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Create and use SET_RESTORE_ROUND{,_NOEX,_53BIT}{,F,L}.
This commit is contained in:
Richard Henderson
parent
7d2e8012cf
commit
eb92c487b3
24
ChangeLog
24
ChangeLog
@ -1,5 +1,29 @@
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2012-03-19 Richard Henderson <rth@twiddle.net>
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* sysdeps/generic/math_private.h (libc_feholdsetround): New.
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(libc_feholdsetroundf, libc_feholdsetroundl): New.
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(libc_feresetround, libc_feresetroundf, libc_feresetroundl): New.
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(libc_feresetround_noex): New.
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(libc_feresetround_noexf): New.
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(libc_feresetround_noexl): New.
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(SET_RESTORE_ROUND, SET_RESTORE_ROUNDF, SET_RESTORE_ROUNDL): New.
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(SET_RESTORE_ROUND_NOEX, SET_RESTORE_ROUND_NOEXF): New.
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(SET_RESTORE_ROUND_NOEXL, SET_RESTORE_ROUND_53BIT): New.
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* sysdeps/ieee754/dbl-64/e_exp.c (__ieee754_exp): Use
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SET_RESTORE_ROUND.
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* sysdeps/ieee754/dbl-64/e_pow.c (__ieee754_pow): Likewise.
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* sysdeps/ieee754/dbl-64/s_sin.c (__sin): Use SET_RESTORE_ROUND_53BIT.
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(__cos): Likewise.
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* sysdeps/ieee754/dbl-64/s_tan.c (__tan): Likewise.
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* sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Use
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SET_RESTORE_ROUND_NOEX.
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* sysdeps/ieee754/dbl-64/e_exp2f.c (__ieee754_exp2f): Use
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SET_RESTORE_ROUND_NOEXF.
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* sysdeps/ieee754/flt-32/e_expf.c (__ieee754_expf): Likewise.
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* sysdeps/x86_64/fpu/math_private.h (libc_feholdsetround): New.
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(libc_feholdsetroundf): New.
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(libc_feresetround, libc_feresetroundf): New.
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* sysdeps/i386/fpu/math_private.h: Include <fenv.h>, <fpu_control.h>.
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(libc_feholdexcept_setround_53bit): Convert from macro to function.
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(libc_feupdateenv_53bit): Likewise. Don't force _FPU_EXTENDED.
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@ -457,6 +457,75 @@ default_libc_feupdateenv (fenv_t *e)
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# define libc_feupdateenv_53bit libc_feupdateenv
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#endif
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/* Save and set the rounding mode. The use of fenv_t to store the old mode
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allows a target-specific version of this function to avoid converting the
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rounding mode from the fpu format. By default we have no choice but to
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manipulate the entire env. */
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#ifndef libc_feholdsetround
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# define libc_feholdsetround libc_feholdexcept_setround
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#endif
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#ifndef libc_feholdsetroundf
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# define libc_feholdsetroundf libc_feholdexcept_setroundf
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#endif
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#ifndef libc_feholdsetroundl
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# define libc_feholdsetroundl libc_feholdexcept_setroundl
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#endif
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/* ... and the reverse. */
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#ifndef libc_feresetround
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# define libc_feresetround libc_feupdateenv
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#endif
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#ifndef libc_feresetroundf
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# define libc_feresetroundf libc_feupdateenvf
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#endif
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#ifndef libc_feresetroundl
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# define libc_feresetroundl libc_feupdateenvl
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#endif
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/* ... and a version that may also discard exceptions. */
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#ifndef libc_feresetround_noex
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# define libc_feresetround_noex libc_fesetenv
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#endif
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#ifndef libc_feresetround_noexf
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# define libc_feresetround_noexf libc_fesetenvf
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#endif
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#ifndef libc_feresetround_noexl
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# define libc_feresetround_noexl libc_fesetenvl
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#endif
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/* Save and restore the rounding mode within a lexical block. */
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#define SET_RESTORE_ROUND(RM) \
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fenv_t __libc_save_rm __attribute__((cleanup(libc_feresetround))); \
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libc_feholdsetround (&__libc_save_rm, (RM))
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#define SET_RESTORE_ROUNDF(RM) \
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fenv_t __libc_save_rm __attribute__((cleanup(libc_feresetroundf))); \
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libc_feholdsetroundf (&__libc_save_rm, (RM))
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#define SET_RESTORE_ROUNDL(RM) \
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fenv_t __libc_save_rm __attribute__((cleanup(libc_feresetroundl))); \
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libc_feholdsetroundl (&__libc_save_rm, (RM))
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/* Save and restore the rounding mode within a lexical block, and also
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the set of exceptions raised within the block may be discarded. */
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#define SET_RESTORE_ROUND_NOEX(RM) \
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fenv_t __libc_save_rm __attribute__((cleanup(libc_feresetround_noex))); \
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libc_feholdsetround (&__libc_save_rm, (RM))
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#define SET_RESTORE_ROUND_NOEXF(RM) \
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fenv_t __libc_save_rm __attribute__((cleanup(libc_feresetround_noexf))); \
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libc_feholdsetroundf (&__libc_save_rm, (RM))
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#define SET_RESTORE_ROUND_NOEXL(RM) \
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fenv_t __libc_save_rm __attribute__((cleanup(libc_feresetround_noexl))); \
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libc_feholdsetroundl (&__libc_save_rm, (RM))
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/* Like SET_RESTORE_ROUND, but also set rounding precision to 53 bits. */
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#define SET_RESTORE_ROUND_53BIT(RM) \
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fenv_t __libc_save_rm __attribute__((cleanup(libc_feupdateenv_53bit))); \
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libc_feholdexcept_setround_53bit (&__libc_save_rm, (RM))
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#define __nan(str) \
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(__builtin_constant_p (str) && str[0] == '\0' ? NAN : __nan (str))
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#define __nanf(str) \
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@ -59,10 +59,9 @@ __ieee754_exp(double x) {
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int4 k;
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#endif
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int4 i,j,m,n,ex;
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fenv_t env;
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double retval;
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libc_feholdexcept_setround (&env, FE_TONEAREST);
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SET_RESTORE_ROUND (FE_TONEAREST);
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junk1.x = x;
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m = junk1.i[HIGH_HALF];
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@ -157,7 +156,6 @@ __ieee754_exp(double x) {
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else { retval = __slowexp(x); goto ret; }
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}
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ret:
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libc_feupdateenv (&env);
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return retval;
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}
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#ifndef __ieee754_exp
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@ -61,57 +61,56 @@ __ieee754_exp2 (double x)
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int tval, unsafe;
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double rx, x22, result;
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union ieee754_double ex2_u, scale_u;
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fenv_t oldenv;
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libc_feholdexcept_setround (&oldenv, FE_TONEAREST);
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{
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SET_RESTORE_ROUND_NOEX (FE_TONEAREST);
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/* 1. Argument reduction.
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Choose integers ex, -256 <= t < 256, and some real
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-1/1024 <= x1 <= 1024 so that
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x = ex + t/512 + x1.
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/* 1. Argument reduction.
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Choose integers ex, -256 <= t < 256, and some real
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-1/1024 <= x1 <= 1024 so that
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x = ex + t/512 + x1.
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First, calculate rx = ex + t/512. */
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rx = x + THREEp42;
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rx -= THREEp42;
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x -= rx; /* Compute x=x1. */
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/* Compute tval = (ex*512 + t)+256.
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Now, t = (tval mod 512)-256 and ex=tval/512 [that's mod, NOT %; and
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/-round-to-nearest not the usual c integer /]. */
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tval = (int) (rx * 512.0 + 256.0);
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First, calculate rx = ex + t/512. */
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rx = x + THREEp42;
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rx -= THREEp42;
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x -= rx; /* Compute x=x1. */
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/* Compute tval = (ex*512 + t)+256.
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Now, t = (tval mod 512)-256 and ex=tval/512 [that's mod, NOT %;
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and /-round-to-nearest not the usual c integer /]. */
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tval = (int) (rx * 512.0 + 256.0);
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/* 2. Adjust for accurate table entry.
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Find e so that
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x = ex + t/512 + e + x2
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where -1e6 < e < 1e6, and
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(double)(2^(t/512+e))
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is accurate to one part in 2^-64. */
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/* 2. Adjust for accurate table entry.
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Find e so that
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x = ex + t/512 + e + x2
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where -1e6 < e < 1e6, and
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(double)(2^(t/512+e))
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is accurate to one part in 2^-64. */
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/* 'tval & 511' is the same as 'tval%512' except that it's always
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positive.
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Compute x = x2. */
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x -= exp2_deltatable[tval & 511];
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/* 'tval & 511' is the same as 'tval%512' except that it's always
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positive.
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Compute x = x2. */
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x -= exp2_deltatable[tval & 511];
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/* 3. Compute ex2 = 2^(t/512+e+ex). */
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ex2_u.d = exp2_accuratetable[tval & 511];
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tval >>= 9;
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unsafe = abs(tval) >= -DBL_MIN_EXP - 1;
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ex2_u.ieee.exponent += tval >> unsafe;
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scale_u.d = 1.0;
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scale_u.ieee.exponent += tval - (tval >> unsafe);
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/* 3. Compute ex2 = 2^(t/512+e+ex). */
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ex2_u.d = exp2_accuratetable[tval & 511];
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tval >>= 9;
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unsafe = abs(tval) >= -DBL_MIN_EXP - 1;
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ex2_u.ieee.exponent += tval >> unsafe;
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scale_u.d = 1.0;
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scale_u.ieee.exponent += tval - (tval >> unsafe);
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/* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial,
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with maximum error in [-2^-10-2^-30,2^-10+2^-30]
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less than 10^-19. */
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/* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial,
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with maximum error in [-2^-10-2^-30,2^-10+2^-30]
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less than 10^-19. */
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x22 = (((.0096181293647031180
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* x + .055504110254308625)
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* x + .240226506959100583)
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* x + .69314718055994495) * ex2_u.d;
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math_opt_barrier (x22);
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x22 = (((.0096181293647031180
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* x + .055504110254308625)
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* x + .240226506959100583)
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* x + .69314718055994495) * ex2_u.d;
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math_opt_barrier (x22);
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}
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/* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */
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libc_fesetenv (&oldenv);
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result = x22 * x + ex2_u.d;
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if (!unsafe)
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@ -85,10 +85,9 @@ __ieee754_pow(double x, double y) {
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(u.i[HIGH_HALF]==0 && u.i[LOW_HALF]!=0)) &&
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/* 2^-1023< x<= 2^-1023 * 0x1.0000ffffffff */
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(v.i[HIGH_HALF]&0x7fffffff) < 0x4ff00000) { /* if y<-1 or y>1 */
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fenv_t env;
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double retval;
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libc_feholdexcept_setround (&env, FE_TONEAREST);
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SET_RESTORE_ROUND (FE_TONEAREST);
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z = log1(x,&aa,&error); /* x^y =e^(y log (X)) */
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t = y*134217729.0;
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@ -105,7 +104,6 @@ __ieee754_pow(double x, double y) {
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t = __exp1(a1,a2,1.9e16*error); /* return -10 or 0 if wasn't computed exactly */
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retval = (t>0)?t:power1(x,y);
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libc_feupdateenv (&env);
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return retval;
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}
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@ -108,10 +108,9 @@ __sin(double x){
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#if 0
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int4 nn;
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#endif
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fenv_t env;
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double retval = 0;
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libc_feholdexcept_setround_53bit (&env, FE_TONEAREST);
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SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
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u.x = x;
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m = u.i[HIGH_HALF];
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@ -365,7 +364,6 @@ __sin(double x){
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}
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ret:
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libc_feupdateenv_53bit (&env);
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return retval;
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}
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@ -383,10 +381,9 @@ __cos(double x)
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mynumber u,v;
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int4 k,m,n;
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fenv_t env;
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double retval = 0;
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libc_feholdexcept_setround_53bit (&env, FE_TONEAREST);
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SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
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u.x = x;
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m = u.i[HIGH_HALF];
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@ -635,7 +632,6 @@ __cos(double x)
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}
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ret:
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libc_feupdateenv_53bit (&env);
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return retval;
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}
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@ -68,13 +68,12 @@ tan(double x) {
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mp_no mpy;
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#endif
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fenv_t env;
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double retval;
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int __branred(double, double *, double *);
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int __mpranred(double, mp_no *, int);
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libc_feholdexcept_setround_53bit (&env, FE_TONEAREST);
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SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
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/* x=+-INF, x=NaN */
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num.d = x; ux = num.i[HIGH_HALF];
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@ -503,7 +502,6 @@ tan(double x) {
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goto ret;
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ret:
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libc_feupdateenv_53bit (&env);
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return retval;
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}
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@ -54,53 +54,52 @@ __ieee754_exp2f (float x)
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int tval, unsafe;
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float rx, x22, result;
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union ieee754_float ex2_u, scale_u;
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fenv_t oldenv;
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libc_feholdexcept_setroundf (&oldenv, FE_TONEAREST);
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{
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SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
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/* 1. Argument reduction.
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Choose integers ex, -128 <= t < 128, and some real
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-1/512 <= x1 <= 1/512 so that
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x = ex + t/512 + x1.
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/* 1. Argument reduction.
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Choose integers ex, -128 <= t < 128, and some real
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-1/512 <= x1 <= 1/512 so that
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x = ex + t/512 + x1.
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First, calculate rx = ex + t/256. */
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rx = x + THREEp14;
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rx -= THREEp14;
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x -= rx; /* Compute x=x1. */
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/* Compute tval = (ex*256 + t)+128.
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Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %; and
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/-round-to-nearest not the usual c integer /]. */
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tval = (int) (rx * 256.0f + 128.0f);
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First, calculate rx = ex + t/256. */
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rx = x + THREEp14;
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rx -= THREEp14;
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x -= rx; /* Compute x=x1. */
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/* Compute tval = (ex*256 + t)+128.
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Now, t = (tval mod 256)-128 and ex=tval/256 [that's mod, NOT %;
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and /-round-to-nearest not the usual c integer /]. */
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tval = (int) (rx * 256.0f + 128.0f);
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/* 2. Adjust for accurate table entry.
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Find e so that
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x = ex + t/256 + e + x2
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where -7e-4 < e < 7e-4, and
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(float)(2^(t/256+e))
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is accurate to one part in 2^-64. */
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/* 2. Adjust for accurate table entry.
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Find e so that
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x = ex + t/256 + e + x2
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where -7e-4 < e < 7e-4, and
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(float)(2^(t/256+e))
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is accurate to one part in 2^-64. */
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/* 'tval & 255' is the same as 'tval%256' except that it's always
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positive.
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Compute x = x2. */
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x -= __exp2f_deltatable[tval & 255];
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/* 'tval & 255' is the same as 'tval%256' except that it's always
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positive.
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Compute x = x2. */
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x -= __exp2f_deltatable[tval & 255];
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/* 3. Compute ex2 = 2^(t/255+e+ex). */
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ex2_u.f = __exp2f_atable[tval & 255];
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tval >>= 8;
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unsafe = abs(tval) >= -FLT_MIN_EXP - 1;
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ex2_u.ieee.exponent += tval >> unsafe;
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scale_u.f = 1.0;
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scale_u.ieee.exponent += tval - (tval >> unsafe);
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/* 3. Compute ex2 = 2^(t/255+e+ex). */
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ex2_u.f = __exp2f_atable[tval & 255];
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tval >>= 8;
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unsafe = abs(tval) >= -FLT_MIN_EXP - 1;
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ex2_u.ieee.exponent += tval >> unsafe;
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scale_u.f = 1.0;
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scale_u.ieee.exponent += tval - (tval >> unsafe);
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/* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
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with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
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less than 1.3e-10. */
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/* 4. Approximate 2^x2 - 1, using a second-degree polynomial,
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with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14]
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less than 1.3e-10. */
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x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
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x22 = (.24022656679f * x + .69314736128f) * ex2_u.f;
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}
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/* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */
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libc_fesetenv (&oldenv);
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result = x22 * x + ex2_u.f;
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if (!unsafe)
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@ -80,40 +80,39 @@ __ieee754_expf (float x)
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||||
double x22, t, result, dx;
|
||||
float n, delta;
|
||||
union ieee754_double ex2_u;
|
||||
fenv_t oldenv;
|
||||
|
||||
libc_feholdexcept_setroundf (&oldenv, FE_TONEAREST);
|
||||
{
|
||||
SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
|
||||
|
||||
/* Calculate n. */
|
||||
n = x * M_1_LN2 + THREEp22;
|
||||
n -= THREEp22;
|
||||
dx = x - n*M_LN2;
|
||||
/* Calculate n. */
|
||||
n = x * M_1_LN2 + THREEp22;
|
||||
n -= THREEp22;
|
||||
dx = x - n*M_LN2;
|
||||
|
||||
/* Calculate t/512. */
|
||||
t = dx + THREEp42;
|
||||
t -= THREEp42;
|
||||
dx -= t;
|
||||
/* Calculate t/512. */
|
||||
t = dx + THREEp42;
|
||||
t -= THREEp42;
|
||||
dx -= t;
|
||||
|
||||
/* Compute tval = t. */
|
||||
tval = (int) (t * 512.0);
|
||||
/* Compute tval = t. */
|
||||
tval = (int) (t * 512.0);
|
||||
|
||||
if (t >= 0)
|
||||
delta = - __exp_deltatable[tval];
|
||||
else
|
||||
delta = __exp_deltatable[-tval];
|
||||
if (t >= 0)
|
||||
delta = - __exp_deltatable[tval];
|
||||
else
|
||||
delta = __exp_deltatable[-tval];
|
||||
|
||||
/* Compute ex2 = 2^n e^(t/512+delta[t]). */
|
||||
ex2_u.d = __exp_atable[tval+177];
|
||||
ex2_u.ieee.exponent += (int) n;
|
||||
/* Compute ex2 = 2^n e^(t/512+delta[t]). */
|
||||
ex2_u.d = __exp_atable[tval+177];
|
||||
ex2_u.ieee.exponent += (int) n;
|
||||
|
||||
/* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
|
||||
with maximum error in [-2^-10-2^-28,2^-10+2^-28]
|
||||
less than 5e-11. */
|
||||
x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
|
||||
/* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
|
||||
with maximum error in [-2^-10-2^-28,2^-10+2^-28]
|
||||
less than 5e-11. */
|
||||
x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
|
||||
}
|
||||
|
||||
/* Return result. */
|
||||
libc_fesetenvf (&oldenv);
|
||||
|
||||
result = x22 * ex2_u.d + ex2_u.d;
|
||||
return (float) result;
|
||||
}
|
||||
|
||||
@ -119,6 +119,29 @@ libc_feupdateenv (fenv_t *e)
|
||||
#define libc_feupdateenv libc_feupdateenv
|
||||
#define libc_feupdateenvf libc_feupdateenv
|
||||
|
||||
static __always_inline void
|
||||
libc_feholdsetround (fenv_t *e, int r)
|
||||
{
|
||||
unsigned int mxcsr;
|
||||
asm (STMXCSR " %0" : "=m" (*&mxcsr));
|
||||
e->__mxcsr = mxcsr;
|
||||
mxcsr = (mxcsr & ~0x6000) | (r << 3);
|
||||
asm volatile (LDMXCSR " %0" : : "m" (*&mxcsr));
|
||||
}
|
||||
#define libc_feholdsetround libc_feholdsetround
|
||||
#define libc_feholdsetroundf libc_feholdsetround
|
||||
|
||||
static __always_inline void
|
||||
libc_feresetround (fenv_t *e)
|
||||
{
|
||||
unsigned int mxcsr;
|
||||
asm (STMXCSR " %0" : "=m" (*&mxcsr));
|
||||
mxcsr = (mxcsr & ~0x6000) | (e->__mxcsr & 0x6000);
|
||||
asm volatile (LDMXCSR " %0" : : "m" (*&mxcsr));
|
||||
}
|
||||
#define libc_feresetround libc_feresetround
|
||||
#define libc_feresetroundf libc_feresetround
|
||||
|
||||
#include_next <math_private.h>
|
||||
|
||||
extern __always_inline double
|
||||
|
||||
Loading…
Reference in New Issue
Block a user