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math: sin cos cleanup

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* use unsigned arithmetics
* use unsigned to store arg reduction quotient (so n&3 is understood)
* remove z=0.0 variables, use literal 0
* raise underflow and inexact exceptions properly when x is small
* fix spurious underflow in tanl
This commit is contained in:
Szabolcs Nagy 2013-05-18 14:40:22 +00:00
parent 1d5ba3bb5a
commit bfda379358
10 changed files with 128 additions and 112 deletions
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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;

11
src/math/tanl.c
View File

@ -53,11 +53,12 @@ long double tanl(long double x)
/* |x| < (double)pi/4 */
if (z.e < M_PI_4) {
/* x = +-0 or x is subnormal */
if (z.bits.exp == 0)
/* inexact and underflow if x!=0 */
return x + x*0x1p-120f;
/* can raise spurious underflow */
/* |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);
}