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 <span id="projectnumber">3.1</span>
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<p>A variety of functions for working with numbers.
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typedef <a class="el" href="class_c_every_n_time_periods.html">CEveryNTimePeriods</a>< uint16_t, <a class="el" href="group__lib8tion.html#ga223820399921e32ddf018a90223ff336">minutes16</a> > </td><td class="memItemRight" valign="bottom"><b>CEveryNMinutes</b></td></tr>
<tr class="separator:ga567d6f1ff78e14a266d5ec93fc53429e"><td class="memSeparator" colspan="2"> </td></tr>
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typedef <a class="el" href="class_c_every_n_time_periods.html">CEveryNTimePeriods</a>< uint8_t, <a class="el" href="group__lib8tion.html#ga837f5a688998f3340994613944e47d41">hours8</a> > </td><td class="memItemRight" valign="bottom"><b>CEveryNHours</b></td></tr>
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</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:gab947c1150e3b9056cb91685a14270173"><td class="memItemLeft" align="right" valign="top">LIB8STATIC float </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gab947c1150e3b9056cb91685a14270173">sfract15ToFloat</a> (sfract15 y)</td></tr>
<tr class="memdesc:gab947c1150e3b9056cb91685a14270173"><td class="mdescLeft"> </td><td class="mdescRight">sfract15ToFloat: conversion from sfract15 fixed point to IEEE754 32-bit float. <a href="#gab947c1150e3b9056cb91685a14270173">More...</a><br /></td></tr>
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<tr class="memitem:gaa2facbc0ec935e34c629aef43d6262c0"><td class="memItemLeft" align="right" valign="top">LIB8STATIC sfract15 </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gaa2facbc0ec935e34c629aef43d6262c0">floatToSfract15</a> (float f)</td></tr>
<tr class="memdesc:gaa2facbc0ec935e34c629aef43d6262c0"><td class="mdescLeft"> </td><td class="mdescRight">conversion from IEEE754 float in the range (-1,1) to 16-bit fixed point. <a href="#gaa2facbc0ec935e34c629aef43d6262c0">More...</a><br /></td></tr>
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void * </td><td class="memItemRight" valign="bottom"><b>memmove8</b> (void *dst, const void *src, uint16_t num)</td></tr>
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void * </td><td class="memItemRight" valign="bottom"><b>memcpy8</b> (void *dst, const void *src, uint16_t num) <a class="el" href="group___bitswap.html#ga01396a2e40133293c3badab349ac99f0">__attribute__</a>((noinline))</td></tr>
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void * </td><td class="memItemRight" valign="bottom"><b>memset8</b> (void *ptr, uint8_t value, uint16_t num) <a class="el" href="group___bitswap.html#ga01396a2e40133293c3badab349ac99f0">__attribute__</a>((noinline))</td></tr>
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LIB8STATIC uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga62ed4425400bc4140902347dc54ffb72">lerp8by8</a> (uint8_t a, uint8_t b, fract8 frac)</td></tr>
<tr class="memdesc:ga62ed4425400bc4140902347dc54ffb72"><td class="mdescLeft"> </td><td class="mdescRight">linear interpolation between two unsigned 8-bit values, with 8-bit fraction <br /></td></tr>
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<tr class="memitem:ga7c02960d0f26e90054c7312e5f9a55b3"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ga7c02960d0f26e90054c7312e5f9a55b3"></a>
LIB8STATIC uint16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga7c02960d0f26e90054c7312e5f9a55b3">lerp16by16</a> (uint16_t a, uint16_t b, fract16 frac)</td></tr>
<tr class="memdesc:ga7c02960d0f26e90054c7312e5f9a55b3"><td class="mdescLeft"> </td><td class="mdescRight">linear interpolation between two unsigned 16-bit values, with 16-bit fraction <br /></td></tr>
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<tr class="memitem:ga8c8f06da86c5d7cf13f55c3a5bfdf251"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ga8c8f06da86c5d7cf13f55c3a5bfdf251"></a>
LIB8STATIC uint16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga8c8f06da86c5d7cf13f55c3a5bfdf251">lerp16by8</a> (uint16_t a, uint16_t b, fract8 frac)</td></tr>
<tr class="memdesc:ga8c8f06da86c5d7cf13f55c3a5bfdf251"><td class="mdescLeft"> </td><td class="mdescRight">linear interpolation between two unsigned 16-bit values, with 8-bit fraction <br /></td></tr>
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<tr class="memitem:gaacea0eaea98a065dfa08bb1c147c52a1"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="gaacea0eaea98a065dfa08bb1c147c52a1"></a>
LIB8STATIC int16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gaacea0eaea98a065dfa08bb1c147c52a1">lerp15by8</a> (int16_t a, int16_t b, fract8 frac)</td></tr>
<tr class="memdesc:gaacea0eaea98a065dfa08bb1c147c52a1"><td class="mdescLeft"> </td><td class="mdescRight">linear interpolation between two signed 15-bit values, with 8-bit fraction <br /></td></tr>
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<tr class="memitem:gad4b09aba4e188e14d3e71d1c9f77f1a5"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="gad4b09aba4e188e14d3e71d1c9f77f1a5"></a>
LIB8STATIC int16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gad4b09aba4e188e14d3e71d1c9f77f1a5">lerp15by16</a> (int16_t a, int16_t b, fract16 frac)</td></tr>
<tr class="memdesc:gad4b09aba4e188e14d3e71d1c9f77f1a5"><td class="mdescLeft"> </td><td class="mdescRight">linear interpolation between two signed 15-bit values, with 8-bit fraction <br /></td></tr>
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<tr class="memitem:gaf65357c7aeca9778e5a2f80a6bac2b5d"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gaf65357c7aeca9778e5a2f80a6bac2b5d">map8</a> (uint8_t in, uint8_t rangeStart, uint8_t rangeEnd)</td></tr>
<tr class="memdesc:gaf65357c7aeca9778e5a2f80a6bac2b5d"><td class="mdescLeft"> </td><td class="mdescRight">map8: map from one full-range 8-bit value into a narrower range of 8-bit values, possibly a range of hues. <a href="#gaf65357c7aeca9778e5a2f80a6bac2b5d">More...</a><br /></td></tr>
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LIB8STATIC uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga381449070b2d6bfba356f87881ab28c0">ease8InOutQuad</a> (uint8_t i)</td></tr>
<tr class="memdesc:ga381449070b2d6bfba356f87881ab28c0"><td class="mdescLeft"> </td><td class="mdescRight">ease8InOutQuad: 8-bit quadratic ease-in / ease-out function Takes around 13 cycles on AVR <br /></td></tr>
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<tr class="memitem:ga3fa6d71702477e71d7c0dd864eb1d568"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ga3fa6d71702477e71d7c0dd864eb1d568"></a>
LIB8STATIC fract8 </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga3fa6d71702477e71d7c0dd864eb1d568">ease8InOutCubic</a> (fract8 i)</td></tr>
<tr class="memdesc:ga3fa6d71702477e71d7c0dd864eb1d568"><td class="mdescLeft"> </td><td class="mdescRight">ease8InOutCubic: 8-bit cubic ease-in / ease-out function Takes around 18 cycles on AVR <br /></td></tr>
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<tr class="memitem:gaa041cdbb17f073dbd352fcae6962dc23"><td class="memItemLeft" align="right" valign="top">LIB8STATIC fract8 </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gaa041cdbb17f073dbd352fcae6962dc23">ease8InOutApprox</a> (fract8 i)</td></tr>
<tr class="memdesc:gaa041cdbb17f073dbd352fcae6962dc23"><td class="mdescLeft"> </td><td class="mdescRight">ease8InOutApprox: fast, rough 8-bit ease-in/ease-out function shaped approximately like 'ease8InOutCubic', it's never off by more than a couple of percent from the actual cubic S-curve, and it executes more than twice as fast. <a href="#gaa041cdbb17f073dbd352fcae6962dc23">More...</a><br /></td></tr>
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<tr class="memitem:gae9e011ff745ade1164ae77b0ef62bfac"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gae9e011ff745ade1164ae77b0ef62bfac">triwave8</a> (uint8_t in)</td></tr>
<tr class="memdesc:gae9e011ff745ade1164ae77b0ef62bfac"><td class="mdescLeft"> </td><td class="mdescRight">triwave8: triangle (sawtooth) wave generator. <a href="#gae9e011ff745ade1164ae77b0ef62bfac">More...</a><br /></td></tr>
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<tr class="memitem:ga209d6cbdb109cc3139e7bb1e46c6228f"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga209d6cbdb109cc3139e7bb1e46c6228f">quadwave8</a> (uint8_t in)</td></tr>
<tr class="memdesc:ga209d6cbdb109cc3139e7bb1e46c6228f"><td class="mdescLeft"> </td><td class="mdescRight">quadwave8: quadratic waveform generator. <a href="#ga209d6cbdb109cc3139e7bb1e46c6228f">More...</a><br /></td></tr>
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<tr class="memitem:ga06b04a0cf955ec107d49b76e0cb35225"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga06b04a0cf955ec107d49b76e0cb35225">cubicwave8</a> (uint8_t in)</td></tr>
<tr class="memdesc:ga06b04a0cf955ec107d49b76e0cb35225"><td class="mdescLeft"> </td><td class="mdescRight">cubicwave8: cubic waveform generator. <a href="#ga06b04a0cf955ec107d49b76e0cb35225">More...</a><br /></td></tr>
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<tr class="memitem:ga17ae8fcfd9c485bb1120d908f836637a"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga17ae8fcfd9c485bb1120d908f836637a">squarewave8</a> (uint8_t in, uint8_t pulsewidth=128)</td></tr>
<tr class="memdesc:ga17ae8fcfd9c485bb1120d908f836637a"><td class="mdescLeft"> </td><td class="mdescRight">squarewave8: square wave generator. <a href="#ga17ae8fcfd9c485bb1120d908f836637a">More...</a><br /></td></tr>
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uint32_t </td><td class="memItemRight" valign="bottom"><b>millis</b> ()</td></tr>
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uint32_t </td><td class="memItemRight" valign="bottom"><b>get_millisecond_timer</b> ()</td></tr>
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<tr class="memitem:ga1b48fc520db5f40910caf79974992395"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga1b48fc520db5f40910caf79974992395">beat88</a> (accum88 beats_per_minute_88, uint32_t timebase=0)</td></tr>
<tr class="memdesc:ga1b48fc520db5f40910caf79974992395"><td class="mdescLeft"> </td><td class="mdescRight">with BPM specified in Q8.8 fixed-point format; e.g. <a href="#ga1b48fc520db5f40910caf79974992395">More...</a><br /></td></tr>
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<tr class="memitem:gade6acbf6fd3c9d346148bccfcafb2fe2"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="gade6acbf6fd3c9d346148bccfcafb2fe2"></a>
LIB8STATIC uint16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gade6acbf6fd3c9d346148bccfcafb2fe2">beat16</a> (accum88 beats_per_minute, uint32_t timebase=0)</td></tr>
<tr class="memdesc:gade6acbf6fd3c9d346148bccfcafb2fe2"><td class="mdescLeft"> </td><td class="mdescRight">beat16 generates a 16-bit 'sawtooth' wave at a given BPM <br /></td></tr>
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<tr class="memitem:ga12014943214a72eec31433d9682d4ebe"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ga12014943214a72eec31433d9682d4ebe"></a>
LIB8STATIC uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga12014943214a72eec31433d9682d4ebe">beat8</a> (accum88 beats_per_minute, uint32_t timebase=0)</td></tr>
<tr class="memdesc:ga12014943214a72eec31433d9682d4ebe"><td class="mdescLeft"> </td><td class="mdescRight">beat8 generates an 8-bit 'sawtooth' wave at a given BPM <br /></td></tr>
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<tr class="memitem:gaf917825ff26c8e1174c5b674a2f3c631"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gaf917825ff26c8e1174c5b674a2f3c631">beatsin88</a> (accum88 beats_per_minute_88, uint16_t lowest=0, uint16_t highest=65535, uint32_t timebase=0, uint16_t phase_offset=0)</td></tr>
<tr class="memdesc:gaf917825ff26c8e1174c5b674a2f3c631"><td class="mdescLeft"> </td><td class="mdescRight">beatsin88 generates a 16-bit sine wave at a given BPM, that oscillates within a given range. <a href="#gaf917825ff26c8e1174c5b674a2f3c631">More...</a><br /></td></tr>
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<tr class="memitem:gaa46e5de1c4c27833359e7a97a18c839b"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gaa46e5de1c4c27833359e7a97a18c839b">beatsin16</a> (accum88 beats_per_minute, uint16_t lowest=0, uint16_t highest=65535, uint32_t timebase=0, uint16_t phase_offset=0)</td></tr>
<tr class="memdesc:gaa46e5de1c4c27833359e7a97a18c839b"><td class="mdescLeft"> </td><td class="mdescRight">beatsin16 generates a 16-bit sine wave at a given BPM, that oscillates within a given range. <a href="#gaa46e5de1c4c27833359e7a97a18c839b">More...</a><br /></td></tr>
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<tr class="memitem:gaecd7cbfc2640407cabf75afcc7d9ddf4"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gaecd7cbfc2640407cabf75afcc7d9ddf4">beatsin8</a> (accum88 beats_per_minute, uint8_t lowest=0, uint8_t highest=255, uint32_t timebase=0, uint8_t phase_offset=0)</td></tr>
<tr class="memdesc:gaecd7cbfc2640407cabf75afcc7d9ddf4"><td class="mdescLeft"> </td><td class="mdescRight">beatsin8 generates an 8-bit sine wave at a given BPM, that oscillates within a given range. <a href="#gaecd7cbfc2640407cabf75afcc7d9ddf4">More...</a><br /></td></tr>
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<tr class="memitem:gaa2abcee2fe76fafd7f3a2aeab03e3b69"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#gaa2abcee2fe76fafd7f3a2aeab03e3b69">seconds16</a> ()</td></tr>
<tr class="memdesc:gaa2abcee2fe76fafd7f3a2aeab03e3b69"><td class="mdescLeft"> </td><td class="mdescRight">Return the current seconds since boot in a 16-bit value. <a href="#gaa2abcee2fe76fafd7f3a2aeab03e3b69">More...</a><br /></td></tr>
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<tr class="memitem:ga223820399921e32ddf018a90223ff336"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga223820399921e32ddf018a90223ff336">minutes16</a> ()</td></tr>
<tr class="memdesc:ga223820399921e32ddf018a90223ff336"><td class="mdescLeft"> </td><td class="mdescRight">Return the current minutes since boot in a 16-bit value. <a href="#ga223820399921e32ddf018a90223ff336">More...</a><br /></td></tr>
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<tr class="memitem:ga837f5a688998f3340994613944e47d41"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint8_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga837f5a688998f3340994613944e47d41">hours8</a> ()</td></tr>
<tr class="memdesc:ga837f5a688998f3340994613944e47d41"><td class="mdescLeft"> </td><td class="mdescRight">Return the current hours since boot in an 8-bit value. <a href="#ga837f5a688998f3340994613944e47d41">More...</a><br /></td></tr>
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<tr class="memitem:ga5f95d6e55b4986bd88f662528cef717e"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga5f95d6e55b4986bd88f662528cef717e">div1024_32_16</a> (uint32_t in32)</td></tr>
<tr class="memdesc:ga5f95d6e55b4986bd88f662528cef717e"><td class="mdescLeft"> </td><td class="mdescRight">Helper routine to divide a 32-bit value by 1024, returning only the low 16 bits. <a href="#ga5f95d6e55b4986bd88f662528cef717e">More...</a><br /></td></tr>
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<tr class="memitem:ga52659d1994f2f21eb05080c97417e93b"><td class="memItemLeft" align="right" valign="top">LIB8STATIC uint16_t </td><td class="memItemRight" valign="bottom"><a class="el" href="group__lib8tion.html#ga52659d1994f2f21eb05080c97417e93b">bseconds16</a> ()</td></tr>
<tr class="memdesc:ga52659d1994f2f21eb05080c97417e93b"><td class="mdescLeft"> </td><td class="mdescRight">bseconds16 returns the current time-since-boot in "binary seconds", which are actually 1024/1000 of a second long. <a href="#ga52659d1994f2f21eb05080c97417e93b">More...</a><br /></td></tr>
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 </td><td class="memItemRight" valign="bottom"><b>INSTANTIATE_EVERY_N_TIME_PERIODS</b> (<a class="el" href="class_c_every_n_time_periods.html">CEveryNMillis</a>, uint32_t, GET_MILLIS)</td></tr>
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<tr class="memitem:ga701c373893bd35aedd1a01a2cccdd020"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ga701c373893bd35aedd1a01a2cccdd020"></a>
 </td><td class="memItemRight" valign="bottom"><b>INSTANTIATE_EVERY_N_TIME_PERIODS</b> (<a class="el" href="class_c_every_n_time_periods.html">CEveryNSeconds</a>, uint16_t, <a class="el" href="group__lib8tion.html#gaa2abcee2fe76fafd7f3a2aeab03e3b69">seconds16</a>)</td></tr>
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 </td><td class="memItemRight" valign="bottom"><b>INSTANTIATE_EVERY_N_TIME_PERIODS</b> (<a class="el" href="class_c_every_n_time_periods.html">CEveryNBSeconds</a>, uint16_t, <a class="el" href="group__lib8tion.html#ga52659d1994f2f21eb05080c97417e93b">bseconds16</a>)</td></tr>
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 </td><td class="memItemRight" valign="bottom"><b>INSTANTIATE_EVERY_N_TIME_PERIODS</b> (<a class="el" href="class_c_every_n_time_periods.html">CEveryNMinutes</a>, uint16_t, <a class="el" href="group__lib8tion.html#ga223820399921e32ddf018a90223ff336">minutes16</a>)</td></tr>
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<tr class="memitem:ga4274871603c32ccf29a2e90ad48dba82"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ga4274871603c32ccf29a2e90ad48dba82"></a>
 </td><td class="memItemRight" valign="bottom"><b>INSTANTIATE_EVERY_N_TIME_PERIODS</b> (<a class="el" href="class_c_every_n_time_periods.html">CEveryNHours</a>, uint8_t, <a class="el" href="group__lib8tion.html#ga837f5a688998f3340994613944e47d41">hours8</a>)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<p>A variety of functions for working with numbers. </p>
<h2 class="groupheader">Function Documentation</h2>
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<td class="memname">LIB8STATIC uint16_t beat88 </td>
<td>(</td>
<td class="paramtype">accum88 </td>
<td class="paramname"><em>beats_per_minute_88</em>, </td>
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<td class="paramtype">uint32_t </td>
<td class="paramname"><em>timebase</em> = <code>0</code> </td>
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<p>with BPM specified in Q8.8 fixed-point format; e.g. </p>
<p>for this function, 120 BPM MUST BE specified as 120*256 = 30720. If you just want to specify "120", use beat16 or beat8. </p>
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<td class="memname">LIB8STATIC uint16_t beatsin16 </td>
<td>(</td>
<td class="paramtype">accum88 </td>
<td class="paramname"><em>beats_per_minute</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">uint16_t </td>
<td class="paramname"><em>lowest</em> = <code>0</code>, </td>
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<td class="paramtype">uint16_t </td>
<td class="paramname"><em>highest</em> = <code>65535</code>, </td>
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<td class="paramtype">uint32_t </td>
<td class="paramname"><em>timebase</em> = <code>0</code>, </td>
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<td class="paramtype">uint16_t </td>
<td class="paramname"><em>phase_offset</em> = <code>0</code> </td>
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<p>beatsin16 generates a 16-bit sine wave at a given BPM, that oscillates within a given range. </p>
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<td class="memname">LIB8STATIC uint8_t beatsin8 </td>
<td>(</td>
<td class="paramtype">accum88 </td>
<td class="paramname"><em>beats_per_minute</em>, </td>
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<td class="paramkey"></td>
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<td class="paramtype">uint8_t </td>
<td class="paramname"><em>lowest</em> = <code>0</code>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>highest</em> = <code>255</code>, </td>
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<td class="paramtype">uint32_t </td>
<td class="paramname"><em>timebase</em> = <code>0</code>, </td>
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<td class="paramtype">uint8_t </td>
<td class="paramname"><em>phase_offset</em> = <code>0</code> </td>
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<p>beatsin8 generates an 8-bit sine wave at a given BPM, that oscillates within a given range. </p>
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<td class="memname">LIB8STATIC uint16_t beatsin88 </td>
<td>(</td>
<td class="paramtype">accum88 </td>
<td class="paramname"><em>beats_per_minute_88</em>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint16_t </td>
<td class="paramname"><em>lowest</em> = <code>0</code>, </td>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype">uint16_t </td>
<td class="paramname"><em>highest</em> = <code>65535</code>, </td>
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<td></td>
<td class="paramtype">uint32_t </td>
<td class="paramname"><em>timebase</em> = <code>0</code>, </td>
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<td class="paramtype">uint16_t </td>
<td class="paramname"><em>phase_offset</em> = <code>0</code> </td>
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<p>beatsin88 generates a 16-bit sine wave at a given BPM, that oscillates within a given range. </p>
<p>For this function, BPM MUST BE SPECIFIED as a Q8.8 fixed-point value; e.g. 120BPM must be specified as 120*256 = 30720. If you just want to specify "120", use beatsin16 or beatsin8. </p>
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<td class="memname">LIB8STATIC uint16_t bseconds16 </td>
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<p>bseconds16 returns the current time-since-boot in "binary seconds", which are actually 1024/1000 of a second long. </p>
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<td>(</td>
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<td class="paramname"><em>in</em></td><td>)</td>
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<p>cubicwave8: cubic waveform generator. </p>
<p>Spends visibly more time at the limits than 'sine' does. </p>
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<td class="memname">LIB8STATIC uint16_t div1024_32_16 </td>
<td>(</td>
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<td class="paramname"><em>in32</em></td><td>)</td>
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<p>Helper routine to divide a 32-bit value by 1024, returning only the low 16 bits. </p>
<p>You'd think this would be just result = (in32 >> 10) & 0xFFFF; and on ARM, that's what you want and all is well. But on AVR that code turns into a loop that executes a four-byte shift ten times: 40 shifts in all, plus loop overhead. This routine gets exactly the same result with just six shifts (vs 40), and no loop overhead. Used to convert millis to 'binary seconds' aka bseconds: one bsecond == 1024 millis. </p>
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<td class="memname">LIB8STATIC uint8_t ease8InOutApprox </td>
<td>(</td>
<td class="paramtype">fract8 </td>
<td class="paramname"><em>i</em></td><td>)</td>
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<p>ease8InOutApprox: fast, rough 8-bit ease-in/ease-out function shaped approximately like 'ease8InOutCubic', it's never off by more than a couple of percent from the actual cubic S-curve, and it executes more than twice as fast. </p>
<p>Use when the cycles are more important than visual smoothness. Asm version takes around 7 cycles on AVR. </p>
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<td class="memname">LIB8STATIC sfract15 floatToSfract15 </td>
<td>(</td>
<td class="paramtype">float </td>
<td class="paramname"><em>f</em></td><td>)</td>
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<p>conversion from IEEE754 float in the range (-1,1) to 16-bit fixed point. </p>
<p>Note that the extremes of one and negative one are NOT representable. The representable range is basically </p>
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<p>Return the current hours since boot in an 8-bit value. </p>
<p>Used as part of the "every N time-periods" mechanism </p>
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<td class="memname">LIB8STATIC uint8_t map8 </td>
<td>(</td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>in</em>, </td>
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<td class="paramtype">uint8_t </td>
<td class="paramname"><em>rangeStart</em>, </td>
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<p>map8: map from one full-range 8-bit value into a narrower range of 8-bit values, possibly a range of hues. </p>
<p>E.g. map myValue into a hue in the range blue..purple..pink..red hue = map8( myValue, HUE_BLUE, HUE_RED);</p>
<p>Combines nicely with the waveform functions (like sin8, etc) to produce continuous hue gradients back and forth: </p><pre class="fragment"> hue = map8( sin8( myValue), HUE_BLUE, HUE_RED);
</pre><p>Mathematically simiar to lerp8by8, but arguments are more like Arduino's "map"; this function is similar to </p><pre class="fragment"> map( in, 0, 255, rangeStart, rangeEnd)
</pre><p>but faster and specifically designed for 8-bit values. </p>
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<td class="memname">LIB8STATIC uint16_t minutes16 </td>
<td>(</td>
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<p>Return the current minutes since boot in a 16-bit value. </p>
<p>Used as part of the "every N time-periods" mechanism </p>
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<td class="memname">LIB8STATIC uint8_t quadwave8 </td>
<td>(</td>
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<td class="paramname"><em>in</em></td><td>)</td>
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<p>quadwave8: quadratic waveform generator. </p>
<p>Spends just a little more time at the limits than 'sine' does. </p>
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<p>Return the current seconds since boot in a 16-bit value. </p>
<p>Used as part of the "every N time-periods" mechanism </p>
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<td class="memname">LIB8STATIC float sfract15ToFloat </td>
<td>(</td>
<td class="paramtype">sfract15 </td>
<td class="paramname"><em>y</em></td><td>)</td>
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<p>sfract15ToFloat: conversion from sfract15 fixed point to IEEE754 32-bit float. </p>
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<td class="memname">LIB8STATIC uint8_t squarewave8 </td>
<td>(</td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>in</em>, </td>
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<td class="paramtype">uint8_t </td>
<td class="paramname"><em>pulsewidth</em> = <code>128</code> </td>
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<p>squarewave8: square wave generator. </p>
<p>Useful for turning a one-byte ever-increasing value into a one-byte value that is either 0 or 255. The width of the output 'pulse' is determined by the pulsewidth argument:</p>
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> If pulsewidth is 255, output is always 255.</div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> If pulsewidth < 255, then</div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>  if input < pulsewidth then output is 255</div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span>  if input >= pulsewidth then output is 0</div>
</div><!-- fragment --><p>the output looking like:</p>
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> 255 +--pulsewidth--+</div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span>  . | |</div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>  0 0 +--------(256-pulsewidth)--------</div>
</div><!-- fragment --><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">in</td><td></td></tr>
<tr><td class="paramname">pulsewidth</td><td></td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>square wave output </dd></dl>
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<td>(</td>
<td class="paramtype">uint8_t </td>
<td class="paramname"><em>in</em></td><td>)</td>
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<p>triwave8: triangle (sawtooth) wave generator. </p>
<p>Useful for turning a one-byte ever-increasing value into a one-byte value that oscillates up and down.</p>
<p>input output 0..127 0..254 (positive slope) 128..255 254..0 (negative slope)</p>
<p>On AVR this function takes just three cycles. </p>
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