From: Keith Packard Date: Sat, 31 May 2014 00:24:51 +0000 (-0700) Subject: altos: Switch APRS altitude encoding computation to fixed point X-Git-Tag: 1.3.2.2~31 X-Git-Url: https://git.gag.com/?p=fw%2Faltos;a=commitdiff_plain;h=a7b0a5613c8e59b4c672b21f8d0890fd5cffd4dc altos: Switch APRS altitude encoding computation to fixed point APRS altitude is logarithmically encoded, so this implementation includes a fixed point log-base-2 function along with a bit of other fixed point stuff. This eliminates all floating point from TeleGPS, saving around 4kB of code space. Signed-off-by: Keith Packard --- diff --git a/src/drivers/ao_aprs.c b/src/drivers/ao_aprs.c index 679dd7bc..8a1b6a4d 100644 --- a/src/drivers/ao_aprs.c +++ b/src/drivers/ao_aprs.c @@ -144,7 +144,6 @@ #endif #include -#include // Public methods, constants, and data structures for each class. @@ -552,6 +551,144 @@ static int tncComment(uint8_t *buf) #endif } +/* + * APRS use a log encoding of altitude with a base of 1.002, such that + * + * feet = 1.002 ** encoded_altitude + * + * meters = (1.002 ** encoded_altitude) * 0.3048 + * + * log2(meters) = log2(1.002 ** encoded_altitude) + log2(0.3048) + * + * log2(meters) = encoded_altitude * log2(1.002) + log2(0.3048) + * + * encoded_altitude = (log2(meters) - log2(0.3048)) / log2(1.002) + * + * encoded_altitude = (log2(meters) + log2(1/0.3048)) * (1/log2(1.002)) + * + * We need 9 bits of mantissa to hold 1/log2(1.002) (~ 347), which leaves us + * 23 bits of fraction. That turns out to be *just* enough to avoid any + * errors in the result (cool, huh?). + */ + +#define fixed23_int(x) ((uint32_t) ((x) << 23)) +#define fixed23_one fixed23_int(1) +#define fixed23_two fixed23_int(2) +#define fixed23_half (fixed23_one >> 1) +#define fixed23_floor(x) ((x) >> 23) +#define fixed23_real(x) ((uint32_t) ((x) * fixed23_one + 0.5)) + +static inline uint64_t +fixed23_mul(uint32_t x, uint32_t y) +{ + return ((uint64_t) x * y + fixed23_half) >> 23; +} + +/* + * Use 30 fraction bits for the altitude. We need two bits at the + * top as we need to handle x, where 0 <= x < 4. We don't + * need 30 bits, but it's actually easier this way as we normalize + * the incoming value to 1 <= x < 2, and having the integer portion + * way up high means we don't have to deal with shifting in both + * directions to cover from 0 to 2**30-1. + */ + +#define fixed30_int(x) ((uint32_t) ((x) << 30)) +#define fixed30_one fixed30_int(1) +#define fixed30_half (fixed30_one >> 1) +#define fixed30_two fixed30_int(2) + +static inline uint32_t +fixed30_mul(uint32_t x, uint32_t y) +{ + return ((uint64_t) x * y + fixed30_half) >> 30; +} + +/* + * Fixed point log2. Takes integer argument, returns + * fixed point result with 23 bits of fraction + */ + +static uint32_t +ao_fixed_log2(uint32_t x) +{ + uint32_t result; + uint32_t frac = fixed23_one; + + /* Bounds check for sanity */ + if (x <= 0) + return 0; + + if (x >= fixed30_one) + return 0xffffffff; + + /* + * Normalize and compute integer log portion + * + * This makes 1 <= x < 2, and computes result to be + * the integer portion of the log2 of x + */ + + for (result = fixed23_int(30); x < fixed30_one; result -= fixed23_one, x <<= 1) + ; + + /* + * Given x, find y and n such that: + * + * x = y * 2**n 1 <= y < 2 + * + * That means: + * + * lb(x) = n + lb(y) + * + * Now, repeatedly square y to find find z and m such that: + * + * z = y ** (2**m) 2 <= z < 4 + * + * This is possible because 1 <= y < 2 + * + * lb(y) = lb(z) / 2**m + * + * (1 + lb(z/2)) + * = ------------- + * 2**m + * + * = 2**-m + 2**-m * lb(z/2) + * + * Note that if 2 <= z < 4, then 1 <= (z/2) < 2, so we can + * iterate to find lb(z/2) + * + * In this implementation, we don't care about the 'm' value, + * instead we only care about 2**-m, which we store in 'frac' + */ + + while (frac != 0 && x != fixed30_one) { + /* Repeatedly square x until 2 <= x < 4 */ + while (x < fixed30_two) { + x = fixed30_mul(x, x); + + /* Divide the fractional result bit by 2 */ + frac >>= 1; + } + + /* Add in this result bit */ + result |= frac; + + /* Make 1 <= x < 2 again and iterate */ + x >>= 1; + } + return result; +} + +#define APRS_LOG_CONVERT fixed23_real(1.714065192056127) +#define APRS_LOG_BASE fixed23_real(346.920048461100941) + +static int +ao_aprs_encode_altitude(int meters) +{ + return fixed23_floor(fixed23_mul(ao_fixed_log2(meters) + APRS_LOG_CONVERT, APRS_LOG_BASE) + fixed23_half); +} + /** * Generate the plain text position packet. */ @@ -580,10 +717,7 @@ static int tncPositionPacket(void) lat = ((uint64_t) 380926 * (900000000 - latitude)) / 10000000; lon = ((uint64_t) 190463 * (1800000000 + longitude)) / 10000000; -#define ALTITUDE_LOG_BASE 0.001998002662673f /* log(1.002) */ - - alt = (altitude * (int32_t) 10000 + (3048/2)) / (int32_t) 3048; - alt = logf((float) altitude) * (1/ALTITUDE_LOG_BASE); + alt = ao_aprs_encode_altitude(altitude); tncCompressInt(buf, lat, 4); buf += 4;