig(NaN) is that NaN;
+ *
+ * Accuracy:
+ * TRIG(x) returns trig(x) nearly rounded
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+double
+sin(double x)
+{
+ double y[2],z=0.0;
+ int32_t n, ix;
+
+ /* High word of x. */
+ GET_HIGH_WORD(ix,x);
+
+ /* |x| ~< pi/4 */
+ ix &= 0x7fffffff;
+ if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);
+
+ /* sin(Inf or NaN) is NaN */
+ else if (ix>=0x7ff00000) return x-x;
+
+ /* argument reduction needed */
+ else {
+ n = __ieee754_rem_pio2(x,y);
+ switch(n&3) {
+ case 0: return __kernel_sin(y[0],y[1],1);
+ case 1: return __kernel_cos(y[0],y[1]);
+ case 2: return -__kernel_sin(y[0],y[1],1);
+ default:
+ return -__kernel_cos(y[0],y[1]);
+ }
+ }
+}
diff --git a/StdLib/LibC/Math/s_tan.c b/StdLib/LibC/Math/s_tan.c new file mode 100644 index 0000000000..6c2a26de5a --- /dev/null +++ b/StdLib/LibC/Math/s_tan.c @@ -0,0 +1,73 @@ +/* @(#)s_tan.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_tan.c,v 1.10 2002/05/26 22:01:58 wiz Exp $");
+#endif
+
+/* tan(x)
+ * Return tangent function of x.
+ *
+ * kernel function:
+ * __kernel_tan ... tangent function on [-pi/4,pi/4]
+ * __ieee754_rem_pio2 ... argument reduction routine
+ *
+ * Method.
+ * Let S,C and T denote the sin, cos and tan respectively on
+ * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
+ * in [-pi/4 , +pi/4], and let n = k mod 4.
+ * We have
+ *
+ * n sin(x) cos(x) tan(x)
+ * ----------------------------------------------------------
+ * 0 S C T
+ * 1 C -S -1/T
+ * 2 -S -C T
+ * 3 -C S -1/T
+ * ----------------------------------------------------------
+ *
+ * Special cases:
+ * Let trig be any of sin, cos, or tan.
+ * trig(+-INF) is NaN, with signals;
+ * trig(NaN) is that NaN;
+ *
+ * Accuracy:
+ * TRIG(x) returns trig(x) nearly rounded
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+double
+tan(double x)
+{
+ double y[2],z=0.0;
+ int32_t n, ix;
+
+ /* High word of x. */
+ GET_HIGH_WORD(ix,x);
+
+ /* |x| ~< pi/4 */
+ ix &= 0x7fffffff;
+ if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
+
+ /* tan(Inf or NaN) is NaN */
+ else if (ix>=0x7ff00000) return x-x; /* NaN */
+
+ /* argument reduction needed */
+ else {
+ n = __ieee754_rem_pio2(x,y);
+ return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
+ -1 -- n odd */
+ }
+}
diff --git a/StdLib/LibC/Math/s_tanh.c b/StdLib/LibC/Math/s_tanh.c new file mode 100644 index 0000000000..f6e17a7b4f --- /dev/null +++ b/StdLib/LibC/Math/s_tanh.c @@ -0,0 +1,79 @@ +/* @(#)s_tanh.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz Exp $");
+#endif
+
+/* Tanh(x)
+ * Return the Hyperbolic Tangent of x
+ *
+ * Method :
+ * x -x
+ * e - e
+ * 0. tanh(x) is defined to be -----------
+ * x -x
+ * e + e
+ * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
+ * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
+ * -t
+ * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
+ * t + 2
+ * 2
+ * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
+ * t + 2
+ * 22.0 < x <= INF : tanh(x) := 1.
+ *
+ * Special cases:
+ * tanh(NaN) is NaN;
+ * only tanh(0)=0 is exact for finite argument.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double one=1.0, two=2.0, tiny = 1.0e-300;
+
+double
+tanh(double x)
+{
+ double t,z;
+ int32_t jx,ix;
+
+ /* High word of |x|. */
+ GET_HIGH_WORD(jx,x);
+ ix = jx&0x7fffffff;
+
+ /* x is INF or NaN */
+ if(ix>=0x7ff00000) {
+ if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
+ else return one/x-one; /* tanh(NaN) = NaN */
+ }
+
+ /* |x| < 22 */
+ if (ix < 0x40360000) { /* |x|<22 */
+ if (ix<0x3c800000) /* |x|<2**-55 */
+ return x*(one+x); /* tanh(small) = small */
+ if (ix>=0x3ff00000) { /* |x|>=1 */
+ t = expm1(two*fabs(x));
+ z = one - two/(t+two);
+ } else {
+ t = expm1(-two*fabs(x));
+ z= -t/(t+two);
+ }
+ /* |x| > 22, return +-1 */
+ } else {
+ z = one - tiny; /* raised inexact flag */
+ }
+ return (jx>=0)? z: -z;
+}
diff --git a/StdLib/LibC/Math/w_acos.c b/StdLib/LibC/Math/w_acos.c new file mode 100644 index 0000000000..7e6aa10254 --- /dev/null +++ b/StdLib/LibC/Math/w_acos.c @@ -0,0 +1,40 @@ +/* @(#)w_acos.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.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_acos.c,v 1.9 2002/05/26 22:01:59 wiz Exp $");
+#endif
+
+/*
+ * wrap_acos(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+double
+acos(double x) /* wrapper acos */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_acos(x);
+#else
+ double z;
+ z = __ieee754_acos(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(fabs(x)>1.0) {
+ return __kernel_standard(x,x,1); /* acos(|x|>1) */
+ } else
+ return z;
+#endif
+}
diff --git a/StdLib/LibC/Math/w_asin.c b/StdLib/LibC/Math/w_asin.c new file mode 100644 index 0000000000..988c42dc1f --- /dev/null +++ b/StdLib/LibC/Math/w_asin.c @@ -0,0 +1,41 @@ +/* @(#)w_asin.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_asin.c,v 1.9 2002/05/26 22:01:59 wiz Exp $");
+#endif
+
+/*
+ * wrapper asin(x)
+ */
+
+
+#include "math.h"
+#include "math_private.h"
+
+
+double
+asin(double x) /* wrapper asin */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_asin(x);
+#else
+ double z;
+ z = __ieee754_asin(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(fabs(x)>1.0) {
+ return __kernel_standard(x,x,2); /* asin(|x|>1) */
+ } else
+ return z;
+#endif
+}
diff --git a/StdLib/LibC/Math/w_atan2.c b/StdLib/LibC/Math/w_atan2.c new file mode 100644 index 0000000000..dbf38de42f --- /dev/null +++ b/StdLib/LibC/Math/w_atan2.c @@ -0,0 +1,40 @@ +/* @(#)w_atan2.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_atan2.c,v 1.9 2002/05/26 22:01:59 wiz Exp $");
+#endif
+
+/*
+ * wrapper atan2(y,x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+double
+atan2(double y, double x) /* wrapper atan2 */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_atan2(y,x);
+#else
+ double z;
+ z = __ieee754_atan2(y,x);
+ if(_LIB_VERSION == _IEEE_||isnan(x)||isnan(y)) return z;
+ if(x==0.0&&y==0.0) {
+ return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */
+ } else
+ return z;
+#endif
+}
diff --git a/StdLib/LibC/Math/w_cosh.c b/StdLib/LibC/Math/w_cosh.c new file mode 100644 index 0000000000..3d73bff961 --- /dev/null +++ b/StdLib/LibC/Math/w_cosh.c @@ -0,0 +1,39 @@ +/* @(#)w_cosh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_cosh.c,v 1.9 2002/05/26 22:02:00 wiz Exp $");
+#endif
+
+/*
+ * wrapper cosh(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+double
+cosh(double x) /* wrapper cosh */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_cosh(x);
+#else
+ double z;
+ z = __ieee754_cosh(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(fabs(x)>7.10475860073943863426e+02) {
+ return __kernel_standard(x,x,5); /* cosh overflow */
+ } else
+ return z;
+#endif
+}
diff --git a/StdLib/LibC/Math/w_exp.c b/StdLib/LibC/Math/w_exp.c new file mode 100644 index 0000000000..29a2bb2906 --- /dev/null +++ b/StdLib/LibC/Math/w_exp.c @@ -0,0 +1,46 @@ +/* @(#)w_exp.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_exp.c,v 1.9 2002/05/26 22:02:00 wiz Exp $");
+#endif
+
+/*
+ * wrapper exp(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+static const double
+o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
+u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
+
+double
+exp(double x) /* wrapper exp */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_exp(x);
+#else
+ double z;
+ z = __ieee754_exp(x);
+ if(_LIB_VERSION == _IEEE_) return z;
+ if(finite(x)) {
+ if(x>o_threshold)
+ return __kernel_standard(x,x,6); /* exp overflow */
+ else if(x<u_threshold)
+ return __kernel_standard(x,x,7); /* exp underflow */
+ }
+ return z;
+#endif
+}
diff --git a/StdLib/LibC/Math/w_fmod.c b/StdLib/LibC/Math/w_fmod.c new file mode 100644 index 0000000000..ef1b1c6875 --- /dev/null +++ b/StdLib/LibC/Math/w_fmod.c @@ -0,0 +1,40 @@ +/* @(#)w_fmod.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_fmod.c,v 1.9 2002/05/26 22:02:00 wiz Exp $");
+#endif
+
+/*
+ * wrapper fmod(x,y)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+double
+fmod(double x, double y) /* wrapper fmod */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_fmod(x,y);
+#else
+ double z;
+ z = __ieee754_fmod(x,y);
+ if(_LIB_VERSION == _IEEE_ ||isnan(y)||isnan(x)) return z;
+ if(y==0.0) {
+ return __kernel_standard(x,y,27); /* fmod(x,0) */
+ } else
+ return z;
+#endif
+}
diff --git a/StdLib/LibC/Math/w_log.c b/StdLib/LibC/Math/w_log.c new file mode 100644 index 0000000000..ae8a5a2338 --- /dev/null +++ b/StdLib/LibC/Math/w_log.c @@ -0,0 +1,40 @@ +/* @(#)w_log.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_log.c,v 1.9 2002/05/26 22:02:02 wiz Exp $");
+#endif
+
+/*
+ * wrapper log(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+double
+log(double x) /* wrapper log */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_log(x);
+#else
+ double z;
+ z = __ieee754_log(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) return z;
+ if(x==0.0)
+ return __kernel_standard(x,x,16); /* log(0) */
+ else
+ return __kernel_standard(x,x,17); /* log(x<0) */
+#endif
+}
diff --git a/StdLib/LibC/Math/w_log10.c b/StdLib/LibC/Math/w_log10.c new file mode 100644 index 0000000000..4c82dfbccc --- /dev/null +++ b/StdLib/LibC/Math/w_log10.c @@ -0,0 +1,43 @@ +/* @(#)w_log10.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_log10.c,v 1.9 2002/05/26 22:02:02 wiz Exp $");
+#endif
+
+/*
+ * wrapper log10(X)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+double
+log10(double x) /* wrapper log10 */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_log10(x);
+#else
+ double z;
+ z = __ieee754_log10(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(x<=0.0) {
+ if(x==0.0)
+ return __kernel_standard(x,x,18); /* log10(0) */
+ else
+ return __kernel_standard(x,x,19); /* log10(x<0) */
+ } else
+ return z;
+#endif
+}
diff --git a/StdLib/LibC/Math/w_log2.c b/StdLib/LibC/Math/w_log2.c new file mode 100644 index 0000000000..35e4d1fccd --- /dev/null +++ b/StdLib/LibC/Math/w_log2.c @@ -0,0 +1,43 @@ +/* @(#)w_log10.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_log2.c,v 1.1 2005/07/21 16:58:39 christos Exp $");
+#endif
+
+/*
+ * wrapper log2(X)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+double
+log2(double x) /* wrapper log10 */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_log2(x);
+#else
+ double z;
+ z = __ieee754_log2(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(x<=0.0) {
+ if(x==0.0)
+ return __kernel_standard(x,x,48); /* log2(0) */
+ else
+ return __kernel_standard(x,x,49); /* log2(x<0) */
+ } else
+ return z;
+#endif
+}
diff --git a/StdLib/LibC/Math/w_pow.c b/StdLib/LibC/Math/w_pow.c new file mode 100644 index 0000000000..f5c4a39a90 --- /dev/null +++ b/StdLib/LibC/Math/w_pow.c @@ -0,0 +1,62 @@ +
+
+/* @(#)w_pow.c 5.2 93/10/01 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_pow.c,v 1.7 2002/05/26 22:02:02 wiz Exp $");
+#endif
+
+/*
+ * wrapper pow(x,y) return x**y
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+
+double
+pow(double x, double y) /* wrapper pow */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_pow(x,y);
+#else
+ double z;
+ z=__ieee754_pow(x,y);
+ if(_LIB_VERSION == _IEEE_|| isnan(y)) return z;
+ if(isnan(x)) {
+ if(y==0.0)
+ return __kernel_standard(x,y,42); /* pow(NaN,0.0) */
+ else
+ return z;
+ }
+ if(x==0.0){
+ if(y==0.0)
+ return __kernel_standard(x,y,20); /* pow(0.0,0.0) */
+ if(finite(y)&&y<0.0)
+ return __kernel_standard(x,y,23); /* pow(0.0,negative) */
+ return z;
+ }
+ if(!finite(z)) {
+ if(finite(x)&&finite(y)) {
+ if(isnan(z))
+ return __kernel_standard(x,y,24); /* pow neg**non-int */
+ else
+ return __kernel_standard(x,y,21); /* pow overflow */
+ }
+ }
+ if(z==0.0&&finite(x)&&finite(y))
+ return __kernel_standard(x,y,22); /* pow underflow */
+ return z;
+#endif
+}
diff --git a/StdLib/LibC/Math/w_sinh.c b/StdLib/LibC/Math/w_sinh.c new file mode 100644 index 0000000000..f653738a3c --- /dev/null +++ b/StdLib/LibC/Math/w_sinh.c @@ -0,0 +1,39 @@ +/* @(#)w_sinh.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_sinh.c,v 1.9 2002/05/26 22:02:03 wiz Exp $");
+#endif
+
+/*
+ * wrapper sinh(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+double
+sinh(double x) /* wrapper sinh */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_sinh(x);
+#else
+ double z;
+ z = __ieee754_sinh(x);
+ if(_LIB_VERSION == _IEEE_) return z;
+ if(!finite(z)&&finite(x)) {
+ return __kernel_standard(x,x,25); /* sinh overflow */
+ } else
+ return z;
+#endif
+}
diff --git a/StdLib/LibC/Math/w_sqrt.c b/StdLib/LibC/Math/w_sqrt.c new file mode 100644 index 0000000000..e55b4d8953 --- /dev/null +++ b/StdLib/LibC/Math/w_sqrt.c @@ -0,0 +1,39 @@ +/* @(#)w_sqrt.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+#include <LibConfig.h>
+#include <sys/EfiCdefs.h>
+#if defined(LIBM_SCCS) && !defined(lint)
+__RCSID("$NetBSD: w_sqrt.c,v 1.9 2002/05/26 22:02:03 wiz Exp $");
+#endif
+
+/*
+ * wrapper sqrt(x)
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+double
+sqrt(double x) /* wrapper sqrt */
+{
+#ifdef _IEEE_LIBM
+ return __ieee754_sqrt(x);
+#else
+ double z;
+ z = __ieee754_sqrt(x);
+ if(_LIB_VERSION == _IEEE_ || isnan(x)) return z;
+ if(x<0.0) {
+ return __kernel_standard(x,x,26); /* sqrt(negative) */
+ } else
+ return z;
+#endif
+}
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