diff options
Diffstat (limited to 'libpixelflinger/fixed.cpp')
-rw-r--r-- | libpixelflinger/fixed.cpp | 339 |
1 files changed, 0 insertions, 339 deletions
diff --git a/libpixelflinger/fixed.cpp b/libpixelflinger/fixed.cpp deleted file mode 100644 index 5b920628b..000000000 --- a/libpixelflinger/fixed.cpp +++ /dev/null @@ -1,339 +0,0 @@ -/* libs/pixelflinger/fixed.cpp -** -** Copyright 2006, The Android Open Source Project -** -** Licensed under the Apache License, Version 2.0 (the "License"); -** you may not use this file except in compliance with the License. -** You may obtain a copy of the License at -** -** http://www.apache.org/licenses/LICENSE-2.0 -** -** Unless required by applicable law or agreed to in writing, software -** distributed under the License is distributed on an "AS IS" BASIS, -** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -** See the License for the specific language governing permissions and -** limitations under the License. -*/ - -#include <stdio.h> - -#include <private/pixelflinger/ggl_context.h> -#include <private/pixelflinger/ggl_fixed.h> - - -// ------------------------------------------------------------------------ - -int32_t gglRecipQNormalized(int32_t x, int* exponent) -{ - const int32_t s = x>>31; - uint32_t a = s ? -x : x; - - // the result will overflow, so just set it to the biggest/inf value - if (ggl_unlikely(a <= 2LU)) { - *exponent = 0; - return s ? FIXED_MIN : FIXED_MAX; - } - - // Newton-Raphson iteration: - // x = r*(2 - a*r) - - const int32_t lz = gglClz(a); - a <<= lz; // 0.32 - uint32_t r = a; - // note: if a == 0x80000000, this means x was a power-of-2, in this - // case we don't need to compute anything. We get the reciprocal for - // (almost) free. - if (a != 0x80000000) { - r = (0x2E800 << (30-16)) - (r>>(2-1)); // 2.30, r = 2.90625 - 2*a - // 0.32 + 2.30 = 2.62 -> 2.30 - // 2.30 + 2.30 = 4.60 -> 2.30 - r = (((2LU<<30) - uint32_t((uint64_t(a)*r) >> 32)) * uint64_t(r)) >> 30; - r = (((2LU<<30) - uint32_t((uint64_t(a)*r) >> 32)) * uint64_t(r)) >> 30; - } - - // shift right 1-bit to make room for the sign bit - *exponent = 30-lz-1; - r >>= 1; - return s ? -r : r; -} - -int32_t gglRecipQ(GGLfixed x, int q) -{ - int shift; - x = gglRecipQNormalized(x, &shift); - shift += 16-q; - x += 1L << (shift-1); // rounding - x >>= shift; - return x; -} - -// ------------------------------------------------------------------------ - -GGLfixed gglFastDivx(GGLfixed n, GGLfixed d) -{ - if ((d>>24) && ((d>>24)+1)) { - n >>= 8; - d >>= 8; - } - return gglMulx(n, gglRecip(d)); -} - -// ------------------------------------------------------------------------ - -static const GGLfixed ggl_sqrt_reciproc_approx_tab[8] = { - // 1/sqrt(x) with x = 1-N/16, N=[8...1] - 0x16A09, 0x15555, 0x143D1, 0x134BF, 0x1279A, 0x11C01, 0x111AC, 0x10865 -}; - -GGLfixed gglSqrtRecipx(GGLfixed x) -{ - if (x == 0) return FIXED_MAX; - if (x == FIXED_ONE) return x; - const GGLfixed a = x; - const int32_t lz = gglClz(x); - x = ggl_sqrt_reciproc_approx_tab[(a>>(28-lz))&0x7]; - const int32_t exp = lz - 16; - if (exp <= 0) x >>= -exp>>1; - else x <<= (exp>>1) + (exp & 1); - if (exp & 1) { - x = gglMulx(x, ggl_sqrt_reciproc_approx_tab[0])>>1; - } - // 2 Newton-Raphson iterations: x = x/2*(3-(a*x)*x) - x = gglMulx((x>>1),(0x30000 - gglMulx(gglMulx(a,x),x))); - x = gglMulx((x>>1),(0x30000 - gglMulx(gglMulx(a,x),x))); - return x; -} - -GGLfixed gglSqrtx(GGLfixed a) -{ - // Compute a full precision square-root (24 bits accuracy) - GGLfixed r = 0; - GGLfixed bit = 0x800000; - int32_t bshift = 15; - do { - GGLfixed temp = bit + (r<<1); - if (bshift >= 8) temp <<= (bshift-8); - else temp >>= (8-bshift); - if (a >= temp) { - r += bit; - a -= temp; - } - bshift--; - } while (bit>>=1); - return r; -} - -// ------------------------------------------------------------------------ - -static const GGLfixed ggl_log_approx_tab[] = { - // -ln(x)/ln(2) with x = N/16, N=[8...16] - 0xFFFF, 0xd47f, 0xad96, 0x8a62, 0x6a3f, 0x4caf, 0x3151, 0x17d6, 0x0000 -}; - -static const GGLfixed ggl_alog_approx_tab[] = { // domain [0 - 1.0] - 0xffff, 0xeac0, 0xd744, 0xc567, 0xb504, 0xa5fe, 0x9837, 0x8b95, 0x8000 -}; - -GGLfixed gglPowx(GGLfixed x, GGLfixed y) -{ - // prerequisite: 0 <= x <= 1, and y >=0 - - // pow(x,y) = 2^(y*log2(x)) - // = 2^(y*log2(x*(2^exp)*(2^-exp)))) - // = 2^(y*(log2(X)-exp)) - // = 2^(log2(X)*y - y*exp) - // = 2^( - (-log2(X)*y + y*exp) ) - - int32_t exp = gglClz(x) - 16; - GGLfixed f = x << exp; - x = (f & 0x0FFF)<<4; - f = (f >> 12) & 0x7; - GGLfixed p = gglMulAddx( - ggl_log_approx_tab[f+1] - ggl_log_approx_tab[f], x, - ggl_log_approx_tab[f]); - p = gglMulAddx(p, y, y*exp); - exp = gglFixedToIntFloor(p); - if (exp < 31) { - p = gglFracx(p); - x = (p & 0x1FFF)<<3; - p >>= 13; - p = gglMulAddx( - ggl_alog_approx_tab[p+1] - ggl_alog_approx_tab[p], x, - ggl_alog_approx_tab[p]); - p >>= exp; - } else { - p = 0; - } - return p; - // ( powf((a*65536.0f), (b*65536.0f)) ) * 65536.0f; -} - -// ------------------------------------------------------------------------ - -int32_t gglDivQ(GGLfixed n, GGLfixed d, int32_t i) -{ - //int32_t r =int32_t((int64_t(n)<<i)/d); - const int32_t ds = n^d; - if (n<0) n = -n; - if (d<0) d = -d; - int nd = gglClz(d) - gglClz(n); - i += nd + 1; - if (nd > 0) d <<= nd; - else n <<= -nd; - uint32_t q = 0; - - int j = i & 7; - i >>= 3; - - // gcc deals with the code below pretty well. - // we get 3.75 cycles per bit in the main loop - // and 8 cycles per bit in the termination loop - if (ggl_likely(i)) { - n -= d; - do { - q <<= 8; - if (n>=0) q |= 128; - else n += d; - n = n*2 - d; - if (n>=0) q |= 64; - else n += d; - n = n*2 - d; - if (n>=0) q |= 32; - else n += d; - n = n*2 - d; - if (n>=0) q |= 16; - else n += d; - n = n*2 - d; - if (n>=0) q |= 8; - else n += d; - n = n*2 - d; - if (n>=0) q |= 4; - else n += d; - n = n*2 - d; - if (n>=0) q |= 2; - else n += d; - n = n*2 - d; - if (n>=0) q |= 1; - else n += d; - - if (--i == 0) - goto finish; - - n = n*2 - d; - } while(true); - do { - q <<= 1; - n = n*2 - d; - if (n>=0) q |= 1; - else n += d; - finish: ; - } while (j--); - return (ds<0) ? -q : q; - } - - n -= d; - if (n>=0) q |= 1; - else n += d; - j--; - goto finish; -} - -// ------------------------------------------------------------------------ - -// assumes that the int32_t values of a, b, and c are all positive -// use when both a and b are larger than c - -template <typename T> -static inline void swap(T& a, T& b) { - T t(a); - a = b; - b = t; -} - -static __attribute__((noinline)) -int32_t slow_muldiv(uint32_t a, uint32_t b, uint32_t c) -{ - // first we compute a*b as a 64-bit integer - // (GCC generates umull with the code below) - uint64_t ab = uint64_t(a)*b; - uint32_t hi = ab>>32; - uint32_t lo = ab; - uint32_t result; - - // now perform the division - if (hi >= c) { - overflow: - result = 0x7fffffff; // basic overflow - } else if (hi == 0) { - result = lo/c; // note: c can't be 0 - if ((result >> 31) != 0) // result must fit in 31 bits - goto overflow; - } else { - uint32_t r = hi; - int bits = 31; - result = 0; - do { - r = (r << 1) | (lo >> 31); - lo <<= 1; - result <<= 1; - if (r >= c) { - r -= c; - result |= 1; - } - } while (bits--); - } - return int32_t(result); -} - -// assumes a >= 0 and c >= b >= 0 -static inline -int32_t quick_muldiv(int32_t a, int32_t b, int32_t c) -{ - int32_t r = 0, q = 0, i; - int leading = gglClz(a); - i = 32 - leading; - a <<= leading; - do { - r <<= 1; - if (a < 0) - r += b; - a <<= 1; - q <<= 1; - if (r >= c) { - r -= c; - q++; - } - asm(""::); // gcc generates better code this way - if (r >= c) { - r -= c; - q++; - } - } - while (--i); - return q; -} - -// this function computes a*b/c with 64-bit intermediate accuracy -// overflows (e.g. division by 0) are handled and return INT_MAX - -int32_t gglMulDivi(int32_t a, int32_t b, int32_t c) -{ - int32_t result; - int32_t sign = a^b^c; - - if (a < 0) a = -a; - if (b < 0) b = -b; - if (c < 0) c = -c; - - if (a < b) { - swap(a, b); - } - - if (b <= c) result = quick_muldiv(a, b, c); - else result = slow_muldiv((uint32_t)a, (uint32_t)b, (uint32_t)c); - - if (sign < 0) - result = -result; - - return result; -} |