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Third Party Musl
提交 83af1dd6 编写于 作者: R Rich Felker
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Merge remote-tracking branch 'nsz/review'

上级 69ee9b2c bfda3793
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Showing with 203 addition and 213 deletion
src/math/__tan.c
浏览文件 @ 83af1dd6
...@@ -12,7 +12,7 @@ ...@@ -12,7 +12,7 @@
* kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 * 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 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.
* 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 * Algorithm
* 1. Since tan(-x) = -tan(x), we need only to consider positive x. * 1. Since tan(-x) = -tan(x), we need only to consider positive x.
...@@ -63,21 +63,22 @@ static const double T[] = { ...@@ -63,21 +63,22 @@ static const double T[] = {
pio4 = 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ pio4 = 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
pio4lo = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */ 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; double_t z, r, v, w, s, a;
int32_t ix, hx; double w0, a0;
uint32_t hx;
int big, sign;
GET_HIGH_WORD(hx,x); GET_HIGH_WORD(hx,x);
ix = hx & 0x7fffffff; /* high word of |x| */ big = (hx&0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */
if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */ if (big) {
if (hx < 0) { sign = hx>>31;
if (sign) {
x = -x; x = -x;
y = -y; y = -y;
} }
z = pio4 - x; x = (pio4 - x) + (pio4lo - y);
w = pio4lo - y;
x = z + w;
y = 0.0; y = 0.0;
} }
z = x * x; z = x * x;
...@@ -90,30 +91,20 @@ double __tan(double x, double y, int iy) ...@@ -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])))); 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]))))); v = z*(T[2] + w*(T[4] + w*(T[6] + w*(T[8] + w*(T[10] + w*T[12])))));
s = z * x; s = z * x;
r = y + z * (s * (r + v) + y); r = y + z*(s*(r + v) + y) + s*T[0];
r += T[0] * s;
w = x + r; w = x + r;
if (ix >= 0x3FE59428) { if (big) {
v = iy; s = 1 - 2*odd;
sign = 1 - ((hx >> 30) & 2); v = s - 2.0 * (x + (r - w*w/(w + s)));
return sign * (v - 2.0 * (x - (w * w / (w + v) - r))); return sign ? -v : v;
} }
if (iy == 1) if (!odd)
return w; return w;
else { /* -1.0/(x+r) has up to 2ulp error, so compute it accurately */
/* w0 = w;
* if allow error up to 2 ulp, simply return SET_LOW_WORD(w0, 0);
* -1.0 / (x+r) here v = r - (w0 - x); /* w0+v = r+x */
*/ a0 = a = -1.0 / w;
/* compute -1.0 / (x+r) accurately */ SET_LOW_WORD(a0, 0);
double_t a; return a0 + a*(1.0 + a0*w0 + a0*v);
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);
}
} }
src/math/__tandf.c
浏览文件 @ 83af1dd6
...@@ -25,7 +25,7 @@ static const double T[] = { ...@@ -25,7 +25,7 @@ static const double T[] = {
0x1362b9bf971bcd.0p-59, /* 0.00946564784943673166728 */ 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; double_t z,r,w,s,t,u;
...@@ -50,6 +50,5 @@ float __tandf(double x, int iy) ...@@ -50,6 +50,5 @@ float __tandf(double x, int iy)
s = z*x; s = z*x;
u = T[0] + z*T[1]; u = T[0] + z*T[1];
r = (x + s*u) + (s*w)*(t + w*r); r = (x + s*u) + (s*w)*(t + w*r);
if(iy==1) return r; return odd ? -1.0/r : r;
else return -1.0/r;
} }
src/math/__tanl.c
浏览文件 @ 83af1dd6
...@@ -45,25 +45,21 @@ T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */ ...@@ -45,25 +45,21 @@ T29 = 0.0000078293456938132840, /* 0x106b59141a6cb3.0p-69 */
T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */ T31 = -0.0000032609076735050182, /* -0x1b5abef3ba4b59.0p-71 */
T33 = 0.0000023261313142559411; /* 0x13835436c0c87f.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 z, r, v, w, s, a, t;
long double osign; int big, sign;
int i;
iy = iy == 1 ? -1 : 1; /* XXX recover original interface */ big = fabsl(x) >= 0.67434;
osign = copysignl(1.0, x); if (big) {
if (fabsl(x) >= 0.67434) { sign = 0;
if (x < 0) { if (x < 0) {
sign = 1;
x = -x; x = -x;
y = -y; y = -y;
} }
z = pio4 - x; x = (pio4 - x) + (pio4lo - y);
w = pio4lo - y;
x = z + w;
y = 0.0; y = 0.0;
i = 1; }
} else
i = 0;
z = x * x; z = x * x;
w = z * z; w = z * z;
r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 + 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) { ...@@ -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 + v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
w * (T27 + w * T31)))))); w * (T27 + w * T31))))));
s = z * x; s = z * x;
r = y + z * (s * (r + v) + y); r = y + z * (s * (r + v) + y) + T3 * s;
r += T3 * s;
w = x + r; w = x + r;
if (i == 1) { if (big) {
v = (long double)iy; s = 1 - 2*odd;
return osign * (v - 2.0 * (x - (w * w / (w + v) - r))); v = s - 2.0 * (x + (r - w * w / (w + s)));
return sign ? -v : v;
} }
if (iy == 1) if (!odd)
return w; return w;
/* /*
......
src/math/cos.c
浏览文件 @ 83af1dd6
...@@ -44,26 +44,28 @@ ...@@ -44,26 +44,28 @@
double cos(double x) double cos(double x)
{ {
double y[2],z=0.0; double y[2];
int32_t n, ix; uint32_t ix;
unsigned n;
GET_HIGH_WORD(ix, x); GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
/* |x| ~< pi/4 */ /* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix <= 0x3fe921fb) { if (ix <= 0x3fe921fb) {
if (ix < 0x3e46a09e) /* if x < 2**-27 * sqrt(2) */ if (ix < 0x3e46a09e) { /* |x| < 2**-27 * sqrt(2) */
/* raise inexact if x != 0 */ /* raise inexact if x!=0 */
if ((int)x == 0) FORCE_EVAL(x + 0x1p120f);
return 1.0; return 1.0;
return __cos(x, z); }
return __cos(x, 0);
} }
/* cos(Inf or NaN) is NaN */ /* cos(Inf or NaN) is NaN */
if (ix >= 0x7ff00000) if (ix >= 0x7ff00000)
return x-x; return x-x;
/* argument reduction needed */ /* argument reduction */
n = __rem_pio2(x, y); n = __rem_pio2(x, y);
switch (n&3) { switch (n&3) {
case 0: return __cos(y[0], y[1]); case 0: return __cos(y[0], y[1]);
......
src/math/cosf.c
浏览文件 @ 83af1dd6
...@@ -26,34 +26,39 @@ c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ ...@@ -26,34 +26,39 @@ c4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
float cosf(float x) float cosf(float x)
{ {
double y; 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 <= 0x3f490fda) { /* |x| ~<= pi/4 */
if (ix < 0x39800000) /* |x| < 2**-12 */ if (ix < 0x39800000) { /* |x| < 2**-12 */
if ((int)x == 0) /* raise inexact if x != 0 */ /* raise inexact if x != 0 */
return 1.0; FORCE_EVAL(x + 0x1p120f);
return 1.0f;
}
return __cosdf(x); return __cosdf(x);
} }
if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */ if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
if (ix > 0x4016cbe3) /* |x| ~> 3*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 { else {
if (hx > 0) if (sign)
return __sindf(c1pio2 - x);
else
return __sindf(x + c1pio2); return __sindf(x + c1pio2);
else
return __sindf(c1pio2 - x);
} }
} }
if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */ if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
if (ix > 0x40afeddf) /* |x| ~> 7*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 { else {
if (hx > 0) if (sign)
return __sindf(x - c3pio2); return __sindf(-x - c3pio2);
else else
return __sindf(-c3pio2 - x); return __sindf(x - c3pio2);
} }
} }
......
src/math/cosl.c
浏览文件 @ 83af1dd6
...@@ -39,30 +39,30 @@ long double cosl(long double x) { ...@@ -39,30 +39,30 @@ long double cosl(long double x) {
long double cosl(long double x) long double cosl(long double x)
{ {
union IEEEl2bits z; union IEEEl2bits z;
int e0; unsigned n;
long double y[2]; long double y[2];
long double hi, lo; long double hi, lo;
z.e = x; z.e = x;
z.bits.sign = 0; 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 x = NaN or Inf, then cos(x) = NaN. */
if (z.bits.exp == 32767) if (z.bits.exp == 0x7fff)
return (x - x) / (x - x); return (x - x) / (x - x);
/* Optimize the case where x is already within range. */ /* |x| < (double)pi/4 */
if (z.e < M_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); return __cosl(z.e, 0);
}
e0 = __rem_pio2l(x, y); n = __rem_pio2l(x, y);
hi = y[0]; hi = y[0];
lo = y[1]; lo = y[1];
switch (n & 3) {
switch (e0 & 3) {
case 0: case 0:
hi = __cosl(hi, lo); hi = __cosl(hi, lo);
break; break;
......
src/math/sin.c
浏览文件 @ 83af1dd6
...@@ -44,21 +44,22 @@ ...@@ -44,21 +44,22 @@
double sin(double x) double sin(double x)
{ {
double y[2], z=0.0; double y[2];
int32_t n, ix; uint32_t ix;
unsigned n;
/* High word of x. */ /* High word of x. */
GET_HIGH_WORD(ix, x); GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
/* |x| ~< pi/4 */ /* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix <= 0x3fe921fb) { if (ix <= 0x3fe921fb) {
if (ix < 0x3e500000) { /* |x| < 2**-26 */ if (ix < 0x3e500000) { /* |x| < 2**-26 */
/* raise inexact if x != 0 */ /* raise inexact if x != 0 and underflow if subnormal*/
if ((int)x == 0) FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
return x; return x;
} }
return __sin(x, z, 0); return __sin(x, 0.0, 0);
} }
/* sin(Inf or NaN) is NaN */ /* sin(Inf or NaN) is NaN */
......
src/math/sincos.c
浏览文件 @ 83af1dd6
...@@ -15,7 +15,8 @@ ...@@ -15,7 +15,8 @@
void sincos(double x, double *sin, double *cos) void sincos(double x, double *sin, double *cos)
{ {
double y[2], s, c; double y[2], s, c;
uint32_t n, ix; uint32_t ix;
unsigned n;
GET_HIGH_WORD(ix, x); GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff; ix &= 0x7fffffff;
...@@ -24,11 +25,10 @@ void sincos(double x, double *sin, double *cos) ...@@ -24,11 +25,10 @@ void sincos(double x, double *sin, double *cos)
if (ix <= 0x3fe921fb) { if (ix <= 0x3fe921fb) {
/* if |x| < 2**-27 * sqrt(2) */ /* if |x| < 2**-27 * sqrt(2) */
if (ix < 0x3e46a09e) { if (ix < 0x3e46a09e) {
/* raise inexact if x != 0 */ /* raise inexact if x!=0 and underflow if subnormal */
if ((int)x == 0) { FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
*sin = x; *sin = x;
*cos = 1.0; *cos = 1.0;
}
return; return;
} }
*sin = __sin(x, 0.0, 0); *sin = __sin(x, 0.0, 0);
......
src/math/sincosf.c
浏览文件 @ 83af1dd6
...@@ -25,21 +25,23 @@ s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ ...@@ -25,21 +25,23 @@ s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
void sincosf(float x, float *sin, float *cos) void sincosf(float x, float *sin, float *cos)
{ {
double y, s, c; double y;
uint32_t n, hx, ix; float_t s, c;
uint32_t ix;
unsigned n, sign;
GET_FLOAT_WORD(hx, x); GET_FLOAT_WORD(ix, x);
ix = hx & 0x7fffffff; sign = ix >> 31;
ix &= 0x7fffffff;
/* |x| ~<= pi/4 */ /* |x| ~<= pi/4 */
if (ix <= 0x3f490fda) { if (ix <= 0x3f490fda) {
/* |x| < 2**-12 */ /* |x| < 2**-12 */
if (ix < 0x39800000) { if (ix < 0x39800000) {
/* raise inexact if x != 0 */ /* raise inexact if x!=0 and underflow if subnormal */
if((int)x == 0) { FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
*sin = x; *sin = x;
*cos = 1.0f; *cos = 1.0f;
}
return; return;
} }
*sin = __sindf(x); *sin = __sindf(x);
...@@ -50,34 +52,35 @@ void sincosf(float x, float *sin, float *cos) ...@@ -50,34 +52,35 @@ void sincosf(float x, float *sin, float *cos)
/* |x| ~<= 5*pi/4 */ /* |x| ~<= 5*pi/4 */
if (ix <= 0x407b53d1) { if (ix <= 0x407b53d1) {
if (ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */ if (ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */
if (hx < 0x80000000) { if (sign) {
*sin = __cosdf(x - s1pio2);
*cos = __sindf(s1pio2 - x);
} else {
*sin = -__cosdf(x + s1pio2); *sin = -__cosdf(x + s1pio2);
*cos = __sindf(x + s1pio2); *cos = __sindf(x + s1pio2);
} else {
*sin = __cosdf(s1pio2 - x);
*cos = __sindf(s1pio2 - x);
} }
return; return;
} }
*sin = __sindf(hx < 0x80000000 ? s2pio2 - x : -s2pio2 - x); /* -sin(x+c) is not correct if x+c could be 0: -0 vs +0 */
*cos = -__cosdf(hx < 0x80000000 ? x - s2pio2 : x + s2pio2); *sin = -__sindf(sign ? x + s2pio2 : x - s2pio2);
*cos = -__cosdf(sign ? x + s2pio2 : x - s2pio2);
return; return;
} }
/* |x| ~<= 9*pi/4 */ /* |x| ~<= 9*pi/4 */
if (ix <= 0x40e231d5) { if (ix <= 0x40e231d5) {
if (ix <= 0x40afeddf) { /* |x| ~<= 7*pi/4 */ 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); *sin = -__cosdf(x - s3pio2);
*cos = __sindf(x - s3pio2); *cos = __sindf(x - s3pio2);
} else {
*sin = __cosdf(x + s3pio2);
*cos = __sindf(-s3pio2 - x);
} }
return; return;
} }
*sin = __sindf(hx < 0x80000000 ? x - s4pio2 : x + s4pio2); *sin = __sindf(sign ? x + s4pio2 : x - s4pio2);
*cos = __cosdf(hx < 0x80000000 ? x - s4pio2 : x + s4pio2); *cos = __cosdf(sign ? x + s4pio2 : x - s4pio2);
return; return;
} }
......
src/math/sincosl.c
浏览文件 @ 83af1dd6
...@@ -10,27 +10,29 @@ void sincosl(long double x, long double *sin, long double *cos) ...@@ -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) void sincosl(long double x, long double *sin, long double *cos)
{ {
union IEEEl2bits u; union IEEEl2bits u;
int n; unsigned n;
long double y[2], s, c; long double y[2], s, c;
u.e = x; u.e = x;
u.bits.sign = 0; u.bits.sign = 0;
/* x = +-0 or subnormal */
if (!u.bits.exp) {
*sin = x;
*cos = 1.0;
return;
}
/* x = nan or inf */ /* x = nan or inf */
if (u.bits.exp == 0x7fff) { if (u.bits.exp == 0x7fff) {
*sin = *cos = x - x; *sin = *cos = x - x;
return; return;
} }
/* |x| < pi/4 */ /* |x| < (double)pi/4 */
if (u.e < M_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); *sin = __sinl(x, 0, 0);
*cos = __cosl(x, 0); *cos = __cosl(x, 0);
return; return;
......
src/math/sinf.c
浏览文件 @ 83af1dd6
...@@ -26,35 +26,38 @@ s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ ...@@ -26,35 +26,38 @@ s4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
float sinf(float x) float sinf(float x)
{ {
double y; double y;
int32_t n, hx, ix; uint32_t ix;
int n, sign;
GET_FLOAT_WORD(hx, x); GET_FLOAT_WORD(ix, x);
ix = hx & 0x7fffffff; sign = ix >> 31;
ix &= 0x7fffffff;
if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
if (ix < 0x39800000) /* |x| < 2**-12 */ if (ix < 0x39800000) { /* |x| < 2**-12 */
/* raise inexact if x != 0 */ /* raise inexact if x!=0 and underflow if subnormal */
if((int)x == 0) FORCE_EVAL(ix < 0x00800000 ? x/0x1p120f : x+0x1p120f);
return x; return x;
}
return __sindf(x); return __sindf(x);
} }
if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */ if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
if (ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */ if (ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */
if (hx > 0) if (sign)
return __cosdf(x - s1pio2);
else
return -__cosdf(x + s1pio2); 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 <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
if (ix <= 0x40afeddf) { /* |x| ~<= 7*pi/4 */ if (ix <= 0x40afeddf) { /* |x| ~<= 7*pi/4 */
if (hx > 0) if (sign)
return -__cosdf(x - s3pio2);
else
return __cosdf(x + s3pio2); 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 */ /* sin(Inf or NaN) is NaN */
......
src/math/sinl.c
浏览文件 @ 83af1dd6
...@@ -37,33 +37,32 @@ long double sinl(long double x) ...@@ -37,33 +37,32 @@ long double sinl(long double x)
long double sinl(long double x) long double sinl(long double x)
{ {
union IEEEl2bits z; union IEEEl2bits z;
int e0, s; unsigned n;
long double y[2]; long double y[2];
long double hi, lo; long double hi, lo;
z.e = x; z.e = x;
s = z.bits.sign;
z.bits.sign = 0; 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 x = NaN or Inf, then sin(x) = NaN. */
if (z.bits.exp == 32767) if (z.bits.exp == 0x7fff)
return (x - x) / (x - x); return (x - x) / (x - x);
/* Optimize the case where x is already within range. */ /* |x| < (double)pi/4 */
if (z.e < M_PI_4) { if (z.e < M_PI_4) {
hi = __sinl(z.e, 0, 0); /* |x| < 0x1p-64 */
return s ? -hi : hi; 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]; hi = y[0];
lo = y[1]; lo = y[1];
switch (n & 3) {
switch (e0 & 3) {
case 0: case 0:
hi = __sinl(hi, lo, 1); hi = __sinl(hi, lo, 1);
break; break;
...@@ -71,10 +70,10 @@ long double sinl(long double x) ...@@ -71,10 +70,10 @@ long double sinl(long double x)
hi = __cosl(hi, lo); hi = __cosl(hi, lo);
break; break;
case 2: case 2:
hi = - __sinl(hi, lo, 1); hi = -__sinl(hi, lo, 1);
break; break;
case 3: case 3:
hi = - __cosl(hi, lo); hi = -__cosl(hi, lo);
break; break;
} }
return hi; return hi;
......
src/math/tan.c
浏览文件 @ 83af1dd6
...@@ -43,27 +43,28 @@ ...@@ -43,27 +43,28 @@
double tan(double x) double tan(double x)
{ {
double y[2], z = 0.0; double y[2];
int32_t n, ix; uint32_t ix;
unsigned n;
/* High word of x. */
GET_HIGH_WORD(ix, x); GET_HIGH_WORD(ix, x);
ix &= 0x7fffffff;
/* |x| ~< pi/4 */ /* |x| ~< pi/4 */
ix &= 0x7fffffff;
if (ix <= 0x3fe921fb) { if (ix <= 0x3fe921fb) {
if (ix < 0x3e400000) /* x < 2**-27 */ if (ix < 0x3e400000) { /* |x| < 2**-27 */
/* raise inexact if x != 0 */ /* raise inexact if x!=0 and underflow if subnormal */
if ((int)x == 0) FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
return x; return x;
return __tan(x, z, 1); }
return __tan(x, 0.0, 0);
} }
/* tan(Inf or NaN) is NaN */ /* tan(Inf or NaN) is NaN */
if (ix >= 0x7ff00000) if (ix >= 0x7ff00000)
return x - x; return x - x;
/* argument reduction needed */ /* argument reduction */
n = __rem_pio2(x, y); 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);
} }
src/math/tanf.c
浏览文件 @ 83af1dd6
...@@ -26,37 +26,39 @@ t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */ ...@@ -26,37 +26,39 @@ t4pio2 = 4*M_PI_2; /* 0x401921FB, 0x54442D18 */
float tanf(float x) float tanf(float x)
{ {
double y; double y;
int32_t n, hx, ix; uint32_t ix;
unsigned n, sign;
GET_FLOAT_WORD(hx, x); GET_FLOAT_WORD(ix, x);
ix = hx & 0x7fffffff; sign = ix >> 31;
ix &= 0x7fffffff;
if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */
if (ix < 0x39800000) /* |x| < 2**-12 */ if (ix < 0x39800000) { /* |x| < 2**-12 */
/* return x and raise inexact if x != 0 */ /* raise inexact if x!=0 and underflow if subnormal */
if ((int)x == 0) FORCE_EVAL(ix < 0x00800000 ? x/0x1p120f : x+0x1p120f);
return x; return x;
return __tandf(x, 1); }
return __tandf(x, 0);
} }
if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */ if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */
if (ix <= 0x4016cbe3) /* |x| ~<= 3pi/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 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 <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */
if (ix <= 0x40afeddf) /* |x| ~<= 7*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 else
return __tandf((hx > 0 ? x-t4pio2 : x+t4pio2), 1); return __tandf((sign ? x+t4pio2 : x-t4pio2), 0);
} }
/* tan(Inf or NaN) is NaN */ /* tan(Inf or NaN) is NaN */
if (ix >= 0x7f800000) if (ix >= 0x7f800000)
return x - x; return x - x;
/* general argument reduction needed */ /* argument reduction */
n = __rem_pio2f(x, &y); n = __rem_pio2f(x, &y);
/* integer parameter: n even: 1; n odd: -1 */ return __tandf(y, n&1);
return __tandf(y, 1-((n&1)<<1));
} }
src/math/tanl.c
浏览文件 @ 83af1dd6
...@@ -41,42 +41,28 @@ long double tanl(long double x) ...@@ -41,42 +41,28 @@ long double tanl(long double x)
long double tanl(long double x) long double tanl(long double x)
{ {
union IEEEl2bits z; union IEEEl2bits z;
int e0, s;
long double y[2]; long double y[2];
long double hi, lo; unsigned n;
z.e = x; z.e = x;
s = z.bits.sign;
z.bits.sign = 0; 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 x = NaN or Inf, then tan(x) = NaN. */
if (z.bits.exp == 32767) if (z.bits.exp == 0x7fff)
return (x - x) / (x - x); return (x - x) / (x - x);
/* Optimize the case where x is already within range. */ /* |x| < (double)pi/4 */
if (z.e < M_PI_4) { if (z.e < M_PI_4) {
hi = __tanl(z.e, 0, 0); /* |x| < 0x1p-64 */
return s ? -hi : hi; 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); n = __rem_pio2l(x, y);
hi = y[0]; return __tanl(y[0], y[1], n&1);
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;
} }
#endif #endif
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