use __expo2 in sinh and cosh, move __cexp to cmath

diff --git a/src/cmath/__cexp.c b/src/cmath/__cexp.c
new file mode 100644 (file)
index 0000000..f603e2b
--- /dev/null
+++ b/src/cmath/__cexp.c
@@ -0,0 +1,87 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/k_exp.c */
+/*-
+ * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#include "libm.h"
+
+static const uint32_t k = 1799; /* constant for reduction */
+static const double kln2 = 1246.97177782734161156; /* k * ln2 */
+
+/*
+ * Compute exp(x), scaled to avoid spurious overflow.  An exponent is
+ * returned separately in 'expt'.
+ *
+ * Input:  ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91
+ * Output: 2**1023 <= y < 2**1024
+ */
+static double __frexp_exp(double x, int *expt)
+{
+       double exp_x;
+       uint32_t hx;
+
+       /*
+        * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to
+        * minimize |exp(kln2) - 2**k|.  We also scale the exponent of
+        * exp_x to MAX_EXP so that the result can be multiplied by
+        * a tiny number without losing accuracy due to denormalization.
+        */
+       exp_x = exp(x - kln2);
+       GET_HIGH_WORD(hx, exp_x);
+       *expt = (hx >> 20) - (0x3ff + 1023) + k;
+       SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20));
+       return exp_x;
+}
+
+/*
+ * __ldexp_cexp(x, expt) compute exp(x) * 2**expt.
+ * It is intended for large arguments (real part >= ln(DBL_MAX))
+ * where care is needed to avoid overflow.
+ *
+ * The present implementation is narrowly tailored for our hyperbolic and
+ * exponential functions.  We assume expt is small (0 or -1), and the caller
+ * has filtered out very large x, for which overflow would be inevitable.
+ */
+double complex __ldexp_cexp(double complex z, int expt)
+{
+       double x, y, exp_x, scale1, scale2;
+       int ex_expt, half_expt;
+
+       x = creal(z);
+       y = cimag(z);
+       exp_x = __frexp_exp(x, &ex_expt);
+       expt += ex_expt;
+
+       /*
+        * Arrange so that scale1 * scale2 == 2**expt.  We use this to
+        * compensate for scalbn being horrendously slow.
+        */
+       half_expt = expt / 2;
+       INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0);
+       half_expt = expt - half_expt;
+       INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0);
+
+       return cpack(cos(y) * exp_x * scale1 * scale2, sin(y) * exp_x * scale1 * scale2);
+}

diff --git a/src/cmath/__cexpf.c b/src/cmath/__cexpf.c
new file mode 100644 (file)
index 0000000..47168e8
--- /dev/null
+++ b/src/cmath/__cexpf.c
@@ -0,0 +1,68 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/k_expf.c */
+/*-
+ * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ */
+
+#include "libm.h"
+
+static const uint32_t k = 235; /* constant for reduction */
+static const float kln2 = 162.88958740F; /* k * ln2 */
+
+/*
+ * See __cexp.c for details.
+ *
+ * Input:  ln(FLT_MAX) <= x < ln(2 * FLT_MAX / FLT_MIN_DENORM) ~= 192.7
+ * Output: 2**127 <= y < 2**128
+ */
+static float __frexp_expf(float x, int *expt)
+{
+       float exp_x;
+       uint32_t hx;
+
+       exp_x = expf(x - kln2);
+       GET_FLOAT_WORD(hx, exp_x);
+       *expt = (hx >> 23) - (0x7f + 127) + k;
+       SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 127) << 23));
+       return exp_x;
+}
+
+float complex __ldexp_cexpf(float complex z, int expt)
+{
+       float x, y, exp_x, scale1, scale2;
+       int ex_expt, half_expt;
+
+       x = crealf(z);
+       y = cimagf(z);
+       exp_x = __frexp_expf(x, &ex_expt);
+       expt += ex_expt;
+
+       half_expt = expt / 2;
+       SET_FLOAT_WORD(scale1, (0x7f + half_expt) << 23);
+       half_expt = expt - half_expt;
+       SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23);
+
+       return cpackf(cosf(y) * exp_x * scale1 * scale2,
+         sinf(y) * exp_x * scale1 * scale2);
+}

diff --git a/src/internal/libm.h b/src/internal/libm.h
index 00c2972..6487015 100644 (file)
--- a/src/internal/libm.h
+++ b/src/internal/libm.h
@@ -124,14 +124,14 @@ int    __rem_pio2(double,double*);
 double __sin(double,double,int);
 double __cos(double,double);
 double __tan(double,double,int);
 double __sin(double,double,int);
 double __cos(double,double);
 double __tan(double,double,int);

-double __ldexp_exp(double,int);
+double __expo2(double);

 double complex __ldexp_cexp(double complex,int);
 
 int    __rem_pio2f(float,double*);
 float  __sindf(double);
 float  __cosdf(double);
 float  __tandf(double,int);
 double complex __ldexp_cexp(double complex,int);
 
 int    __rem_pio2f(float,double*);
 float  __sindf(double);
 float  __cosdf(double);
 float  __tandf(double,int);

-float  __ldexp_expf(float,int);
+float  __expo2f(float);

 float complex __ldexp_cexpf(float complex,int);
 
 long double __sinl(long double, long double, int);
 float complex __ldexp_cexpf(float complex,int);
 
 long double __sinl(long double, long double, int);

diff --git a/src/math/__exp.c b/src/math/__exp.c
index 83f8ac3..ef14e5f 100644 (file)
--- a/src/math/__exp.c
+++ b/src/math/__exp.c
@@ -27,72 +27,25 @@
 
 #include "libm.h"
 
 
 #include "libm.h"
 

-static const uint32_t k = 1799; /* constant for reduction */
-static const double kln2 = 1246.97177782734161156; /* k * ln2 */
-
-/*
- * Compute exp(x), scaled to avoid spurious overflow.  An exponent is
- * returned separately in 'expt'.
- *
- * Input:  ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91
- * Output: 2**1023 <= y < 2**1024
- */
-static double __frexp_exp(double x, int *expt)
-{
-       double exp_x;
-       uint32_t hx;
-
-       /*
-        * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to
-        * minimize |exp(kln2) - 2**k|.  We also scale the exponent of
-        * exp_x to MAX_EXP so that the result can be multiplied by
-        * a tiny number without losing accuracy due to denormalization.
-        */
-       exp_x = exp(x - kln2);
-       GET_HIGH_WORD(hx, exp_x);
-       *expt = (hx >> 20) - (0x3ff + 1023) + k;
-       SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20));
-       return exp_x;
-}
-

 /*
 /*

- * __ldexp_exp(x, expt) and __ldexp_cexp(x, expt) compute exp(x) * 2**expt.
- * They are intended for large arguments (real part >= ln(DBL_MAX))
- * where care is needed to avoid overflow.
- *
- * The present implementation is narrowly tailored for our hyperbolic and
- * exponential functions.  We assume expt is small (0 or -1), and the caller
- * has filtered out very large x, for which overflow would be inevitable.
+ * We use exp(x) = exp(x - kln2) * 2**k,
+ * k is carefully chosen to minimize |exp(kln2) - 2**k|

  */
  */

-double __ldexp_exp(double x, int expt)
-{
-       double exp_x, scale;
-       int ex_expt;
+static const uint32_t k = 1799;
+static const double kln2 = 1246.97177782734161156;

 
 

-       exp_x = __frexp_exp(x, &ex_expt);
-       expt += ex_expt;
-       INSERT_WORDS(scale, (0x3ff + expt) << 20, 0);
-       return exp_x * scale;
-}
-
-double complex __ldexp_cexp(double complex z, int expt)
+/* exp(x)/2 when x is huge */
+double __expo2(double x)

 {
 {

-       double x, y, exp_x, scale1, scale2;
-       int ex_expt, half_expt;
-
-       x = creal(z);
-       y = cimag(z);
-       exp_x = __frexp_exp(x, &ex_expt);
-       expt += ex_expt;
+       double scale;
+       int n;

 
        /*
 
        /*

-        * Arrange so that scale1 * scale2 == 2**expt.  We use this to
-        * compensate for scalbn being horrendously slow.
+        * efficient scalbn(y, k-1):
+        * 2**(k-1) cannot be represented
+        * so we use that k-1 is even and scale in two steps

         */
         */

-       half_expt = expt / 2;
-       INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0);
-       half_expt = expt - half_expt;
-       INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0);
-
-       return cpack(cos(y) * exp_x * scale1 * scale2, sin(y) * exp_x * scale1 * scale2);
+       n = (k - 1)/2;
+       INSERT_WORDS(scale, (0x3ff + n) << 20, 0);
+       return exp(x - kln2) * scale * scale;

 }
 }

diff --git a/src/math/__expf.c b/src/math/__expf.c
index fa4fcdc..192838f 100644 (file)
--- a/src/math/__expf.c
+++ b/src/math/__expf.c
@@ -27,53 +27,25 @@
 
 #include "libm.h"
 
 
 #include "libm.h"
 

-static const uint32_t k = 235; /* constant for reduction */
-static const float kln2 = 162.88958740F; /* k * ln2 */
-

 /*
 /*

- * See __exp.c for details.
- *
- * Input:  ln(FLT_MAX) <= x < ln(2 * FLT_MAX / FLT_MIN_DENORM) ~= 192.7
- * Output: 2**127 <= y < 2**128
+ * We use exp(x) = exp(x - kln2) * 2**k,
+ * k is carefully chosen to minimize |exp(kln2) - 2**k|

  */
  */

-static float __frexp_expf(float x, int *expt)
-{
-       float exp_x;
-       uint32_t hx;
-
-       exp_x = expf(x - kln2);
-       GET_FLOAT_WORD(hx, exp_x);
-       *expt = (hx >> 23) - (0x7f + 127) + k;
-       SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 127) << 23));
-       return exp_x;
-}
-
-float __ldexp_expf(float x, int expt)
-{
-       float exp_x, scale;
-       int ex_expt;
-
-       exp_x = __frexp_expf(x, &ex_expt);
-       expt += ex_expt;
-       SET_FLOAT_WORD(scale, (0x7f + expt) << 23);
-       return exp_x * scale;
-}
+static const uint32_t k = 235;
+static const float kln2 = 162.88958740f;

 
 

-float complex __ldexp_cexpf(float complex z, int expt)
+/* expf(x)/2 when x is huge */
+float __expo2f(float x)

 {
 {

-       float x, y, exp_x, scale1, scale2;
-       int ex_expt, half_expt;
-
-       x = crealf(z);
-       y = cimagf(z);
-       exp_x = __frexp_expf(x, &ex_expt);
-       expt += ex_expt;
-
-       half_expt = expt / 2;
-       SET_FLOAT_WORD(scale1, (0x7f + half_expt) << 23);
-       half_expt = expt - half_expt;
-       SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23);
-
-       return (cpackf(cosf(y) * exp_x * scale1 * scale2,
-               sinf(y) * exp_x * scale1 * scale2));
+       float scale;
+       int n;
+
+       /*
+        * efficient scalbnf(y, k-1):
+        * 2**(k-1) cannot be represented
+        * so we use that k-1 is even and scale in two steps
+        */
+       n = (k - 1)/2;
+       SET_FLOAT_WORD(scale, (0x7f + n) << 23);
+       return expf(x - kln2) * scale * scale;

 }
 }

diff --git a/src/math/cosh.c b/src/math/cosh.c
index 5b871db..5f38b27 100644 (file)
--- a/src/math/cosh.c
+++ b/src/math/cosh.c
@@ -67,7 +67,7 @@ double cosh(double x)
 
        /* |x| in [log(maxdouble), overflowthresold] */
        if (ix <= 0x408633CE)
 
        /* |x| in [log(maxdouble), overflowthresold] */
        if (ix <= 0x408633CE)

-               return __ldexp_exp(fabs(x), -1);
+               return __expo2(fabs(x));

 
        /* |x| > overflowthresold, cosh(x) overflow */
        return huge*huge;
 
        /* |x| > overflowthresold, cosh(x) overflow */
        return huge*huge;

diff --git a/src/math/coshf.c b/src/math/coshf.c
index 6a0db52..9e87afc 100644 (file)
--- a/src/math/coshf.c
+++ b/src/math/coshf.c
@@ -50,7 +50,7 @@ float coshf(float x)
 
        /* |x| in [log(maxfloat), overflowthresold] */
        if (ix <= 0x42b2d4fc)
 
        /* |x| in [log(maxfloat), overflowthresold] */
        if (ix <= 0x42b2d4fc)

-               return __ldexp_expf(fabsf(x), -1);
+               return __expo2f(fabsf(x));

 
        /* |x| > overflowthresold, cosh(x) overflow */
        return huge*huge;
 
        /* |x| > overflowthresold, cosh(x) overflow */
        return huge*huge;

diff --git a/src/math/sinh.c b/src/math/sinh.c
index 5e037e5..935879c 100644 (file)
--- a/src/math/sinh.c
+++ b/src/math/sinh.c
@@ -64,8 +64,7 @@ double sinh(double x)
 
        /* |x| in [log(maxdouble), overflowthresold] */
        if (ix <= 0x408633CE)
 
        /* |x| in [log(maxdouble), overflowthresold] */
        if (ix <= 0x408633CE)

-               // FIXME: 0.5 * 2.0 * huge == huge ?
-               return h*2.0*__ldexp_exp(fabs(x), -1);
+               return h * 2.0 * __expo2(fabs(x)); /* h is for sign only */

 
        /* |x| > overflowthresold, sinh(x) overflow */
        return x*huge;
 
        /* |x| > overflowthresold, sinh(x) overflow */
        return x*huge;

diff --git a/src/math/sinhf.c b/src/math/sinhf.c
index 15c5013..056b5f8 100644 (file)
--- a/src/math/sinhf.c
+++ b/src/math/sinhf.c
@@ -50,8 +50,7 @@ float sinhf(float x)
 
        /* |x| in [logf(maxfloat), overflowthresold] */
        if (ix <= 0x42b2d4fc)
 
        /* |x| in [logf(maxfloat), overflowthresold] */
        if (ix <= 0x42b2d4fc)

-               // FIXME: 0.5f * 2.0f * huge == huge ?
-               return h*2.0F*__ldexp_expf(fabsf(x), -1);
+               return h * 2.0f * __expo2f(fabsf(x)); /* h is for sign only */

 
        /* |x| > overflowthresold, sinh(x) overflow */
        return x*huge;
 
        /* |x| > overflowthresold, sinh(x) overflow */
        return x*huge;