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Issue #3366: Add expm1 function to math module. Thanks Eric Smith for
testing on Windows.
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Lines changed: 162 additions & 10 deletions

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‎Doc/library/math.rst‎

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@@ -164,6 +164,20 @@ Power and logarithmic functions
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Return ``e**x``.
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.. function:: expm1(x)
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Return ``e**x - 1``. For small floats *x*, the subtraction in
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``exp(x) - 1`` can result in a significant loss of precision; the
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:func:`expm1` function provides a way to compute this quantity to
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full precision::
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>>> from math import exp, expm1
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>>> exp(1e-5) - 1 # gives result accurate to 11 places
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1.0000050000069649e-05
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>>> expm1(1e-5) # result accurate to full precision
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1.0000050000166668e-05
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.. function:: log(x[, base])
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With one argument, return the natural logarithm of *x* (to base *e*).

‎Lib/test/math_testcases.txt‎

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@@ -249,3 +249,73 @@ gam0132 gamma -4503599627370495.5 -> 0.0
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-- thanks to loss of accuracy in 1-x
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gam0140 gamma -63.349078729022985 -> 4.1777971677761880e-88
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gam0141 gamma -127.45117632943295 -> 1.1831110896236810e-214
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-----------------------------------------------------------
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-- expm1: exp(x) - 1, without precision loss for small x --
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-----------------------------------------------------------
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-- special values
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expm10000 expm1 0.0 -> 0.0
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expm10001 expm1 -0.0 -> -0.0
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expm10002 expm1 inf -> inf
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expm10003 expm1 -inf -> -1.0
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expm10004 expm1 nan -> nan
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-- expm1(x) ~ x for tiny x
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expm10010 expm1 5e-324 -> 5e-324
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expm10011 expm1 1e-320 -> 1e-320
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expm10012 expm1 1e-300 -> 1e-300
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expm10013 expm1 1e-150 -> 1e-150
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expm10014 expm1 1e-20 -> 1e-20
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expm10020 expm1 -5e-324 -> -5e-324
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expm10021 expm1 -1e-320 -> -1e-320
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expm10022 expm1 -1e-300 -> -1e-300
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expm10023 expm1 -1e-150 -> -1e-150
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expm10024 expm1 -1e-20 -> -1e-20
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-- moderate sized values, where direct evaluation runs into trouble
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expm10100 expm1 1e-10 -> 1.0000000000500000e-10
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expm10101 expm1 -9.9999999999999995e-08 -> -9.9999995000000163e-8
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expm10102 expm1 3.0000000000000001e-05 -> 3.0000450004500034e-5
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expm10103 expm1 -0.0070000000000000001 -> -0.0069755570667648951
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expm10104 expm1 -0.071499208740094633 -> -0.069002985744820250
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expm10105 expm1 -0.063296004180116799 -> -0.061334416373633009
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expm10106 expm1 0.02390954035597756 -> 0.024197665143819942
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expm10107 expm1 0.085637352649044901 -> 0.089411184580357767
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expm10108 expm1 0.5966174947411006 -> 0.81596588596501485
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expm10109 expm1 0.30247206212075139 -> 0.35319987035848677
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expm10110 expm1 0.74574727375889516 -> 1.1080161116737459
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expm10111 expm1 0.97767512926555711 -> 1.6582689207372185
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expm10112 expm1 0.8450154566787712 -> 1.3280137976535897
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expm10113 expm1 -0.13979260323125264 -> -0.13046144381396060
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expm10114 expm1 -0.52899322039643271 -> -0.41080213643695923
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expm10115 expm1 -0.74083261478900631 -> -0.52328317124797097
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expm10116 expm1 -0.93847766984546055 -> -0.60877704724085946
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expm10117 expm1 10.0 -> 22025.465794806718
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expm10118 expm1 27.0 -> 532048240600.79865
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expm10119 expm1 123 -> 2.6195173187490626e+53
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expm10120 expm1 -12.0 -> -0.99999385578764666
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expm10121 expm1 -35.100000000000001 -> -0.99999999999999944
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-- extreme negative values
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expm10201 expm1 -37.0 -> -0.99999999999999989
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expm10200 expm1 -38.0 -> -1.0
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expm10210 expm1 -710.0 -> -1.0
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-- the formula expm1(x) = 2 * sinh(x/2) * exp(x/2) doesn't work so
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-- well when exp(x/2) is subnormal or underflows to zero; check we're
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-- not using it!
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expm10211 expm1 -1420.0 -> -1.0
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expm10212 expm1 -1450.0 -> -1.0
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expm10213 expm1 -1500.0 -> -1.0
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expm10214 expm1 -1e50 -> -1.0
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expm10215 expm1 -1.79e308 -> -1.0
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-- extreme positive values
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expm10300 expm1 300 -> 1.9424263952412558e+130
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expm10301 expm1 700 -> 1.0142320547350045e+304
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expm10302 expm1 709.78271289328393 -> 1.7976931346824240e+308
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expm10303 expm1 709.78271289348402 -> inf overflow
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expm10304 expm1 1000 -> inf overflow
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expm10305 expm1 1e50 -> inf overflow
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expm10306 expm1 1.79e308 -> inf overflow

‎Lib/test/test_math.py‎

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@@ -987,17 +987,16 @@ def test_mtestfile(self):
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if math.isnan(expected) and math.isnan(got):
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continue
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if not math.isnan(expected) and not math.isnan(got):
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# we use different closeness criteria for
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# different functions.
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if fn == 'gamma':
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accuracy_failure = ulps_check(expected, got, 20)
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elif fn == 'lgamma':
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if fn == 'lgamma':
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# we use a weaker accuracy test for lgamma;
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# lgamma only achieves an absolute error of
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# a few multiples of the machine accuracy, in
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# general.
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accuracy_failure = acc_check(expected, got,
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rel_err = 5e-15,
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abs_err = 5e-15)
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else:
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raise ValueError("don't know how to check accuracy "
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"for this function")
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accuracy_failure = ulps_check(expected, got, 20)
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if accuracy_failure is None:
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continue
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‎Misc/NEWS‎

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@@ -1683,7 +1683,7 @@ Extension Modules
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- Issue #7078: Set struct.__doc__ from _struct.__doc__.
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- Issue #3366: Add gamma, lgamma functions to math module.
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- Issue #3366: Add expm1, gamma, lgamma functions to math module.
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- Issue #6823: Allow time.strftime() to accept a tuple with a isdst field
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outside of the range of [-1, 1] by normalizing the value to within that

‎Modules/Setup.dist‎

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@@ -169,7 +169,7 @@ GLHACK=-Dclear=__GLclear
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#array arraymodule.c # array objects
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#cmath cmathmodule.c # -lm # complex math library functions
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#math mathmodule.c # -lm # math library functions, e.g. sin()
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#math mathmodule.c _math.c # -lm # math library functions, e.g. sin()
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#_struct _struct.c # binary structure packing/unpacking
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#time timemodule.c # -lm # time operations and variables
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#operator operator.c # operator.add() and similar goodies

‎Modules/_math.c‎

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/* Definitions of some C99 math library functions, for those platforms
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that don't implement these functions already. */
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#include <float.h>
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#include <math.h>
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/* Mathematically, expm1(x) = exp(x) - 1. The expm1 function is designed
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to avoid the significant loss of precision that arises from direct
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evaluation of the expression exp(x) - 1, for x near 0. */
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double
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_Py_expm1(double x)
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{
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/* For abs(x) >= log(2), it's safe to evaluate exp(x) - 1 directly; this
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also works fine for infinities and nans.
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For smaller x, we can use a method due to Kahan that achieves close to
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full accuracy.
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*/
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if (fabs(x) < 0.7) {
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double u;
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u = exp(x);
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if (u == 1.0)
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return x;
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else
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return (u - 1.0) * x / log(u);
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}
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else
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return exp(x) - 1.0;
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}

‎Modules/_math.h‎

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double _Py_expm1(double x);
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#ifdef HAVE_EXPM1
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#define m_expm1 expm1
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#else
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/* if the system doesn't have expm1, use the substitute
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function defined in Modules/_math.c. */
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#define m_expm1 _Py_expm1
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#endif

‎Modules/mathmodule.c‎

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*/
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#include "Python.h"
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#include "_math.h"
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#include "longintrepr.h" /* just for SHIFT */
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#ifdef _OSF_SOURCE
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"cosh(x)\n\nReturn the hyperbolic cosine of x.")
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FUNC1(exp, exp, 1,
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"exp(x)\n\nReturn e raised to the power of x.")
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FUNC1(expm1, m_expm1, 1,
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"expm1(x)\n\nReturn exp(x)-1.\n"
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"This function avoids the loss of precision involved in the direct "
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"evaluation of exp(x)-1 for small x.")
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FUNC1(fabs, fabs, 0,
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"fabs(x)\n\nReturn the absolute value of the float x.")
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FUNC1(floor, floor, 0,
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{"cosh", math_cosh, METH_O, math_cosh_doc},
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{"degrees", math_degrees, METH_O, math_degrees_doc},
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{"exp", math_exp, METH_O, math_exp_doc},
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{"expm1", math_expm1, METH_O, math_expm1_doc},
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{"fabs", math_fabs, METH_O, math_fabs_doc},
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{"factorial", math_factorial, METH_O, math_factorial_doc},
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{"floor", math_floor, METH_O, math_floor_doc},

‎PC/VC6/pythoncore.dsp‎

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‎PC/VS7.1/pythoncore.vcproj‎

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<File
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RelativePath="..\..\Modules\_lsprof.c">
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</File>
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<File
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RelativePath="..\..\Modules\_math.c">
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</File>
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<File
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RelativePath="..\..\Modules\_randommodule.c">
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</File>

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