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Merge remote-tracking branch 'nsz/review'

This commit is contained in:
Rich Felker 2013-05-18 12:06:42 -04:00
parent 69ee9b2cb1 bfda379358
commit 83af1dd65a
15 changed files with 203 additions and 213 deletions
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57
src/math/__tan.c
View File

@ -12,7 +12,7 @@
* kernel tan function on ~[-pi/4, pi/4] (except on -0), 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.
* Input odd indicates whether tan (if odd = 0) or -1/tan (if odd = 1) is returned.
*
* Algorithm
* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
@ -63,21 +63,22 @@ static const double T[] = {
pio4 = 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
pio4lo = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */
double __tan(double x, double y, int iy)
double __tan(double x, double y, int odd)
{
double_t z, r, v, w, s, sign;
int32_t ix, hx;
double_t z, r, v, w, s, a;
double w0, a0;
uint32_t hx;
int big, sign;
GET_HIGH_WORD(hx,x);
ix = hx & 0x7fffffff; /* high word of |x| */
if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */
if (hx < 0) {
big = (hx&0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */
if (big) {
sign = hx>>31;
if (sign) {
x = -x;
y = -y;
}
z = pio4 - x;
w = pio4lo - y;
x = z + w;
x = (pio4 - x) + (pio4lo - y);
y = 0.0;
}
z = x * x;
@ -90,30 +91,20 @@ double __tan(double x, double y, int iy)
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;
r = y + z*(s*(r + v) + y) + s*T[0];
w = x + r;
if (ix >= 0x3FE59428) {
v = iy;
sign = 1 - ((hx >> 30) & 2);
return sign * (v - 2.0 * (x - (w * w / (w + v) - r)));
if (big) {
s = 1 - 2*odd;
v = s - 2.0 * (x + (r - w*w/(w + s)));
return sign ? -v : v;
}
if (iy == 1)
if (!odd)
return w;
else {
/*
* if allow error up to 2 ulp, simply return
* -1.0 / (x+r) here
*/
/* compute -1.0 / (x+r) accurately */
double_t a;
double z, 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);
}
/* -1.0/(x+r) has up to 2ulp error, so compute it accurately */
w0 = w;
SET_LOW_WORD(w0, 0);
v = r - (w0 - x); /* w0+v = r+x */
a0 = a = -1.0 / w;
SET_LOW_WORD(a0, 0);
return a0 + a*(1.0 + a0*w0 + a0*v);
}

5
src/math/__tandf.c
View File

@ -25,7 +25,7 @@ static const double T[] = {
0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */
};
float __tandf(double x, int iy)
float __tandf(double x, int odd)
{
double_t z,r,w,s,t,u;
@ -50,6 +50,5 @@ float __tandf(double x, int iy)
s = z*x;
u = T[0] + z*T[1];
r = (x + s*u) + (s*w)*(t + w*r);
if(iy==1) return r;
else return -1.0/r;
return odd ? -1.0/r : r;
}

32
src/math/__tanl.c
View File

@ -45,25 +45,21 @@ T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */
T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */
T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.0p-71 */
long double __tanl(long double x, long double y, int iy) {
long double __tanl(long double x, long double y, int odd) {
long double z, r, v, w, s, a, t;
long double osign;
int i;
int big, sign;
iy = iy == 1 ? -1 : 1; /* XXX recover original interface */
osign = copysignl(1.0, x);
if (fabsl(x) >= 0.67434) {
big = fabsl(x) >= 0.67434;
if (big) {
sign = 0;
if (x < 0) {
sign = 1;
x = -x;
y = -y;
}
z = pio4 - x;
w = pio4lo - y;
x = z + w;
x = (pio4 - x) + (pio4lo - y);
y = 0.0;
i = 1;
} else
i = 0;
}
z = x * x;
w = z * z;
r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
@ -71,14 +67,14 @@ long double __tanl(long double x, long double y, int iy) {
v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
w * (T27 + w * T31))))));
s = z * x;
r = y + z * (s * (r + v) + y);
r += T3 * s;
r = y + z * (s * (r + v) + y) + T3 * s;
w = x + r;
if (i == 1) {
v = (long double)iy;
return osign * (v - 2.0 * (x - (w * w / (w + v) - r)));
if (big) {
s = 1 - 2*odd;
v = s - 2.0 * (x + (r - w * w / (w + s)));
return sign ? -v : v;
}
if (iy == 1)
if (!odd)
return w;
/*

20
src/math/cos.c
View File

@ -44,26 +44,28 @@
double cos(double x)
{
double y[2],z=0.0;
int32_t n, ix;
double y[2];
uint32_t ix;
unsigned n;
GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix <= 0x3fe921fb) {
if (ix < 0x3e46a09e) /* if x < 2**-27 * sqrt(2) */
/* raise inexact if x != 0 */
if ((int)x == 0)
return 1.0;
return __cos(x, z);
if (ix < 0x3e46a09e) { /* |x| < 2**-27 * sqrt(2) */
/* raise inexact if x!=0 */
FORCE_EVAL(x + 0x1p120f);
return 1.0;
}
return __cos(x, 0);
}
/* cos(Inf or NaN) is NaN */
if (ix >= 0x7ff00000)
return x-x;
/* argument reduction needed */
/* argument reduction */
n = __rem_pio2(x, y);
switch (n&3) {
case 0: return __cos(y[0], y[1]);

33
src/math/cosf.c
View File

@ -26,34 +26,39 @@ c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
float cosf(float x)
{
double y;
int32_t n, hx, ix;
uint32_t ix;
unsigned n, sign;
GET_FLOAT_WORD(ix, x);
sign = ix >> 31;
ix &= 0x7fffffff;
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
if (ix < 0x39800000) /* |x| < 2**-12 */
if ((int)x == 0) /* raise inexact if x != 0 */
return 1.0;
if (ix < 0x39800000) { /* |x| < 2**-12 */
/* raise inexact if x != 0 */
FORCE_EVAL(x + 0x1p120f);
return 1.0f;
}
return __cosdf(x);
}
if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
if (ix > 0x4016cbe3) /* |x| ~> 3*pi/4 */
return -__cosdf(hx > 0 ? x-c2pio2 : x+c2pio2);
return -__cosdf(sign ? x+c2pio2 : x-c2pio2);
else {
if (hx > 0)
return __sindf(c1pio2 - x);
else
if (sign)
return __sindf(x + c1pio2);
else
return __sindf(c1pio2 - x);
}
}
if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
if (ix > 0x40afeddf) /* |x| ~> 7*pi/4 */
return __cosdf(hx > 0 ? x-c4pio2 : x+c4pio2);
return __cosdf(sign ? x+c4pio2 : x-c4pio2);
else {
if (hx > 0)
return __sindf(x - c3pio2);
if (sign)
return __sindf(-x - c3pio2);
else
return __sindf(-c3pio2 - x);
return __sindf(x - c3pio2);
}
}

22
src/math/cosl.c
View File

@ -39,30 +39,30 @@ long double cosl(long double x) {
long double cosl(long double x)
{
union IEEEl2bits z;
int e0;
unsigned n;
long double y[2];
long double hi, lo;
z.e = x;
z.bits.sign = 0;
/* If x = +-0 or x is a subnormal number, then cos(x) = 1 */
if (z.bits.exp == 0)
return 1.0;
/* If x = NaN or Inf, then cos(x) = NaN. */
if (z.bits.exp == 32767)
if (z.bits.exp == 0x7fff)
return (x - x) / (x - x);
/* Optimize the case where x is already within range. */
if (z.e < M_PI_4)
/* |x| < (double)pi/4 */
if (z.e < M_PI_4) {
/* |x| < 0x1p-64 */
if (z.bits.exp < 0x3fff - 64)
/* raise inexact if x!=0 */
return 1.0 + x;
return __cosl(z.e, 0);
}
e0 = __rem_pio2l(x, y);
n = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (e0 & 3) {
switch (n & 3) {
case 0:
hi = __cosl(hi, lo);
break;

15
src/math/sin.c
View File

@ -44,21 +44,22 @@
double sin(double x)
{
double y[2], z=0.0;
int32_t n, ix;
double y[2];
uint32_t ix;
unsigned n;
/* High word of x. */
GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix <= 0x3fe921fb) {
if (ix < 0x3e500000) { /* |x| < 2**-26 */
/* raise inexact if x != 0 */
if ((int)x == 0)
return x;
/* raise inexact if x != 0 and underflow if subnormal*/
FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
return x;
}
return __sin(x, z, 0);
return __sin(x, 0.0, 0);
}
/* sin(Inf or NaN) is NaN */

12
src/math/sincos.c
View File

@ -15,7 +15,8 @@
void sincos(double x, double *sin, double *cos)
{
double y[2], s, c;
uint32_t n, ix;
uint32_t ix;
unsigned n;
GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
@ -24,11 +25,10 @@ void sincos(double x, double *sin, double *cos)
if (ix <= 0x3fe921fb) {
/* if |x| < 2**-27 * sqrt(2) */
if (ix < 0x3e46a09e) {
/* raise inexact if x != 0 */
if ((int)x == 0) {
*sin = x;
*cos = 1.0;
}
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
*sin = x;
*cos = 1.0;
return;
}
*sin = __sin(x, 0.0, 0);

45
src/math/sincosf.c
View File

@ -25,21 +25,23 @@ s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
void sincosf(float x, float *sin, float *cos)
{
double y, s, c;
uint32_t n, hx, ix;
double y;
float_t s, c;
uint32_t ix;
unsigned n, sign;
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
GET_FLOAT_WORD(ix, x);
sign = ix >> 31;
ix &= 0x7fffffff;
/* |x| ~<= pi/4 */
if (ix <= 0x3f490fda) {
/* |x| < 2**-12 */
if (ix < 0x39800000) {
/* raise inexact if x != 0 */
if((int)x == 0) {
*sin = x;
*cos = 1.0f;
}
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
*sin = x;
*cos = 1.0f;
return;
}
*sin = __sindf(x);
@ -50,34 +52,35 @@ void sincosf(float x, float *sin, float *cos)
/* |x| ~<= 5*pi/4 */
if (ix <= 0x407b53d1) {
if (ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */
if (hx < 0x80000000) {
*sin = __cosdf(x - s1pio2);
*cos = __sindf(s1pio2 - x);
} else {
if (sign) {
*sin = -__cosdf(x + s1pio2);
*cos = __sindf(x + s1pio2);
} else {
*sin = __cosdf(s1pio2 - x);
*cos = __sindf(s1pio2 - x);
}
return;
}
*sin = __sindf(hx < 0x80000000 ? s2pio2 - x : -s2pio2 - x);
*cos = -__cosdf(hx < 0x80000000 ? x - s2pio2 : x + s2pio2);
/* -sin(x+c) is not correct if x+c could be 0: -0 vs +0 */
*sin = -__sindf(sign ? x + s2pio2 : x - s2pio2);
*cos = -__cosdf(sign ? x + s2pio2 : x - s2pio2);
return;
}
/* |x| ~<= 9*pi/4 */
if (ix <= 0x40e231d5) {
if (ix <= 0x40afeddf) { /* |x| ~<= 7*pi/4 */
if (hx < 0x80000000) {
if (sign) {
*sin = __cosdf(x + s3pio2);
*cos = -__sindf(x + s3pio2);
} else {
*sin = -__cosdf(x - s3pio2);
*cos = __sindf(x - s3pio2);
} else {
*sin = __cosdf(x + s3pio2);
*cos = __sindf(-s3pio2 - x);
}
return;
}
*sin = __sindf(hx < 0x80000000 ? x - s4pio2 : x + s4pio2);
*cos = __cosdf(hx < 0x80000000 ? x - s4pio2 : x + s4pio2);
*sin = __sindf(sign ? x + s4pio2 : x - s4pio2);
*cos = __cosdf(sign ? x + s4pio2 : x - s4pio2);
return;
}

20
src/math/sincosl.c
View File

@ -10,27 +10,29 @@ void sincosl(long double x, long double *sin, long double *cos)
void sincosl(long double x, long double *sin, long double *cos)
{
union IEEEl2bits u;
int n;
unsigned n;
long double y[2], s, c;
u.e = x;
u.bits.sign = 0;
/* x = +-0 or subnormal */
if (!u.bits.exp) {
*sin = x;
*cos = 1.0;
return;
}
/* x = nan or inf */
if (u.bits.exp == 0x7fff) {
*sin = *cos = x - x;
return;
}
/* |x| < pi/4 */
/* |x| < (double)pi/4 */
if (u.e < M_PI_4) {
/* |x| < 0x1p-64 */
if (u.bits.exp < 0x3fff - 64) {
/* raise underflow if subnormal */
if (u.bits.exp == 0) FORCE_EVAL(x*0x1p-120f);
*sin = x;
/* raise inexact if x!=0 */
*cos = 1.0 + x;
return;
}
*sin = __sinl(x, 0, 0);
*cos = __cosl(x, 0);
return;

33
src/math/sinf.c
View File

@ -26,35 +26,38 @@ s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
float sinf(float x)
{
double y;
int32_t n, hx, ix;
uint32_t ix;
int n, sign;
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
GET_FLOAT_WORD(ix, x);
sign = ix >> 31;
ix &= 0x7fffffff;
if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
if (ix < 0x39800000) /* |x| < 2**-12 */
/* raise inexact if x != 0 */
if((int)x == 0)
return x;
if (ix < 0x39800000) { /* |x| < 2**-12 */
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(ix < 0x00800000 ? x/0x1p120f : x+0x1p120f);
return x;
}
return __sindf(x);
}
if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
if (ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */
if (hx > 0)
return __cosdf(x - s1pio2);
else
if (sign)
return -__cosdf(x + s1pio2);
else
return __cosdf(x - s1pio2);
}
return __sindf(hx > 0 ? s2pio2 - x : -s2pio2 - x);
return __sindf(sign ? -(x + s2pio2) : -(x - s2pio2));
}
if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
if (ix <= 0x40afeddf) { /* |x| ~<= 7*pi/4 */
if (hx > 0)
return -__cosdf(x - s3pio2);
else
if (sign)
return __cosdf(x + s3pio2);
else
return -__cosdf(x - s3pio2);
}
return __sindf(hx > 0 ? x - s4pio2 : x + s4pio2);
return __sindf(sign ? x + s4pio2 : x - s4pio2);
}
/* sin(Inf or NaN) is NaN */

29
src/math/sinl.c
View File

@ -37,33 +37,32 @@ long double sinl(long double x)
long double sinl(long double x)
{
union IEEEl2bits z;
int e0, s;
unsigned n;
long double y[2];
long double hi, lo;
z.e = x;
s = z.bits.sign;
z.bits.sign = 0;
/* If x = +-0 or x is a subnormal number, then sin(x) = x */
if (z.bits.exp == 0)
return x;
/* If x = NaN or Inf, then sin(x) = NaN. */
if (z.bits.exp == 32767)
if (z.bits.exp == 0x7fff)
return (x - x) / (x - x);
/* Optimize the case where x is already within range. */
/* |x| < (double)pi/4 */
if (z.e < M_PI_4) {
hi = __sinl(z.e, 0, 0);
return s ? -hi : hi;
/* |x| < 0x1p-64 */
if (z.bits.exp < 0x3fff - 64) {
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(z.bits.exp == 0 ? x/0x1p120f : x+0x1p120f);
return x;
}
return __sinl(x, 0.0, 0);
}
e0 = __rem_pio2l(x, y);
n = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (e0 & 3) {
switch (n & 3) {
case 0:
hi = __sinl(hi, lo, 1);
break;
@ -71,10 +70,10 @@ long double sinl(long double x)
hi = __cosl(hi, lo);
break;
case 2:
hi = - __sinl(hi, lo, 1);
hi = -__sinl(hi, lo, 1);
break;
case 3:
hi = - __cosl(hi, lo);
hi = -__cosl(hi, lo);
break;
}
return hi;

23
src/math/tan.c
View File

@ -43,27 +43,28 @@
double tan(double x)
{
double y[2], z = 0.0;
int32_t n, ix;
double y[2];
uint32_t ix;
unsigned n;
/* High word of x. */
GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix <= 0x3fe921fb) {
if (ix < 0x3e400000) /* x < 2**-27 */
/* raise inexact if x != 0 */
if ((int)x == 0)
return x;
return __tan(x, z, 1);
if (ix < 0x3e400000) { /* |x| < 2**-27 */
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
return x;
}
return __tan(x, 0.0, 0);
}
/* tan(Inf or NaN) is NaN */
if (ix >= 0x7ff00000)
return x - x;
/* argument reduction needed */
/* argument reduction */
n = __rem_pio2(x, y);
return __tan(y[0], y[1], 1 - ((n&1)<<1)); /* n even: 1, n odd: -1 */
return __tan(y[0], y[1], n&1);
}

32
src/math/tanf.c
View File

@ -26,37 +26,39 @@ t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
float tanf(float x)
{
double y;
int32_t n, hx, ix;
uint32_t ix;
unsigned n, sign;
GET_FLOAT_WORD(hx, x);
ix = hx & 0x7fffffff;
GET_FLOAT_WORD(ix, x);
sign = ix >> 31;
ix &= 0x7fffffff;
if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
if (ix < 0x39800000) /* |x| < 2**-12 */
/* return x and raise inexact if x != 0 */
if ((int)x == 0)
return x;
return __tandf(x, 1);
if (ix < 0x39800000) { /* |x| < 2**-12 */
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(ix < 0x00800000 ? x/0x1p120f : x+0x1p120f);
return x;
}
return __tandf(x, 0);
}
if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
if (ix <= 0x4016cbe3) /* |x| ~<= 3pi/4 */
return __tandf((hx > 0 ? x-t1pio2 : x+t1pio2), -1);
return __tandf((sign ? x+t1pio2 : x-t1pio2), 1);
else
return __tandf((hx > 0 ? x-t2pio2 : x+t2pio2), 1);
return __tandf((sign ? x+t2pio2 : x-t2pio2), 0);
}
if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
if (ix <= 0x40afeddf) /* |x| ~<= 7*pi/4 */
return __tandf((hx > 0 ? x-t3pio2 : x+t3pio2), -1);
return __tandf((sign ? x+t3pio2 : x-t3pio2), 1);
else
return __tandf((hx > 0 ? x-t4pio2 : x+t4pio2), 1);
return __tandf((sign ? x+t4pio2 : x-t4pio2), 0);
}
/* tan(Inf or NaN) is NaN */
if (ix >= 0x7f800000)
return x - x;
/* general argument reduction needed */
/* argument reduction */
n = __rem_pio2f(x, &y);
/* integer parameter: n even: 1; n odd: -1 */
return __tandf(y, 1-((n&1)<<1));
return __tandf(y, n&1);
}

38
src/math/tanl.c
View File

@ -41,42 +41,28 @@ long double tanl(long double x)
long double tanl(long double x)
{
union IEEEl2bits z;
int e0, s;
long double y[2];
long double hi, lo;
unsigned n;
z.e = x;
s = z.bits.sign;
z.bits.sign = 0;
/* If x = +-0 or x is subnormal, then tan(x) = x. */
if (z.bits.exp == 0)
return x;
/* If x = NaN or Inf, then tan(x) = NaN. */
if (z.bits.exp == 32767)
if (z.bits.exp == 0x7fff)
return (x - x) / (x - x);
/* Optimize the case where x is already within range. */
/* |x| < (double)pi/4 */
if (z.e < M_PI_4) {
hi = __tanl(z.e, 0, 0);
return s ? -hi : hi;
/* |x| < 0x1p-64 */
if (z.bits.exp < 0x3fff - 64) {
/* raise inexact if x!=0 and underflow if subnormal */
FORCE_EVAL(z.bits.exp == 0 ? x/0x1p120f : x+0x1p120f);
return x;
}
return __tanl(x, 0, 0);
}
e0 = __rem_pio2l(x, y);
hi = y[0];
lo = y[1];
switch (e0 & 3) {
case 0:
case 2:
hi = __tanl(hi, lo, 0);
break;
case 1:
case 3:
hi = __tanl(hi, lo, 1);
break;
}
return hi;
n = __rem_pio2l(x, y);
return __tanl(y[0], y[1], n&1);
}
#endif