Performance of measuring text width in AppKit

Is there a way in AppKit to measure the width of a large number of NSString objects(say a million) really fast? I have tried 3 different ways to do this:

[NSString sizeWithAttributes:]

[NSAttributedString size]

NSLayoutManager (get text width instead of height)

Here are some performance metrics

Count\Mechanism    sizeWithAttributes    NSAttributedString    NSLayoutManager

1000               0.057                 0.031                 0.007

10000              0.329                 0.325                 0.064

100000             3.06                  3.14                  0.689

1000000            29.5                  31.3                  7.06

NSLayoutManager is clearly the way to go, but the problem being

High memory footprint(more than 1GB according to profiler) because of the creation of heavyweight NSTextStorage objects.

High creation time. All of the time taken is during creation of the above strings, which is a dealbreaker in itself.(subsequently measuring NSTextStorage objects which have glyphs created and laid out only takes about 0.0002 seconds).

7 seconds is still too slow for what I am trying to do. Is there a faster way? To measure a million strings in about a second?

In case you want to play around, Here is the github project.

Here are some ideas I haven't tried.

Use Core Text directly. The other APIs are built on top of it.
Parallelize. All modern Macs (and even all modern iOS devices) have multiple cores. Divide up the string array into several subarrays. For each subarray, submit a block to a global GCD queue. In the block, create the necessary Core Text or NSLayoutManager objects and measure the strings in the subarray. Both APIs can be used safely this way. (Core Text) (NSLayoutManager)
Regarding “High memory footprint”: Use Local Autorelease Pool Blocks to Reduce Peak Memory Footprint.
Regarding “All of the time taken is during creation of the above strings, which is a dealbreaker in itself”: Are you saying all the time is spent in these lines:
```
double random = (double)arc4random_uniform(1000) / 1000;
NSString *randomNumber = [NSString stringWithFormat:@"%f", random];
```
Formatting a floating-point number is expensive. Is this your real use case? If you just want to format a random rational of the form n/1000 for 0 ≤ n < 1000, there are faster ways. Also, in many fonts, all digits have the same width, so that it's easy to typeset columns of numbers. If you pick such a font, you can avoid measuring the strings in the first place.

UPDATE

Here's the fastest code I've come up with using Core Text. The dispatched version is almost twice as fast as the single-threaded version on my Core i7 MacBook Pro. My fork of your project is here.

static CGFloat maxWidthOfStringsUsingCTFramesetter(
        NSArray *strings, NSRange range) {
    NSString *bigString =
        [[strings subarrayWithRange:range] componentsJoinedByString:@"\n"];
    NSAttributedString *richText =
        [[NSAttributedString alloc]
            initWithString:bigString
            attributes:@{ NSFontAttributeName: (__bridge NSFont *)font }];
    CGPathRef path =
        CGPathCreateWithRect(CGRectMake(0, 0, CGFLOAT_MAX, CGFLOAT_MAX), NULL);
    CGFloat width = 0.0;
    CTFramesetterRef setter =
        CTFramesetterCreateWithAttributedString(
            (__bridge CFAttributedStringRef)richText);
    CTFrameRef frame =
        CTFramesetterCreateFrame(
            setter, CFRangeMake(0, bigString.length), path, NULL);
    NSArray *lines = (__bridge NSArray *)CTFrameGetLines(frame);
    for (id item in lines) {
        CTLineRef line = (__bridge CTLineRef)item;
        width = MAX(width, CTLineGetTypographicBounds(line, NULL, NULL, NULL));
    }
    CFRelease(frame);
    CFRelease(setter);
    CFRelease(path);
    return (CGFloat)width;
}

static void test_CTFramesetter() {
    runTest(__func__, ^{
        return maxWidthOfStringsUsingCTFramesetter(
            testStrings, NSMakeRange(0, testStrings.count));
    });
}

static void test_CTFramesetter_dispatched() {
    runTest(__func__, ^{
        dispatch_queue_t gatherQueue = dispatch_queue_create(
            "test_CTFramesetter_dispatched result-gathering queue", nil);
        dispatch_queue_t runQueue =
            dispatch_get_global_queue(QOS_CLASS_UTILITY, 0);
        dispatch_group_t group = dispatch_group_create();

        __block CGFloat gatheredWidth = 0.0;

        const size_t Parallelism = 16;
        const size_t totalCount = testStrings.count;
        // Force unsigned long to get 64-bit math to avoid overflow for
        // large totalCounts.
        for (unsigned long i = 0; i < Parallelism; ++i) {
            NSUInteger start = (totalCount * i) / Parallelism;
            NSUInteger end = (totalCount * (i + 1)) / Parallelism;
            NSRange range = NSMakeRange(start, end - start);
            dispatch_group_async(group, runQueue, ^{
                double width =
                    maxWidthOfStringsUsingCTFramesetter(testStrings, range);
                dispatch_sync(gatherQueue, ^{
                    gatheredWidth = MAX(gatheredWidth, width);
                });
            });
        }

        dispatch_group_wait(group, DISPATCH_TIME_FOREVER);

        return gatheredWidth;
    });
}

UPDATE

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