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[PATCH 1/3] New generic sincosf
- From: Rajalakshmi Srinivasaraghavan <raji at linux dot vnet dot ibm dot com>
- To: libc-alpha at sourceware dot org
- Cc: Rajalakshmi Srinivasaraghavan <raji at linux dot vnet dot ibm dot com>
- Date: Wed, 13 Dec 2017 11:13:19 +0530
- Subject: [PATCH 1/3] New generic sincosf
- Authentication-results: sourceware.org; auth=none
- References: <1513143801-3290-1-git-send-email-raji@linux.vnet.ibm.com>
This implementation is based on generic s_sinf.c and s_cosf.c.
Tested on s390x, powerpc64le and powerpc32.
2017-12-12 Rajalakshmi Srinivasaraghavan <raji@linux.vnet.ibm.com>
* sysdeps/ieee754/flt-32/s_cosf.c: Move reduced() and
constants to s_sincos.h file.
* sysdeps/ieee754/flt-32/s_sinf.c: Likewise.
* sysdeps/ieee754/flt-32/s_sincosf.c: New implementation.
* sysdeps/ieee754/flt-32/s_sincos.h: New file.
---
sysdeps/ieee754/flt-32/s_cosf.c | 100 ++-------------------
sysdeps/ieee754/flt-32/s_sincos.h | 155 +++++++++++++++++++++++++++++++++
sysdeps/ieee754/flt-32/s_sincosf.c | 172 +++++++++++++++++++++++++++----------
sysdeps/ieee754/flt-32/s_sinf.c | 107 ++---------------------
4 files changed, 297 insertions(+), 237 deletions(-)
create mode 100644 sysdeps/ieee754/flt-32/s_sincos.h
diff --git a/sysdeps/ieee754/flt-32/s_cosf.c b/sysdeps/ieee754/flt-32/s_cosf.c
index ac6d044449..d19397faca 100644
--- a/sysdeps/ieee754/flt-32/s_cosf.c
+++ b/sysdeps/ieee754/flt-32/s_cosf.c
@@ -20,6 +20,7 @@
#include <math.h>
#include <math_private.h>
#include <libm-alias-float.h>
+#include "s_sincos.h"
#ifndef COSF
# define COSF_FUNC __cosf
@@ -27,95 +28,6 @@
# define COSF_FUNC COSF
#endif
-/* Chebyshev constants for cos, range -PI/4 - PI/4. */
-static const double C0 = -0x1.ffffffffe98aep-2;
-static const double C1 = 0x1.55555545c50c7p-5;
-static const double C2 = -0x1.6c16b348b6874p-10;
-static const double C3 = 0x1.a00eb9ac43ccp-16;
-static const double C4 = -0x1.23c97dd8844d7p-22;
-
-/* Chebyshev constants for sin, range -PI/4 - PI/4. */
-static const double S0 = -0x1.5555555551cd9p-3;
-static const double S1 = 0x1.1111110c2688bp-7;
-static const double S2 = -0x1.a019f8b4bd1f9p-13;
-static const double S3 = 0x1.71d7264e6b5b4p-19;
-static const double S4 = -0x1.a947e1674b58ap-26;
-
-/* Chebyshev constants for cos, range 2^-27 - 2^-5. */
-static const double CC0 = -0x1.fffffff5cc6fdp-2;
-static const double CC1 = 0x1.55514b178dac5p-5;
-
-/* PI/2 with 98 bits of accuracy. */
-static const double PI_2_hi = 0x1.921fb544p+0;
-static const double PI_2_lo = 0x1.0b4611a626332p-34;
-
-static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */
-
-#define FLOAT_EXPONENT_SHIFT 23
-#define FLOAT_EXPONENT_BIAS 127
-
-static const double pio2_table[] = {
- 0 * M_PI_2,
- 1 * M_PI_2,
- 2 * M_PI_2,
- 3 * M_PI_2,
- 4 * M_PI_2,
- 5 * M_PI_2
-};
-
-static const double invpio4_table[] = {
- 0x0p+0,
- 0x1.45f306cp+0,
- 0x1.c9c882ap-28,
- 0x1.4fe13a8p-58,
- 0x1.f47d4dp-85,
- 0x1.bb81b6cp-112,
- 0x1.4acc9ep-142,
- 0x1.0e4107cp-169
-};
-
-static const double ones[] = { 1.0, -1.0 };
-
-/* Compute the cosine value using Chebyshev polynomials where
- THETA is the range reduced absolute value of the input
- and it is less than Pi/4,
- N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
- whether a sine or cosine approximation is more accurate and
- the sign of the result. */
-static inline float
-reduced (double theta, unsigned int n)
-{
- double sign, cx;
- const double theta2 = theta * theta;
-
- /* Determine positive or negative primary interval. */
- n += 2;
- sign = ones[(n >> 2) & 1];
-
- /* Are we in the primary interval of sin or cos? */
- if ((n & 2) == 0)
- {
- /* Here cosf() is calculated using sin Chebyshev polynomial:
- x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
- cx = S3 + theta2 * S4;
- cx = S2 + theta2 * cx;
- cx = S1 + theta2 * cx;
- cx = S0 + theta2 * cx;
- cx = theta + theta * theta2 * cx;
- }
- else
- {
- /* Here cosf() is calculated using cos Chebyshev polynomial:
- 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
- cx = C3 + theta2 * C4;
- cx = C2 + theta2 * cx;
- cx = C1 + theta2 * cx;
- cx = C0 + theta2 * cx;
- cx = 1. + theta2 * cx;
- }
- return sign * cx;
-}
-
float
COSF_FUNC (float x)
{
@@ -161,7 +73,7 @@ COSF_FUNC (float x)
pio2_table must go to 5 (9 / 2 + 1). */
unsigned int n = (abstheta * inv_PI_4) + 1;
theta = abstheta - pio2_table[n / 2];
- return reduced (theta, n);
+ return reduced_cos (theta, n);
}
else if (isless (abstheta, INFINITY))
{
@@ -171,7 +83,7 @@ COSF_FUNC (float x)
double x = n / 2;
theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
/* Argument reduction needed. */
- return reduced (theta, n);
+ return reduced_cos (theta, n);
}
else /* |theta| >= 2^23. */
{
@@ -199,7 +111,7 @@ COSF_FUNC (float x)
e += c;
e += d;
e *= M_PI_4;
- return reduced (e, l + 1);
+ return reduced_cos (e, l + 1);
}
else
{
@@ -209,14 +121,14 @@ COSF_FUNC (float x)
if (e <= 1.0)
{
e *= M_PI_4;
- return reduced (e, l + 1);
+ return reduced_cos (e, l + 1);
}
else
{
l++;
e -= 2.0;
e *= M_PI_4;
- return reduced (e, l + 1);
+ return reduced_cos (e, l + 1);
}
}
}
diff --git a/sysdeps/ieee754/flt-32/s_sincos.h b/sysdeps/ieee754/flt-32/s_sincos.h
new file mode 100644
index 0000000000..b0110fc2af
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/s_sincos.h
@@ -0,0 +1,155 @@
+/* Used by sinf, cosf and sincosf functions.
+ Copyright (C) 2017 Free Software Foundation, Inc.
+ This file is part of the GNU C Library.
+
+ The GNU C Library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ The GNU C Library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with the GNU C Library; if not, see
+ <http://www.gnu.org/licenses/>. */
+
+/* Chebyshev constants for cos, range -PI/4 - PI/4. */
+static const double C0 = -0x1.ffffffffe98aep-2;
+static const double C1 = 0x1.55555545c50c7p-5;
+static const double C2 = -0x1.6c16b348b6874p-10;
+static const double C3 = 0x1.a00eb9ac43ccp-16;
+static const double C4 = -0x1.23c97dd8844d7p-22;
+
+/* Chebyshev constants for sin, range -PI/4 - PI/4. */
+static const double S0 = -0x1.5555555551cd9p-3;
+static const double S1 = 0x1.1111110c2688bp-7;
+static const double S2 = -0x1.a019f8b4bd1f9p-13;
+static const double S3 = 0x1.71d7264e6b5b4p-19;
+static const double S4 = -0x1.a947e1674b58ap-26;
+
+/* Chebyshev constants for sin, range 2^-27 - 2^-5. */
+static const double SS0 = -0x1.555555543d49dp-3;
+static const double SS1 = 0x1.110f475cec8c5p-7;
+
+/* Chebyshev constants for cos, range 2^-27 - 2^-5. */
+static const double CC0 = -0x1.fffffff5cc6fdp-2;
+static const double CC1 = 0x1.55514b178dac5p-5;
+
+/* PI/2 with 98 bits of accuracy. */
+static const double PI_2_hi = 0x1.921fb544p+0;
+static const double PI_2_lo = 0x1.0b4611a626332p-34;
+
+static const double SMALL = 0x1p-50; /* 2^-50. */
+static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */
+
+#define FLOAT_EXPONENT_SHIFT 23
+#define FLOAT_EXPONENT_BIAS 127
+
+static const double pio2_table[] = {
+ 0 * M_PI_2,
+ 1 * M_PI_2,
+ 2 * M_PI_2,
+ 3 * M_PI_2,
+ 4 * M_PI_2,
+ 5 * M_PI_2
+};
+
+static const double invpio4_table[] = {
+ 0x0p+0,
+ 0x1.45f306cp+0,
+ 0x1.c9c882ap-28,
+ 0x1.4fe13a8p-58,
+ 0x1.f47d4dp-85,
+ 0x1.bb81b6cp-112,
+ 0x1.4acc9ep-142,
+ 0x1.0e4107cp-169
+};
+
+static const double ones[] = { 1.0, -1.0 };
+
+/* Compute the sine value using Chebyshev polynomials where
+ THETA is the range reduced absolute value of the input
+ and it is less than Pi/4,
+ N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
+ whether a sine or cosine approximation is more accurate and
+ SIGNBIT is used to add the correct sign after the Chebyshev
+ polynomial is computed. */
+static inline float
+reduced_sin (const double theta, const unsigned int n,
+ const unsigned int signbit)
+{
+ double sx;
+ const double theta2 = theta * theta;
+ /* We are operating on |x|, so we need to add back the original
+ signbit for sinf. */
+ double sign;
+ /* Determine positive or negative primary interval. */
+ sign = ones[((n >> 2) & 1) ^ signbit];
+ /* Are we in the primary interval of sin or cos? */
+ if ((n & 2) == 0)
+ {
+ /* Here sinf() is calculated using sin Chebyshev polynomial:
+ x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
+ sx = S3 + theta2 * S4; /* S3+x^2*S4. */
+ sx = S2 + theta2 * sx; /* S2+x^2*(S3+x^2*S4). */
+ sx = S1 + theta2 * sx; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
+ sx = S0 + theta2 * sx; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
+ sx = theta + theta * theta2 * sx;
+ }
+ else
+ {
+ /* Here sinf() is calculated using cos Chebyshev polynomial:
+ 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
+ sx = C3 + theta2 * C4; /* C3+x^2*C4. */
+ sx = C2 + theta2 * sx; /* C2+x^2*(C3+x^2*C4). */
+ sx = C1 + theta2 * sx; /* C1+x^2*(C2+x^2*(C3+x^2*C4)). */
+ sx = C0 + theta2 * sx; /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))). */
+ sx = 1.0 + theta2 * sx;
+ }
+
+ /* Add in the signbit and assign the result. */
+ return sign * sx;
+}
+
+/* Compute the cosine value using Chebyshev polynomials where
+ THETA is the range reduced absolute value of the input
+ and it is less than Pi/4,
+ N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
+ whether a sine or cosine approximation is more accurate and
+ the sign of the result. */
+static inline float
+reduced_cos (double theta, unsigned int n)
+{
+ double sign, cx;
+ const double theta2 = theta * theta;
+
+ /* Determine positive or negative primary interval. */
+ n += 2;
+ sign = ones[(n >> 2) & 1];
+
+ /* Are we in the primary interval of sin or cos? */
+ if ((n & 2) == 0)
+ {
+ /* Here cosf() is calculated using sin Chebyshev polynomial:
+ x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
+ cx = S3 + theta2 * S4;
+ cx = S2 + theta2 * cx;
+ cx = S1 + theta2 * cx;
+ cx = S0 + theta2 * cx;
+ cx = theta + theta * theta2 * cx;
+ }
+ else
+ {
+ /* Here cosf() is calculated using cos Chebyshev polynomial:
+ 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
+ cx = C3 + theta2 * C4;
+ cx = C2 + theta2 * cx;
+ cx = C1 + theta2 * cx;
+ cx = C0 + theta2 * cx;
+ cx = 1. + theta2 * cx;
+ }
+ return sign * cx;
+}
diff --git a/sysdeps/ieee754/flt-32/s_sincosf.c b/sysdeps/ieee754/flt-32/s_sincosf.c
index 4946a6eb54..b9f775d45b 100644
--- a/sysdeps/ieee754/flt-32/s_sincosf.c
+++ b/sysdeps/ieee754/flt-32/s_sincosf.c
@@ -1,7 +1,6 @@
/* Compute sine and cosine of argument.
- Copyright (C) 1997-2017 Free Software Foundation, Inc.
+ Copyright (C) 2017 Free Software Foundation, Inc.
This file is part of the GNU C Library.
- Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
@@ -19,9 +18,9 @@
#include <errno.h>
#include <math.h>
-
#include <math_private.h>
#include <libm-alias-float.h>
+#include "s_sincos.h"
#ifndef SINCOSF
# define SINCOSF_FUNC __sincosf
@@ -32,50 +31,137 @@
void
SINCOSF_FUNC (float x, float *sinx, float *cosx)
{
- int32_t ix;
-
- /* High word of x. */
- GET_FLOAT_WORD (ix, x);
-
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if (ix <= 0x3f490fd8)
- {
- *sinx = __kernel_sinf (x, 0.0, 0);
- *cosx = __kernel_cosf (x, 0.0);
- }
- else if (ix>=0x7f800000)
+ double cx;
+ double theta = x;
+ double abstheta = fabs (theta);
+ /* If |x|< Pi/4. */
+ if (isless (abstheta, M_PI_4))
{
- /* sin(Inf or NaN) is NaN */
- *sinx = *cosx = x - x;
- if (ix == 0x7f800000)
- __set_errno (EDOM);
+ if (abstheta >= 0x1p-5) /* |x| >= 2^-5. */
+ {
+ const double theta2 = theta * theta;
+ /* Chebyshev polynomial of the form for sin and cos. */
+ cx = C3 + theta2 * C4;
+ cx = C2 + theta2 * cx;
+ cx = C1 + theta2 * cx;
+ cx = C0 + theta2 * cx;
+ cx = 1.0 + theta2 * cx;
+ *cosx = cx;
+ cx = S3 + theta2 * S4;
+ cx = S2 + theta2 * cx;
+ cx = S1 + theta2 * cx;
+ cx = S0 + theta2 * cx;
+ cx = theta + theta * theta2 * cx;
+ *sinx = cx;
+ }
+ else if (abstheta >= 0x1p-27) /* |x| >= 2^-27. */
+ {
+ /* A simpler Chebyshev approximation is close enough for this range:
+ for sin: x+x^3*(SS0+x^2*SS1)
+ for cos: 1.0+x^2*(CC0+x^3*CC1). */
+ const double theta2 = theta * theta;
+ cx = CC0 + theta * theta2 * CC1;
+ cx = 1.0 + theta2 * cx;
+ *cosx = cx;
+ cx = SS0 + theta2 * SS1;
+ cx = theta + theta * theta2 * cx;
+ *sinx = cx;
+ }
+ else
+ {
+ /* Handle some special cases. */
+ if (theta)
+ *sinx = theta - (theta * SMALL);
+ else
+ *sinx = theta;
+ *cosx = 1.0 - abstheta;
+ }
}
- else
+ else /* |x| >= Pi/4. */
{
- /* Argument reduction needed. */
- float y[2];
- int n;
-
- n = __ieee754_rem_pio2f (x, y);
- switch (n & 3)
+ unsigned int signbit = isless (x, 0);
+ if (isless (abstheta, 9 * M_PI_4)) /* |x| < 9*Pi/4. */
+ {
+ /* There are cases where FE_UPWARD rounding mode can
+ produce a result of abstheta * inv_PI_4 == 9,
+ where abstheta < 9pi/4, so the domain for
+ pio2_table must go to 5 (9 / 2 + 1). */
+ unsigned int n = (abstheta * inv_PI_4) + 1;
+ theta = abstheta - pio2_table[n / 2];
+ *sinx = reduced_sin (theta, n, signbit);
+ *cosx = reduced_cos (theta, n);
+ }
+ else if (isless (abstheta, INFINITY))
+ {
+ if (abstheta < 0x1p+23) /* |x| < 2^23. */
+ {
+ unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
+ double x = n / 2;
+ theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
+ /* Argument reduction needed. */
+ *sinx = reduced_sin (theta, n, signbit);
+ *cosx = reduced_cos (theta, n);
+ }
+ else /* |x| >= 2^23. */
+ {
+ x = fabsf (x);
+ int exponent;
+ GET_FLOAT_WORD (exponent, x);
+ exponent
+ = (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;
+ exponent += 3;
+ exponent /= 28;
+ double a = invpio4_table[exponent] * x;
+ double b = invpio4_table[exponent + 1] * x;
+ double c = invpio4_table[exponent + 2] * x;
+ double d = invpio4_table[exponent + 3] * x;
+ uint64_t l = a;
+ l &= ~0x7;
+ a -= l;
+ double e = a + b;
+ l = e;
+ e = a - l;
+ if (l & 1)
+ {
+ e -= 1.0;
+ e += b;
+ e += c;
+ e += d;
+ e *= M_PI_4;
+ *sinx = reduced_sin (e, l + 1, signbit);
+ *cosx = reduced_cos (e, l + 1);
+ }
+ else
+ {
+ e += b;
+ e += c;
+ e += d;
+ if (e <= 1.0)
+ {
+ e *= M_PI_4;
+ *sinx = reduced_sin (e, l + 1, signbit);
+ *cosx = reduced_cos (e, l + 1);
+ }
+ else
+ {
+ l++;
+ e -= 2.0;
+ e *= M_PI_4;
+ *sinx = reduced_sin (e, l + 1, signbit);
+ *cosx = reduced_cos (e, l + 1);
+ }
+ }
+ }
+ }
+ else
{
- case 0:
- *sinx = __kernel_sinf (y[0], y[1], 1);
- *cosx = __kernel_cosf (y[0], y[1]);
- break;
- case 1:
- *sinx = __kernel_cosf (y[0], y[1]);
- *cosx = -__kernel_sinf (y[0], y[1], 1);
- break;
- case 2:
- *sinx = -__kernel_sinf (y[0], y[1], 1);
- *cosx = -__kernel_cosf (y[0], y[1]);
- break;
- default:
- *sinx = -__kernel_cosf (y[0], y[1]);
- *cosx = __kernel_sinf (y[0], y[1], 1);
- break;
+ int32_t ix;
+ /* High word of x. */
+ GET_FLOAT_WORD (ix, abstheta);
+ /* sin/cos(Inf or NaN) is NaN. */
+ *sinx = *cosx = x - x;
+ if (ix == 0x7f800000)
+ __set_errno (EDOM);
}
}
}
diff --git a/sysdeps/ieee754/flt-32/s_sinf.c b/sysdeps/ieee754/flt-32/s_sinf.c
index 418d4487c5..c682bc64fc 100644
--- a/sysdeps/ieee754/flt-32/s_sinf.c
+++ b/sysdeps/ieee754/flt-32/s_sinf.c
@@ -20,6 +20,7 @@
#include <math.h>
#include <math_private.h>
#include <libm-alias-float.h>
+#include "s_sincos.h"
#ifndef SINF
# define SINF_FUNC __sinf
@@ -27,100 +28,6 @@
# define SINF_FUNC SINF
#endif
-/* Chebyshev constants for cos, range -PI/4 - PI/4. */
-static const double C0 = -0x1.ffffffffe98aep-2;
-static const double C1 = 0x1.55555545c50c7p-5;
-static const double C2 = -0x1.6c16b348b6874p-10;
-static const double C3 = 0x1.a00eb9ac43ccp-16;
-static const double C4 = -0x1.23c97dd8844d7p-22;
-
-/* Chebyshev constants for sin, range -PI/4 - PI/4. */
-static const double S0 = -0x1.5555555551cd9p-3;
-static const double S1 = 0x1.1111110c2688bp-7;
-static const double S2 = -0x1.a019f8b4bd1f9p-13;
-static const double S3 = 0x1.71d7264e6b5b4p-19;
-static const double S4 = -0x1.a947e1674b58ap-26;
-
-/* Chebyshev constants for sin, range 2^-27 - 2^-5. */
-static const double SS0 = -0x1.555555543d49dp-3;
-static const double SS1 = 0x1.110f475cec8c5p-7;
-
-/* PI/2 with 98 bits of accuracy. */
-static const double PI_2_hi = -0x1.921fb544p+0;
-static const double PI_2_lo = -0x1.0b4611a626332p-34;
-
-static const double SMALL = 0x1p-50; /* 2^-50. */
-static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */
-
-#define FLOAT_EXPONENT_SHIFT 23
-#define FLOAT_EXPONENT_BIAS 127
-
-static const double pio2_table[] = {
- 0 * M_PI_2,
- 1 * M_PI_2,
- 2 * M_PI_2,
- 3 * M_PI_2,
- 4 * M_PI_2,
- 5 * M_PI_2
-};
-
-static const double invpio4_table[] = {
- 0x0p+0,
- 0x1.45f306cp+0,
- 0x1.c9c882ap-28,
- 0x1.4fe13a8p-58,
- 0x1.f47d4dp-85,
- 0x1.bb81b6cp-112,
- 0x1.4acc9ep-142,
- 0x1.0e4107cp-169
-};
-
-static const double ones[] = { 1.0, -1.0 };
-
-/* Compute the sine value using Chebyshev polynomials where
- THETA is the range reduced absolute value of the input
- and it is less than Pi/4,
- N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide
- whether a sine or cosine approximation is more accurate and
- SIGNBIT is used to add the correct sign after the Chebyshev
- polynomial is computed. */
-static inline float
-reduced (const double theta, const unsigned int n,
- const unsigned int signbit)
-{
- double sx;
- const double theta2 = theta * theta;
- /* We are operating on |x|, so we need to add back the original
- signbit for sinf. */
- double sign;
- /* Determine positive or negative primary interval. */
- sign = ones[((n >> 2) & 1) ^ signbit];
- /* Are we in the primary interval of sin or cos? */
- if ((n & 2) == 0)
- {
- /* Here sinf() is calculated using sin Chebyshev polynomial:
- x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */
- sx = S3 + theta2 * S4; /* S3+x^2*S4. */
- sx = S2 + theta2 * sx; /* S2+x^2*(S3+x^2*S4). */
- sx = S1 + theta2 * sx; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */
- sx = S0 + theta2 * sx; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */
- sx = theta + theta * theta2 * sx;
- }
- else
- {
- /* Here sinf() is calculated using cos Chebyshev polynomial:
- 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */
- sx = C3 + theta2 * C4; /* C3+x^2*C4. */
- sx = C2 + theta2 * sx; /* C2+x^2*(C3+x^2*C4). */
- sx = C1 + theta2 * sx; /* C1+x^2*(C2+x^2*(C3+x^2*C4)). */
- sx = C0 + theta2 * sx; /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))). */
- sx = 1.0 + theta2 * sx;
- }
-
- /* Add in the signbit and assign the result. */
- return sign * sx;
-}
-
float
SINF_FUNC (float x)
{
@@ -171,7 +78,7 @@ SINF_FUNC (float x)
pio2_table must go to 5 (9 / 2 + 1). */
unsigned int n = (abstheta * inv_PI_4) + 1;
theta = abstheta - pio2_table[n / 2];
- return reduced (theta, n, signbit);
+ return reduced_sin (theta, n, signbit);
}
else if (isless (abstheta, INFINITY))
{
@@ -179,9 +86,9 @@ SINF_FUNC (float x)
{
unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;
double x = n / 2;
- theta = x * PI_2_lo + (x * PI_2_hi + abstheta);
+ theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;
/* Argument reduction needed. */
- return reduced (theta, n, signbit);
+ return reduced_sin (theta, n, signbit);
}
else /* |x| >= 2^23. */
{
@@ -209,7 +116,7 @@ SINF_FUNC (float x)
e += c;
e += d;
e *= M_PI_4;
- return reduced (e, l + 1, signbit);
+ return reduced_sin (e, l + 1, signbit);
}
else
{
@@ -219,14 +126,14 @@ SINF_FUNC (float x)
if (e <= 1.0)
{
e *= M_PI_4;
- return reduced (e, l + 1, signbit);
+ return reduced_sin (e, l + 1, signbit);
}
else
{
l++;
e -= 2.0;
e *= M_PI_4;
- return reduced (e, l + 1, signbit);
+ return reduced_sin (e, l + 1, signbit);
}
}
}
--
2.11.0