From 25215b63b9aa93089a9a05d1cffc3784109228c6 Mon Sep 17 00:00:00 2001 From: nsz Date: Mon, 12 Mar 2012 22:53:59 +0100 Subject: [PATCH] use __expo2 in sinh and cosh, move __cexp to cmath --- src/cmath/__cexp.c | 87 +++++++++++++++++++++++++++++++++++++++++++++ src/cmath/__cexpf.c | 68 +++++++++++++++++++++++++++++++++++ src/internal/libm.h | 4 +-- src/math/__exp.c | 75 ++++++++------------------------------ src/math/__expf.c | 62 +++++++++----------------------- src/math/cosh.c | 2 +- src/math/coshf.c | 2 +- src/math/sinh.c | 3 +- src/math/sinhf.c | 3 +- 9 files changed, 192 insertions(+), 114 deletions(-) create mode 100644 src/cmath/__cexp.c create mode 100644 src/cmath/__cexpf.c diff --git a/src/cmath/__cexp.c b/src/cmath/__cexp.c new file mode 100644 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 + * 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 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 + * 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 --- 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 __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); -float __ldexp_expf(float,int); +float __expo2f(float); 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 --- a/src/math/__exp.c +++ b/src/math/__exp.c @@ -27,72 +27,25 @@ #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 --- a/src/math/__expf.c +++ b/src/math/__expf.c @@ -27,53 +27,25 @@ #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 --- 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) - return __ldexp_exp(fabs(x), -1); + return __expo2(fabs(x)); /* |x| > overflowthresold, cosh(x) overflow */ return huge*huge; diff --git a/src/math/coshf.c b/src/math/coshf.c index 6a0db52..9e87afc 100644 --- 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) - return __ldexp_expf(fabsf(x), -1); + return __expo2f(fabsf(x)); /* |x| > overflowthresold, cosh(x) overflow */ return huge*huge; diff --git a/src/math/sinh.c b/src/math/sinh.c index 5e037e5..935879c 100644 --- 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) - // 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; diff --git a/src/math/sinhf.c b/src/math/sinhf.c index 15c5013..056b5f8 100644 --- 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) - // 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; -- 2.20.1