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Specialize fdlibm to jerry

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Keep IEEE code paths only:
* removed SVID, XOPEN, POSIX code paths from everywhere.
* deleted s_lib_version.c, as version is only useful if multiple
  standards are supported.
* deleted k_standard.c, as it handles non-IEEE exception cases only.
* renamed the e_{acos,asin,atan2,exp,fmod,log,pow,sqrt}.c sources as
  s_.*, dropped the __ieee754_ prefix from the names of the
  appropriate functions therein, and deleted the
  w_{acos,asin,atan2,exp,fmod,log,pow,sqrt}.c wrapper code.

Keep C99 declaration variants only:
* removed old C-style function declaration variants.
* removed data declaration variants where const qualifier was not
  used.

Clean unused sources/functions:
* removed s_{rint,significand,tanh}.c and the appropriate functions
  defined therein.

JerryScript-DCO-1.0-Signed-off-by: Akos Kiss akiss@inf.u-szeged.hu
This commit is contained in:
Akos Kiss 2016-03-13 22:30:47 +01:00
parent d674b92f26
commit 397dff81ee
38 changed files with 266 additions and 1905 deletions
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59
third-party/fdlibm/e_rem_pio2.c vendored
View File

@ -13,39 +13,31 @@
*/
/* __ieee754_rem_pio2(x,y)
*
* return the remainder of x rem pi/2 in y[0]+y[1]
*
* return the remainder of x rem pi/2 in y[0]+y[1]
* use __kernel_rem_pio2()
*/
#include "fdlibm.h"
/*
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
*/
#ifdef __STDC__
static const int two_over_pi[] = {
#else
static int two_over_pi[] = {
#endif
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,
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,
};
#ifdef __STDC__
static const int npio2_hw[] = {
#else
static int npio2_hw[] = {
#endif
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
@ -64,11 +56,7 @@ static int npio2_hw[] = {
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
#ifdef __STDC__
static const double
#else
static double
#endif
static const double
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
@ -80,12 +68,7 @@ pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
#ifdef __STDC__
int __ieee754_rem_pio2(double x, double *y)
#else
int __ieee754_rem_pio2(x,y)
double x,y[];
#endif
int __ieee754_rem_pio2(double x, double *y)
{
double z,w,t,r,fn;
double tx[3];
@ -126,7 +109,7 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
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]) {
if(n<32&&ix!=npio2_hw[n-1]) {
y[0] = r-w; /* quick check no cancellation */
} else {
j = ix>>20;
@ -134,16 +117,16 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
i = j-(((__HI(y[0]))>>20)&0x7ff);
if(i>16) { /* 2nd iteration needed, good to 118 */
t = r;
w = fn*pio2_2;
w = fn*pio2_2;
r = t-w;
w = fn*pio2_2t-((t-r)-w);
w = fn*pio2_2t-((t-r)-w);
y[0] = r-w;
i = j-(((__HI(y[0]))>>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);
w = fn*pio2_3t-((t-r)-w);
y[0] = r-w;
}
}
@ -152,7 +135,7 @@ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
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 */

174
third-party/fdlibm/include/fdlibm.h vendored
View File

@ -24,56 +24,17 @@
#ifdef __LITTLE_ENDIAN
#define __HI(x) *(1+(int*)&x)
#define __LO(x) *(int*)&x
#define __HIp(x) *(1+(int*)x)
#define __LOp(x) *(int*)x
#else
#define __HI(x) *(int*)&x
#define __LO(x) *(1+(int*)&x)
#define __HIp(x) *(int*)x
#define __LOp(x) *(1+(int*)x)
#endif
#ifdef __STDC__
#define __P(p) p
#else
#define __P(p) ()
#endif
/*
* ANSI/POSIX
*/
extern int signgam;
#define MAXFLOAT ((float)3.40282346638528860e+38)
enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix};
#define _LIB_VERSION_TYPE enum fdversion
#define _LIB_VERSION _fdlib_version
/* if global variable _LIB_VERSION is not desirable, one may
* change the following to be a constant by:
* #define _LIB_VERSION_TYPE const enum version
* In that case, after one initializes the value _LIB_VERSION (see
* s_lib_version.c) during compile time, it cannot be modified
* in the middle of a program
*/
extern _LIB_VERSION_TYPE _LIB_VERSION;
#define _IEEE_ fdlibm_ieee
#define _SVID_ fdlibm_svid
#define _XOPEN_ fdlibm_xopen
#define _POSIX_ fdlibm_posix
struct exception {
int type;
char *name;
double arg1;
double arg2;
double retval;
};
#define HUGE MAXFLOAT
/*
@ -93,126 +54,39 @@ struct exception {
/*
* ANSI/POSIX
*/
extern double acos __P((double));
extern double asin __P((double));
extern double atan __P((double));
extern double atan2 __P((double, double));
extern double cos __P((double));
extern double sin __P((double));
extern double tan __P((double));
extern double acos (double);
extern double asin (double);
extern double atan (double);
extern double atan2 (double, double);
extern double cos (double);
extern double sin (double);
extern double tan (double);
extern double cosh __P((double));
extern double sinh __P((double));
extern double tanh __P((double));
extern double exp (double);
extern double log (double);
extern double exp __P((double));
extern double frexp __P((double, int *));
extern double ldexp __P((double, int));
extern double log __P((double));
extern double log10 __P((double));
extern double modf __P((double, double *));
extern double pow (double, double);
extern double sqrt (double);
extern double pow __P((double, double));
extern double sqrt __P((double));
extern double ceil (double);
extern double fabs (double);
extern double floor (double);
extern double fmod (double, double);
extern double ceil __P((double));
extern double fabs __P((double));
extern double floor __P((double));
extern double fmod __P((double, double));
extern double erf __P((double));
extern double erfc __P((double));
extern double gamma __P((double));
extern double hypot __P((double, double));
extern int isnan __P((double));
extern int finite __P((double));
extern double j0 __P((double));
extern double j1 __P((double));
extern double jn __P((int, double));
extern double lgamma __P((double));
extern double y0 __P((double));
extern double y1 __P((double));
extern double yn __P((int, double));
extern double acosh __P((double));
extern double asinh __P((double));
extern double atanh __P((double));
extern double cbrt __P((double));
extern double logb __P((double));
extern double nextafter __P((double, double));
extern double remainder __P((double, double));
#ifdef _SCALB_INT
extern double scalb __P((double, int));
#else
extern double scalb __P((double, double));
#endif
extern int matherr __P((struct exception *));
/*
* IEEE Test Vector
*/
extern double significand __P((double));
extern int isnan (double);
extern int finite (double);
/*
* Functions callable from C, intended to support IEEE arithmetic.
*/
extern double copysign __P((double, double));
extern int ilogb __P((double));
extern double rint __P((double));
extern double scalbn __P((double, int));
/*
* BSD math library entry points
*/
extern double expm1 __P((double));
extern double log1p __P((double));
/*
* Reentrant version of gamma & lgamma; passes signgam back by reference
* as the second argument; user must allocate space for signgam.
*/
#ifdef _REENTRANT
extern double gamma_r __P((double, int *));
extern double lgamma_r __P((double, int *));
#endif /* _REENTRANT */
extern double copysign (double, double);
extern double scalbn (double, int);
/* ieee style elementary functions */
extern double __ieee754_sqrt __P((double));
extern double __ieee754_acos __P((double));
extern double __ieee754_acosh __P((double));
extern double __ieee754_log __P((double));
extern double __ieee754_atanh __P((double));
extern double __ieee754_asin __P((double));
extern double __ieee754_atan2 __P((double,double));
extern double __ieee754_exp __P((double));
extern double __ieee754_cosh __P((double));
extern double __ieee754_fmod __P((double,double));
extern double __ieee754_pow __P((double,double));
extern double __ieee754_lgamma_r __P((double,int *));
extern double __ieee754_gamma_r __P((double,int *));
extern double __ieee754_lgamma __P((double));
extern double __ieee754_gamma __P((double));
extern double __ieee754_log10 __P((double));
extern double __ieee754_sinh __P((double));
extern double __ieee754_hypot __P((double,double));
extern double __ieee754_j0 __P((double));
extern double __ieee754_j1 __P((double));
extern double __ieee754_y0 __P((double));
extern double __ieee754_y1 __P((double));
extern double __ieee754_jn __P((int,double));
extern double __ieee754_yn __P((int,double));
extern double __ieee754_remainder __P((double,double));
extern int __ieee754_rem_pio2 __P((double,double*));
#ifdef _SCALB_INT
extern double __ieee754_scalb __P((double,int));
#else
extern double __ieee754_scalb __P((double,double));
#endif
extern int __ieee754_rem_pio2 (double,double*);
/* fdlibm kernel function */
extern double __kernel_standard __P((double,double,int));
extern double __kernel_sin __P((double,double,int));
extern double __kernel_cos __P((double,double));
extern double __kernel_tan __P((double,double,int));
extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const 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*);

29
third-party/fdlibm/k_cos.c vendored
View File

@ -15,7 +15,7 @@
* __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.
* Input y is the tail of x.
*
* Algorithm
* 1. Since cos(-x) = cos(x), we need only to consider positive x.
@ -26,14 +26,14 @@
* 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
* | 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
* 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))
@ -48,11 +48,7 @@
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
static const double
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
@ -61,12 +57,7 @@ C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
#ifdef __STDC__
double __kernel_cos(double x, double y)
#else
double __kernel_cos(x, y)
double x,y;
#endif
double __kernel_cos(double x, double y)
{
double a,hz,z,r,qx;
int ix;
@ -76,7 +67,7 @@ C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
}
z = x*x;
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
if(ix < 0x3FD33333) /* if |x| < 0.3 */
if(ix < 0x3FD33333) /* if |x| < 0.3 */
return one - (0.5*z - (z*r - x*y));
else {
if(ix > 0x3fe90000) { /* x > 0.78125 */

73
third-party/fdlibm/k_rem_pio2.c vendored
View File

@ -14,12 +14,12 @@
/*
* __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
*
* __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
* 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
@ -28,10 +28,10 @@
* (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
* 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
* 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]:
@ -61,15 +61,15 @@
*
* nx dimension of x[]
*
* prec an integer indicating the precision:
* 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
* 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)).
@ -80,12 +80,12 @@
*
* Here is the description of some local variables:
*
* jk jk+1 is the initial number of terms of ipio2[] needed
* 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.
* jz local integer variable indicating the number of
* terms of ipio2[] used.
*
* jx nx - 1
*
@ -98,16 +98,16 @@
*
* jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
*
* q[] double array with integral value, representing the
* 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.
* into 24 bits chunks.
*
* f[] ipio2[] in floating point
* f[] ipio2[] in floating point
*
* iq[] integer array by breaking up q[] in 24-bits chunk.
*
@ -121,25 +121,17 @@
/*
* 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
* 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 "fdlibm.h"
#ifdef __STDC__
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
#else
static int init_jk[] = {2,3,4,6};
#endif
#ifdef __STDC__
static const double PIo2[] = {
#else
static double PIo2[] = {
#endif
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
@ -150,22 +142,13 @@ static double PIo2[] = {
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
};
#ifdef __STDC__
static const double
#else
static double
#endif
static const double
zero = 0.0,
one = 1.0,
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
#ifdef __STDC__
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
#else
int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
double x[], y[]; int e0,nx,prec; int ipio2[];
#endif
int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
{
int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
double z,fw,f[20],fq[20],q[20];
@ -258,7 +241,7 @@ recompute:
while(iq[jz]==0) { jz--; q0-=24;}
} else { /* break z into 24-bit if necessary */
z = scalbn(z,-q0);
if(z>=two24) {
if(z>=two24) {
fw = (double)((int)(twon24*z));
iq[jz] = (int)(z-two24*fw);
jz += 1; q0 += 24;
@ -283,29 +266,29 @@ recompute:
case 0:
fw = 0.0;
for (i=jz;i>=0;i--) fw += fq[i];
y[0] = (ih==0)? fw: -fw;
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;
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;
y[1] = (ih==0)? fw: -fw;
break;
case 3: /* painful */
for (i=jz;i>0;i--) {
fw = fq[i-1]+fq[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];
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];
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 {

27
third-party/fdlibm/k_sin.c vendored
View File

@ -15,10 +15,10 @@
* 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).
* 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.
* 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]
@ -26,13 +26,13 @@
* 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 |
*
* |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
* For better accuracy, let
* 3 2 2 2 2
* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
* then 3 2
@ -41,11 +41,7 @@
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
static const double
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
@ -54,12 +50,7 @@ S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
#ifdef __STDC__
double __kernel_sin(double x, double y, int iy)
#else
double __kernel_sin(x, y, iy)
double x,y; int iy; /* iy=0 if y is zero */
#endif
double __kernel_sin(double x, double y, int iy)
{
double z,r,v;
int ix;

733
third-party/fdlibm/k_standard.c vendored
View File

@ -1,733 +0,0 @@
/* @(#)k_standard.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 "fdlibm.h"
#include <errno.h>
#ifndef _USE_WRITE
#include <stdio.h> /* fputs(), stderr */
// #define WRITE2(u,v) fputs(u, stderr)
#else /* !defined(_USE_WRITE) */
#include <unistd.h> /* write */
// #define WRITE2(u,v) write(2, u, v)
#undef fflush
#endif /* !defined(_USE_WRITE) */
static double zero = 0.0; /* used as const */
/*
* Standard conformance (non-IEEE) on exception cases.
* Mapping:
* 1 -- acos(|x|>1)
* 2 -- asin(|x|>1)
* 3 -- atan2(+-0,+-0)
* 4 -- hypot overflow
* 5 -- cosh overflow
* 6 -- exp overflow
* 7 -- exp underflow
* 8 -- y0(0)
* 9 -- y0(-ve)
* 10-- y1(0)
* 11-- y1(-ve)
* 12-- yn(0)
* 13-- yn(-ve)
* 14-- lgamma(finite) overflow
* 15-- lgamma(-integer)
* 16-- log(0)
* 17-- log(x<0)
* 18-- log10(0)
* 19-- log10(x<0)
* 20-- pow(0.0,0.0)
* 21-- pow(x,y) overflow
* 22-- pow(x,y) underflow
* 23-- pow(0,negative)
* 24-- pow(neg,non-integral)
* 25-- sinh(finite) overflow
* 26-- sqrt(negative)
* 27-- fmod(x,0)
* 28-- remainder(x,0)
* 29-- acosh(x<1)
* 30-- atanh(|x|>1)
* 31-- atanh(|x|=1)
* 32-- scalb overflow
* 33-- scalb underflow
* 34-- j0(|x|>X_TLOSS)
* 35-- y0(x>X_TLOSS)
* 36-- j1(|x|>X_TLOSS)
* 37-- y1(x>X_TLOSS)
* 38-- jn(|x|>X_TLOSS, n)
* 39-- yn(x>X_TLOSS, n)
* 40-- gamma(finite) overflow
* 41-- gamma(-integer)
* 42-- pow(NaN,0.0)
*/
#ifdef __STDC__
double __kernel_standard(double x, double y, int type)
#else
double __kernel_standard(x,y,type)
double x,y; int type;
#endif
{
struct exception exc;
#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */
#define HUGE_VAL inf
double inf = 0.0;
__HI(inf) = 0x7ff00000; /* set inf to infinite */
#endif
#ifdef _USE_WRITE
(void) fflush(stdout);
#endif
exc.arg1 = x;
exc.arg2 = y;
switch(type) {
case 1:
/* acos(|x|>1) */
exc.type = DOMAIN;
exc.name = "acos";
exc.retval = zero;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if(_LIB_VERSION == _SVID_) {
// // (void) WRITE2("acos: DOMAIN error\n", 19);
// }
// errno = EDOM;
// }
break;
case 2:
/* asin(|x|>1) */
exc.type = DOMAIN;
exc.name = "asin";
exc.retval = zero;
// if(_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if(_LIB_VERSION == _SVID_) {
// // (void) WRITE2("asin: DOMAIN error\n", 19);
// }
// errno = EDOM;
// }
break;
case 3:
/* atan2(+-0,+-0) */
exc.arg1 = y;
exc.arg2 = x;
exc.type = DOMAIN;
exc.name = "atan2";
exc.retval = zero;
// if(_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if(_LIB_VERSION == _SVID_) {
// // (void) WRITE2("atan2: DOMAIN error\n", 20);
// }
// errno = EDOM;
// }
break;
case 4:
/* hypot(finite,finite) overflow */
exc.type = OVERFLOW;
exc.name = "hypot";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 5:
/* cosh(finite) overflow */
exc.type = OVERFLOW;
exc.name = "cosh";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 6:
/* exp(finite) overflow */
exc.type = OVERFLOW;
exc.name = "exp";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 7:
/* exp(finite) underflow */
exc.type = UNDERFLOW;
exc.name = "exp";
exc.retval = zero;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 8:
/* y0(0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "y0";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("y0: DOMAIN error\n", 17);
// }
// errno = EDOM;
// }
break;
case 9:
/* y0(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "y0";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("y0: DOMAIN error\n", 17);
// }
// errno = EDOM;
// }
break;
case 10:
/* y1(0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "y1";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("y1: DOMAIN error\n", 17);
// }
// errno = EDOM;
// }
break;
case 11:
/* y1(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "y1";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("y1: DOMAIN error\n", 17);
// }
// errno = EDOM;
// }
break;
case 12:
/* yn(n,0) = -inf */
exc.type = DOMAIN; /* should be SING for IEEE */
exc.name = "yn";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("yn: DOMAIN error\n", 17);
// }
// errno = EDOM;
// }
break;
case 13:
/* yn(x<0) = NaN */
exc.type = DOMAIN;
exc.name = "yn";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("yn: DOMAIN error\n", 17);
// }
// errno = EDOM;
// }
break;
case 14:
/* lgamma(finite) overflow */
exc.type = OVERFLOW;
exc.name = "lgamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 15:
/* lgamma(-integer) or lgamma(0) */
exc.type = SING;
exc.name = "lgamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("lgamma: SING error\n", 19);
// }
// errno = EDOM;
// }
break;
case 16:
/* log(0) */
exc.type = SING;
exc.name = "log";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("log: SING error\n", 16);
// }
// errno = EDOM;
// }
break;
case 17:
/* log(x<0) */
exc.type = DOMAIN;
exc.name = "log";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("log: DOMAIN error\n", 18);
// }
// errno = EDOM;
// }
break;
case 18:
/* log10(0) */
exc.type = SING;
exc.name = "log10";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("log10: SING error\n", 18);
// }
// errno = EDOM;
// }
break;
case 19:
/* log10(x<0) */
exc.type = DOMAIN;
exc.name = "log10";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("log10: DOMAIN error\n", 20);
// }
// errno = EDOM;
// }
break;
case 20:
/* pow(0.0,0.0) */
/* error only if _LIB_VERSION == _SVID_ */
exc.type = DOMAIN;
exc.name = "pow";
exc.retval = zero;
// if (_LIB_VERSION != _SVID_) exc.retval = 1.0;
// else if (!matherr(&exc)) {
// // (void) WRITE2("pow(0,0): DOMAIN error\n", 23);
// errno = EDOM;
// }
break;
case 21:
/* pow(x,y) overflow */
exc.type = OVERFLOW;
exc.name = "pow";
if (_LIB_VERSION == _SVID_) {
exc.retval = HUGE;
y *= 0.5;
if(x<zero&&rint(y)!=y) exc.retval = -HUGE;
} else {
exc.retval = HUGE_VAL;
y *= 0.5;
if(x<zero&&rint(y)!=y) exc.retval = -HUGE_VAL;
}
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 22:
/* pow(x,y) underflow */
exc.type = UNDERFLOW;
exc.name = "pow";
exc.retval = zero;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 23:
/* 0**neg */
exc.type = DOMAIN;
exc.name = "pow";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("pow(0,neg): DOMAIN error\n", 25);
// }
// errno = EDOM;
// }
break;
case 24:
/* neg**non-integral */
exc.type = DOMAIN;
exc.name = "pow";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = zero/zero; /* X/Open allow NaN */
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("neg**non-integral: DOMAIN error\n", 32);
// }
// errno = EDOM;
// }
break;
case 25:
/* sinh(finite) overflow */
exc.type = OVERFLOW;
exc.name = "sinh";
if (_LIB_VERSION == _SVID_)
exc.retval = ( (x>zero) ? HUGE : -HUGE);
else
exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL);
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 26:
/* sqrt(x<0) */
exc.type = DOMAIN;
exc.name = "sqrt";
if (_LIB_VERSION == _SVID_)
exc.retval = zero;
else
exc.retval = zero/zero;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("sqrt: DOMAIN error\n", 19);
// }
// errno = EDOM;
// }
break;
case 27:
/* fmod(x,0) */
exc.type = DOMAIN;
exc.name = "fmod";
if (_LIB_VERSION == _SVID_)
exc.retval = x;
else
exc.retval = zero/zero;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("fmod: DOMAIN error\n", 20);
// }
// errno = EDOM;
// }
break;
case 28:
/* remainder(x,0) */
exc.type = DOMAIN;
exc.name = "remainder";
exc.retval = zero/zero;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("remainder: DOMAIN error\n", 24);
// }
// errno = EDOM;
// }
break;
case 29:
/* acosh(x<1) */
exc.type = DOMAIN;
exc.name = "acosh";
exc.retval = zero/zero;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("acosh: DOMAIN error\n", 20);
// }
// errno = EDOM;
// }
break;
case 30:
/* atanh(|x|>1) */
exc.type = DOMAIN;
exc.name = "atanh";
exc.retval = zero/zero;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("atanh: DOMAIN error\n", 20);
// }
// errno = EDOM;
// }
break;
case 31:
/* atanh(|x|=1) */
exc.type = SING;
exc.name = "atanh";
exc.retval = x/zero; /* sign(x)*inf */
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("atanh: SING error\n", 18);
// }
// errno = EDOM;
// }
break;
case 32:
/* scalb overflow; SVID also returns +-HUGE_VAL */
exc.type = OVERFLOW;
exc.name = "scalb";
exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 33:
/* scalb underflow */
exc.type = UNDERFLOW;
exc.name = "scalb";
exc.retval = copysign(zero,x);
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 34:
/* j0(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "j0";
exc.retval = zero;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2(exc.name, 2);
// // (void) WRITE2(": TLOSS error\n", 14);
// }
// errno = ERANGE;
// }
break;
case 35:
/* y0(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "y0";
exc.retval = zero;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2(exc.name, 2);
// // (void) WRITE2(": TLOSS error\n", 14);
// }
// errno = ERANGE;
// }
break;
case 36:
/* j1(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "j1";
exc.retval = zero;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2(exc.name, 2);
// // (void) WRITE2(": TLOSS error\n", 14);
// }
// errno = ERANGE;
// }
break;
case 37:
/* y1(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "y1";
exc.retval = zero;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2(exc.name, 2);
// // (void) WRITE2(": TLOSS error\n", 14);
// }
// errno = ERANGE;
// }
break;
case 38:
/* jn(|x|>X_TLOSS) */
exc.type = TLOSS;
exc.name = "jn";
exc.retval = zero;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2(exc.name, 2);
// // (void) WRITE2(": TLOSS error\n", 14);
// }
// errno = ERANGE;
// }
break;
case 39:
/* yn(x>X_TLOSS) */
exc.type = TLOSS;
exc.name = "yn";
exc.retval = zero;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2(exc.name, 2);
// // (void) WRITE2(": TLOSS error\n", 14);
// }
// errno = ERANGE;
// }
break;
case 40:
/* gamma(finite) overflow */
exc.type = OVERFLOW;
exc.name = "gamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = ERANGE;
// else if (!matherr(&exc)) {
// errno = ERANGE;
// }
break;
case 41:
/* gamma(-integer) or gamma(0) */
exc.type = SING;
exc.name = "gamma";
if (_LIB_VERSION == _SVID_)
exc.retval = HUGE;
else
exc.retval = HUGE_VAL;
// if (_LIB_VERSION == _POSIX_)
// errno = EDOM;
// else if (!matherr(&exc)) {
// if (_LIB_VERSION == _SVID_) {
// // (void) WRITE2("gamma: SING error\n", 18);
// }
// errno = EDOM;
// }
break;
case 42:
/* pow(NaN,0.0) */
/* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */
exc.type = DOMAIN;
exc.name = "pow";
exc.retval = x;
// if (_LIB_VERSION == _IEEE_ ||
// _LIB_VERSION == _POSIX_) exc.retval = 1.0;
// else if (!matherr(&exc)) {
// errno = EDOM;
// }
// break;
}
return exc.retval;
}

12
third-party/fdlibm/k_tan.c vendored
View File

@ -10,7 +10,6 @@
* ====================================================
*/
/* INDENT OFF */
/* __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.
@ -26,9 +25,9 @@
* tan(x) ~ x + T1*x + ... + T13*x
* where
*
* |tan(x) 2 4 26 | -59.2
* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
* | x |
* |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
@ -68,10 +67,9 @@ static const double xxx[] = {
#define pio4 xxx[14]
#define pio4lo xxx[15]
#define T xxx
/* INDENT ON */
double
__kernel_tan(double x, double y, int iy) {
double __kernel_tan(double x, double y, int iy)
{
double z, r, v, w, s;
int ix, hx;

25
third-party/fdlibm/e_acos.c → third-party/fdlibm/s_acos.c vendored
View File

@ -11,15 +11,15 @@
* ====================================================
*/
/* __ieee754_acos(x)
* Method :
/* 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))
* 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
@ -37,13 +37,9 @@
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
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 */
@ -57,12 +53,7 @@ qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
#ifdef __STDC__
double __ieee754_acos(double x)
#else
double __ieee754_acos(x)
double x;
#endif
double acos(double x)
{
double z,p,q,r,w,s,c,df;
int hx,ix;

25
third-party/fdlibm/e_asin.c → third-party/fdlibm/s_asin.c vendored
View File

@ -11,13 +11,13 @@
* ====================================================
*/
/* __ieee754_asin(x)
* Method :
/* 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
* 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)
*
@ -44,11 +44,7 @@
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
huge = 1.000e+300,
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
@ -66,12 +62,7 @@ qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
#ifdef __STDC__
double __ieee754_asin(double x)
#else
double __ieee754_asin(x)
double x;
#endif
double asin(double x)
{
double t = 0,w,p,q,c,r,s;
int hx,ix;
@ -80,8 +71,8 @@ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
if(ix>= 0x3ff00000) { /* |x|>= 1 */
if(((ix-0x3ff00000)|__LO(x))==0)
/* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
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*/
@ -109,6 +100,6 @@ qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
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;
}
if(hx>0) return t; else return -t;
}

35
third-party/fdlibm/s_atan.c vendored
View File

@ -26,41 +26,29 @@
* [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
* 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 "fdlibm.h"
#ifdef __STDC__
static const double atanhi[] = {
#else
static double atanhi[] = {
#endif
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 */
};
#ifdef __STDC__
static const double atanlo[] = {
#else
static double atanlo[] = {
#endif
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 */
};
#ifdef __STDC__
static const double aT[] = {
#else
static double aT[] = {
#endif
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
@ -74,20 +62,11 @@ static double aT[] = {
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
};
#ifdef __STDC__
static const double
#else
static double
#endif
static const double
one = 1.0,
huge = 1.0e300;
#ifdef __STDC__
double atan(double x)
#else
double atan(x)
double x;
#endif
double atan(double x)
{
double w,s1,s2,z;
int ix,hx,id;
@ -109,9 +88,9 @@ huge = 1.0e300;
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);
id = 0; x = (2.0*x-one)/(2.0+x);
} else { /* 11/16<=|x|< 19/16 */
id = 1; x = (x-one)/(x+one);
id = 1; x = (x-one)/(x+one);
}
} else {
if (ix < 0x40038000) { /* |x| < 2.4375 */

23
third-party/fdlibm/e_atan2.c → third-party/fdlibm/s_atan2.c vendored
View File

@ -12,10 +12,10 @@
*
*/
/* __ieee754_atan2(y,x)
/* 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):
* 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,
*
@ -33,19 +33,15 @@
* 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
* 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 "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
static const double
tiny = 1.0e-300,
zero = 0.0,
pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
@ -53,12 +49,7 @@ pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
#ifdef __STDC__
double __ieee754_atan2(double y, double x)
#else
double __ieee754_atan2(y,x)
double y,x;
#endif
double atan2(double y, double x)
{
double z;
int k,m,hx,hy,ix,iy;

15
third-party/fdlibm/s_ceil.c vendored
View File

@ -22,18 +22,9 @@
#include "fdlibm.h"
#ifdef __STDC__
static const double huge = 1.0e300;
#else
static double huge = 1.0e300;
#endif
#ifdef __STDC__
double ceil(double x)
#else
double ceil(x)
double x;
#endif
double ceil(double x)
{
int i0,i1,j0;
unsigned i,j;
@ -43,7 +34,7 @@ static double huge = 1.0e300;
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;}
if(i0<0) {i0=0x80000000;i1=0;}
else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;}
}
} else {
@ -62,7 +53,7 @@ static double huge = 1.0e300;
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;
if(j0==20) i0+=1;
else {
j = i1 + (1<<(52-j0));
if(j<i1) i0+=1; /* got a carry */

7
third-party/fdlibm/s_copysign.c vendored
View File

@ -19,12 +19,7 @@
#include "fdlibm.h"
#ifdef __STDC__
double copysign(double x, double y)
#else
double copysign(x,y)
double x,y;
#endif
double copysign(double x, double y)
{
__HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000);
return x;

13
third-party/fdlibm/s_cos.c vendored
View File

@ -20,8 +20,8 @@
* __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
* 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
*
@ -39,17 +39,12 @@
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
* TRIG(x) returns trig(x) nearly rounded
*/
#include "fdlibm.h"
#ifdef __STDC__
double cos(double x)
#else
double cos(x)
double x;
#endif
double cos(double x)
{
double y[2],z=0.0;
int n, ix;

41
third-party/fdlibm/e_exp.c → third-party/fdlibm/s_exp.c vendored
View File

@ -10,7 +10,7 @@
* ====================================================
*/
/* __ieee754_exp(x)
/* exp(x)
* Returns the exponential of x.
*
* Method
@ -18,36 +18,36 @@
* 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.
* x = k*ln2 + r, |r| <= 0.5*ln2.
*
* Here r will be represented as r = hi-lo for better
* 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 Remes algorithm on [0,0.34658] to generate
* a polynomial of degree 5 to approximate R. The maximum error
* We use a special Remes 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)
* (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
* | 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)
* 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)
@ -62,24 +62,20 @@
* 1 ulp (unit in the last place).
*
* Misc. info.
* For IEEE double
* 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
* 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 "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
halF[2] = {0.5,-0.5,},
huge = 1.0e+300,
@ -98,12 +94,7 @@ P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
#ifdef __STDC__
double __ieee754_exp(double x) /* default IEEE double exp */
#else
double __ieee754_exp(x) /* default IEEE double exp */
double x;
#endif
double exp(double x) /* default IEEE double exp */
{
double y,hi,lo,c,t;
int k = 0,xsb;
@ -125,7 +116,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
}
/* argument reduction */
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
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 {
@ -135,7 +126,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
lo = t*ln2LO[0];
}
x = hi - lo;
}
}
else if(hx < 0x3e300000) { /* when |x|<2**-28 */
if(huge+x>one) return one+x;/* trigger inexact */
}
@ -144,7 +135,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
/* 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);
if(k==0) return one-((x*c)/(c-2.0)-x);
else y = one-((lo-(x*c)/(2.0-c))-hi);
if(k >= -1021) {
__HI(y) += (k<<20); /* add k to y's exponent */

7
third-party/fdlibm/s_fabs.c vendored
View File

@ -17,12 +17,7 @@
#include "fdlibm.h"
#ifdef __STDC__
double fabs(double x)
#else
double fabs(x)
double x;
#endif
double fabs(double x)
{
__HI(x) &= 0x7fffffff;
return x;

9
third-party/fdlibm/s_finite.c vendored
View File

@ -18,14 +18,9 @@
#include "fdlibm.h"
#ifdef __STDC__
int finite(double x)
#else
int finite(x)
double x;
#endif
int finite(double x)
{
int hx;
int hx;
hx = __HI(x);
return (unsigned)((hx&0x7fffffff)-0x7ff00000)>>31;
}

15
third-party/fdlibm/s_floor.c vendored
View File

@ -22,18 +22,9 @@
#include "fdlibm.h"
#ifdef __STDC__
static const double huge = 1.0e300;
#else
static double huge = 1.0e300;
#endif
#ifdef __STDC__
double floor(double x)
#else
double floor(x)
double x;
#endif
double floor(double x)
{
int i0,i1,j0;
unsigned i,j;
@ -43,7 +34,7 @@ static double huge = 1.0e300;
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;}
if(i0>=0) {i0=i1=0;}
else if(((i0&0x7fffffff)|i1)!=0)
{ i0=0xbff00000;i1=0;}
}
@ -63,7 +54,7 @@ static double huge = 1.0e300;
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;
if(j0==20) i0+=1;
else {
j = i1+(1<<(52-j0));
if(j<i1) i0 +=1 ; /* got a carry */

17
third-party/fdlibm/e_fmod.c → third-party/fdlibm/s_fmod.c vendored
View File

@ -12,25 +12,18 @@
*/
/*
* __ieee754_fmod(x,y)
* fmod(x,y)
* Return x mod y in exact arithmetic
* Method: shift and subtract
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, Zero[] = {0.0, -0.0,};
#else
static double one = 1.0, Zero[] = {0.0, -0.0,};
#endif
static const double
one = 1.0,
Zero[] = {0.0, -0.0,};
#ifdef __STDC__
double __ieee754_fmod(double x, double y)
#else
double __ieee754_fmod(x,y)
double x,y ;
#endif
double fmod(double x, double y)
{
int n,hx,hy,hz,ix,iy,sx,i;
unsigned lx,ly,lz;

9
third-party/fdlibm/s_isnan.c vendored
View File

@ -18,17 +18,12 @@
#include "fdlibm.h"
#ifdef __STDC__
int isnan(double x)
#else
int isnan(x)
double x;
#endif
int isnan(double x)
{
int hx,lx;
hx = (__HI(x)&0x7fffffff);
lx = __LO(x);
hx |= (unsigned)(lx|(-lx))>>31;
hx |= (unsigned)(lx|(-lx))>>31;
hx = 0x7ff00000 - hx;
return ((unsigned)(hx))>>31;
}

35
third-party/fdlibm/s_lib_version.c vendored
View File

@ -1,35 +0,0 @@
/* @(#)s_lib_version.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.
* ====================================================
*/
/*
* MACRO for standards
*/
#include "fdlibm.h"
/*
* define and initialize _LIB_VERSION
*/
#ifdef _POSIX_MODE
_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_;
#else
#ifdef _XOPEN_MODE
_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_;
#else
#ifdef _SVID3_MODE
_LIB_VERSION_TYPE _LIB_VERSION = _SVID_;
#else /* default _IEEE_MODE */
_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_;
#endif
#endif
#endif

47
third-party/fdlibm/e_log.c → third-party/fdlibm/s_log.c vendored
View File

@ -11,28 +11,28 @@
* ====================================================
*/
/* __ieee754_log(x)
/* log(x)
* Return the logrithm of x
*
* Method :
* 1. Argument Reduction: find k and f such that
* x = 2^k * (1+f),
* 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
* 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)
* (the values of Lg1 to Lg7 are listed in the program)
* and
* | 2 14 | -58.45
* | Lg1*s +...+Lg7*s - R(z) | <= 2
* | 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
@ -40,14 +40,14 @@
* 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).
* 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:
* 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(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.
*
@ -56,19 +56,15 @@
* 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
* 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 "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
@ -80,14 +76,9 @@ Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
static double zero = 0.0;
static const double zero = 0.0;
#ifdef __STDC__
double __ieee754_log(double x)
#else
double __ieee754_log(x)
double x;
#endif
double log(double x)
{
double hfsq,f,s,z,R,w,t1,t2,dk;
int k,hx,i,j;
@ -118,14 +109,14 @@ static double zero = 0.0;
if(k==0) return f-R; else {dk=(double)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
s = f/(2.0+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)));
t1= w*(Lg2+w*(Lg4+w*Lg6));
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
i |= j;
R = t2+t1;
if(i>0) {

51
third-party/fdlibm/e_pow.c → third-party/fdlibm/s_pow.c vendored
View File

@ -10,14 +10,14 @@
* ====================================================
*/
/* __ieee754_pow(x,y) return x**y
/* 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 muti-precision
* 2. Perform y*log2(x) = n+y' by simulating muti-precision
* arithmetic, where |y'|<=0.5.
* 3. Return x**y = 2**n*exp(y'*log2)
*
@ -45,23 +45,19 @@
* Accuracy:
* pow(x,y) returns x**y nearly rounded. In particular
* pow(integer,integer)
* always returns the correct integer provided it is
* 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
* 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 "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
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 */
@ -94,12 +90,7 @@ 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*/
#ifdef __STDC__
double __ieee754_pow(double x, double y)
#else
double __ieee754_pow(x,y)
double x, y;
#endif
double 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;
@ -113,12 +104,12 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
/* y==zero: x**0 = 1 */
if((iy|ly)==0) return one;
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;
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
@ -126,7 +117,7 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
* yisint = 2 ... y is an even int
*/
yisint = 0;
if(hx<0) {
if(hx<0) {
if(iy>=0x43400000) yisint = 2; /* even integer y */
else if(iy>=0x3ff00000) {
k = (iy>>20)-0x3ff; /* exponent */
@ -137,11 +128,11 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
j = iy>>(20-k);
if((j<<(20-k))==iy) yisint = 2-(j&1);
}
}
}
}
}
/* special value of y */
if(ly==0) {
if(ly==0) {
if (iy==0x7ff00000) { /* y is +-inf */
if(((ix-0x3ff00000)|lx)==0)
return y - y; /* inf**+-1 is NaN */
@ -156,7 +147,7 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
if(hy==0x40000000) return x*x; /* y is 2 */
if(hy==0x3fe00000) { /* y is 0.5 */
if(hx>=0) /* x >= +0 */
return sqrt(x);
return sqrt(x);
}
}
@ -169,13 +160,13 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
if(hx<0) {
if(((ix-0x3ff00000)|yisint)==0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
} else if(yisint==1)
} else if(yisint==1)
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
}
n = (hx>>31)+1;
/* (x<0)**(non-int) is NaN */
@ -193,7 +184,7 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
/* 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
/* 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));
@ -225,7 +216,7 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
__LO(s_h) = 0;
/* t_h=ax+bp[k] High */
t_h = zero;
__HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
__HI(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) */
@ -287,7 +278,7 @@ ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
n = ((n&0x000fffff)|0x00100000)>>(20-k);
if(j<0) n = -n;
p_h -= t;
}
}
t = p_l+p_h;
__LO(t) = 0;
u = t*lg2_h;

84
third-party/fdlibm/s_rint.c vendored
View File

@ -1,84 +0,0 @@
/* @(#)s_rint.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.
* ====================================================
*/
/*
* rint(x)
* Return x rounded to integral value according to the prevailing
* rounding mode.
* Method:
* Using floating addition.
* Exception:
* Inexact flag raised if x not equal to rint(x).
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
TWO52[2]={
4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
-4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */
};
#ifdef __STDC__
double rint(double x)
#else
double rint(x)
double x;
#endif
{
int i0,j0,sx;
unsigned i,i1;
double w,t;
i0 = __HI(x);
sx = (i0>>31)&1;
i1 = __LO(x);
j0 = ((i0>>20)&0x7ff)-0x3ff;
if(j0<20) {
if(j0<0) {
if(((i0&0x7fffffff)|i1)==0) return x;
i1 |= (i0&0x0fffff);
i0 &= 0xfffe0000;
i0 |= ((i1|-i1)>>12)&0x80000;
__HI(x)=i0;
w = TWO52[sx]+x;
t = w-TWO52[sx];
i0 = __HI(t);
__HI(t) = (i0&0x7fffffff)|(sx<<31);
return t;
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
i>>=1;
if(((i0&i)|i1)!=0) {
if(j0==19) i1 = 0x40000000; else
i0 = (i0&(~i))|((0x20000)>>j0);
}
}
} else if (j0>51) {
if(j0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((unsigned)(0xffffffff))>>(j0-20);
if((i1&i)==0) return x; /* x is integral */
i>>=1;
if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20));
}
__HI(x) = i0;
__LO(x) = i1;
w = TWO52[sx]+x;
return w-TWO52[sx];
}

23
third-party/fdlibm/s_scalbn.c vendored
View File

@ -11,31 +11,22 @@
* ====================================================
*/
/*
/*
* scalbn (double x, int n)
* scalbn(x,n) returns x* 2**n computed by exponent
* manipulation rather than by actually performing an
* scalbn(x,n) returns x* 2**n computed by exponent
* manipulation rather than by actually performing an
* exponentiation or a multiplication.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
huge = 1.0e+300,
tiny = 1.0e-300;
#ifdef __STDC__
double scalbn (double x, int n)
#else
double scalbn (x,n)
double x; int n;
#endif
double scalbn (double x, int n)
{
int k,hx,lx;
hx = __HI(x);
@ -45,7 +36,7 @@ tiny = 1.0e-300;
if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
x *= two54;
hx = __HI(x);
k = ((hx&0x7ff00000)>>20) - 54;
k = ((hx&0x7ff00000)>>20) - 54;
if (n< -50000) return tiny*x; /*underflow*/
}
if (k==0x7ff) return x+x; /* NaN or Inf */

30
third-party/fdlibm/s_significand.c vendored
View File

@ -1,30 +0,0 @@
/* @(#)s_significand.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.
* ====================================================
*/
/*
* significand(x) computes just
* scalb(x, (double) -ilogb(x)),
* for exercising the fraction-part(F) IEEE 754-1985 test vector.
*/
#include "fdlibm.h"
#ifdef __STDC__
double significand(double x)
#else
double significand(x)
double x;
#endif
{
return __ieee754_scalb(x,(double) -ilogb(x));
}

13
third-party/fdlibm/s_sin.c vendored
View File

@ -20,8 +20,8 @@
* __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
* 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
*
@ -39,17 +39,12 @@
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
* TRIG(x) returns trig(x) nearly rounded
*/
#include "fdlibm.h"
#ifdef __STDC__
double sin(double x)
#else
double sin(x)
double x;
#endif
double sin(double x)
{
double y[2],z=0.0;
int n, ix;

102
third-party/fdlibm/e_sqrt.c → third-party/fdlibm/s_sqrt.c vendored
View File

@ -11,15 +11,15 @@
* ====================================================
*/
/* __ieee754_sqrt(x)
/* 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)
* 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:
* 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
@ -28,9 +28,9 @@
* 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
*
* To compute q from q , one checks whether
* i+1 i
*
* -(i+1) 2
* (q + 2 ) <= y. (2)
@ -45,7 +45,7 @@
* s + 2 <= y (3)
* i i
*
* The advantage of (3) is that s and y can be computed by
* The advantage of (3) is that s and y can be computed by
* i i
* the following recurrence formula:
* if (3) is false
@ -57,10 +57,10 @@
* -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).
*
* 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
* 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.
@ -70,7 +70,7 @@
* 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
@ -83,21 +83,14 @@
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, tiny=1.0e-300;
#else
static double one = 1.0, tiny=1.0e-300;
#endif
static const double
one = 1.0,
tiny = 1.0e-300;
#ifdef __STDC__
double __ieee754_sqrt(double x)
#else
double __ieee754_sqrt(x)
double x;
#endif
double sqrt(double x)
{
double z;
int sign = (int)0x80000000;
int sign = (int)0x80000000;
unsigned r,t1,s1,ix1,q1;
int ix0,s0,q,m,t,i;
@ -108,7 +101,7 @@ static double one = 1.0, tiny=1.0e-300;
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 */
@ -142,12 +135,12 @@ static double one = 1.0, tiny=1.0e-300;
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;
}
t = s0+r;
if(t<=ix0) {
s0 = t+r;
ix0 -= t;
q += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
@ -155,9 +148,9 @@ static double one = 1.0, tiny=1.0e-300;
r = sign;
while(r!=0) {
t1 = s1+r;
t1 = s1+r;
t = s0;
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
s1 = t1+r;
if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
ix0 -= t;
@ -178,7 +171,7 @@ static double one = 1.0, tiny=1.0e-300;
if (q1==(unsigned)0xffffffff) { q1=0; q += 1;}
else if (z>one) {
if (q1==(unsigned)0xfffffffe) q+=1;
q1+=2;
q1+=2;
} else
q1 += (q1&1);
}
@ -195,18 +188,18 @@ static double one = 1.0, tiny=1.0e-300;
/*
Other methods (use floating-point arithmetic)
-------------
(This is a copy of a drafted paper by Prof W. Kahan
(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)
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,
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
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.
@ -216,7 +209,7 @@ 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
a floating point number x (in IEEE double format) respectively
1 11 52 ...widths
------------------------------------------------------
@ -224,7 +217,7 @@ A. sqrt(x) by Newton Iteration
------------------------------------------------------
msb lsb msb lsb ...order
------------------------ ------------------------
x0: |s| e | f1 | x1: | f2 |
------------------------ ------------------------
@ -249,7 +242,7 @@ A. sqrt(x) by Newton Iteration
(2) Iterative refinement
Apply Heron's rule three times to y, we have y approximates
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
@ -274,12 +267,12 @@ A. sqrt(x) by Newton Iteration
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
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
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
@ -310,7 +303,7 @@ A. sqrt(x) by Newton Iteration
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;
@ -329,7 +322,7 @@ B. sqrt(x) by Reciproot Iteration
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
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)
@ -350,9 +343,9 @@ B. sqrt(x) by Reciproot Iteration
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
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)
@ -361,7 +354,7 @@ B. sqrt(x) by Reciproot Iteration
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;
(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.
@ -408,27 +401,27 @@ B. sqrt(x) by Reciproot Iteration
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
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 then the foregoing red tape, the
If multiplication is cheaper then 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
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 |
z1: | f2 |
--------------------
bit 31 bit 0
@ -445,7 +438,6 @@ B. sqrt(x) by Reciproot Iteration
11 01 even
-------------------------------------------------
(4) Special cases (see (4) of Section A).
(4) Special cases (see (4) of Section A).
*/

13
third-party/fdlibm/s_tan.c vendored
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@ -19,8 +19,8 @@
* __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
* 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
*
@ -38,17 +38,12 @@
* trig(NaN) is that NaN;
*
* Accuracy:
* TRIG(x) returns trig(x) nearly rounded
* TRIG(x) returns trig(x) nearly rounded
*/
#include "fdlibm.h"
#ifdef __STDC__
double tan(double x)
#else
double tan(x)
double x;
#endif
double tan(double x)
{
double y[2],z=0.0;
int n, ix;

82
third-party/fdlibm/s_tanh.c vendored
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@ -1,82 +0,0 @@
/* @(#)s_tanh.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.
* ====================================================
*/
/* 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 "fdlibm.h"
#ifdef __STDC__
static const double one=1.0, two=2.0, tiny = 1.0e-300;
#else
static double one=1.0, two=2.0, tiny = 1.0e-300;
#endif
#ifdef __STDC__
double tanh(double x)
#else
double tanh(x)
double x;
#endif
{
double t,z;
int jx,ix;
/* High word of |x|. */
jx = __HI(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;
}

39
third-party/fdlibm/w_acos.c vendored
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@ -1,39 +0,0 @@
/* @(#)w_acos.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.
* ====================================================
*/
/*
* wrap_acos(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double acos(double x) /* wrapper acos */
#else
double acos(x) /* wrapper acos */
double x;
#endif
{
#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
}

41
third-party/fdlibm/w_asin.c vendored
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@ -1,41 +0,0 @@
/* @(#)w_asin.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.
* ====================================================
*
*/
/*
* wrapper asin(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double asin(double x) /* wrapper asin */
#else
double asin(x) /* wrapper asin */
double x;
#endif
{
#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
}

40
third-party/fdlibm/w_atan2.c vendored
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@ -1,40 +0,0 @@
/* @(#)w_atan2.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.
* ====================================================
*
*/
/*
* wrapper atan2(y,x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double atan2(double y, double x) /* wrapper atan2 */
#else
double atan2(y,x) /* wrapper atan2 */
double y,x;
#endif
{
#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
}

48
third-party/fdlibm/w_exp.c vendored
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@ -1,48 +0,0 @@
/* @(#)w_exp.c 1.4 04/04/22 */
/*
* ====================================================
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
*
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* wrapper exp(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double
#else
static double
#endif
o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
#ifdef __STDC__
double exp(double x) /* wrapper exp */
#else
double exp(x) /* wrapper exp */
double x;
#endif
{
#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
}

39
third-party/fdlibm/w_fmod.c vendored
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@ -1,39 +0,0 @@
/* @(#)w_fmod.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.
* ====================================================
*/
/*
* wrapper fmod(x,y)
*/
#include "fdlibm.h"
#ifdef __STDC__
double fmod(double x, double y) /* wrapper fmod */
#else
double fmod(x,y) /* wrapper fmod */
double x,y;
#endif
{
#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
}

39
third-party/fdlibm/w_log.c vendored
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@ -1,39 +0,0 @@
/* @(#)w_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.
* ====================================================
*/
/*
* wrapper log(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double log(double x) /* wrapper log */
#else
double log(x) /* wrapper log */
double x;
#endif
{
#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
}

59
third-party/fdlibm/w_pow.c vendored
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@ -1,59 +0,0 @@
/* @(#)w_pow.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.
* ====================================================
*/
/*
* wrapper pow(x,y) return x**y
*/
#include "fdlibm.h"
#ifdef __STDC__
double pow(double x, double y) /* wrapper pow */
#else
double pow(x,y) /* wrapper pow */
double x,y;
#endif
{
#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
}

38
third-party/fdlibm/w_sqrt.c vendored
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@ -1,38 +0,0 @@
/* @(#)w_sqrt.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.
* ====================================================
*/
/*
* wrapper sqrt(x)
*/
#include "fdlibm.h"
#ifdef __STDC__
double sqrt(double x) /* wrapper sqrt */
#else
double sqrt(x) /* wrapper sqrt */
double x;
#endif
{
#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
}