Hello Shelley Chen, Hung-Te Lin, Yu-Ping Wu,
I'd like you to do a code review. Please visit
https://review.coreboot.org/c/coreboot/+/42993
to review the following change.
Change subject: libpayload: Add simple 32.32 fixed-point math API ......................................................................
libpayload: Add simple 32.32 fixed-point math API
struct fraction is slooooooooooow. This patch adds a simple 64-bit (32-bits integral, 32-bits fractional) fixed-point math API that is *much* faster when doing intensive graphics operations. It is optimized for speed over accuracy so some operations may lose a bit more precision than expected, but overall it's still plenty of bits for most use cases.
Also includes support for basic trigonometric functions with a small lookup table.
Signed-off-by: Julius Werner jwerner@chromium.org Change-Id: Id0f9c23980e36ce0ac0b7c5cd0bc66153bca1fd0 --- A payloads/libpayload/include/fpmath.h M payloads/libpayload/libc/Makefile.inc A payloads/libpayload/libc/fpmath.c 3 files changed, 384 insertions(+), 0 deletions(-)
git pull ssh://review.coreboot.org:29418/coreboot refs/changes/93/42993/1
diff --git a/payloads/libpayload/include/fpmath.h b/payloads/libpayload/include/fpmath.h new file mode 100644 index 0000000..db7cc21 --- /dev/null +++ b/payloads/libpayload/include/fpmath.h @@ -0,0 +1,234 @@ +/* + * + * Copyright (C) 2020 Google, Inc. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. The name of the author may not be used to endorse or promote products + * derived from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include <stdint.h> + +/* + * This file implements operations for a simple 32.32 fixed-point math type. + * This is intended for speed-critical stuff (e.g. graphics) so there are + * intentionally no overflow checks or assertions, and operations are written + * to prefer speed over precision (e.g. multiplying by 1 may lose precision). + * For best results, only use for applications where 16.16 would fit. + */ + +typedef struct { /* wrap in struct to prevent direct access */ + int64_t v; +} fpmath_t; + +#define FPMATH_SHIFT 32 /* define where to place the decimal point */ + +/* Turn an integer into an fpmath_t. */ +static inline fpmath_t fp(int32_t a) +{ + return (fpmath_t){ .v = (int64_t)a << FPMATH_SHIFT }; +} + +/* Create an fpmath_t from a fraction. (numerator / denominator) */ +static inline fpmath_t fpfrac(int32_t numerator, int32_t denominator) +{ + return (fpmath_t){ .v = ((int64_t)numerator << FPMATH_SHIFT) / denominator }; +} + +/* Turn an fpmath_t back into an integer, rounding towards -INF. */ +static inline int32_t fpfloor(fpmath_t a) +{ + return a.v >> FPMATH_SHIFT; +} + +/* Turn an fpmath_t back into an integer, rounding towards nearest. */ +static inline int32_t fpround(fpmath_t a) +{ + return (a.v + ((int64_t)1 << (FPMATH_SHIFT - 1))) >> FPMATH_SHIFT; +} + +/* Turn an fpmath_t back into an integer, rounding towards +INF. */ +static inline int32_t fpceil(fpmath_t a) +{ + return (a.v + ((int64_t)1 << FPMATH_SHIFT) - 1) >> FPMATH_SHIFT; +} + +/* Add two fpmath_t. (a + b) */ +static inline fpmath_t fpadd(fpmath_t a, fpmath_t b) +{ + return (fpmath_t){ .v = a.v + b.v }; +} + +/* Add an fpmath_t and an integer. (a + b) */ +static inline fpmath_t fpaddi(fpmath_t a, int32_t b) +{ + return (fpmath_t){ .v = a.v + ((int64_t)b << FPMATH_SHIFT) }; +} + +/* Subtract one fpmath_t from another. (a + b) */ +static inline fpmath_t fpsub(fpmath_t a, fpmath_t b) +{ + return (fpmath_t){ .v = a.v - b.v }; +} + +/* Subtract an integer from an fpmath_t. (a - b) */ +static inline fpmath_t fpsubi(fpmath_t a, int32_t b) +{ + return (fpmath_t){ .v = a.v - ((int64_t)b << FPMATH_SHIFT) }; +} + +/* Subtract an fpmath_t from an integer. (a - b) */ +static inline fpmath_t fpisub(int32_t a, fpmath_t b) +{ + return (fpmath_t){ .v = ((int64_t)a << FPMATH_SHIFT) - b.v }; +} + +/* Multiply two fpmath_t. (a * b) + Looses 16 bits fractional precision on each. */ +static inline fpmath_t fpmul(fpmath_t a, fpmath_t b) +{ + return (fpmath_t){ .v = (a.v >> (FPMATH_SHIFT/2)) * (b.v >> (FPMATH_SHIFT/2)) }; +} + +/* Multiply an fpmath_t and an integer. (a * b) */ +static inline fpmath_t fpmuli(fpmath_t a, int32_t b) +{ + return (fpmath_t){ .v = a.v * b }; +} + +/* Divide an fpmath_t by another. (a / b) + Looses 16 bits integral precision on each! Careful with this one! */ +static inline fpmath_t fpdiv(fpmath_t a, fpmath_t b) +{ + return (fpmath_t){ .v = (a.v << (FPMATH_SHIFT/2)) / (b.v >> (FPMATH_SHIFT/2)) }; +} + +/* Divide an fpmath_t by an integer. (a / b) */ +static inline fpmath_t fpdivi(fpmath_t a, int32_t b) +{ + return (fpmath_t){ .v = a.v / b }; +} + +/* Calculate absolute value of an fpmath_t. (ABS(a)) */ +static inline fpmath_t fpabs(fpmath_t a) +{ + return (fpmath_t){ .v = (a.v < 0 ? -a.v : a.v) }; +} + +/* Return true iff two fpmath_t are exactly equal. (a == b) + Like with floats, you probably don't want to use this most of the time. */ +static inline int fpequals(fpmath_t a, fpmath_t b) +{ + return a.v == b.v; +} + +/* Return true iff one fpmath_t is less than another. (a < b) */ +static inline int fpless(fpmath_t a, fpmath_t b) +{ + return a.v < b.v; +} + +/* Return true iff one fpmath_t is more than another. (a > b) */ +static inline int fpmore(fpmath_t a, fpmath_t b) +{ + return a.v > b.v; +} + +/* Return the smaller of two fpmath_t. (MIN(a, b)) */ +static inline fpmath_t fpmin(fpmath_t a, fpmath_t b) +{ + if (a.v < b.v) + return a; + else + return b; +} + +/* Return the larger of two fpmath_t. (MAX(a, b)) */ +static inline fpmath_t fpmax(fpmath_t a, fpmath_t b) +{ + if (a.v > b.v) + return a; + else + return b; +} + +/* Return the constant PI as an fpmath_t (to as much precision as I was willing to bother). */ +static inline fpmath_t fppi(void) +{ + /* Can have one more digit when dividing unsigned, will be small enough to fit after. */ + return (fpmath_t){ .v = ((uint64_t)3141592654 << FPMATH_SHIFT) / 1000000000 }; +} + +/* + * Returns the "one-based" sine of an fpmath_t, meaning the input is interpreted as if the range + * 0.0-1.0 corresponded to 0.0-PI/2 for radians. This is mostly here as the base primitives for + * the other trig stuff, but it may be useful to use directly if your input value already needs + * to be multiplied by some factor of PI and you want to save the instructions (and precision) + * for multiplying it in just so that the trig functions can divide it right out again. + */ +fpmath_t fpsin1(fpmath_t x); + +/* Returns the "one-based" cosine of an fpmath_t (analogous definition to fpsin1()). */ +static inline fpmath_t fpcos1(fpmath_t x) +{ + return fpsin1(fpaddi(x, 1)); +} + +/* Returns the sine of an fpmath_t interpreted as radians. */ +static inline fpmath_t fpsinr(fpmath_t radians) +{ + return fpsin1(fpdiv(radians, fpdivi(fppi(), 2))); +} + +/* Returns the sine of an fpmath_t interpreted as degrees. */ +static inline fpmath_t fpsind(fpmath_t degrees) +{ + return fpsin1(fpdivi(degrees, 90)); +} + +/* Returns the cosine of an fpmath_t interpreted as radians. */ +static inline fpmath_t fpcosr(fpmath_t radians) +{ + return fpcos1(fpdiv(radians, fpdivi(fppi(), 2))); +} + +/* Returns the cosine of an fpmath_t interpreted as degrees. */ +static inline fpmath_t fpcosd(fpmath_t degrees) +{ + return fpcos1(fpdivi(degrees, 90)); +} + +/* Returns the tangent of an fpmath_t interpreted as radians. + No safety rails, don't call this at the poles! */ +static inline fpmath_t fptanr(fpmath_t radians) +{ + fpmath_t one_based = fpdiv(radians, fpdivi(fppi(), 2)); + return fpdiv(fpsin1(one_based), fpcos1(one_based)); +} + +/* Returns the tangent of an fpmath_t interpreted as degrees. + No safety rails, don't call this at the poles! */ +static inline fpmath_t fptand(fpmath_t degrees) +{ + fpmath_t one_based = fpdivi(degrees, 90); + return fpdiv(fpsin1(one_based), fpcos1(one_based)); +} diff --git a/payloads/libpayload/libc/Makefile.inc b/payloads/libpayload/libc/Makefile.inc index 2999023..f9006ae 100644 --- a/payloads/libpayload/libc/Makefile.inc +++ b/payloads/libpayload/libc/Makefile.inc @@ -38,3 +38,4 @@ libc-$(CONFIG_LP_LIBC) += die.c libc-$(CONFIG_LP_LIBC) += coreboot.c libc-$(CONFIG_LP_LIBC) += fmap.c +libc-$(CONFIG_LP_LIBC) += fpmath.c diff --git a/payloads/libpayload/libc/fpmath.c b/payloads/libpayload/libc/fpmath.c new file mode 100644 index 0000000..4c2a6ac --- /dev/null +++ b/payloads/libpayload/libc/fpmath.c @@ -0,0 +1,149 @@ +/* + * + * Copyright (C) 2020 Google, Inc. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. The name of the author may not be used to endorse or promote products + * derived from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include <fpmath.h> + +/* + * This table represents one ascending arc of the sine curve, i.e. the values sin(x) for + * 0.0 <= x < PI/2. We divide that range into 256 equidistant points and store the corresponding + * sine values for those points. Since the values lie in the range 0.0 <= sin(x) < 1.0, in order + * to make the most use of the bytes we store, we map them to the range from 0 to UINT16_MAX. + * + * Generated with: + * + * for (i = 0; i < 256; i++) { + * double s = sin((double)i * M_PI / 2 / 256); + * uint16_t u = fmin(round(s * (1 << 16)), (1 << 16)); + * printf("0x%04x,%s", u, i % 8 == 7 ? "\n" : " "); + * } + * + * In order to make sure the second access for linear interpolation (see below) cannot overrun + * the array, we stick a final 257th value 0xffff at the end. (It should really be 0x10000, + * but... this is good enough.) + */ + +/* Table size as power of two. If we ever want to change the table size, updating this value + should make everything else fall back into place again (hopefully). */ +#define TP2 8 + +static const uint16_t fpsin_table[(1 << TP2) + 1] = { + 0x0000, 0x0192, 0x0324, 0x04b6, 0x0648, 0x07da, 0x096c, 0x0afe, + 0x0c90, 0x0e21, 0x0fb3, 0x1144, 0x12d5, 0x1466, 0x15f7, 0x1787, + 0x1918, 0x1aa8, 0x1c38, 0x1dc7, 0x1f56, 0x20e5, 0x2274, 0x2402, + 0x2590, 0x271e, 0x28ab, 0x2a38, 0x2bc4, 0x2d50, 0x2edc, 0x3067, + 0x31f1, 0x337c, 0x3505, 0x368e, 0x3817, 0x399f, 0x3b27, 0x3cae, + 0x3e34, 0x3fba, 0x413f, 0x42c3, 0x4447, 0x45cb, 0x474d, 0x48cf, + 0x4a50, 0x4bd1, 0x4d50, 0x4ecf, 0x504d, 0x51cb, 0x5348, 0x54c3, + 0x563e, 0x57b9, 0x5932, 0x5aaa, 0x5c22, 0x5d99, 0x5f0f, 0x6084, + 0x61f8, 0x636b, 0x64dd, 0x664e, 0x67be, 0x692d, 0x6a9b, 0x6c08, + 0x6d74, 0x6edf, 0x7049, 0x71b2, 0x731a, 0x7480, 0x75e6, 0x774a, + 0x78ad, 0x7a10, 0x7b70, 0x7cd0, 0x7e2f, 0x7f8c, 0x80e8, 0x8243, + 0x839c, 0x84f5, 0x864c, 0x87a1, 0x88f6, 0x8a49, 0x8b9a, 0x8ceb, + 0x8e3a, 0x8f88, 0x90d4, 0x921f, 0x9368, 0x94b0, 0x95f7, 0x973c, + 0x9880, 0x99c2, 0x9b03, 0x9c42, 0x9d80, 0x9ebc, 0x9ff7, 0xa130, + 0xa268, 0xa39e, 0xa4d2, 0xa605, 0xa736, 0xa866, 0xa994, 0xaac1, + 0xabeb, 0xad14, 0xae3c, 0xaf62, 0xb086, 0xb1a8, 0xb2c9, 0xb3e8, + 0xb505, 0xb620, 0xb73a, 0xb852, 0xb968, 0xba7d, 0xbb8f, 0xbca0, + 0xbdaf, 0xbebc, 0xbfc7, 0xc0d1, 0xc1d8, 0xc2de, 0xc3e2, 0xc4e4, + 0xc5e4, 0xc6e2, 0xc7de, 0xc8d9, 0xc9d1, 0xcac7, 0xcbbc, 0xccae, + 0xcd9f, 0xce8e, 0xcf7a, 0xd065, 0xd14d, 0xd234, 0xd318, 0xd3fb, + 0xd4db, 0xd5ba, 0xd696, 0xd770, 0xd848, 0xd91e, 0xd9f2, 0xdac4, + 0xdb94, 0xdc62, 0xdd2d, 0xddf7, 0xdebe, 0xdf83, 0xe046, 0xe107, + 0xe1c6, 0xe282, 0xe33c, 0xe3f4, 0xe4aa, 0xe55e, 0xe610, 0xe6bf, + 0xe76c, 0xe817, 0xe8bf, 0xe966, 0xea0a, 0xeaab, 0xeb4b, 0xebe8, + 0xec83, 0xed1c, 0xedb3, 0xee47, 0xeed9, 0xef68, 0xeff5, 0xf080, + 0xf109, 0xf18f, 0xf213, 0xf295, 0xf314, 0xf391, 0xf40c, 0xf484, + 0xf4fa, 0xf56e, 0xf5df, 0xf64e, 0xf6ba, 0xf724, 0xf78c, 0xf7f1, + 0xf854, 0xf8b4, 0xf913, 0xf96e, 0xf9c8, 0xfa1f, 0xfa73, 0xfac5, + 0xfb15, 0xfb62, 0xfbad, 0xfbf5, 0xfc3b, 0xfc7f, 0xfcc0, 0xfcfe, + 0xfd3b, 0xfd74, 0xfdac, 0xfde1, 0xfe13, 0xfe43, 0xfe71, 0xfe9c, + 0xfec4, 0xfeeb, 0xff0e, 0xff30, 0xff4e, 0xff6b, 0xff85, 0xff9c, + 0xffb1, 0xffc4, 0xffd4, 0xffe1, 0xffec, 0xfff5, 0xfffb, 0xffff, + 0xffff, +}; + +/* x is in the "one-based" scale, so x == 1.0 is the top of the curve (PI/2 in radians). */ +fpmath_t fpsin1(fpmath_t x) +{ + /* + * When doing things like sin(x)/x, tiny errors can quickly become big problems, so just + * returning the nearest table value we have is not good enough (our fpmath_t has four + * times as much fractional precision as the sine table). A good and fast enough remedy + * is to linearly interpolate between the two nearest table values v1 and v2. + * (There are better but slower interpolations so we intentionally choose this one.) + * + * Most of this math can be done in 32 bits (because we're just operating on fractional + * parts in the 0.0-1.0 range anyway), so to help our 32-bit platforms a bit we keep it + * there as long as possible and only go back to an int64_t at the end. + */ + uint32_t v1, v2; + + /* + * Since x is "one-based" the part that maps to our curve (0.0 to PI/2 in radians) just + * happens to be exactly the fractional part of the fpmath_t, easy to extract. + */ + int index = (x.v >> (FPMATH_SHIFT - TP2)) & ((1 << TP2) - 1); + + /* + * In our one-based input domain, the period of the sine function is exactly 4.0. By + * extracting the first bit of the integral part of the fpmath_t we can check if it is + * odd-numbered (1.0-2.0, 3.0-4.0, etc.) or even numbered (0.0-1.0, 2.0-3.0, etc.), and + * that tells us whether we are in a "rising" (away from 0) or "falling" (towards 0) + * part of the sine curve. Our table curve is rising, so for the falling parts we have + * to mirror the curve horizontally by using the complement of our input index. + */ + if (x.v & ((int64_t)1 << FPMATH_SHIFT)) { + v1 = fpsin_table[(1 << TP2) - index]; + v2 = fpsin_table[(1 << TP2) - index - 1]; + } else { + v1 = fpsin_table[index]; + v2 = fpsin_table[index + 1]; + } + + /* + * Linear interpolation: sin(x) is interpolated as the closest number sin(x0) to the + * left of x we have in our table, plus the distance of that value to the closest number + * to the right of x (sin(x1)) times the fractional distance of x to x0. Since the table + * is conveniently exactly 256 values, x0 is exactly the upper 8 bits of the fractional + * part of x, meaning all fractional bits below that represent exactly the distance we + * need to interpolate over. (There are 24 of them but we need to multiply them with + * 16-bit table values to fit exactly 32 bits, so we discard the lowest 8 bits.) + */ + uint32_t val = (v1 << (FPMATH_SHIFT - 16)) + + (v2 - v1) * ((x.v >> (16 - TP2)) & 0xffff); + + /* + * Just like the first integral bit told us whether we need to mirror horizontally, the + * second can tell us to mirror vertically. In 2.0-4.0, 6.0-8.0, etc. of the input range + * the sine is negative, and in 0.0-2.0, 4.0-6.0, etc. it is positive. + */ + if (x.v & ((int64_t)2 << FPMATH_SHIFT)) + return (fpmath_t){ .v = -(int64_t)val }; + else + return (fpmath_t){ .v = val }; +}