Merge tag 'android-11.0.0_r16' into android-10.0

Android 11.0.0 release 16 - twrp bringup patch
diff --git a/libpixelflinger/include/private/pixelflinger/ggl_context.h b/libpixelflinger/include/private/pixelflinger/ggl_context.h
new file mode 100644
index 0000000..563b0f1
--- /dev/null
+++ b/libpixelflinger/include/private/pixelflinger/ggl_context.h
@@ -0,0 +1,565 @@
+/*
+ * Copyright (C) 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.
+ */
+
+#ifndef ANDROID_GGL_CONTEXT_H
+#define ANDROID_GGL_CONTEXT_H
+
+#include <stdint.h>
+#include <stddef.h>
+#include <string.h>
+#include <sys/types.h>
+#include <endian.h>
+
+#include <pixelflinger/pixelflinger.h>
+#include <private/pixelflinger/ggl_fixed.h>
+
+namespace android {
+
+// ----------------------------------------------------------------------------
+
+#if BYTE_ORDER == LITTLE_ENDIAN
+
+inline uint32_t GGL_RGBA_TO_HOST(uint32_t v) {
+    return v;
+}
+inline uint32_t GGL_HOST_TO_RGBA(uint32_t v) {
+    return v;
+}
+
+#else
+
+inline uint32_t GGL_RGBA_TO_HOST(uint32_t v) {
+#if defined(__mips__) && __mips_isa_rev>=2
+    uint32_t r;
+    __asm__("wsbh %0, %1;"
+        "rotr %0, %0, 16"
+        : "=r" (r)
+        : "r" (v)
+        );
+    return r;
+#else
+    return (v<<24) | (v>>24) | ((v<<8)&0xff0000) | ((v>>8)&0xff00);
+#endif
+}
+inline uint32_t GGL_HOST_TO_RGBA(uint32_t v) {
+#if defined(__mips__) && __mips_isa_rev>=2
+    uint32_t r;
+    __asm__("wsbh %0, %1;"
+        "rotr %0, %0, 16"
+        : "=r" (r)
+        : "r" (v)
+        );
+    return r;
+#else
+    return (v<<24) | (v>>24) | ((v<<8)&0xff0000) | ((v>>8)&0xff00);
+#endif
+}
+
+#endif
+
+// ----------------------------------------------------------------------------
+
+const int GGL_DITHER_BITS = 6;  // dither weights stored on 6 bits
+const int GGL_DITHER_ORDER_SHIFT= 3;
+const int GGL_DITHER_ORDER      = (1<<GGL_DITHER_ORDER_SHIFT);
+const int GGL_DITHER_SIZE       = GGL_DITHER_ORDER * GGL_DITHER_ORDER;
+const int GGL_DITHER_MASK       = GGL_DITHER_ORDER-1;
+
+// ----------------------------------------------------------------------------
+
+const int GGL_SUBPIXEL_BITS = 4;
+
+// TRI_FRACTION_BITS defines the number of bits we want to use
+// for the sub-pixel coordinates during the edge stepping, the
+// value shouldn't be more than 7, or bad things are going to
+// happen when drawing large triangles (8 doesn't work because
+// 32 bit muls will loose the sign bit)
+
+#define  TRI_FRACTION_BITS  (GGL_SUBPIXEL_BITS)
+#define  TRI_ONE            (1 << TRI_FRACTION_BITS)
+#define  TRI_HALF           (1 << (TRI_FRACTION_BITS-1))
+#define  TRI_FROM_INT(x)    ((x) << TRI_FRACTION_BITS)
+#define  TRI_FRAC(x)        ((x)                 &  (TRI_ONE-1))
+#define  TRI_FLOOR(x)       ((x)                 & ~(TRI_ONE-1))
+#define  TRI_CEIL(x)        (((x) + (TRI_ONE-1)) & ~(TRI_ONE-1))
+#define  TRI_ROUND(x)       (((x) +  TRI_HALF  ) & ~(TRI_ONE-1))
+
+#define  TRI_ROUDNING       (1 << (16 - TRI_FRACTION_BITS - 1))
+#define  TRI_FROM_FIXED(x)  (((x)+TRI_ROUDNING) >> (16-TRI_FRACTION_BITS))
+
+#define  TRI_SNAP_NEXT_HALF(x)   (TRI_CEIL((x)+TRI_HALF) - TRI_HALF)
+#define  TRI_SNAP_PREV_HALF(x)   (TRI_CEIL((x)-TRI_HALF) - TRI_HALF)
+
+// ----------------------------------------------------------------------------
+
+const int GGL_COLOR_BITS = 24;
+
+// To maintain 8-bits color chanels, with a maximum GGLSurface
+// size of 4096 and GGL_SUBPIXEL_BITS=4, we need 8 + 12 + 4 = 24 bits
+// for encoding the color iterators
+
+inline GGLcolor gglFixedToIteratedColor(GGLfixed c) {
+    return (c << 8) - c;
+}
+
+// ----------------------------------------------------------------------------
+
+template<bool> struct CTA;
+template<> struct CTA<true> { };
+
+#define GGL_CONTEXT(con, c)         context_t *(con) = static_cast<context_t *>(c) /* NOLINT */
+#define GGL_OFFSETOF(field)         uintptr_t(&(((context_t*)0)->field))
+#define GGL_INIT_PROC(p, f)         p.f = ggl_ ## f;
+#define GGL_BETWEEN(x, L, H)        (uint32_t((x)-(L)) <= ((H)-(L)))
+
+#define ggl_likely(x)	__builtin_expect(!!(x), 1)
+#define ggl_unlikely(x)	__builtin_expect(!!(x), 0)
+
+const int GGL_TEXTURE_UNIT_COUNT    = 2;
+const int GGL_TMU_STATE             = 0x00000001;
+const int GGL_CB_STATE              = 0x00000002;
+const int GGL_PIXEL_PIPELINE_STATE  = 0x00000004;
+
+// ----------------------------------------------------------------------------
+
+#define GGL_RESERVE_NEEDS(name, l, s)                               \
+    const uint32_t  GGL_NEEDS_##name##_MASK = (((1LU<<(s))-1)<<(l));  \
+    const uint32_t  GGL_NEEDS_##name##_SHIFT = (l);
+
+#define GGL_BUILD_NEEDS(val, name)                                  \
+    (((val)<<(GGL_NEEDS_##name##_SHIFT)) & GGL_NEEDS_##name##_MASK)
+
+#define GGL_READ_NEEDS(name, n)                                     \
+    (uint32_t((n) & GGL_NEEDS_##name##_MASK) >> GGL_NEEDS_##name##_SHIFT)
+
+#define GGL_NEED_MASK(name)     (uint32_t(GGL_NEEDS_##name##_MASK))
+#define GGL_NEED(name, val)     GGL_BUILD_NEEDS(val, name)
+
+GGL_RESERVE_NEEDS( CB_FORMAT,       0, 6 )
+GGL_RESERVE_NEEDS( SHADE,           6, 1 )
+GGL_RESERVE_NEEDS( W,               7, 1 )
+GGL_RESERVE_NEEDS( BLEND_SRC,       8, 4 )
+GGL_RESERVE_NEEDS( BLEND_DST,      12, 4 )
+GGL_RESERVE_NEEDS( BLEND_SRCA,     16, 4 )
+GGL_RESERVE_NEEDS( BLEND_DSTA,     20, 4 )
+GGL_RESERVE_NEEDS( LOGIC_OP,       24, 4 )
+GGL_RESERVE_NEEDS( MASK_ARGB,      28, 4 )
+
+GGL_RESERVE_NEEDS( P_ALPHA_TEST,    0, 3 )
+GGL_RESERVE_NEEDS( P_AA,            3, 1 )
+GGL_RESERVE_NEEDS( P_DEPTH_TEST,    4, 3 )
+GGL_RESERVE_NEEDS( P_MASK_Z,        7, 1 )
+GGL_RESERVE_NEEDS( P_DITHER,        8, 1 )
+GGL_RESERVE_NEEDS( P_FOG,           9, 1 )
+GGL_RESERVE_NEEDS( P_RESERVED1,    10,22 )
+
+GGL_RESERVE_NEEDS( T_FORMAT,        0, 6 )
+GGL_RESERVE_NEEDS( T_RESERVED0,     6, 1 )
+GGL_RESERVE_NEEDS( T_POT,           7, 1 )
+GGL_RESERVE_NEEDS( T_S_WRAP,        8, 2 )
+GGL_RESERVE_NEEDS( T_T_WRAP,       10, 2 )
+GGL_RESERVE_NEEDS( T_ENV,          12, 3 )
+GGL_RESERVE_NEEDS( T_LINEAR,       15, 1 )
+
+const int GGL_NEEDS_WRAP_CLAMP_TO_EDGE  = 0;
+const int GGL_NEEDS_WRAP_REPEAT         = 1;
+const int GGL_NEEDS_WRAP_11             = 2;
+
+inline uint32_t ggl_wrap_to_needs(uint32_t e) {
+    switch (e) {
+    case GGL_CLAMP:         return GGL_NEEDS_WRAP_CLAMP_TO_EDGE;
+    case GGL_REPEAT:        return GGL_NEEDS_WRAP_REPEAT;
+    }
+    return 0;
+}
+
+inline uint32_t ggl_blendfactor_to_needs(uint32_t b) {
+    if (b <= 1) return b;
+    return (b & 0xF)+2;
+}
+
+inline uint32_t ggl_needs_to_blendfactor(uint32_t n) {
+    if (n <= 1) return n;
+    return (n - 2) + 0x300;
+}
+
+inline uint32_t ggl_env_to_needs(uint32_t e) {
+    switch (e) {
+    case GGL_REPLACE:   return 0;
+    case GGL_MODULATE:  return 1;
+    case GGL_DECAL:     return 2;
+    case GGL_BLEND:     return 3;
+    case GGL_ADD:       return 4;
+    }
+    return 0;
+}
+
+inline uint32_t ggl_needs_to_env(uint32_t n) {
+    const uint32_t envs[] = { GGL_REPLACE, GGL_MODULATE, 
+            GGL_DECAL, GGL_BLEND, GGL_ADD };
+    return envs[n];
+
+}
+
+// ----------------------------------------------------------------------------
+
+enum {
+    GGL_ENABLE_BLENDING     = 0x00000001,
+    GGL_ENABLE_SMOOTH       = 0x00000002,
+    GGL_ENABLE_AA           = 0x00000004,
+    GGL_ENABLE_LOGIC_OP     = 0x00000008,
+    GGL_ENABLE_ALPHA_TEST   = 0x00000010,
+    GGL_ENABLE_SCISSOR_TEST = 0x00000020,
+    GGL_ENABLE_TMUS         = 0x00000040,
+    GGL_ENABLE_DEPTH_TEST   = 0x00000080,
+    GGL_ENABLE_STENCIL_TEST = 0x00000100,
+    GGL_ENABLE_W            = 0x00000200,
+    GGL_ENABLE_DITHER       = 0x00000400,
+    GGL_ENABLE_FOG          = 0x00000800,
+    GGL_ENABLE_POINT_AA_NICE= 0x00001000
+};
+
+// ----------------------------------------------------------------------------
+
+struct needs_filter_t;
+struct needs_t {
+    inline int match(const needs_filter_t& filter);
+    inline bool operator == (const needs_t& rhs) const {
+        return  (n==rhs.n) &&
+                (p==rhs.p) &&
+                (t[0]==rhs.t[0]) &&
+                (t[1]==rhs.t[1]);
+    }
+    inline bool operator != (const needs_t& rhs) const {
+        return !operator == (rhs);
+    }
+    uint32_t    n;
+    uint32_t    p;
+    uint32_t    t[GGL_TEXTURE_UNIT_COUNT];
+};
+
+inline int compare_type(const needs_t& lhs, const needs_t& rhs) {
+    return memcmp(&lhs, &rhs, sizeof(needs_t));
+}
+
+struct needs_filter_t {
+    needs_t     value;
+    needs_t     mask;
+};
+
+int needs_t::match(const needs_filter_t& filter) {
+    uint32_t result = 
+        ((filter.value.n ^ n)       & filter.mask.n)    |
+        ((filter.value.p ^ p)       & filter.mask.p)    |
+        ((filter.value.t[0] ^ t[0]) & filter.mask.t[0]) |
+        ((filter.value.t[1] ^ t[1]) & filter.mask.t[1]);
+    return (result == 0);
+}
+
+// ----------------------------------------------------------------------------
+
+struct context_t;
+class Assembly;
+
+struct blend_state_t {
+	uint32_t			src;
+	uint32_t			dst;
+	uint32_t			src_alpha;
+	uint32_t			dst_alpha;
+	uint8_t				reserved;
+	uint8_t				alpha_separate;
+	uint8_t				operation;
+	uint8_t				equation;
+};
+
+struct mask_state_t {
+    uint8_t             color;
+    uint8_t             depth;
+    uint32_t            stencil;
+};
+
+struct clear_state_t {
+    GGLclampx           r;
+    GGLclampx           g;
+    GGLclampx           b;
+    GGLclampx           a;
+    GGLclampx           depth;
+    GGLint              stencil;
+    uint32_t            colorPacked;
+    uint32_t            depthPacked;
+    uint32_t            stencilPacked;
+    uint32_t            dirty;
+};
+
+struct fog_state_t {
+    uint8_t     color[4];
+};
+
+struct logic_op_state_t {
+    uint16_t            opcode;
+};
+
+struct alpha_test_state_t {
+    uint16_t            func;
+    GGLcolor            ref;
+};
+
+struct depth_test_state_t {
+    uint16_t            func;
+    GGLclampx           clearValue;
+};
+
+struct scissor_t {
+    uint32_t            user_left;
+    uint32_t            user_right;
+    uint32_t            user_top;
+    uint32_t            user_bottom;
+    uint32_t            left;
+    uint32_t            right;
+    uint32_t            top;
+    uint32_t            bottom;
+};
+
+struct pixel_t {
+    uint32_t    c[4];
+    uint8_t     s[4];
+};
+
+struct surface_t {
+    union {
+        GGLSurface          s;
+        // Keep the following struct field types in line with the corresponding
+        // GGLSurface fields to avoid mismatches leading to errors.
+        struct {
+            GGLsizei        reserved;
+            GGLuint         width;
+            GGLuint         height;
+            GGLint          stride;
+            GGLubyte*       data;
+            GGLubyte        format;
+            GGLubyte        dirty;
+            GGLubyte        pad[2];
+        };
+    };
+    void                (*read) (const surface_t* s, context_t* c,
+                                uint32_t x, uint32_t y, pixel_t* pixel);
+    void                (*write)(const surface_t* s, context_t* c,
+                                uint32_t x, uint32_t y, const pixel_t* pixel);
+};
+
+// ----------------------------------------------------------------------------
+
+struct texture_shade_t {
+    union {
+        struct {
+            int32_t             is0;
+            int32_t             idsdx;
+            int32_t             idsdy;
+            int                 sscale;
+            int32_t             it0;
+            int32_t             idtdx;
+            int32_t             idtdy;
+            int                 tscale;
+        };
+        struct {
+            int32_t             v;
+            int32_t             dx;
+            int32_t             dy;
+            int                 scale;
+        } st[2];
+    };
+};
+
+struct texture_iterators_t {
+    // these are not encoded in the same way than in the
+    // texture_shade_t structure
+    union {
+        struct {
+            GGLfixed			ydsdy;
+            GGLfixed            dsdx;
+            GGLfixed            dsdy;
+            int                 sscale;
+            GGLfixed			ydtdy;
+            GGLfixed            dtdx;
+            GGLfixed            dtdy;
+            int                 tscale;
+        };
+        struct {
+            GGLfixed			ydvdy;
+            GGLfixed            dvdx;
+            GGLfixed            dvdy;
+            int                 scale;
+        } st[2];
+    };
+};
+
+struct texture_t {
+	surface_t			surface;
+	texture_iterators_t	iterators;
+    texture_shade_t     shade;
+	uint32_t			s_coord;
+	uint32_t            t_coord;
+	uint16_t			s_wrap;
+	uint16_t            t_wrap;
+	uint16_t            min_filter;
+	uint16_t            mag_filter;
+    uint16_t            env;
+    uint8_t             env_color[4];
+	uint8_t				enable;
+	uint8_t				dirty;
+};
+
+struct raster_t {
+    GGLfixed            x;
+    GGLfixed            y;
+};
+
+struct framebuffer_t {
+    surface_t           color;
+    surface_t           read;
+	surface_t			depth;
+	surface_t			stencil;
+    int16_t             *coverage;
+    size_t              coverageBufferSize;
+};
+
+// ----------------------------------------------------------------------------
+
+struct iterators_t {
+	int32_t             xl;
+	int32_t             xr;
+    int32_t             y;
+	GGLcolor			ydady;
+	GGLcolor			ydrdy;
+	GGLcolor			ydgdy;
+	GGLcolor			ydbdy;
+	GGLfixed			ydzdy;
+	GGLfixed			ydwdy;
+	GGLfixed			ydfdy;
+};
+
+struct shade_t {
+	GGLcolor			a0;
+    GGLcolor            dadx;
+    GGLcolor            dady;
+	GGLcolor			r0;
+    GGLcolor            drdx;
+    GGLcolor            drdy;
+	GGLcolor			g0;
+    GGLcolor            dgdx;
+    GGLcolor            dgdy;
+	GGLcolor			b0;
+    GGLcolor            dbdx;
+    GGLcolor            dbdy;
+	uint32_t            z0;
+    GGLfixed32          dzdx;
+    GGLfixed32          dzdy;
+	GGLfixed            w0;
+    GGLfixed            dwdx;
+    GGLfixed            dwdy;
+	uint32_t			f0;
+    GGLfixed            dfdx;
+    GGLfixed            dfdy;
+};
+
+// these are used in the generated code
+// we use this mirror structure to improve
+// data locality in the pixel pipeline
+struct generated_tex_vars_t {
+    uint32_t    width;
+    uint32_t    height;
+    uint32_t    stride;
+    uintptr_t   data;
+    int32_t     dsdx;
+    int32_t     dtdx;
+    int32_t     spill[2];
+};
+
+struct generated_vars_t {
+    struct {
+        int32_t c;
+        int32_t dx;
+    } argb[4];
+    int32_t     aref;
+    int32_t     dzdx;
+    int32_t     zbase;
+    int32_t     f;
+    int32_t     dfdx;
+    int32_t     spill[3];
+    generated_tex_vars_t    texture[GGL_TEXTURE_UNIT_COUNT];
+    int32_t     rt;
+    int32_t     lb;
+};
+
+// ----------------------------------------------------------------------------
+
+struct state_t {
+	framebuffer_t		buffers;
+	texture_t			texture[GGL_TEXTURE_UNIT_COUNT];
+    scissor_t           scissor;
+    raster_t            raster;
+	blend_state_t		blend;
+    alpha_test_state_t  alpha_test;
+    depth_test_state_t  depth_test;
+    mask_state_t        mask;
+    clear_state_t       clear;
+    fog_state_t         fog;
+    logic_op_state_t    logic_op;
+    uint32_t            enables;
+    uint32_t            enabled_tmu;
+    needs_t             needs;
+};
+
+// ----------------------------------------------------------------------------
+
+struct context_t {
+	GGLContext          procs;
+	state_t             state;
+    shade_t             shade;
+	iterators_t         iterators;
+    generated_vars_t    generated_vars                __attribute__((aligned(32)));
+    uint8_t             ditherMatrix[GGL_DITHER_SIZE] __attribute__((aligned(32)));
+    uint32_t            packed;
+    uint32_t            packed8888;
+    const GGLFormat*    formats;
+    uint32_t            dirty;
+    texture_t*          activeTMU;
+    uint32_t            activeTMUIndex;
+
+    void                (*init_y)(context_t* c, int32_t y);
+	void                (*step_y)(context_t* c);
+	void                (*scanline)(context_t* c);
+    void                (*span)(context_t* c);
+    void                (*rect)(context_t* c, size_t yc);
+    
+    void*               base;
+    Assembly*           scanline_as;
+    GGLenum             error;
+};
+
+// ----------------------------------------------------------------------------
+
+void ggl_init_context(context_t* context);
+void ggl_uninit_context(context_t* context);
+void ggl_error(context_t* c, GGLenum error);
+int64_t ggl_system_time();
+
+// ----------------------------------------------------------------------------
+
+};
+
+#endif // ANDROID_GGL_CONTEXT_H
+
diff --git a/libpixelflinger/include/private/pixelflinger/ggl_fixed.h b/libpixelflinger/include/private/pixelflinger/ggl_fixed.h
new file mode 100644
index 0000000..4217a89
--- /dev/null
+++ b/libpixelflinger/include/private/pixelflinger/ggl_fixed.h
@@ -0,0 +1,878 @@
+/*
+ * Copyright (C) 2005 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.
+ */
+
+#ifndef ANDROID_GGL_FIXED_H
+#define ANDROID_GGL_FIXED_H
+
+#include <math.h>
+#include <pixelflinger/pixelflinger.h>
+
+// ----------------------------------------------------------------------------
+
+#define CONST           __attribute__((const))
+#define ALWAYS_INLINE   __attribute__((always_inline))
+
+const GGLfixed FIXED_BITS = 16;
+const GGLfixed FIXED_EPSILON  = 1;
+const GGLfixed FIXED_ONE  = 1L<<FIXED_BITS;
+const GGLfixed FIXED_HALF = 1L<<(FIXED_BITS-1);
+const GGLfixed FIXED_MIN  = 0x80000000L;
+const GGLfixed FIXED_MAX  = 0x7FFFFFFFL;
+
+inline GGLfixed gglIntToFixed(GGLfixed i)       ALWAYS_INLINE ;
+inline GGLfixed gglFixedToIntRound(GGLfixed f)  ALWAYS_INLINE ;
+inline GGLfixed gglFixedToIntFloor(GGLfixed f)  ALWAYS_INLINE ;
+inline GGLfixed gglFixedToIntCeil(GGLfixed f)   ALWAYS_INLINE ;
+inline GGLfixed gglFracx(GGLfixed v)            ALWAYS_INLINE ;
+inline GGLfixed gglFloorx(GGLfixed v)           ALWAYS_INLINE ;
+inline GGLfixed gglCeilx(GGLfixed v)            ALWAYS_INLINE ;
+inline GGLfixed gglCenterx(GGLfixed v)          ALWAYS_INLINE ;
+inline GGLfixed gglRoundx(GGLfixed v)           ALWAYS_INLINE ;
+
+GGLfixed gglIntToFixed(GGLfixed i) {
+    return i<<FIXED_BITS;
+}
+GGLfixed gglFixedToIntRound(GGLfixed f) {
+    return (f + FIXED_HALF)>>FIXED_BITS;
+}
+GGLfixed gglFixedToIntFloor(GGLfixed f) {
+    return f>>FIXED_BITS;
+}
+GGLfixed gglFixedToIntCeil(GGLfixed f) {
+    return (f + ((1<<FIXED_BITS) - 1))>>FIXED_BITS;
+}
+
+GGLfixed gglFracx(GGLfixed v) {
+    return v & ((1<<FIXED_BITS)-1);
+}
+GGLfixed gglFloorx(GGLfixed v) {
+    return gglFixedToIntFloor(v)<<FIXED_BITS;
+}
+GGLfixed gglCeilx(GGLfixed v) {
+    return gglFixedToIntCeil(v)<<FIXED_BITS;
+}
+GGLfixed gglCenterx(GGLfixed v) {
+    return gglFloorx(v + FIXED_HALF) | FIXED_HALF;
+}
+GGLfixed gglRoundx(GGLfixed v) {
+    return gglFixedToIntRound(v)<<FIXED_BITS;
+}
+
+// conversion from (unsigned) int, short, byte to fixed...
+#define GGL_B_TO_X(_x)      GGLfixed( ((int32_t(_x)+1)>>1)<<10 )
+#define GGL_S_TO_X(_x)      GGLfixed( ((int32_t(_x)+1)>>1)<<2 )
+#define GGL_I_TO_X(_x)      GGLfixed( ((int32_t(_x)>>1)+1)>>14 )
+#define GGL_UB_TO_X(_x)     GGLfixed(   uint32_t(_x) +      \
+                                        (uint32_t(_x)<<8) + \
+                                        (uint32_t(_x)>>7) )
+#define GGL_US_TO_X(_x)     GGLfixed( (_x) + ((_x)>>15) )
+#define GGL_UI_TO_X(_x)     GGLfixed( (((_x)>>1)+1)>>15 )
+
+// ----------------------------------------------------------------------------
+
+GGLfixed gglPowx(GGLfixed x, GGLfixed y) CONST;
+GGLfixed gglSqrtx(GGLfixed a) CONST;
+GGLfixed gglSqrtRecipx(GGLfixed x) CONST;
+int32_t gglMulDivi(int32_t a, int32_t b, int32_t c);
+
+int32_t gglRecipQNormalized(int32_t x, int* exponent);
+int32_t gglRecipQ(GGLfixed x, int q) CONST;
+
+inline GGLfixed gglRecip(GGLfixed x) CONST;
+inline GGLfixed gglRecip(GGLfixed x) {
+    return gglRecipQ(x, 16);
+}
+
+inline GGLfixed gglRecip28(GGLfixed x) CONST;
+int32_t gglRecip28(GGLfixed x) {
+    return gglRecipQ(x, 28);
+}
+
+// ----------------------------------------------------------------------------
+
+#if defined(__arm__) && !defined(__thumb__)
+
+// inline ARM implementations
+inline GGLfixed gglMulx(GGLfixed x, GGLfixed y, int shift) CONST;
+__attribute__((always_inline)) inline GGLfixed gglMulx(GGLfixed x, GGLfixed y, int shift) {
+    GGLfixed result, t;
+    if (__builtin_constant_p(shift)) {
+    asm("smull  %[lo], %[hi], %[x], %[y]            \n"
+        "movs   %[lo], %[lo], lsr %[rshift]         \n"
+        "adc    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
+        : [lo]"=r"(result), [hi]"=r"(t), [x]"=r"(x)
+        : "%[x]"(x), [y]"r"(y), [lshift] "I"(32-shift), [rshift] "I"(shift)
+        : "cc"
+        );
+    } else {
+    asm("smull  %[lo], %[hi], %[x], %[y]            \n"
+        "movs   %[lo], %[lo], lsr %[rshift]         \n"
+        "adc    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
+        : [lo]"=&r"(result), [hi]"=&r"(t), [x]"=&r"(x)
+        : "%[x]"(x), [y]"r"(y), [lshift] "r"(32-shift), [rshift] "r"(shift)
+        : "cc"
+        );
+    }
+    return result;
+}
+
+inline GGLfixed gglMulAddx(GGLfixed x, GGLfixed y, GGLfixed a, int shift) CONST;
+__attribute__((always_inline)) inline GGLfixed gglMulAddx(GGLfixed x, GGLfixed y, GGLfixed a,
+                                                          int shift) {
+    GGLfixed result, t;
+    if (__builtin_constant_p(shift)) {
+    asm("smull  %[lo], %[hi], %[x], %[y]            \n"
+        "add    %[lo], %[a],  %[lo], lsr %[rshift]  \n"
+        "add    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
+        : [lo]"=&r"(result), [hi]"=&r"(t), [x]"=&r"(x)
+        : "%[x]"(x), [y]"r"(y), [a]"r"(a), [lshift] "I"(32-shift), [rshift] "I"(shift)
+        );
+    } else {
+    asm("smull  %[lo], %[hi], %[x], %[y]            \n"
+        "add    %[lo], %[a],  %[lo], lsr %[rshift]  \n"
+        "add    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
+        : [lo]"=&r"(result), [hi]"=&r"(t), [x]"=&r"(x)
+        : "%[x]"(x), [y]"r"(y), [a]"r"(a), [lshift] "r"(32-shift), [rshift] "r"(shift)
+        );
+    }
+    return result;
+}
+
+inline GGLfixed gglMulSubx(GGLfixed x, GGLfixed y, GGLfixed a, int shift) CONST;
+inline GGLfixed gglMulSubx(GGLfixed x, GGLfixed y, GGLfixed a, int shift) {
+    GGLfixed result, t;
+    if (__builtin_constant_p(shift)) {
+    asm("smull  %[lo], %[hi], %[x], %[y]            \n"
+        "rsb    %[lo], %[a],  %[lo], lsr %[rshift]  \n"
+        "add    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
+        : [lo]"=&r"(result), [hi]"=&r"(t), [x]"=&r"(x)
+        : "%[x]"(x), [y]"r"(y), [a]"r"(a), [lshift] "I"(32-shift), [rshift] "I"(shift)
+        );
+    } else {
+    asm("smull  %[lo], %[hi], %[x], %[y]            \n"
+        "rsb    %[lo], %[a],  %[lo], lsr %[rshift]  \n"
+        "add    %[lo], %[lo], %[hi], lsl %[lshift]  \n"
+        : [lo]"=&r"(result), [hi]"=&r"(t), [x]"=&r"(x)
+        : "%[x]"(x), [y]"r"(y), [a]"r"(a), [lshift] "r"(32-shift), [rshift] "r"(shift)
+        );
+    }
+    return result;
+}
+
+inline int64_t gglMulii(int32_t x, int32_t y) CONST;
+inline int64_t gglMulii(int32_t x, int32_t y)
+{
+    // 64-bits result: r0=low, r1=high
+    union {
+        struct {
+            int32_t lo;
+            int32_t hi;
+        } s;
+        int64_t res;
+    };
+    asm("smull %0, %1, %2, %3   \n"
+        : "=r"(s.lo), "=&r"(s.hi)
+        : "%r"(x), "r"(y)
+        :
+        );
+    return res;
+}
+#elif defined(__mips__) && __mips_isa_rev < 6
+
+/*inline MIPS implementations*/
+inline GGLfixed gglMulx(GGLfixed a, GGLfixed b, int shift) CONST;
+inline GGLfixed gglMulx(GGLfixed a, GGLfixed b, int shift) {
+    GGLfixed result,tmp,tmp1,tmp2;
+
+    if (__builtin_constant_p(shift)) {
+        if (shift == 0) {
+            asm ("mult %[a], %[b] \t\n"
+              "mflo  %[res]   \t\n"
+            : [res]"=&r"(result),[tmp]"=&r"(tmp)
+            : [a]"r"(a),[b]"r"(b)
+            : "%hi","%lo"
+            );
+        } else if (shift == 32)
+        {
+            asm ("mult %[a], %[b] \t\n"
+            "li  %[tmp],1\t\n"
+            "sll  %[tmp],%[tmp],0x1f\t\n"
+            "mflo %[res]   \t\n"
+            "addu %[tmp1],%[tmp],%[res] \t\n"
+            "sltu %[tmp1],%[tmp1],%[tmp]\t\n"   /*obit*/
+            "sra %[tmp],%[tmp],0x1f \t\n"
+            "mfhi  %[res]   \t\n"
+            "addu %[res],%[res],%[tmp]\t\n"
+            "addu %[res],%[res],%[tmp1]\t\n"
+            : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1)
+            : [a]"r"(a),[b]"r"(b),[shift]"I"(shift)
+            : "%hi","%lo"
+            );
+        } else if ((shift >0) && (shift < 32))
+        {
+            asm ("mult %[a], %[b] \t\n"
+            "li  %[tmp],1 \t\n"
+            "sll  %[tmp],%[tmp],%[shiftm1] \t\n"
+            "mflo  %[res]   \t\n"
+            "addu %[tmp1],%[tmp],%[res] \t\n"
+            "sltu %[tmp1],%[tmp1],%[tmp] \t\n"  /*obit?*/
+            "addu  %[res],%[res],%[tmp] \t\n"
+            "mfhi  %[tmp]   \t\n"
+            "addu  %[tmp],%[tmp],%[tmp1] \t\n"
+            "sll   %[tmp],%[tmp],%[lshift] \t\n"
+            "srl   %[res],%[res],%[rshift]    \t\n"
+            "or    %[res],%[res],%[tmp] \t\n"
+            : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+            : [a]"r"(a),[b]"r"(b),[lshift]"I"(32-shift),[rshift]"I"(shift),[shiftm1]"I"(shift-1)
+            : "%hi","%lo"
+            );
+        } else {
+            asm ("mult %[a], %[b] \t\n"
+            "li  %[tmp],1 \t\n"
+            "sll  %[tmp],%[tmp],%[shiftm1] \t\n"
+            "mflo  %[res]   \t\n"
+            "addu %[tmp1],%[tmp],%[res] \t\n"
+            "sltu %[tmp1],%[tmp1],%[tmp] \t\n"  /*obit?*/
+            "sra  %[tmp2],%[tmp],0x1f \t\n"
+            "addu  %[res],%[res],%[tmp] \t\n"
+            "mfhi  %[tmp]   \t\n"
+            "addu  %[tmp],%[tmp],%[tmp2] \t\n"
+            "addu  %[tmp],%[tmp],%[tmp1] \t\n"            /*tmp=hi*/
+            "srl   %[tmp2],%[res],%[rshift]    \t\n"
+            "srav  %[res], %[tmp],%[rshift]\t\n"
+            "sll   %[tmp],%[tmp],1 \t\n"
+            "sll   %[tmp],%[tmp],%[norbits] \t\n"
+            "or    %[tmp],%[tmp],%[tmp2] \t\n"
+            "movz  %[res],%[tmp],%[bit5] \t\n"
+            : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+            : [a]"r"(a),[b]"r"(b),[norbits]"I"(~(shift)),[rshift]"I"(shift),[shiftm1] "I"(shift-1),[bit5]"I"(shift & 0x20)
+            : "%hi","%lo"
+            );
+        }
+    } else {
+        asm ("mult %[a], %[b] \t\n"
+        "li  %[tmp],1 \t\n"
+        "sll  %[tmp],%[tmp],%[shiftm1] \t\n"
+        "mflo  %[res]   \t\n"
+        "addu %[tmp1],%[tmp],%[res] \t\n"
+        "sltu %[tmp1],%[tmp1],%[tmp] \t\n"  /*obit?*/
+        "sra  %[tmp2],%[tmp],0x1f \t\n"
+        "addu  %[res],%[res],%[tmp] \t\n"
+        "mfhi  %[tmp]   \t\n"
+        "addu  %[tmp],%[tmp],%[tmp2] \t\n"
+        "addu  %[tmp],%[tmp],%[tmp1] \t\n"            /*tmp=hi*/
+        "srl   %[tmp2],%[res],%[rshift]    \t\n"
+        "srav  %[res], %[tmp],%[rshift]\t\n"
+        "sll   %[tmp],%[tmp],1 \t\n"
+        "sll   %[tmp],%[tmp],%[norbits] \t\n"
+        "or    %[tmp],%[tmp],%[tmp2] \t\n"
+        "movz  %[res],%[tmp],%[bit5] \t\n"
+         : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+         : [a]"r"(a),[b]"r"(b),[norbits]"r"(~(shift)),[rshift] "r"(shift),[shiftm1]"r"(shift-1),[bit5] "r"(shift & 0x20)
+         : "%hi","%lo"
+         );
+        }
+
+        return result;
+}
+
+inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) CONST;
+inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) {
+    GGLfixed result,t,tmp1,tmp2;
+
+    if (__builtin_constant_p(shift)) {
+        if (shift == 0) {
+                 asm ("mult %[a], %[b] \t\n"
+                 "mflo  %[lo]   \t\n"
+                 "addu  %[lo],%[lo],%[c]    \t\n"
+                 : [lo]"=&r"(result)
+                 : [a]"r"(a),[b]"r"(b),[c]"r"(c)
+                 : "%hi","%lo"
+                 );
+                } else if (shift == 32) {
+                    asm ("mult %[a], %[b] \t\n"
+                    "mfhi  %[lo]   \t\n"
+                    "addu  %[lo],%[lo],%[c]    \t\n"
+                    : [lo]"=&r"(result)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c)
+                    : "%hi","%lo"
+                    );
+                } else if ((shift>0) && (shift<32)) {
+                    asm ("mult %[a], %[b] \t\n"
+                    "mflo  %[res]   \t\n"
+                    "mfhi  %[t]   \t\n"
+                    "srl   %[res],%[res],%[rshift]    \t\n"
+                    "sll   %[t],%[t],%[lshift]     \t\n"
+                    "or  %[res],%[res],%[t]    \t\n"
+                    "addu  %[res],%[res],%[c]    \t\n"
+                    : [res]"=&r"(result),[t]"=&r"(t)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c),[lshift]"I"(32-shift),[rshift]"I"(shift)
+                    : "%hi","%lo"
+                    );
+                } else {
+                    asm ("mult %[a], %[b] \t\n"
+                    "nor %[tmp1],$zero,%[shift]\t\n"
+                    "mflo  %[res]   \t\n"
+                    "mfhi  %[t]   \t\n"
+                    "srl   %[res],%[res],%[shift]    \t\n"
+                    "sll   %[tmp2],%[t],1     \t\n"
+                    "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
+                    "or  %[tmp1],%[tmp2],%[res]    \t\n"
+                    "srav  %[res],%[t],%[shift]     \t\n"
+                    "andi %[tmp2],%[shift],0x20\t\n"
+                    "movz %[res],%[tmp1],%[tmp2]\t\n"
+                    "addu  %[res],%[res],%[c]    \t\n"
+                    : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"I"(shift)
+                    : "%hi","%lo"
+                    );
+                }
+            } else {
+                asm ("mult %[a], %[b] \t\n"
+                "nor %[tmp1],$zero,%[shift]\t\n"
+                "mflo  %[res]   \t\n"
+                "mfhi  %[t]   \t\n"
+                "srl   %[res],%[res],%[shift]    \t\n"
+                "sll   %[tmp2],%[t],1     \t\n"
+                "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
+                "or  %[tmp1],%[tmp2],%[res]    \t\n"
+                "srav  %[res],%[t],%[shift]     \t\n"
+                "andi %[tmp2],%[shift],0x20\t\n"
+                "movz %[res],%[tmp1],%[tmp2]\t\n"
+                "addu  %[res],%[res],%[c]    \t\n"
+                : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+                : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"r"(shift)
+                : "%hi","%lo"
+                );
+            }
+            return result;
+}
+
+inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) CONST;
+inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) {
+    GGLfixed result,t,tmp1,tmp2;
+
+    if (__builtin_constant_p(shift)) {
+        if (shift == 0) {
+                 asm ("mult %[a], %[b] \t\n"
+                 "mflo  %[lo]   \t\n"
+                 "subu  %[lo],%[lo],%[c]    \t\n"
+                 : [lo]"=&r"(result)
+                 : [a]"r"(a),[b]"r"(b),[c]"r"(c)
+                 : "%hi","%lo"
+                 );
+                } else if (shift == 32) {
+                    asm ("mult %[a], %[b] \t\n"
+                    "mfhi  %[lo]   \t\n"
+                    "subu  %[lo],%[lo],%[c]    \t\n"
+                    : [lo]"=&r"(result)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c)
+                    : "%hi","%lo"
+                    );
+                } else if ((shift>0) && (shift<32)) {
+                    asm ("mult %[a], %[b] \t\n"
+                    "mflo  %[res]   \t\n"
+                    "mfhi  %[t]   \t\n"
+                    "srl   %[res],%[res],%[rshift]    \t\n"
+                    "sll   %[t],%[t],%[lshift]     \t\n"
+                    "or  %[res],%[res],%[t]    \t\n"
+                    "subu  %[res],%[res],%[c]    \t\n"
+                    : [res]"=&r"(result),[t]"=&r"(t)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c),[lshift]"I"(32-shift),[rshift]"I"(shift)
+                    : "%hi","%lo"
+                    );
+                } else {
+                    asm ("mult %[a], %[b] \t\n"
+                    "nor %[tmp1],$zero,%[shift]\t\n"
+                     "mflo  %[res]   \t\n"
+                     "mfhi  %[t]   \t\n"
+                     "srl   %[res],%[res],%[shift]    \t\n"
+                     "sll   %[tmp2],%[t],1     \t\n"
+                     "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
+                     "or  %[tmp1],%[tmp2],%[res]    \t\n"
+                     "srav  %[res],%[t],%[shift]     \t\n"
+                     "andi %[tmp2],%[shift],0x20\t\n"
+                     "movz %[res],%[tmp1],%[tmp2]\t\n"
+                     "subu  %[res],%[res],%[c]    \t\n"
+                     : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+                     : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"I"(shift)
+                     : "%hi","%lo"
+                     );
+                    }
+                } else {
+                asm ("mult %[a], %[b] \t\n"
+                "nor %[tmp1],$zero,%[shift]\t\n"
+                "mflo  %[res]   \t\n"
+                "mfhi  %[t]   \t\n"
+                "srl   %[res],%[res],%[shift]    \t\n"
+                "sll   %[tmp2],%[t],1     \t\n"
+                "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
+                "or  %[tmp1],%[tmp2],%[res]    \t\n"
+                "srav  %[res],%[t],%[shift]     \t\n"
+                "andi %[tmp2],%[shift],0x20\t\n"
+                "movz %[res],%[tmp1],%[tmp2]\t\n"
+                "subu  %[res],%[res],%[c]    \t\n"
+                : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+                : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"r"(shift)
+                : "%hi","%lo"
+                );
+            }
+    return result;
+}
+
+inline int64_t gglMulii(int32_t x, int32_t y) CONST;
+inline int64_t gglMulii(int32_t x, int32_t y) {
+    union {
+        struct {
+#if defined(__MIPSEL__)
+            int32_t lo;
+            int32_t hi;
+#elif defined(__MIPSEB__)
+            int32_t hi;
+            int32_t lo;
+#endif
+        } s;
+        int64_t res;
+    }u;
+    asm("mult %2, %3 \t\n"
+        "mfhi %1   \t\n"
+        "mflo %0   \t\n"
+        : "=r"(u.s.lo), "=&r"(u.s.hi)
+        : "%r"(x), "r"(y)
+	: "%hi","%lo"
+        );
+    return u.res;
+}
+
+#elif defined(__aarch64__)
+
+// inline AArch64 implementations
+
+inline GGLfixed gglMulx(GGLfixed x, GGLfixed y, int shift) CONST;
+inline GGLfixed gglMulx(GGLfixed x, GGLfixed y, int shift)
+{
+    GGLfixed result;
+    GGLfixed round;
+
+    asm("mov    %x[round], #1                        \n"
+        "lsl    %x[round], %x[round], %x[shift]      \n"
+        "lsr    %x[round], %x[round], #1             \n"
+        "smaddl %x[result], %w[x], %w[y],%x[round]   \n"
+        "lsr    %x[result], %x[result], %x[shift]    \n"
+        : [round]"=&r"(round), [result]"=&r"(result) \
+        : [x]"r"(x), [y]"r"(y), [shift] "r"(shift)   \
+        :
+       );
+    return result;
+}
+inline GGLfixed gglMulAddx(GGLfixed x, GGLfixed y, GGLfixed a, int shift) CONST;
+inline GGLfixed gglMulAddx(GGLfixed x, GGLfixed y, GGLfixed a, int shift)
+{
+    GGLfixed result;
+    asm("smull  %x[result], %w[x], %w[y]                     \n"
+        "lsr    %x[result], %x[result], %x[shift]            \n"
+        "add    %w[result], %w[result], %w[a]                \n"
+        : [result]"=&r"(result)                               \
+        : [x]"r"(x), [y]"r"(y), [a]"r"(a), [shift] "r"(shift) \
+        :
+        );
+    return result;
+}
+
+inline GGLfixed gglMulSubx(GGLfixed x, GGLfixed y, GGLfixed a, int shift) CONST;
+inline GGLfixed gglMulSubx(GGLfixed x, GGLfixed y, GGLfixed a, int shift)
+{
+
+    GGLfixed result;
+
+    asm("smull  %x[result], %w[x], %w[y]                     \n"
+        "lsr    %x[result], %x[result], %x[shift]            \n"
+        "sub    %w[result], %w[result], %w[a]                \n"
+        : [result]"=&r"(result)                               \
+        : [x]"r"(x), [y]"r"(y), [a]"r"(a), [shift] "r"(shift) \
+        :
+        );
+    return result;
+}
+inline int64_t gglMulii(int32_t x, int32_t y) CONST;
+inline int64_t gglMulii(int32_t x, int32_t y)
+{
+    int64_t res;
+    asm("smull  %x0, %w1, %w2 \n"
+        : "=r"(res)
+        : "%r"(x), "r"(y)
+        :
+        );
+    return res;
+}
+
+#elif defined(__mips__) && __mips_isa_rev == 6
+
+/*inline MIPS implementations*/
+inline GGLfixed gglMulx(GGLfixed a, GGLfixed b, int shift) CONST;
+inline GGLfixed gglMulx(GGLfixed a, GGLfixed b, int shift) {
+    GGLfixed result,tmp,tmp1,tmp2;
+
+    if (__builtin_constant_p(shift)) {
+        if (shift == 0) {
+            asm ("mul %[res], %[a], %[b] \t\n"
+            : [res]"=&r"(result)
+            : [a]"r"(a),[b]"r"(b)
+            );
+        } else if (shift == 32)
+        {
+            asm ("mul %[res], %[a], %[b] \t\n"
+            "li  %[tmp],1\t\n"
+            "sll  %[tmp],%[tmp],0x1f\t\n"
+            "addu %[tmp1],%[tmp],%[res] \t\n"
+            "muh %[res], %[a], %[b] \t\n"
+            "sltu %[tmp1],%[tmp1],%[tmp]\t\n"   /*obit*/
+            "sra %[tmp],%[tmp],0x1f \t\n"
+            "addu %[res],%[res],%[tmp]\t\n"
+            "addu %[res],%[res],%[tmp1]\t\n"
+            : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1)
+            : [a]"r"(a),[b]"r"(b),[shift]"I"(shift)
+            );
+        } else if ((shift >0) && (shift < 32))
+        {
+            asm ("mul %[res], %[a], %[b] \t\n"
+            "li  %[tmp],1 \t\n"
+            "sll  %[tmp],%[tmp],%[shiftm1] \t\n"
+            "addu %[tmp1],%[tmp],%[res] \t\n"
+            "sltu %[tmp1],%[tmp1],%[tmp] \t\n"  /*obit?*/
+            "addu  %[res],%[res],%[tmp] \t\n"
+            "muh %[tmp], %[a], %[b] \t\n"
+            "addu  %[tmp],%[tmp],%[tmp1] \t\n"
+            "sll   %[tmp],%[tmp],%[lshift] \t\n"
+            "srl   %[res],%[res],%[rshift]    \t\n"
+            "or    %[res],%[res],%[tmp] \t\n"
+            : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+            : [a]"r"(a),[b]"r"(b),[lshift]"I"(32-shift),[rshift]"I"(shift),[shiftm1]"I"(shift-1)
+            );
+        } else {
+            asm ("mul %[res], %[a], %[b] \t\n"
+            "li  %[tmp],1 \t\n"
+            "sll  %[tmp],%[tmp],%[shiftm1] \t\n"
+            "addu %[tmp1],%[tmp],%[res] \t\n"
+            "sltu %[tmp1],%[tmp1],%[tmp] \t\n"  /*obit?*/
+            "sra  %[tmp2],%[tmp],0x1f \t\n"
+            "addu  %[res],%[res],%[tmp] \t\n"
+            "muh  %[tmp], %[a], %[b]   \t\n"
+            "addu  %[tmp],%[tmp],%[tmp2] \t\n"
+            "addu  %[tmp],%[tmp],%[tmp1] \t\n"            /*tmp=hi*/
+            "srl   %[tmp2],%[res],%[rshift]    \t\n"
+            "srav  %[res], %[tmp],%[rshift]\t\n"
+            "sll   %[tmp],%[tmp],1 \t\n"
+            "sll   %[tmp],%[tmp],%[norbits] \t\n"
+            "or    %[tmp],%[tmp],%[tmp2] \t\n"
+            "seleqz  %[tmp],%[tmp],%[bit5] \t\n"
+            "selnez  %[res],%[res],%[bit5] \t\n"
+            "or    %[res],%[res],%[tmp] \t\n"
+            : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+            : [a]"r"(a),[b]"r"(b),[norbits]"I"(~(shift)),[rshift]"I"(shift),[shiftm1] "I"(shift-1),[bit5]"I"(shift & 0x20)
+            );
+        }
+    } else {
+        asm ("mul %[res], %[a], %[b] \t\n"
+        "li  %[tmp],1 \t\n"
+        "sll  %[tmp],%[tmp],%[shiftm1] \t\n"
+        "addu %[tmp1],%[tmp],%[res] \t\n"
+        "sltu %[tmp1],%[tmp1],%[tmp] \t\n"  /*obit?*/
+        "sra  %[tmp2],%[tmp],0x1f \t\n"
+        "addu  %[res],%[res],%[tmp] \t\n"
+        "muh  %[tmp], %[a], %[b] \t\n"
+        "addu  %[tmp],%[tmp],%[tmp2] \t\n"
+        "addu  %[tmp],%[tmp],%[tmp1] \t\n"            /*tmp=hi*/
+        "srl   %[tmp2],%[res],%[rshift]    \t\n"
+        "srav  %[res], %[tmp],%[rshift]\t\n"
+        "sll   %[tmp],%[tmp],1 \t\n"
+        "sll   %[tmp],%[tmp],%[norbits] \t\n"
+        "or    %[tmp],%[tmp],%[tmp2] \t\n"
+        "seleqz  %[tmp],%[tmp],%[bit5] \t\n"
+        "selnez  %[res],%[res],%[bit5] \t\n"
+        "or    %[res],%[res],%[tmp] \t\n"
+         : [res]"=&r"(result),[tmp]"=&r"(tmp),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+         : [a]"r"(a),[b]"r"(b),[norbits]"r"(~(shift)),[rshift] "r"(shift),[shiftm1]"r"(shift-1),[bit5] "r"(shift & 0x20)
+         );
+        }
+        return result;
+}
+
+inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) CONST;
+inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) {
+    GGLfixed result,t,tmp1,tmp2;
+
+    if (__builtin_constant_p(shift)) {
+        if (shift == 0) {
+                 asm ("mul %[lo], %[a], %[b] \t\n"
+                 "addu  %[lo],%[lo],%[c]    \t\n"
+                 : [lo]"=&r"(result)
+                 : [a]"r"(a),[b]"r"(b),[c]"r"(c)
+                 );
+                } else if (shift == 32) {
+                    asm ("muh %[lo], %[a], %[b] \t\n"
+                    "addu  %[lo],%[lo],%[c]    \t\n"
+                    : [lo]"=&r"(result)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c)
+                    );
+                } else if ((shift>0) && (shift<32)) {
+                    asm ("mul %[res], %[a], %[b] \t\n"
+                    "muh  %[t], %[a], %[b] \t\n"
+                    "srl   %[res],%[res],%[rshift]    \t\n"
+                    "sll   %[t],%[t],%[lshift]     \t\n"
+                    "or  %[res],%[res],%[t]    \t\n"
+                    "addu  %[res],%[res],%[c]    \t\n"
+                    : [res]"=&r"(result),[t]"=&r"(t)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c),[lshift]"I"(32-shift),[rshift]"I"(shift)
+                    );
+                } else {
+                    asm ("mul %[res], %[a], %[b] \t\n"
+                    "muh %[t], %[a], %[b] \t\n"
+                    "nor %[tmp1],$zero,%[shift]\t\n"
+                    "srl   %[res],%[res],%[shift]    \t\n"
+                    "sll   %[tmp2],%[t],1     \t\n"
+                    "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
+                    "or  %[tmp1],%[tmp2],%[res]    \t\n"
+                    "srav  %[res],%[t],%[shift]     \t\n"
+                    "andi %[tmp2],%[shift],0x20\t\n"
+                    "seleqz %[tmp1],%[tmp1],%[tmp2]\t\n"
+                    "selnez %[res],%[res],%[tmp2]\t\n"
+                    "or %[res],%[res],%[tmp1]\t\n"
+                    "addu  %[res],%[res],%[c]    \t\n"
+                    : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"I"(shift)
+                    );
+                }
+            } else {
+                asm ("mul %[res], %[a], %[b] \t\n"
+                "muh %[t], %[a], %[b] \t\n"
+                "nor %[tmp1],$zero,%[shift]\t\n"
+                "srl   %[res],%[res],%[shift]    \t\n"
+                "sll   %[tmp2],%[t],1     \t\n"
+                "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
+                "or  %[tmp1],%[tmp2],%[res]    \t\n"
+                "srav  %[res],%[t],%[shift]     \t\n"
+                "andi %[tmp2],%[shift],0x20\t\n"
+                "seleqz %[tmp1],%[tmp1],%[tmp2]\t\n"
+                "selnez %[res],%[res],%[tmp2]\t\n"
+                "or %[res],%[res],%[tmp1]\t\n"
+                "addu  %[res],%[res],%[c]    \t\n"
+                : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+                : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"r"(shift)
+                );
+            }
+            return result;
+}
+
+inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) CONST;
+inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) {
+    GGLfixed result,t,tmp1,tmp2;
+
+    if (__builtin_constant_p(shift)) {
+        if (shift == 0) {
+                 asm ("mul %[lo], %[a], %[b] \t\n"
+                 "subu  %[lo],%[lo],%[c]    \t\n"
+                 : [lo]"=&r"(result)
+                 : [a]"r"(a),[b]"r"(b),[c]"r"(c)
+                 );
+                } else if (shift == 32) {
+                    asm ("muh %[lo], %[a], %[b] \t\n"
+                    "subu  %[lo],%[lo],%[c]    \t\n"
+                    : [lo]"=&r"(result)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c)
+                    );
+                } else if ((shift>0) && (shift<32)) {
+                    asm ("mul %[res], %[a], %[b] \t\n"
+                    "muh %[t], %[a], %[b] \t\n"
+                    "srl   %[res],%[res],%[rshift]    \t\n"
+                    "sll   %[t],%[t],%[lshift]     \t\n"
+                    "or  %[res],%[res],%[t]    \t\n"
+                    "subu  %[res],%[res],%[c]    \t\n"
+                    : [res]"=&r"(result),[t]"=&r"(t)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c),[lshift]"I"(32-shift),[rshift]"I"(shift)
+                    );
+                } else {
+                    asm ("mul %[res], %[a], %[b] \t\n"
+                    "muh %[t], %[a], %[b] \t\n"
+                    "nor %[tmp1],$zero,%[shift]\t\n"
+                    "srl   %[res],%[res],%[shift]    \t\n"
+                    "sll   %[tmp2],%[t],1     \t\n"
+                    "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
+                    "or  %[tmp1],%[tmp2],%[res]    \t\n"
+                    "srav  %[res],%[t],%[shift]     \t\n"
+                    "andi %[tmp2],%[shift],0x20\t\n"
+                    "seleqz %[tmp1],%[tmp1],%[tmp2]\t\n"
+                    "selnez %[res],%[res],%[tmp2]\t\n"
+                    "or %[res],%[res],%[tmp1]\t\n"
+                    "subu  %[res],%[res],%[c]    \t\n"
+                    : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+                    : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"I"(shift)
+                     );
+                    }
+                } else {
+                asm ("mul %[res], %[a], %[b] \t\n"
+                "muh %[t], %[a], %[b] \t\n"
+                "nor %[tmp1],$zero,%[shift]\t\n"
+                "srl   %[res],%[res],%[shift]    \t\n"
+                "sll   %[tmp2],%[t],1     \t\n"
+                "sllv  %[tmp2],%[tmp2],%[tmp1]     \t\n"
+                "or  %[tmp1],%[tmp2],%[res]    \t\n"
+                "srav  %[res],%[t],%[shift]     \t\n"
+                "andi %[tmp2],%[shift],0x20\t\n"
+                "seleqz %[tmp1],%[tmp1],%[tmp2]\t\n"
+                "selnez %[res],%[res],%[tmp2]\t\n"
+                "or %[res],%[res],%[tmp1]\t\n"
+                "subu  %[res],%[res],%[c]    \t\n"
+                : [res]"=&r"(result),[t]"=&r"(t),[tmp1]"=&r"(tmp1),[tmp2]"=&r"(tmp2)
+                : [a]"r"(a),[b]"r"(b),[c]"r"(c),[shift]"r"(shift)
+                );
+            }
+    return result;
+}
+
+inline int64_t gglMulii(int32_t x, int32_t y) CONST;
+inline int64_t gglMulii(int32_t x, int32_t y) {
+    union {
+        struct {
+#if defined(__MIPSEL__)
+            int32_t lo;
+            int32_t hi;
+#elif defined(__MIPSEB__)
+            int32_t hi;
+            int32_t lo;
+#endif
+        } s;
+        int64_t res;
+    }u;
+    asm("mul %0, %2, %3 \t\n"
+        "muh %1, %2, %3 \t\n"
+        : "=r"(u.s.lo), "=&r"(u.s.hi)
+        : "%r"(x), "r"(y)
+        );
+    return u.res;
+}
+
+#else // ----------------------------------------------------------------------
+
+inline GGLfixed gglMulx(GGLfixed a, GGLfixed b, int shift) CONST;
+inline GGLfixed gglMulx(GGLfixed a, GGLfixed b, int shift) {
+    return GGLfixed((int64_t(a)*b + (1<<(shift-1)))>>shift);
+}
+inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) CONST;
+inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) {
+    return GGLfixed((int64_t(a)*b)>>shift) + c;
+}
+inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) CONST;
+inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c, int shift) {
+    return GGLfixed((int64_t(a)*b)>>shift) - c;
+}
+inline int64_t gglMulii(int32_t a, int32_t b) CONST;
+inline int64_t gglMulii(int32_t a, int32_t b) {
+    return int64_t(a)*b;
+}
+
+#endif
+
+// ------------------------------------------------------------------------
+
+inline GGLfixed gglMulx(GGLfixed a, GGLfixed b) CONST;
+inline GGLfixed gglMulx(GGLfixed a, GGLfixed b) {
+    return gglMulx(a, b, 16);
+}
+inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c) CONST;
+inline GGLfixed gglMulAddx(GGLfixed a, GGLfixed b, GGLfixed c) {
+    return gglMulAddx(a, b, c, 16);
+}
+inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c) CONST;
+inline GGLfixed gglMulSubx(GGLfixed a, GGLfixed b, GGLfixed c) {
+    return gglMulSubx(a, b, c, 16);
+}
+
+// ------------------------------------------------------------------------
+
+inline int32_t gglClz(int32_t x) CONST;
+inline int32_t gglClz(int32_t x)
+{
+#if (defined(__arm__) && !defined(__thumb__)) || defined(__mips__) || defined(__aarch64__)
+    return __builtin_clz(x);
+#else
+    if (!x) return 32;
+    int32_t exp = 31;
+    if (x & 0xFFFF0000) { exp -=16; x >>= 16; }
+    if (x & 0x0000ff00) { exp -= 8; x >>= 8; }
+    if (x & 0x000000f0) { exp -= 4; x >>= 4; }
+    if (x & 0x0000000c) { exp -= 2; x >>= 2; }
+    if (x & 0x00000002) { exp -= 1; }
+    return exp;
+#endif
+}
+
+// ------------------------------------------------------------------------
+
+int32_t gglDivQ(GGLfixed n, GGLfixed d, int32_t i) CONST;
+
+inline int32_t gglDivQ16(GGLfixed n, GGLfixed d) CONST;
+inline int32_t gglDivQ16(GGLfixed n, GGLfixed d) {
+    return gglDivQ(n, d, 16);
+}
+
+inline int32_t gglDivx(GGLfixed n, GGLfixed d) CONST;
+inline int32_t gglDivx(GGLfixed n, GGLfixed d) {
+    return gglDivQ(n, d, 16);
+}
+
+// ------------------------------------------------------------------------
+
+inline GGLfixed gglRecipFast(GGLfixed x) CONST;
+inline GGLfixed gglRecipFast(GGLfixed x)
+{
+    // This is a really bad approximation of 1/x, but it's also
+    // very fast. x must be strictly positive.
+    // if x between [0.5, 1[ , then 1/x = 3-2*x
+    // (we use 2.30 fixed-point)
+    const int32_t lz = gglClz(x);
+    return (0xC0000000 - (x << (lz - 1))) >> (30-lz);
+}
+
+// ------------------------------------------------------------------------
+
+inline GGLfixed gglClampx(GGLfixed c) CONST;
+inline GGLfixed gglClampx(GGLfixed c)
+{
+#if defined(__thumb__)
+    // clamp without branches
+    c &= ~(c>>31);  c = FIXED_ONE - c;
+    c &= ~(c>>31);  c = FIXED_ONE - c;
+#else
+#if defined(__arm__)
+    // I don't know why gcc thinks its smarter than me! The code below
+    // clamps to zero in one instruction, but gcc won't generate it and
+    // replace it by a cmp + movlt (it's quite amazing actually).
+    asm("bic %0, %1, %1, asr #31\n" : "=r"(c) : "r"(c));
+#elif defined(__aarch64__)
+    asm("bic %w0, %w1, %w1, asr #31\n" : "=r"(c) : "r"(c));
+#else
+    c &= ~(c>>31);
+#endif
+    if (c>FIXED_ONE)
+        c = FIXED_ONE;
+#endif
+    return c;
+}
+
+// ------------------------------------------------------------------------
+
+#endif // ANDROID_GGL_FIXED_H