diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/e_exp.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_exp.c | 62 |
1 files changed, 17 insertions, 45 deletions
diff --git a/sysdeps/ieee754/dbl-64/e_exp.c b/sysdeps/ieee754/dbl-64/e_exp.c index 7a9daa5858..1bcb382c77 100644 --- a/sysdeps/ieee754/dbl-64/e_exp.c +++ b/sysdeps/ieee754/dbl-64/e_exp.c @@ -23,10 +23,10 @@ /* exp1 */ /* */ /* FILES NEEDED:dla.h endian.h mpa.h mydefs.h uexp.h */ -/* mpa.c mpexp.x slowexp.c */ +/* mpa.c mpexp.x */ /* */ /* An ultimate exp routine. Given an IEEE double machine number x */ -/* it computes the correctly rounded (to nearest) value of e^x */ +/* it computes an almost correctly rounded (to nearest) value of e^x */ /* Assumption: Machine arithmetic operations are performed in */ /* round to nearest mode of IEEE 754 standard. */ /* */ @@ -46,10 +46,6 @@ # define SECTION #endif -double __slowexp (double); - -/* An ultimate exp routine. Given an IEEE double machine number x it computes - the correctly rounded (to nearest) value of e^x. */ double SECTION __ieee754_exp (double x) @@ -93,17 +89,10 @@ __ieee754_exp (double x) rem = (bet + bet * eps) + al * eps; res = al + rem; - cor = (al - res) + rem; - if (res == (res + cor * err_0)) - { - retval = res * binexp.x; - goto ret; - } - else - { - retval = __slowexp (x); - goto ret; - } /*if error is over bound */ + /* Maximum relative error is 7.8e-22 (70.1 bits). + Maximum ULP error is 0.500007. */ + retval = res * binexp.x; + goto ret; } if (n <= smallint) @@ -166,38 +155,22 @@ __ieee754_exp (double x) if (ex >= -1022) { binexp.i[HIGH_HALF] = (1023 + ex) << 20; - if (res == (res + cor * err_0)) - { - retval = res * binexp.x; - goto ret; - } - else - { - retval = __slowexp (x); - goto check_uflow_ret; - } /*if error is over bound */ + /* Does not underflow: res >= 1.0, binexp >= 0x1p-1022 + Maximum relative error is 7.8e-22 (70.1 bits). + Maximum ULP error is 0.500007. */ + retval = res * binexp.x; + goto ret; } ex = -(1022 + ex); binexp.i[HIGH_HALF] = (1023 - ex) << 20; res *= binexp.x; cor *= binexp.x; - eps = 1.0000000001 + err_0 * binexp.x; t = 1.0 + res; y = ((1.0 - t) + res) + cor; res = t + y; - cor = (t - res) + y; - if (res == (res + eps * cor)) - { - binexp.i[HIGH_HALF] = 0x00100000; - retval = (res - 1.0) * binexp.x; - goto check_uflow_ret; - } - else - { - retval = __slowexp (x); - goto check_uflow_ret; - } /* if error is over bound */ - check_uflow_ret: + /* Maximum ULP error is 0.5000035. */ + binexp.i[HIGH_HALF] = 0x00100000; + retval = (res - 1.0) * binexp.x; if (retval < DBL_MIN) { double force_underflow = tiny * tiny; @@ -210,10 +183,9 @@ __ieee754_exp (double x) else { binexp.i[HIGH_HALF] = (junk1.i[LOW_HALF] + 767) << 20; - if (res == (res + cor * err_0)) - retval = res * binexp.x * t256.x; - else - retval = __slowexp (x); + /* Maximum relative error is 7.8e-22 (70.1 bits). + Maximum ULP error is 0.500007. */ + retval = res * binexp.x * t256.x; if (isinf (retval)) goto ret_huge; else |