/* * * 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) Truncates integral part of a to 16 bits! 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. */ static inline fpmath_t fppi(void) { /* Rounded (uint64_t)(M_PI * (1UL << 60)) to nine hex digits. */ return (fpmath_t){ .v = 0x3243f6a89 }; } /* * 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 guard rails, don't call this at the poles or you'll divide by 0! */ 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 guard rails, don't call this at the poles or you'll divide by 0! */ static inline fpmath_t fptand(fpmath_t degrees) { fpmath_t one_based = fpdivi(degrees, 90); return fpdiv(fpsin1(one_based), fpcos1(one_based)); }