• d-bugmail puremagic.com Jan 28 2010
• d-bugmail puremagic.com Jan 28 2010
• d-bugmail puremagic.com Jan 28 2010
• d-bugmail puremagic.com Jan 28 2010
• d-bugmail puremagic.com Jan 28 2010
• d-bugmail puremagic.com Jan 28 2010
• d-bugmail puremagic.com Jan 31 2010

d-bugmail puremagic.com writes:

http://d.puremagic.com/issues/show_bug.cgi?id=3749

           Summary: cannot evaluate ylog2x at compile time
           Product: D
           Version: 2.041
          Platform: Other
        OS/Version: Linux
            Status: NEW
          Severity: normal
          Priority: P2
         Component: DMD
        AssignedTo: nobody puremagic.com
        ReportedBy: baryluk smp.if.uj.edu.pl


--- Comment #0 from Witold Baryluk <baryluk smp.if.uj.edu.pl> 2010-01-28
12:19:56 PST ---
import std.stdio;
import std.math;

double iter(double x) {
    static immutable a = log(4.0);
    return x*a;
}

void main() {
    writefln("%s", iter(5.0));
}


/usr/include/d/dmd2-posix/phobos/import/std/math.d(1415): Error: cannot
evaluate yl2x(x,0xb.17217f7d1cf79acp-4L) at compile time
aaaa.d(6): Error: cannot evaluate log(4L) at compile time
aaaa.d(6): Error: cannot evaluate log(4L) at compile time


This also means that currently DMD compiler will not perform constant folding
on a.

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--- Comment #1 from Witold Baryluk <baryluk smp.if.uj.edu.pl> 2010-01-28
12:29:09 PST ---
Same problem is with exp function.


/usr/include/d/dmd2-posix/phobos/import/std/math.d(895): Error: cannot evaluate
exp2(0xb.8aa3b295c17f0bcp-3L * x) at compile time
/usr/include/d/dmd2-posix/phobos/import/std/math.d(903): Error: cannot evaluate
exp(cast(real)x) at compile time
aaaa.d(6): Error: cannot evaluate exp(4F) at compile time
aaaa.d(6): Error: cannot evaluate exp(4F) at compile time

I know it can solved by using CTFE functions, but for example sqrt or sin, cos
are working correctly. I really don't want to put by hand obscure numerical
constants, and then don't know from where they came :)


Releated to bug1475.

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Witold Baryluk <baryluk smp.if.uj.edu.pl> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
           Severity|normal                      |minor


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David Simcha <dsimcha yahoo.com> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
                 CC|                            |dsimcha yahoo.com


--- Comment #2 from David Simcha <dsimcha yahoo.com> 2010-01-28 12:46:12 PST ---
A patch has just been submitted fairly recently for if(__ctfe).  Once that's
released, people (myself included) will start submitting patches to make
compile-time versions of most of std.math.  Most of the runtime implementations
use assembly language somewhere for efficiency, or call the C standard lib
implementations.  We'll have to write more naive compile-time versions of these
functions.

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Don <clugdbug yahoo.com.au> changed:

           What    |Removed                     |Added
----------------------------------------------------------------------------
                 CC|                            |clugdbug yahoo.com.au


--- Comment #3 from Don <clugdbug yahoo.com.au> 2010-01-28 13:01:46 PST ---
(In reply to comment #2)
 A patch has just been submitted fairly recently for if(__ctfe).  Once that's
 released, people (myself included) will start submitting patches to make
 compile-time versions of most of std.math.  Most of the runtime implementations
 use assembly language somewhere for efficiency, or call the C standard lib
 implementations.  We'll have to write more naive compile-time versions of these
 functions.


if(__ctfe) is in the next release. yl2x() probably should have built-in
support, though. Since it's an intrinsic, if (__ctfe) won't work for it.

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--- Comment #4 from Witold Baryluk <baryluk smp.if.uj.edu.pl> 2010-01-28
15:55:35 PST ---
So I release this as public domain. I written this code as workaround to lack
of log and exp. They looks to be accurate to 16 digital digits on whole real
line.
Results can be slightly different than values returned by std.math.{log,exp}
unfortunetly. Anybody want to review this code or know better methods?

/** Calculate natural logarithm of x.
 *
 *
 * Performs reduction of large values to (0..3) inverval, using log(x 3^n) =
log(x) + n*log(3)
 *
 * Then uses truncated Taylor series in variable y=(x-1)/(x+1) for x > 0.
 *
 * For values x < 1, calculate -log(1/x)
 *
 */
double ctfe_log(double x_) {
    if (x_ == 0.0) {
        return -double.infinity;
    }
    if (x_ < 0.0) {
        return double.nan;
    }
    if (x_ == double.infinity) {
        return double.infinity;
    }

    if (x_ == 1.0) {
        return 0.0;
    }

    if (!(x_ == x_)) { // nan
        return double.nan;
    }

    real x = x_;

    if (x > 1.0) {
        uint m = 0;
        // reduce to (1 .. 3) interval
        while (x > 3.0) {
            x = x / 3.0;
            m = m + 1;
        }
        real y = (x-1.0)/(x+1.0);

        real y2 = y*y;

        /* Evaluate Horner's scheme on polynomial
         * log(x) = log((1+y) / (1-y)) = 2 y (1 + y^2/3 + y^4/5  + y^6/7 + ...
y^70/71)
         */
        real temp = 0.0;

        for (int i = 71; i >= 3; i -= 2) {
            temp += 1.0/cast(real)i;
            temp *= y2;
        }
        temp += 1.0;

        y = 2.0*y*temp;
        if (m) {
            return y + m*ctfe_log(3.0);
        } else {
            return y;
        }
    } else {
        return -ctfe_log(1.0/x);
    }
}

/** Compute exponential function of x.
 *
 * Uses truncated Taylor series expeansion of exp function.
 *
 * Performs reduction for |x| > 2, of the form exp(x 2^m) = exp(x)^(2^m)
 */
double ctfe_exp(double x_) {
    if (x_ == 0.0) {
        return 1.0;
    }

    if (x_ >= 710.0) { // includes +infinity
        return double.infinity;
    }
    if (x_ <= -746.0) { // includes -infinity
        return 0.0;
    }
    if (!(x_ == x_)) { // nan
        return double.nan;
    }

    real x = x_;

    int m = 0;

    // reduce to (-2 .. 2) interval
    if (x > 0.0) {
        while (x > 2.0) {
            x = x / 2.0;
            m = m + 1;
        }
    } else {
        while (x < -2.0) {
            x = x / 2.0;
            m = m - 1;
        }
    }


    real temp = 1.0;
    real term = 1.0;

    for (int i = 1; i <= 25; i++) {
        term *= x/cast(real)i;
        temp += term;
    }

    if (m) {
        real exp2 = ctfe_exp(2.0);
        if (m > 0) {
            for (int i = 0; i < m; i++) {
                temp = temp*temp;
            }
        } else {
            for (int i = 0; i < -m; i++) {
                temp = temp*temp;
            }
        }
        return temp;
    } else {
        return temp;
    }
}

int tests(double[] xs, int min, int max) {
    assert(min <= max);
    int r = 0;
    double c = 1.0;
    if (min < 0) {
        for (int i = 0; i < -min; i++) {
            c = c / 2.0;
        }
    }
    if (min > 0) {
        for (int i = 0; i < -min; i++) {
            c = c * 2.0;
        }
    }
    for (int i = min; i <= max; i++) {
        foreach (x0; xs) {
            auto x = c * x0;
            if ( (ctfe_exp(ctfe_log(x)) - x) / x < 1.0e-16 ) {
                // ok
            } else {
                r = r + 1;
            }
        }
    }
    return r;
}

enum c = tests(
    [0.1, 0.1001, 0.11, 0.2, 0.24, 0.3, 0.341, 0.387123, 0.4,
    0.5, 0.55, 0.6, 0.7, 0.732, 0.8, 0.88, 0.9, 0.98, 0.9991, 0.999992],
    -300, 300);
static assert(c == 0);
static assert(ctfe_exp(0.0) == 1.0);
static assert(ctfe_exp(-1000.0) == 0.0);
static assert(ctfe_exp(1000.0) == double.infinity);
static assert(ctfe_log(0.0) == -double.infinity);

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--- Comment #5 from Witold Baryluk <baryluk smp.if.uj.edu.pl> 2010-01-31
08:03:28 PST ---
Small but important error in unittest (c was not multiplied correctly. Also
-300..300 range was somehow too big, compilations was very long.

int tests(double[] xs, int min, int max) {
    assert(min <= max);
    int r = 0;
    double c = 1.0;
    if (min < 0) {
        for (int i = 0; i < -min; i++) {
            c = c / 2.0;
        }
    }
    if (min > 0) {
        for (int i = 0; i < min; i++) {
            c = c * 2.0;
        }
    }
    for (int i = min; i <= max; i++) {
        foreach (x0; xs) {
            auto x = c * x0;
            if ( (ctfe_exp(ctfe_log(x)) - x) / x < 1.0e-16 ) {
                ;
            } else {
                r = r + 1;
            }
        }
        c = c * 2.0;
    }
    return r;
}

unittest {
    enum c = tests(
        [0.1, 0.1001, 0.11, 0.2, 0.24, 0.3, 0.341, 0.387123, 0.4,
        0.5, 0.55, 0.6, 0.7, 0.732, 0.8, 0.88, 0.9, 0.98, 0.9991, 0.999992],
        -30, 30);
    static assert(c == 0);
}
static assert(ctfe_exp(0.0) == 1.0);
static assert(ctfe_exp(-1000.0) == 0.0);
static assert(ctfe_exp(1000.0) == double.infinity);
static assert(ctfe_log(0.0) == -double.infinity);

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